.. _sec-module.keno:
KENO: A Monte Carlo Criticality Program
=======================================
*K. B. Bekar*, *C. Celik*, *M. E. Dunn,*\ :sup:`1` *S. Goluoglu,*\ :sup:`1`
*D. F. Hollenbach*,\ :sup:`1` *N. F. Landers,*\ :sup:`1` *C. M.Perfetti,*\ :sup:`1`
*L. M. Petrie,*\ :sup:`1` *B. T. Rearden,*\ :sup:`1`
KENO is a three-dimensional (3D) Monte Carlo criticality transport
program developed and maintained for use as part of the SCALE Code
System. It can be used as part of a sequence or as a standalone program.
There are two versions of the code currently supported in SCALE.
KENO V.a is the older of the two. KENO-VI contains all current KENO V.a
features plus a more flexible geometry package known as the SCALE
Generalized Geometry Package. The geometry package in KENO-VI is capable
of modeling any volume that can be constructed using quadratic
equations. In addition, such features as geometry intersections, body
rotations, hexagonal and dodecahedral arrays, and array boundaries have
been included to make the code more flexible.
The simpler geometry features supported by KENO V.a allow for
significantly shorter execution times than KENO-VI, while the additional
geometry features supported in KENO-VI make the code appropriate for
cases where geometry modeling is not possible with KENO V.a. In
particular, KENO-VI allows intersections, body truncations with planes,
and a much wider variety of geometrical bodies. KENO-VI also has the
ability to rotate bodies so that volumes no longer must be positioned
parallel to a major axis. Hexagonal arrays are available in KENO-VI and
dohecahedral arrays enable the code to model pebble bed reactors and
other systems composed of close packed spheres. The use of array
boundaries makes it possible to fill a non-cuboidal volume with an
array, specifying the boundary where a particle leaves and enters the
array.
Except for geometry capabilities, the two versions of KENO share most of
the computational capabilities and the input flexibility specific to
most SCALE modules. They can both operate in multigroup or continuous
energy mode, run as standalone codes, or integrated in computational
sequences such as CSAS, TSUNAMI-3D, or TRITON. Both versions of the code
are continually updated and are written in FORTRAN 90.
Computational capabilities shared by the two versions of KENO include
the determination of k-effective, neutron lifetime, generation time,
energy-dependent leakages, energy- and region-dependent absorptions,
fissions, the system mean-free-path, the region-dependent
mean-free-path, average neutron energy, flux densities, fission
densities, reaction rate tallies, mesh tallies, source convergence
diagnostics, problem-dependent continuous energy temperature treatments,
parallel calculations, restart capabilities, and many more.
:sup:`1`\ Formerly with Oak Ridge National Laboratory
ACKNOWLEDGMENTS
---------------
Many individuals have contributed significantly to the development of
KENO. Special recognition is given to G. E. Whitesides, former Director
of the Computing Applications Division, who was responsible for the
concept and development of the original KENO code. He has also
contributed significantly to some of the techniques used in both KENO
versions. The late J. T. Thomas offered many ideas that have been
implemented in the code. R. M. Westfall, retired from ORNL, provided
early consultation, encouragement, and benchmarks for validating the
code. The special abilities of J. R. Knight, retired from ORNL,
contributed substantially to debugging early versions of the code. S. W.
D. Hart was instrumental in implementing continuous energy temperature
treatments. W. J. Marshall has provided substantial validation and
quality assurance reviews. Appreciation is expressed to C. V. Parks and
S. M. Bowman for their support of KENO and the KENO3D visualization
tool. The late P. B. Fox provided many of the figures in this document.
D. Ilas, B. J. Marshall, and D. E. Mueller consolidated the previous
KENO V.a and KENO-VI manuals into this present form. The efforts of
L. F. Norris (retired), W. C. Carter (retired), S. J. Poarch, D. J.
Weaver (retired), S. Y. Walker and R. B. Raney in preparing this
document are gratefully acknowledged.
The authors thank the U. S. Nuclear Regulatory Commission and the DOE
Nuclear Criticality Safety Program for sponsorship of the continuous
energy, source convergence diagnostics, and grid geometry features in
the current version.
.. _sec-module.keno.intro:
Introduction to KENO
--------------------
KENO, a functional module in the SCALE system, is a Monte Carlo
criticality program used to calculate :math:`k_{eff}`, fluxes, reaction rates,
and other data for three-dimensional (3-D) systems. Special features
include multigroup or continuous energy mode, simplified data input, the
ability to specify origins for spherical and cylindrical geometry
regions, a P\ :sub:`n` scattering treatment, and restart capability.
The KENO data input features flexibility in the order of input. The only
restrictions are that the sequence identifier, title, and cross section
library must be entered first. A large portion of the data has been
assigned default values found to be adequate for many
problems. This feature enables the user to run a problem with a minimum
of input data.
In addition to the features listed above, KENO-VI uses the SCALE
Generalized Geometry Package (SGGP), which contains a much larger set of
geometrical bodies, including cuboids, cylinders, spheres, cones,
dodecahedrons, elliptical cylinders, ellipsoids, hoppers,
parallelepipeds, planes, rhomboids, and wedges. The code's flexibility
is increased by allowing: intersecting geometry regions; hexagonal,
dodecahedral, and cuboidal arrays; bodies and holes rotated to any angle
and translated to any position; and a specified array boundary that
contains only that portion of the array located inside the boundary.
Users should be aware that the added geometry features in KENO-VI can
result in significantly longer run times than KENO V.a. A KENO-VI
problem that can be modeled in KENO V.a will typically run about four
times as long with KENO-VI as it does with KENO V.a. Therefore KENO-VI
is not a replacement for KENO V.a, but rather an additional version for
more complex geometries that could not be modeled previously.
Blocks of input data are entered in the form
``READ XXXX** *input_data* ``END XXXX``
where ``XXXX`` is the keyword for the type of data being entered. The
types of data entered include parameters, geometry region data, array
definition data, biasing or weighting data, albedo boundary conditions,
starting distribution information, the cross section mixing table, extra
one-dimensional (1-D) (reaction rate) cross section IDs for special
applications, energy group boundaries for tallying in the continuous
energy mode, a mesh grid for collecting flux moments, and printer plot
information.
A block of data can be omitted unless it is needed or desired for the
problem. Within the blocks of data, most of the input is activated by
using keywords to override default values.
The treatment of the energy variable can be either multigroup or
continuous. Changing the calculation mode from multigroup to continuous
energy or vice versa is established by simply changing the cross section
library used. All available calculated entities in the multigroup mode
can also be calculated in the continuous energy mode. If the calculated
entity is energy or group dependent, it is automatically tallied into
the appropriate group structure in the continuous energy mode.
The KENO V.a geometry input consists of spheres, hemispheres, cylinders,
hemicylinders, and cuboids. Although the origin of the cylinders,
hemicylinders, spheres, and hemispheres is zero by default, they may be
specified to any value that will allow the geometry to fit in the
problem. This feature allows the use of nonconcentric cylindrical and
spherical shapes and provides a great deal of freedom in positioning
them. Another feature that expands the generality of the code is the
ability to place the cut surface of the hemicylinders and hemispheres at
any distance between the radius and the origin.
An additional convenience is the availability of an alternative method
for specifying the array definition unit-location data. This method uses
FIDO-like options for filling the array.
As mentioned above, KENO-VI uses the SGGP, which contains a much more
flexible geometry package than the one in KENO V.a. In KENO-VI, geometry
regions are constructed and processed as sets of quadratic equations. A
set of geometric shapes (including all of those used in KENO V.a plus
others) is available in KENO-VI, as well as the ability to build more
complex geometric shapes using sets of quadratic equations. Unlike
KENO V.a, KENO-VI allows intersections between geometry regions within a
unit, and it provides the ability to specify an array boundary that
intersects the array.
The most flexible KENO V.a geometry features are the
"``ARRAY``-of-\ ``ARRAY``\ s" and "``HOLE``\ s" capabilities. The
``ARRAY``-of-\ ``ARRAY``\ s option allows the construction of ``ARRAY``\ s
from other ``ARRAY``\ s. The depth of nesting is limited only by
computer space restrictions. This option greatly simplifies the setup
for ``ARRAY``\ s involving different ``UNIT``\ s at different spacings.
The ``HOLE`` option allows a ``UNIT`` or an ``ARRAY`` to be placed at
any desired location within a geometry region. The emplaced ``UNIT`` or
``ARRAY`` cannot intersect any geometry region and must be wholly
contained within a region. As many ``HOLE``\ s as will snugly fit
without intersecting can be placed in a region. This option is
especially useful for describing shipping casks and reflectors that have
gaps or other geometrical features. Any number of ``HOLE``\ s can be
described in a problem, and ``HOLE``\ s can be nested to any depth.
The primary difference between the KENO V.a and KENO-VI geometry input
is the methodology used to represent the geometry/material regions in a
unit. KENO-VI uses two geometry records (cards) to describe a region.
The first record, called the GEOMETRY record, contains the geometry
(``shape``) keyword, region boundary definitions, and any geometry
modification data. Using geometry modification data, regions can be
rotated and translated to any angle and position within a unit. The
second record, the ``CONTENT`` record, contains the ``MEDIA`` keyword;
the material, ``HOLE``, or ``ARRAY`` ID number; the bias ID number; and
the region definition vector. KENO-VI requires that a ``GLOBAL UNIT`` be
specified in all problems, including single unit problems.
In addition to the *cuboidal* ``ARRAY``\ s available in KENO V.a,
*hexagonal* ``ARRAY``\ s and *dodecahedral* ``ARRAY``\ s can be directly
constructed in KENO-VI. Also, the ability to specify an ``ARRAY``
boundary that intersects the ``ARRAY`` makes it possible to construct a
lattice in a cylinder using one ``ARRAY`` in KENO-VI instead of multiple
``ARRAY``\ s and ``HOLE``\ s as would be required in KENO V.a.
Anisotropic scattering is treated by using discrete scattering angles.
The angles and associated probabilities are generated in a manner that
preserves the moments of the angular scattering distribution for the
selected group-to-group transfer. These moments can be derived from the
coefficients of a P\ :sub:`n` Legendre polynomial expansion. All moments
through the 2n - 1 moment are preserved for n discrete scattering
angles. A one-to-one correspondence exists such that n Legendre
coefficients yield n moments. The cases of zero and one scattering angle
are treated in a special manner. Even when the user specifies multiple
scattering angles, KENO can recognize that the distribution is
isotropic, and therefore KENO selects from a continuous isotropic
distribution. If the user specifies one scattering angle, the code
selects the scattering angle from a linear function if it is positive
between -1 and +1, and otherwise it performs semicontinuous scattering
by picking scattering angle cosines uniformly over some range between -1
and +1. The probability is zero over the rest of the range.
The KENO restart option is easy to activate. Certain changes can be made
when a problem is restarted, including using a different random sequence
or turning off certain print options such as fluxes or the fissions and
absorptions by region.
KENO can also compute angular fluxes and flux moments in multigroup
calculations, which are required to compute scattering terms for
generation of sensitivity coefficients with the SAMS module or the
TSUNAMI-3D sequence. Fluxes can also be accumulated in a Cartesian
mesh that is superimposed over the user-defined geometry in an automated
manner.
KENO can perform Monte Carlo transport calculations concurrently on a
number of computational nodes. By introducing a simple master-slave
approach via MPI, KENO runs different random walks concurrently on the
replicated geometry within the same generation. Fission source and other
tallied quantities are gathered at the end of each generation by the
master process and are then processed either for final edits or
subsequent generations. Code parallel performance is strongly dependent
on the size of the problem simulated and the size of the tallied
quantities.
.. _sec-module.keno.data_guide:
KENO Data Guide
---------------
KENO may be run stand alone or as part of a SCALE criticality safety or
sensitivity and uncertainty analysis sequence. If KENO is run stand
alone in the multigroup mode, cross section data can be used from an
AMPX :cite:`KENO-dugr2002` working format library or from a Monte Carlo format cross
section library. If KENO uses an AMPX working format library, a mixing
table data block must be entered. If a Monte Carlo format library is
used, a mixing table data block is not entered, and the mixtures
specified in the KENO geometry description must be consistent with the
mixtures created on the Monte Carlo format library file.
If KENO is run stand alone in the continuous energy mode, a mixing table
data block must be provided unless the restart option is used.
If KENO is run as part of a SCALE sequence, the mixtures are defined in
the sequence input; therefore, a mixing table data block cannot be entered in
KENO. Furthermore, the mixture numbers used in the KENO geometry
description must correspond to those defined in the composition data
block of the sequence input. To use a cell-weighted mixture in
KENO, the keyword ``CELLMIX=``, followed by a unique mixture
number, must be specified in the cell data input block of the sequence.
Note that cell data are applicable only in the multigroup mode.
The mixture number used in the KENO input is the unique
mixture number immediately following the keyword ``CELLMIX``. A
cell-weighted mixture is available only in SCALE sequences that use
XSDRN to perform a cell-weighting calculation using a multigroup cross
section library. :numref:`tab-module.keno.parameters` through :numref:`tab8-1-14` summarize the KENO
input data blocks. These input data blocks are discussed in detail in
the following sections. See CSAS, TRITON, and TSUNAMI manuals for more
details and tips about how KENO is used as part of these sequences.
To run KENO in parallel (standalone execution), the user must
provide the module name with the ``%`` prefix in the input file (e.g., ``=%kenovi``),
and provide the required arguments in the command line for parallel execution.
The ``%`` prefix is not required if KENO is run as part of a SCALE sequence.
Sequences such as CSAS, TRITON, and TSUNAMI-3D automatically
initiate parallel KENO execution if the user provides the required arguments
in the command line while running this code.
.. warning:: KENO can be run in parallel if SCALE has been built with MPI.
SCALE pre-built binaries disseminated with each SCALE release are usually
not MPI-enabled binaries.
.. tabularcolumns:: |\Y{0.08}|\Y{0.09}|\Y{0.10}|\Y{0.17}|\Y{0.20}|\Y{0.27}|
.. table:: Summary of KENO parameter data
:name: tab-module.keno.parameters
:align: left
:widths: 8 9 10 17 20 27
:class: longtable
+--------------------------+------------------------------------------------------------------------------------------------------+
| PARAMETERS: | |
| | Format: ``READ PARAM`` *parameter_data* ``END PARAM`` |
| | |
| | If parameters are entered, they must follow the sequence ID, title, and cross section library name |
| | See :numref:`sec-module.keno.parameters`, :numref:`sec-module.keno.file_unit`, and |
| | :numref:`sec-module.keno.parameter` for further details. |
+============+=============+=====================================+============+=============+=====================================+
| **KEY** | **DEFAULT** | **DEFINITION** | **KEY** | **DEFAULT** | **DEFINITION** |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``RND=`` | given | random number | ``WTL=`` | 1/WTH | Russian Roulette weight |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``TME=`` | no limit | execution time (min) | ``TTL=`` | -1.0 | CE temperature tolerance |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``TBA=`` | 10 min | batch time (min) | ``THC=`` | 10.0 | thermal energy cutoff (eV) |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``SIG=`` | 0.0 | deviation limit | ``DBH=`` | 210 | DBRC upper energy cutoff (eV) |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``WTA=`` | 0.5 | average weight | ``DBL=`` | 0.4 | DBRC lower energy cutoff (eV) |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``WTH=`` | 3.0 | weight for splitting | ``MSH=`` | 0.0 | mesh size of the cubic mesh |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``GEN=`` | 203 | number of generations | ``CET=`` | 0 | CE TSUNAMI calculation mode |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``NPG=`` | 1000 | number per generation | ``CFP=`` | -1 | number of latent generations for |
| | | | | | CE-TSUNAMI |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``NSK=`` | 3 | generations skipped | ``X1D=`` | 0 or 1 | number of of extra 1-Ds |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``RES=`` | 0 | generations between restart | ``NB8=`` | 1000 | blocks for direct access unit |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``BEG=`` | 1 | restart at this generation | ``NL8=`` | 512 | length of direct access block |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``NGP=`` | 252 | number of energy groups for tallying| ``NFB=`` | NPG | fission bank positions |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``DBR=`` | 0 | use DBRC for scattering | ``NBK=`` | NPG+25 | neutron bank positions |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``DBX=`` | 2 | Doppler Broadening method | ``XNB=`` | 0 | extra bank entries |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``NQD=`` | 0 | quadrature order for angular | ``XFB=`` | 0 | extra bank entries |
| | | flux moments | | | |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``PNM=`` | 0 | order of flux moments | ``AMX=`` | NO | all mixture xsecs |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``CEP=`` | NO | continuous energy directory file | ``XAP=`` | NO | xsec angles & probabilities |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``XS1=`` | NO | 1-D xsecs | ``XS2=`` | NO | 2-D xsecs |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``APP=`` | NO | append restart data | ``XSL=`` | NO | 2-D Pl xsecs |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``ADJ=`` | NO | adjoint calculation | ``PKI=`` | NO | fission spectrum |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``PTB=`` | YES | use probability tables | ``P1D=`` | NO | extra 1-D xsecs |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``PNU=`` | NO | use prompt neutron spectrum only | ``PWT=`` | NO | print average weight |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``FRE=`` | YES | use analytic free gas kernels | ``PGM=`` | NO | print unprocessed geometry |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``UUM=`` | NO | use unionized mixture xsec | ``PAX=`` | NO | albedo-xsec array |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``M2U=`` | NO | use unionized nuclide xsec | ``PMF=`` | NO | print angular fluxes |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``CFX=`` | NO | collect fluxes | ``PMS=`` | NO | print mesh fluxes |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``FLX=`` | NO | collect and print region fluxes | ``PMM=`` | NO | print mesh flux angular moments |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``FDN=`` | YES | fision densities | ``PMV=`` | NO | print mesh volumes |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``FAR=`` | NO | fission and absorption per region | ``TFM=`` | NO | coordinate transform |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``GAS=`` | FAR | FAR by energy | ``FST=`` | NO | print F*(r) 3dmap |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``NUB=`` | YES | neutrons per fission | ``SCX=`` | NO | save CE-xsec to restart file |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``MFP=`` | NO | compute and print mean free paths | ``SCD=`` | NO | fission source convergence diag. |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``SMU=`` | NO | self-multiplication | ``CDS=`` | NO | accumulate neutron production |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``MKP=`` | NO | matrix keff by location in array | ``FIS=`` | NO | fission rate mesh tally |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``CKP=`` | NO | cofactor keff by location | ``GFX=`` | NO | compute grid fluxes |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``FMP=`` | NO | fission production by location | ``MFX=`` | NO | compute mesh fluxes |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``MKU=`` | NO | matrix keff by unit | ``CGD=`` | NO | use mesh for CLUTCH F\*(r) calc. |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``CKU=`` | NO | cofactor keff by unit | ``HTM=`` | YES | produce HTML |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``FMU=`` | NO | fission production by unit | ``RUN=`` | YES | execute problem |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``MKA=`` | NO | matrix keff by array | ``PLT=`` | YES | print plots |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``CKA=`` | NO | cofactor keff by array | ``BUG=`` | NO | debug print |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``FMA=`` | NO | fission production by array | ``TRK=`` | NO | print neutron tracks |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``MKH=`` | NO | matrix keff by hole | ``GRP=`` | 0 | group structure library |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``CKH=`` | NO | cofactor keff by hole | ``RST=`` | 0 | read restart |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``FMH=`` | NO | fission production by hole | ``WRS=`` | 0 | write restart |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``HAL=`` | NO | MKA at highest level | ``SKT=`` | 16 | scratch |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``HHL=`` | NO | MKH at highest level | ``LIB=`` | 0 | working xsecs |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``XSC=`` | 14 | mixed xsecs | ``FNI=`` | | input restart file identifier |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``ALB=`` | 79 | albedo | ``FNO=`` | | output restart file identifier |
+------------+-------------+-------------------------------------+------------+-------------+-------------------------------------+
| ``WTS=`` | 80 | weights | |
+------------+-------------+-------------------------------------+----------------------------------------------------------------+
.. list-table:: Summary of array data.
:name: tab8-1-2
:align: center
* - .. image:: figs/Keno/tab2.svg
:align: center
:width: 1000
.. list-table:: Summary of biasing data.
:name: tab8-1-3
:align: center
* - .. image:: figs/Keno/tab3.svg
:align: center
:width: 1000
.. |br| raw:: html
.. raw:: latex
\begin{landscape}
.. tabularcolumns:: |p{1.6cm}|p{1.4cm}|p{1.8cm}|p{1.3cm}|p{1.6cm}|p{1.3cm}|p{1.6cm}|p{1.3cm}|p{1.6cm}|
.. table:: Summary of boundary condition data.
:name: tab8-1-4
:class: longtable
+----------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| ``BNDS`` | Format: |
| **(albedo or** | |
| **boundary** | KENO V.a: ``READ BNDS`` face code albedo name ``END BNDS`` |br| |
| **conditions)** | KENO-VI : ``READ BNDS`` [BODY=label] face code albedo name ``END BNDS`` |
| | |
| | See :numref:`sec-module.keno.albedo` |
+----------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | The sequence *FACE CODE ALBEDO NAME* is entered as many times as necessary to define the appropriate albedo boundary conditions. |br| |
| | KENO-VI’s BODY parameter must be used to define the appropriate albedo boundary conditions when the boundary definition vector of the global unit has more than one body label. |br| |
| | The default for all faces is vacuum. |
| +--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | FACE CODES FOR ENTERING BOUNDARY (ALBEDO) CONDITIONS |
| +-------------------------+-----------------------------------+-------------------+----------------------+----------------------------+----------------------------------+-----------+-------------------------+
| | FACE | DEFINITION | FACE | DEFINITION | FACE | DEFINITION | FACE | DEFINITION |
| | CODE | | CODE | | CODE | | CODE | |
| +-------------------------+-----------------------------------+-------------------+----------------------+----------------------------+----------------------------------+-----------+-------------------------+
| | ``SURFACE(k)`` | albedo surface enumeration | ``+XB=`` | positive X face | **&FC=** | all positive faces | **+YZ=** | positive Y and Z faces |
| | | indicates any :math:`k^{th}` face +-------------------+----------------------+----------------------------+----------------------------------+-----------+-------------------------+
| | | of the boundary shape. Used for | ``&XB=`` | positive X face | **-FC=** | all negative faces | **+ZY=** | positive Y and Z faces |
| | | both **cuboidal and** +-------------------+----------------------+----------------------------+----------------------------------+-----------+-------------------------+
| | | **non-cuboidal boundary shapes.** | ``-XB=`` | negative X face | **XYF=** | all X and Y faces | **&YZ=** | positive Y and Z faces |
| | | +-------------------+----------------------+----------------------------+----------------------------------+-----------+-------------------------+
| | | | ``+YB=`` | positive Y face | **XZF=** | all X and Z faces | **&ZY=** | positive Y and Z faces |
| | | +-------------------+----------------------+----------------------------+----------------------------------+-----------+-------------------------+
| | | | ``&YB=`` | positive Y face | **YZF=** | all Y and Z faces | **-XY=** | negative X and Y faces |
| | | +-------------------+----------------------+----------------------------+----------------------------------+-----------+-------------------------+
| | | | ``-YB=`` | negative Y face | **+XY=** | positive X and Y faces | **-XZ=** | negative X and Z faces |
| | | +-------------------+----------------------+----------------------------+----------------------------------+-----------+-------------------------+
| | | shape-specific albedo numbers | ``+ZB=`` | positive Z face | **+YX=** | positive X and Y faces | **-YZ=** | negative Y and Z faces |
| | | for both KENO V.a and. +-------------------+----------------------+----------------------------+----------------------------------+-----------+-------------------------+
| | | KENO-VI are listed in | ``&ZB=`` | positive Z face | **&YX=** | positive X and Y faces | **YXF=** | all X and Y faces |
| | | :numref:`keno-table-alb-enum-k5` +-------------------+----------------------+----------------------------+----------------------------------+-----------+-------------------------+
| | | and :numref:`tab8-1-2-5` | ``-ZB=`` | negative Z face | **&XY=** | positive X and Y faces | **ZXF=** | all X and Z faces |
| | | +-------------------+----------------------+----------------------------+----------------------------------+-----------+-------------------------+
| | | | ``XFC=`` | both X faces | **+XZ=** | positive X and Z faces | **ZYF=** | all Y and Z faces |
| | | +-------------------+----------------------+----------------------------+----------------------------------+-----------+-------------------------+
| | | | ``YFC=`` | both Y faces | **+ZX=** | positive X and Z faces | **-YX=** | negative X and Y faces |
| +-------------------------+-----------------------------------+-------------------+----------------------+----------------------------+----------------------------------+-----------+-------------------------+
| | ``ALL=`` | all faces of a single or multiple | ``ZFC=`` | both Z faces | **&XZ=** | positive X and Z faces | **-ZX=** | negative X and Z faces |
| | | boundary shape(s) +-------------------+----------------------+----------------------------+----------------------------------+-----------+-------------------------+
| | | | ``+FC=`` | all positive faces | **&ZX=** | positive X and Z faces | **-ZY=** | negative Y and Z faces |
| | | +-------------------+----------------------+----------------------------+----------------------------------+-----------+-------------------------+
| | | | Above face codes are applicable for **only cuboidal boundary shapes** (cube or cuboid). |
| | | | |
+----------------------+-------------------------+-----------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------+
.. tabularcolumns:: |p{1.4cm}|p{1.6cm}|p{1.3cm}|p{1.4cm}|p{1.6cm}|p{1.3cm}|p{1.3cm}|p{1.4cm}|p{1.4cm}|
.. table:: Summary of boundary condition data (continued).
:class: longtable
+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| **ALBEDO NAMES AVAILABLE ON THE KENO ALBEDO LIBRARY, FOR USE WITH THE FACE CODES** |
+--------------------+----------------------------------------------+------+---------------------+-------------------------------+-------+-----------------+-----------------------------+-----------+
| ALBEDO | DESC. | MODE | ALBEDO | DESC. | MODE | ALBEDO | DESC. | MODE |
| NAME | | | NAME | | | NAME | | |
+====================+==============================================+======+=====================+===============================+=======+=================+=============================+===========+
| DP0H2O | 12 in. double P0 water differential albedo | MG | CONC-4 | 4 in. concrete differential | MG | VACUUM | vacuum condition | MG and CE |
| | with 4 incident angles | | | albedo with 4 incident angles | | | | |
| DP0H2O | | | CON4 | | | VOID | | |
| | | | | | | | | |
| DP0 | | | CONC4 | | | VACU | | |
| | | | | | | | | |
| DP0 | | | | | | VAC | | |
| | | +---------------------+-------------------------------+-------+-----------------+-----------------------------+-----------+
| | | | CONC-8 | 8 in. concrete differential | MG | | | |
+--------------------+----------------------------------------------+------+ | albedo with 4 incident angles | | | | |
| H2O | 12 in. water differential albedo with 4 | MG | CON8 | | | SPECULAR | mirror image reflection | MG and CE |
| | incident angles | | | | | | | |
| WATER | | | CONC8 | | | MIRROR | | |
| | | | | | | | | |
| | | | | | | MIRR | | |
+--------------------+----------------------------------------------+------+---------------------+-------------------------------+-------+ | | |
| PARAFFIN | 12 in. paraffin differential albedo with 4 | MG | CONC-12 | 12 in. concrete differential | MG | SPEC | | |
| | incident angles | | | albedo with 4 incident angles | | | | |
| PARA | | | CON12 | | | SPE | | |
| | | | | | | | | |
| WAX | | | CONC12 | | | MIR | | |
+--------------------+----------------------------------------------+------+---------------------+-------------------------------+-------+-----------------+-----------------------------+-----------+
| CARBON | 200 cm carbon differential albedo with 4 | MG | CONC-16 | 16 in. concrete differential | MG | PERIODIC | periodic boundary condition | MG and CE |
| | incident angles | | | albedo with 4 incident angles | | | | |
| GRAPHITE | | | CON16 | | | PERI | | |
| | | | | | | | | |
| C | | | CONC16 | | | PER | | |
+--------------------+----------------------------------------------+------+---------------------+-------------------------------+-------+-----------------+-----------------------------+-----------+
| ETHYLENE | 12 in. polyethylene differential albedo with | MG | CONC-24 | 24 in. concrete differential | MG | WHITE | White boundary condition | MG and CE |
| | 4 incident angles | | | albedo with 4 incident angles | | | | |
| POLY | | | CONC | | | | | |
| | | | | | | | | |
| CH2 | | | CONC24 | | | | | |
+--------------------+----------------------------------------------+------+---------------------+-------------------------------+-------+-----------------+-----------------------------+-----------+
.. raw:: latex
\end{landscape}
.. table:: Summary of boundary condition data specific to KENO V.a
:name: keno-table-alb-enum-k5
:align: center
:class: longtable
+---------------------------------------------------------------------------------------------+
| ALBEDO SURFACE NUMBERS RELATED TO KENO V.a GEOMETRY SHAPES |
+===================+===========+================+===========+================+========+======+
| | | | | | | |
| GEOMETRY SHAPE | 1 | 2 | 3 | 4 | 5 | 6 |
+-------------------+-----------+----------------+-----------+----------------+--------+------+
| | | | | | | |
| CUBE | +X | -X | | | | |
+-------------------+-----------+----------------+-----------+----------------+--------+------+
| | | | | | | |
| CUBOID | +X | -X | +Y | -Y | +Z | -Z |
+-------------------+-----------+----------------+-----------+----------------+--------+------+
| | | | | | | |
| CYLINDER | Radial | +Z | -Z | | | |
+-------------------+-----------+----------------+-----------+----------------+--------+------+
| | | | | | | |
| HEMISPHERE | Radial | Cut surface | | | | |
+-------------------+-----------+----------------+-----------+----------------+--------+------+
| | | | | | | |
| HEMICYLINDER | Radial | Top | Bottom | Cut surface | | |
+-------------------+-----------+----------------+-----------+----------------+--------+------+
| | | | | | | |
| SPHERE | Radial | | | | | |
+-------------------+-----------+----------------+-----------+----------------+--------+------+
| | | | | | | |
| XCYLINDER | Radial | +X | -X | | | |
+-------------------+-----------+----------------+-----------+----------------+--------+------+
| | | | | | | |
| YCYLINDER | Radial | +Y | -Y | | | |
+-------------------+-----------+----------------+-----------+----------------+--------+------+
| | | | | | | |
| ZCYLINDER | Radial | +Z | -Z | | | |
+-------------------+-----------+----------------+-----------+----------------+--------+------+
.. raw:: latex
\begin{landscape}
.. tabularcolumns:: |p{1.4cm}|p{.8cm}|p{.8cm}|p{.8cm}|p{.8cm}|p{.8cm}|p{.8cm}|p{.8cm}|p{.8cm}|p{.8cm}|p{.8cm}|p{.8cm}|p{.8cm}
.. table:: Summary of boundary condition data specific to KENO-VI.
:name: tab8-1-2-5
:class: longtable
+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| **ALBEDO SURFACE NUMBERS RELATED TO KENO-VI GEOMETRY BODIES** |
+==================+=================+=================+==========+==========+===========+===========+===========+===========+===========+===========+===========+===========+
| | | | | | | | | | | | | |
| GEOMETRY BODY | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| CONE | Radial | +Z | -Z | | | | | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| CUBOID | +X | -X | +Y | -Y | +Z | -Z | | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| CYLINDER | Radial | +Z | -Z | | | | | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | |+X |br| +Y |-X |br| -\Y|-X |br| +Y |+X |br| -Y |-X |br| -Y |+X |br| +Y |+X |br| -Y |-X |br| +Y |
| DODECAHEDRON | +X | -X | +Y | -Y ||br| +Z ||br| -\Z ||br| +Z ||br| -Z ||br| +Z ||br| -Z ||br| +Z ||br| -Z |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| ECYLINDER | Radial | +Z | -Z | | | | | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| ELLIPSOID | Radial | | | | | | | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| HEXPRISM | +X | -X |+X |br| +Y|-X |br| -Y|-X |br| +Y |+X |br| -Y | +Z | -Z | | | | |
| | | | | | | | | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| HOPPER | +X | -X | +Y | -Y | +Z | -Z | | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| PENTAGON | -Y | +X |br| -Y |+X |br| +Y|-X |br| +Y|-X |br| -\Y| +Z | -Z | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| PLANE | Surface | | | | | | | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| QUADRATIC | | | | | | | | | | | | |
| | Surface | | | | | | | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| RHEXPRISM | +Y | -Y |-X |br| +Y|+X |br| -Y|+X |br| +Y |-X |br| -\Y| +Z | -Z | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| RING | Inner Radius | Outer Radius | +Z | -Z | | | | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| SPHERE | Radial | | | | | | | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| WEDGE | -Y | -X |br| +Y |+X |br| +Y| +Z | -Z | | | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| XCYLINDER | Radial | +X | -X | | | | | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| XPPLANE | +X | -X | | | | | | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| YCYLINDER | Radial | +Y | -Y | | | | | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| YPPLANE | +Y | -Y | | | | | | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| ZCYLINDER | Radial | +Z | -Z | | | | | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| ZPPLANE | +Z | -Z | | | | | | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| |
| Surfaces refer to the pre-rotation surface of the body that occurs in the indicated quadrant. |
| |
| Refer to :numref:`fig8-1-1` through :numref:`fig8-1-22` for illustrations of each geometry body. |
+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
.. raw:: latex
\end{landscape}
.. list-table:: Summary of geometry data in KENO V.a.
:name: tabsec-module.keno.albedo
:align: center
* - .. image:: figs/Keno/tab6.svg
* - .. image:: figs/Keno/tab6cont.svg
.. list-table:: Summary of geometry data in KENO-VI.
:name: tab8-1-7
:align: center
* - .. image:: figs/Keno/tab7.svg
.. list-table:: Summary of mixing table data.
:name: tab8-1-8
:align: center
* - .. image:: figs/Keno/tab8.svg
.. list-table:: Summary of plot data.
:name: tab8-1-9
:align: center
* - .. image:: figs/Keno/tab9.svg
:align: center
:width: 1000
.. list-table:: Summary of starting data.
:name: tab8-1-10
:align: center
* - .. image:: figs/Keno/tab8-1-10.svg
:align: center
:width: 1000
.. list-table:: Summary of volume data (KENO-VI).
:name: tab8-1-11
:align: center
* - .. image:: figs/Keno/tab11.svg
:width: 1000
:align: center
.. list-table:: Summary of grid geometry data.
:name: tab8-1-12
:align: center
* - .. image:: figs/Keno/tab12.svg
:width: 1000
:align: center
.. tabularcolumns:: |p{2cm}|p{10cm}|
.. table:: Summary of energy group boundaries data.
:name: tab8-1-13
:class: longtable
+-----------------------------------+-----------------------------------------+
| ENERGY | Format: READ ENERGY energy group |
| | boundaries END ENERGY |
| | |
| | Enter upper energy boundary for |
| | each group in eV. The last entry |
| | is the lower energy boundary of |
| | the last group. For N groups, |
| | there are N+1 entries. Entries |
| | must be in descending order and |
| | in units of eV. |
+-----------------------------------+-----------------------------------------+
.. list-table:: Summary of reaction data.
:name: tab8-1-14
:align: center
* - .. image:: figs/Keno/tab14.svg
:width: 1000
:align: center
.. _sec-module.keno.input_outline:
Keno input outline
~~~~~~~~~~~~~~~~~~
The data input for KENO is outlined below. Default data for KENO have
been found to be adequate for many problems. These values should be
carefully considered when entering data.
Blocks of input data are entered in the form:
``READ XXXX`` *input_data* ``END XXXX``
where ``XXXX`` is the keyword for the type of data being entered. The
keywords that can be used are listed in :numref:`tab8-1-15`. A minimum of four
characters is required for a keyword, and some keyword names may be as
long as twelve characters (``READ PARAMETER``, ``READ GEOMETRY``, etc.).
Keyword inputs are not case sensitive. Data input is activated by
entering the words ``READ XXXX`` followed by one or more blanks. All
input data pertinent to ``XXXX`` are then entered. Data for ``XXXX`` are
terminated by entering ``END XXXX`` followed by two or more blanks. Note
that multiple ``READ GRID`` blocks are used if multiple grid definitions
are needed.
.. table:: Types of input data.
:align: center
:name: tab8-1-15
+-----------------------------------+-------------------------------------+
| **Type of data** | **Keyword** |
+-----------------------------------+-------------------------------------+
| Parameters | ``PARAMETER``, ``PARA`` or ``PARM`` |
+-----------------------------------+-------------------------------------+
| Geometry | ``GEOMETRY``, ``GEOM`` |
+-----------------------------------+-------------------------------------+
| Biasing | ``BIAS`` |
+-----------------------------------+-------------------------------------+
| Boundary conditions | ``BOUNDS``, ``BOUN`` or ``BNDS`` |
+-----------------------------------+-------------------------------------+
| Start | ``START``, ``STAR`` or ``STRT`` |
+-----------------------------------+-------------------------------------+
| Energy | ``ENERGY`` or ``ENER`` |
+-----------------------------------+-------------------------------------+
| Array (unit orientation) | ``ARRAY`` or ``ARRA`` |
+-----------------------------------+-------------------------------------+
| Extra 1-D cross sections | ``X1DS`` |
+-----------------------------------+-------------------------------------+
| Cross section mixing table\ | ``MIXT`` or ``MIX`` |
| :sup:`a` | |
+-----------------------------------+-------------------------------------+
| Plot\ :sup:`a` | ``PLOT`` or ``PLT`` or ``PICT`` |
+-----------------------------------+-------------------------------------+
| Volumes | ``VOLUME`` |
+-----------------------------------+-------------------------------------+
| Grid geometry | ``GRIDGEOMETRY``, ``GRIDGEOM``, or |
| | ``GRID`` |
+-----------------------------------+-------------------------------------+
| Reactions | ``REACTION``, ``REAC`` |
+-----------------------------------+-------------------------------------+
| :sup:`a` MIX and PLT must include a trailing blank, which is considered |
| part of the keyword. |
+-------------------------------------------------------------------------+
Three data records **must** be entered for every problem:
(1) the SCALE sequence identifier,
(2) the problem title,
(3) and the ``END DATA`` to terminate the problem.
KENO V.a or KENO-VI are typically run as part of CSAS, TRITON, or TSUNAMI
sequences, but it may also be run standalone. For standalone KENO execution,
the sequence identifier is specified using one line similar to:
::
=kenovi
A problem title **must be entered** and must immediately follow the sequence
identifier (limit 80 characters, including blanks; extra characters will be
discarded). See :numref:`sec-module.keno.parameters`.
The following guidance generally assumes the user is running KENO stand
alone. If KENO is to be run using of the other sequences (e.g., CSAS5),
see the appropriate manual section for additional guidance.
``READ PARA`` *parameter_data* ``END PARA``
Enter parameter input as needed to describe a problem. If parameter
data are desired in standalone KENO calculations (i.e., non-CSAS),
they must immediately follow the problem title. Default values are
assigned to all parameters. A problem **can** be run without entering
any parameter data if the default values are acceptable.
Parameter data must begin with the words ``READ PARA``, ``READ PARM``,
or ``READ PARAMETER``. Parameter data may be entered in any
order. If a parameter is entered more than once, the last value is
used. The words ``END PARA`` or ``END PARM``, or ``END PARAMETER``
terminate the parameter data. See :numref:`sec-module.keno.parameters`.
(n\ :sub:`1`)...( n\ :sub:`13`) The following data may be entered in any
order. Data not needed to describe the problem may be omitted.
(n\ :sub:`1`) ``READ GEOM`` *all_geometry_region_data* ``END GEOM``
Geometry region data must be entered for every problem that is not a
restart problem. Geometry data must begin with the words ``READ GEOM``
or ``READ GEOMETRY``. The words ``END GEOM`` or ``END GEOMETRY``
terminate the geometry region data. See :numref:`sec-module.keno.geom`.
(n\ :sub:`2`) ``READ ARRA`` *array_definition_data* ``END ARRA``
Enter array definition data as needed to describe the problem. Array
definition data define the array size and position units (defined in
the geometry data) in a 3-D lattice that represents the physical
problem being analyzed. Array data must begin with the words
``READ ARRA`` or ``READ ARRAY`` and must terminate with the words
``END ARRA`` or ``END ARRAY``. See :numref:`sec-module.keno.geom.array_data`.
(n\ :sub:`4`) ``READ BOUN`` *albedo_boundary_conditions* ``END BOUN``
Enter albedo boundary conditions as needed to describe the problem.
Albedo data must begin with the words ``READ BOUN``, ``READ BNDS``,
``READ BOUND``, or ``READ BOUNDS``, and it must terminate with the
words ``END BOUN``, ``ENDS BNDS``, ``END BOUND``, or ``END BOUNDS``.
See :numref:`sec-module.keno.albedo`.
(n\ :sub:`3`) ``READ BIAS`` *biasing_information* ``END BIAS``
The *biasing_information* is used to define the weight given to a
neutron surviving Russian roulette. Biasing data must begin with the
words ``READ BIAS``. The words ``END BIAS`` terminate the biasing
data. See :numref:`sec-module.keno.biasing`.
(n\ :sub:`5`) ``READ STAR`` *starting_distribution_information* ``END STAR``
Enter starting information data for starting the initial source
neutrons only if a uniform starting distribution is undesirable.
Start data must begin with the words ``READ STAR``, ``READ STRT`` or
``READ START``, and it must terminate with the words ``END STAR``,
``END STRT`` or ``END START``. See :numref:`sec-module.keno.start_data`.
(n\ :sub:`6`) ``READ ENER`` *energy_group_boundaries* ``END ENER``
Enter upper energy boundaries for each neutron energy group to be
used for tallying in the continuous energy mode. Energy bin data
begin with the words ``READ ENER`` or ``READ ENERGY`` and terminate
with the words ``END ENER`` or ``END ENERGY``. The last entry is the
lower energy boundary of the last group. The values must be in
descending order. This block is only applicable to continuous energy
KENO calculations. See :numref:`8-1-2-12`.
(n\ :sub:`7`) ``READ MIXT`` *cross_section_mixing_table* ``END MIXT``
Enter a mixing table to define all the mixtures to be used in the
problem. The mixing table must begin with the words ``READ MIXT`` or
``READ MIX`` and must end with the words ``END MIXT`` or ``END MIX``.
Do not enter mixing table data if KENO is being executed as a part of
a SCALE sequence. See :numref:`sec-module.keno.mixing_table`.
(n\ :sub:`8`) ``READ X1DS`` *extra_1-D_cross_section_IDs* ``END X1DS``
Enter the IDs of any extra 1-D cross sections to be used in the
problem. These must be available on the mixture cross section
library. Extra 1-D cross section data must begin with the words
``READ X1DS`` and terminate with the words ``END X1DS``. See
:numref:`sec-module.keno.xs1d`.
(n\ :sub:`9`) ``READ PLOT`` *plot_data* ``END PLOT``
Enter the data needed to provide a 2-D character or color plot of a
slice through a specified portion of the 3-D geometrical
representation of the problem. Plot data must begin with the words
``READ PLOT``, ``READ PLT``, or ``READ PICT`` and terminate with the
words ``END PLOT``, ``END PLT``, or ``END PICT``. See :numref:`8-1-2-11`.
(n\ :sub:`10`) ``READ VOLUME`` *volume_data* ``END VOLUME``
Enter the data needed to specify the volumes of the geometry data.
Volume data must begin with the words ``READ VOLUME`` and end with
the words ``END VOLUME``. See :numref:`8-1-2-13`.
(n\ :sub:`11`) ``READ GRID`` *mesh_grid_data* ``END GRID``
Enter the data needed to specify a simple Cartesian grid over either
the entire problem or part of the problem geometry for tallying
fluxes, moments, fission sources, etc. Grid data may be entered using
the keywords ``READ GRID``, ``READ GRIDGEOM``, or ``READ GRIDGEOMETRY``,
and they are terminated with either ``END GRID``, ``END GRIDGEOM``,
or ``END GRIDGEOMETRY``. Multiple grids may be
defined by repeating the ``READ GRID`` block several times,
specifying a different mesh grid identification number for each so
defined grid. See :numref:`8-1-2-14` for further information.
(n\ :sub:`12`) ``READ REAC`` *reaction_data* ``END REAC``
Enter the data needed to specify filters for the reaction tally
calculations. Reaction data must begin with the words ``READ REAC``
and terminate with ``END REAC``. This block is only applicable to
calculations in the continuous energy mode. See :numref:`8-1-2-15`.
(n\ :sub:`13`) ``END DATA must be entered``
Terminate the data for the problem.
.. _sec-module.keno.input_procedure:
Procedure for data input
~~~~~~~~~~~~~~~~~~~~~~~~
For a standalone KENO problem, the first data records **must** be the
sequence identifier (e.g., ``=kenovi`` or ``=kenova``) and the title. The next
block of data **must** be the parameters if they are to be entered. A
problem can be run without entering the parameters, which causes KENO to
use default values for input parameters. The remaining blocks of data
can be entered in any order.
Keywords are deonated using ``FIXED-WIDTH``. A keyword is used to identify the
data that follow it. When a keyword is used, it must be entered
exactly as shown in the data guide. All keywords except those ending
with an equal sign must be followed by at least one blank.
*small_italics* correlate data with a program variable name. The
actual values are entered in place of the program variable name and
are terminated by a blank or a comma.
*CAPITAL ITALICS* identify general data items. General data items are
general classes of data including:
(1) geometry data such as *UNIT INITIALIZATION* and *UNIT NUMBER*
*DEFINITION*, *GEOMETRY REGION DESCRIPTION*, *GEOMETRY WORD*,
*MIXTURE NUMBER*, *BIAS ID*, and *REGION DIMENSIONS*,
(2) albedo data such as *FACE CODES* and *ALBEDO NAMES*,
(3) weighting data such as *BIAS ID NUMBERS*, etc.
The square brackets, [ and ], are used to show that an entry is optional.
The broken line, \|, is used as a logical "or" symbol to
show that the entries to its left and right are alternatives that
cannot be used simultaneously.
.. _sec-module.keno.parameters:
Title and parameter data
~~~~~~~~~~~~~~~~~~~~~~~~
A *title*, a character string, must be entered at the top of the input
file. The syntax is:
*title* a string of characters with a length of up to 80 characters,
including blanks.
The ``PARAMETER`` block may contain parameter initializations for those
parameters that need to be changed from their default value. The syntax
for the ``PARAMETER`` block is:
``READ PARA``\ [``METER``] *p\ 1 ... p\ N* ``END PARA``\ [``METER``]
or
``READ PARM`` *p\ 1 … p\ N* ``END PARM``
*p\ 1 ... p\ N* are *N* (*N* greater than or equal to zero) keyworded
parameters that together make up the *PARAMETER DATA*
The commonly changed parameters are ``TME``, ``GEN``, ``NSK``,
and ``NPG``. Seldom-changed parameters are ``NBK``, ``NFB``,
``XNB``, ``XFB``, ``WTH``, ``WTL``, ``TBA``,
``BUG``, ``TRK``, and ``LNG``.
The *PARAMETER DATA*, *p\ 1 … p\ N*, consists of one or more of the
parameters described below.
Some of the parameters are valid either for only multigroup or continuous-energy mode. All below parameters and their values are printed in the
Numeric Parameters or Logical Parameters output edits, regardless
of whether the parameter is valid in the current transport mode (either
multigroup or continous energy).
Floating point parameters
``RND`` = *rndnum* input hexadecimal random number, a default value is
provided.
``TME`` = *tmax* execution time (in minutes) for the problem, default =
0.0 (no limit).
.. caution::
Note that it is only tested at the end of each generation whether
the given time limit has been exceeded. The job may be terminated
without completing all generations or finalizing all results for
output editing if *tmax* has not been entered carefully.
``TBA`` = *tbtch* time allotted for each generation (in minutes),
default = 10 minutes. If *tbtch* is exceeded in any generation, the
problem is assumed to be looping. Execution is terminated, and final
edits are performed. The problem can loop indefinitely on a computer if
the system-dependent routine to interrupt the problem (PULL) is not
functional. ``TBA=`` is also used to set the amount of time available
for generating the initial starting points.
``SIG`` = *tsigma* if entered and > 0.0, this is the standard deviation
at which the problem will terminate, default = 0.0, which means do not
check sigma.
``WTA`` = *dwtav* the default average weight given a neutron that
survives Russian roulette, *dwtav* default = 0.5.
``WTH`` = *wthigh* the default value of *wthigh* is 3.0 and should be
changed only if the user has a valid reason to do so. The weight at
which splitting occurs is defined to be *wthigh x wtavg*, where *wtavg*
is the weight given to a neutron that survives Russian roulette.
``WTL`` = *wtlow* Russian roulette is played when the weight of a
neutron is less than *wtlow x wtavg*. The *wtlow* default =
1.0/\ *wthigh*.
.. note:: The default values of *wthigh* and *wtlow* have been determined
to minimize the deviation per unit running time for many problems.
``TTL`` = *temperature_tolerance* the continuous energy cross sections
must be within the *temperature_tolerance* (in degrees Kelvin) of the
requested temperature for the problem to run. A negative value specifies
the use of the closest temperature to that requested. TTL is ignored
when ``DBX`` is nonzero. The default = -1.0.
.. note:: If a parameter entered is not valid for the current transport
mode (either multigroup or continuous energy mode), KENO usually ignores
this parameter without a warning. Although a parameter is ignored, its
user-defined value may appear in Numeric Parameters or Logical Parameters
output edits.
``THC`` = *ethermal_cutoff* the thermal cutoff energy for bound and
free-gas moderators in continuous-energy transport. The cutoff energy
for the thermal neutron transport treatments is represented by a single
energy for all nuclides. If the incident energy is below ``THC``,
then thermal scattering kinematics are governed by :math:`S(\alpha, \beta)`
data or the free-gas treatment. If incident energy is greater than ``THC``,
then the energy of the motion of the nuclei is considered negligible
compared to the neutron energy. See :numref:`sec-module.keno.ce_physics.tsl` for more details.
The default = 10.0 eV.
``DBH`` = *dbrc_high* the energy cutoff (in eV) up to which the Doppler
Broadening Rejection Correction (DBRC) method will be used on nuclides
for which DBRC is enabled, and cross section libraries are available.
DBH is used only in continuous-energy mode. Default = 210.0 eV.
``DBL`` = *dbrc_low* the energy cutoff (in eV) down to which DBRC will
be used on nuclides for which DBRC is enabled and cross section
libraries are available. Only used in continuous-energy mode. Default = 0.4 eV.
``MSH`` = *mesh_size* length (cm) of one side of a cubic mesh for
tallying fluxes, fission source or fission densities. Default = 0.0.
A positive non-zero value must be entered if one of ``MFX``, ``CDS``,
``FIS``, or ``GFX`` parameters is defined as *YES* and **KENO grid data**
input is not entered. See :numref:`8-1-3-10` for more details.
Integer parameters
``GEN`` = *nba* number of generations to be run, default = 203.
``NPG`` = *npb* number of neutrons per generation, default = 1000.
``NSK`` = *nskip* number of generations (1 through *nskip*) to be
omitted when collecting results, default = 3.
``RES`` = *nrstrt* number of generations between writing restart data,
default = 0. If ``RES`` is zero, restart data are not written. When
restarting a problem, ``RES`` is defaulted to the value that was used
when the restart data block was written. Thus, it must be entered as
zero to terminate writing restart data for a restarted problem.
``BEG`` = *nbas* beginning generation number, default = 1. If ``BEG`` is
greater than 1, then restart data must be available. ``BEG`` must be 1
greater than the number of generations retrieved from the restart file.
**NGP** = *ngp* number of neutron energy groups to be used for tallying
in continuous-energy mode. If **NGP** corresponds to a standard SCALE
group structure, then the SCALE group structure will be used. If it does
not correspond to a standard structure, then an equally spaced in lethargy
group structure will be used. If nothing is specified for a
continuous-energy problem, the SCALE 252-group structure will be used.
.. note:: In multigroup mode, default energy boundaries used for tallying are
always obtained from the multigroup library used by transport, and
**NGP** is defaulted accordingly. In continuous-energy mode, energy
group boundaries read from **ENERGY** block override the default
ngp value. **NGP** value printed in numeric parameters output edit may
not reflect this update. The final **NGP** value is correctly printed
in additional information output edit (shown as number of energy groups).
**DBR** = *lusedbrc* use the Doppler broadening rejection correction method.
See :numref:`8-1-6-2-9` for more details. Used only in continuous-energy mode.
Default = 2.
0 = no DBRC
1 = DBRC for :sup:`238`\ U only
2 = DBRC for all available nuclides (:sup:`232`\ Th, :sup:`234`\ U,
:sup:`235`\ U, :sup:`236`\ U, :sup:`238`\ U, :sup:`237`\ Np,
:sup:`239`\ Pu, :sup:`240`\ Pu)
**DBX** = *db_xs_mode* option for performing problem-dependent or on-the-fly Doppler
Broadening. See :numref:`8-1-6-2-10` for more details. Default = 2.
0 = no problem-dependent or on-the-fly Doppler Broadening
1 = perform problem-dependent Doppler Broadening for 1D cross
sections only.
2 = perform problem-dependent Doppler Broadening for both 1D and 2D
(thermal scattering data) cross sections.
**CET** = *ce_tsunami_mode* mode for CE TSUNAMI (See TSUNAMI-3D manual).
0 = no sensitivity calculations
1 = CLUTCH sensitivity calculation
2 = IFP sensitivity calculation
4 = GEAR-MC calculation (with CLUTCH only)
5 = GEAR-MC calculation (with CLUTCH+IFP)
7 = undersampling metric calculation
**CFP** = *number_of_latent_generations* number of latent generations used
for IFP sensitivity or :math:`F^{*}\left( r \right)` calculations (See TSUNAMI-3D manual).
If CET=1 and CFP= -1 then :math:`F^{*}\left( r \right)` is assumed to equal one everywhere.
If CET=4 and CFP= -1 then :math:`F^{*}\left( r \right)` is assumed to equal zero everywhere.
**NQD** = *nquad* quadrature order for angular flux tallies, default =
0, which means do not collect. Angular fluxes are typically only needed
for TSUNAMI-3D calculations(See TSUNAMI-3D manual).
**PNM** = *isctr* highest order of flux moment tallies, default = 0.
Flux moments are typically only tallied for TSUNAMI-3D calculations (See TSUNAMI-3D manual).
**X1D** = *numx1d* number of extra 1D cross sections, default = 0.
**NB8** = *nb8* number of blocks allocated for the first direct-access
unit, default = 1000.
**NL8** = *nl8* length of blocks allocated for the first direct-access
unit, default = 512.
**NBK** = *nbank* number of positions in the neutron bank, default =
*npb* + 25.
**XNB** = *nxnbk* number of extra entries in the neutron bank, default =
0.
**NFB** = *nfbnk* number of positions in the fission bank, default =
*npb.*
**XFB** = *nxfbk* number of extra entries in the fission bank, default =
0.
Alphanumeric parameter data
**CEP** = *lcep* key for choosing the calculation mode in stand alone
KENO calculations. The parameter is set to the appropriate value by the
calling sequence if not stand alone KENO. For stand alone KENO, enter NO
for multigroup mode, or enter the continuous energy directory filename
for the continuous energy mode. The directory file is the file
containing pointers to files significant for the continuous energy run.
**FNI** = *mode_in* extra field in the input restart file name
[restart\_*mode_in*.keno_input] and
[restart\_*mode_in*.keno_calculated]. The default is an empty field.
**FNO** = *mode_out* extra field in the output restart filename
[restart\_*mode_out*.keno_input] and
[restart\_*mode_out*.keno_calculated]. The default is an empty field.
Logical parameter data … enter *YES* or *NO*
**APP** = *lappend* key for appending the restart data, default = NO.
**ADJ** = *nadj* key for running adjoint calculation, default = NO.
Adjoint cross sections must be available to run an adjoint problem. If
LIB= is specified, the cross sections will be adjointed by the code. If
XSC= is specified, the cross sections must already be in adjoint order.
**PTB** = *ptb* key for using probability tables in the continuous
energy mode, default = YES
**PNU =** *lpromptnu* key for using prompt-only :math:`\nu` in the
continuous energy mode, default = NO -- use total.
**FRE** = *lfree_analytic* no longer supported (**obsolete parameter**).
**UUM** = *lUnionizedMix* use unionized mixture cross section,
default = NO. Only used in continuous-energy mode. See :numref:`8-1-6-2-3` for
more details.
**M2U =** *luseMap2Union* store cross sections for each nuclide on a
unionized energy grid, default=NO. Only used in the continuous energy mode.
See :numref:`8-1-6-2-3` for further details.
**CFX** = *nflx* collect fluxes, default = NO.
**FLX** = *nflx* key for collecting and printing fluxes, default = NO.
**FDN** = *nfden* key for collecting and printing fission densities,
default = YES.
**FAR** = *lfa* key for generating region-dependent fissions and
absorptions for each energy group, default = NO.
**GAS** = *lgas* key for printing region-dependent fissions and
absorptions by energy group, applicable only if FAR = YES. Default =
FAR. GAS = YES prints region-dependent data by energy group. GAS = NO
suppresses region-dependent data by energy group.
**NUB** = *nubar* calculate the average number of neutrons per fission
and the average energy group at which fission occurred, default = YES.
**MFP** = *mean-free-path* compute and print the mean-free-path of a
neutron by region, default = NO.
**SMU** = *lmult* calculate the average self-multiplication of a unit,
default = NO.
**MKP** = *larpos* calculate and print matrix k-effective by unit
location, default = NO. Unit location may also be referred to as array
position or position index.
**CKP** = *lckp* calculate and print cofactor k-effective by unit
location, default = NO. Unit location may also be referred to as array
position or position index.
**FMP** = *pmapos* print fission production matrix by array position,
default = NO.
**MKU** = *lunit* calculate and print matrix k-effective by unit type,
default = NO.
**CKU** = *lcku* calculate and print cofactor k-effective by unit type,
default = NO.
**FMU** = *pmunit* print fission production matrix by unit type,
default = NO.
**MKH** = *lmhole* calculate and print matrix k-effective by hole number,
default = NO.
**CKH** = *lckh* calculate and print cofactor k-effective by hole number,
default = NO.
**FMH** = *pmhole* print fission production matrix by hole number,
default = NO.
**MKA** = *lmarry* calculate and print matrix k-effective by array number,
default = NO.
**CKA** = *lcka* calculate and print cofactor k-effective by array number,
default = NO.
**FMA** = *pmarry* print fission production matrix by array number,
default = NO.
**HHL** = *lhhgh* collect matrix information by hole number at the
highest hole nesting level, default = NO.
**HAL** = *langh* collect matrix information by array number at the
highest array nesting level, default = NO.
**AMX** = *amx* key for printing all mixture cross section data. This is
the same as activating *XAP, XS1, XS2, PKI*, and *P1D*. If any of these
are entered in addition to *AMX*, then that portion of *AMX* will be
overridden, default = NO.
**XAP** = *prtap* key for printing discrete scattering angles and
probabilities for the mixture cross sections, default = NO.
**XS1** = *prtp0* key for printing mixture 1D cross sections, default =
NO.
**XS2** = *prt1* key for printing mixture 2D cross sections, default =
NO.
**XSL** = *prtl* key for printing mixture 2D P\ :sub:`L` cross
sections, default = NO. The Legendre expansion order L is automatically
read from the cross section library.
**PKI** = *prtchi* print input fission spectrum, default = NO.
**P1D** = *prtex* print extra 1D cross sections, default = NO.
**PWT** = *lpwt* print weight average array, default = NO.
**PGM** = *lgeom* print unprocessed geometry as it is read, default =
NO.
**PAX** = *lcorsp* print the arrays defining the correspondence between
the cross section energy group structure and the albedo energy group
structure, default = NO.
**PMF** = *prtmore* print angular fluxes or flux moments if calculated,
default = NO.
**PMS** = *print_mesh_flux* print mesh fluxes if computed, default = NO.
**PMM** = *print_mesh_moments* print the angular moments of the mesh flux,
if computed, default = NO.
**PMV** = *print_mesh_volumes* print the volume of each mesh interval,
if computed. Default = NO.
**TFM** = *ltfm* perform coordinate transform for flux moments and
angular flux calculations, default = NO.
**FST** = *lprint_FStar* create a .3dmap file that contains the *F*\ :sup:`*`\ (r) mesh used by
a CE-TSUNAMI CLUTCH sensitivity calculation.
**SCX** = *lxsecSave* save CE cross sections to restart file, default=NO.
**HTM** = *html_output* produce HTML formatted output for interactive browsing,
sorting, and plotting of results, default = YES.
**BUG** = *ldbug* print debug information, default = NO. Enter *YES* for code
debug purposes only.
**TRK** = *ltrk* print tracking information, default = NO. Enter *YES* for code
debug purposes only.
**RUN** = *lrun* key for determining if the problem is to be executed when data checking
is complete, default = YES.
**PLT** = *lplot* key for drawing specified plots of the problem geometry,
default = YES.
.. note:: The parameters RUN and PLT can also be entered in the PLOT
data. See :numref:`8-1-2-11`. It is recommended that these parameters be
entered only in the parameter data to ensure that the data
printed in the Logical Parameters table is actually performed. If RUN
and/or PLT are entered in both the parameter data and plot data, the
results vary depending on whether the problem is run (1) stand alone,
(2) as a restarted problem, (3) as CSAS with parm=check, or (4) as CSAS
without parm=check. These conditions are detailed below.
KENO standalone and CSAS with PARM=CHECK
The values of RUN and/or PLT entered in KENO parameter data are printed in
the Logical Parameters table of the problem output. However, values for RUN
and/or PLT entered in the **KENO plot data** will override the values entered
in the parameter data.
Restarted KENO
The values of RUN and/or PLT printed in the Logical Parameters table of the
problem output are the final values from the parent problem unless those values
are overridden by values entered in the **KENO parameter data** of the
restarted problem. If the problem is restarted at generation 1,
**KENO plot data** can be entered, and the values for RUN and/or PLT will
override the values printed in the Logical Parameters table.
CSAS Without PARM=CHECK
The values of RUN and/or PLT entered in the **KENO parameter data** override values
entered in the KENO plot data. The values printed in the Logical Parameters
table control whether the problem is to be executed and whether a plot is
performed.
Parameters that are either Logical or Integer ... enter YES or NO, or an integer number
**SCD**\ = *l_grid_entropy or mp_grid_entropy*
score Shannon entropy on a grid,
and then perform fission source convergence diagnostics(ScnvgDiag), default=YES,
default grid ID = 10001. See :numref:`8-1-6-7` for further details.
**CDS** = *lgrid_prod_dens or mp_grid_prod_dens*
accumulate neutron fissions on a mesh grid either constructed with **MSH** or defined
by **KENO grid data** input
to use as fission source in subsequent MAVRIC/Monaco shielding calculation or for
visualization, default = NO.
**FIS** = *lgrid_fis_rate or mp_grid_fis_rate*
compute fission rates on a mesh grid either constructed with **MSH**
or defined by **KENO grid data** input, default = NO.
**GFX** = *lgrid_flux or mp_grid_flux*
compute grid fluxes on a mesh grid either constructed with **MSH**
or defined by **KENO grid data** input, default = NO.
**MFX** = *lgrid_mat_avg_flux or mp_grid_mat_avg_flux*
compute mesh fluxes (averaged over the volume of mixtures/materials in each mesh voxel)
on a mesh grid either constructed with **MSH**
or defined by **KENO grid data** input, default = NO.
**CGD** = *lgrid_fstar or mp_grid_fstart*
compute the *F*\ :sup:`*`\ (r) mesh tally
for continuous-energy CLUTCH sensitivity calculations. This mesh is defined
with either **MSH** parameter or **KENO grid data**, default = NO.
The KENO codes in SCALE versions prior to 6.2 allowed for only one mesh
definition in the user input, with either the **MSH** parameter or the **KENO grid data**
input, and calculation of a single mesh-based quantity, such as MFX (mesh fluxes)
or CDS (fission source accumulation on a mesh), per KENO simulation. Either
of these mesh-based quantities can be enabled only by entering **MSH=yes** or
**CDS=yes** in the parameter input.
Starting with SCALE 6.2, the option to define multiple spatial meshes during
a single simulation was implemented in the KENO codes to add flexibility to
mesh-based quantity calculations. This enabled computing desired quantities
on different spatial meshes in a single KENO simulation: a finer mesh can be used for grid fluxes
to increase the resolution while overlaying these data on the geometry for a
problem with a full-core reactor model, whereas a coarser mesh can be used for
Shannon entropy tally for source convergence diagnostics for the same problem.
The new implementation requires that each mesh definition in the **KENO grid data**
input have a unique NUMBER (grid ID), which is used for
mesh assignment. Users can assign any spatial grid to mesh-based quantities
by setting the mesh parameters to this grid NUMBER (e.g., **GFX=id1**
**MFX=id2**, etc.)
To support both definition formats (logical entries or integer entries),
the parameter processor was redesigned for the parameters **SCD**, **CDS**,
**GFX**, **MFX** and **CGD** to allow either integer or logical entries.
Integer entries are required if multiple mesh-based quantities are requested
with different meshes. In this case, each integer entry must point to a grid ID
specified in any **KENO grid data**. See :numref:`8-1-3-10` for
several examples for the use of these parameter definitions.
KENO codes in SCALE 6.3 introduce a new mesh-based quantity, fission rates
on a mesh grid, which is controlled by parameter **FIS** in the parameter
block. Like the above parameters, **FIS** also allows both logical and
integer entries.
These entries for all above parameters are detailed below.
**SCD**\ = yes
enable source convergence diagnostics using the fission
source accumulation on the default mesh, which is 5 :math:`\times` 5 :math:`\times` 5 Cartesian
mesh overlaying the whole problem geometry, generated automatically.
See :numref:`8-1-6-7`.
**SCD**\ =\ *id*
enable source convergence diagnostics using the
fission source accumulation on the mesh defined with **KENO grid data**
with grid ID, *id*.
**CGD**\ =\ *id*
enable a mesh grid defined by the **KENO grid data** with grid ID, *id* for CLUTCH :math:`F^{*}\left( r \right)`
calculations.
**MFX**\ =yes
compute mesh fluxes on intervals defined by the **MSH** parameter
or by the first specified **grid data** block.
**MFX**\ =\ *id*
compute mesh fluxes on a mesh grid defined by the **KENO grid data** with grid ID, *id*.
**CDS**\ =yes
accumulate fission sources on intervals defined by
**MSH** or by the first specified **grid data** block.
**CDS**\ =\ *id*
accumulate fission source on a mesh grid defined by
the specified **KENO grid data** with grid ID, *id*.
**FIS**\ =yes
compute fission rates on intervals defined
by **MSH** or by the first specified **grid data** block.
**FIS**\ =\ *id*
compute fission rates on a mesh grid defined by the
**KENO grid data** with grid ID, *id*.
**GFX**\ =yes
compute grid fluxes (fluxes averaged over a voxel
volume) on intervals defined by **MSH** or by the first
specified **grid data** block.
**GFX**\ =\ *id*
compute grid fluxes on a mesh grid defined by the **KENO grid data** with grid
ID, *id*.
All of the above quantities may be requested in a single input using
either the same or different grids. See :numref:`8-1-3-10` for more details.
I/O Unit Numbers
**XSC** = *xsecs*
I/O unit number for a Monte Carlo format mixed cross
section library. When LIB :math:`\neq` 0, default = 14. To read a mixed cross section
library from a Monte Carlo format library file or CSASI, XSC must be
specified.
**ALB** = *albdo*
I/O unit number for albedo data, default = 79.
**WTS** = *wts*
I/O unit number for weights, default = 80.
**LIB** = *lib*
I/O unit number for *AMPX* working format cross section
library, default = 0.
**SKT** = *skrt*
I/O unit number for scratch space, default = 16.
**RST** = *rstrt*
I/O unit number for reading restart data, default = 0.
Enter a logical unit number to restart if *BEG* > 1.
**WRS** = *wstrt*
I/O unit number for writing restart data, default = 0. A non-zero value
must be entered if *RES* > 0.
**GRP** = *grpbs*
I/O unit number for an energy group boundary library, default = 77.
Example:
Default values for the parameters **NPG** and **FLX** are overridden by the
user-defined values. Code continues calculations with 203 particles per
generation, and tallies region-averaged fluxes in starting after **NSK**
generations skipped.
::
READ PARAM
NPG=203 FLX=yes
END PARAM
Example:
**NSK** has been defined more than once. The last **NSK** value 50 is used.
A cubic Cartesian mesh grid with 3 cm side length is
constructed using the extents of the bounding box enclosing the global
unit (or outermost geometry). Then, fluxes (averaged over voxel volumes)
are tallied on this mesh grid after 50 generations skipped.
::
READ PARA
NSK=13
MSH=3.0 GFX=yes NSK=50
END PARA
.. _sec-module.keno.geom:
Geometry data
~~~~~~~~~~~~~
The *GEOMETRY\_ DATA* consists of a series of **UNIT** descriptions, one
of which may be the **GLOBAL UNIT**. The **UNIT** is the basic geometry
piece in KENO and often corresponds to a well-defined physical entity
(e.g., a fuel pin). A **UNIT**, therefore, may consist of multiple
*material regions*. Each **UNIT** has its own, local coordinate system.
The **UNIT**\ s are assembled to construct the problem's global geometry
for KENO. The *GEOMETRY\_ DATA* must be entered unless the problem is
being restarted. See :numref:`sec-module.keno.geom_guide` for detailed examples.
.. _sec-module.keno.geom.units:
UNITS
^^^^^
Geometric arrangements in KENO are achieved in a manner similar to using
a child's building blocks. Each building block is called a **UNIT**. An
**ARRAY** or lattice is constructed by stacking these **UNIT**\ s. Once
an **ARRAY** or lattice has been constructed, it can be placed in a
**UNIT** by using an **ARRAY** specification.
Each **UNIT** in an **ARRAY** or lattice has its own coordinate system.
In KENO V.a, all coordinate systems in all **UNIT**\ s must have the
same orientation. This restriction is removed in KENO-VI. All geometry
data used in a problem are correlated to the absolute coordinate system
by specifying a **GLOBAL UNIT**. **UNIT**\ s are constructed of
combinations from several allowed **shape**\ s or geometric regions.
These regions can be placed anywhere within a **UNIT**. In KENO V.a the
regions are oriented along the coordinate system of the **UNIT** and do
not intersect other regions. This means, for example, that a
**CYLINDER** must have its axis parallel to one of the coordinate axes,
while a rectangular parallelepiped must have its faces perpendicular to
a coordinate axis. The most stringent KENO V.a geometry restriction is
that none of the options allow geometry regions to intersect. In KENO
V.a, each region in a unit must entirely contain each preceding region.
The orientation, intersection, and containment restrictions are
eliminated in KENO-VI. :numref:`fig8-1-1` shows some situations that are not
allowed in KENO V.a, but are allowed in KENO-VI.
.. figure:: figs/Keno/fig1.png
:align: center
:name: fig8-1-1
Examples of geometry allowed in KENO-VI but not allowed in KENO V.a.
For KENO V.a, unless special options are invoked, each geometric region
in a **UNIT** must completely enclose each interior region. Regions may
touch at points of tangency and may share faces. See :numref:`fig8-1-2` for
examples of allowable situations.
.. figure:: figs/Keno/fig2.png
:align: center
:name: fig8-1-2
Examples of correct KENO V.a units.
Special options are provided to circumvent the complete enclosure
restriction in KENO V.a or to enhance the basic geometry package in
KENO-VI. These options include **ARRAY** and **HOLE** descriptions. The
**HOLE** option is the simplest of these and allows placing a **UNIT**
anywhere within a region of another **UNIT.** In KENO V.a, **HOLE**\ s
are not allowed to intersect the region into which they are placed; this
restriction does not apply in KENO-VI (see :numref:`fig8-1-3`). In both geometry
packages, a **HOLE** cannot intersect the **UNIT** boundary. It is
recommended that the outer boundary of a **UNIT** used as a **HOLE**
should not be tangent to or share a boundary with another **HOLE** or a
region of the **UNIT** containing the **HOLE** because the code may find
that the regions are intersecting due to precision and round-off. Since
a particle must check every region to determine its location within a
**UNIT**, using **HOLE**\ s to contain complex sections of a problem may
decrease the CPU time needed for the problem in KENO-VI. Inclusion of
**HOLE**\ s increases run-time in KENO V.a, but in many cases cannot be
avoided. An arbitrary number of **HOLE**\ s can be placed in a region in
combination with a series of surrounding regions. The only restrictions
on **HOLE**\ s are (1) when they are placed in a **UNIT,** they must be
entirely contained within the **UNIT**, and (2) they cannot intersect
other **HOLE**\ s or nested **ARRAY**\ s. **HOLE**\ s in KENO V.a cannot
intersect an **ARRAY**; in KENO-VI, the **HOLE** cannot intersect the
**ARRAY** boundary.
.. figure:: figs/Keno/fig3.png
:align: center
:name: fig8-1-3
Example demonstrating HOLE capability in KENO.
Lattices or arrays are created by stacking **UNIT**\ s. In KENO V.a,
only rectangular parallelepipeds can be organized in an **ARRAY**.
**HEXPRISM**\ s and **DODECAHEDRON**\ s are allowed in KENO-VI to
construct triangular pitched or closed-packed dodecahedral **ARRAY**\ s,
respectively. The adjacent faces of adjacent **UNIT**\ s stacked in this
manner must match exactly. See :numref:`8-1-3-6-4` for additional
clarification and :numref:`fig8-1-4` and :numref:`fig8-1-5` for typical examples.
.. figure:: figs/Keno/fig4.png
:align: center
:width: 400
:name: fig8-1-4
Example of triangular pitched ARRAY construction.
.. figure:: figs/Keno/fig5.png
:align: center
:name: fig8-1-5
Example of ARRAY construction.
The **ARRAY** option is provided to allow for placing an **ARRAY** or
lattice within a **UNIT**. In KENO-VI, an **ARRAY** is placed in a
**UNIT** by inserting it directly into a geometry/material region as a
content record. In KENO V.a, the **ARRAY** is placed directly in the
unit like a **CUBOID**: it must be the first region in the **UNIT**, or
the **ARRAY** elements must intersect with the smaller region.
Subsequent regions in the **UNIT** containing the **ARRAY** must contain
it entirely. In KENO-VI, the reverse is true: the region boundary
containing the **ARRAY** must coincide with or be contained within the
**ARRAY** boundary. Therefore, in KENO-VI the region boundary becomes
the **ARRAY** boundary, with the problem ignoring any part of the
**ARRAY** outside the boundary. A particle enters or leaves the
**ARRAY** when the region boundary is crossed. In KENO V.a, only one
**ARRAY** can be placed directly in a UNIT. However, multiple
**ARRAY**\ s can be placed within a **UNIT** by using **HOLE**\ s. When
an **ARRAY** is placed in a **UNIT** via a **HOLE**, the **UNIT** that
contains the **ARRAY** (rather than the **ARRAY** itself) is placed in
the **UNIT**. **ARRAY**\ s of dissimilar **ARRAY**\ s can be created by
stacking **UNIT**\ s that contain **ARRAY**\ s. In KENO-VI, it is
possible to place multiple **ARRAY**\ s in a **UNIT** by placing them in
separate regions. Also in KENO-VI, using **HOLE**\ s to insert
**ARRAY**\ s allows the **ARRAY**\ s to be rotated when placed. See
:numref:`fig8-1-6` for an example of an **ARRAY** composed of **UNIT**\ s
containing **HOLE**\ s and **ARRAY**\ s.
.. figure:: figs/Keno/fig6.png
:align: center
:name: fig8-1-6
Example of an ARRAY composed of UNITs containing ARRAYs and HOLEs.
The method of entering *GEOMETRY_DATA* in the geometry data block
follows:
``READ GEOM`` *GEOMETRY\_ DATA* ``END GEOM``
.. _sec-module.keno.geom.units.init:
UNIT initialization
'''''''''''''''''''
The description of a ``UNIT`` starts out with the ``UNIT``
*INITIALIZATION* and is terminated by encountering another ``UNIT``
*INITIALIZATION* or ``END GEOM``.
The ``UNIT`` *INITIALIZATION* has the following format:
[``GLOBAL``] ``UNIT`` *u*
*u* is the identification number (positive integer) assigned to the
particular ``UNIT``. It may be used later to reference a ``UNIT``
previously constructed that the user wishes to place in a ``HOLE``, or
it may be used in an ``ARRAY`` (see below for more details).
``GLOBAL`` is an attribute that specifies that the respective ``UNIT``
is the most comprehensive ``UNIT`` in the KENO problem to be solved, the
``UNIT`` that includes all the other ``UNIT``\ s and defines the overall
geometric boundaries of the problem. In general, a \ ``GLOBAL UNIT``
must be entered for each problem.
.. note::
In KENO V.a, the ``GLOBAL`` specification is optional. If it is used,
it can precede either a ``UNIT`` command or an ``ARRAY``
*PLACEMENT_DESCRIPTION*. If it is not entered and the problem does
not contain ``ARRAY`` data, ``UNIT`` 1 is the default ``GLOBAL UNIT``.
If there is no ``GLOBAL UNIT`` specified and ``UNIT`` 1 is
absent from the geometry description, an error message is printed. If
the geometry description contains an ``ARRAY``, KENO V.a defaults the
global array to the array referenced by the last ``ARRAY``
*PLACEMENT_DESCRIPTION* that is not immediately preceded by a unit
description. Otherwise, it is the largest array number specified in
the array data (:numref:`sec-module.keno.geom.array_data`).
Examples of initiating a ``UNIT``:
1. Initiate input data for ``UNIT`` No. 6.
..
``UNIT`` 6
2. Initiate input data for the **GLOBAL UNIT** which is **UNIT** No. 4.
..
``GLOBAL UNIT`` 4
For each ``UNIT``, the ``UNIT``\ 's *DESCRIPTION* follows the
``UNIT``\ 's *INITIALIZATION*. The *DESCRIPTION* is realized by
combining the commands listed below. The basic principles for
constructing a ``UNIT`` are different between KENO V.a and KENO-VI. A
brief discussion of these principles, together with a few examples, is
presented at the end of this section following the description of the
basic input used to build the geometry of a ``UNIT``. The keywords that
may be used to define a ``UNIT`` in KENO are as follows:
``shape``
``COM=``
``HOLE``
``ARRAY``
``REPLICATE`` (KENO V.a only)
``REFLECTOR`` (KENO V.a only)
``MEDIA`` (KENO-VI only)
``BOUNDARY`` (KENO-VI only)
.. _sec-module.keno.geom.units.shape:
Shape
'''''
**Shape** is a generic keyword used to describe a basic geometric shape
that may be used in building the geometry of a particular **UNIT**. The
general format varies between KENO V.a and KENO-VI. In KENO V.a, the
**shape** defines a region containing a material, so the user is
required to provide both a material and a *bias ID*. In KENO-VI the
**shape** is used strictly as a surface, which is later used to define
the mono-material regions (using the **MEDIA** card). The user is
therefore required to enter a label for this surface so that the
**shape** can be referenced later.
KENO V.a:
**shape** *m* *b* *d*\ :sub:`1` … *d*\ :sub:`N` [*a*\ :sub:`1` …* [*a*\ :sub:`M` ]…]
KENO-VI:
**shape** *l* *d*\ :sub:`1` … *d*\ :sub:`N` [*a*\ :sub:`1` …* [*a*\ :sub:`M` ]…]
**shape** is a generic keyword that describes a basic predefined KENO
shape (e.g., **CUBOID**, **CYLINDER**) that is used to build the
geometry of the **UNIT**. The predefined shapes differ between KENO V.a
and KENO-VI. See :numref:`sec-scale.keno5.shapes` for a description of the KENO V.a basic
shapes and :numref:`sec-scale.keno6.shapes` for the KENO-VI shapes.
*m* is the mixture number of the material (positive integer) that fills
the particular shape in KENO V.a **UNIT** description. A material number
of zero indicates a void region (i.e., no material is present in the
volume defined by the **shape**).
*b* is the bias identification number (*bias ID*, a positive integer)
assigned to the particular region defined by the **shape** in the KENO
V.a **UNIT** description.
*l* is the label (positive integer) assigned to the particular **shape**
in the KENO-VI **UNIT** description. This label is used later to define
a certain mono-material region within the **UNIT**.
*d*\ :sub:`1` … *d*\ :sub:`N` represent the *N* dimensions (floating point numbers) that
define the particular **shape** (e.g., radius of a sphere or cylinder).
See :numref:`sec-scale.keno5.shapes` and :numref:`sec-scale.keno6.shapes`
for the particular value of *N* and how each **shape** is described.
*a*\ :sub:`1` … *a*\ :sub:`M` are *M* optional *ATTRIBUTES* for the **shape**. The
attributes provide additional flexibility in the **shape** description.
The attributes that may be used with either KENO V.a or KENO-VI are
described below (see shape ATTRIBUTES).
shape ATTRIBUTES
The *ATTRIBUTES* that can be used to enhance the **shape** description
are **CHORD**, **ORIG**\ [**IN**], **CENTER**, and **ROTATE** (KENO-VI
only).
The CHORD attribute
This attribute has different formats in KENO V.a and KENO-VI. The user
will notice that it is more restrictive in KENO V.a. Only the
**HEMISPHERE and HEMICYLINDER shape**\ s can be **CHORD**\ ed in KENO
V.a, but all 3-D shapes may be **CHORD**\ ed in KENO-VI.
KENO V.a:
**CHORD** :math:`\rho`
KENO-VI:
**CHORD** [**+X**\ =\ *x\ +*] [-**X**\ =\ *x\ -*] [**+Y**\ =\ *y\ +*]
[-**Y**\ =\ *y\ -*] [**+Z**\ =\ *z\ +*] [-**Z**\ =\ *z\ -*]
:math:`p` is the distance :math:`\rho` from the cut surface to the center of the sphere
or the axis of a hemicylinder. See :numref:`fig8-1-7` and :numref:`fig8-1-8`. Negative
values of :math:`\rho` indicate that less than half of the **shape** is retained,
while positive values indicate that more than half of the **shape** will
be retained.
**+X=**, -**X=**, **+Y=**, -**Y=**, **+Z=**, -**Z=**
are subordinate
keywords that define the axis parallel to the chord. The "+" and "-"
signs are used to define the side of the chord which is included in the
volume. A "+" in the keyword indicates that the more positive side of
the chord is included in the volume. A "-" in the keyword indicates that
the more negative side of the chord is included in the volume.
*x\ +, x\ -, y\ +, y\ -, z\ +, z\ -*
are the coordinates of the plane
perpendicular to the chord. For each chord added to a body, the keyword
**CHORD** must be used, followed by one of the subordinate keywords and
its dimension.
In KENO V.a, the CHORD attribute is applicable for only hemispherical
and hemicylindrical shapes, *not* for SPHERE, XCYLINDER, YCYLINDER,
CYLINDER, ZCYLINDER, CUBE, or CUBOID.
.. figure:: figs/Keno/fig7.png
:align: center
:name: fig8-1-7
Partial hemisphere or hemicylinder; less than half exists (less than half is defined by
:math:`\rho < 0`).
.. figure:: figs/Keno/fig8.png
:align: center
:name: fig8-1-8
Partial hemisphere of hemicylinder; more than half exists (more than half is defined by
:math:`\rho > 0`).
:numref:`fig8-1-9` provides two examples of the use of the CHORD option in
KENO-VI.
.. figure:: figs/Keno/fig9.png
:align: center
:name: fig8-1-9
Examples of the CHORD option in KENO-VI.
The ORIG\ [IN] attribute
The format is slightly different between KENO V.a and KENO-VI. Since the
entries in KENO-VI are key worded, the user has more flexibility in
choosing the order of these entries or in using default values. Only
non-zero values must be entered in KENO-VI, but all applicable values,
whether zero or non-zero, must be entered in KENO V.a.
KENO V.a:
**ORIG**\ [**IN**] *a b* [*c*]
KENO-VI:
**ORIGIN** [**X**\ =\ *x*\ :sub:`0`] [**Y**\ =\ *y*\ :sub:`0`] [**Z**\ =\ *z*\ :sub:`0`]
:math:`a`
is the X coordinate of the origin of a sphere or hemisphere; the X
coordinate of the centerline of a Z or Y cylinder or hemicylinder; the Y
coordinate of the centerline of an X cylinder or hemicylinder.
:math:`b`
is the Y coordinate of the origin of a sphere or hemisphere; the Y
coordinate of the centerline of a Z cylinder or hemicylinder; the Z
coordinate of the centerline of an X or Y cylinder or hemicylinder.
:math:`c`
is the Z coordinate of the origin of a sphere or hemisphere; it must
be omitted for all cylinders or hemicylinders.
**X=**, **Y=**, **Z=**
are the subordinate keywords used to define the
new position of the origin of the **shape**. If the a subordinate
keyword appears more than once after the **ORIGIN** keyword, the values
are summed. If the new value is zero, the particular coordinate does not
need to be specified.
*x*\ :sub:`0`, *y*\ :sub:`0`, *z*\ :sub:`0`
are the values for the new coordinates where the
origin of the **shape** is to be translated.
The CENTER attribute
This attribute establishes the reference center for the flux moment
calculations, which can be useful in TSUNAMI calculations. The syntax
for this attribute is:
**CENTER** *center_type* [*u*] [*x y z*]
*center_type*
is the reference center value, as described in
:numref:`tab8-1-16`. The default value is **global**.
*u*
is the **UNIT** number to be used as a reference center for this
region when the *center_type* is **unit**.
*x*, *y*, *z*
are the offset from the point specified by the
*center_type*. The default is 0.0 for all three entries.
.. table:: Reference center values
:align: center
:name: tab8-1-16
+-----------------------------------+-----------------------------------+
| **center_type** | **Reference point** |
+-----------------------------------+-----------------------------------+
| **unit** | Reference is defined as the |
| | origin of **UNIT** *unit_number* |
| | plus the offset defined by |
| | *x*, \ *y*, and *z*. |
+-----------------------------------+-----------------------------------+
| **global** | Reference is defined as system |
| | origin-i.e., (0,0,0) point of the |
| | **GLOBAL UNIT**-plus the offset |
| | defined by *x*, *y*, and *z*. |
+-----------------------------------+-----------------------------------+
| **local** | Reference is defined as the |
| | origin of the current **UNIT** |
| | plus the offset defined by *x*, |
| | *y*, and *z*. |
+-----------------------------------+-----------------------------------+
| **fuelcenter** | Reference is defined as the |
| | center of all fissile material in |
| | the system plus the offset |
| | defined by *x*, *y*, and *z*. |
+-----------------------------------+-----------------------------------+
| **wholeunit** | When entered for the first region |
| | in a unit, the reference for all |
| | regions in the unit are defined |
| | as the origin of the current unit |
| | plus the offset defined by |
| | *x*, \ *y*, and *z*. |
+-----------------------------------+-----------------------------------+
The ROTATE attribute
This attribute can only be used in the KENO-VI input. It allows for the
rotation of the **shape** or **HOLE** to which it is applied. If
**ORIGIN** and **ROTATE** data follow the same **shape** or **HOLE**
record, the **shape** is always rotated prior to translation, regardless
of the order in which the data appear. :numref:`fig8-1-10` provides an example
of the use of the **ROTATE** option. Its syntax is:
**ROTATE** [**A1**\ =\ *a*\ :sub:`1`] [**A2**\ =\ *a*\ :sub:`2`] [**A3**\ =\ *a*\ :sub:`3`]
**A1**\ =, **A2**\ =, **A3**\ =
are subordinate keywords to specify the
angles of rotation of the particular shape with respect to the origin of
the coordinate system. The Euler X-convention is used for rotation.
*a*\ :sub:`1`, *a*\ :sub:`2`, *a*\ :sub:`3`
are the values of the Euler rotation angles in
degrees. The default is 0 degrees. If a subordinate keyword appears more
than once following the ROTATE keyword, the values are summed.
.. figure:: figs/Keno/fig10.png
:align: center
:width: 500
:name: fig8-1-10
Explanation of the ROTATE option.
Examples of **shape**\ s:
1. Specify a hemisphere labeled 10, containing material 2 with a radius
of 5.0 cm which contains only material where Z > 2.0 within the
sphere centered at the origin, and its origin translated to X=1.0,
Y=1.5, and Z=3.0.
KENO V.a (no label, but material and bias ID are the first two numerical entries):
**HEMISPHERE** 2 1 5.0 **CHORD** -2.0 **ORIGIN** 1.0 1.5 3.0
or
**HEMISPHE+Z** 2 1 5.0 **CHORD** -2.0 **ORIGIN** 1.0 1.5 3.0
KENO-VI (no material; this is to be specified with **MEDIA**):
**SPHERE** 10 5.0 **CHORD** **+Z**\ =2.0 **ORIGIN** **X**\ =1.0
**Y**\ =1.5 **Z**\ =3.0
2. Specify a hemicylinder labeled 10, containing material 1, having a
radius of 5.0 cm and a length extending from Z=2.0 cm to Z=7.0 cm.
The hemicylinder has been truncated perpendicular to the X axis at
X= -3 such that material 1 does not exist between X= -3 and X= -5.
Position the origin of the truncated hemicylinder at X=10 cm and
Y=15 cm with respect to the origin of the unit, and rotate it (in
KENO-VI input) so it is in the YZ plane at X=10 and at a 45\ :math:`^{\circ}` angle
with the Y plane.
KENO V.a (no rotation possible, no label):
**ZHEMICYL+X** 1 1 5.0 7.0 2.0 **CHORD** 3.0 **ORIGIN** 10.0 15.0
KENO-VI (no material; this is to be specified with **MEDIA** card):
**CYLINDER** 10 5.0 7.0 2.0 **CHORD** **+X**\ = -3.0 **ORIGIN**
**X**\ =10.0 **Y**\ =15.0 **ROTATE** **A2**\ = -45
COM=
''''
The keyword **COM**\ = signals that a comment is to be read. The
optional comment can be placed anywhere within a unit definition. Its
syntax is:
**COM** = *delim comment delim*
*delim*
is the delimiter, which may be any one of " , ` , \* , ^ , or !
*comment*
is the comment string, up to 132 characters long.
Example of comment within a **UNIT**:
**COM**\="This is a fuel pin"
HOLE
''''
This entry is used to position a **UNIT** within a surrounding **UNIT**
relative to the origin of the surrounding **UNIT**. **HOLE**\ s may
share surfaces with but may not intersect other **HOLE**\ s, the
**BOUNDARY** of the **UNIT** which contains the **HOLE**, or an
**ARRAY** boundary. In KENO-VI, the **BOUNDARY** record of a **UNIT**
placed in a **HOLE** may contain more than one geometry label, but all
labels must be positive, indicating inside the respective geometry
bodies. The syntax for **HOLE** is:
KENO V.a:
**HOLE** *u x y z*
KENO-VI:
**HOLE** *u* [*a*\ :sub:`1` … [*a*\ :sub:`M` ]…]
*u*
is the unit previously defined that is to be placed within the
**HOLE**.
*x y z*
is the position of the **HOLE** in the KENO V.a host **UNIT**.
*a\ 1 … a\ M*
are optional KENO-VI *ATTRIBUTES* for the **HOLE**. The
*ATTRIBUTES* can be **ORIGIN** or **ROTATE** and follow the same syntax
previously defined for KENO-VI **shape** *ATTRIBUTES*. These
*ATTRIBUTES* allow for the translation and/or rotation of the **HOLE**
within the host region.
Examples of **HOLE** use:
Place **UNIT** 2 in the surrounding **UNIT** such that the **ORIGIN** of
**UNIT** 2 is at **X**\ =3, **Y**\ =3.5, **Z**\ =4 relative to the
origin of the surrounding **UNIT**.
KENO V.a:
**HOLE** 2 3 3.5 4
KENO-VI:
**HOLE** 2 **ORIGIN** **X**\ =3.0 **Y**\ =3.5 **Z**\ =4.0
ARRAY
'''''
When used within a **UNIT** description, this entry provides an
**ARRAY** placement description. In KENO V.a, it always starts a new
**UNIT** and generates a rectangular parallelepiped that fits the outer
boundaries of the specified **ARRAY**. The specified **ARRAY** is
positioned in the **UNIT** according to the most negative point in the
**ARRAY** with respect to the coordinate system of the surrounding
**UNIT**. Thus, the location of the minimum x, minimum y, and minimum z
point in the array is specified in the coordinate system of the **UNIT**
into which the **ARRAY** is being placed.
In KENO-VI, the **ARRAY** keyword is used to position an **ARRAY**
within a region in a surrounding **UNIT** relative to the origin of the
surrounding **UNIT**. When the subordinate keyword **PLACE** is entered,
it is followed by six numbers that precisely locate the **ARRAY** within
the surrounding **UNIT** as shown in the example below. The first three
numbers consist of the element in the **ARRAY** of the **UNIT** selected
to position the **ARRAY**. The next three numbers consist of the
position of the origin of the selected **UNIT** in the surrounding
**UNIT**. Higher level **ARRAY** boundaries may intersect lower level
**ARRAY** boundaries as long as they do not intersect **HOLE**\ s in the
**UNIT**\ s contained in the **ARRAY** or in **UNIT**\ s contained in
lower level **ARRAY**\ s.
The syntax for the **ARRAY** card is as follows:
KENO V.a:
**ARRAY** *array_id* *x y z*
KENO-VI:
**ARRAY** *array_id* *l*\ :sub:`1` … *l*\ :sub:`N` [**PLACE** *N*\ :sub:`x` *N*\ :sub:`y` *N*\ :sub:`z` *x y
z*]
*array_id*
is the label that identifies the array to be placed.
*l\ 1* … *l\ N*
is the *REGION DEFINITION VECTOR*. These are previously
defined **shape** labels, and together they define the region in which
the array *array_id* is to be placed. This is used only in KENO-VI.
*N\ x N\ y N\ z*
are three integers that define the element in the
**ARRAY** of the **UNIT** selected to position the **ARRAY**. This is
used only in KENO-VI.
*x y z*
specify the position of the **ARRAY** in the **UNIT**.
In KENO V.a, the x, y, and z values are the point where the most
negative x, y, and z point of the **ARRAY** is to be located in the
**UNIT**\ 's coordinates.
In KENO-VI, the x, y, and z values are the point where the origin of the
**UNIT** specified by *N\ x*, *N\ y*, and *N\ z* is to be located in the
**shape** specified by the *REGION DEFINITION VECTOR*.
Example of **ARRAY** use:
In KENO V.a, position the most negative point of **ARRAY** 6 at X = 2.0,
Y = 3.0, Z = 4.0 relative to the origin of the containing **UNIT**.
**ARRAY** 6 2.0 3.0 4.0
In KENO-VI, position instead the origin of **UNIT** (1,2,3) of **ARRAY**
6 at X = 2.0, Y = 3.0, Z = 4.0 and specify the **ARRAY** boundary to be
the region that is inside the geometry **shape**\ s labeled 10 and 20
and outside the geometry **shape** labeled 30 used to describe the
surrounding **UNIT**.
**ARRAY** 6 10 20 -30 **PLACE** 1 2 3 2.0 3.0 4.0
REPLICATE and REFLECTOR
'''''''''''''''''''''''
These keywords specific to KENO V.a are used to generate additional
geometry regions having the **shape** of the previous region. The
geometry keyword **REFLECTOR** is a synonym for **REPLICATE**. The
desired weighting functions can be applied to those regions by
specifying biasing data as described in :numref:`sec-module.keno.biasing`. The total
thickness generated for each surface is the thickness per region for
that surface times the number of regions to be generated, *nreg*.
The replicate specification is frequently used to generate weighting
regions external to an ``ARRAY`` placement description. Thus an
``ARRAY`` placement description followed by a ``REPLICATE`` description
would generate regions of a cuboidal shape. A cylindrical reflector
could be generated by following the ``ARRAY`` placement description with
a ``CYLINDER`` and then a ``REPLICATE``. A ``HOLE`` cannot immediately
follow a ``REPLICATE``.
Extra regions using default weights can be generated by specifying the
first importance region, *imp*, to be one that was not defined in the
*BIASING INFORMATION* provided in a ``READ BIAS`` block. This capability
can be used to generate extra regions for collecting information such as
fluxes, leakage, etc.
Multiple replicate descriptions can be used in any problem. This
capability can be used to model different reflector materials of
different thicknesses on different faces.
The number of appropriate region dimensions needed for specifying
``REPLICATE`` is determined by the preceding region. For example, if the
previous region were a ``SPHERE``, one entry (i.e., *t*\ :sub:`1`) would be
required. If the previous region were a ``CYLINDER``, the first entry,
*t*\ :sub:`1`, would be the thickness/region in the radial direction, the
second entry, *t*\ :sub:`2`, would the thickness/region in the positive length
direction, the third entry, *t*\ :sub:`3`, would be the thickness/region in the
negative length direction, etc. The ``REPLICATE`` specification
requirements for a ``CUBE`` are the same as for a ``CUBOID``.
Syntax:
``REPLICATE|REFLECTOR`` *m* *b* *t*\ :sub:`1` … *t*\ :sub:`N` *nreg*
*m*
is the number of the material (non-negative integer) that fills the
particular REPLICATE/REFLECTOR region in the **UNIT** description. A
material of zero indicates a void region (i.e., no material is present
in the volume defined by the **shape**).
*b*
is the bias identification number (positive integer) assigned to the
particular region defined by the ``shape`` in the KENO V.a ``UNIT``
description. If the specified bias ID is defined in a ``READ BIAS``
block, the bias ID number will be incremented automatically, increasing
one for each additional region up to *nreg*.
*t*\ :sub:`1` … *t*\ :sub:`N`
represent the thickness (floating point number) per region
for each of the *N* surfaces that define the particular ``shape``. If
the specified bias ID is one that is defined in the ``READ BIAS`` block, the
region thicknesses should be consistent with the thicknesses used to
generate the bias data being used. See :numref:`sec-module.xsdrnpm.fixed_sources`.
*nreg*
is the number of regions (integer) to be generated.
Example:
Create five regions of material 4, each being 3 cm thick, outside a
cuboid region (a cuboid has six dimensions). The inner-most of the five
generated regions has a *bias id* of 2. The following four regions have
*bias id* of 3, 4, 5, and 6.
MEDIA
'''''
This card is used in the KENO-VI input file to define the location of a
mixture relative to the geometric ``shape``\ s in the ``UNIT``.
:numref:`fig8-1-11` shows the input for a set of three intersecting
``SPHERE``\ s in a ``CUBOID``. The total volume data for a region in the
problem may be entered as the last entry on the ``MEDIA`` card by using
the ``VOL=`` keyword immediately followed by the volume in
cm\ :sup:`3`. The volume entered is the volume of the region in the unit
multiplied by the number of times the unit occurs in the problem minus
any volume excluded from the problem by ``ARRAY`` boundaries and
``HOLE``\ s. The volumes for any or all regions may be entered. If the
volume is entered here, this value will be used even if volumes are also
entered as a file or calculated (See :numref:`8-1-2-13`). Volumes not
entered will be determined by the input specified in the VOLUME DATA
block. If no volume is supplied, the KENO-VI default volume of -1 will
be used. This only affects volume-averaged quantities, i.e., not
*k*\ :sub:`eff`.
Syntax:
``MEDIA`` *m* *b* *l*\ :sub:`1` ... *l*\ :sub:`N` [``VOL`` = *v*]
*m*
is the material (positive integer or zero for vacuum) that fills the
region defined by ``MEDIA``.
*b*
is the *bias id* for the material sector being defined.
*l*\ :sub:`1` ... *l*\ :sub:`N`
is the region definition vector (*N* integers). These
are *N* previously defined **shape** labels that together define the
material sector.
``VOL`` =
is an optional sub-keyword used to input the material sector
volume.
*v*
is the volume in cm\ :sup:`3` of the material sector defined by the
``MEDIA`` card.
.. figure:: figs/Keno/fig11.png
:align: center
:width: 500
:name: fig8-1-11
Example of the MEDIA record.
BOUNDARY
''''''''
This card is used in KENO-VI to define the outer boundary of the
``UNIT``. In KENO V.a, the outer boundary of the ``UNIT`` is implicitly
defined by the last ``shape`` in the ``UNIT``. Each ``UNIT`` must have
one and only one ``BOUNDARY`` card.
Syntax:
``BOUNDARY`` *l\ 1* … *l\ N*
*l*\ :sub:`1` … *l*\ :sub:`N`
is the ``UNIT`` *BOUNDARY DEFINITION VECTOR* (*N*
integers). These are *N* previously defined **shape** labels that
together define the outer boundary of the **UNIT**. All entries must be
positive for the ``UNIT`` being defined to be used subsequently as a
``HOLE``.
.. _sec-module.keno.geom.array_data:
ARRAY Data
~~~~~~~~~~
The array definition data block is used to define the size of an
**ARRAY** and to position **UNIT**\ s (defined in the geometry data) in
a 3-D lattice that represents the **ARRAY** being described. As many
arrays as are necessary can be described in a problem, subject to
computer storage limitations. In KENO V.a, only one **ARRAY** may be
placed directly in a **UNIT**, but as many **ARRAY**\ s as are needed
may be placed in the **UNIT** by using **HOLE**\ s. In KENO-VI,
any number of arrays can be placed in any **UNIT** either directly or
indirectly using **HOLE**\ s. There is no default global array. If a
global array is desired it must be explicitly defined.
The **ARRAY** definition data is entered as:
READ ARRAY ARRAY_ DATA END ARRAY
The *ARRAY\_ DATA* consists of *ARRAY_PARAMETERS* and
*UNIT_ORIENTATION_DESCRIPTION*.
.. _sec-module.keno.geom.array_param:
ARRAY Parameters
^^^^^^^^^^^^^^^^
The ARRAY parameters that can be used in the definition of an ARRAY are:
**ARA**\ =
**GBL**\ =
**NUX**\ =, **NUY**\ =, **NUZ**\ =
**PRT**\ =
**COM**\ =
**TYP**\ = (KENO-VI only)
.. _sec-module.keno.geom.array.ara:
ARA=
''''
The **ARA**\ = parameter defines a reference number for an **ARRAY**. It
has no default in KENO-VI. In KENO V.a, if is missing, the default is 1.
Syntax:
**ARA**\ =\ *a*
*a*
is the reference number for the **ARRAY**. It has no default in
KENO-VI. In KENO V.a, if is missing, the default is 1.
.. _sec-module.keno.geom.array.gbl:
GBL=
''''
This is used to input the number of the global array.
Syntax:
**GBL**\ =\ *g*
*g*
is the reference number for the global **ARRAY**. In KENO V.a it
must not be entered more than once. The default is the largest value for
*a*, the reference number for the **ARRAY**. In KENO-VI it is no default
value and if entered more than once, the last value is used.
.. _sec-module.keno.geom.array.prt:
PRT=
''''
This entry is used to enable printing the **ARRAY** of **UNIT** numbers.
Syntax:
**PRT**\ =\ *print*
*print*
is a logical constant which defaults to YES, indicating that the
**ARRAY** of **UNIT** numbers is printed. If the value is NO, then a
summary table is printed instead containing the number of times each
unit is used in each array.
.. _sec-module.keno.geom.array.nu:
NUX=, NUY=, NUZ=
''''''''''''''''
These entries are used to input the number of units in the X, Y, and Z
directions, respectively.
Syntax:
**NUX**\ =\ *n*\ :sub:`x` **NUY**\ =\ *n*\ :sub:`y` **NUZ**\ =\ *n*\ :sub:`z`
*n*\ :sub:`x` *n*\ :sub:`y` *n*\ :sub:`z`
are the number of units in the X, Y, and Z directions,
respectively. There is no default in KENO-VI. In KENO V.a, each of them
defaults to 1.
.. _sec-module.keno.geom.array.type:
TYPE=
'''''
This entry is used to specify the type of **ARRAY** and is specific to
KENO-VI, where more than one type of arrays can be used. It cannot be
used in KENO V.a.
Syntax:
**TYP**\ =\ *atyp*
*atyp*
type of array (**cuboidal** or **square**, **hexagonal** or
**triangular**, **rhexagonal**, **shexagonal**, **dodecahedral**),
default = **cuboidal**
.. _sec-module.keno.geom.array.com:
COM=
''''
This keyword is used to enter a comment.
Syntax:
**COM**\ =\ *delim comment delim*
*delim*
is a delimiter. Acceptable delimiters are ", \`, \* , ^ , or !.
*comment*
is the comment string. Maximum *comment* length is
132 characters.
.. _sec-module.keno.array_orient:
ARRAY orientation data
^^^^^^^^^^^^^^^^^^^^^^
There are two methods to enter the **UNIT** numbers constituting an
**ARRAY**: **LOOP** and **FILL**.
.. _sec-module.keno.geom.array.loop:
LOOP Construct
''''''''''''''
The ``LOOP`` construct resembles a FORTRAN DO-loop construct.
The arrangement of ``UNIT``\ s may be considered as consisting of a 3-D
matrix of ``UNIT`` numbers, with the ``UNIT`` position increasing in the
positive X, Y, and Z directions, respectively.
Syntax:
``LOOP`` *u* *ix*\ :sub:`1` *ix*\ :sub:`2` incx *iy*\ :sub:`1` *iy*\ :sub:`2` incy *iz*\ :sub:`1` *iz*\ :sub:`2` *incz* ``END
LOOP``
*u*
is the ``UNIT`` identification number (a positive integer).
*ix*\ :sub:`1`
is the starting position in the X direction; *ix*\ :sub:`1` must be at
least 1 and less than or equal to *n*\ :sub:`x` of :numref:`sec-module.keno.geom.array.nu`.
*ix*\ :sub:`2` is the ending position in the X direction; *ix*\ :sub:`2` must be at
least 1 and less than or equal to *n\ x*.
*incx*
is the number of ``UNIT``\ s by which increments are made in the
positive X direction; *incx* must be greater than zero and less than or
equal to *n*\ :sub:`x`.
*iy*\ :sub:`1`
is the starting position in the Y direction; *iy*\ :sub:`1` must be at
least 1 and less than or equal to *n*\ :sub:`y`.
*iy*\ :sub:`2`
is the ending position in the Y direction; *iy*\ :sub:`2` must be at
least 1 and less than or equal to *n*\ :sub:`y`.
*incy*
is the number of **UNIT**\ s by which increments are made in the
positive Y direction; *incy* must be greater than zero and less than or
equal to *n*\ :sub:`y`.
*iz*\ :sub:`1`
is the starting position in the Z direction; *iz*\ :sub:`1` must be at
least 1 and less than or equal to *n*\ :sub:`z`.
*iz*\ :sub:`2`
is the ending position in the Z direction;, *iz*\ :sub:`2` must be at
least 1 and less than or equal to *n*\ :sub:`z`.
*incz*
is the number of **UNIT**\ s by which increments are made in the
positive Z direction; *incz* must be greater than zero and less than or
equal to *n*\ :sub:`z`.
The syntax for ending the **LOOP** construct is:
``END LOOP``
The sequence *u* through *incz* is repeated until the entire **ARRAY**
is described. If any portion of an **ARRAY** is defined in a conflicting
manner, the last entry to define that portion will determine the
**ARRAY**\ 's configuration. To use this feature, fill the entire
**ARRAY** with the most relevant **UNIT** number and superimpose the
other **UNIT** numbers in their proper places. An example showing the
use of the **LOOP** option is given below. This 5 :math:`\times` 4 :math:`\times` 3 **ARRAY** of
**UNIT**\ s is a matrix of **UNIT**\ s that has 5 \ **UNIT**\ s stacked
in the X direction, 4 \ **UNIT**\ s in the Y direction, and
3 \ **UNIT**\ s in the Z direction. X increases from left to right, and
Y increases from bottom to top. Each Z layer is shown separately.
Given:
.. code-block:: none
1 2 1 2 1 2 1 2 1 2 1 1 1 1 1
1 1 1 1 1 2 2 2 2 2 1 3 3 3 1
1 1 1 1 1 2 2 2 2 2 1 3 3 3 1
1 2 1 2 1 2 1 2 1 2 1 1 1 1 1
Z Layer 1 Z Layer 2 Z Layer 3
The data for this array could be entered using the following entries.
(1) 1 1 5 1 1 4 1 1 3 1
This fills the entire array with 1s.
(2) 2 2 5 2 1 4 3 1 1 1
This loads the four 2s in the first Z layer.
(3) 2 1 5 1 2 3 1 2 2 1
This loads the second and third rows of 2s in the second Z layer.
(4) 2 1 5 2 1 4 3 2 2 1
This loads the desired 2s in the first and fourth rows of the second Z layer.
(5) 3 2 4 1 2 3 1 3 3 1
This loads the 3s in the third Z layer and completes the array data input.
The second layer could have been defined by substituting the following data for entries (3) and (4):
(3) 2 1 5 1 1 4 1 2 2 1
This completely fills the second layer with 2s.
(4) 1 2 4 2 1 4 3 2 2 1
This loads the four 1s in the second layer.
When using the **LOOP** option, there is no single correct method of
entering the data. If a **UNIT** is improperly positioned in the
**ARRAY** or if some positions in the **ARRAY** are left undefined, it
is often easier to add data to correctly define the **ARRAY** than to
try to correct the existing data.
.. _sec-module.keno.geom.array.fill:
FILL Construct
''''''''''''''
The **FILL** construct enters data by stringing in **UNIT** numbers
starting at X=1, Y=1, Z=1, and varying X, then Y, and then Z to fill the
**ARRAY**. *n*\ :sub:`x` x *n*\ :sub:`y` x *n*\ :sub:`z` entries are required. FIDO-like
input options specified in :numref:`tab8-1-17` are also available for filling
the **ARRAY**.
Syntax:
``FILL`` *u*\ :sub:`1` … *u*\ :sub:`N` {``END FILL}``\ \|\ ``T``
*u*\ :sub:`1` … *u*\ :sub:`N` are the *N*\ =\ *n*\ :sub:`x` x *n*\ :sub:`y` x *n*\ :sub:`z` ``UNIT`` numbers
that make up the ``ARRAY``
The syntax for ending the ``FILL`` construct is
``END FILL``
An alternative to end the ``UNIT`` data in ``FILL`` is by entering the
letter ``T``.
.. tabularcolumns:: |p{2cm}|p{2cm}|p{2cm}|p{5cm}|
.. table:: FIDO-like input for mixed box orientation fill option.
:name: tab8-1-17
:class: longtable
+-----------------+-----------------+-----------------+-----------------+
| Count | Option | Operand | Function |
| | | | |
| field | field | field | |
+-----------------+-----------------+-----------------+-----------------+
| | | *j* | stores *j* at |
| | | | the current |
| | | | position in the |
| | | | array |
+-----------------+-----------------+-----------------+-----------------+
| *i* | R | *j* | stores *j* in |
| | | | the next *i* |
| | | | positions in |
| | | | the array |
+-----------------+-----------------+-----------------+-----------------+
| *i* | \* | *j* | stores *j* in |
| | | | the next *i* |
| | | | positions in |
| | | | the array |
+-----------------+-----------------+-----------------+-----------------+
| *i* | $ | *j* | stores *j* in |
| | | | the next *i* |
| | | | positions in |
| | | | the array |
+-----------------+-----------------+-----------------+-----------------+
| | F | *j* | fills the |
| | | | remainder of |
| | | | the array with |
| | | | unit number |
| | | | *j*, starting |
| | | | with the |
| | | | current |
| | | | position in the |
| | | | array |
+-----------------+-----------------+-----------------+-----------------+
| | A | *j* | sets the |
| | | | current |
| | | | position in the |
| | | | array to *j* |
+-----------------+-----------------+-----------------+-----------------+
| *i* | S | | increments the |
| | | | current |
| | | | position in the |
| | | | array by *i* |
| | | | (This allows |
| | | | for skipping |
| | | | *i* positions; |
| | | | *i* may be |
| | | | positive or |
| | | | negative.) |
+-----------------+-----------------+-----------------+-----------------+
| *i* | Q | *j* | repeats the |
| | | | previous *j* |
| | | | entries *i* |
| | | | times (default |
| | | | value of *i* is |
| | | | 1) |
+-----------------+-----------------+-----------------+-----------------+
| *i* | N | *j* | repeats |
| | | | previous *j* |
| | | | entries *i* |
| | | | times, |
| | | | inverting the |
| | | | sequence each |
| | | | time. (default |
| | | | value of *i* is |
| | | | 1) |
+-----------------+-----------------+-----------------+-----------------+
| *i* | B | *j* | backs *i* |
| | | | entries. From |
| | | | that position, |
| | | | repeats the |
| | | | previous *j* |
| | | | entries in |
| | | | reverse order |
| | | | (default value |
| | | | of *i* is 1) |
+-----------------+-----------------+-----------------+-----------------+
| *i* | I | *j k* | provides the |
| | | | end points j |
| | | | and k, with i |
| | | | entries |
| | | | linearly |
| | | | interpolated |
| | | | between them |
| | | | (i.e., a total |
| | | | of i+2 points). |
| | | | At least one |
| | | | blank must |
| | | | separate j and |
| | | | k. When used |
| | | | for an integer |
| | | | array, the |
| | | | I option should |
| | | | only be used to |
| | | | generate |
| | | | integer |
| | | | steps-i.e., (k-\|
| | | | j)/(i+1) |
| | | | should be a |
| | | | whole number |
+-----------------+-----------------+-----------------+-----------------+
| | T | | terminates the |
| | | | data reading |
| | | | for the array |
+-----------------+-----------------+-----------------+-----------------+
.. note:: When entering data using the options in this table, the *count field*
and *option field* must be adjacent with no imbedded blanks.
The operand field may be separated from the option field by one or
more blanks.
Example: Consider a 3 :math:`\times` 3 :math:`\times` 1 ``ARRAY`` filled with 8
``UNIT`` 1s and a ``UNIT`` 2, as shown below.
.. code-block:: none
1 1 1
1 2 1
1 1 1
The input data to describe this ``ARRAY`` could be entered as follows:
Option (1) ``1 1 1 1 2 1 1 1 1 T``
This fills the array one position at a time,
starting at the lower left corner. The ``T`` terminates the data.
or
Option (2) ``F1 A5 2 END FILL``
The F1 fills the entire array with 1s, the A5
locates the fifth position in the array, and the 2 loads a 2 in that
position. The ``END FILL`` terminates the data.
.. _sec-module.keno.albedo:
Albedo data
~~~~~~~~~~~
Albedo boundary conditions are entered using a *FACE CODE* to define
where albedo conditions are to be used, and using an *ALBEDO NAME* to
indicate which albedo condition is to be used on that face. The default
value for each face is vacuum or void. The default values are overridden
only on faces for which other albedo names are specified. Albedo boundary
conditions are applied only to the outermost region of a problem
(global boundaries). Different albedo options are allowed for
different global boundaries, and this may show some differences in both
KENO V.a and KENO-VI.
In previous SCALE versions, KENO V.a would have allowed the use of
albedo boundary conditions to the boundary faces if and only if the
outermost geometry region was a cuboid. For non-cuboidal outermost geometries,
only the void or vacuum albedo option could have been applied. This limitation
has been relaxed in SCALE 6.3; KENO V.a now allows some albedo options
for non-cuboidal boundary shapes.
Unlike KENO V.a, KENO-VI allows a combination of geometry shapes to be
used to define the boundaries of the global unit. Combinations of more than
one geometry shape may result in re-entrant surfaces in the model.
KENO-VI users need to be aware that when a neutron reaches a surface
with a vacuum albedo, that neutron exits the model and the history ends.
If a model contains features
that are reentrant, that is a neutron could exit the model and reenter
the model on the other side of an unmodeled region, all neutrons passing
through the problem boundary are lost when they reach the unmodeled
region. Neutrons are not "transported" across unmodeled areas between
reentrant surfaces. It is not possible to create a KENO V.a model with
reentrant problem outer boundary surfaces.
The syntax for entering the albedo boundary conditions is as follows. Note
that ``BODY`` is no longer considered as a *FACE CODE* in the KENO-VI albedo
boundary conditions capability, unlike the previous versions of SCALE.
KENO V.a:
``READ BOUNDS`` **fc**\ :sub:`1`\ =\ *a*\ :sub:`1` [**fc**\ :sub:`2`\ =\ *a*\ :sub:`2`]\ …
[**fc**\ :sub:`N`\ =\ *a*\ :sub:`N`] ``END BOUNDS``
KENO-VI:
``READ BOUNDS`` [**BODY**\ =\ *body_label* ] **fc**\ :sub:`1`\ =\ *a*\ :sub:`1` [**fc**\ :sub:`2`\ =\ *a*\ :sub:`2`]\ … [**fc**\ :sub:`N`\ =\ *a*\ :sub:`N`] ``END BOUNDS``
**fc**\ :sub:`1` … **fc**\ :sub:`N` are **N** *FACE CODE*\ s, each refers
to a single or combination of multiple faces of the global
boundaries (faces of the outermost region of a problem). *FACE CODE*\ s
for different outer shapes are defined in :numref:`tab8-1-18`.
*a*\ :sub:`1` … *a*\ :sub:`N` are the *ALBEDO NAME*\ s as defined in :numref:`tab8-1-19`.
**BODY=** refers to the body or shape label in the global unit input.
This optional parameter is available only for KENO-VI. The use of **BODY**
with any face code combination is an optional feature for the problems
in which the boundary definition vector of the global unit consists
of a single body label (e.g. **BOUNDARY 10**). However, any face code used
to specify an albedo condition on any face of a boundary shape must
follow the **BODY=** parameter when the boundary definition vector
of the global unit has more than one boundary labels (e.g., **BOUNDARY 10 20 30**).
In such a case, all albedo boundary condition specifications following
the **BODY=** definition are applied only on the faces of the body
given with that **BODY=** definition.
*body_label* is the integer label of one of the shapes or bodies listed
in the boundary definition vector of the global unit.
Albedo boundary conditions may be entered on each face of the global
boundaries multiple times. The boundary condition that applies to the
boundary face is the last one entered. If no boundary data are entered
or if no albedo boundary condition is applied to a boundary face, then
this boundary face is assumed to have a void or vacuum boundary condition.
Similarly, albedo boundary conditions may be entered on each face of
a boundary body listed in the boundary definition vector of the global unit
multiple times. In this KENO-VI specific case, the boundary condition
that applies to the boundary face of that body is the last one entered.
Example:
Apply the reflective albedo boundary condition to all faces of
a cuboidal outer boundary except the positive *X* face.
In this sample problem, KENO with the **ALL** face code first applies
the reflective albedo boundary condition to all faces of the outermost
geometry. Then, the **+XB=** face code overrides the albedo type
as *VACUUM* for the positive *X* face of the cuboidal outer boundary.
KENO V.a:
.. code-block:: scale
READ BOUNDS
ALL=mirror +XB=vacuum
END BOUNDS
KENO-VI:
.. code-block:: scale
read geometry
...
global unit 1
CUBOID 10 ...
...
BOUNDARY 10
end geometry
READ BOUNDS
ALL=mirror +XB=vacuum
END BOUNDS
' following albedo specification is identical with the above one
' READ BOUNDS
' BODY=10 ALL=mirror +XB=vacuum
' END BOUNDS
Example:
Apply a material-specific albedo *H2O* to all faces of the global boundaries
except the bottom face of the cuboid, which is one of the boundary shapes. Another
material-specific albedo *CONC24* is applied to the bottom face of this cuboid.
This sample problem demonstrates the albedo boundary condition specification
for a KENO-VI model in which outer boundary of the global unit is defined
by a combination of a cuboid and a sphere (CUBOID 10 and SPHERE 20).
KENO-VI, with this input, first applies a material-specific albedo, *H2O*, to
all faces of BODY 10. Then, it overrides the boundary condition of the
bottom face of the cuboid with another material-specific albedo, *CONC24*.
Finally, material-specific albedo *H2O* is also applied to the spherical face
of BODY 20.
KENO-VI:
.. code-block:: scale
read geometry
...
global unit 1
CUBOID 10 ...
SPHERE 20 ...
...
BOUNDARY 10 20
end geometry
READ BOUNDS
BODY=10 ALL=H2O -ZB=CONC24
BODY=20 ALL=H2O
END BOUNDS
' following albedo specification is identical with the above one
' READ BOUNDS
' BODY=10 ALL=H2O
' BODY=20 ALL=H2O
' BODY=10 -ZB=CONC24
' END BOUNDS
All available **FACE CODE**\ s are described in :numref:`tab8-1-18`. Note that
the listed **FACE CODE**\ s are supported by both KENO V.a and KENO-VI.
.. tabularcolumns:: |p{3cm}|p{10cm}|
.. table:: Face codes and surface numbers for entering boundary (albedo) conditions.
:align: center
:name: tab8-1-18
:class: longtable
+-----------------------------------+----------------------------------------------+
| Face codes | Faces defined by face codes |
+-----------------------------------+----------------------------------------------+
| ALL= | All faces of a single or multiple boundary |
| | shape(s) |
| | |
+-----------------------------------+----------------------------------------------+
| SURFACE( k )= | Albedo surface enumeration indicates any |
| | :math:`k^{th}` face of the boundary shape |
| | |
| | (:numref:`kenova-surf-enum` and |
| | :numref:`kenovi-surf-enum` list |
| | shape-specific albedo surface numbers) |
+-----------------------------------+----------------------------------------------+
| +XB= | Positive X face of a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| &XB= | Positive X face of a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| -XB= | Negative X face of a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| +YB= | Positive Y face of a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| &YB= | Positive Y face of a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| -YB= | Negative Y face of a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| +ZB= | Positive Z face of a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| &ZB= | Positive Z face of a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| -ZB= | Negative Z face of a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| XFC= | Both positive and negative X faces of |
| | a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| YFC= | Both positive and negative Y faces of |
| | a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| ZFC= | Both positive and negative Z faces of |
| | a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| +FC= | Positive X, Y, and Z faces faces of |
| | a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| &FC= | Positive X, Y, and Z faces of |
| | a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| -FC= | Negative X, Y, and Z faces of |
| | a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| XYF= | Positive and negative X and Y faces of |
| | a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| XZF= | Positive and negative X and Z faces of |
| | a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| YZF= | Positive and negative Y and Z faces of |
| | a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| +XY= | Positive X and Y faces of |
| | a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| +YX= | Positive X and Y faces of |
| | a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| &XY= | Positive X and Y faces of |
| | a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| &YZ= | Positive X and Y faces of |
| | a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| +XZ= | Positive X and Z faces of |
| | a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| +ZX= | Positive X and Z faces of |
| | a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| &XZ= | Positive X and Z faces of |
| | a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| &ZX= | Positive X and Z faces of |
| | a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| +YZ= | Positive Y and Z faces of |
| | a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| +ZY= | Positive Y and Z faces of |
| | a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| &YZ= | Positive Y and Z faces of |
| | a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| &ZY= | Positive Y and Z faces of |
| | a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| -XY= | Negative X and Y faces of |
| | a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| -XZ= | Negative X and Z faces of |
| | a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| -YZ= | Negative Y and Z faces of |
| | a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| YXF= | Positive and negative X and Y faces of |
| | a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| ZXF= | Positive and negative X and Z faces of |
| | a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| ZYF= | Positive and negative Y and Z faces of |
| | a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| -YX= | Negative X and Y faces of |
| | a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| -ZX= | Negative X and Z faces of |
| | a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
| -ZY= | Negative Y and Z faces of |
| | a cuboidal boundary shape |
+-----------------------------------+----------------------------------------------+
.. warning::
In SCALE 6.3:
- Face codes, which are specific to the cuboidal boundary shape, cannot be used
with non-cuboidal boundary shapes.
- **SURFACE(..)** face code **cannot be used** together with any cuboidal
face codes listed in :numref:`tab8-1-18` if the outermost geometry is cube or cuboid.
- The **ALL** face code refers to all faces of the global boundaries.
Unlike the albedo boundary conditions capability in KENO codes of previous SCALE versions,
*FACE CODE* definitions and their use are slightly different in SCALE 6.3.
**SURFACE(..)=** face code is a valid option for both KENO V.a and KENO-VI.
**SURFACE(..)=** face code with a corresponding albedo surface number
can be used to apply an albedo boundary condition to the specified surface
of **any boundary shape** (cuboidal or non-cuboidal). Albedo surface enumerations
for all geometric shapes supported by KENO V.a and KENO-VI are listed in
:numref:`kenova-surf-enum` and :numref:`kenovi-surf-enum`, respectively.
Note that entering an illegal albedo surface number with **SURFACE(..)** face
code in bounds data input block fails the execution
(i.e., SURFACE(2)=... for a sphere, SURFACE(9) for a hexprism, etc.)
The **ALL=** face code will apply the listed boundary condition to all
surfaces of a single boundary shape, or multiple boundary shapes (KENO-VI only).
It can be used with any boundary shape available in both KENO V.a and KENO-VI.
If it follows a **BODY=** definition, then it refers to all the faces
of the body given with that **BODY=** definition (KENO-VI only).
All the face codes, which are listed in :numref:`tab8-1-18`, except **ALL=** and
**SURFACE(..)**, are specific to the cuboidal boundary shape, and
they may be applied only to the cuboid or cube boundaries.
.. table:: Albedo surface numbers related to KENO V.a geometry shapes
:name: kenova-surf-enum
:align: center
+-------------------+-------------------------------------------------------------------------+
| GEOMETRY SHAPE | ALBEDO SURFACE ENUMERATION |
| +-----------+----------------+-----------+----------------+--------+------+
| | 1 | 2 | 3 | 4 | 5 | 6 |
+-------------------+-----------+----------------+-----------+----------------+--------+------+
| | | | | | | |
| CUBE | +X | -X | | | | |
+-------------------+-----------+----------------+-----------+----------------+--------+------+
| | | | | | | |
| CUBOID | +X | -X | +Y | -Y | +Z | -Z |
+-------------------+-----------+----------------+-----------+----------------+--------+------+
| | | | | | | |
| CYLINDER | Radial | +Z | -Z | | | |
+-------------------+-----------+----------------+-----------+----------------+--------+------+
| | | | | | | |
| HEMISPHERE | Radial | Cut surface | | | | |
+-------------------+-----------+----------------+-----------+----------------+--------+------+
| | | | | | | |
| HEMICYLINDER | Radial | Top | Bottom | Cut surface | | |
+-------------------+-----------+----------------+-----------+----------------+--------+------+
| | | | | | | |
| SPHERE | Radial | | | | | |
+-------------------+-----------+----------------+-----------+----------------+--------+------+
| | | | | | | |
| XCYLINDER | Radial | +X | -X | | | |
+-------------------+-----------+----------------+-----------+----------------+--------+------+
| | | | | | | |
| YCYLINDER | Radial | +Y | -Y | | | |
+-------------------+-----------+----------------+-----------+----------------+--------+------+
| | | | | | | |
| ZCYLINDER | Radial | +Z | -Z | | | |
+-------------------+-----------+----------------+-----------+----------------+--------+------+
.. raw:: latex
\begin{landscape}
.. tabularcolumns:: |p{1.4cm}|p{.8cm}|p{.8cm}|p{.8cm}|p{.8cm}|p{.8cm}|p{.8cm}|p{.8cm}|p{.8cm}|p{.8cm}|p{.8cm}|p{.8cm}|p{.8cm}
.. table:: Albedo surface numbers related to KENO-VI geometry bodies.
:name: kenovi-surf-enum
:class: longtable
+------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------+
| GEOMETRY BODY | ALBEDO SURFACE ENUMERATION |
+ +-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| CONE | Radial | +Z | -Z | | | | | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| CUBOID | +X | -X | +Y | -Y | +Z | -Z | | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| CYLINDER | Radial | +Z | -Z | | | | | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | |+X |br| +Y |-X |br| -\Y|-X |br| +Y |+X |br| -Y |-X |br| -Y |+X |br| +Y |+X |br| -Y |-X |br| +Y |
| DODECAHEDRON | +X | -X | +Y | -Y ||br| +Z ||br| -\Z ||br| +Z ||br| -Z ||br| +Z ||br| -Z ||br| +Z ||br| -Z |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| ECYLINDER | Radial | +Z | -Z | | | | | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| ELLIPSOID | Radial | | | | | | | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| HEXPRISM | +X | -X |+X |br| +Y|-X |br| -Y|-X |br| +Y |+X |br| -Y | +Z | -Z | | | | |
| | | | | | | | | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| HOPPER | +X | -X | +Y | -Y | +Z | -Z | | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| PENTAGON | -Y | +X |br| -Y |+X |br| +Y|-X |br| +Y|-X |br| -Y | +Z | -Z | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| PLANE | Surface | | | | | | | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| QUADRA\ | | | | | | | | | | | | |
| TIC | Surface | | | | | | | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| RHEXPRISM | +Y | -Y |-X |br| +Y|+X |br| -Y|+X |br| +Y |-X |br| -\Y| +Z | -Z | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| RING | Inner Radius | Outer Radius | +Z | -Z | | | | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| SPHERE | Radial | | | | | | | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| WEDGE | -Y | -X |br| +Y |+X |br| +Y| +Z | -Z | | | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| XCYLINDER | Radial | +X | -X | | | | | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| XPPLANE | +X | -X | | | | | | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| YCYLINDER | Radial | +Y | -Y | | | | | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| YPPLANE | +Y | -Y | | | | | | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| ZCYLINDER | Radial | +Z | -Z | | | | | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| | | | | | | | | | | | | |
| ZPPLANE | +Z | -Z | | | | | | | | | | |
+------------------+-----------------+-----------------+----------+----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+
| |
| Surfaces refer to the pre-rotation surface of the body that occurs in the indicated quadrant. |
| |
| Refer to :numref:`fig8-1-1` through :numref:`fig8-1-22` for illustrations of each geometry body. |
+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
.. raw:: latex
\end{landscape}
All albedo names available in both KENO codes are given in :numref:`tab8-1-19`.
:numref:`tab8-1-19` lists also some material-specific albedo sets. Care must be
exercised when using material-specific albedo types. These data sets
were generated using a real problem, and they implicitly reflect the
neutron energy spectrum, materials, and geometry from that model. Where
neutron energy spectra, materials, and geometry vary from that model,
the material-specific albedos may give significantly incorrect results.
This may be checked by comparing results from a sample of calculations
performed with both explicitly modeled reflectors and material-specific
albedos. In general, use of material-specific albedos is not
recommended.
.. warning:: The user should thoroughly understand material-specific
albedos (e.g., DP0H2O, CON24, etc.) before attempting to use these
reflectors. Misapplication of these problem-specific albedo data can
cause the code to produce incorrect results without obvious symptoms.
.. table:: Albedo names available on the KENO albedo library for use with the face codes \*
:align: center
:name: tab8-1-19
+-----------------------------------+-----------------------------------+
| DP0H2O, DPOH2O, DP0, DPO | 12 in. (30.48 cm) double |
| | P\ :sub:`0` water differential |
| | albedo with 4 incident angles |
+-----------------------------------+-----------------------------------+
| H2O, WATER | 12 in. (30.48 cm) water |
| | differential albedo with |
| | 4 incident angles |
+-----------------------------------+-----------------------------------+
| PARAFFIN, PARA, WAX | 12 in. (30.48 cm) paraffin |
| | differential albedo with |
| | 4 incident angles |
+-----------------------------------+-----------------------------------+
| CARBON, GRAPHITE, C | 78.74 in. (200.00 cm) carbon |
| | differential albedo with |
| | 4 incident angles |
+-----------------------------------+-----------------------------------+
| ETHYLENE, POLY, CH2 | 12 in. (30.48 cm) polyethylene |
| | differential albedo with |
| | 4 incident angles |
+-----------------------------------+-----------------------------------+
| CONC-4, CON4, CONC4 | 4 in. (10.16 cm) concrete |
| | differential albedo with |
| | 4 incident angles |
+-----------------------------------+-----------------------------------+
| CONC-8, CON8, CONC8 | 8 in. (20.32 cm) concrete |
| | differential albedo with |
| | 4 incident angles |
+-----------------------------------+-----------------------------------+
| CONC-12, CON12, CONC12 | 12 in. (30.48 cm) concrete |
| | differential albedo with |
| | 4 incident angles |
+-----------------------------------+-----------------------------------+
| CONC-16, CON16, CONC16 | 16 in. (40.64 cm) concrete |
| | differential albedo with |
| | 4 incident angles |
+-----------------------------------+-----------------------------------+
| CONC-24, CON24, CONC24 | 24 in. (60.96 cm) concrete |
| | differential albedo with |
| | 4 incident angles |
+-----------------------------------+-----------------------------------+
| VACUUM, VOID | Vacuum condition |
+-----------------------------------+-----------------------------------+
| SPECULAR, MIRROR, REFLECT | Mirror image reflection |
+-----------------------------------+-----------------------------------+
| PERIODIC | Periodic boundary condition |
+-----------------------------------+-----------------------------------+
| WHITE | White boundary condition |
+-----------------------------------+-----------------------------------+
| \* Material-specific albedos (differential albedos) may not be used |
| in continuous energy mode |
+-----------------------------------------------------------------------+
.. note:: Differential albedos (material specific albedos), e.g., H2O and CONC,
may not be used in continuous energy calculations. In multigroup mode,
none of the differential albedos are allowed for the adjoint transport
mode.
Different albedo options are allowed for different global boundaries. If the
global boundary is a single cube or cuboids, then any available albedo option
is allowed on any face of this cuboidal global boundary. However, if a
periodic boundary condition is to be used, then it must be specified on opposing
faces simultaneously.
.. warning::
There is no consistency check for the surfaces on which **PERIODIC**
boundary condition has been specified. It is the user's responsibility to
specify the **PERIODIC** boundary condition on opposing faces simultaneously.
Albedo options for non-cuboidal global boundaries may show some differences in
KENO V.a and KENO-VI:
KENO V.a:
- Albedo boundary conditions other than **VACUUM** are not allowed if the
outermost geometry is either a hemisphere or a hemicylinder.
- Material-specific albedos cannot be applied to the curvilinear faces of
the outermost geometry.
- **MIRROR** and **PERIODIC** boundary conditions are not allowed on the
curvilinear faces of the outermost geometry.
- Whereas **WHITE** or **VACUUM** may be applied to the radial face of a
cylinder, any albedo options can be used for the top and bottom faces.
Example:
Use a 24-in. concrete albedo boundary condition on the -Z face of the
problem and use mirror image reflection on the +X and -X faces to represent
an infinite linear array on a 2 ft thick concrete pad.
.. code-block:: scale
READ BOUNDS
XFC=mirror -ZB=CONC24
END BOUNDS
Example:
A cylinder with arbitrarily chosen length is specularly reflected on the
top and bottom faces to create an infinitely long cylinder.
.. code-block:: scale
READ BOUNDS
SURFACE(2)=mirror SURFACE(3)=mirror
END BOUNDS
KENO-VI:
- Any CHORDed surfaces that are global unit boundaries will use the
default (VOID) boundary condition, and this cannot be changed.
Because KENO-VI does not provide any input method to assign a non-vacuum
albedo boundary condition to the CHORDed surface(s), this restriction
may need to be considered when building the geometry of the global unit.
- If the boundary definition vector of the global unit contains only a single
body label, then all albedo boundary conditions are allowed on any face of the global
boundary.
- If the boundary definition vector of the global unit contains multiple body
labels and all these body labels are positive numbers (e.g. **BOUNDARY 10 20 30**),
then all albedo boundary conditions may be applied to any of the faces of each
body.
- If the boundary definition vector of the global unit contains multiple body
labels and any of these body labels are negative numbers
(e.g. **BOUNDARY 10 20 -30**), then only the **VACUUM** albedo is allowed on
the faces of all bodies.
.. caution:: No non-vacuum albedo boundary conditions can be applied to a CHORDed
surface that is global unit boundary.
Example:
A cylinder with an arbitrarily chosen length is specularly reflected on the
top and bottom faces to create an infinitely long cylinder.
.. code-block:: scale
read geometry
...
global unit 1
CYLINDER 10 ...
...
BOUNDARY 10
end geometry
READ BOUNDS
ALL=mirror SURFACE(1)=void
END BOUNDS
' identical boundary condition can be applied with another definition
' READ BOUNDS
' BODY=10 SURFACE(2)=reflective SURFACE(3)=mirror
' END BOUNDS
Example:
Use a 24 in. concrete albedo boundary condition on the -Z face of the problem
and use mirror image reflection on the +X and -X faces to represent an infinite
linear array on a 2 ft thick concrete pad.
.. code-block:: scale
read geometry
...
global unit 1
CUBOID 101 ...
...
BOUNDARY 101
end geometry
READ BOUNDS
SURFACE(1)=mirror SURFACE(2)=mirror SURFACE(6)=CON24
END BOUNDS
' identical boundary condition can be applied with another definition
' READ BOUNDS
' BODY=101 XFC=reflective -ZB=CONC24
' END BOUNDS
Example:
Use a 24-in. concrete albedo boundary condition on the -Z face of
a problem with a hexagonal boundary and use mirror image reflection on
all side faces of the hexprism to represent an infinite planar array
on a 2-ft-thick concrete pad.
.. code-block:: scale
read geometry
...
global unit 1
HEXPRISM 201 ...
...
BOUNDARY 201
end geometry
READ BOUNDS
SURFACE(1)=mirror SURFACE(2)=mirror
SURFACE(3)=mirror SURFACE(4)=mirror
SURFACE(5)=mirror SURFACE(6)=mirror
SURFACE(7)=vacuum SURFACE(8)=conc24
END BOUNDS
' an alternative albedo specification for the same boundary conditions
' READ BOUNDS
' ALL=mirror SURFACE(7)=vacuum SURFACE(8)=con24
' END BOUNDS
'
' an alternative albedo specification for the same boundary conditions
' READ BOUNDS
' BODY=201 ALL=mirror SURFACE(7)=vacuum SURFACE(8)=con24
' END BOUNDS
'
' an alternative albedo specification for the same boundary conditions
' READ BOUNDS
' ALL=mirror
' BODY=201 SURFACE(7)=vacuum SURFACE(8)=con24
' END BOUNDS
'
Example:
The outer boundary of the global unit consists of a cuboid
(body label 10) and a sphere (body label 20). The sphere is large enough
to cut the corners of the cuboid leaving most of the cuboid intact. Use
a 24 in. concrete albedo boundary condition on the -Z face of the cuboid
to represent a 2 ft. thick concrete pad. Use the DP0H2O on the other
surfaces to represent an infinite water reflector.
.. code-block:: scale
read geometry
...
global unit 1
CUBOID 10 ...
SPHERE 20 ...
...
BOUNDARY 10 20
end geometry
READ BOUNDS
BODY=10 ALL=DP0H2O -ZB=CONC24
BODY=20 SURFACE(1)=DPOH2O
END BOUNDS
' an alternative albedo specification for the same boundary conditions
' READ BOUNDS
' ALL=DPOH2O
' BODY=10 -ZB=CONC24
' END BOUNDS
Note that the **ALL** face code is used in two different ways in the above example:
(1) Used with body 10 to apply **DPOH2O** albedo *to all faces of this body*
(2) Used without body, which is legitimate for KENO-VI, to apply **DPOH2O**
albedo *to all faces of both body 10 and 20* (global unit boundaries defined
by CUBOID 10 and SPHERE 20).
Example:
KENO geometry specification allows modeling the same physical problem with
different geometry definitions. For some cases, boundary condition specification
becomes more critical to represent the same problem with different
geometry configurations. Users must be extra cautious when building
their model and examine the limitations listed in this section carefully
to prevent unexpected results.
This example was designed to demonstrate how ignoring such limitations
for albedo boundary condition setup affects results in analysis. In this
example, a model of a simplified version of a GODIVA sphere was attempted
with three different geometry definitions as shown below.
KENO-VI, full GODIVA sphere:
.. code-block:: scale
...
READ GEOMETRY
global unit 1
sphere 30 8.75
media 1 1 30
boundary 30
END GEOMETRY
READ BOUNDS
ALL=vacuum
END BOUNDS
KENO-VI, half GODIVA sphere defined by combination of a sphere and a cuboid:
.. code-block:: scale
...
READ GEOMETRY
global unit 1
sphere 30 8.75
cuboid 40 8.75 0.0 4p8.75
media 1 1 30 40
boundary 30 40
END GEOMETRY
READ BOUNDS
ALL=mirror
BODY=30 surface(1)=void
END BOUNDS
KENO-VI, half GODIVA sphere defined by a sphere and a CHORD modifier:
.. code-block:: scale
...
READ GEOMETRY
global unit 1
sphere 30 8.75 chord +x=0.0
media 1 1 30
boundary 30
END GEOMETRY
READ BOUNDS
ALL=mirror surface(1)=void
END BOUNDS
The first geometry definition uses only a sphere to define the Godiva
sphere. The second sample input uses the combination of a sphere and
a cuboid to define a hemisphere and an appropriate boundary condition
on each outer boundary to simulate the Godiva sphere. Similarly, in
the third sample input, a modified CHORD was used with a sphere to define
a hemisphere and an appropriate boundary condition on each outer
boundary to simulate the Godiva sphere.
But even if the sample input with the CHORDed surface given above
seems correct at first glance, it cannot model the same physical problem as
the other two because the
albedo boundary condition specification with ALL=MIRROR is not applied
to the CHORDed surface. Therefore, that CHORDed sphere models a
half GODIVA sphere rather than a full one. Results from these three
models, presented in :numref:`tab-module.keno.albedo_chord`, indicate that
using code capabilities improperly might result in significant bias in the
results.
.. table:: k-eff results of GODIVA models used in this example
:align: center
:name: tab-module.keno.albedo_chord
+----------------------------------------------------+---------------------+
| **Model** | **k-eff** |
+----------------------------------------------------+---------------------+
| Full sphere | 1.02680 +/- 0.00100 |
+----------------------------------------------------+---------------------+
| Half sphere defined by a sphere and a cuboid | 1.02962 +/- 0.00075 |
+----------------------------------------------------+---------------------+
| Half sphere defined by a sphere and a CHORD | 0.78745 +/- 0.00078 |
+----------------------------------------------------+---------------------+
Unlike KENO codes in previous versions, in SCALE 6.3, KENO codes print several
warning messages to remind the user about such limitations and their potential
effects if ignored.
.. caution:: There is no input method to assign a non-vacuum boundary condition
to a CHORDed boundary surface (external boundary). Therefore, KENO-VI always
applies VACUUM boundary condition to the CHORDed boundary surfaces, and this
cannot be changed.
.. _sec-module.keno.biasing:
Biasing or weighting data
~~~~~~~~~~~~~~~~~~~~~~~~~
The biasing data block is used (in only multigroup mode) to define the
weight that is given to a neutron surviving Russian roulette. The
average weight of a neutron that survives Russian roulette, *wtavg*, is
defaulted to *dwtav* (**WTA**\ = in the parameter data [see :numref:`sec-module.keno.parameters`])
for all *BIAS IDs* and can be overridden by entering biasing
information.
The *biasing_information* is used to relate a *BIAS ID* to the desired
energy-dependent values of *wtavg*. This concept is similar to the way
the *MIXTURE ID, mat*, is related to the macroscopic cross section data.
The weighting functions used in KENO are energy-dependent values of
*wtavg* that are applicable over a given thickness interval of a
material. For example, the weighting function for water is composed of
sets of energy-dependent values of *wtavg* for 11 intervals, each
interval being 3 cm thick. The first set of *wtavg's* is for the 0--3 cm
interval of water, the second set of *wtavg's* is for the 3--6 cm
interval of water, etc. The eleventh set of *wtavg's* is for the 30--33
cm interval of water.
To input biasing information, a *BIAS ID* must be assigned to correspond
to a set of *wtavg*. Biasing data can specify a *MATERIAL ID* from the
existing KENO V.a weighting library or from the *AUXILIARY DATA* input.
The materials available from the KENO weighting library are listed in
:numref:`tab8-1-20`.
The *biasing_information* is entered in one of the following two forms.
The first set is said to input the *CORRELATION DATA*, while the second
form is said to input the *AUXILIARY DATA*.
``READ BIAS ID**\ =\ *m ib ie* ``END BIAS``
or
``READ BIAS WT``\ [``S``\ ]=\ *wttitl id s* *t*\ :sub:`1` *i*\ :sub:`1` *g*\ :sub:`1` *w*\ :sub:`1,1` …
*w*\ :sub:`1,i1xg1` … *t*\ :sub:`s` *i*\ :sub:`s` *g*\ :sub:`s` *w*\ :sub:`s,1` … *w*\ :sub:`s,isxgs` ``END BIAS``
``ID=`` specifies that *CORRELATION DATA* will be entered next.
``WT=`` or ``WTS=`` specifies that *AUXILIARY DATA* will be entered
next.
*m*
is the identification (material ID) for the material whose weighting
function is to be used. A material ID can be chosen from the existing
KENO weighting library (:numref:`tab8-1-20`) or from the *auxiliary data* input
using the second form of the **BIAS** block as described later. If a
material ID appears in both the KENO weighting library and the
*auxiliary data*, the *weights* from the *auxiliary data* will be used.
*ib*
is the bias ID of the weighting function for the first interval of
material *m*. The geometry record having the bias ID equal to *ib* will
use the group-dependent *weights* from the first interval of material
*m*.
*ie*
is the bias ID of the group-dependent *weights* from the (*ie* -
*ib* + 1)\ *th* interval of material *m*.
*wttitl*
is an arbitrary title name (12 characters maximum), such as
CONCRETE, WATER, SPECIALH2O, etc., to identify the material for which
the user is entering data. Embedded blanks are not allowed.
*id*
is an identification number (material ID). The value is arbitrary.
However, if the data are to be utilized in the problem, this ID must
also be used at least once in the first form of the **BIAS** block.
*s*
is the number of sets of group structures for which *weights* will
be read for this ID.
*t*\ :sub:`1`\ … *t*\ :sub:`s`
are *s* thicknesses of each increment for which *weights*
will be read for this ID.
*i*\ :sub:`1`\ … *i*\ :sub:`s`
are *s* numbers of increments for which *weights* will be
read for this ID.
*g*\ :sub:`1`\ … *g*\ :sub:`s`
are *s* numbers of energy groups for which *weights* will
be read.
*w*\ :sub:`1,i1xg1`\ … *w*\ :sub:`s,isxgs`
are *s* sets of *weights*, each set containing
a number of *weights* equal to the product of number of increments times
the number of groups for that set. The group index varies the fastest.
.. tabularcolumns:: |p{2cm}|p{2cm}|p{3cm}|p{3cm}|p{3cm}|
.. table:: IDs, group structure and incremental thickness for weighting data available on the KENO weighting library.
:class: longtable
:name: tab8-1-20
+-------------+-------------+-------------+-------------+-------------+
| Material | Material | Group | Increment | Total |
| | ID | structure | :sup:`a` | number of |
| | | for which | thickness | increments |
| | | weights | (cm) | available |
| | | are | | |
| | | available | | |
+-------------+-------------+-------------+-------------+-------------+
| Concrete | 301 | 27 | 5 | 20 |
| | | | | |
| | | 28 | 5 | 20 |
| | | | | |
| | | 56 | 5 | 20 |
| | | | | |
| | | 200 | 5 | 20 |
| | | | | |
| | | 238 | 5 | 20 |
| | | | | |
| | | 252 | 5 | 20 |
+-------------+-------------+-------------+-------------+-------------+
| Paraffin | 400 | 27 | 3 | 10 |
| | | | | |
| | | 28 | 3 | 10 |
| | | | | |
| | | 56 | 3 | 10 |
| | | | | |
| | | 200 | 3 | 10 |
| | | | | |
| | | 238 | 3 | 10 |
| | | | | |
| | | 252 | 3 | 10 |
+-------------+-------------+-------------+-------------+-------------+
| Water | 500 | 27 | 3 | 10 |
| | | | | |
| | | 28 | 3 | 10 |
| | | | | |
| | | 56 | 3 | 10 |
| | | | | |
| | | 200 | 3 | 10 |
| | | | | |
| | | 238 | 3 | 10 |
| | | | | |
| | | 252 | 3 | 10 |
+-------------+-------------+-------------+-------------+-------------+
| Graphite | 6100 | 27 | 20 | 10 |
| | | | | |
| | | 28 | 20 | 10 |
| | | | | |
| | | 56 | 20 | 10 |
| | | | | |
| | | 200 | 20 | 10 |
| | | | | |
| | | 238 | 20 | 10 |
| | | | | |
| | | 252 | 20 | 10 |
+-------------+-------------+-------------+-------------+-------------+
| :sup:`a` Group-dependent weight averages are supplied for each |
| increment of the specified incremental thickness (i.e., for any |
| given material) the first ngp (number of energy groups) weights |
| apply to the first increment of the thickness specified here, the |
| next ngp weights apply to the next increment of that thickness, etc|
| CAUTION--If bias IDs defined in the weighting information data are |
| used in the geometry, the region thickness should be consistent |
| with the incremental thickness of the weighting data in order to |
| avoiid overbiasing or underbiasing. |
+---------------------------------------------------------------------+
.. Warning:: The user should thoroughly understand weighted tracking
before attempting to generate and use auxiliary data for biasing. Incorrect
weighting can cause the code to produce incorrect results without obvious symptoms.
.. caution:: 1. Each set of *AUXILIARY* or *CORRELATION* data must be completely
described in conjunction with its keyword. Complete sets of these data
can be interspersed in an arbitrary order but data within each set must
be entered in the specified order.
2. *AUXILIARY DATA*: If the same *m* is specified in more than one set
of data, the last set having the group structure used in the problem is
the set that will be utilized. When *AUXILIARY DATA* are entered,
*CORRELATION DATA* must also be entered in order to use the *AUXILIARY
DATA*.
3. *CORRELATION DATA*: If biasing data define the same bias ID (from the
geometry data) more than once, the value that is entered last supersedes
previous entries. *Be well aware that multiple definitions for the same
bias ID can cause erroneous answers due to overbiasing.*
4. Bias data may not be used in continuous energy mode.
.. centered:: Examples
1. Use the first form of the **BIAS** block to utilize the water biasing
factors in bias IDs 2 through 11. From :numref:`tab8-1-20`, water has
material ID m=500 and has bias parameters for 10 intervals that are
each 3 cm thick.
``READ BIAS ID``\ =500 2 11 ``END BIAS``
2. Use the second form of the ``BIAS`` block to specify biasing factors
for ``SPECIALWATER`` to be used in bias IDs 6 and 7. The ``SPECIALWATER``
biasing factors have a value of 0.69 for BIAS ID 6 and 0.86 for bias
ID 7 in each energy group. Sixteen-group cross sections are being
used. Each weighting region is 3.048 cm thick. The material ID is
arbitrarily chosen to be 510. Note that the first form of the
``BIAS`` block must be entered to allow the second form of the
``BIAS`` block to be used for BIAS IDs 6 and 7.
``READ BIAS WT = SPECIALWATER`` 510 1 3.048 2 16 16*0.69 16*0.86
``ID``\ =510 6 7 ``END BIAS``
3. An example of multiple definitions for the same bias ID follows:
``READ BIAS ID``\ =400 2 7 ``ID``\ =500 5 7 ``END BIAS``
The data for paraffin (``ID``\ =400) will be used for bias IDs 2, 3, and
4, and the data for water (``ID``\ =500) will be used for bias IDs 5, 6,
and 7. The paraffin data for bias IDs 5, 6, and 7 have been overwritten
by water data.
Multiple definitions for the same bias ID are not necessarily incorrect,
but the user should be cautious about using multiple definitions and
should ensure that the desired biasing or weighting functions are used
in the desired geometry regions.
4. An example of how the *bias ID* relates to the energy-dependent
values of *weights* is given below.
Assume that a paraffin reflector is to be used, and it is desirable to
use the weighting function from the KENO weighting library to minimize
the running time for the problem. Also assume that these weighting
functions are to be used in the volumes defined in the geometry records
having the *bias ID* (defined on a **shape** or ``MEDIA`` card for KENO
V.a and KENO-VI, respectively) equal to 6, 7, 8, and 9. *Correlation
data* are then entered and *auxiliary data* will not be entered.
The biasing data would be:
``READ BIAS ID``\ =400 6 9 ``END BIAS``
The results of these data are
(1) the group-dependent *weights* for the 0--3 cm interval of paraffin
will be used in the volume defined by the geometry region having *bias
ID*\ = 6.
(2) the group-dependent *weights* for the 3--6 cm interval of paraffin
will be used in the volume defined by the geometry region having *bias
ID*\ = 7.
(3) the group-dependent *weights* for the 6--9 cm interval of paraffin
will be used in the volume defined by the geometry region having *bias
ID*\ = 8.
(4) the group-dependent *weights* for the 9--12 cm interval of paraffin
will be used in the volume defined by the geometry region having *bias
ID*\ = 9.
.. _sec-module.keno.start_data:
Start data
~~~~~~~~~~
Special start options are available for controlling the initial neutron
distribution. The default starting distribution for **a global array** is flat
over the overall array dimensions, in fissile material only. The default
starting distribution for a single unit is flat over the system, in
fissile material only. See :numref:`tab8-1-21` for the starting distributions
available in KENO. The syntax for the **START** block is:
``READ START`` *p\ 1* …\ *p\ N* ``END START``
*p*\ :sub:`1` …\ *p*\ :sub:`N` are *N* initializations for the parameters listed
below.
The starting information that can be entered is given below. Enter only
the data necessary to describe the desired starting distribution.
``NST =`` *ntypst*
start type, default = 0
:numref:`tab8-1-21` lists the available options under the heading, "Start
type."
``TFX =`` *tfx*
the X coordinate of the point at which neutrons are to
be started. Default = 0.0. Use for start types 3, 4, and 6.
``TFY =`` *tfy*
the Y coordinate of the point at which neutrons are to
be started. Default = 0.0. Use for start types 3, 4, and 6.
``TFZ =`` *tfz*
the Z coordinate of the point at which neutrons are to
be started. Default = 0.0.
Use for start types 3, 4, and 6.
``NXS =`` *nbxs*
the x index of the unit's position in the global array.
Default = 0.
Use for start types 2, 3, and 6.
``NYS =`` *nbys*
the y index of the unit's position in the global array.
Default = 0.
Use for start types 2, 3, and 6.
``NZS =`` *nbzs*
the z index of the unit's position in the global array.
Default = 0.
Use for start types 2, 3, and 6.
``KFS =`` *kfis*
the mixture whose fission spectrum is to be used for
starting neutrons that are not in a fissionable medium. Defaulted to the
fissionable mixture having the smallest mixture number. Available for
start types 3, 4, and 6.
``LNU =`` *lfin*
the final neutron to be started at a point. Default =
0. Each *lfin* should be greater than zero, and each successive *lfin*
should be greater than the previous one. Use only for start type 6.
``NBX =`` *nboxst*
the unit in which neutrons will be started. Default =
0.
Use for start types 4 and 5.
``FCT =`` *fract*
the fraction of neutrons that will be started as a
spike or the relative fraction of each segment
when using to specify a segmented distribution in z. Default = 0.
Use for start type 2 and type 8.
``XSM =`` *xsm*
the -X dimension of the cuboid in which the neutrons will
be started. Default = 0.0. For an array problem, XSM is defaulted to
the minimum X coordinate of the global array. If the outermost geometry
is a cube or cuboid, then XSM is defaulted to the minimum X coordinate of
this cuboid. Use for start types 0, 1, 2, 7, and 8.
``XSP =`` *xsp*
the +X dimension of the cuboid in which the neutrons
will be started. Default = 0.0. For an array problem, XSP is defaulted to
the maximum X coordinate of the global array. If the outermost geometry
is a cube or cuboid, then XSP is defaulted to the maximum X coordinate of
this cuboid. Use for start types 0, 1, 2, 7, and 8.
``YSM =`` *ysm*
the -Y dimension of the cuboid in which the neutrons will
be started. Default = 0.0. For an array problem, YSM is defaulted to
the minimum Y coordinate of the global array. If the outermost geometry
is a cube or cuboid, then YSM is defaulted to the minimum Y coordinate of
this cuboid. Use for start types 0, 1, 2, 7, and 8.
``YSP =`` *ysp*
the +Y dimension of the cuboid in which the neutrons
will be started. Default = 0.0. For an array problem, YSP is defaulted to
the maximum Y coordinate of the global array. If the outermost geometry
is a cube or cuboid, then YSP is defaulted to the maximum Y coordinate of
this cuboid. Use for start types 0, 1, 2, 7, and 8.
``ZSM =`` *zsm*
the -Z dimension of the cuboid in which the neutrons
will be started. Default = 0.0 for only start types 0, 1, 2, and 7.
For an array problem, ZSM is defaulted to the minimum Z coordinate of
the global array. If the outermost geometry is a cube or cuboid, then ZSM
is defaulted to the minimum Z coordinate of this cuboid.
Use for start types 0, 1, 2, 7, and 8.
``ZSP =`` *zsp*
the +Z dimension of the cuboid in which the neutrons
will be started. Default = 0.0 for only start types 0, 1, 2, and 7.
For an array problem, ZSP is defaulted to the maximum Z coordinate of
the global array. If the outermost geometry is a cube or cuboid, then ZSP
is defaulted to the minimum Z coordinate of this cuboid.
Use for start types 0, 1, 2, 7, and 8.
``RFL =`` *rflkey*
No longer supported (obsolete parameter).
``PS6 =`` *lprt6*
the key for printing start type 6 input data. If the
key is YES, then start type 6 data are printed. If it is NO, then start
type 6 data are not printed. Enter YES or NO. Default = NO.
Available for start type 6.
``PSP =`` *lpstp*
the key for printing the neutron starting points using
the tracking format. If the key is YES, then print the neutron starting
points. If it is NO, then do not print the starting points. Enter YES or
NO. Default = NO.
Available for all start types.
``RDU =`` *rdu*
the file from which ASCII start data are to be read for
start type 6.
``WS6`` = *ws6*
the file to which ASCII start data are written. Available for all start types.
``MSS`` = *filename.msl*
the file from which ASCII start data are to be
read. *filename* may include a valid pathname. Available for start type
9.
.. note:: All start types can write the initial neutron starting points at the
last generation to an ASCII start data file specified by WS6. However,
only start type 6 can read starting data from an ASCII start data file specified
by RDU. The ASCII start data file format is described in :numref:`sec-module.keno.start_data.ascii`.
.. tabularcolumns:: |p{1.2cm}|p{1.5cm}|p{1.5cm}|p{7cm}|
.. |8123| replace:: :numref:`sec-module.keno.parameters`
.. table:: Starting distributions available in KENO.
:align: center
:name: tab8-1-21
:class: longtable
+-----------------+-----------------+-----------------+-----------------------+
| Start | Required | Optional | Starting |
| | | | distribution |
| type | data | data | |
+-----------------+-----------------+-----------------+-----------------------+
| 0 | None | NST | Uniform |
| | | | throughout |
| | | XSM | fissile |
| | | | material within |
| | | XSP | the volume |
| | | | defined by |
| | | YSM | (1) the outer region |
| | | | of a single unit, |
| | | YSP | (2) the boundary of |
| | | | the global array, |
| | | ZSM | or (3) a cuboid |
| | | | specified by |
| | | ZSP | XSM, XSP, YSM, |
| | | | YSP, ZSM, and |
| | | PSP | ZSP. |
| | | | |
| | | WS6 | |
| | | | |
| | | RFL \ :sup:`a` | |
+-----------------+-----------------+-----------------+-----------------------+
| 1 | NST | XSM | The starting |
| | | | points are |
| | | XSP | chosen |
| | | | according to a |
| | | YSM | cosine |
| | | | distribution |
| | | YSP | throughout the |
| | | | volume of a |
| | | ZSM | cuboid defined |
| | | | by XSM, XSP, |
| | | ZSP | YSM, YSP, ZSM, |
| | | | and ZSP. Points |
| | | PSP | that are not in |
| | | | fissile |
| | | WS6 | material are |
| | | | discarded. |
| | | RFL \ :sup:`a` | |
+-----------------+-----------------+-----------------+-----------------------+
| 2 | NST | XSM | An arbitrary |
| | | | fraction (FCT) |
| | NXS | XSP | of neutrons are |
| | | | started |
| | NYS | YSM | uniformly in |
| | | | the unit |
| | NZS | YSP | located at |
| | | | position NXS, |
| | FCT | ZSM | NYS, NZS in the |
| | | | global array. |
| | | ZSP | The remainder |
| | | | of the neutrons |
| | | PSP | is started in |
| | | | fissile |
| | | WS6 | material, from |
| | | | points chosen |
| | | RFL \ :sup:`a` | from a cosine |
| | | | distribution |
| | | | throughout the |
| | | | volume of a |
| | | | cuboid defined |
| | | | by XSM, XSP, |
| | | | YSM, YSP, ZSM, |
| | | | ZSP. |
+-----------------+-----------------+-----------------+-----------------------+
| 3 | NST | KFS | All neutrons |
| | | | are started at |
| | TFX | PSP | position TFX, |
| | | | TFY, TFZ within |
| | TFY | WS6 | the unit |
| | | | located at |
| | TFZ | | position NXS, |
| | | | NYS, NZS in the |
| | NXS | | global array. |
| | | | |
| | NYS | | |
| | | | |
| | NZS | | |
+-----------------+-----------------+-----------------+-----------------------+
| 4 | NST | KFS | All neutrons |
| | | | are started at |
| | TFX | PSP | position TFX, |
| | | | TFY, TFZ within |
| | TFY | WS6 | units NBX in |
| | | | the global |
| | TFZ | | array. |
| | | | |
| | NBX | | |
+-----------------+-----------------+-----------------+-----------------------+
| 5 | NST | PSP | Neutrons are started |
| | | | uniformly in |
| | NBX | WS6 | fissile material in |
| | | | units NBX in the |
| | | | global array. |
+-----------------+-----------------+-----------------+-----------------------+
| 6 | NST | NXS | The starting |
| | | | distribution is |
| | TFX | NYS | arbitrarily |
| | | | input. LNU is |
| | TFY | NZS | the final |
| | | | neutron to be |
| | TFZ | KFS | started at a |
| | | | point TFX, TFY, |
| | LNU \ :sup:`b` | PS6 | TFZ relative to |
| | | | the global |
| | | PSP | coordinate |
| | | | system or at a |
| | | RDU \ :sup:`c` | point TFX, TFY, |
| | | | TFZ, relative |
| | | WS6 | to the unit |
| | | | located at the |
| | | | global array |
| | | | position NXS, |
| | | | NYS, NZS. |
+-----------------+-----------------+-----------------+-----------------------+
| 7 | | XSM | The starting |
| | | | points are |
| | | XSP | chosen |
| | | | according to a |
| | | YSM | flat |
| | | | distribution in |
| | | YSP | the X- and |
| | | | Y-dimensions |
| | | ZSM | and a (1.0 - |
| | | | cos(z))\ |
| | | ZSP | :sup:`2` |
| | | | distribution in |
| | | PSP | the Z-dimension |
| | | | throughout the |
| | | WS6 | volume of a |
| | | | cuboid defined |
| | | | by XSM, XSP, |
| | | | YSM, YSP, ZSM, |
| | | | and ZSP. Points |
| | | | that are not in |
| | | | fissile |
| | | | material are |
| | | | discarded. |
+-----------------+-----------------+-----------------+-----------------------+
| 8 | NST | XSM | Neutrons are |
| | | | started with |
| | ZSM | XSP | flat |
| | | | distribution in |
| | ZSP | YSM | X and Y, and a |
| | | | segmented |
| | FCT | YSP | distribution in |
| | | | Z, with the X-Y |
| | | PSP | limits defined |
| | | | by XSM, XSP, |
| | | WS6 | YSM, YSP and |
| | | | the relative |
| | | | fraction in |
| | | | ZSP-ZSM defined |
| | | | by FCT. FCT |
| | | | must be the |
| | | | last **entry** |
| | | | for each segment. |
+-----------------+-----------------+-----------------+-----------------------+
| 9 | NST | | Mesh source from |
| | | | Sourcerer :sup:`d`. |
| | MSS | | The starting |
| | | | distribution is |
| | | | read from a |
| | | | previously |
| | | | created mesh |
| | | | source file |
| | | | declared with |
| | | | MSS=\ *filename.msl*\,|
| | | | where |
| | | | *filename* may |
| | | | include a valid |
| | | | pathname. |
+-----------------+-----------------+-----------------+-----------------------+
| :sup:`a` RFL parameter is no longer supported (obsolete parameter) |
| |
| :sup:`b` When entering data for start 6, LNU must be the last entry for each|
| set of data, and the LNU in each successive set of data must be larger than |
| the previous value of LNU. A set of data consists of required and optional |
| data. |
| |
| :sup:`c` Starting points can be read from either a single or multiple ASCII |
| start data file(s) specified with RDU. Each set of data with RDU must be |
| followed by LNU that controls the number of starting points read from each |
| file. Starting points read from an ASCII start data file can be also |
| combined with any set of starting data specified with TFX/TFY/TFZ and/or |
| NXS/NYS/NZS. |
| |
| :sup:`d` Sourcerer sequence has temporarily been removed from SCALE 6.3 |
| because its design relied on legacy SCALE components. A new development |
| has been in progress to redesign Sourcerer capability as a new START data |
| type for both KENO and Shift transport codes, which will be available in |
| next SCALE release. |
| |
+-----------------+-----------------+-----------------+-----------------------+
.. Warning:: Start data input block does not allow multiple start types defined
together. Both KENO V.a and KENO-VI only process the start data entered in the
first start data input block and discard the others if multiple start data
input block defined in user input.
Example-1:
Both KENO V.a and KENO-VI read only start data from the first start data input block and
ignore the second one. All starting points are uniformly sampled throughout the fissile
materials iside the user-defined box (+x=3.0 -x=-3.0 +y= 1.0 -y=-1.0 +z= 2.0 -z=-2.0).
.. code-block:: scale
...
READ START
NST=0 XSP=3.0 XSM=-3.0 YSP=1.0 YSM=-1.0 ZSP=2.0 ZSM=-2.0
END START
READ START
NST=6 TFX=2.0 TFY= 3.0 TFZ=0.0 LNU=25
END START
end data
end
Optional parameters, **XSM**, **XSP**, **YSM**, **YSP**, **ZSM**, and **ZSP**
allowed in start types 0, 1, 2, 7, and 8 are defaulted to 0.0. The default values
are internally updated for the problems either with a global array or with a
global unit with cuboid booundary shape as described above. User-defined values
always override these defaults, and the last user entry always overrides the
previous one. See :numref:`sec-module.keno.start_dist` for details and more examples.
.. note:: User input specification with **XSM** > **XSP** or **YSM** > **YSP** or
**ZSM** > **ZSP** is **not** considered as an error, and calculation is continued
by swapping the values. Start type edit in output does not reflect the
swapping operations.
.. note:: KENO-VI and KENO V.a has different interpretation for the source sampling when
the user-defined cuboid is not inside the outermost geometry.
In such a case, some starting points could be outside the global geometry,
even though they are sampled inside the user-defined cuboid, and these points
are considered as an error by KENO V.a; therefore, code terminates the
execution after a couple errors have occurred. In contrast, rather than
terminating execution, KENO-VI discards the points sampled outside the
global geometry, and continues source sampling until all
starting points have been sampled in the fissile regions inside the global unit.
.. note:: Unlike KENO V.a, the outer boundary can be any shape (or combination of shapes)
in KENO-VI. For such a case, KENO-VI samples starting positions in the volume of
**the first body** entered in the boundary definition vector of the global unit
if and only if none of translation and transformation operations are performed
on this body.
The start type 6 capability allows neutrons to be started at the arbitrary
starting points defined by a set of data. The last entry for each start
6 data set must be ``LNU``, and the ``LNU`` value of each successive set
of data must be larger than the last. Start 6 data set with any of
``TFX``, ``TFY``, and ``TFZ``, followed by ``LNU`` defines points relative
to the global coordinate system, and with any of ``NXS``, ``NYS``,
``NZS``, ``TFX``, ``TFY``, and ``TFZ`` followed by ``LNU`` defines points
relative to the unit located at global array position (``NXS``, ``NYS``, ``NZS``).
In the start type 6 capabilitiy, ``TFX``, ``TFY``, and ``TFZ`` values
are defaulted to 0.0, and ``NXS``, ``NYS``, and ``NZS`` values are defaulted to 0.
This capability does not allow multiple entries of ``NXS``, ``NYS``, ``NZS``,
``TFX``, ``TFY``, and ``TFZ`` in the same start 6 data set.
``NXS``, ``NYS``, ``NZS``, ``TFX``, ``TFY``, and ``TFZ`` values entered in each
start type 6 data set override their default values. A start type 6 data set
with one or more missing ``TFX``, ``TFY``, and ``TFZ`` entries does not halt
the execution. Instead, the last updated values of ``TFX``, ``TFY``, and ``TFZ``
are used for the missing one.
Start type 6 is capable of reading starting points from an ASCII start data
file, which could be created by writing starting points from a previous
calculation, defined by RDU in a start type 6 data set. See
:numref:`sec-module.keno.start_data.ascii` for the details about a typical ASCII start data file
currently supported, and :numref:`sec-module.keno.start_dist` for more examples.
The following example was designed to illustrate the starting source distributions
provided by start data types. Note that only start types 0, 1, 2, 5, 7, and 8
was used for this specific example.
Example-2:
In this example, a 2 :math:`\times` 2 :math:`\times` 1 rectangular array filled with
four different units is used to demonstrate the different starting point
distributions that can be generated by the starting types available in
the start data capability. Spatial distribution of the starting points
sampled with only start types 0, 1, 2, 5, 7, and 8 are overlayed on the
problem geometry.
.. code-block:: scale
=kenovi
2x2 pin cell model for starting distribution demonstration
read parameters
cep=ce_v7.1_endf gen=10 npg=5000 nsk=0 htm=no
end parameter
read mixt
mix=1
8016 3.91376E-02 92235 8.73674E-04 92238 1.87428E-02
mix=2
8016 3.91376E-02 92235 8.73674E-04 92238 1.87428E-02
mix=31
40090 2.17623E-02 40091 4.74582E-03 40092 7.25409E-03
40094 7.35137E-03 40096 1.18434E-03
mix=32
40090 2.17623E-02 40091 4.74582E-03 40092 7.25409E-03
40094 7.35137E-03 40096 1.18434E-03
mix=41
1001 4.77898E-02 1002 5.49646E-06 5010 4.75767E-06
5011 1.91502E-05 8016 2.38396E-02 8017 9.08111E-06
mix=42
1001 4.77898E-02 1002 5.49646E-06 5010 4.75767E-06
5011 1.91502E-05 8016 2.38396E-02 8017 9.08111E-06
end mixt
read geom
unit 1
com='UO2 Fuel Rod'
cylinder 10 0.3860 6.0 0.0
cylinder 20 0.4582 6.0 0.0
cuboid 30 4p0.6375 6.0 0.0
media 1 1 10
media 31 1 20 -10
media 41 1 30 -20
boundary 30
unit 2
com='UO2 Fuel Rod'
cylinder 10 0.3860 6.0 0.0
cylinder 20 0.4582 6.0 0.0
cuboid 30 4p0.6375 6.0 0.0
media 2 1 10
media 32 1 20 -10
media 42 1 30 -20
boundary 30
unit 3
com='UO2 Fuel Rod'
cylinder 10 0.3860 6.0 0.0
cylinder 20 0.4582 6.0 0.0
cuboid 30 4p0.6375 6.0 0.0
media 1 1 10
media 31 1 20 -10
media 41 1 30 -20
boundary 30
unit 4
com='UO2 Fuel Rod'
cylinder 10 0.3860 6.0 0.0
cylinder 20 0.4582 6.0 0.0
cuboid 30 4p0.6375 6.0 0.0
media 2 1 10
media 32 1 20 -10
media 42 1 30 -20
boundary 30
global unit 5
cuboid 10 4p1.275 6.0 0.0
array 1 10 place 2 2 1 0.6375 0.6375 0.0
boundary 10
end geom
read array
ara=1 typ=square nux=2 nuy=2 nuz=1 gbl=1
fill 1 3
2 4
end fill
end array
read bounds
all=mirror
end bounds
end data
end
- **start type 0** (default starting type), samples neutrons initial
starting points uniformly throughout four fissile cylinders inside
the global unit. :numref:`fig7-1-2-8-1` shows spatial distributions
of the initial neutrons.
.. figure:: figs/Keno/keno_starttype0.png
:align: center
:name: fig7-1-2-8-1
Starting point distribution obtained with start type 0 overlayed on the geometry
.. note:: Overlaying starting distribution on Fulcrum-visualized geometry
is not currently implemented in Fulcrum. Initial starting points obtained with
**PSP** option for all these start type configurations were used with an
external utility to overlay them on the geometry visualized by Fulcrum.
- **start type 1**, samples neutrons initial starting points with a
cosine distribution (in each dimension) within a user-defined box
given in start data input. All points except the ones in four fissile
cylinders inside the global unit are discarded. Start type 1 produces
initial neutron distributions concentrated in the middle of the
problem as depicted in :numref:`fig7-1-2-8-2`.
.. code-block:: scale
...
READ START
NST=1 XSP=1.275 XSM=-1.275 YSP=1.275 YSM=-1.275 ZSP=6.0 ZSM=0.0
PSP=YES WS6=keno1.src
END START
.. figure:: figs/Keno/keno_starttype1.png
:align: center
:name: fig7-1-2-8-2
Starting point distribution obtained with start type 1 overlayed on the geometry
- **start type 2** is used with the array problems. With the following start
data definition, an arbitrary fraction (FCT=0.5 in this case) of neutrons
is started uniformly in the unit (unit=1) located at position NXS=1
NYS=1 and NZS=1 in the global array. The remainder of the neutrons are started
in fissile material, from points chosen from a cosine distribution
throughout the volume of a cuboid defined by +x=1.275 -x=-1.275 +y=1.275
-y=-1.275 +z=6.0 -z=0.0. All points except the ones in four fissile
cylinders inside the user-defined cuboid are discarded. Start type 2
produces initial neutron distributions concentrated both in the middle
of the problem and in the unit=1 located at the specified global array
element. :numref:`fig7-1-2-8-3` shows both vertical and horizontal
spatial distributions of the initial neutrons sampled with this
start type.
.. code-block:: scale
...
READ START
NST=2 XSP=1.275 XSM=-1.275 YSP=1.275 YSM=-1.275 ZSP=6.0 ZSM=0.0
FCT=0.5 NXS=1 NYS=1 NZS=1
PSP=YES WS6=keno2.src
END START
.. figure:: figs/Keno/keno_starttype2.png
:align: center
:name: fig7-1-2-8-3
Starting point distribution obtained with start type 2 overlayed on the geometry
- **start type 5** uniformly samples initial starting points inside the unit=2
in the global array. :numref:`fig7-1-2-8-4` shows the both vertical and
horizontal spatial distributions of the initial neutrons sampled with
this start type.
.. code-block:: scale
...
READ START
NST=5
NBX=2
PSP=YES WS6=keno5.src
END START
.. figure:: figs/Keno/keno_starttype5.png
:align: center
:name: fig7-1-2-8-4
Starting point distribution obtained with start type 5 overlayed on the geometry
- **start type 7** samples neutrons initial starting points with a uniform
distribution in X-Y and a :math:`(1-cos)^2` distribution in Z inside
the cuboid defined by +x=1.275 -x=-1.275 +y=1.275 -y=-1.275 +z=6.0 -z=0.0.
Start type 7 produces an initial neutron distributions concentrated
to the top and bottom parts of the problem as shown in :numref:`fig7-1-2-8-5`.
.. code-block:: scale
...
READ START
NST=7 XSP=1.275 XSM=-1.275 YSP=1.275 YSM=-1.275 ZSP=6.0 ZSM=0.0
PSP=YES WS6=keno7.src
END START
.. figure:: figs/Keno/keno_starttype7.png
:align: center
:name: fig7-1-2-8-5
Starting point distribution obtained with start type 7 overlayed on the geometry
- **start type 8** samples the neutrons initial starting points with a
uniform distribution in X-Y and a segmented distribution in Z inside
the cuboid defined by +x=1.275 -x=-1.275 +y=1.275 -y=-1.275 +z=6.0 -z=0.0.
Start type 8 with the specified input places the majority of the neutrons
in the bottom of the problem and gradually decreases the neutron
population from bottom to top using the user-provided segmented
distribution as shown in :numref:`fig7-1-2-8-6`.
.. code-block:: scale
...
READ START
NST=8
PSP=YES WS6=keno8.src
XSP=1.275 XSM=-1.275 YSP=1.275 YSM=-1.275
ZSM=0.0 ZSP=1.0 FCT=0.30
ZSM=1.0 ZSP=2.0 FCT=0.25
ZSM=2.0 ZSP=3.0 FCT=0.20
ZSM=3.0 ZSP=4.0 FCT=0.13
ZSM=4.0 ZSP=5.0 FCT=0.10
ZSM=5.0 ZSP=6.0 FCT=0.02
END START
.. figure:: figs/Keno/keno_starttype8.png
:align: center
:name: fig7-1-2-8-6
Starting point distribution obtained with start type 8 overlayed on the geometry
.. _sec-module.keno.start_data.ascii:
ASCII Start Data File Format
^^^^^^^^^^^^^^^^^^^^^^^^^^^^
A sample ASCII start data file is shown below. In a typical ASCII
start data file, each line defines a data set. The first three
columns are ``TFX``, ``TFY``, and ``TFZ`` values, the next four
columns are ``NXS``, ``NYS``, ``NZS``, and ``KFS``, and the last column
is always ``LNU``. The file must be ended with a termination line with ``LNU``
=0. The file format is given with ``(3es20.9,5i12)``.
.. raw:: latex
\begin{landscape}
.. code-block:: none
-1.000000000e-01 -2.000000000e+00 -3.300000000e+00 0 0 0 1 1
-3.000000000e-01 -2.400000000e+00 -3.300000000e+00 0 0 0 1 15
-3.000000000e-01 -2.500000000e+00 -3.300000000e+00 0 0 0 1 36
-4.000000000e-01 -2.600000000e+00 -3.300000000e+00 0 0 0 1 37
-4.000000000e-01 -2.700000000e+00 -3.300000000e+00 0 0 0 1 38
-5.000000000e-01 -2.800000000e+00 -3.300000000e+00 0 0 0 1 39
-5.000000000e-01 -2.900000000e+00 -3.300000000e+00 0 0 0 1 40
-5.000000000e-01 -2.900000000e+00 -3.300000000e+00 0 0 0 1 0
.. raw:: latex
\end{landscape}
.. _sec-module.keno.xs1d:
Extra 1-D XSECS IDs data
~~~~~~~~~~~~~~~~~~~~~~~~
Extra 1-D cross section IDs are not required. They are allowed as input
in order to simplify future modifications to calculate reaction rates,
etc., as well as for compatibility with other SCALE codes. The syntax
for the extra 1-D cross section data block is:
``READ X1DS NEUTRON`` *i\ 1 …i\ x1d* ``END X1DS``
``NEUTRON``
is a keyword to indicate that the following ID identifies a
neutron interaction.
*i*\ :sub:`1` … *i*\ :sub:`x1d`
``X1D`` 1-D identification numbers or keyword identifiers
for the 1-D cross section to be used. These cross sections must be
available on the mixture cross section library. ``X1D`` entries are
expected to be read (see integer PARAMETER data).
.. _sec-module.keno.mixing_table:
Mixing table data
~~~~~~~~~~~~~~~~~
A cross section mixing table must be entered if KENO is being run stand
alone and a Monte Carlo cross section format library is not being used
in the multigroup mode, or KENO is being run stand alone in the
continuous energy mode. If the parameter ``LIB=`` (:numref:`sec-module.keno.parameters`) is
entered, then mixing table data must be entered. A cross section mixing
table is entered using the following syntax:
``READ MIXT`` *p*\ :sub:`1` … *p*\ :sub:`N` ``END MIXT``
*p*\ :sub:`1` … *p*\ :sub:`N`
are *N* parameters that might or might not be keyworded.
The possible parameters that can be used in a ``MIXT`` block are
described below.
``SCT =`` *nsct*
is used to input the number of scattering angles and
only applies in multigroup mode. *nsct* is the number of discrete
scattering angles, default = 1. The number of scattering angles
specifies the number of discrete scattering angles to be used for the
cross sections. If SCT is not set (i.e., SCT= -1), then the number of
scattering angles is determined from the cross section library
specified. The number of scattering angles defaults to (ncoef+1)/2,
where ncoef is the largest Legendre polynomial order used in the
problem. It needs to be entered only once for a problem. If more than
one value is entered, the last one is used for the problem. For
assistance in determining the number of discrete scattering angles for
the cross sections, see :numref:`8-1-3-4-3`.
``EPS =`` *pbxs*
is used to enter the cross section message cutoff
value, and it only applies in multigroup mode. *pbxs* is the value of
the P\ :sub:`0` cross section for each transfer, above which generated
warning messages will be printed, default = 3 × 10\ :sup:`-5`. The
primary purpose of entering this cutoff value is to suppress printing
these messages when they are generated during cross section processing.
For assistance in determining a value for EPS, see :numref:`8-1-3-4-4`.
``MIX =`` *mix*
is used to input the identification number of the
mixture being described. *mix* defines the mixture being described.
``NCM =`` *ncmx*
is used to input the nuclide mixture IDs to be used for
this mixture. *ncmx* defines the nuclide mixture ID. When
``MIX=``\ *mix* is read, *ncmx* is defaulted to *mix* also. Then, as
long as all the nuclides that need to be mixed into *mix* already have
*mix* specified as their nuclide mixture (frequently the case when using
SCALE), the user does not need to specify ``NCM``. The most usual case
where ``NCM`` must be specified is when the mixtures were specified as a
different mixture number when they were created in SCALE as compared to
the mixture number used for them in KENO. Cell homogenized mixtures also
need ``NCM`` specified.
``TMP``\ \|\ ``TEM`` = *temperature*
is used to input the desired
temperature of the CE cross section data.
``nucl``
is the nuclide ID number from the AMPX working format cross
section library.
``XS=``\ *fname*
is used to input the optional continuous energy cross
section filename to override the default cross sections. *fname* is the
name of the file.
``dens``
is the number density (atoms/b-cm) associated with nuclide ID
number *nucl*.
The sequence "\ *nucl* ``NCM``\ =\ *ncmx* [``XS``\ =\ *fname*] *dens*\ "
may be repeated until the mixture defined by ``MIX``\ =\ *mix* has been
completely described.
The sequence "\ ``MIX =`` *mix* ``NCM`` = *ncmx* ``TMP``\ \|\ ``TEM`` =
*temperature nucl* ``NCM``\ =\ *ncmx* [``XS``\ =\ *fname*] *dens*\ " may
be repeated until all the mixtures have been described.
.. note:: If a given nuclide ID is entered more than once in the same
mixture, then the number densities for that nuclide are summed.
If a mixture number is used as a nuclide ID, then it is treated as a
nuclide and the number density associated with it is used as a
density modifier. (If the density is entered as 1, then the mixture
is mixed in at full density. If it is entered as 0.5, the mixture is
mixed in at one half of its full density.) A Monte Carlo formatted
cross section library is generated on the unit defined by the
parameter ``XSC=``. If this data set is saved, subsequent cases can
utilize these mixtures without remixing.
The entry ``XS``\ =\ *fname* is optional. If a nuclide is entered
more than once in a mixture and this entry is specified, then they
must be the same (i.e., cannot use more than one continuous energy
cross section sets for a nuclide in a given mixture). Different
mixtures may have the same nuclide with different continuous energy
cross section sets.
.. _8-1-2-11:
Plot data
~~~~~~~~~
Plots of slices specified through the geometry can be generated and
displayed (1) as character plots using alphanumeric characters to
represent mixture numbers, unit numbers or bias ID numbers or (2) as
color plots which generate a PNG file using colors to represent mixture
numbers, unit numbers or bias ID numbers. Color plots require an
independent program to display the PNG file to a PC or workstation
monitor or to convert the file to be displayed using a plotting device.
The keyword ``SCR=`` is used to control the plot display method.
``SCR=YES``, the default value, uses the color plot display method.
``SCR=NO`` uses the character plot display method. The value of
``SCR`` determines the plot display method for all the plots specified
in a problem. If ``SCR=`` is entered more than once, the last entry
determines the plot display method. In other words, all plots generated
by a problem will be either character plots or color plots.
The plot data can include the data for any or all types of plots. A plot
by mixture number is the default. The kind of plot is defined by the
parameter ``PIC=``. Character plots are printed after the volumes are
printed and before the final preparations for tracking are completed.
Plot data are not required for a problem, but theyb can be used to
verify the problem description. The actual plotting of the picture can
be suppressed by entering ``PLT= NO`` in the parameter data or plot
data. This allows plot data to be kept in the problem input for
reference purposes without actually plotting the picture(s). Entering a
value for ``PLT`` in the plot data will override any value entered in
the parameter data. However, if a problem is restarted, the value of
``PLT`` from the parameter data is used. The upper left and lower right
coordinates of the plot must be specified relative to the origin of the
problem. See :numref:`8-1-3-9` for a discussion of plot origins and plot
data.
Enter the plot data using the following syntax:
``READ PLOT`` *p*\ :sub:`1` … *p*\ :sub:`N` ``END PLOT``
*p*\ :sub:`1` … *p*\ :sub:`N`
are *N* parameters entered using keywords followed by the
appropriate data. The plot title and the plot character string must be
contained within delimiters. Enter as many picture parameters as
necessary to describe the plot. Multiple sets of plot data can be
entered. The parameter input for each plot is terminated by a labeled or
unlabeled ``END``. The labeled ``END`` cannot use the word ``PLOT`` as
the first four characters of the label. For example, ``END PLT1`` is a
valid label, but ``END PLOT1`` is not. If an unlabeled ``END`` is used,
it cannot start in column 1.
The possible parameters that can be used in a ``PLOT`` block are
described below.
``TTL=`` *delim ptitl delim*
Enter a one-character delimiter *delim* to
signal the beginning of the title (132 characters maximum). The title is
terminated when *delim* is encountered the second time. Acceptable
delimiters include " , ` , \* , ^ , or !.
Default = title of the KENO case.
``PIC=`` *wrd*
The plot type, *wrd*, is followed by one or more blanks
and must be one of the keywords listed below. The plot type is
initialized to MAT; the default is the value from the previous plot.
+-----------------------------------+-----------------------------------+
| MAT | These keywords will cause the |
| | plot to represent the mixture |
| MIX[T[URE]] | numbers used in the specified |
| | geometry slice. |
| MEDI[A] | |
+-----------------------------------+-----------------------------------+
| UNT | These keywords will cause the |
| | plot to represent the units used |
| UNIT[TYPE] | in the specified geometry slice. |
| | In the legend of the color plot, |
| | the material number actually |
| | refers to the units. |
+-----------------------------------+-----------------------------------+
| IMP | These keywords will cause the |
| | plot to represent the bias ID |
| BIAS[ID] | numbers used in the specified |
| | geometry slice. In the legend of |
| WTS | the color plot, the material |
| | number actually refers to the |
| WEIG[HTS] | bias ID numbers. |
| | |
| WGT[S] | |
+-----------------------------------+-----------------------------------+
``TYP =``
Enter the type desired.
XY for an X-Y plot
XZ for an X-Z plot
YZ for a Y-Z plot
Direction cosines do not need to be entered if TYP is entered.
Plot coordinates
Enter values for the upper left and lower right
coordinates of the plot as described below. **Data must be entered for
all nonzero coordinates unless all six values from the previous plot are
to be used.**
Upper left coordinates
Enter the X, Y, and Z coordinates of the upper
left-hand corner of the plot.
``XUL=``\ *xul*
is used to enter the X coordinate of the upper
left-hand corner of the plot.
Default = value from previous plot; initialized to zero if any other
coordinates are entered.
``YUL=``\ *yul*
is used to enter the Y coordinate of the upper left-hand
corner of the plot. Default = value from previous plot; initialized to
zero if any other coordinates are entered.
``ZUL=``\ *zul*
is used to enter the Z coordinate of the upper left-hand
corner of the plot. Default = value from previous plot; initialized to
zero if any other coordinates are entered.
Lower right coordinates
Enter the X, Y, and Z coordinates of the lower
right-hand corner of the plot.
``XLR=``\ *xlr*
is used to enter the X coordinate of the lower right-hand
corner of the plot. Default = value from previous plot; initialized to
zero if any other coordinates are entered.
``YLR=``\ *ylr*
is used to enter the Y coordinate of the lower right-hand
corner of the plot.
Default = value from previous plot; initialized to zero if any other
coordinates are entered.
``ZLR=``\ *zlr*
is used to enter the Z coordinate of the lower right-hand
corner of the plot. Default = value from previous plot; initialized to zero if any other
coordinates are entered.
Direction cosines across the plot
Enter direction numbers proportional to the direction cosines for the AX axis of the plot.
The AX axis is from left to right across the plot. If any one of the AX direction cosines is entered,
the other two are set to zero. The direction cosines are normalized by the code.
``UAX=``\ *uax* is used to enter the X component of the direction
cosines for the AX axis of the plot. Default = value from previous
plot; initialized to zero if any other direction cosines are entered.
``VAX=``\ *vax* is used to enter the Y component of the direction
cosines for the AX axis of the plot. Default = value from previous
plot; initialized to zero if any other direction cosines are entered.
``WAX=``\ *wax* is used to enter the Z component of the direction
cosines for the AX axis of the plot. Default = value from previous
plot; initialized to zero if any other direction cosines are entered.
Direction cosines down the plot
Enter direction numbers proportional
to the direction cosines for the DN axis of the plot.
The DN axis is from top to bottom down the plot. If any one of the DN direction
cosines is entered, the other two are set to zero. The direction cosines are normalized
by the code.
``UDN=``\ *udn* is used to enter the X component of the direction
cosines for the DN axis of the plot. Default = value from previous
plot; initialized to zero if any other direction cosines are entered.
``VDN=``\ *vdn* is used to enter the Y component of the direction
cosines for the DN axis of the plot. Default = value from previous
plot; initialized to zero if any other direction cosines are entered.
``WDN=``\ *wdn* is used to enter the Z component of the direction
cosines for the DN axis of the plot. Default = value from previous
plot; initialized to zero if any other direction cosines are entered.
Scaling parameters
Enter one or more scaling parameters to define the
size of the plot.
.. note:: If any of the scaling parameters are entered for a plot,
the value of those that were not entered is recalculated. If none of
the scaling parameters are specified for a plot, the values from the
previous plot are used.
``DLX=``\ *dlx*
is used to input the horizontal spacing between points on
the plot. Default = value from previous plot; initialized to zero if
``NAX`` or ``NDN`` is entered.
``DLD=``\ *dld*
is used to input the vertical spacing between points on
the plot. Default = value from previous plot; initialized to zero if
``NAX`` or ``NDN`` is entered.
.. note:: If either DLX or DLD is entered, the code will calculate the
value of the other. If both are entered, the plot may be distorted.
``NAX=``\ *nax*
is used to input the number of intervals to be printed
across the plot. Default = value from previous plot; initialized to zero
if ``DLX`` or ``DLD`` is entered.
``NDN=``\ *ndn*
is used to input the number of intervals to be printed
down the plot. Default = value from previous plot; initialized to zero
if ``DLX`` or ``DLD`` is entered.
Global scaling parameter
``LPI=``\ *lpi*
is used to input a scaling factor used to control the
horizontal to vertical proportionality of a plot or plots. SCALE 4.3 and
later versions allow *lpi* to be input as a floating point number. For
an undistorted character plot, *lpi* should be specified as the number
of characters down the page that occupy the same distance as ten
characters across the page. For an undistorted color plot, *lpi* should
be entered as ten times the ratio of the vertical pixel dimension to the
horizontal pixel dimension. The default value of *lpi* is 8.0 for a
character plot and 10.0 for a color plot. *lpi*\ =10 will usually
display an undistorted color plot.
The value entered for *lpi* applies to all plot data following it
until a new value of *lpi* is specified.
.. note:: Plot data must include the specification of the upper left
corner of the plot and the direction cosines across and down the
plot.
Additional data required to generate a plot are one of the following
combinations:
1. the lower right corner of the plot, the global scaling parameter,
``LPI``, and one of the scaling parameters (``DLX``, ``DLD``,
``NAX``, ``NDN``).
2. the lower right corner of the plot, one of the scaling parameters
related to the horizontal specifications of the plot (``DLX`` or
``NAX``), and one of the scaling parameters related to the vertical
specification of the plot (``DLD`` or ``NDN``). ``LPI``, even if
specified will not be used.
3. ``NAX`` and ``NDN`` and any two of ``LPI, DLX``, and ``DLD``. If
``LPI, DLX``, and ``DLD`` are all specified, ``LPI`` is not used.
The data required to generate a plot may be supplied from
(1) defaulted values, (2) data from the previous plot, or (3) data
that are specifically entered for the current plot.
Miscellaneous parameters
Enter miscellaneous parameters
``RUN=``\ *run*
is used to determine if the problem is executed or is
terminated after data checking. A value of YES for *run* means the
problem will be executed if all the data were acceptable. A value of NO
specifies the problem will be terminated after data checking is
completed. The default value of ``RUN`` is YES.
``PLT=``\ *plt*
is used to specify if a plot is to be made. A value of
YES for *plt* specifies that a plot is to be made. If plot data are
entered, ``PLT`` is defaulted to YES.
.. note:: The parameters ``RUN`` and ``PLT`` can also be entered in the
PARAMETER data. See :numref:`sec-module.keno.parameters`. It is recommended that these
parameters be entered only in the parameter data block in order to
ensure that the data printed in the "Logical Parameters" table are what
is actually performed.
``SCR=`` *src*
This is used to determine the plot display method. The
plot display method is specified by entering either YES or NO for *src*.
The default value is YES. ``SCR``\ =YES uses the color plot display
method. ``SCR``\ =NO uses the character plot display method. If ``SCR``
is entered more than once in a problem, the last value entered is the
one that is used.
``NCH=`` *delim char delim*
Enter only if plots are to be made utilizing
the character plot display method (``SCR=``\ NO). Enter a delimiter
(i.e., " , ` , \* , ^ , or !) to signal the beginning of character
string *char*. The character string is terminated when the *delim*
character is encountered the second time. Do not use the initial
delimiter in the *char* string, as it will be read as terminating the
string. *char* is a character string with each entry representing a
plottable quantity (i.e., media {mixture} number, unit number, or bias
ID). These are the characters that will be used in the plot. The first
entry represents media, unit, or bias ID zero; the second entry
represents the smallest media, unit, or bias ID used in the problem; the
third entry represents the next larger media, unit, or bias ID used in
the problem; etc. For example, assume ``PIC``\ =MAT is specified, and
15 mixtures are defined in the mixing table, and the geometry data use
only mixtures 3 and 7. By default, a blank will be printed for mixture
zero, a 1 will be printed for mixture 3, and a 2 will be printed for
mixture 7. If you wish to print a zero for a void (mixture 0), a 3 for
mixture 3, and a 7 for mixture 7, enter NCH=`037'.
The default values of CHAR are the following:
.. |.| replace:: :math:`\cdot`
.. tabularcolumns:: |p{1.2cm}|p{.5cm}|p{.5cm}|p{.5cm}|p{.5cm}|p{.5cm}|p{.5cm}|p{.5cm}|p{.5cm}|p{.5cm}|p{.5cm}|p{.5cm}|p{.5cm}|p{.5cm}|p{.5cm}|p{.5cm}|p{.5cm}|
.. table::
:class: longtable
+----------+-----+-----+-----+-----+-----+-------+-----+-----+-----+-----+-----+-----+-----+-----+-----+----+
| Quantity | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
+----------+-----+-----+-----+-----+-----+-------+-----+-----+-----+-----+-----+-----+-----+-----+-----+----+
| SYMBOL | | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F |
+----------+-----+-----+-----+-----+-----+-------+-----+-----+-----+-----+-----+-----+-----+-----+-----+----+
| | | | | | | | | | | | | | | | | |
+----------+-----+-----+-----+-----+-----+-------+-----+-----+-----+-----+-----+-----+-----+-----+-----+----+
| Quantity | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 |
+----------+-----+-----+-----+-----+-----+-------+-----+-----+-----+-----+-----+-----+-----+-----+-----+----+
| SYMBOL | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V |
+----------+-----+-----+-----+-----+-----+-------+-----+-----+-----+-----+-----+-----+-----+-----+-----+----+
| | | | | | | | | | | | | | | | | |
+----------+-----+-----+-----+-----+-----+-------+-----+-----+-----+-----+-----+-----+-----+-----+-----+----+
| Quantity | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | |
+----------+-----+-----+-----+-----+-----+-------+-----+-----+-----+-----+-----+-----+-----+-----+-----+----+
| SYMBOL | W | X | Y | Z | # | , | $ | \- | \+ | ) | | | & | > | : | ; | |
+----------+-----+-----+-----+-----+-----+-------+-----+-----+-----+-----+-----+-----+-----+-----+-----+----+
| | | | | | | | | | | | | | | | | |
+----------+-----+-----+-----+-----+-----+-------+-----+-----+-----+-----+-----+-----+-----+-----+-----+----+
| Quantity | 47 | 48 | 49 | 50 | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | | | | |
+----------+-----+-----+-----+-----+-----+-------+-----+-----+-----+-----+-----+-----+-----+-----+-----+----+
| SYMBOL | |.| | \- | "%" | "*" | """ | "=" | "!" | "(" | "@" | "<" | "/" | 0 | | | | |
+----------+-----+-----+-----+-----+-----+-------+-----+-----+-----+-----+-----+-----+-----+-----+-----+----+
``CLR=`` *n*\ :sub:`1` *r*(*n*\ :sub:`1`) *g*(*n*\ :sub:`1`) *b*(*n*\ :sub:`1`) … *n*\ :sub:`N` *r*(*n*\ :sub:`N`) *g*(*n*\ :sub:`N`) *b*(*n*\ :sub:`N`) ``END COLOR``
this entry is used to define the colors to be used by the color plot.
It may be entered only if plots are to be made utilizing the color
plot display method (``SCR``\ =YES). After entering the keyword
``CLR=``, 4 numbers are entered *N* times. The first number, *n*\ :sub:`1`,
represents a media (mixture) number, unit number, or bias ID. The
next three numbers, whose values can range from 0 through 255, define
the *red, green, and blue* components of the color that will
represent this *n*\ :sub:`1` in the plot. The sequence of 4 numbers is
repeated until the colors associated with all of the media (mixture)
numbers, unit numbers, or bias IDs used in the problem have been
defined. The smallest number that can be entered for *n*\ :sub:`i` is -1,
representing undefined regions in the plot. An *n\ i* of 0 represents
void regions; *n*\ :sub:`i` of 1 represents the smallest media, unit, or
bias ID used in the problem; *n*\ :sub:`i` of 2 represents the next larger
media, unit, or bias ID used in the problem, etc. The color plot
definition data are terminated by entering the keywords ``END COLOR``.
A total of 256 default colors are provided in :numref:`tab8-1-22`
Two of those colors represent undefined regions, *n*\ :sub:`i`\ =-1*, as
black and void regions, and *n*\ :sub:`i`\ =0 as gray. The remaining 254
colors represent the default values for mixtures, bias IDs, or unit
numbers used in the problem. If **num** is entered as **-1**, the
next three numbers define the color that will be used to represent
undefined regions of the plot. The default color for undefined
regions is black, represented as 0 0 0. If *n*\ :sub:`i` is entered as 0,
the next three numbers define the color that will represent void
regions in the plot. The default color for void is gray, represented
as 200 200 200. For example, assume a color plot is to be made for a
problem that uses void regions and mixture numbers 1, 3, and 5. By
default, the undefined regions (Index -1) will be black; void regions
(Index 0) will be gray; the first mixture, mixture 1 (Index 1), will
be medium blue; the next larger mixture, mixture 3 (Index 2), will be
turquoise2; and the last mixture, mixture 5 (Index 3), will be
green2. If these values are acceptable, data do not need to be
entered for ``CLR=``\ . If the user decides to define void to be
white (255 255 255), mixture 1 to be red (255 0 0), mixture 3 to be
bright blue (0 0 255), and mixture 5 to be green (0 255 0), then the
following data could be entered:
``CLR``\ =0 255 255 255 1 255 0 0 2 0 0 255 3 0 255 0 ``END COLOR``
In this example, the first number (0) defines the void, and the next
three numbers are the *red, green, and blue* components that combine
as the color white. The fifth number (1) represents the smallest
mixture number (mixture 1), and the next three numbers are the *red,
green, and blue* components of red. The ninth number (2) represents
the next larger mixture number (mixture 3), and the next three
numbers are the *red, green, and blue* components of bright blue. The
thirteenth number (3) represents the next larger mixture number
(mixture 5), and the next three numbers are the red, green, and blue
components of green. The ``END COLOR`` terminates the color
definition data. Because color data were not entered for *n\ i* of
-1, undefined regions will be represented by the color black, the
default specification from :numref:`tab8-1-22`. The *red, green, and blue*
components of some bright colors are listed below.
+---------------------+---------+-----------+----------+
| **Display Color** | **red** | **green** | **blue** |
+=====================+=========+===========+==========+
| black | 0 | 0 | 0 |
+---------------------+---------+-----------+----------+
| white | 255 | 255 | 255 |
+---------------------+---------+-----------+----------+
| "default void gray" | 200 | 200 | 200 |
+---------------------+---------+-----------+----------+
| red | 255 | 0 | 0 |
+---------------------+---------+-----------+----------+
| green | 0 | 255 | 0 |
+---------------------+---------+-----------+----------+
| brightest blue | 0 | 0 | 255 |
+---------------------+---------+-----------+----------+
| yellow | 255 | 255 | 0 |
+---------------------+---------+-----------+----------+
| brightest cyan | 0 | 255 | 255 |
+---------------------+---------+-----------+----------+
| magenta | 255 | 0 | 255 |
+---------------------+---------+-----------+----------+
The 256 default colors are listed in :numref:`tab8-1-22`.
.. list-table:: Default color specifications for the color plot display method
:name: tab8-1-22
:align: center
* - .. image:: figs/Keno/tab22_Page_01.png
:width: 400
:align: center
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* - .. image:: figs/Keno/tab22_Page_02.png
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* - .. image:: figs/Keno/tab22_Page_11.png
:width: 400
:align: center
.. _8-1-2-12:
Energy group boundary data
~~~~~~~~~~~~~~~~~~~~~~~~~~
Upper energy group boundary data in eV are entered to determine the
groups into which the tallies will be collected in the continuous energy
mode. For *G* groups *G*\ +1 entries are entered. The last entry is the
lower energy boundary of the last group. The values must be in
descending order. The parameter ``NGP`` is set equal to the number of
entries-1. The syntax is:
``READ ENERGY`` *u*\ :sub:`1` …u\ *G* *u*\ :sub:`G+1` ``END ENERGY``
*u*\ :sub:`1` … *u*\ :sub:`G`
are the upper energy limits of energy groups 1 … *G*,
respectively.
*u*\ :sub:`G+1`
is the lower energy limit of energy group *G*.
Example:
.. code-block:: scale
READ ENERGY
2e7 1e5 1 1e-5
END ENERGY
Defines a 3-group structure with group 1 (2e+7 eV to 1e+5 eV), group 2
(1e+5 eV to 1 eV), and group 3 (1 eV to 1e-5 eV) and sets ``NGP``\ =3.
Energy group boundary data are optional. Default values for the energy
group boundaries in the calculations are determined as in the following
order:
i. Use energy group boundaries from ``ENERGY`` block if specified
in the input. The number of entries in the ``ENERGY`` block is
``NGP``\ +1.
ii. If only ``NGP`` is specified (in ``PARAMETER`` block) in the input
and ``NGP`` is equal to the number of energy groups in one of the
SCALE neutron cross section libraries, the energy group structure
from that library will be used.
iii. If only ``NGP`` is specified (in ``PARAMETER`` block) in the input
and ``NGP`` is not equal to the number of energy groups in one of
the SCALE neutron cross section libraries, ``NGP`` equal lethargy
bins will be used.
iv. Use SCALE 252-group structure as default, ``NGP``\ =252.
.. _8-1-2-13:
Volume data
~~~~~~~~~~~
If volumes are needed (for calculating fission densities, fluxes, etc.),
then the data necessary to determine them are entered. The syntax for
this block is:
``READ VOLUME`` *p*\ :sub:`1` … *p*\ :sub:`N` ``END VOLUME``
*p*\ :sub:`1` … *p*\ :sub:`N`
are *N* parameters entered using keywords followed by the
appropriate data.
The possible parameters that can be used in a ``VOLUME`` block are
described below.
``READVOL=``\ *vol*
used to input the file name (up to 256 characters)
of the file from which user-specified volumes are read. This is an
optional parameter and only works for KENO-VI. The data are read in
sections for each ``UNIT`` contained in the problem. First the keyword
"\ ``UNIT``\ " is read, followed by the ``UNIT`` number. For that
``UNIT`` the data for each region containing material in the order shown
in the input is read as follows: the keyword "\ ``MEDIA``\ " is read,
followed by the mixture number, followed by the keyword "\ ``VOL``\ =",
followed by the total volume for that region. Regions containing
``ARRAY``\ s and ``HOLE``\ s are skipped. An example of the data
contained in a volume file is given later in this section.
``TYPE=``\ *vcalc*
used to determine the type of volume calculation.
*vcalc* can have the values:
NONE: (only works in KENO-VI, where it is also the default) No volume
calculation, volumes are set to -1.0 (only in KENO-VI).
TRACE: A trapezoidal integration will be performed (only in KENO-VI).
RANDOM: A Monte Carlo integration will be performed.
``NRAYS=``\ *ntotal*
the number of intervals used in the trapezoidal
integration (default 100,000). Used only with TYPE=TRACE (KENO-VI).
``BATCHES=``\ *nloop*
the number of batches to be used in the
Monte Carlo integration (default 500). Used only with TYPE=RANDOM.
``POINTS=``\ *nplp*
the number of points per batch used in the Monte Carlo
integration (default 1000). Used only with TYPE=RANDOM.
``XP=``\ *xp*
the pls X face of the encompassing cuboid.
``XM=``\ *xm*
the minus X face of the encompassing cuboid.
``YP=``\ *yp*
the plus Y face of the encompassing cuboid.
``YM=``\ *ym*
the minus Y face of the encompassing cuboid.
``ZP=``\ *zp*
the plus Z face of the encompassing cuboid.
``ZM``\ *zm*
the minus Z face of the encompassing cuboid.
``SAMPLE_DEN=``\ *sampleden*
the density of sampling points per
cm\ :sup:`3` per batch. Used only with TYPE=RANDOM.
``IFACE`` =\ *fname*
the face of the enclosing cuboid where the
trapezoidal integration will be performed. Enter either ``XFACE``,
``YFACE``, or ``ZFACE``. KENO-VI will integrate over the face with the
smallest area by default. This allows specifying a different face. Used
only for ``TYPE=TRACE`` (KENO-VI).
The volume parameters include specifying the type of calculation to
determine the volumes and additional parameters needed for the selected
type. In KENO-VI the default type is NONE (i.e., no volume calculation
will be performed), and the volumes for regions not containing
``HOLE``\ s or ``ARRAY``\ s will be set to -1.0. No other data are
needed for this type.
In KENO-VI the volume data may be entered for any or all regions within
the geometry data by placing the keyword ``VOL``\ = followed by the
total volume of that region in the problem at the end of the ``MEDIA``
card. See :numref:`sec-module.keno.geom` (Geometry Data) for more details.
For KENO-VI, in the same problem, volumes may be entered using a
combination of three methods: (1) in the geometry data using ``VOL``\ =,
(2) read from a volume file, and (3) calculated. The calculated volumes
(method 3) are obtained for both the regions, and the meshes are defined
by a grid (such as in TSUNAMI runs). As for KENO V.a, the mesh volumes
must always be calculated (i.e., there is no method to input the mesh
volumes). If volumes are entered or calculated using more than one
method, the following hierarchy is used to determine which volume is
used for the regions.
1. Volumes entered as part of a ``MEDIA`` card using ``VOL``\ = are
always used.
2. Volumes read from the volume file are used if that volume for the
region was not specified using VOL= following a ``MEDIA`` card.
3. Calculated volumes are used if they are not specified using
``VOL=`` and if there is no volume file or data for that region on
the volume file.
4. Volumes that have not been set or calculated will be set to -1.0.
This may result in negative fluxes and fission densities for these
regions.
5. Volumes are only calculated for regions containing material. Regions
containing ``ARRAY``\ s or ``HOLE``\ s have no volume. Those volumes
are associated with the ``UNIT`` contained in the ``ARRAY`` or
``HOLE``.
In KENO V.a, the region volumes are always calculated by the code
without the user's intervention. This is possible because KENO V.a has
no region intersections, so calculation of the volumes is always
possible using analytical methods. The use of the (RANDOM) calculated
volumes using the ``VOLUME`` block is then only justified when the user
needs to calculate the volumes defined by a grid, such as for TSUNAMI
calculations.
When volumes are calculated using either RANDOM or TRACE, then a file
containing volumes and named \_volxxxx (where xxxx is an 18-digit number
with the leftmost unused digits padded with zeros) is created in the
temporary directory. The program searches the temporary directory for a
file name beginning with \_vol. If it is not found, the volume file that
is created is named \_vol000000000000000000. If a file exists, then a
new file will be created where the file number is the largest number
associated with a previous volume file incremented by 1. The file is
automatically copied to the user directory with the input file base name
prepended to it, such as inputfile.volxxxx.volumes.
Below is an example of the ``VOLUME`` data block associated with a case
in which volumes are being calculated using ray tracing. The number of
rays used is set to one million, and if the outer unit volume is not a
cuboid, then a cuboid will be placed around the global region prior to
calculating volumes.
.. code-block:: scale
read volume
type=trace nrays=1000000
XP=10 XM=-15 YP=15 YM=-15 ZP=15 ZM=-15
end volume
Below is an example of the ``VOLUME`` data block associated with a case
where volumes are being calculated using random sampling. The number of
particles per batch is set to 100,000, and the number of batches used is
set to 500. After being calculated, the volume data will be written to a
file in the temporary directory as discussed above.
.. code-block:: scale
read volume
type=random points=100000 batches=500
XP=10 XM=-10 YP=15 YM=-15 ZP=25 ZM=15
end volume
Below is an example of the ``VOLUME`` data block associated with a case
where volumes are both read in from the file VOLUME_DATA and calculated
using random sampling. The number of particles per generation is set to
1,000,000, and the number of generations used is set to 500. The file
VOLUME_DATA must be formatted as shown below. The calculated volume data
are written in the temporary working directory to a file as discussed
above. Calculating volume data for some volume regions and providing
input volume data for others may be useful if only part of the volume
data is known and the remaining data need to be calculated.
.. code-block:: scale
read volume
type=random points=1000000 batches=500
readvol=volume_DAta
end volume
Example volume file VOLUME_DATA:
.. code-block:: scale
UNIT 1
MEDIA 1 VOL=110.0
MEDIA 2 VOL=2435.8
MEDIA 2 VOL=3242.9
UNIT 2
MEDIA 2 VOL=342.8
MEDIA 0 VOL=4235.0
Below is an example of a sample problem in which volumes are being
calculated using random sampling. The number of particles per generation
is set to 100,000, and the number of generations used is set to 500.
After being calculated, the ``VOLUME`` data will be written as described
above.
.. code-block:: scale
=CSAS6
SAMPLE PROBLEM WITH VOLUMES CALCULATED AND PRINTED TO FILE
v7.1-252n
READ COMP
URANIUM 1 DEN=18.76 1 293 92235 93.2 92238 5.6 92234 1.0 92236 0.2 END
END COMP
READ GEOMETRY
UNIT 3
COM='SINGLE UNIT CENTERED'
SPHERE 10 4.000
CUBOID 20 6P6.0
MEDIA 1 1 10
MEDIA 0 1 20 -10
BOUNDARY 20
UNIT 1
COM='SINGLE UNIT CENTERED'
SPHERE 10 5.000
CUBOID 20 6P6.0
MEDIA 1 1 10
MEDIA 0 1 20 -10
BOUNDARY 20
GLOBAL UNIT 2
COM='Global UNIT'
CUBOID 10 6P18.0
ARRAY 1 10 PLACE 2 2 2 3R0.0
BOUNDARY 10
END GEOMETRY
READ ARRAY ARA=1 NUX=3 NUY=3 NUZ=3 TYP=CUBOIDAL FILL
1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 1 1 1 1 1 1 1 1 1 END ARRAY
READ VOLUME
TYPE=RANDOM POINTS=100000 BATCHES=500
END VOLUME
END DATA
END
Example volume file _volxxxx:
.. code-block:: scale
UNIT 1
MEDIA 1 VOL=9423.45
MEDIA 0 VOL=21678.6
UNIT 3
MEDIA 1 VOL=2410.81
MEDIA 0 VOL=13143.1
Below is an example of a problem with the volumes entered in the
geometry data block using ``VOL=`` followed by the volume for all
``MEDIA`` type content records. Note that the keyword ``VOL=``
should never follow a ``HOLE`` or ``ARRAY`` content record.
.. code-block:: scale
=csas26
Sample problem with volumes input in geometry data
v7.1-252n
read comp
uranium 1 den=18.76 1 293 92235 93.2 92238 5.6 92234 1.0 92236 0.2 end
end comp
read geometry
unit 3
com='unit 3'
sphere 10 4.000
cuboid 20 6p6.0
media 1 1 10 vol=2412.7
media 0 1 20 -10 vol=13139.3
boundary 20
unit 1
com='UNIT 1'
sphere 10 5.000
cuboid 20 6p6.0
media 1 1 10 vol=9424.8
media 0 1 20 -10 vol=21679.2
boundary 20
global unit 2
com='GLOBAL Unit 2'
cuboid 10 6p18.0
array 1 10 place 2 2 2 3r0.0
boundary 10
end geometry
read array ara=1 nux=3 nuy=3 nuz=3 typ=cuboidal fill
1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 1 1 1 1 1 1 1 1 1 end array
end data
end
.. _8-1-2-14:
Grid geometry data
~~~~~~~~~~~~~~~~~~
This data block is used to input the data needed to define a Cartesian
grid for tallying purposes.
``READ GRID N`` *p*\ :sub:`1` … *p*\ :sub:`L` ``END GRID``
*N*
mesh grid identifier, always entered.
*p*\ :sub:`1` … *p*\ :sub:`L`
are *L* parameters chosen from the list below. The
parameters are entered using keywords followed by the appropriate data,
except for the grid identifier, which is always entered first as an
integer.
``N``\ [``UM``]\ ``XCELLS=``\ *numx*
number of cells in the x
direction, default = 1.
``N``\ [``UM``]\ ``YCELLS=``\ *numy*
number of cells in the y
direction, default = 1.
``N``\ [``UM``]\ ``ZCELLS=``\ *numz*
number of cells in the z
direction, default = 1.
``XMIN=``\ *xmin*
minimum cell boundary in the x direction, default = 0.
``XMAX=``\ *xmax*
maximum cell boundary in the x direction, default =
1.
``YMIN=``\ *ymin*
minimum cell boundary in the y direction, default =
0.
``YMAX=``\ *ymax*
maximum cell boundary on the y direction, default =
1.
``ZMIN``\ =\ *zmin*
minimum cell boundary in the z direction, default =
0.
``ZMAX=``\ *zmax*
maximum cell boundary in the z direction, default = 1.
``XPLANES``\ *xplanes*
the cell boundaries in the x direction
followed by end, default = 0, 1 end.
``YPLANES``\ *yplanes*
the cell boundaries in the y direction
followed by end, default = 0, 1 end.
``ZPLANES=``\ *zplanes*
the cell boundaries in the z direction
followed by end, default = 0, 1 end.
``XLINEAR=``\ *numcellsx *x*\ :sub:`min` *x*\ :sub:`max`
generate y-z planes from
x\ :sub:`min` to x\ :sub:`max` creating *numcellsx* intervals.
``YLINEAR=``\ *numcellsy *y*\ :sub:`min` *y*\ :sub:`max`
generate x-z planes from
y\ :sub:`min` to y\ :sub:`max`, creating *numcellsy* intervals.
``ZLINEAR=``\ *numcellsz *z*\ :sub:`min` *z*\ :sub:`max`
generate x-y planes from
z\ :sub:`min` to z\ :sub:`max`, creating *numcellsz* intervals.
``TITLE=``\ *title*
optional title for this mesh grid. Only used in
KENO if an error in the grid causes a debug print.
If *numx, xmin, xmax* are entered, then the code will calculate *numx*
equally spaced cells in the x direction between *xmin* and *xmax*.
If *xplanes* is entered, then the code will count the number of unique
*xplanes*, and order them from minimum to maximum, deleting any
duplicates.
If the user inputs both sets of data, then the code will use the
*xplanes* data.
If *xplanes* and *xlinear* are both entered, then the code will retain
all unique planes from *xplanes* and all *xlinear* entries provided. The
above also applies to Y and Z.
``NOTE``: The user **MUST** set the minimum and maximum values in each
direction so that the actual geometry is totally covered by the mesh for
mesh flux tally that is used in TSUNAMI sensitivity calculations.
KENO checks for and eliminates duplicate or nearly duplicate planes.
The user may specify multiple mesh grids; each must be defined in
separate ``READ GRID`` blocks. In this case, each grid should have
different *N* (grid ID number). See :numref:`8-1-3-10` for details and
samples.
.. _8-1-2-15:
Reaction data
~~~~~~~~~~~~~
The reaction data block is used to specify the type of tally (e.g.,
reaction rates, flux, and few group reaction cross sections) and the
reaction/nuclide pairs in any mixture used in the problem for reaction
tally calculations. This block is operational only with the continuous
energy mode, and it provides the specifications for reaction rate,
neutron flux, and reaction cross section tallies. See :numref:`8-1-6-6` for
more details. For multigroup KENO calculations, use KMART5 or KMART6,
which are described in the KMART section of the SCALE manual.
A reaction data block consists of *REACTION FILTERS*, *TALLY TYPE*,
*ENERGY GROUP BOUNDARIES*, and *OUTPUT EDITS*. These data types can be entered in
any order. A combination of parameters for describing the *REACTION FILTERS*
and *TALLY TYPE* must be entered for any reaction or cross section
tally calculation. *ENERGY GROUP BOUNDARIES* and *OUTPUT EDITS* data are
optional. Tally calculations can be performed for multiple reactions
specified by the *REACTION FILTERS*. Only one energy grid, either
specified with the data in *ENERGY GROUP BOUNDARIES* or from the
``READ ENERGY`` block or from the code defaults, is used for all reaction tally
calculations. To provide data for the continuous energy depletion
calculations, another energy grid can be specified and used for tallying
only the mixture flux.
Enter *REACTION DATA* in the form:
``READ REACTION`` *REACTION FILTERS [TALLY TYPE] [ENERGY GROUP BOUNDARIES][OUTPUT EDITS]* ``END REACTION``
*REACTION FILTERS*
define a reaction map that is used in reaction tally
calculations. The *REACTION FILTERS* must be entered in the following
order; mixture data (``MIX`` or ``MIXLIST``) followed by nuclide data
(``NUC`` or ``NUCLIST``) followed by reaction IDs (``MT`` or
``MTLIST``). Each filter is defined using a combination of the following
keywords:
``MIX=``\ *mixnum*
Mixture number, no default value. Specified mixture
number must exist in the mixing table and be used in the problem for a
valid filter generation. A wildcard ``*`` can be used to define a
filter applicable for all mixtures in the problem.
``MIXLIST`` *mixnum*\ :sub:`1` *mixnum*\ :sub:`2` … *mixnum*\ :sub:`N`\ ``END``
A list of mixture
numbers followed by *end,* no default values. Specified mixture numbers
must exist in the mixing table and be used in the problem for a valid
reaction tally calculation. Within each filter, use either ``MIX`` or
``MIXLIST``, but not both.
``NUC=``\ *nucid*
Nuclide identifier, no default value. Specified
nuclide must be a constituent of the mixtures used in this filter
definition (specified with MIX or MIXLIST). A wildcard "*" can be used
to define a filter applicable for all nuclides in each mixture in this
filter definition. Nuclide identifiers are listed for all isotopes in
the :ref:`Standard Composition Library section ` of the SCALE manual.
``NUCLIST`` *nucid*\ :sub:`1` *nucid*\ :sub:`2` … *nucid*\ :sub:`N`\ ``END``
A list of nuclide
identifiers followed by *end,* no default values. Specified nuclides
must be the constituents of the mixtures used in this filter definition
(specified by ``MIX`` or ``MIXLIST``). Within each filter, use either
``NUC`` or ``NUCLIST``, but not both.
``MT=``\ *mt*
Reaction MT number, no default value. Specified reaction
MT number should be available for the nuclides defined in this filter
definition (specified by ``NUC`` or ``NUCLIST``). Otherwise, the code
skips the filter definition with this given reaction MT. A wildcard "*"
can be used to define a filter with all reaction MTs. Valid SCALE
library MT values are listed in the :ref:`sec-data.mt`.
``MTLIST`` *mt*\ :sub:`1` *mt*\ :sub:`2` … *mt*\ :sub:`N`\ ``END``
A list of reaction ``MT``
numbers followed by *end,* no default values. Specified MT numbers
should be available for the nuclides defined in this filter definition
(specified by ``MIX`` or ``MIXLIST``). Otherwise, KENO skips that
reaction specified in the filter for the reaction tally calculations.
Within each filter, use either ``MT`` or ``MTLIST``, but not both.
A reaction filter consists of either single or multiple mixture, nuclide
and reaction definitions. A valid reaction filter starts with mixture
specification, followed by nuclide specification, and ends with reaction
specification. Mixture(s) must be specified with either ``MIX`` or
``MIXLIST`` keywords. Nuclide(s) in these mixtures must be entered with
either ``NUC`` or ``NUCLIST``, and reactions for each nuclide must be
specified with either ``MT`` or ``MTLIST``.
Mixture, nuclide, and reaction number are required for mixture average
fluxes, even though the nuclide and reaction numbers are not used for
the neutron flux tallies.
Multiple reaction filter definitions are allowed. KENO processes all the
definitions and creates a reaction map based on them. The following
examples demonstrate the reaction filter specifications for different
problems. In these examples, reaction filters are specified based on the
following composition data used in the problem:
compositions in the example problem
+---------+------------------------+
| mixture | nuclides |
+=========+========================+
| 10 | 92235, 92238, 8016 |
+---------+------------------------+
| 20 | 92238, 94239, 8016 |
+---------+------------------------+
| 30 | 92235, 92238, 8016 |
+---------+------------------------+
| 40 | 1001, 8016 |
+---------+------------------------+
| 100 | 1001, 8016, 5010, 5011 |
+---------+------------------------+
.. code-block:: scale
:name: keno-ex1
:caption: Defines a reaction filter used to tally only fission reaction (``MT=18``) of :sup:`235`\ U in mixture 10.
READ REACTION
MIX=10 NUC=92235 MT=18
...
END REACTION
.. code-block:: scale
:name: keno-ex2
:caption: Defines a reaction filter used to tally all available reactions of :sup:`235`\ U in mixture 10
READ REACTION
MIX=10 NUC=92235 MT=*
...
END REACTION
.. code-block:: scale
:caption: Defines a reaction filter used to tally the elastic scattering (mt=2), fission (mt=18), and capture (mt=102) reactions of :sup:`235`\ U in mixture 10
:name: keno-ex3
READ REACTION
MIX=10 NUC=92235 MTLIST 2 18 102 END
...
END REACTION
.. code-block:: scale
:name: keno-ex4
:caption: Defines a reaction filter used to tally the elastic scattering (``MT=2``), fission (``MT=18``), and capture (``MT=102``) reactions of :sup:`235`\ U in mixture 10. Reaction filter definition in this example is identical to the filter definition given in :numref:`keno-ex3`.
READ REACTION
MIX=10 NUC=92235 MT=2
MIX=10 NUC=92235 MT=18
MIX=10 NUC=92235 MT=102
...
END REACTION
.. code-block:: scale
:name: keno-ex5
:caption: Defines a reaction filter used to tally the fission reaction (``MT=18``) of :sup:`235`\ U and :sup:`238`\ U in mixture 10. Code skips the reaction tally request for :sup:`16`\ O since the requested reaction is not available for this nuclide in the data library.
READ REACTION
MIX=10 NUC=* MT=18
...
END REACTION
.. code-block:: scale
:name: keno-ex6
:caption: Defines a reaction filter used to tally the fission reaction (``MT=18``) of :sup:`235`\ U and :sup:`238`\ U in mixture 10. Reaction filter definition in this example is identical to the filter definition given in :numref:`keno-ex5`.
READ REACTION
MIX=10 NUC=92235 MT=18
MIX=10 NUC=92238 MT=18
...
END REACTION
.. code-block:: scale
:name: keno-ex7
:caption: A reaction filter used to tally the capture reaction (``MT=102``) of :sup:`16`\ O in all mixtures.
READ REACTION
MIX=* NUC=8016 MT=102
...
END REACTION
.. code-block:: scale
:name: keno-ex8
:caption: Areaction filter used to tally the capture reaction (``MT=102``) of :sup:`16`\ O in mixtures 10, 20, 30, 40, and 100 respectively. Reaction filter definition in this example is identical to the filter definition given in :numref:`keno-ex7`.
READ REACTION
MIX=10 NUC=8016 MT=102
MIX=20 NUC=8016 MT=102
MIX=30 NUC=8016 MT=102
MIX=40 NUC=8016 MT=102
MIX=100 NUC=8016 MT=102
...
END REACTION
.. code-block:: scale
:name: keno-ex9
:caption: A reaction filter used to tally the capture reaction (``MT=102``) of :sup:`16`\ O in mixtures 10, 20, 30, 40, and 100 respectively. Reaction filter definition in this example is identical to the filter definition given in :numref:`keno-ex7` and :numref:`keno-ex8`.
READ REACTION
MIXLIST 10 20 30 40 100 END NUC=8016 MT=102
...
END REACTION
.. code-block:: scale
:name: keno-ex10
:caption: Complex reaction tally for U-238, Pu-239, H-1, and O-16 across several mixtures.
READ REACTION
MIXLIST 10 20 30 END NUC=92238 MT=102
MIX=20 NUC=94239 MT=18
MIX=40 NUC=1001 MT=*
MIX=* NUC=8016 MT=2
MIX=* NUC=* MT=27
...
END REACTION
:numref:`keno-ex10` defines a complex reaction filter used to tally:
a) Capture reaction (**MT**\ =102) of :sup:`238`\ U in mixtures 10, 20
and 30 respectively,
b) Fission reaction (**MT**\ =18) of :sup:`239`\ Pu in mixture 20,
c) All reactions of :sup:`1`\ H in mixture 40,
d) Elastic scattering reaction of :sup:`16`\ O in all mixtures,
e) Total absorption reaction of all nuclides in all mixtures.
Parameters of TALLY TYPE are logical parameters used to select
quantities (reaction cross section, reaction rate, and mixture flux)
that are tallied for the given problem. The user specifies any
combination of these TALLY TYPEs once for all filters:
``XSTALLY=``\ *lCEXSTally*
Enter YES or NO. A value of YES specifies that reaction cross
sections be tallied for the reactions listed in *REACTION FILTERS*.
The default value of ``XSTALLY`` is NO. Computed reaction cross
sections are saved in a file named *BASENAME_keno_micro_xs.0* in
RTNDIR, which is a SCALE environment variable for the directory from
where the calculation was started. BASENAME is a SCALE environment
variable that is the base name of the input file. (BASENAME is equal
to *"mytest"* if the SCALE input name is *"mytest.inp."*)
``RRTALLY=``\ *lCERRTally*
Enter YES or NO. A value of YES specifies that reaction rates be
tallied for the reactions listed in *REACTION FILTERS*. The default
value of RRTALLY is NO. Computed reaction rates are saved in a file
named *BASENAME_keno_micro_rr.0* in RTNDIR.
.. note:: KENO combines and saves reaction rate and reaction cross
section tallies to the same file, named *BASENAME_keno_micro_xs_rr.0* in
RTNDIR, if both ``XSTALLY`` and ``RRTALLY`` are set to YES.
``MIXFLX=``\ *lCEMixFlux*
Enter YES or NO. A value of YES specifies that mixture fluxes are to
be tallied for the mixtures listed in *REACTION FILTERS*. The default
value of ``MIXFLX`` is NO. Computed mixture fluxes are saved in a
file named *BASENAME_keno_mixture_flux.0* in RTNDIR.
Mixture, nuclide, and reaction number are required for mixture
average fluxes, even though the nuclide and reaction numbers are not
used for the neutron flux tallies.
.. code-block:: scale
:name: keno-ex11
:caption: Defines a reaction filter, which uses fission reaction (``MT=18``) of :sup:`235`\ U in mixture 10, for tallying reaction cross sections.
READ REACTION
MIX=10 NUC=92235 MT=18
XSTALLY=YES
...
END REACTION
.. note:: Computed data are saved in a file named
*BASENAME_keno_micro_xs.0*
.. code-block:: scale
:name: keno-ex12
:caption: Defines a reaction filter, which uses fission reaction (``MT=18``) of :sup:`235`\ U in mixture 10, for tallying reaction rates as well as the reaction cross sections.
READ REACTION
MIX=10 NUC=92235 MT=18
XSTALLY=YES RRTALLY=YES
...
END REACTION
.. note:: Computed data are saved in files named
*BASENAME_keno_micro_xs_rr.0*
.. code-block:: scale
:name: keno-ex13
:caption: Defines a reaction filter, which uses fission reaction (``MT=18``) of :sup:`235`\ U in mixture 10, for tallying reaction cross sections. In addition, mixture flux is tallied for mixture 10 given in this reaction filter.
READ REACTION
MIX=10 NUC=92235 MT=18
XSTALLY=YES MIXFLX=YES
...
END REACTION
.. note:: Computed data are saved in files named
*BASENAME_keno_micro_xs.0*, and *BASENAME_keno_mixture_flux.0*,
respectively.
*ENERGY GROUP BOUNDARIES* data define energy group structure other than
the defaults for tallying both reaction cross sections/reaction rates
and mixture fluxes.
``ENER_XS`` *e\ 1 e\ 2 e\ 3 …*\ ``END`` Upper energy boundary for each
group. The last entry is the lower energy boundary of the last group.
For N groups, there are N+1 entries. Entries must be in descending
order. This may be specified once in the REACTION block and, if used, is
applied to all cross section and reaction rate tallies.
``ENER_FLX`` *e\ 1 e\ 2 e\ 3 …*\ ``END`` Upper energy boundary for each
group, default is ``NGP``-group data. The last entry is the lower energy
boundary of the last group. For N groups, there are N +1 entries.
Entries must be in descending order. This may be specified once in the
REACTION block and, if used, is applied to all mixture flux tallies.
.. note:: Default values for the energy group boundaries in reaction
tally calculations are determined as in the order described in :numref:`8-1-2-12`.
.. code-block:: scale
:name: keno-ex14
:caption: No ``READ ENERGY`` block, no ``NGP`` in ``READ PARAMETER`` block, no energy group
READ REACTION
MIX=10 NUCLIST 92235 92238 END
MTLIST 16 17 18 END
MIXFLX=YES XSTALLY=YES
...
END REACTION
Default SCALE 252-group energy structure is used for tallying both
mixture flux and reaction cross sections.
.. code-block:: scale
:name: keno-ex15
:caption: Energy group bounds specified in ``READ ENERGY`` block. 2-group energy structure given in ``READ ENERGY`` block is used for tallying both mixture flux and reaction cross sections.
READ ENERGY
20.E6 0.6 1.E-4
END ENERGY
...
READ REACTION
MIX=10 NUCLIST 92235 92238 END
MTLIST 16 17 18 END
MIXFLX=YES XSTALLY=YES
...
END REACTION
.. code-block:: scale
:name: keno-ex16
:caption: ``NGP`` is set in ``READ PARAMETER`` block; 4-group energy group structure (4-equal lethargy bins) is used for tallying both mixture flux and reaction cross sections.
READ PARAMETER
...
NGP=4
END PARAMETER
...
READ REACTION
MIX=10 NUCLIST 92235 92238 END
MTLIST 16 17 18 END
MIXFLX=YES XSTALLY=YES
...
END REACTION
.. code-block:: scale
:name: keno-ex17
:caption: 3-group energy group structure given in ``reaction data`` block is used for tallying reaction cross sections, and default SCALE 252-group energy structure is used for tallying mixture flux.
READ REACTION
MIX=10 NUCLIST 92235 92238 END
MTLIST 16 17 18 END
MIXFLX=YES XSTALLY=YES
ENER_XS 20.E6 1.E3 1.0 1.E-4 END
…
END REACTION
.. code-block:: scale
:name: keno-ex18
:caption: 2-group energy group structure given in ``reaction data`` block is used for tallying reaction cross sections, and 3-group energy group structure given in ``reaction data`` block is used for tallying mixture flux.
READ REACTION
MIX=10 NUCLIST 92235 92238 END
MTLIST 16 17 18 END
MIXFLX=YES XSTALLY=YES
ENER_FLX 20.E6 1.E3 1.0 1.E-4 END
ENER_XS 20.E6 1.0 1.E-4 END
…
END REACTION
Parameters of *OUTPUT EDITS* are logical parameters used to print
reaction tallies and mixture fluxes in separate files. These parameters
are optional parameters.
``PRNTXS=``\ *lCEprintXS* Enter YES or NO. A value of YES specifies that
reaction cross sections tallies for each mixture be written in separate
files in RTNDIR (*BASENAME_keno_micro_xs_mix{mixnum}.0, mixnum* is the
mixture numbers specified in the reaction filters)\ *.* The default
value of ``PRNTXS`` is NO.
``PRNTRR=``\ *lCEprintRR* Enter YES or NO. A value of YES specifies that
reaction rate tallies for each mixture be written in separate files in
RTNDIR (*BASENAME_keno_micro_rr_mix{mixnum}.0, mixnum* is the mixture
numbers specified in the reaction filters)\ *.* The default value of
``PRNTRR`` is NO.
``PRNTFLX=``\ *lCEprintMixFlux* Enter YES or NO. A value of YES
specifies that mixture flux tallies for each mixture be written in
separate files in RTNDIR (*BASENAME_keno_mixture_flux_mix{mixnum}.0,
mixnum* is the mixture numbers specified in the reaction filters)\ *.*
The default value of ``PRNTFLX`` is NO.
Notes for KENO Users
--------------------
This section provides assorted tips designed to assist the KENO user with problem mockups.
Some information concerning methods used by KENO is also included.
Data entry
~~~~~~~~~~
The KENO data is entered in blocks that begin and end with keywords as
described in :numref:`sec-module.keno.input_outline`. Only one set of parameter data can be
entered for a problem. However, for other data blocks, it is possible to
enter more than one block of the same kind of data. When this is done,
only the last block of that kind of data is retained for use by the
problem, except for the GRID block for which all blocks are retained.
Within data blocks, a number, x, can be repeated n times by specifying
nRx, n*x, or n$x.
Numbers in engineering notation may be specified with or without an "E"
between the base and the exponent. For example; 0.0011 may be specified
as 1.1e-3 or as 1.1-3.
Multiple and scattered entries in the mixing table
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
In the following examples, assume 1001 is the nuclide ID for hydrogen,
8016 is the nuclide ID for oxygen, 92235 is the nuclide ID for
:sup:`235`\ U, and 92238 is the nuclide ID for :sup:`238`\ U. If a given
nuclide ID is used more than once in the same mixture, the result is the
summing of all the number densities associated with that nuclide. For
example:
``MIX =1 92235 4.3e-2 92238 2.6e-3 1001 3.7e-2 92235 1.1e-3 8016 1.8e-2``
would be the same as entering:
``MIX =1 92235 4.41e-2 92238 2.6e-3 1001 3.7e-2 8016 1.8e-2``
A belated entry for a mixture can be made as follows:
``MIX =1 1001 6.6e-2 MIX=2 92235 4.3e-2 92238 2.6e-3 MIX=1 8016 3.3e-2``
This is the same as entering:
``MIX =1 1001 6.6e-2 8016 3.3e-2 MIX=2 92235 4.3e-2 92238 2.6e-3``
Multiple entries in geometry data
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Individual geometry regions cannot be replaced by adding an additional
description. However, entire unit descriptions can be replaced by adding
a new description having the same unit number. The last description
entered for a unit is used in the calculation. For example, the
following geometry descriptions are equivalent in KENO V.a and KENO-VI,
respectively:
In KENO V.a:
.. code-block:: scale
READ GEOM UNIT 1 SPHERE 1 1 5.0 CUBE 0 1 10.0 -10.0
UNIT 2 CYLINDER 1 1 2.0 5.0 -5.0 CUBE 0 1 10.0 -10.0
UNIT 1 CUBOID 1 1 1.0 -1.5 2.5 -2.0 5.0 -6.0 CUBE 0 1 10.0 -10.0
END GEOM
is the same as entering:
.. code-block:: scale
READ GEOM UNIT 1 CUBOID 1 1 1.0 -1.5 2.5 -2.0 5.0 -6.0
CUBE 0 1 10.0 -10.0
UNIT 2 CYLINDER 1 1 2.0 5.0 -5.0 CUBE 0 1 10.0 -10.0 END GEOM
or
.. code-block:: scale
READ GEOM UNIT 2 CYLINDER 1 1 2.0 5.0 -5.0 CUBE 0 1 10.0 -10.0
UNIT 1 CUBOID 1 1 1.0 -1.5 2.5 -2.0 5.0 -6.0 CUBE 0 1 10.0 -10.0
END GEOM
In KENO-VI:
.. code-block:: scale
READ GEOM
UNIT 1 SPHERE 10 5.0
CUBOID 20 10.0 -10.0 10.0 -10.0 10.0 -10.0
MEDIA 1 1 10
MEDIA 0 1 20 -10
BOUNDARY 20
UNIT 2
CYLINDER 10 2.0 5.0 -5.0
CUBOID 20 10.0 -10.0 10.0 -10.0 10.0 -10.0
MEDIA 1 1 10
MEDIA 0 1 20 -10
BOUNDARY 20
UNIT 1
CUBOID 10 1.0 -1.5 2.5 -2.0 5.0 -6.0
CUBOID 20 10.0 -10.0 10.0 -10.0 10.0 -10.0
MEDIA 1 1 10
MEDIA 0 1 -10 20
BOUNDARY 20
END GEOM
is the same as entering
.. code-block:: scale
READ GEOM
UNIT 1
CUBOID 10 1.0 -1.5 2.5 -2.0 5.0 -6.0
CUBOID 20 10.0 -10.0 10.0 -10.0 10.0 -10.0
MEDIA 1 1 10
BOUNDARY 20
MEDIA 0 1 -10 20
UNIT 2
CYLINDER 10 2.0 5.0 -5.0
CUBOID 20 10.0 -10.0 10.0 -10 10.0 -10.0
MEDIA 1 1 10
MEDIA 0 1 -10 20
BOUNDARY 20
END GEOM
or
.. code-block:: scale
READ GEOM
UNIT 2
CYLINDER 30 2.0 5.0 -5.0
CUBOID 40 6P10.0
MEDIA 1 1 30
MEDIA 0 1 -30 40
BOUNDARY 40
UNIT 1
CUBOID 20 1.0 -1.5 2.5 -2.0 5.0 -6.0
CUBOID 10 6P10.0
MEDIA 1 1 20
MEDIA 0 1 10 -20
BOUNDARY 10
END GEOM
The order of entry for ``UNIT`` descriptions is not important because
the ``UNIT`` number is assigned as the value following the word
``UNIT``. They do not need to be entered sequentially, and they do not
need to be numbered sequentially. It is perfectly acceptable to enter
``UNIT``\ s 2, 3, and 5, omitting Units 1 and 4 as long as ``UNIT``\ s 1
and 4 are not referenced in the problem. It is also acceptable to
scramble the order of entry as in entering ``UNIT``\ s 3, 2, and 5.
.. _sec-module.keno.file_unit:
Default logical unit numbers for KENO
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The logical unit numbers for data used by KENO are listed in
:numref:`tab8-1-23`.
.. tabularcolumns:: |p{5cm}|p{1.5cm}|p{1.5cm}|p{2cm}|
.. table:: KENO logical unit numbers
:name: tab8-1-23
:class: longtable
+-----------------+-----------------+-----------------+-----------------+
| Function | Parameter | Unit | Variable |
| | name | number | name |
+-----------------+-----------------+-----------------+-----------------+
| Problem input | | 5 | INPT |
| data (ASCII) | | | |
+-----------------+-----------------+-----------------+-----------------+
| Problem input | | 95 | BIN |
| data (binary) | | | |
+-----------------+-----------------+-----------------+-----------------+
| Program output | | 6 | OUTPT |
| (ASCII) | | | |
+-----------------+-----------------+-----------------+-----------------+
| Albedo data | ALB= | 79 | ALBDO |
+-----------------+-----------------+-----------------+-----------------+
| Scratch unit | SKT= | 16 | SKRT |
+-----------------+-----------------+-----------------+-----------------+
| Read restart | RST= | 0\ :sup:`a` | RSTRT |
| data | | | |
+-----------------+-----------------+-----------------+-----------------+
| | | 34\ :sup:`b` | RSTRT |
+-----------------+-----------------+-----------------+-----------------+
| Write restart | WRS= | 0\ :sup:`a` | WSTRT |
| data | | | |
+-----------------+-----------------+-----------------+-----------------+
| | | 35\ :sup:`c` | WSTRT |
+-----------------+-----------------+-----------------+-----------------+
| Direct access | | 8 | DIRECT(1) |
| storage for | | | |
| input data | | | |
+-----------------+-----------------+-----------------+-----------------+
| Direct access | | 9 | DIRECT(2) |
| storage for | | | |
| supergrouped | | | |
| data | | | |
+-----------------+-----------------+-----------------+-----------------+
| Direct access | | 10 | DIRECT(3) |
| storage for | | | |
| cross section | | | |
| mixing | | | |
+-----------------+-----------------+-----------------+-----------------+
| Mixed cross | XSC= | 14\ :sup:`d` | ICEXS |
| section data | | | |
| set | | | |
+-----------------+-----------------+-----------------+-----------------+
| Group-dependent | WTS= | 80 | WTS |
| weights | | | |
+-----------------+-----------------+-----------------+-----------------+
| AMPX working | LIB= | 0\ :sup:`a` | AMPXS |
| format cross | | | |
| sections | | | |
+-----------------+-----------------+-----------------+-----------------+
| Group boundary | GRP= | 77 | GRPBS |
| Library | | | |
| (KENO-VI) | | | |
+-----------------+-----------------+-----------------+-----------------+
| :sup:`a` Defaulted to zero |
| |
| :sup:`b` Defaulted to 34 if ``BEG=`` a number greater than 1 and |
| ``RSTRT=0``. |
| |
| :sup:`c Defaulted to 35 if ``RES=`` a number greater than zero and |
| ``WSTRT=0``. |
| |
| :sup:`d` Defaulted to 0; if ``LIB=`` a number greater than zero, |
| ``ICEXS`` is defaulted to 14. |
+-----------------------------------------------------------------------+
.. _sec-module.keno.parameter:
Parameter input
~~~~~~~~~~~~~~~
When the parameter data block is entered for a problem, the same keyword
may be entered several times. The last value that is entered is used in
the problem. Data may be entered as follows:
.. code-block:: scale
READ PARAM FLX=YES NPG=1000 TME=0.5 TME=1.0
NPG=50 TME=10.0 FLX=NO
NPG=500
END PARA
This will result in the problem having ``FLX=NO``, ``TME=10.0``, and
``NPG=500``. It may be more convenient for the user to insert a new
value than to change the existing data.
Certain parameter default values should not be overridden unless the
user has a very good reason to do so. These parameters are as follows:
1. ``X1D=`` which defines the number of extra 1-D cross sections. The
use of extra 1-D cross sections-other than the use of the fission
cross section for calculating the average number of neutrons per
fission-requires programming changes to the code;
2. ``NFB=`` which defines the number of neutrons that can be entered
in the fission bank (the fission bank is where the information
related to a fission is stored);
3. ``XFB=`` which defines the number of extra positions in the
fission bank;
4. ``NBK=`` which defines the number of neutrons that can be entered
in the neutron bank (the neutron bank contains information about each
history);
5. ``XNB=`` which defines the number of extra positions in the
neutron bank;
6. ``WTH=`` which defines the factor that determines when splitting
occurs;
7. ``WTA=`` which defines the default average weight given to a
neutron that survives Russian roulette;
8. ``WTL=`` which defines the factor that determines when Russian
roulette is played; and
9. ``LNG=`` which sets the maximum words of storage available to the
program.
It is recommended that ``BUG=``, the flag for printing debug
information, ``never`` be set to YES. The user would have to look at the
FORTRAN coding to determine what information is printed. ``BUG``\ =YES
prints massive amounts of sparsely labeled information. The user should
only rarely consider using ``TRK``\ =YES. This generates thousands of
lines of well-labeled output that provides information about each
history at key locations during the tracking procedure. All other
parameters can be changed at will to provide features the user wishes to
activate.
Cross sections
~~~~~~~~~~~~~~
In multi-energy group mode, KENO always uses cross sections from a mixed
cross section data file. The format of this file is the Monte Carlo
processed cross section file. A mixed cross section file can be created
by previous KENO run, or by using an AMPX working format library and
entering mixing table data in KENO.
Use a mixed cross section Monte Carlo format library
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
A mixed cross section Monte Carlo format library (premixed cross section
data file) from a previous KENO case may be used. This file is specified
using the parameter ``XSC``\ =. If a mixing table data block is entered,
the premixed cross section data file will be rewritten. Therefore, a
mixing table should not be entered if a premixed cross section data file
is used. The user should verify that the mixtures created by a previous
KENO case are consistent with those used in the geometry data of the
problem.
Use an AMPX working format library
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
When an AMPX working format library is used, it must be specified using
the parameter ``LIB``\ =, and mixing table data must always be entered.
IDs used in the mixing table must match the IDs on the AMPX working
format library. The user must provide a file with the correct cross
sections with a name that matches the pattern ftNNf001, with NN being
the number of the logical unit.
.. _8-1-3-4-3:
Number of scattering angles
^^^^^^^^^^^^^^^^^^^^^^^^^^^
The number of scattering angles is defaulted to 1 (defaulted to 2 when
KENO-VI is run as part of the CSAS6 sequence). This stand alone default
is not adequate for many applications. The user should specify the
scattering angle to be consistent with the cross sections being used.
The number of scattering angles is entered in the cross section mixing
table by using the keyword ``SCT``\ =. See :numref:`sec-module.keno.mixing_table`.
The order of the last Legendre coefficient to be preserved in the
scattering distribution is equal to (2 :math:`\times` SCT - 1). ``SCT``\ =1 could be
used with a P\ :sub:`1` cross section set such as the 16-group
Hansen-Roach cross section library, and ``SCT``\ =2, for a P\ :sub:`3`
cross section set such as the SCALE 27-group cross section library.
ENDF/B-VII cross section libraries such as the 44-group or 252-group
libraries contain many nuclides having P\ :sub:`5` cross section sets.
Isotropic scattering is achieved by entering ``SCT``\ =0.
.. _8-1-3-4-4:
Cross section message cutoff
^^^^^^^^^^^^^^^^^^^^^^^^^^^^
The cross section message cutoff value, *pbxs*, is defaulted to
3 :math:`\times` 10\ :sup:`-5`. Warning messages generated when errors are
encountered in the P\ :sub:`L` expansion of the group-to-group transfers
will be suppressed if the P\ :sub:`0` cross section for that particular
energy transfer is less than *pbxs*. The value of *pbxs* is specified in
the cross section mixing table by using the keyword ``EPS``\ =. See
:numref:`sec-module.keno.mixing_table`.
The default value of *pbxs* is sufficient to assure that warning
messages will not be printed for most of the SCALE P\ :sub:`1` and
P\ :sub:`3` cross section libraries. However, the v7.0-n library may
print a few errors if P\ :sub:`5` cross sections are specified.
The error messages below were printed for a problem using the 238-group
cross section library and *pbxs* = 3.0 :math:`\times` 10\ :sup:`-5`. If the default
value of *pbxs* allows too many warning messages to be printed, a value
can be determined which does not print the error messages from the
printed messages by choosing a number larger than the P\ :sub:`0`
component on the first line, as shown below.
THE LEGENDRE EXPANSION OF THE CROSS SECTION (P\ :sub:`0`\-P\ :sub:`N`) IS
P\ :sub:`0` P\ :sub:`1` P\ :sub:`2` ... P\ :sub:`n`
THE MOMENTS CORRESPONDING TO THIS DISTRIBUTION ARE
M\ :sub:`1` M\ :sub:`2` ... M\ :sub:`n`
THE MOMENTS CORRESPONDING TO THE GENERATED DISTRIBUTION ARE
M\ :sub:`1` M\ :sub:`2` ... M\ :sub:`n`
THE LEGENDRE EXPANSION CORRESPONDING TO THESE MOMENTS IS
P\ :sub:`0` P\ :sub:`1` P\ :sub:`2` ... P\ :sub:`n`
___ MOMENTS WERE ACCEPTED
For the following messages, ``EPS``\ =6.9e-5 would cause all three
messages to be suppressed. A value less than 5.615159e-5 and greater
than 4.767635e-5 would suppress the second message, and a value less
than 6.855362e-5 and greater than 5.615159e-5 would suppress the first
two messages.
.. code-block:: none
KMSG060 THE ANGULAR SCATTERING DISTRIBUTION FOR MIXTURE 2 HAS BAD MOMENTS FOR THE TRANSFER FROM GROUP 28 TO GROUP 72
1 MOMENTS WERE ACCEPTED
THE LEGENDRE EXPANSION OF THE CROSS SECTION (P0-PN) IS
5.615159E-05 1.155527E-06 -2.804013E-05 -1.732067E-06
THE MOMENTS CORRESPONDING TO THIS DISTRIBUTION ARE
2.057870E-02 4.234578E-04 8.710817E-06
THE MOMENTS CORRESPONDING TO THE GENERATED DISTRIBUTION ARE
2.057870E-02 4.235078E-04 8.710817E-06
THE LEGENDRE EXPANSION CORRESPONDING TO THESE MOMENTS IS
5.615159E-05 1.155527E-06 -2.804011E-05 -1.732066E-06
THE WEIGHTS/ANGLES FOR THIS DISTRIBUTION ARE
9.999995E-01 5.268617E-07
2.057881E-02 -1.973451E-01
THE MOMENTS CORRESPONDING TO THIS DISTRIBUTION ARE
2.057870E-02 4.235078E-04 8.710817E-06
KMSG060 THE ANGULAR SCATTERING DISTRIBUTION FOR MIXTURE 2 HAS BAD MOMENTS FOR THE TRANSFER FROM GROUP 31 TO GROUP 75
1 MOMENTS WERE ACCEPTED
THE LEGENDRE EXPANSION OF THE CROSS SECTION (P0-PN) IS
4.767635E-05 7.834378E-07 -2.381887E-05 -1.174626E-06
THE MOMENTS CORRESPONDING TO THIS DISTRIBUTION ARE
1.643242E-02 2.700205E-04 4.451724E-06
THE MOMENTS CORRESPONDING TO THE GENERATED DISTRIBUTION ARE
1.643242E-02 2.700282E-04 4.437279E-06
THE LEGENDRE EXPANSION CORRESPONDING TO THESE MOMENTS IS
4.767635E-05 7.834378E-07 -2.381885E-05 -1.174627E-06
THE WEIGHTS/ANGLES FOR THIS DISTRIBUTION ARE
9.999858E-01 1.420136E-05
1.643265E-02 -2.334324E-07
THE MOMENTS CORRESPONDING TO THIS DISTRIBUTION ARE
1.643242E-02 2.700282E-04 4.437279E-06
KMSG060 THE ANGULAR SCATTERING DISTRIBUTION FOR MIXTURE 2 HAS BAD MOMENTS FOR THE TRANSFER FROM GROUP
32 TO GROUP 74 (1)
1 MOMENTS WERE ACCEPTED (2)
THE LEGENDRE EXPANSION OF THE CROSS SECTION (P0-PN) IS (3)
6.855362E-05 1.341944E-06 -3.423741E-05 -2.011613E-06 (4)
THE MOMENTS CORRESPONDING TO THIS DISTRIBUTION ARE (5)
1.957510E-02 3.831484E-04 7.601939E-06 (6)
THE MOMENTS CORRESPONDING TO THE GENERATED DISTRIBUTION ARE (7)
1.957510E-02 3.832207E-04 7.502292E-06 (8)
THE LEGENDRE EXPANSION CORRESPONDING TO THESE MOMENTS IS (9)
6.855362E-05 1.341944E-06 -3.423740E-05 -2.011629E-06 (10)
THE WEIGHTS/ANGLES FOR THIS DISTRIBUTION ARE (11)
9.999056E-01 9.437981E-05 (12)
1.957695E-02 -1.848551E-06 (13)
THE MOMENTS CORRESPONDING TO THIS DISTRIBUTION ARE (14)
1.957510E-02 3.832207E-04 7.502292E-06 (15)
The user does not need to attempt to suppress all these messages. They
are printed to inform the user of the fact that the moments of the
angular distribution are not moments of a valid probability
distribution. The original P\ :sub:`n` coefficients and their moments
are listed in lines 3--6 of the message. Lines 7--10 list the new
corrected moments and their corresponding P\ :sub:`n` coefficients.
The weights and angles printed in lines 11--13 were generated from the
corrected moments. The last two lines of the message list the moments
generated from those weights and angles. They should match line 8, which
lists the moments corresponding to the generated distribution.
For most criticality problems, the first moment contributions are much
more significant than the contributions of the higher order moments.
Thus, the higher order moments may not affect the results significantly.
The user may compare the original moments and corrected moments to make
a judgment as to the significance of the change in the moments.
Mixing table
~~~~~~~~~~~~
Mixtures can be used in defining other mixtures. When defining mixture
numbers, care should be taken to avoid using a mixture number that is
identical to a nuclide ID number if the mixture is to be used in
defining another mixture. If a mixture number is defined more than once,
it results in a summing effect.
The nuclide mixing loop is done before the mixture mixing loop, which
performs mixing in the order of data entry. Thus, the order of mixing
mixtures into other mixtures is important because a mixture must be
defined before it can be used in another mixture. Some examples of
correct and incorrect mixing are shown below, using 1001 as the nuclide
ID for hydrogen, 8016 as the nuclide ID for oxygen, 92235 as the nuclide
ID for :sup:`235`\ U, and 92238 as the nuclide ID for :sup:`238`\ U.
EXAMPLES OF CORRECT USAGE
.. code-block:: scale
READ MIXT
MIX=1 1001 6.6e-2 8016 3.3e-2
MIX=2 1 0.5
END MIXT
This results in mixture 1 being full-density water and mixture 2 being half-density water.
.. code-block:: scale
READ MIXT
MIX=1 2 0.5
MIX=3 1 0.5
MIX=2 1001 6.6e-2 8016 3.3e-2
END MIXT
This results in mixture 1 being half-density water, mixture 2 being
full-density water, and mixture 3 being quarter-density water. Because
the nuclide mixing loop is done first, mixture 2 is created first and is
available to create mixture 1, which is then available to create
mixture 3.
.. code-block:: scale
READ MIXT
MIX=1 1001 6.6e-2 8016 3.3e-2
MIX=2 92235 7.5e-4 92238 2.3e-2 8016 4.6e-2 1 .01
END MIXT
This results in mixture 1 being full-density water and mixture 2 being uranium oxide containing 0.01 density water.
.. code-block:: scale
READ MIXT
MIX=1 1001 6.6e-2 8016 3.3e-2
MIX=2 92235 4.4e-2 92238 2.6e-3
MIX=1 1 0.5
END MIXT
This results in mixture 1 being water at 1.5 density (1001 9.9e-2 and 8016 4.95e-2)
and mixture 2 is highly enriched uranium metal.
EXAMPLES OF INCORRECT USAGE
.. code-block:: scale
READ MIXT
MIX=3 1 0.75
MIX=1 2 0.5
MIX=2 1001 6.6e-2 8016 3.3e-2
END MIXT
Here the intent is for mixture 2 to be full-density water, mixture 1 to
be half-density water, and mixture 3 to be 3/8 (0.75 × 0.5) density
water. Instead, the result for mixture 3 is a void, mixture 1 is
half-density water, and mixture 2 is full-density water. This is because
the nuclide mixing loop is done first, thus defining mixture 2. The
mixture mixing loop is done next. Mixture 3 is defined to be mixture 1
multiplied by 0.75, but since mixture 1 has not been defined yet, 0.75
of zero is zero. Mixture 1 is then defined to be mixture 2 multiplied by
0.5. If the definition of mixture 1 preceded the definition of
mixture 3, as in item (2) under examples of correct usage, it would work
correctly.
.. code-block:: scale
READ MIXT
MIX=1 1001 6.6e-2 8016 3.3e-2
MIX=1001 92235 4.4e-2 92238 2.6e-3
MIX=2 1001 0.5
END MIXT
This results in mixture 1 being full-density water, mixture 1001 being
uranium metal, and mixture 2 being hydrogen with a number density of 0.5
because 1001 is the nuclide ID number for hydrogen. When a mixture
number is identical to a nuclide ID and is used in mixing, that number
is assumed to be a nuclide ID rather than a mixture number. The intent
was for mixture 1 to be full-density water, mixture 1001 to be uranium
metal, and mixture 2 to be half-density uranium metal.
.. _sec-module.keno.geom_guide:
Geometry Considerations
~~~~~~~~~~~~~~~~~~~~~~~
In general, KENO geometry descriptions consist of (1) geometry data
(:numref:`sec-module.keno.geom`) defining the geometrical shapes present in the problem,
and (2) array data (:numref:`sec-module.keno.geom.array_data`) defining the placement of the units
that were defined in the geometry data. The geometry data block is
prefaced by ``READ GEOM``, and the array data block is prefaced by
``READ ARRAY``.
When a 3-D geometrical configuration is described as KENO geometry data,
it may be necessary to describe portions of the configuration
individually. These individual partial descriptions of the configuration
are called ``UNIT``\ s. KENO geometry modeling is subject to the
following restrictions:
1. Units are composed of regions. These regions are created using
geometric bodies and surfaces (``shape``\ s) that are previously
defined.
1. In KENO-VI the geometric bodies and surfaces may intersect.
Regions are defined relative to the geometric bodies and surfaces
in a ``UNIT``. ``HOLE``\ s provide a means of creating complex
geometries in a ``UNIT`` and then inserting the ``UNIT`` into
existing ``UNIT``\ s. For complex geometries the use of
``HOLE``\ s may decrease the CPU time required for the problem.
2. In KENO V.a, each geometry region in a ``UNIT`` must completely
enclose all geometry regions which precede it. Boundaries of the
surfaces of the regions may be shared or tangent, but they must
not intersect. The use of ``HOLE``\ s in KENO V.a provides an
exception to this complete enclosure rule. The use of ``HOLE``\ s
in KENO V.a will increase the CPU time required for the problem.
2. All geometrical surfaces must be describable in KENO V.a as spheres,
hemispheres, cylinders, hemicylinders, cubes, cuboids, or as a set
of quadratic equations in KENO-VI.
3. When specifying an ``ARRAY``, each ``UNIT`` used in a cuboidal
``ARRAY`` must have a ``CUBE`` or ``CUBOID`` as its outer region
(this is the only option in KENO V.a); a hexprism as the outer
boundary if it is a hexagonal, triangular, or shexagonal
``ARRAY``; a rhexprism as the outer boundary if it is a rhexagonal
``ARRAY``; and a dodecahedron as the outer boundary if it is a
dodecahedral ``ARRAY``. In addition, the outer boundary of a
``UNIT`` cannot be rotated or translated in KENO V.a.
4. When several ``UNIT``\ s are used to describe an ``ARRAY``, the
adjacent faces of the ``UNIT``\ s in contact with each other must
be the same size and shape.
5. ``UNIT``\ s are placed directly into regions using ``HOLE``\ s. As
many ``HOLE``\ s as will fit without intersecting other
``HOLE``\ s, nested ``ARRAY``\ s or ``HOLE``\ s, or the ``UNIT``
``BOUNDARY`` can be placed in a ``UNIT`` without intersecting each
other. In KENO V.a, ``HOLE``\ s cannot intersect any of the
regions within the ``UNIT`` in which they are placed. ``HOLE``\ s
are described in more detail in :numref:`sec-module.keno.geom.holes`, and nested
``HOLE``\ s are described in :numref:`sec-module.keno.geom.nesting_holes`.
6. Multiple ``ARRAY``\ s may be required to describe a complicated
system. In KENO V.a, only one ``ARRAY`` may be placed directly
into a ``UNIT``. However, multiple ``ARRAY``\ s may be placed in a
``UNIT`` by placing the ``ARRAY``\ s in other ``UNIT``\ s and
placing those ``UNIT``\ s in the original ``UNIT`` using
``HOLE``\ s. Multiple ``ARRAY``\ s may be placed directly into a
``UNIT`` in KENO-VI. These ``UNIT``\ s may then be used to create
other ``ARRAY``\ s, or they may be placed in other ``UNIT``\ s
using ``HOLE``\ s. ``UNIT``\ s placed in ``ARRAY``\ s or
``HOLE``\ s that are contained in other ``HOLE``\ s or
``ARRAY``\ s are said to be nested. The nesting level of a
``UNIT`` is the number of ``ARRAY``\ s and ``HOLE``\ s between the
``ARRAY`` or ``HOLE`` in the ``GLOBAL UNIT`` or ``ARRAY`` and the
``UNIT``. Multiple ``ARRAY``\ s are described in more detail in
:numref:`8-1-3-6-3`.
The KENO V.a geometry package allows any applicable ``shape`` to be
enclosed by any other applicable ``shape``, subject only to the complete
enclosure restriction. The KENO-VI geometry package allows any ``shape``
describable using quadratic equations to be enclosed or intersected by
any other allowable ``shape``. The implication of this type of
description is that the entire volume between two adjacent geometrical
surfaces contains only one mixture, ``HOLE``, or ``ARRAY``. A void is
specified by a mixture ID of zero. If ``HOLE``\ s are present in the
volume between two surfaces, the volume of that region is reduced by the
``HOLE``\ 's volume(s).
In KENO V.a geometry, if the problem requires several ``UNIT``\ s to
describe its geometrical characteristics, each ``UNIT`` that is used in
an ``ARRAY`` must have a rectangular parallelepiped as its outer
surface. This restriction is relaxed in KENO-VI, where the outer surface
may be a rectangular parallelepiped, a hexagonal prism, a 90\ :math:`^{\circ}` rotated
hexagonal prism, or a dodecahedron, but all units placed in an array
must use the same shape as their outer ``BOUNDARY``. In order to
describe the composite overall geometrical characteristics of the
problem, these ``UNIT``\ s may be arranged in a rectangular ``ARRAY``
for KENO V.a geometry, or in either a rectangular, hexagonal,
shexagaonal, rhexagonal, or dodecahedral ``ARRAY`` for KENO-VI geometry.
This is done by specifying the number of units in the X, Y, and
Z directions. If more than one ``UNIT`` is involved, data must be
entered to define the number assigned to the ``ARRAY`` and the placement
of the individual ``UNIT``\ s in the ``ARRAY``. The ``ARRAY`` number,
the number of ``UNIT``\ s in the X, Y, and Z directions, and the
placement data are called *array data* (:numref:`sec-module.keno.geom.array_data`).
In the KENO V.a geometry description, the surrounding regions of any
``shape`` may be placed around an ``ARRAY``, and they may consist of any
number of regions in any order subject to the complete enclosure
restriction. ``ARRAY``\ s are positioned relative to the ``UNIT ORIGIN``
by specifying the location of the most negative point in the array, i.e.
the most negative X, most negative Y, and most negative Z corner of the
``ARRAY``. In KENO-VI geometry, an ``ARRAY`` may be placed in a region
of any shape if the region boundary is contained within the ``ARRAY`` or
shares the ``ARRAY`` boundary and does not cut across nested
``ARRAY``\ s or ``HOLE``\ s. In this case, only the section of the
``ARRAY`` contained within the region is recognized by the problem.
``ARRAY``\ s are positioned relative to the ``UNIT`` ``ORIGIN`` by
placing the ``ORIGIN`` of a specified ``UNIT`` in the ``ARRAY`` at a
specified location in the ``UNIT``.
To create a geometry mockup from a physical configuration, the user
should keep the restrictions mentioned earlier in mind. There may be
several ways of correctly describing the same physical configuration.
Careful analysis of the system can result in a simpler mockup and
shorter computer running time. A mockup with fewer geometry regions may
run faster than the same mockup with extraneous regions. The number of
``UNIT``\ s used can affect the running time, because a transformation
of coordinates must be made every time a history moves from one ``UNIT``
into another. Thus, if the size of a ``UNIT`` is small relative to the
mean free path, a larger percentage of time is spent processing the
transformation of coordinates. Because all boundaries in a ``UNIT`` must
be checked for crossings, it may be more efficient to break up complex
``UNIT``\ s into several smaller, simpler ``UNIT``\ s. The trade-off
involves the time required to process more boundary crossings vs the
time required to transform coordinate systems when ``UNIT`` boundaries
are crossed.
``Geometry dimensions:`` The use of FIDO syntax may help simplify the
description of the geometry. For example, a 20 :math:`\times` 20 :math:`\times` 2.5 cm rectangular
parallelepiped would have been described as ``CUBOID`` 1 1 10.0 -10.0
10.0 -10.0 1.25 -1.25 in KENO V.a and ``CUBOID`` 1 10.0 10.0 10.0 10.0
1.25 1.25 in KENO-VI. By using the P option (see :numref:`tab8-1-17`), the
same rectangular parallelepiped could be described as ``CUBOID`` 1 1
4P10.0 2P1.25 in KENO V.a and or ``CUBOID`` 1 4P10.0 2P1.25 in KENO-VI,
where the last 6 entries describe the geometry. The P option simply
repeats the dimension following the P for the number of times stated
before the P, and it reverses the sign every time. Therefore, 6P8.0 is
equivalent to 8.0 -8.0 8.0 -8.0 8.0 -8.0.
``Geometry comments:`` One comment can be entered for each ``UNIT`` in
the *geometry region data*. Similarly, one comment can be entered for
each ``ARRAY`` in the *array definition data*. A comment can be entered
using the keyword ``COM``\ =. This is followed by a comment with a
maximum length of 132 characters. The comment must be preceded and
terminated by a delimiter character. Acceptable delimiters include " , `
, \* , ^ , or !. One comment is allowed for each ``UNIT`` in the
*geometry region data*. If multiple comments are entered for a ``UNIT``,
the last comment is used. The comment can be entered anywhere after the
``UNIT`` number where a keyword is expected (:numref:`sec-module.keno.geom`). See the
following example.
KENO V.a:
.. code-block:: scale
READ GEOM
UNIT 1
COM=*SPHERICAL METAL UNIT*
SPHERE 1 1 5.0
CUBE 0 1 2P5.0
UNIT 2
CYLINDER 1 1 5.0 2P5.0
CUBE 0 1 2P5.0
COM=!CYLINDRICAL METAL UNIT!
UNIT 3
HEMISPHE+X 1 1 5.0
COM='HEMISPHERICAL METAL UNIT'
CUBE 0 1 2P5.0
UNIT 4
COM=^ARRAY OF SPHERICAL UNITS^
ARRAY 1 3*0.0
UNIT 5
COM="ARRAY OF CYLINDRICAL UNITS"
ARRAY 2 3*0.0
UNIT 6
COM='ARRAY OF HEMISPHERICAL UNITS'
ARRAY 3 3*0.0
END GEOM
KENO-VI:
.. code-block:: scale
READ GEOM
UNIT 1
COM=*SPHERICAL METAL UNIT*
SPHERE 1 5.0
CUBOID 2 6P5.0
MEDIA 1 1 1
MEDIA 0 1 -1 2
BOUNDARY 2
UNIT 2
CYLINDER 1 5.0 2P5.0
CUBOID 2 6P5.0
MEDIA 1 1 1
COM=!CYLINDRICAL METAL UNIT!
MEDIA 0 1 -1 2
BOUNDARY 2
UNIT 3
SPHERE 1 5.0 CHORD +X=0.0
MEDIA 1 1 1
COM='HEMISPHERICAL METAL UNIT'
CUBOID 2 6P5.0
MEDIA 0 1 -1 2
BOUNDARY 2
UNIT 4
COM='ARRAY OF SPHERICAL UNITS'
CUBOID 1 6P15
ARRAY 1 1 PLACE 2 2 2 3*0.0
BOUNDARY 1
UNIT 5
CUBOID 1 6P15.0
COM='ARRAY OF CYLINDRICAL UNITS'
ARRAY 2 1 PLACE 2 2 2 3*0.0
BOUNDARY 1
UNIT 6
COM='ARRAY OF HEMISPHERICAL UNITS'
CUBOID 1 6P15.0
ARRAY 3 1 PLACE 2 2 2 3*0.0
BOUNDARY 1
GLOBAL UNIT 7
COM='ARRAY OF ARRAYS'
CUBOID 1 4P15.0 2P45.0
ARRAY 4 1 PLACE 1 1 2 3*0.0
BOUNDARY 1
END GEOM
One comment is allowed for each array in the *array definition data*.
The rules governing these comments are the same as those listed above.
However, the comment for an ``ARRAY`` must precede the ``UNIT``
arrangement description, and it can precede the ``ARRAY`` number
(:numref:`sec-module.keno.geom.array_data`). Examples of correct ``ARRAY`` comments are given below.
KENO V.a:
.. code-block:: scale
READ ARRAY
COM='ARRAY OF SPHERICAL METAL UNITS'
ARA=1 NUX=2 NUY=2 NUZ=2 FILL F1 END FILL
ARA=2 COM='ARRAY OF CYLINDRICAL METAL UNITS'
NUX=2 NUY=2 NUZ=2 FILL F2 END FILL
ARA=3 NUX=2 NUY=2 NUZ=2
COM='ARRAY OF HEMISPHERICAL METAL UNITS'
FILL F3 END FILL
ARA=4 COM='COMPOSITE ARRAY OF ARRAYS. Z=1 IS SPHERES, Z=2 IS CYLINDERS, Z=3 IS HEMISPHERES'
NUX=1 NUY=1 NUZ=3 FILL 4 5 6 END FILL
END ARRAY
KENO-VI:
.. code-block:: scale
READ ARRAY
COM='ARRAY OF SPHERICAL METAL UNITS'
ARA=1 NUX=3 NUY=3 NUZ=3 FILL F1 END FILL
ARA=2 COM='ARRAY OF CYLINDRICAL METAL UNITS'
NUX=3 NUY=3 NUZ=3 FILL F2 END FILL
ARA=3 NUX=3 NUY=3 NUZ=3
COM='ARRAY OF HEMISPHERICAL METAL UNITS'
FILL F3 END FILL
ARA=4 COM='COMPOSITE ARRAY OF ARRAYS. Z=1 IS SPHERES, Z=2 IS CYLINDERS, Z=3 IS HEMISPHERES'
NUX=1 NUY=1 NUZ=3 FILL 4 5 6 END FILL
END ARRAY
Some of the basics of KENO geometry are illustrated in the following examples:
EXAMPLE 1. Assume a stack of six cylindrical disks each measuring 5 cm
in radius and 2 cm thick. The bottom disk is composed of material 1, and
the next disk is composed of material 2, etc., alternating throughout
the stack. A square plate of material 3 that is 20 cm on a side and
2.5 cm thick is centered on top of the stack. This configuration is
shown in :numref:`fig8-1-12`.
.. figure:: figs/Keno/fig12.png
:align: center
:width: 400
:name: fig8-1-12
Stack of disks with a square top.
This problem can be described as a single ``UNIT`` problem, describing
the cylindrical portion first. In this instance, the origin has been
chosen at the center bottom of the bottom disk. The bottom disk is
defined by the first cylinder description, and the next disk is defined
by the difference between the first and second cylinder descriptions.
Since both disks have a radius of 5.0 and a -Z length of 0.0, the first
cylinder containing material 1 exists from Z = 0.0 to Z = 2.0, and the
second cylinder containing material 2 exists from Z = 2.0 to Z = 4.0.
When all the disks have been described, a void cuboid having the same X
and Y dimensions as the square plate and the same Z dimensions as the
stack of disks is defined. The square plate of material 3 is then
defined on top of the stack. Omission of the first cuboid description
would result in the stack of disks being encased in a solid cuboid of
material 3 instead of having a flat plate on top of the stack. The
geometry input is shown below.
.. centered:: Data description 1, Example 1.
KENO V.a:
.. code-block:: scale
READ GEOM
CYLINDER 1 1 5.0 2.0 0.0
CYLINDER 2 1 5.0 4.0 0.0
CYLINDER 1 1 5.0 6.0 0.0
CYLINDER 2 1 5.0 8.0 0.0
CYLINDER 1 1 5.0 10.0 0.0
CYLINDER 2 1 5.0 12.0 0.0
CUBOID 0 1 10.0 -10.0 10.0 -10.0 12.0 0.0
CUBOID 3 1 10.0 -10.0 10.0 -10.0 14.5 0.0
KENO-VI:
.. code-block:: scale
READ GEOM
GLOBAL UNIT 1
CYLINDER 1 5.0 2.0 0.0
CYLINDER 2 5.0 4.0 2.0
CYLINDER 3 5.0 6.0 4.0
CYLINDER 4 5.0 8.0 6.0
CYLINDER 5 5.0 10.0 8.0
CYLINDER 6 5.0 12.0 10.0
CUBOID 7 10.0 -10.0 10.0 -10.0 12.0 0.0
CUBOID 8 10.0 -10.0 10.0 -10.0 14.5 0.0
MEDIA 1 1 1
MEDIA 2 1 2
MEDIA 1 1 3
MEDIA 2 1 4
MEDIA 1 1 5
MEDIA 2 1 6
MEDIA 0 1 -1 -2 -3 -4 -5 -6 7
MEDIA 3 1 -7 8
BOUNDARY 8
END GEOM
An alternative description of the same example is given below. The
origin has been chosen at the center of the disk of material 1 nearest
the center of the stack. This disk of material 1 is defined by the first
cylinder description, and the disks of material 2 on either side of it
are defined by the second cylinder description. The top and bottom disks
of material 1 are defined by the third cylinder, and the top disk of
material 2 is defined by the last cylinder. The square plate is defined
by the two cuboids. This description is more efficient than the previous
one because there are fewer surfaces to check for crossings.
.. centered:: Data description 2, Example 1.
KENO V.a:
.. code-block:: scale
READ GEOM
CYLINDER 1 1 5.0 1.0 -1.0
CYLINDER 2 1 5.0 3.0 -3.0
CYLINDER 1 1 5.0 5.0 -5.0
CYLINDER 2 1 5.0 7.0 -5.0
CUBOID 0 1 10.0 -10.0 10.0 -10.0 7.0 -5.0
CUBOID 3 1 10.0 -10.0 10.0 -10.0 9.5 -5.0
KENO-VI:
.. code-block:: scale
READ GEOM
GLOBAL UNIT 1
CYLINDER 10 5.0 1.0 -1.0
CYLINDER 20 5.0 3.0 -3.0
CYLINDER 30 5.0 5.0 -5.0
CYLINDER 40 5.0 7.0 -5.0
CUBOID 50 10.0 -10.0 10.0 -10.0 7.0 -5.0
CUBOID 60 10.0 -10.0 10.0 -10.0 9.5 -5.0
MEDIA 1 1 10
MEDIA 2 1 -10 20
MEDIA 1 1 -20 30
MEDIA 2 1 -30 40
MEDIA 0 1 -40 50
MEDIA 3 1 -50 60
BOUNDARY 60
END GEOM
Example 1 can also be described as an ``ARRAY``. Define three different
``UNIT`` types. ``UNIT`` 1 will define a disk of material 1, ``UNIT`` 2
will define a disk of material 2, and ``UNIT`` 3 will define the square
plate of material 3. The origin of each ``UNIT`` is defined at the
center bottom of the disk or plate being described. As mentioned
earlier, only ``UNIT``\ s with a ``CUBE`` or ``CUBOID`` as their outer
boundary can be placed in a cuboidal ``ARRAY``. The geometry input for
this arrangement is shown below.
.. centered:: Data description 3, Example 1.
KENO V.a:
.. code-block:: scale
READ GEOM
UNIT 1
CYLINDER 1 1 5.0 2.0 0.0
CUBOID 0 1 10.0 -10.0 10.0 -10.0 2.0 0.0
UNIT 2
CYLINDER 2 1 5.0 2.0 0.0
CUBOID 0 1 10.0 -10.0 10.0 -10.0 2.0 0.0
UNIT 3
CUBOID 3 1 10.0 -10.0 10.0 -10.0 2.5 0.0
END GEOM
READ ARRAY NUX=1 NUY=1 NUZ=7 FILL 1 2 1 2 1 2 3 END ARRAY
.. note:: The ``ARRAY`` is assumed to be the ``GLOBAL ARRAY`` because
only a single ``ARRAY`` is defined.
KENO-VI:
.. code-block:: scale
READ GEOM
UNIT 1
CYLINDER 1 5.0 2.0 0.0
CUBOID 2 10.0 -10.0 10.0 -10.0 2.0 0.0
MEDIA 1 1 1
MEDIA 0 1 -1 2
BOUNDARY 2
UNIT 2
CYLINDER 1 5.0 2.0 0.0
CUBOID 2 10.0 -10.0 10.0 -10.0 2.0 0.0
MEDIA 2 1 1
MEDIA 0 1 2 -1
BOUNDARY 2
UNIT 3
CUBOID 1 10.0 -10.0 10.0 -10.0 2.5 0.0
MEDIA 3 1 1
BOUNDARY 1
GLOBAL UNIT 4
CUBOID 1 10 -10 10 -10 14.5 0.0
ARRAY 1 1 PLACE 1 1 1 3*0.0
BOUNDARY 1
END GEOM
READ ARRAY ARA=1 NUX=1 NUY=1 NUZ=7 FILL 1 2 1 2 1 2 3 END ARRAY
If the user prefers for the origin of each unit to be at its center, the
geometry region data can be entered as shown below. The array data would
be identical to that of data description 3, Example 1.
.. centered:: Data description 4, Example 1.
KENO V.a:
.. code-block:: scale
READ GEOM
UNIT 1
CYLINDER 1 1 5.0 1.0 -1.0
CUBOID 0 1 10.0 -10.0 10.0 -10.0 1.0 -1.0
UNIT 2
CYLINDER 2 1 5.0 1.0 -1.0
CUBOID 0 1 10.0 -10.0 10.0 -10.0 1.0 -1.0
UNIT 3
CUBOID 3 1 10.0 -10.0 10.0 -10.0 1.25 -1.25
END GEOM
KENO-VI:
.. code-block:: scale
READ GEOM
UNIT 1
CYLINDER 1 5.0 1.0 -1.0
CUBOID 2 10.0 -10.0 10.0 -10.0 1.0 -1.0
MEDIA 1 1 1
MEDIA 0 1 -1 2
BOUNDARY 2
UNIT 2
CYLINDER 1 5.0 1.0 -1.0
CUBOID 2 10.0 -10.0 10.0 -10.0 1.0 -1.0
MEDIA 2 1 1
MEDIA 0 1 -1 2
BOUNDARY 2
UNIT 3
CUBOID 1 10.0 -10.0 10.0 -10.0 1.25 -1.25
MEDIA 3 1 1
BOUNDARY 1
GLOBAL UNIT 4
CUBOID 1 10 -10 10 -10 14.5 0.0
ARRAY 1 1 PLACE 1 1 1 0.0 0.0 1.0
BOUNDARY 1
END GEOM
Be aware that each ``UNIT`` in a geometry description can have its
origin defined independent of the other ``UNIT``\ s. It would be correct
to use ``UNIT``\ s 1 and 3 from data descriptions 3, and ``UNIT`` 2 from
data description 4. The *array data* would remain the same as data
description 3, Example 1. The user should define the origin of each unit
to be as convenient as possible for the chosen description. Care should
be taken when assigning coordinates to the ``UNIT`` used to ``PLACE``
the ``ARRAY`` in its surrounding region.
Another method of describing Example 1 as a bare array is to define
``UNIT`` 1 to be a disk of material 1 topped by a disk of material 2.
The origin has been chosen at the center bottom of the disk of
material 1. ``UNIT`` 2 is the square plate of material 3 with the origin
at the center of the ``UNIT``. The ``ARRAY`` consists of three
``UNIT`` 1s, topped by a ``UNIT`` 2, as shown below.
.. centered:: Data description 5, Example 1.
KENO V.a:
.. code-block:: scale
READ GEOM
UNIT 1
CYLINDER 1 1 5.0 2.0 0.0
CYLINDER 2 1 5.0 4.0 0.0
CUBOID 0 1 10.0 -10.0 10.0 -10.0 4.0 0.0
UNIT 2
CUBOID 3 1 10.0 -10.0 10.0 -10.0 1.25 -1.25
END GEOM
READ ARRAY NUX=1 NUY=1 NUZ=4 FILL 3R1 2 END ARRAY
KENO-VI:
.. code-block:: scale
READ GEOM
UNIT 1
CYLINDER 1 5.0 2.0 0.0
CYLINDER 2 5.0 4.0 2.0
CUBOID 3 10.0 -10.0 10.0 -10.0 4.0 0.0
MEDIA 1 1 1
MEDIA 2 1 2
MEDIA 0 1 -1 -2 3
BOUNDARY 3
UNIT 2
CUBOID 1 10.0 -10.0 10.0 -10.0 1.25 -1.25
MEDIA 3 1 1
BOUNDARY 1
GLOBAL UNIT 3
CUBOID 1 10 -10 10 -10 14.5 0.0
ARRAY 1 1 PLACE 1 1 1 3*0.0
BOUNDARY 1
END GEOM
READ ARRAY ARA=1 NUX=1 NUY=1 NUZ=4 FILL 3R1 2 END ARRAY
Example 1 can be described as a reflected ``ARRAY`` by treating the
square plate as a reflector in the positive Z direction. One means of
describing this situation is to define ``UNIT``\ s 1 and 2 as in data
description 3, Example 1. The origin of the ``GLOBAL UNIT`` is defined
to be at the center of the ``ARRAY``. The corresponding input geometry
is shown below.
.. centered:: Data description 6, Example 1.
KENO V.a:
.. code-block:: scale
READ GEOM
UNIT 1
CYLINDER 1 1 5.0 2.0 0.0
CUBOID 0 1 10.0 -10.0 10.0 -10.0 2.0 0.0
UNIT 2
CYLINDER 2 1 5.0 2.0 0.0
CUBOID 0 1 10.0 -10.0 10.0 -10.0 2.0 0.0
GLOBAL UNIT 3
ARRAY 1 -10.0 -10.0 -6.0
CUBOID 3 1 10.0 -10.0 10.0 -10.0 8.5 -6.0
END GEOM
READ ARRAY NUX=1 NUY=1 NUZ=6 FILL 1 2 1 2 1 2 END ARRAY
KENO-VI:
.. code-block:: scale
READ GEOM
UNIT 1
CYLINDER 1 5.0 2.0 0.0
CUBOID 2 10.0 -10.0 10.0 -10.0 2.0 0.0
MEDIA 1 1 1
MEDIA 0 1 -1 2
BOUNDARY 2
UNIT 2
CYLINDER 1 5.0 2.0 0.0
CUBOID 2 10.0 -10.0 10.0 -10.0 2.0 0.0
MEDIA 2 1 1
MEDIA 0 1 -1 2
BOUNDARY 2
GLOBAL UNIT 3
CUBOID 1 10.0 -10.0 10.0 -10.0 6.0 -6.0
CUBOID 2 10.0 -10.0 10.0 -10.0 8.5 -6.0
ARRAY 1 1 PLACE 1 1 1 0.0 0.0 -6.0
MEDIA 3 1 -1 2
BOUNDARY 2
END GEOM
READ ARRAY ARA=1 NUX=1 NUY=1 NUZ=6 FILL 1 2 1 2 1 2 END ARRAY
The user could have chosen the origin of the ``ARRAY`` boundary to be at
the center bottom of the ``ARRAY``, in which case the geometry
description for the ``GLOBAL UNIT`` would be:
KENO V.a:
.. code-block:: scale
ARRAY 1 -10.0 -10.0 0.0
CUBOID 3 1 10.0 -10.0 10.0 -10.0 14.5 0.0
or
.. code-block:: scale
ARRAY 1 -10.0 -10.0 0.0
REPLICATE 3 4*0.0 2.5 0 1
The reflector region at the top of the array can be added by using a
``CUBOID`` or by using a ``REPLICATE`` description in KENO V.a. Recall
that there is no ``REPLICATE`` function in KENO-VI.
A simpler method of describing Example 1 as a reflected array is to
define only one unit as in data description 5, Example 1. The square
plate is treated as a reflector, as in data description 6, Example 1.
The input for this arrangement is given below.
.. centered:: Data description 7, Example 1.
KENO V.a:
.. code-block:: scale
READ GEOM
UNIT 1
CYLINDER 1 1 5.0 2.0 0.0
CYLINDER 2 1 5.0 4.0 0.0
CUBOID 0 1 10.0 -10.0 10.0 -10.0 4.0 0.0
GLOBAL UNIT 2
ARRAY 1 -10.0 -10.0 0.0
CUBOID 3 1 10.0 -10.0 10.0 -10.0 14.5 0.0
END GEOM
READ ARRAY NUX=1 NUY=1 NUZ=3 END ARRAY
KENO-VI:
.. code-block:: scale
READ GEOM
UNIT 1
CYLINDER 1 5.0 2.0 0.0
CYLINDER 2 5.0 4.0 2.0
CUBOID 3 10.0 -10.0 10.0 -10.0 4.0 0.0
MEDIA 1 1 1
MEDIA 2 1 2
MEDIA 0 1 -1 -2 3
BOUNDARY 3
GLOBAL UNIT 2
CUBOID 1 10.0 -10.0 10.0 -10.0 12.0 0.0
CUBOID 2 10.0 -10.0 10.0 -10.0 14.5 0.0
ARRAY 1 1 PLACE 1 1 1 3*0.0
MEDIA 3 1 -1 2
BOUNDARY 2
END GEOM
READ ARRAY ARA=1 NUX=1 NUY=1 NUZ=3 FILL F1 END FILL END ARRAY
EXAMPLE 2. Assume that the stack of six disks in Example 1 is placed at
the center bottom of a cylindrical container composed of material 6
whose inside diameter is 16.0 cm. The bottom and sides of the container
are 0.25 cm thick, the top is open, and the total height of the
container is 18.25 cm. Assume the square plate of Example 1 is centered
on top of the container.
The geometry input can be described utilizing most of the data
description methods associated with Example 1. One method of describing
Example 2 as a single ``UNIT`` is given below.
.. centered:: Data description 1, Example 2.
KENO V.a:
.. code-block:: scale
READ GEOM
UNIT 1
CYLINDER 1 1 5.0 1.0 -1.0
CYLINDER 2 1 5.0 3.0 -3.0
CYLINDER 1 1 5.0 5.0 -5.0
CYLINDER 2 1 5.0 7.0 -5.0
CYLINDER 0 1 8.0 13.0 -5.0
CYLINDER 6 1 8.25 13.0 -5.25
CUBOID 0 1 10.0 -10.0 10.0 -10.0 13.0 -5.25
CUBOID 3 1 10.0 -10.0 10.0 -10.0 15.5 -5.25
END GEOM
KENO-VI:
.. code-block:: scale
READ GEOM
GLOBAL UNIT 1
CYLINDER 1 5.0 1.0 -1.0
CYLINDER 2 5.0 3.0 -3.0
CYLINDER 3 5.0 5.0 -5.0
CYLINDER 4 5.0 7.0 -5.0
CYLINDER 5 8.0 13.0 -5.0
CYLINDER 6 8.25 13.0 -5.25
CUBOID 7 10.0 -10.0 10.0 -10.0 13.0 -5.25
CUBOID 8 10.0 -10.0 10.0 -10.0 15.5 -5.25
MEDIA 1 1 1
MEDIA 2 1 -1 2
MEDIA 1 1 -2 3
MEDIA 2 1 -3 4
MEDIA 0 1 -4 5
MEDIA 6 1 -5 6
MEDIA 0 1 -6 7
MEDIA 3 1 -7 8
BOUNDARY 8
END GEOM
In the above description, the origin is defined to be at the center of
the disk of material 1 nearest the center of the stack. This disk is
defined by the first cylinder description. The disks of material 2 above
and below it are defined by the second cylinder description. The disks
of material 1 above and below them are defined by the third cylinder
description. The top disk of material 2 is defined by the fourth
cylinder description. The void interior of the container is defined by
the fifth cylinder description. The container is defined by the last
cylinder description. The first cuboid description is used to define a
void whose X and Y dimensions are the same as the square plate and whose
Z dimensions are the same as the container. The last cuboid description
defines the square plate. Omission of the first cuboid description would
result in the container being encased in a solid cuboid of material 3.
Thus, both cuboids are necessary to properly define the square plate.
Example 2 can be described as a reflected **ARRAY**. One of the
descriptions uses only one **UNIT** and is similar to data
description 7, Example 1. This description is shown below.
.. centered:: Data description 2, Example 2.
KENO V.a:
.. code-block:: scale
READ GEOM
UNIT 1
CYLINDER 1 1 5.0 2.0 0.0
CYLINDER 2 1 5.0 4.0 0.0
CUBOID 0 1 5.0 -5.0 5.0 -5.0 4.0 0.0
GLOBAL UNIT 2
ARRAY 1 -5.0 -5.0 0.0
CYLINDER 0 1 8.0 18.0 0.0
CYLINDER 6 1 8.25 18.0 -0.25
CUBOID 0 1 10.0 -10.0 10.0 -10.0 18.0 -0.25
CUBOID 3 1 10.0 -10.0 10.0 -10.0 20.5 -0.25
END GEOM
READ ARRAY NUX=1 NUY=1 NUZ=3 END ARRAY
KENO-VI:
.. code-block:: scale
READ GEOM
UNIT 1
CYLINDER 1 5.0 2.0 0.0
CYLINDER 2 5.0 4.0 2.0
CUBOID 3 5.0 -5.0 5.0 -5.0 4.0 0.0
MEDIA 1 1 1
MEDIA 2 1 2
MEDIA 0 1 -1 -2 3
BOUNDARY 3
GLOBAL UNIT 2
CUBOID 1 5.0 -5.0 5.0 -5.0 12.0 0.0
ARRAY 1 1 PLACE 1 1 1 3*0.0
CYLINDER 2 8.0 18.0 0.0
MEDIA 0 1 -1 2
CYLINDER 3 8.25 18.0 -0.25
MEDIA 6 1 -2 3
CUBOID 4 10.0 -10.0 10.0 -10.0 20.5 18.0
CUBOID 5 10.0 -10.0 10.0 -10.0 20.5 -0.25
MEDIA 3 1 4
MEDIA 0 1 -3 -4 5
BOUNDARY 5
END GEOM
READ ARRAY ARA NUX=1 NUY=1 NUZ=3 FILL F1 END FILL END ARRAY
In the above data description, the first two cylinder descriptions
define a disk of material 1 with a disk of material 2 directly on top of
it. A tight fitting void cuboid is placed around them so they can be
stacked three high to achieve the stack of disks shown in Example 1,
:numref:`fig8-1-12`. This array comprises the array portion of the geometry
region description. The origin of the array boundary, a tight fitting
cube or cuboid that encompasses the array, is defined by the **ARRAY**
description. Everything after the **ARRAY** record is considered part of
the reflector. The first cylinder after the **ARRAY** record defines the
void interior of the cylindrical container. The next cylinder defines
the walls of the container. The second-to-last cuboid defines a void
volume outside the container from its bottom to its top and having the
same X and Y dimensions as the square plate. The last cuboid defines the
square plate of material 3 that is sitting on top of the container.
Another method to describe Example 2 is as an array composed of units
that contain both the stack and container. This description requires a
minimum of four units to describe the problem. This configuration is
given below in data description 3, Example 2.
.. centered:: Data description 3, Example 2.
KENO V.a:
.. code-block:: scale
READ GEOM
UNIT 1
CYLINDER 6 1 8.25 0.25 0.0
CUBOID 0 1 10.0 -10.0 10.0 -10.0 0.25 0.0
UNIT 2
CYLINDER 1 1 5.0 2.0 0.0
CYLINDER 2 1 5.0 4.0 0.0
CYLINDER 0 1 8.0 4.0 0.0
CYLINDER 6 1 8.25 4.0 0.0
CUBOID 0 1 10.0 -10.0 10.0 -10.0 4.0 0.0
UNIT 3
CYLINDER 0 1 8.0 3.0 -3.0
CYLINDER 6 1 8.25 3.0 -3.0
CUBOID 0 1 10.0 -10.0 10.0 -10.0 3.0 -3.0
CUBOID 3 1 10.0 -10.0 10.0 -10.0 5.5 -3.0
END GEOM
READ ARRAY NUX=1 NUY=1 NUZ=5 FILL 1 3R2 3 END ARRAY
KENO-VI:
.. code-block:: scale
READ GEOM
UNIT 1
CYLINDER 1 8.25 0.25 0.0
CUBOID 2 10.0 -10.0 10.0 -10.0 0.25 0.0
MEDIA 6 1 1
MEDIA 0 1 2 -1
BOUNDARY 2
UNIT 2
CYLINDER 10 5.0 2.0 0.0
CYLINDER 20 5.0 4.0 0.0
CYLINDER 30 8.0 4.0 0.0
CYLINDER 40 8.25 4.0 0.0
CUBOID 50 10.0 -10.0 10.0 -10.0 4.0 0.0
MEDIA 1 1 10
MEDIA 2 1 20 -10
MEDIA 0 1 30 -20
MEDIA 6 1 40 -30
MEDIA 0 1 50 -40
BOUNDARY 50
UNIT 3
CYLINDER 1 8.0 3.0 -3.0
CYLINDER 2 8.25 3.0 -3.0
CUBOID 3 10.0 -10.0 10.0 -10.0 5.5 3.0
CUBOID 4 10.0 -10.0 10.0 -10.0 5.5 -3.0
MEDIA 0 1 1
MEDIA 6 1 2 -1
MEDIA 3 1 3
MEDIA 0 1 4 -3 -2
BOUNDARY 4
GLOBAL UNIT 4
CUBOID 1 10.0 -10.0 10.0 -10.0 20.75 0.0
ARRAY 1 1 PLACE 1 1 1 3*0.0
BOUNDARY 1
END GEOM
READ ARRAY NUX=1 NUY=1 NUZ=5 FILL 1 3R2 3 END ARRAY
In the above description, ``UNIT`` 1 is the bottom of the cylindrical
container. The void ``CUBOID`` is only as tall as the bottom of the
container, and its X and Y dimensions are the same as the square plate
on top of the container. If all the ``UNIT``\ s in the ``ARRAY`` use
these same dimensions in the X and Y directions, the requirement that
adjacent faces of units in contact with each other must be the same size
and shape is satisfied. This ``ARRAY`` is stacked in the Z direction, so
all ``UNIT``\ s must have the same overall dimensions in the X direction
and in the Y direction. ``UNIT`` 2 will be used in the ``ARRAY`` three
times to create the stack of disks. It contains a disk of material 1
topped by a disk of material 2. The portion of the container that
contains the disks and the cuboid that defines the outer boundaries of
the unit are included in ``UNIT`` 2. ``UNIT`` 3 describes the empty top
portion of the container and the square plate on top of it. The
Z dimensions of ``UNIT`` 3 were determined by subtracting three times
the total Z dimension of ``UNIT`` 2 from the inside height of the
container [18.0 - (3 :math:`\times` 4.0) = 6.0]. This can also be determined from the
overall height of the container by subtracting off the bottom thickness
of the container and three times the height of ``UNIT`` 2 [18.25 - 0.25
- (3 :math:`\times` 4.0) = 6.0]. The origin of ``UNIT`` 3 is located at the center of
this distance. For the KENO-VI input, a ``GLOBAL UNIT`` is also
provided, ``UNIT`` 4, containing the ``ARRAY`` built with ``UNIT``\ s 1,
2, 3.
EXAMPLE 3. Refer to Example 1, :numref:`fig8-1-12`, and imagine a ``HOLE``
1.5 cm in diameter is drilled along the centerline of the stack through
the disks and the square plate. In KENO V.a this ``HOLE`` would
eliminate the possibility of describing the system as a single unit
because the ``HOLE`` in the center of the alternating materials of the
stack cannot be described in a manner that allows each successive
geometry region to encompass the regions interior to it. Therefore, it
must be described as an ``ARRAY``. The square plate on the top of the
disks is defined as a ``UNIT`` in the ``ARRAY``. In the geometry
description given below, the square plate is defined in ``UNIT`` 3.
KENO-VI can easily describe this configuration as a single ``UNIT``.
.. centered:: Data description 1, Example 3.
KENO V.a:
.. code-block:: scale
READ GEOM
UNIT 1
CYLINDER 0 1 0.75 2.0 0.0
CYLINDER 1 1 5.0 2.0 0.0
CUBOID 0 1 10.0 -10.0 10.0 -10.0 2.0 0.0
UNIT 2
CYLINDER 0 1 0.75 2.0 0.0
CYLINDER 2 1 5.0 2.0 0.0
CUBOID 0 1 10.0 -10.0 10.0 -10.0 2.0 0.0
UNIT 3
CYLINDER 0 1 0.75 2.5 0.0
CUBOID 3 1 10.0 -10.0 10.0 -10.0 2.5 0.0
END GEOM
READ ARRAY NUX=1 NUY=1 NUZ=7 FILL 1 2 2Q2 3 END FILL END ARRAY
KENO-VI:
.. code-block:: scale
READ GEOM
GLOBAL UNIT 1
CYLINDER 1 0.75 7.0 -5.0
CYLINDER 2 5.0 1.0 -1.0
CYLINDER 3 5.0 3.0 -3.0
CYLINDER 4 5.0 5.0 -5.0
CYLINDER 5 5.0 7.0 -5.0
CYLINDER 6 8.0 13.0 -5.0
CYLINDER 7 8.25 13.0 -5.25
CUBOID 8 10.0 -10.0 10.0 -10.0 15.5 13.0
CUBOID 9 10.0 -10.0 10.0 -10.0 15.5 -5.25
MEDIA 0 1 1
MEDIA 1 1 -1 2
MEDIA 2 1 -1 -2 3
MEDIA 1 1 -1 -3 4
MEDIA 2 1 -1 -4 5
MEDIA 0 1 -5 6
MEDIA 6 1 -6 7
MEDIA 3 1 8
MEDIA 0 1 -7 -8 9
BOUNDARY 9
END GEOM
In data description 1, Example 3 above, KENO V.a input, ``UNIT`` 1
describes a disk of material 1 with a ``HOLE`` through its centerline.
The first ``CYLINDER`` defines the ``HOLE``, the second defines the rest
of the disk, and the ``CUBOID`` defines the size of the ``UNIT`` to be
consistent with the square plate so they can be stacked together in an
``ARRAY``. ``UNIT`` 2 describes a disk of material 2 in similar fashion.
``UNIT`` 3 describes the square plate of material 3 with a ``HOLE``
through its center. The ``CYLINDER`` defines the ``HOLE`` and the
``CUBOID`` defines the square plate. These three ``UNIT``\ s are stacked
in the Z direction to achieve the composite system. This is represented
by ``FILL 1 2 2Q2 3``. The ``2Q2`` repeats the two entries preceding the ``2Q2``
twice. Alternatively, this can be achieved by entering
``FILL 1 2 1 2 1 2 3 END FILL``. The same ``ARRAY`` can also be achieved using the
``LOOP`` option. An example of the data for this option is:
``LOOP 1 6R1 1 5 2 2 6R1 2 6 2 3 6R1 7 7 1 END LOOP``.
``UNIT`` 1 is placed at the X = 1, Y = 1, and Z = 1,3,5 positions of the
``ARRAY`` by entering 1 6R1 1 5 2. ``UNIT`` 2 is positioned at the X =
1, Y = 1 and Z = 2,4,6 positions in the ``ARRAY`` by entering 2 6R1 2 6
2. ``UNIT`` 3 is placed at the X = 1, Y = 1, Z = 7 position of the
``ARRAY`` by entering 3 6R1 7 7 1. See :numref:`sec-module.keno.geom.array_data` for additional
information regarding ``ARRAY`` specifications.
For the KENO-VI input, ``UNIT`` 1 contains the entire problem
description. The first ``CYLINDER`` describes the 1.5 cm diameter hole
through the stack. The next four ``CYLINDER``\ s define the stack. The
sixth and seventh ``CYLINDER``\ s describe the void and container. The
two ``CUBOID``\ s describe the top plate and surrounding global region
of void. The ``MEDIA`` cards are used to place the materials in the
appropriate regions.
EXAMPLE 4. Assume two large cylinders that are 2.5 cm in radius and 5 cm
long are connected by a smaller cylinder that is 0.5 cm in radius and
10 cm long, as shown in :numref:`fig8-1-13`. All three cylinders are composed of
material 1. By starting the geometry description in the small cylinder,
this system can be described as a single unit.
.. figure:: figs/Keno/fig13.png
:align: center
:width: 400
:name: fig8-1-13
Two large cylinders joined axially by a small cylinder.
.. centered:: Data description 1, Example 4.
KENO-VI:
.. code-block:: scale
READ GEOM
GLOBAL UNIT 1
XCYLINDER 1 0.5 5.0 -5.0
XCYLINDER 2 2.5 5.0 -5.0
XCYLINDER 3 2.5 10.0 -10.0
MEDIA 1 1 1
MEDIA 0 1 2 -1
MEDIA 1 1 3 -2
BOUNDARY 3
END GEOM
KENO V.a:
.. code-block:: scale
READ GEOM
CYLINDER 1 1 0.5 5.0 -5.0
CYLINDER 0 1 2.5 5.0 -5.0
CYLINDER 1 1 2.5 10.0 -10.0
END GEOM
The origin is at the center of the small cylinder, which is described by
the first cylinder description. The second cylinder description defines
a void cylinder surrounding the small cylinder. Its radius is the same
as the large cylinders, and its height (length) coincides with that of
the small cylinder. The last cylinder description defines the large
cylinders on either end of the small cylinder. In KENO V.a, because this
problem does not specify otherwise, the length of the ``CYLINDER``\ s is
assumed to coincide with the Z axis. In KENO-VI, because the problem was
created using ``XCYLINDER``\ s, the long axes of the ``CYLINDER``\ s
coincide with the X axis.
EXAMPLE 5. Assume two large cylinders with a center-to-center spacing of
15 cm, each having a radius of 2.5 cm and length of 5 cm, are connected
radially by a small cylinder having a radius of 1.5 cm, as shown in :numref:`fig8-1-14`.
.. figure:: figs/Keno/fig14.png
:align: center
:width: 400
:name: fig8-1-14
Two large cylinders radially connected by a small cylinder.
This system cannot be described rigorously in KENO V.a geometry because
the intersection of the cylinders cannot be described. However, it can
be approximated two ways, as shown in :numref:`fig8-1-15`. The top approximation
is described in data description 1, Example 5. The bottom approximation
is described in data description 2, Example 5, and data description 3,
Example 5. These may be poor approximations for criticality safety
calculations.
.. figure:: figs/Keno/fig15.png
:align: center
:width: 400
:name: fig8-1-15
KENO V.a approximations of cylindrical intersections.
.. centered:: Data description 1, Example 5.
KENO V.a:
.. code-block:: scale
READ GEOM
UNIT 1
CYLINDER 1 1 2.5 2.5 -2.5
CUBE 0 1 2.5 -2.5
UNIT 2
XCYLINDER 1 1 1.5 5.0 -5.0
CUBOID 0 1 5.0 -5.0 2.5 -2.5 2.5 -2.5
END GEOM
READ ARRAY NUX=3 NUY=1 NUZ=1 FILL 1 2 1 END ARRAY
``UNIT`` 1 defines a large ``CYLINDER``, and ``UNIT`` 2 describes the
small ``CYLINDER``. In both ``UNIT``\ s the origin is at the center of
the ``CYLINDER``. The large ``CYLINDER``\ s have their centerlines along
the Z axis and the small ``CYLINDER`` has its length along the X axis.
.. centered:: Data description 2, Example 5.
KENO V.a:
.. code-block:: scale
READ GEOMETRY
UNIT 1
CYLINDER 1 1 2.5 1.0 0.0
CUBOID 0 1 4P2.5 1.0 0.0
UNIT 2
ZHEMICYL-X 1 1 2.5 2P1.5 CHORD 2.0
CUBOID 0 1 2.0 3P-2.5 2P1.5
UNIT 3
ZHEMICYL+X 1 1 2.5 2P1.5 CHORD 2.0
CUBOID 0 1 2.5 -2.0 2P2.5 2P1.5
UNIT 4
XCYLINDER 1 1 1.5 2P5.5
CUBOID 0 1 2P5.5 2P2.5 2P1.5
UNIT 5
CUBOID 0 1 2P5.0 2P2.5 1.0 0.0
UNIT 6
ARRAY 1 3*0.0
UNIT 7
ARRAY 2 3*0.0
END GEOMETRY
READ ARRAY ARA=1 NUX=3 NUY=1 NUZ=1 FILL 1 5 1 END FILL
ARA=2 NUX=3 NUY=1 NUZ=1 FILL 2 4 3 END FILL
ARA=3 NUX=1 NUY=1 NUZ=3 FILL 6 7 6 END FILL
END ARRAY
The above geometry description uses ``ARRAY``\ s of ``ARRAY``\ s (see
:numref:`8-1-3-6-3`) to describe the bottom approximation of :numref:`fig8-1-15`.
``UNIT`` 1 defines a large ``CYLINDER`` that has a radius of 2.5 cm and
a height of 10 cm inside a close-fitting ``CUBOID``. This is used in
both large ``CYLINDER``\ s as the portion of the large ``CYLINDER`` that
exists above and below the region where the small ``CYLINDER`` joins it.
``UNIT`` 5 is the spacing between the tops of the two large
``CYLINDER``\ s and the spacing between the bottoms of the two large
``CYLINDER``\ s. ``ARRAY`` 1 thus defines the bottom of the system:
two short ``CYLINDER``\ s (``UNIT`` 1s) separated by 10 cm (``UNIT`` 5
is the separation). ``UNIT`` 6 contains ``ARRAY`` 1.
``UNIT`` 2 is the left hemicylinder that adjoins the horizontal
``CYLINDER``, and ``UNIT`` 3 is the right hemicylinder that adjoins the
horizontal ``CYLINDER``. ``UNIT`` 4 defines the horizontal ``CYLINDER``.
``ARRAY`` 2 contains ``UNIT``\ s 2, 4, and 3 from left to right. This
defines the central portion of the system where the horizontal
``CYLINDER`` adjoins the two hemicylinders. These hemicylinders are
larger than half ``CYLINDER``\ s. ``UNIT`` 7 contains ``ARRAY`` 2. The
entire system is achieved by stacking a ``UNIT`` 6 above and below the
``UNIT`` 7 as defined in ``ARRAY`` 3, the ``GLOBAL ARRAY``.
.. centered:: Data description 3, Example 5.
KENO V.a:
.. code-block:: scale
READ GEOMETRY
UNIT 1
CYLINDER 1 1 2.5 1.0 0.0
UNIT 2
CYLINDER 1 1 2.5 1.0 0.0
CUBOID 0 1 17.5 -2.5 2P2.5 1.0 0.0
HOLE 1 15.0 0.0 0.0
UNIT 3
ZHEMICYL-X 1 1 2.5 2P1.5 CHORD 2.0
UNIT 4
ZHEMICYL+X 1 1 2.5 2P1.5 CHORD 2.0
UNIT 5
XCYLINDER 1 1 1.5 2P5.5
CUBOID 0 1 2P10.0 2P2.5 2P1.5
HOLE 3 -7.5 2*0.0
HOLE 4 7.5 2*0.0
END GEOMETRY
READ ARRAY
ARA=1 NUX=1 NUY=1 NUZ=3 FILL 2 5 2 END FILL
END ARRAY
The above geometry description uses ``HOLE``\ s (see :numref:`sec-module.keno.geom.holes`) to
describe the bottom approximation of :numref:`fig8-1-15`. ``UNIT`` 1 defines a
large ``CYLINDER`` with a radius of 2.5 cm and a height of 1.0 cm.
``UNIT`` 2 defines the same ``CYLINDER`` within a ``CUBOID`` that
extends from X = -2.5 to X = 17.5, from Y = -2.5 to Y = 2.5, and Z = 0.0
to Z = 1.0. The origin of the ``CYLINDER`` is at (0.0,0.0,0.0). Thus
``UNIT`` 2 describes the top and bottom of the ``CYLINDER`` on the left.
``UNIT`` 1 is positioned within this ``CUBOID`` as a ``HOLE`` with its
origin at (15.0,0.0,0.0) to describe the top and bottom of the
``CYLINDER`` on the right. ``UNIT`` 3 is the left hemicylinder that
adjoins the horizontal ``CYLINDER``, and ``UNIT`` 4 is the right
hemicylinder that adjoins the horizontal ``CYLINDER``. ``UNIT`` 5
defines the horizontal ``CYLINDER`` with its origin at the center within
a ``CUBOID`` that extends from X = -10.0 to X = +10.0, Y = -2.5 to Y =
2.5, and Z = -1.5 to Z = 1.5. ``UNIT`` 3 is positioned to the left of
the horizontal ``CYLINDER``, and ``UNIT`` 4 is positioned to the right
of the horizontal ``CYLINDER`` by using ``HOLE``\ s. The entire system
is achieved by stacking a ``UNIT`` 2 above and below ``UNIT`` 5 as shown
in the ``ARRAY`` data.
This same geometry description can be used with ``UNIT`` 2 redefined,
having its origin defined so that it extends from X = -10 to X = 10, Y =
-2.5 to Y = 2.5, and Z = 0.0 to Z = 1. In this instance, the geometry
data would be identical except for ``UNIT`` 2. This alternative
description of ``UNIT`` 2 is
KENO V.a:
.. code-block:: scale
UNIT 2
CYLINDER 1 1 2.5 1.0 0.0 ORIGIN -7.5 0.0
CUBOID 0 1 2P10.0 2P2.5 1.0 0.0
HOLE 1 7.5 0.0 0.0
This system can be easily described in KENO-VI geometry because
intersections are allowed. The small ``CYLINDER`` is rotated in data
description 1, Example 5.
.. centered:: Data description 1, Example 5.
KENO-VI:
.. code-block:: scale
READ GEOM
GLOBAL UNIT 1
CYLINDER 1 2.5 2.5 -2.5
CYLINDER 2 2.5 2.5 -2.5 ORIGIN Y=15.0
YCYLINDER 3 1.5 15.0 0.0
CUBOID 4 5.0 -5.0 17.5 -2.5 2.5 -2.5
MEDIA 1 1 1
MEDIA 1 1 2
MEDIA 1 1 3 -1 -2
MEDIA 0 1 4 -3 -2 -1
BOUNDARY 4
END GEOM
The first and second ``CYLINDER``\ s define the two large
``CYLINDER``\ s, and the third ``CYLINDER`` describes the small
connecting ``CYLINDER``. The two large ``CYLINDER``\ s are oriented
along the Z axis. The second large cylinder is translated so its origin
is at position (0.0, 15.0, 0.0). The small ``CYLINDER`` is oriented
along the Y axis. Region 1 consists of the material in the first large
``CYLINDER``. Region 2 consists of the material in the second large
``CYLINDER``. Region 3 consists of the material in the small
``CYLINDER`` but not in either of the large ``CYLINDER``\ s. Region 4 is
the ``BOUNDARY`` region.
EXAMPLE 6. Assume 2 small cylinders 1.0 cm in radius and 10 cm long are
connected by a large cylinder 2.5 cm in radius and 5 cm long as shown in
:numref:`fig8-1-16`.
.. figure:: figs/Keno/fig16.png
:align: center
:width: 200
:name: fig8-1-16
Two small cylinders joined axially by a large cylinder.
This problem is very similar to Example 4. It can be described as a
single ``UNIT`` in KENO-VI, but not in KENO V.a where it must be
described as an array. In KENO V.a, ``UNIT`` 1 defines the large
cylinder, and ``UNIT`` 2 defines the small cylinder. The origin of each
``UNIT`` is at its center. The composite system consists of two
``UNIT`` 2s and one ``UNIT`` 1 as shown below. In KENO-VI,
``CYLINDER`` 1 defines the long thin cylinder, and ``CYLINDER`` 2
defines the short thick cylinder. The origin of each cylinder is at its
center. In both KENO V.a and KENO-VI, the centerline of the cylinders
lies along the Z axis.
.. centered:: Data description 1, Example 6.
KENO V.a:
.. code-block:: scale
READ GEOM
UNIT 1
CYLINDER 1 1 2.5 2.5 -2.5
CUBE 0 1 2.5 -2.5
UNIT 2
CYLINDER 1 1 1.0 5.0 -5.0
CUBOID 0 1 2.5 -2.5 2.5 -2.5 5.0 -5.0
END GEOM
READ ARRAY NUX=1 NUY=1 NUZ=3 FILL 2 1 2 END ARRAY
KENO-VI:
.. code-block:: scale
READ GEOM
GLOBAL UNIT 1
CYLINDER 1 1.0 12.5 -12.5
CYLINDER 2 2.5 2.5 -2.5
CUBOID 3 4P2.5 12.5 -12.5
MEDIA 1 1 1
MEDIA 1 1 2 -1
MEDIA 0 1 3 -2 -1
BOUNDARY 3
END GEOM
EXAMPLE 7. Assume an 11 :math:`\times` 5 :math:`\times` 3 square-pitched array of spheres of
material 1, radius 3.75 cm, with a center-to-center spacing of 10 cm in
the X, Y, and Z directions. The data for this system are given below.
.. centered:: Data description 1, Example 7.
KENO V.a:
.. code-block:: scale
READ GEOM
SPHERE 1 1 3.75
CUBE 0 1 5.0 -5.0
END GEOM
READ ARRAY NUX=11 NUY=5 NUZ=3 END ARRAY
KENO-VI:
.. code-block:: scale
READ GEOM
UNIT 1
SPHERE 1 3.75
CUBOID 2 6P5.0
MEDIA 1 1 1
MEDIA 0 1 2 -1
BOUNDARY 2
GLOBAL UNIT 2
CUBOID 10 55.0 -55.0 25.0 -25.0 15.0 -15.0
ARRAY 1 10 PLACE 6 3 2 3*0.0
BOUNDARY 10
END GEOM
READ ARRAY NUX=11 NUY=5 NUZ=3 FILL F1 END FILL END ARRAY
EXAMPLE 8. Assume an 11 :math:`\times` 5 :math:`\times` 3 rectangular-pitched array of spheres of
material 1, whose radius is 3.75 cm and whose center-to-center spacing
is 10 cm in the X direction, 15 cm in the Y direction, and 20 cm in the
Z direction. The input for this geometry is given below.
.. centered:: Data description 1, Example 8.
KENO V.a:
.. code-block:: scale
READ GEOM
SPHERE 1 1 3.75
CUBOID 0 1 5.0 -5.0 7.5 -7.5 10.0 -10.0
END GEOM
READ ARRAY NUX=11 NUY=5 NUZ=3 END ARRAY
KENO-VI:
.. code-block:: scale
READ GEOM
UNIT 1
SPHERE 1 3.75
CUBOID 2 5.0 -5.0 7.5 -7.5 10.0 -10.0
MEDIA 1 1 1
MEDIA 0 1 2 -1
BOUNDARY 2
GLOBAL UNIT 2
CUBOID 1 55.0 -55.0 37.5 -37.5 30.0 -30.0
ARRAY 1 1 PLACE 6 3 2 3*0.0
BOUNDARY 1
END GEOM
READ ARRAY NUX=11 NUY=5 NUZ=3 FILL F1 END FILL END ARRAY
EXAMPLE 9. Assume an 11 :math:`\times` 5 :math:`\times` 3 square-pitched array of spheres of
material 1 with a 3.75 cm radius and 10 cm center-to-center spacing in
the X, Y, and Z directions. This array is reflected by 30 cm of
material 2 (water) on all faces, and weighted tracking (biasing) is to
be used in the water reflector. The array spacing defines the
perpendicular distance from the outer layer of spheres to the reflector
to be 5 cm in the X, Y, and Z directions. The geometry input for this
system is given below.
.. centered:: Data description 1, Example 9.
KENO V.a:
.. code-block:: scale
READ GEOM
UNIT 1
SPHERE 1 1 3.75
CUBE 0 1 5.0 -5.0
GLOBAL UNIT 2
ARRAY 1 -55.0 -25.0 -15.0
REFLECTOR 2 2 6*3.0 10
END GEOM
READ ARRAY NUX=11 NUY=5 NUZ=3 END ARRAY
READ BIAS ID=500 2 11 END BIAS
KENO-VI:
.. code-block:: scale
READ GEOM
UNIT 1
SPHERE 1 3.75
CUBOID 2 6P5.0
MEDIA 1 1 1
MEDIA 0 1 2 -1
BOUNDARY 2
GLOBAL UNIT 2
CUBOID 1 55.0 -55.0 25.0 -25.0 15.0 -15.0
CUBOID 2 58.0 -58.0 28.0 -28.0 18.0 -18.0
CUBOID 3 61.0 -61.0 31.0 -31.0 21.0 -21.0
CUBOID 4 64.0 -64.0 34.0 -34.0 24.0 -24.0
CUBOID 5 67.0 -67.0 37.0 -37.0 27.0 -27.0
CUBOID 6 70.0 -70.0 40.0 -40.0 30.0 -30.0
CUBOID 7 73.0 -73.0 43.0 -43.0 33.0 -33.0
CUBOID 8 76.0 -76.0 46.0 -46.0 36.0 -36.0
CUBOID 9 79.0 -79.0 49.0 -49.0 39.0 -39.0
CUBOID 10 82.0 -82.0 52.0 -52.0 42.0 -42.0
CUBOID 11 85.0 -85.0 55.0 -55.0 45.0 -45.0
ARRAY 1 1 PLACE 6 3 2 3*0.0
MEDIA 2 2 2 -1
MEDIA 2 3 3 -2
MEDIA 2 4 4 -3
MEDIA 2 5 5 -4
MEDIA 2 6 6 -5
MEDIA 2 7 7 -6
MEDIA 2 8 8 -7
MEDIA 2 9 9 -8
MEDIA 2 10 10 -9
MEDIA 2 11 11 -10
BOUNDARY 11
END GEOM
READ ARRAY NUX=11 NUY=5 NUZ=3 FILL F1 END FILL END ARRAY
READ BIAS ID=500 2 11 END BIAS
In the KENO V.a input, the ``ARRAY`` boundary defines the origin of the
``REFLECTOR`` to be at the center of the ``ARRAY``. The 6*3.0 in the
``REFLECTOR`` description repeats the 3.0 six times. The ``REFLECTOR``
record is used to generate ten ``REFLECTOR`` regions, each of which is
3.0 cm thick, on all six faces of the ``ARRAY``.
In the KENO-VI input, the basic ``UNIT`` used to construct the ``ARRAY``
is defined in ``UNIT`` 1. The ``ARRAY`` is positioned in ``UNIT`` 2
(the ``GLOBAL UNIT``) using the ``ARRAY`` card and the ``PLACE`` option.
The ``ARRAY`` is then surrounded by ten \ ``REFLECTOR`` regions, each
3.0 cm thick, on all sides.
The first bias ``ID`` is 2, so the last bias ``ID`` will be 11 if
10 regions are created. The biasing data block is necessary to apply
the desired weighting or biasing function to the reflector. The
biasing material ID is obtained from :numref:`tab8-1-20`. IDs, group
structure and incremental thickness for
weighting data available on the KENO weighting library. If the
biasing data block is omitted from the problem description, the 10
reflector regions will not have a biasing function applied to them,
and the default value of the average weight will be used. This may
cause the problem to execute more slowly, and therefore require the
use of more computer time.
EXAMPLE 10. Assume the reflector in Example 9 is present only on both
X faces, both Y faces, and the negative Z face. The reflector is only
15.24 cm thick on these faces. The top of the array (positive Z face) is
unreflected.
.. centered:: Data description 1, Example 10.
KENO V.a:
.. code-block:: scale
READ GEOM
UNIT 1
SPHERE 1 1 3.75
CUBE 0 1 5.0 -5.0
GLOBAL UNIT 2
ARRAY 1 -55.0 -25.0 -15.0
REFLECTOR 2 2 4*3.0 0.0 3.0 5
REFLECTOR 2 7 4*0.24 0.0 0.24 1
READ ARRAY NUX=11 NUY=5 NUZ=3 END ARRAY
READ BIAS ID=500 2 7 END BIAS
KENO-VI:
.. code-block:: scale
READ GEOM
UNIT 1
SPHERE 1 3.75
CUBOID 2 6P5.0
MEDIA 1 1 1
MEDIA 0 1 2 -1
BOUNDARY 2
GLOBAL UNIT 2
CUBOID 1 55.0 -55.0 25.0 -25.0 15.0 -15.0
CUBOID 2 58.0 -58.0 28.0 -28.0 15.0 -18.0
CUBOID 3 61.0 -61.0 31.0 -31.0 15.0 -21.0
CUBOID 4 64.0 -64.0 34.0 -34.0 15.0 -24.0
CUBOID 5 67.0 -67.0 37.0 -37.0 15.0 -27.0
CUBOID 6 70.24 -70.24 40.24 -40.24 15.0 -30.24
ARRAY 1 1 PLACE 6 3 2 3*0.0
MEDIA 2 2 2 -1
MEDIA 2 3 3 -2
MEDIA 2 4 4 -3
MEDIA 2 5 5 -4
MEDIA 2 6 6 -5
BOUNDARY 6
END GEOM
READ ARRAY NUX=11 NUY=5 NUZ=3 FILL F1 END FILL END ARRAY
READ BIAS ID=500 2 6 END BIAS
In the KENO V.a input, the first ``REFLECTOR`` description generates
five regions around the ``ARRAY``, each region being 3.0 cm thick in the
+X, -X, +Y, -Y, and -Z directions, and of zero thickness in the
+Z direction. This defines a total thickness of 15 cm of reflector
material on the appropriate faces. The second ``REFLECTOR`` description
generates the last 0.24 cm of material 2 on those faces. Thus, the total
reflector thickness is 15.24 cm on each face of the array, except the
top which has no reflector. Five reflector regions were generated by the
first ``REFLECTOR`` description, and one was generated by the second
``REFLECTOR`` description; so, six biasing regions must be defined in
the biasing data. Thus, the beginning bias ``ID`` is 2, and the ending
bias ID is 7.
In the KENO-VI input, the first ``CUBOID`` in Unit 2 represents the
boundary for the ``ARRAY``. The next four ``CUBOID``\ s represent the
first four regions around the ``ARRAY``, each region being 3.0 cm thick
in the +X, X, +Y, -Y, and -Z directions, and of zero thickness in the
+Z direction. A total thickness of 12 cm of reflector material is on the
appropriate faces. The last ``CUBOID`` represents the last 3.24 cm of
material 2 on those faces. Thus, the total reflector thickness is
15.24 cm on each face of the array, except the top which has no
reflector. The beginning bias ID is 2, and the ending bias ID is 6. The
last region could either be larger or smaller than the recommended
thickness to complete the reflector.
The biasing material ``ID`` and thickness per region are obtained from
:numref:`tab8-1-20`. The thickness per region should be very nearly the
thickness per region from the table to avoid over biasing in the
reflector. Partial increments at the outer region of a reflector are
exempt from this recommendation. If a biasing function is not to be
applied to a region generated by the ``REFLECTOR`` record, the thickness
per region can be any desired thickness and the biasing data block is
omitted.
EXAMPLE 11. Assume the array of Example 7 has the central unit of the
array replaced by a cylinder of material 4, 5 cm in radius and 10 cm
tall. Assume a 20 cm thick spherical reflector of material 3 (concrete)
is positioned so its inner radius is 65 cm from the center of the array.
The minimum inner radius of a spherical reflector for this array is
62.25 cm (:math:`\sqrt{55^{2} + 25^{2} + 15^{2} }`). If the inner radius is smaller than this, the problem
cannot be described using KENO V.a geometry.
.. centered:: Data description 1, Example 11.
KENO V.a:
.. code-block:: scale
READ GEOM
UNIT 1
SPHERE 1 1 3.75
CUBE 0 1 5.0 -5.0
UNIT 2
CYLINDER 4 1 5.0 5.0 -5.0
CUBE 0 1 5.0 -5.0
GLOBAL UNIT 2
ARRAY 1 -55.0 -25.0 -15.0
SPHERE 0 1 65.0
REPLICATE 3 2 5.0 4
END GEOM
READ ARRAY
NUX=11 NUY=5 NUZ=3
LOOP 1 1 11 1 1 5 1 1 3 1 2 6 6 1 3 3 1 2 2 1 END LOOP
END ARRAY
READ BIAS ID=301 2 5 END BIAS
KENO-VI:
.. code-block:: scale
READ GEOM
UNIT 1
SPHERE 1 3.75
CUBOID 2 6P5.0
MEDIA 1 1 1
MEDIA 0 1 2 -1
BOUNDARY 2
UNIT 2
CYLINDER 1 5.0 5.0 -5.0
CUBOID 2 6P5.0
MEDIA 4 1 1
MEDIA 0 1 2 -1
BOUNDARY 2
GLOBAL UNIT 3
CUBOID 1 55.0 -55.0 25.0 -25.0 15.0 -15.0
SPHERE 2 65.0
SPHERE 3 70.0
SPHERE 4 75.0
SPHERE 5 80.0
SPHERE 6 85.0
ARRAY 1 1 PLACE 6 3 2 3*0.0
MEDIA 0 1 2 -1
MEDIA 3 2 3 -2
MEDIA 3 3 4 -3
MEDIA 3 4 5 -4
MEDIA 3 5 6 -5
BOUNDARY 6
END GEOM
READ ARRAY
NUX=11 NUY=5 NUZ=3
LOOP 1 1 11 1 1 5 1 1 3 1 2 6 6 1 3 3 1 2 2 1 END LOOP
END ARRAY
READ BIAS ID=301 2 5 END BIAS
``UNIT`` 1 describes the ``SPHERE`` and spacing used in the ``ARRAY``.
``UNIT`` 2 defines the ``CYLINDER`` located at the center of the
``ARRAY``. In KENO V.a, the ``ARRAY`` record defines the origin of the
reflector to be at the center of the ``ARRAY``, while in KENO-VI it
defines the origin of the ``ARRAY`` to be at the center of the ``GLOBAL
UNIT``. The first ``SPHERE`` in the ``GLOBAL UNIT`` defines the inner
radius of the reflector. The next four ``SPHERE`` and four ``MEDIA``
records of the KENO-VI input and the ``REPLICATE`` record of the KENO
V.a input will generate four spherical regions of material 3, each
5.0 cm thick. The data for the ``BIAS`` block is generated in a similar
manner to previous examples, except that concrete (ID=301) is used. The
recommended reflector thickness is 5 cm; this thickness is incorporated
explicitly in the KENO-VI model and with 4 repetitions of the 5 cm thick
reflector via ``REPLICATE`` in the KENO V.a model. The first 10 entries
following the word ``LOOP`` fills the 11 :math:`\times` 5 :math:`\times` 3 ``ARRAY`` with
``UNIT``\ s 1. The next 10 entries position ``UNIT`` 2 at the center of
the ``ARRAY`` (X = 6, Y = 3, and Z = 2), replacing the ``UNIT`` 1 that
had been placed there by the first 10 entries.
EXAMPLE 12. Assume a data profile such as fission densities is desired
in a cylinder at 0.5 cm intervals in the radial direction and 1.5 cm
intervals axially. The cylinder is composed of material 1 and has a
radius of 5 cm and a height of 15 cm. The ``REPLICATE`` or ``REFLECTOR``
description can be used to generate these regions in KENO V.a. A biasing
data block is not entered because default biasing is desired throughout
the cylinder.
.. centered:: Data description 1, Example 12.
KENO V.a:
.. code-block:: scale
READ GEOM
CYLINDER 1 1 0.5 1.5 0
REFLECTOR 1 1 0.5 1.5 0 9
END GEOM
KENO-VI:
.. code-block:: scale
READ GEOM
GLOBAL UNIT 1
CYLINDER 1 0.5 1.5 0
CYLINDER 2 1.0 3.0 0
CYLINDER 3 1.5 4.5 0
CYLINDER 4 2.0 6.0 0
CYLINDER 5 2.5 7.5 0
CYLINDER 6 3.0 9.0 0
CYLINDER 7 3.5 10.5 0
CYLINDER 8 4.0 12.0 0
CYLINDER 9 4.5 13.5 0
CYLINDER 10 5.0 15.0 0
MEDIA 1 1 1
MEDIA 1 1 2 -1
MEDIA 1 1 3 -2
MEDIA 1 1 4 -3
MEDIA 1 1 5 -4
MEDIA 1 1 6 -5
MEDIA 1 1 7 -6
MEDIA 1 1 8 -7
MEDIA 1 1 9 -8
MEDIA 1 1 10 -9
BOUNDARY 10
END GEOM
EXAMPLE 13. (KENO-VI due to pipe junctions) Assume a cross composed of
two Plexiglas cylinders (material 3) having an inner diameter of
13.335 cm and an outer diameter of 16.19 cm. The bottom and side legs of
the cross are closed by a 3.17 cm thick piece of Plexiglas. From the
center of the intersection, the bottom and side legs are 91.44 cm long
and the top leg is 121.92 cm long. The cross is filled with a
UO\ :sub:`2`\ F\ :sub:`2` solution (material 1) to a height of 28.93 cm
above the center of the cylinder intersection. The cross is then
surrounded by a water reflector (material 2) that extends from the
center of the intersection: 111.74 cm in the :math:`\pm`\ X directions, 20.64 cm in
the :math:`\pm`\ Y directions, 29.03 cm in the +Z direction, and -118.428 cm in the
-Z direction. A schematic of the assembly is shown in :numref:`fig8-1-17`.
.. figure:: figs/Keno/fig17.png
:align: center
:width: 400
:name: fig8-1-17
Plexiglas UO\ :sub:`2`\ F\ :sub:`2`-filled cross.
.. centered:: Data description of Example 13 (KENO-VI only).
.. code-block:: scale
READ GEOMETRY
GLOBAL UNIT 1
CYLINDER 10 13.335 28.93 -88.27
CYLINDER 20 13.335 121.92 -88.27
CYLINDER 30 16.19 121.92 -91.44
YCYLINDER 40 13.335 88.27 -88.27
YCYLINDER 50 16.19 91.44 -91.44
CUBOID 60 2P111.74 2P20.64 29.03 -118.428
CUBOID 70 2P111.74 2P20.64 121.92 -118.428
MEDIA 1 1 10
MEDIA 0 1 20 -10
MEDIA 3 1 30 -20 -40
MEDIA 1 1 40 -10
MEDIA 3 1 50 -40 -30
MEDIA 2 1 60 -30 -50
MEDIA 0 1 70 -30 -60
BOUNDARY 70
END GEOMETRY
EXAMPLE 14. (KENO-VI only because of rotation) Assume a Y-shaped
aluminum cylinder (material 2) with a 13.95 cm inner radius and a 0.16
cm wall thickness is filled with a UO\ :sub:`2`\ F\ :sub:`2` solution
(material 1). From the center where the Y intersects the cylinder, the
bottom leg is 76.7 cm long, the top leg is 135.4 cm long, and the Y leg
is 126.04 cm long, canted at a 29.26-degree angle. The bottom of the
bottom leg and the top of the Y leg are sealed with 1.3 cm caps. The
Y cylinder is filled to a height of 52.8 cm above the center where the
Y leg intersects the vertical cylinder. The cylinder is surrounded by a
water reflector (material 3) that extends out 37.0 cm in the
:math:`\pm`X direction, 100.0 and -37.0 cm in the :math:`\pm`Y direction, and 135.4 and
-99.6 in the :math:`\pm`Z direction. A schematic of the assembly is shown in
:numref:`fig8-1-18`.
.. figure:: figs/Keno/fig18.png
:align: center
:width: 400
:name: fig8-1-18
Y-shaped UO\ :sub:`2`\ F\ :sub:`2`-filled aluminum cylinder.
.. centered:: Data description of Example 14 (KENO-VI only).
.. code-block:: scale
READ GEOMETRY
GLOBAL UNIT 1
COM='30 DEG Y CYLINDER'
CYLINDER 10 13.95 135.4 -75.4
CYLINDER 20 14.11 135.4 -76.7
CYLINDER 30 13.95 124.74 0.0 ROTATE A2=-29.26
CYLINDER 40 14.11 126.04 0.0 ROTATE A2=-29.26
CUBOID 50 2P37.0 100.0 -37.0 52.8 -75.4
CUBOID 60 2P37.0 100.0 -37.0 135.4 -99.6
MEDIA 1 1 10 50
MEDIA 2 1 20 -10 -30
MEDIA 1 1 30 50 -10
MEDIA 2 1 40 -30 -20
MEDIA 0 1 10 -50
MEDIA 0 1 30 -50 -10
MEDIA 3 1 60 -20 -40
BOUNDARY 60
END GEOMETRY
.. _sec-module.keno.geom.holes:
Use of holes in the geometry
^^^^^^^^^^^^^^^^^^^^^^^^^^^^
:numref:`sec-module.keno.geom_guide` tells how each KENO V.a geometry region in a ``UNIT``
must completely enclose all previously described regions in that
``UNIT`` and how KENO-VI geometry allows regions in a ``UNIT`` to
intersect, thus eliminating the need for ``HOLE``\ s. ``HOLE``\ s can be
used to circumvent the complete enclosure restriction in KENO V.a to
some degree. In KENO-VI, they can be useful in simplifying the input of
a problem and decreasing the total CPU time needed for a problem.
A ``HOLE`` is a means of placing an entire ``UNIT`` within a geometry
region. A separate ``HOLE`` description is required for every location
in a geometry region where a ``UNIT`` is to be placed. The information
contained in a ``HOLE`` description is (1) the keyword ``HOLE``, (2) the
``UNIT`` number of the ``UNIT`` to be placed, and (3) any modification
data needed to correctly position and rotate (in KENO-VI) the specified
``UNIT`` within the containing ``UNIT``. In KENO V.a, a ``HOLE`` is
placed inside the geometry region that precedes it. This excludes
``HOLE``\ s ... (i.e., if a ``CUBE`` geometry region is followed by four
``HOLE`` descriptions, all four ``HOLE``\ s are located within the
``CUBE``). In KENO V.a, ``HOLE``\ s are subject to the restriction that
they cannot intersect any other geometry region. ``HOLE``\ s can be
nested to any depth (see :numref:`sec-module.keno.geom.nesting_holes`). It is not advisable to use
``HOLE``\ s tangent to other ``HOLE``\ s or geometry, because round-off
error may cause them to overlap. It is not uncommon for a problem that
runs on one type of computer to fail on another type using the same
data. Therefore, it is recommended that tangency and boundaries shared
with ``HOLE``\ s be avoided. This may be accomplished by separating the
otherwise collocated or tangent surfaces by a very small (i.e.,
10\ :sup:`-6` cm) distance.
In KENO V.a, tracking in regions that contain holes is less efficient
than tracking in regions that do not contain holes. Therefore, holes
should be used only when the system cannot be easily described by
conventional methods. One example of the use of holes is shown in
:numref:`fig8-1-19`, representing nine close-packed rods in an annulus.
In KENO-VI, tracking in regions that contain ``HOLE``\ s can be more
efficient than tracking in regions that do not contain ``HOLE``\ s
because every region boundary in a ``UNIT`` must be checked for a
crossing whenever a crossing is possible. Putting small but complex
geometries in a hole will lessen the number of boundaries that need to
be checked for possible crossings. However, the indiscriminate use of
holes is not advised since the particle must change coordinate systems
every time a hole is entered or exited. Therefore, holes should be used
carefully and only when the system can be simplified significantly by
their use.
EXAMPLE 15. One example of a unit that requires holes in KENO V.a is
better described not using holes in KENO-VI as shown in :numref:`fig8-1-19`,
representing nine close-packed rods in an annulus. The large rods are
1.4 cm in radius and composed of mixture 3. The small rods are 0.6 cm
in radius and composed of mixture 1. The inside radius of the annulus
is 3.6 cm, and the outside radius is 3.8 cm. The annulus is made of
mixture 2. The rods and annulus are both 30 cm long. The annulus is
centered in a cuboid having an 8 cm\ :sup:`2` cross section and a
length of 32 cm. The black and gray areas in
:numref:`fig8-1-19` are void.
.. figure:: figs/Keno/fig19.png
:align: center
:width: 400
:name: fig8-1-19
Close-packed cylinders in an annulus.
.. centered:: Data description of Example 15.
KENO V.a:
.. code-block:: scale
READ GEOM
UNIT 1
CYLINDER 1 1 0.6 2P15.0
UNIT 2
CYLINDER 3 1 1.4 2P15.0
GLOBAL UNIT 3
CYLINDER 1 1 0.6 2P15.0
CYLINDER 0 1 3.6 2P15.0
HOLE 2 0.0 -2.0 0.0
HOLE 1 2.0 -2.0 0.0
HOLE 2 2.0 0.0 0.0
HOLE 1 2.0 2.0 0.0
HOLE 2 0.0 2.0 0.0
HOLE 1 -2.0 2.0 0.0
HOLE 2 -2.0 0.0 0.0
HOLE 1 -2.0 -2.0 0.0
CYLINDER 2 1 3.8 2P15.0
CUBOID 0 1 4P4.0 2P16.0
END GEOM
KENO-VI:
.. code-block:: scale
READ GEOM
GLOBAL UNIT 1
CYLINDER 1 0.6 2P15.0
CYLINDER 2 0.6 2P15.0 ORIGIN X=2.0 Y=-2.0
CYLINDER 3 0.6 2P15.0 ORIGIN X=2.0 Y=2.0
CYLINDER 4 0.6 2P15.0 ORIGIN X=-2.0 Y=2.0
CYLINDER 5 0.6 2P15.0 ORIGIN X=-2.0 Y=-2.0
CYLINDER 6 1.4 2P15.0 ORIGIN X=2.0
CYLINDER 7 1.4 2P15.0 ORIGIN Y=2.0
CYLINDER 8 1.4 2P15.0 ORIGIN X=-2.0
CYLINDER 9 1.4 2P15.0 ORIGIN Y=-2.0
CYLINDER 10 3.6 2P15.0
CYLINDER 11 3.8 2P15.0
CUBOID 12 4P4.0 2P16.0
MEDIA 1 1 1
MEDIA 1 1 2
MEDIA 1 1 3
MEDIA 1 1 4
MEDIA 1 1 5
MEDIA 3 1 6
MEDIA 3 1 7
MEDIA 3 1 8
MEDIA 3 1 9
MEDIA 0 1 10 -1 -2 -3 -4 -5 -6 -7 -8 -9
MEDIA 2 1 11 -10
MEDIA 0 1 12 -11
BOUNDARY 12
END GEOM
The first ``HOLE`` description in the KENO V.a input represents the
bottom large rod. It takes ``UNIT`` 2 and places its ``ORIGIN`` at
(0.0,-2.0,0.0) relative to the ``ORIGIN`` of ``UNIT`` 3. The second
``HOLE`` description represents the small rod to the right of the large
rod just discussed. It places the origin of ``UNIT`` 1 at (2.0,-2.0,0.0)
in ``UNIT`` 3. The third ``HOLE`` description represents the large rod
to the right. It places the origin of ``UNIT`` 2 at (2.0,0.0,0.0) in
``UNIT`` 3. This procedure is repeated in a counterclockwise direction
until all eight rods have been placed within the region that defines the
inner surface of the annulus. The ``CYLINDER`` that defines the outer
surface of the annulus is described after all the ``HOLE``\ s for the
previous region have been placed. Then the outer ``CUBOID`` is
described. This example illustrates that a ``UNIT`` that is to be placed
using a ``HOLE`` description need not have a ``CUBE`` or ``CUBOID`` as
its last region. Note that including the central rod directly in
``UNIT`` 3 reduces the CPU time required for transport compared to the
case of all 9 rods being inserted as ``HOLE``\ s. It is also important
that the 9 ``HOLE``\ s are inserted *after* the void cylinder into which
they are inserted. Entering the ``HOLE``\ s in any other position in the
input would generated region intersection errors. The order of the HOLE
records in any given region is not important, as they can be
interchanged with each other randomly. However, they must always appear
immediately after the region in which they are placed.
The KENO-VI input does not need to use ``HOLE``\ s. The first
``CYLINDER`` description in this case represents the middle small rod.
The next four ``CYLINDER`` records describe the four remaining small
rods surrounding the middle rod. The ``ORIGIN`` attribute is used to
shift the origin of each ``CYLINDER`` to the appropriate location. The
following four ``CYLINDER`` records represent the four large rods.
Again, the ``ORIGIN`` attribute is used to shift the ``ORIGIN`` of each
``CYLINDER`` to the appropriate location. Only the nonzero dimensions
need to be entered in the ``ORIGIN`` data. The tenth ``CYLINDER`` record
is the void in the annulus that contains the rods. The last ``CYLINDER``
record defines the outer surface of the annulus. Finally, the ``CUBOID``
record describes the surrounding ``UNIT`` boundary.
In KENO-VI, holes may not extend across any array outer boundary, may
not intersect with other holes, and may not cross the host UNIT outer
boundary. Thus a hole may be placed so that it crosses several regions
within an array. The hole description replaces the unit description
within the hole domain. Since the holes are placed using the host UNIT
coordinate system, the location of the hole record in the unit
definition is not relevant.
An array of the arrangement shown in :numref:`fig8-1-19` can be easily described
by altering the array description data. For example, a 5 :math:`\times` 3 :math:`\times` 2 array
of these shapes with a center-to-center spacing of 8 cm in X and Y and
32 cm in Z can be achieved by using the following array data:
.. code-block:: scale
READ ARRAY NUX=5 NUY=3 NUZ=2 FILL F3 END FILL END ARRAY
or
.. code-block:: scale
READ ARRAY NUX=5 NUY=3 NUZ=2 FILL 30*3 END FILL END ARRAY
or
.. code-block:: scale
READ ARRAY NUX=5 NUY=3 NUZ=2 LOOP 3 1 5 1 1 3 1 1 2 1 END LOOP END ARRAY
.. _sec-module.keno.geom.nesting_holes:
Nesting holes
^^^^^^^^^^^^^
This section illustrates how holes are nested. Holes can be nested to
any level. Consider the configuration illustrated in :numref:`fig8-1-19` and
replace the large rods with a complicated geometric arrangement. The
resulting Fig. is shown in :numref:`fig8-1-20`. :numref:`fig8-1-21` shows the
complicated geometric arrangement that replaced the large rods of
:numref:`fig8-1-19`. :numref:`fig8-1-22` shows a component of the arrangement shown in
:numref:`fig8-1-20`.
.. figure:: figs/Keno/fig20.png
:align: center
:width: 400
:name: fig8-1-20
Configuration using nested holes.
.. figure:: figs/Keno/fig21.png
:align: center
:width: 400
:name: fig8-1-21
Complicated geometric arrangement by Unit 7.
.. figure:: figs/Keno/fig22.png
:align: center
:width: 400
:name: fig8-1-22
Geometric component represented by Unit 4.
EXAMPLE 16. There is no predetermined preferred method to create a
geometry mockup for a given physical system. The user should determine
the most convenient order. To describe the configuration shown in :numref:`fig8-1-20`
using nested ``HOLE``\ s, it is likely most convenient to start
the geometry mockup at the deepest nesting level, as shown in
:numref:`fig8-1-21`. The small ``CYLINDER``\ s are composed of mixture 1, and
they are each 0.1 cm in radius and 30 cm long. There are five small
``CYLINDER``\ s used in :numref:`fig8-1-22`. Their centers are located at
(0,0,0) for the central one, at (0,-0.4,0) for the bottom one, at
(0.4,0,0) for the right one, at (0,0.4,0) for the top one, and at
(-0.4,0,0) for the left one. The rectangular parallelepipeds
(``CUBOID``\ s) are composed of mixture 2. Each one is 30 cm long and
0.1 cm by 0.2 cm in cross section. The large ``CYLINDER`` containing the
configuration is composed of mixture 3, is 30 cm long and has a radius
of 0.5 cm.
A possible geometry mockup for this system is described as follows in
KENO V.a:
(1) define a small cylinder to be ``UNIT`` 1,
(2) define a small ``CUBOID`` with its length in the X direction to
be ``UNIT`` 2,
(3) define a small ``CUBOID`` with its length in the Y direction to
be ``UNIT`` 3,
(4) define ``UNIT`` 4 to be the large cylinder and place the
``CYLINDER``\ s and ``CUBOID``\ s in it using ``HOLE``\ s.
::
UNIT 1
CYLINDER 1 1 0.1 2P15.0
UNIT 2
CUBOID 2 1 2P0.1 2P0.05 2P15.0
UNIT 3
CUBOID 2 1 2P0.05 2P0.1 2P15.0
UNIT 4
CYLINDER 1 1 0.1 2P15.0
CYLINDER 3 1 0.5 2P15.0
HOLE 1 0.0 -0.4 0.0
HOLE 1 0.4 0.0 0.0
HOLE 1 0.0 0.4 0.0
HOLE 1 -0.4 0.0 0.0
HOLE 2 -0.2 0.0 0.0
HOLE 2 0.2 0.0 0.0
HOLE 3 0.0 -0.2 0.0
HOLE 3 0.0 0.2 0.0
The first cylinder description in ``UNIT`` 4 places the central rod,
the second cylinder description in ``UNIT`` 4 places the outer cylinder,
the *first* ``HOLE`` places the bottom ``CYLINDER``,
the *second* ``HOLE`` places the ``CYLINDER`` at the right,
the *third* ``HOLE`` places the top ``CYLINDER``,
the *fourth* ``HOLE`` places the ``CYLINDER`` at the left,
the *fifth* ``HOLE`` places the left ``CUBOID`` whose length is in X,
the *sixth* ``HOLE`` places the right ``CUBOID`` whose length is in X,
the *seventh* ``HOLE`` places the bottom ``CUBOID`` whose length is in
Y, and
the *eighth* ``HOLE`` places the top ``CUBOID`` whose length is in Y.
A possible geometry mockup for this system is described as follows in
KENO-VI:
1. define ``UNIT`` 1 to contain the five small cylinders and four
blocks,
2. define ``UNIT`` 2 to contain the next two larger-sized cylinders and
``UNIT`` 1 as ``HOLE``\ s, and
3. define ``GLOBAL UNIT`` 3 to contain the large cylinders and
``UNIT`` 2 as ``HOLE``\ s.
.. code-block:: scale
UNIT 1
CYLINDER 1 0.1 2P15.0
CYLINDER 2 0.1 2P15.0 ORIGIN Y=-0.4
CYLINDER 3 0.1 2P15.0 ORIGIN X=0.4
CYLINDER 4 0.1 2P15.0 ORIGIN Y=0.4
CYLINDER 5 0.1 2P15.0 ORIGIN X=-0.4
CUBOID 6 -0.3 -0.1 2P0.05 2P15.0
CUBOID 7 0.3 0.1 2P0.05 2P15.0
CUBOID 8 2P0.05 -0.3 -0.1 2P15.0
CUBOID 9 2P0.05 0.3 0.1 2P15.0
CYLINDER 10 0.5 2P15.0
MEDIA 1 1 1
MEDIA 1 1 2
MEDIA 1 1 3
MEDIA 1 1 4
MEDIA 1 1 5
MEDIA 2 1 6
MEDIA 2 1 7
MEDIA 2 1 8
MEDIA 2 1 9
MEDIA 3 1 10 -1 -2 -3 -4 -5 -6 -7 -8 -9
BOUNDARY 10
geometry record *1* places the central rod,
geometry record *2* places the bottom ``CYLINDER``,
geometry record *3* places the ``CYLINDER`` at the right,
geometry record *4* places the top ``CYLINDER``,
geometry record *5* places the ``CYLINDER`` at the left,
geometry record *6* places the left ``CUBOID`` whose length is in X,
geometry record *7* places the right ``CUBOID`` whose length is in X,
geometry record *8* places the bottom ``CUBOID`` whose length is in Y,
geometry record *9* places the top ``CUBOID`` whose length is in Y, and
geometry record *10* is the surrounding ``CYLINDER`` that defines the
unit boundary.
In :numref:`fig8-1-21`, the large plain cylinders are composed of mixture 1 and
are 0.5 cm in radius and 30 cm long. The cylindrical component of
``UNIT`` 4 for KENO V.a or ``UNIT`` 1 for KENO-VI is the same size: an
outer radius of 0.5 cm and a length of 30 cm. The small cylinders
located in the interstices between the large cylinders are composed of
mixture 2, are 0.2 cm in radius, and are 30 cm long. The annulus is
composed of mixture 4, has a 1.3 cm inside radius and a 1.4 cm outer
radius. The volume between the inner cylinders is void. The large
cylinders each have a radius of 0.5 cm and are tangent. Therefore, their
origins are offset from the origin of the ``UNIT`` by 0.707107. This is
from X\ :sup:`2` + Y\ :sup:`2` = 1.0, where X and Y are equal.
For KENO V.a, define ``UNIT`` 5 to be the large plain cylinder,
``UNIT`` 6 to be the small cylinder, and ``UNIT`` 7 as the annulus that
contains the cylinders. Its origin is at its center. The geometry mockup
for this portion of the problem follows:
KENO V.a:
.. code-block:: scale
UNIT 5
CYLINDER 1 1 0.5 2P15.0
UNIT 6
CYLINDER 2 1 0.2 2P15.0
UNIT 7
CYLINDER 2 1 0.2 2P15.0
CYLINDER 0 1 1.3 2P15.0
HOLE 5 0.707107 0.0 0.0
HOLE 6 0.707107 0.707107 0.0
HOLE 4 0.0 0.707107 0.0
HOLE 6 -0.707107 0.707107 0.0
HOLE 5 -0.707107 0.0 0.0
HOLE 6 -0.707107 -0.707107 0.0
HOLE 4 0.0 -0.707107 0.0
HOLE 6 0.707107 -0.707107 0.0
CYLINDER 4 1 1.4 2P15.0
The *first* ``HOLE`` places the larger ``CYLINDER`` of mixture 1 at the
right with its origin at (0.707107,0.0,0.0),
the *second* ``HOLE`` places the small ``CYLINDER`` in the upper right
quadrant,
the *third* ``HOLE`` places the top ``CYLINDER`` that contains the
geometric component defined in ``UNIT`` 4,
the *fourth* ``HOLE`` places the small ``CYLINDER`` in the upper left
quadrant,
the *fifth* ``HOLE`` places the larger ``CYLINDER`` of mixture 1 at the
left,
the *sixth* ``HOLE`` places the small ``CYLINDER`` in the lower lower
left quadrant,
the *seventh* ``HOLE`` places the bottom ``CYLINDER`` that contains the
geometric component defined in ``UNIT`` 4, and
the *eighth* ``HOLE`` places the small ``CYLINDER`` in the lower right
quadrant.
The last ``CYLINDER`` defines the outer surface of the annulus.
For KENO-VI, ``UNIT`` 2 is the annulus that contains the cylinders.
KENO-VI:
.. code-block:: scale
UNIT 2
CYLINDER 1 0.2 2P15.0
CYLINDER 2 0.2 2P15.0 ORIGIN X=0.707107 Y=0.707107
CYLINDER 3 0.2 2P15.0 ORIGIN X=-0.707107 Y=0.707107
CYLINDER 4 0.2 2P15.0 ORIGIN X=-0.707107 Y=-0.707107
CYLINDER 5 0.2 2P15.0 ORIGIN X=0.707107 Y=-0.707107
CYLINDER 6 0.5 2P15.0 ORIGIN X=0.707107
CYLINDER 7 0.5 2P15.0 ORIGIN X=-0.707107
CYLINDER 10 1.3 2P15.0
CYLINDER 11 1.4 2P15.0
MEDIA 2 1 1
MEDIA 2 1 2
MEDIA 2 1 3
MEDIA 2 1 4
MEDIA 2 1 5
MEDIA 1 1 6
MEDIA 1 1 7
HOLE 1 ORIGIN Y=0.707107
HOLE 1 ORIGIN Y=-0.707107
MEDIA 0 1 10 -1 -2 -3 -4 -5 -6 -7
MEDIA 4 1 11 -10
BOUNDARY 11
In Unit 2 of the above KENO-VI geometry,
``CYLINDER`` *1* places a small ``CYLINDER`` of mixture 2 at the origin,
``CYLINDER`` *2* places the small ``CYLINDER`` of mixture 2 in the upper
right quadrant,
``CYLINDER`` *3* places the small ``CYLINDER`` of mixture 2 in the upper
left quadrant,
``CYLINDER`` *4* places the small ``CYLINDER`` of mixture 2 in the lower
left quadrant,
``CYLINDER`` *5* places the small ``CYLINDER`` of mixture 2 in the lower
right quadrant,
``CYLINDER`` *6* places the larger ``CYLINDER`` of mixture 1 at the
right with its origin at (0.707107,0.0,0.0),
``CYLINDER`` *7* places the larger ``CYLINDER`` of mixture 1 at the left
with its origin at (0.0,0.707107.0.0),
``CYLINDER`` *10* defines the inner surface of the annulus,
``CYLINDER`` *11* defines the outer surface of the annulus and the
``UNIT`` boundary,
the first ``HOLE`` places the top ``CYLINDER`` that contains the
geometric component defined in ``UNIT`` 1, and
the second ``HOLE`` places the bottom ``CYLINDER`` that contains the
geometric component defined in ``UNIT`` 1.
To complete the geometry mockup, consider :numref:`fig8-1-20`.
For KENO V.a geometry, define ``UNIT`` 8 to be a cylinder of mixture 2
having a radius of 0.6 cm and a length of 30 cm. Define ``UNIT`` 9 to be
the central rod and the large annulus of 3.6 cm inner radius, 3.8 cm
outer radius, and 30 cm length centered in a ``CUBOID`` having an 8
cm\ :sup:`2` cross section and being 32 cm long.
KENO V.a:
.. code-block:: scale
UNIT 8
CYLINDER 2 1 0.6 2P15.0
UNIT 9
CYLINDER 2 1 0.6 2P15.0
CYLINDER 0 1 3.6 2P15
HOLE 7 2.0 0.0 0.0
HOLE 8 2*2.0 0.0
HOLE 7 0.0 2.0 0.0
HOLE 8 -2.0 2.0 0.0
HOLE 7 -2.0 2*0.0
HOLE 8 2*-2.0 0.0
HOLE 7 0.0 -2.0 0.0
HOLE 8 2P2.0 0.0
CYLINDER 4 1 3.8 2P15.0
CUBOID 0 1 4P4.0 2P16.0
In ``UNIT`` 9 of the KENO V.a description, the first ``CYLINDER``
defines the rod of mixture 2, centered in the annulus. The second
``CYLINDER`` defines the void volume between the central rod and the
annulus.
The *first* ``HOLE`` places the composite annulus of ``UNIT`` 7 to the
right of the central rod,
the *second* ``HOLE`` places a rod defined by ``UNIT`` 8 in the upper
right quadrant of the annulus,
the *third* ``HOLE`` places the composite annulus of ``UNIT`` 7 above
the central rod,
the *fourth* ``HOLE`` places a rod defined by ``UNIT`` 8 in the upper
left quadrant of the annulus,
the *fifth* ``HOLE`` places the composite annulus of ``UNIT`` 7 to the
left of the central rod,
the *sixth* ``HOLE`` places a rod defined by ``UNIT`` 8 in the lower
left quadrant,
the *seventh* ``HOLE`` places the composite annulus of ``UNIT`` 7 below
the central rod, and
the *eighth* ``HOLE`` places a rod defined by ``UNIT`` 8 in the lower
right quadrant.
The last ``CYLINDER`` defines the outer surface of the annulus. The
outer ``CUBOID`` is the last region.
For KENO-VI geometry, define ``UNIT`` 3 to be the central rod and four
outer rods of 0.6 cm radius and 30.0 cm length, and the large annulus of
3.6 cm inner radius, 3.8 cm outer radius, and 30 cm length centered in a
cuboid having an 8 cm\ :sup:`2` cross section and a length of 32 cm.
KENO-VI:
.. code-block:: scale
GLOBAL UNIT 3
CYLINDER 1 0.6 2P15.0
CYLINDER 2 0.6 2P15.0 ORIGIN X=2.0 Y=2.0
CYLINDER 3 0.6 2P15.0 ORIGIN X=-2.0 Y=2.0
CYLINDER 4 0.6 2P15.0 ORIGIN X=-2.0 Y=-2.0
CYLINDER 5 0.6 2P15.0 ORIGIN X=2.0 Y=-2.0
CYLINDER 10 3.6 2P15.0
CYLINDER 11 3.8 2P15.0
CUBOID 12 4P4.0 2P16.0
MEDIA 2 1 1
MEDIA 2 1 2
MEDIA 2 1 3
MEDIA 2 1 4
MEDIA 2 1 5
HOLE 2 ORIGEN X=2
HOLE 2 ORIGEN Y=2
HOLE 2 ORIGEN X=-2
HOLE 2 ORIGEN Y=-2
MEDIA 0 1 10 -1 -2 -3 -4 -5
MEDIA 4 1 11 -10
MEDIA 0 1 12 -11
BOUNDARY 12
In ``UNIT`` 3 of the above KENO-VI description,
``CYLINDER`` *1* defines the rod of mixture 2, centered in the annulus,
``CYLINDER`` *2* places a rod of mixture 2 in the upper right quadrant
of the annulus,
``CYLINDER`` *3* places a rod of mixture 2 in the upper left quadrant of
the annulus,
``CYLINDER`` *4* places a rod of mixture 2 in the lower left quadrant,
``CYLINDER`` *5* places a rod of mixture 2 in the lower right quadrant,
``CYLINDER`` *10* defines the void volume between the central rod and
the annulus,
``CYLINDER`` *11* defines the outer surface of the annulus,
``CUBOID`` *12* defines the unit boundary,
the first ``HOLE`` places ``UNIT`` 2 to the right of the central rod,
the second ``HOLE`` places ``UNIT`` 2 above the central rod,
the third ``HOLE`` places ``UNIT`` 2 to the left of the central rod,
and
the fourth ``HOLE`` places ``UNIT`` 2 below the central rod.
This problem illustrates three levels of ``HOLE`` nesting. The total
input data for the problem is given below. The geometry description
accurately recreates the geometry arrangement of :numref:`fig8-1-20`. The 2D
color plot output is shown in :numref:`fig8-1-23`.
.. figure:: figs/Keno/fig23.png
:align: center
:width: 400
:name: fig8-1-23
Color plot of nested holes example problem.
KENO V.a:
NESTED HOLES SAMPLE
.. code-block:: scale
READ GEOM
UNIT 1
CYLINDER 1 1 0.1 2P15.0
UNIT 2
CUBOID 2 1 2P0.1 2P0.05 2P15.0
UNIT 3
CUBOID 2 1 2P0.05 2P0.1 2P15.0
UNIT 4
CYLINDER 1 1 0.1 2P15.0
CYLINDER 3 1 0.5 2P15.0
HOLE 1 0.0 -0.4 0.0
HOLE 1 0.4 0.0 0.0
HOLE 1 0.0 0.4 0.0
HOLE 1 -0.4 0.0 0.0
HOLE 2 -0.2 0.0 0.0
HOLE 2 0.2 0.0 0.0
HOLE 3 0.0 -0.2 0.0
HOLE 3 0.0 0.2 0.0
UNIT 5
CYLINDER 1 1 0.5 2P15.0
UNIT 6
CYLINDER 2 1 0.2 2P15.0
UNIT 7
CYLINDER 2 1 0.2 2P15.0
CYLINDER 0 1 1.3 2P15.0
HOLE 5 0.707107 2*0.0
HOLE 6 0.707107 0.707107 0.0
HOLE 4 0.0 0.707107 0.0
HOLE 6 -0.707107 0.707107 0.0
HOLE 5 -0.707107 0.0 0.0
HOLE 6 -0.707107 -0.707107 0.0
HOLE 4 0.0 -0.707107 0.0
HOLE 6 0.707107 -0.707107 0.0
CYLINDER 4 1 1.4 2P15.0
UNIT 8
CYLINDER 2 1 0.6 2P15.0
GLOBAL UNIT 9
CYLINDER 2 1 0.6 2P15.0
CYLINDER 0 1 3.6 2P15.0
HOLE 7 2.0 0.0 0.0
HOLE 8 2*2.0 0.0
HOLE 7 0.0 2.0 0.0
HOLE 8 -2.0 2.0 0.0
HOLE 7 -2.0 2*0.0
HOLE 8 2*-2.0 0.0
HOLE 7 0.0 -2.0 0.0
HOLE 8 2P2.0 0.0
CYLINDER 4 1 3.8 2P15.0
CUBOID 0 1 4P4.0 2P16.0
END GEOM
READ PLOT
TTL='X-Y SLICE AT Z MIDPOINT. NESTED HOLES'
XUL=-0.1 YUL=8.1 ZUL=16.0
XLR=8.1 YLR=-0.1 ZLR=16
UAX=1.0 VDN=-1.0 NAX=260 NCH=' *-.X' SCR=NO
END PLOT
END DATA
END
KENO-VI:
.. code-block:: scale
READ GEOM
UNIT 1
CYLINDER 1 0.1 2P15.0
CYLINDER 2 0.1 2P15.0 ORIGIN Y=-0.4
CYLINDER 3 0.1 2P15.0 ORIGIN X=0.4
CYLINDER 4 0.1 2P15.0 ORIGIN Y=0.4
CYLINDER 5 0.1 2P15.0 ORIGIN X=-0.4
CUBOID 6 -0.3 -0.1 2P0.05 2P15.0
CUBOID 7 0.3 0.1 2P0.05 2P15.0
CUBOID 8 2P0.05 -0.3 -0.1 2P15.0
CUBOID 9 2P0.05 0.3 0.1 2P15.0
CYLINDER 10 0.5 2P15.0
MEDIA 1 1 1 -6 -7 -8 -9
MEDIA 1 1 2 -8
MEDIA 1 1 3 -7
MEDIA 1 1 4 -9
MEDIA 1 1 5 -6
MEDIA 2 1 6 -1 -5
MEDIA 2 1 7 -1 -3
MEDIA 2 1 8 -1 -2
MEDIA 2 1 9 -1 -4
MEDIA 3 1 -1 -2 -3 -4 -5 -6 -7 -8 -9 10
BOUNDARY 10
UNIT 2
CYLINDER 1 0.2 2P15.0
CYLINDER 2 0.2 2P15.0 ORIGIN X=0.707107 Y=0.707107
CYLINDER 3 0.2 2P15.0 ORIGIN X=-0.707107 Y=0.707107
CYLINDER 4 0.2 2P15.0 ORIGIN X=-0.707107 Y=-0.707107
CYLINDER 5 0.2 2P15.0 ORIGIN X=0.707107 Y=-0.707107
CYLINDER 6 0.5 2P15.0 ORIGIN X=0.707107
CYLINDER 7 0.5 2P15.0 ORIGIN X=-0.707107
CYLINDER 10 1.3 2P15.0
CYLINDER 11 1.4 2P15.0
MEDIA 2 1 1
MEDIA 2 1 2
MEDIA 2 1 3
MEDIA 2 1 4
MEDIA 2 1 5
MEDIA 1 1 6
MEDIA 1 1 7
HOLE 1 ORIGIN Y=0.707107
HOLE 1 ORIGIN Y=-0.707107
MEDIA 0 1 10 -1 -2 -3 -4 -5 -6 -7
MEDIA 4 1 11 -10
BOUNDARY 11
GLOBAL UNIT 3
CYLINDER 1 0.6 2P15.0
CYLINDER 2 0.6 2P15.0 ORIGIN X=2.0 Y=2.0
CYLINDER 3 0.6 2P15.0 ORIGIN X=-2.0 Y=2.0
CYLINDER 4 0.6 2P15.0 ORIGIN X=-2.0 Y=-2.0
CYLINDER 5 0.6 2P15.0 ORIGIN X=2.0 Y=-2.0
CYLINDER 10 3.6 2P15.0
CYLINDER 11 3.8 2P15.0
CUBOID 12 4P4.0 2P16.0
MEDIA 2 1 1
MEDIA 2 1 2
MEDIA 2 1 3
MEDIA 2 1 4
MEDIA 2 1 5
HOLE 2 ORIGIN X=2
HOLE 2 ORIGIN Y=2
HOLE 2 ORIGIN X=-2
HOLE 2 ORIGIN Y=-2
MEDIA 0 1 10 -1 -2 -3 -4 -5
MEDIA 4 1 11 -10
MEDIA 0 1 12 -11
BOUNDARY 12
END GEOM
READ PLOT
TTL='X-Y SLICE AT Z MIDPOINT. NESTED HOLES'
XUL=-4.1 YUL=4.1 ZUL=0.0
XLR=4.1 YLR=-4.1 ZLR=0
UAX=1.0 VDN=-1.0 NAX=800
END PLOT
END DATA
END
.. _8-1-3-6-3:
Multiple arrays
^^^^^^^^^^^^^^^
EXAMPLE 17. :numref:`sec-module.keno.geom_guide` demonstrates how ``UNIT``\ s are composed of
geometry regions and how these ``UNIT``\ s can be stacked in an
``ARRAY``. This same procedure can be extended to create multiple
``ARRAY``\ s. Furthermore, ``ARRAY``\ s can be used as building blocks
within other ``ARRAY``\ s.
Consider Sample Problem 19 from :numref:`sec-module.keno.examples`. This problem is a critical
experiment consisting of a composite array :cite:`KENO-thomas_critical_1973,KENO-thomas_critical_1964` of four
highly enriched uranium metal cylinders and four cylindrical Plexiglas
containers filled with uranyl nitrate solution. A photograph of the
experiment is given in :numref:`fig8-1c-3`. The coordinate system is defined to
be Z up the page, Y across the page, and X out of the page.
The Plexiglas containers have an inside radius of 9.525 cm and an
outside radius of 10.16 cm. The inside height is 17.78 cm, and the
outside height is 19.05 cm. Four of these containers are stacked with a
center-to-center spacing of 21.75 cm in the Y direction and 20.48 cm in
the Z direction (vertical). This arrangement of four Plexiglas
containers can be described as follows: mixture 2 is the uranyl nitrate
and mixture 3 is Plexiglas, so the Plexiglas container with its
appropriate spacing ``CUBOID`` can be described as ``UNIT`` 1. This
considers the ``ARRAY`` to be bare and suspended with no supports.
KENO V.a:
.. code-block:: scale
UNIT 1
CYLINDER 2 1 9.525 2P8.89
CYLINDER 3 1 10.16 2P9.525
CUBOID 0 1 4P10.875 2P10.24
KENO-VI:
.. code-block:: scale
UNIT 1
CYLINDER 1 9.525 2P8.89
CYLINDER 2 10.16 2P9.525
CUBOID 3 4P10.875 2P10.24
MEDIA 2 1 1
MEDIA 3 1 2 -1
MEDIA 0 1 3 -2
BOUNDARY 3
The ``ARRAY`` of four Plexiglas containers can be described as
``ARRAY`` 1 in the array data as follows:
``ARA=1 NUX=1 NUY=2 NUZ=2 FILL F1 END FILL``
The four metal cylinders, comprised of mixture 1, each have a radius of
5.748 cm and are 10.765 cm tall. They have a center-to-center spacing of
13.18 cm in the Y direction and 12.45 cm in the Z direction (vertical).
Thus, one of the metal cylinders with its appropriate spacing ``CUBOID``
can be described as ``UNIT`` 2. This ``ARRAY`` is also considered to be
bare and unsupported.
KENO V.a:
.. code-block:: scale
UNIT 2
CYLINDER 1 1 5.748 2P5.3825
CUBOID 0 1 4P6.59 2P6.225
KENO-VI:
.. code-block:: scale
UNIT 2
CYLINDER 1 5.748 2P5.3825
CUBOID 2 4P6.59 2P6.225
MEDIA 1 1 1
MEDIA 0 1 2 -1
BOUNDARY 2
The array of four metal cylinders can be described as ``ARRAY`` 2 in the
array data.
``ARA=2 NUX=1 NUY=2 NUZ=2 FILL F2 END FILL``
Now two ``ARRAY``\ s have been described. The overall dimensions of the
``ARRAY`` of Plexiglas containers are 21.75 cm in X, 43.5 cm in Y, and
40.96 cm in Z. The overall dimensions of the ``ARRAY`` of metal
cylinders are 13.18 cm in X, 26.36 cm in Y, and 24.9 cm in Z.
In order to describe the composite ``ARRAY``, these two ``ARRAY``\ s
must be positioned within ``UNIT``\ s and stacked together into one
``ARRAY``. In order for them to be stacked into one ``ARRAY``, the
adjacent faces must match. This is accomplished by defining a ``UNIT`` 3
which contains ``ARRAY`` 1, the ``ARRAY`` of Plexiglas solution
containers. The overall dimensions of this ``UNIT`` are 21.75 cm in X,
43.5 cm in Y, and 40.96 cm in Z. These dimensions are calculated by the
code and need not be specified. ``UNIT`` 3 is defined as follows:
KENO V.a:
.. code-block:: scale
UNIT 3
ARRAY 1 3*0.0
KENO-VI:
.. code-block:: scale
UNIT 3
CUBOID 1 2P10.875 2P21.75 2P20.48
ARRAY 1 1 PLACE 1 1 1 0.0 -10.875 -10.24
BOUNDARY 1
The ``ARRAY`` of metal cylinders will be defined to be ``UNIT`` 4.
However, this ``ARRAY`` is 17.14 cm smaller in the Y and 16.06 cm
smaller in the Z dimensions than the ``ARRAY`` of Plexiglas ``UNIT``\ s.
Therefore, a void region must be placed around the ``ARRAY`` in those
directions so ``UNIT`` 4 and ``UNIT`` 3 will be the same size in Y and
Z.
KENO V.a:
.. code-block:: scale
UNIT 4
ARRAY 2 3*0.0
REPLICATE 0 1 2*0.0 2*8.57 2*8.03 1
KENO-VI:
.. code-block::scale
UNIT 4
CUBOID 1 2P6.59 2P13.18 2P12.45
CUBOID 2 2P6.59 2P21.75 2P20.48
ARRAY 2 1 PLACE 1 1 1 0.0 -6.59 -6.225
MEDIA 0 1 2 -1
BOUNDARY 2
Now that ``UNIT`` 3 and ``UNIT`` 4 have been defined, they must be
placed in the global or universe ``ARRAY`` to define the physical
arrangement of the eight pieces. This procedure is implemented via a
``GLOBAL`` ``ARRAY`` in KENO V.a, while KENO-VI uses a ``GLOBAL UNIT`` 3
as follows:
KENO V.a:
.. code-block:: scale
GBL=3 ARA=3 NUX=2 NUY=1 NUZ=1 FILL 4 3 END FILL
KENO-VI:
.. code-block:: scale
GLOBAL UNIT 5
CUBOID 1 34.93 0.0 43.5 0.0 40.96 0.0
ARRAY 3 1 PLACE 1 1 1 6.59 21.75 20.48
BOUNDARY 1
The description of ``ARRAY`` 3 in KENO-VI is identical to that shown for
KENO V.a.
This completes the geometry description for the problem. The complete
geometry input description for the problem is given below.
KENO V.a:
.. code-block:: scale
=KENOVA
SAMPLE PROBLEM 19 4 AQUEOUS 4 METAL ARRAY OF ARRAYS
READ PARAM LIB=4 RUN=NO END PARAM
READ MIXT SCT=1
MIX=1
1092238 3.2275e-3
1092235 4.4802e-2
MIX=2
20011023 5.81e-2
2007014 1.9753e-3
2008016 3.6927e-2
20092235 9.8471e-4
20092238 7.7697e-5
MIX=3
11006012 3.5552e-2
11011023 5.6884e-2
11008016 1.4221e-2
END MIXT
READ GEOM
UNIT 1
CYLINDER 2 1 9.525 8.89 -8.89
CYLINDER 3 1 10.16 2P9.525
CUBOID 0 1 4P10.875 2P10.24
UNIT 2
CYLINDER 1 1 5.748 2P5.3825
CUBOID 0 1 4P6.59 2P6.225
UNIT 3
ARRAY 1 3*0.0
UNIT 4
ARRAY 2 3*0.0
REPLICATE 0 1 2*0.0 2*8.57 2*8.03 1
END GEOM
READ ARRAY
ARA=1 NUX=1 NUY=2 NUZ=2 FILL F1 END FILL
ARA=2 NUX=1 NUY=2 NUZ=2 FILL F2 END FILL
GBL=3 ARA=3 NUX=2 NUY=1 NUZ=1 FILL 4 3 END FILL
END ARRAY
READ PLOT TTL='X-Y SLICE AT Z=10.24'
XUL=-1.0 YUL=44.5 ZUL=10.24
XLR=35.93 YLR=-1.0 ZLR=10.24
UAX=1.0 VDN=-1.0 NAX=640 PIC=MIX END
TTL='X-Z SLICE AT Y=10.875'
XUL=-1.0 YUL=10.875 ZUL=41.96 XLR=35.93 YLR=10.875 ZLR=-1.0
UAX=1.0 WDN=-1.0 PIC=MIX END END PLOT
END DATA
END
KENO-VI:
.. code-block:: scale
=KENO-VI
SAMPLE PROBLEM 19 4 AQUEOUS 4 METAL ARRAY OF ARRAYS
READ PARAM
LIB=4 FLX=YES FDN=YES NUB=YES SMU=YES MKP=YES MKU=YES FMP=YES FMU=YES
END PARAM
READ MIXT
SCT=2
MIX=1
1092234 4.82717E-04
1092235 4.47971E-02
1092236 9.57233E-05
1092238 2.65767E-03
MIX=2
2001001 5.77931E-02
2007014 2.13092E-03
2008016 3.74114E-02
2092234 1.06784E-05
2092235 9.84602E-04
2092236 5.29386E-06
2092238 6.19414E-05
MIX=3
11001001 5.67873E-02
11006000 3.54921E-02
11008016 1.41968E-02
END MIXT
READ GEOM
UNIT 1
CYLINDER 1 9.525 2P8.89
CYLINDER 2 10.16 2P9.525
CUBOID 3 4P10.875 2P10.24
MEDIA 2 1 1
MEDIA 3 1 2 -1
MEDIA 0 1 3 -2
BOUNDARY 3
UNIT 2
CYLINDER 1 5.748 2P5.3825
CUBOID 2 4P6.59 2P6.225
MEDIA 1 1 1
MEDIA 0 1 2 -1
BOUNDARY 2
UNIT 3
CUBOID 1 2P10.875 2P21.75 2P20.48
ARRAY 1 1 PLACE 1 1 1 0.0 -10.875 -10.24
BOUNDARY 1
UNIT 4
CUBOID 1 2P6.59 2P13.18 2P12.45
CUBOID 2 2P6.59 2P21.75 2P20.48
ARRAY 2 1 PLACE 1 1 1 0.0 -6.59 -6.225
MEDIA 0 1 2 -1
BOUNDARY
GLOBAL UNIT 5
CUBOID 1 34.93 0.0 43.5 0.0 40.96 0.0
ARRAY 3 1 PLACE 1 1 1 6.59 21.75 20.48
BOUNDARY 1
END GEOM
READ ARRAY
ARA=1 NUX=1 NUY=2 NUZ=2 FILL F1 END FILL
ARA=2 NUX=1 NUY=2 NUZ=2 FILL F2 END FILL
GBL=3 ARA=3 NUX=2 NUY=1 NUZ=1 FILL 4 3 END FILL
END ARRAY
READ PLOT TTL='X-Y SLICE AT Z=10.24'
XUL=-1.0 YUL=44.5 ZUL=10.24
XLR=35.93 YLR=-1.0 ZLR=10.24
UAX=1.0 VDN=-1.0 NAX=130 NCH=' *.-' PIC=MIX END
TTL='X-Z SLICE AT Y=10.875'
XUL=-1.0 YUL=10.875 ZUL=41.96
XLR=35.93 YLR=10.875 ZLR=-1.0
UAX=1.0 WDN=-1.0 PIC=MIX END
END PLOT
END DATA
END
A plot of an X-Y slice taken through the bottom layer of the array is
shown in :numref:`fig8-1-24`. A plot of an X-Z slice taken through the +Y half
of the array is shown in :numref:`fig8-1-25`. These plots were used to verify
the geometry mockup.
.. figure:: figs/Keno/fig24.png
:align: center
:width: 400
:name: fig8-1-24
X-Y plot of mixed array.
.. figure:: figs/Keno/fig25.png
:align: center
:width: 400
:name: fig8-1-25
X-Z plot of mixed array.
.. centered:: STORAGE ARRAY
EXAMPLE 18. Consider a storage array of highly enriched uranium buttons,
each 1 in. tall and 4 in. in diameter. These buttons are stored on
stainless steel shelves with a center-to-center spacing of 60.96 cm
(2 ft) between them in the Y direction, and only one button on each
shelf in the X direction. The shelves are 0.635 cm
(:sup:`1`/:sub:`4`\ in.) thick (Z dimension), 45.72 cm (18 in.) wide (X
dimension), 609.6 cm (20 ft) long (Y dimension), and are 45.72 cm
(18 in.) from the top of a shelf to the bottom of the shelf above it.
Each rack of storage shelves is four shelves high, with the first shelf
being 15.24 cm (6 in.) above the floor. The storage room is 586.56 cm
(19.5 ft) in the X direction by 1293.44 cm (43 ft) in the Y direction
with 365.76 cm (12 ft. ) ceilings in the Z direction. The walls,
ceiling, and floor are composed of concrete, 30.48 cm (1 ft) thick. All
the aisles between the storage racks are 91.44 cm (3 ft) wide. The racks
are arranged with their length in the Y direction and an aisle between
them. The arrays of racks are arranged with two in the Y direction and
five in the X direction. Mixture 1 is the uranium metal, mixture 2 is
the stainless steel, and mixture 3 is the concrete.
The metal button and its center-to-center spacing are described first.
The void vertical spacing has arbitrarily been chosen to extend from the
bottom of the button to the next shelf above the button. The shelf of
stainless steel is described under the button.
KENO V.a:
.. code-block:: scale
UNIT 1
COM='METAL BUTTONS'
CYLINDER 1 1 5.08 2.54 0.0
CUBOID 0 1 2P22.86 2P30.48 45.72 0.0
CUBOID 2 1 2P22.86 2P30.48 45.72 -0.635
KENO-VI:
.. code-block::scale
UNIT 1
CYLINDER 1 5.08 2.54 0.0
CUBOID 2 2P22.86 2P30.48 45.72 0.0
CUBOID 3 2P22.86 2P30.48 45.72 -0.635
MEDIA 1 1 1
MEDIA 0 1 2 -1
MEDIA 2 1 3 -2
BOUNDARY 3
``ARRAY`` 1 creates an ``ARRAY`` of these buttons that fills one shelf.
``UNIT`` 2 then contains one of the shelves shown in :numref:`fig8-1-26`.
.. figure:: figs/Keno/fig26.png
:align: center
:width: 400
:name: fig8-1-26
Two racks of uranium buttons.
KENO V.a:
.. code-block:: scale
ARA=1 COM='SINGLE SHELF CONTAINING 10 METAL BUTTONS'
NUX=1 NUY=10 NUZ=1 FILL F1 END FILL
UNIT 2
COM='SINGLE SHELF (1 X 10 X 1 ARRAY OF METAL BUTTONS ON A SHELF)'
ARRAY 1 3*0.0
KENO-VI:
.. code-block:: scale
ARA=1 NUX=1 NUY=10 NUZ=1 FILL F1 END FILL
UNIT 2
CUBOID 1 45.72 0.0 609.60 0.0 46.355 0.0
ARRAY 1 1 PLACE 1 1 1 22.86 30.48 0.635
BOUNDARY 1
.. note:: The origin of ``UNIT`` 2 is on the bottom of the bottom shelf; it
has been moved from the bottom of the button. The X and Y position of
the origin is at the front, left-hand corner of the bottom of this
lowest shelf.
Stack four ``UNIT`` 2s vertically to obtain one of the racks shown in
:numref:`fig8-1-26`. One rack is defined by array 2.
.. code-block:: scale
ARA=2 COM='SINGLE RACK OF 4 SHELVES'
NUX=1 NUY=1 NUZ=4 FILL F2 END FILL
Generate a ``UNIT`` 3 that contains a rack of shelves and a ``UNIT`` 4
that is the aisle between the ends of the two racks in the Y direction.
KENO V.a:
.. code-block:: scale
UNIT 3
COM='SINGLE RACK (4 SHELVES TALL)'
ARRAY 2 3*0.0
UNIT 4
COM='CENTRAL AISLE UNIT SAME HEIGHT AS 4 SHELVES'
CUBOID 0 1 2P22.86 2P45.72 185.42 0.0
KENO-VI:
.. code-block:: scale
UNIT 3
CUBOID 1 45.72 0.0 609.60 0.0 185.42 0.0
ARRAY 2 1 PLACE 1 1 1 3*0.0
BOUNDARY 1
UNIT 4
CUBOID 1 2P22.86 2P45.72 185.42 0.0
MEDIA 0 1 1
BOUNDARY 1
Stack ``UNIT``\ s 3 and 4 together in the Y direction to create
``UNIT`` 5 which contains both racks in the Y direction and the aisle
between them. This configuration is shown in :numref:`fig8-1-26`.
KENO V.a:
.. code-block:: scale
ARA=3 COM='TWO RACKS END TO END WITH CENTRAL AISLE'
NUX=1 NUY=3 NUZ=1 FILL 3 4 3 END FILL
UNIT 5
COM='SET OF TWO RACKS END TO END SEPARATED BY THE CENTRAL AISLE'
ARRAY 3 3*0.0
KENO-VI:
.. code-block:: scale
ARA=3 NUX=1 NUY=3 NUZ=1 FILL 3 4 3 END FILL
UNIT 5
CUBOID 1 45.72 0.0 1310.64 0.0 185.42 0.0
ARRAY 3 1 PLACE 1 1 1 3*0.0
BOUNDARY 1
Create a ``UNIT`` 6, which is an aisle 91.44 cm (3 ft) wide in the
X direction and 1310.64 cm (43 ft) in the Y direction (full length of
the room).
KENO V.a:
.. code-block:: scale
UNIT 6
COM='AISLE BETWEEN ADJACENT SETS OF TWO RACKS & CENTRAL AISLE (UNITS 5)'
CUBOID 0 1 91.44 0.0 1310.64 0.0 185.42 0.0
KENO-VI:
.. code-block:: scale
UNIT 6
CUBOID 1 91.44 0.0 1310.64 0.0 185.42 0.0
MEDIA 0 1 1
BOUNDARY 1
Stack ``UNIT``\ s 5 and 6 in the X direction to achieve the array of
racks in the room. Then put the 6 in. spacing below the bottom of the
racks, the spacing between the top of the top rack and the ceiling, and
add the concrete floor, walls, and ceiling around the array. ``ARRAY`` 4
describes the array of racks in the room. ``ARRAY`` record (first
``CUBOID`` description in KENO-VI) encompasses this ``ARRAY``, and the
first ``REFLECTOR`` (second ``CUBOID`` in KENO-VI) descriptions are used
to add the spacing between the top rack and the ceiling. The last two
``REFLECTOR`` (``CUBOID``\ s 3 through 9 in KENO-VI) descriptions add
the ceiling, walls, and floor in 5.0 cm increments to bias the concrete.
A perspective of the room is shown in :numref:`fig8-1-27`.
KENO V.a:
.. code-block:: scale
ARA=4 COM='ENTIRE STORAGE ARRAY'
NUX=9 NUY=1 NUZ=1 FILL 5 6 3Q2 5 END FILL
GLOBAL
UNIT 7
COM='STORAGE ARRAY IN THE ROOM WITH WALLS, FLOOR AND CEILING'
ARRAY 4 3*0.0
REFLECTOR 0 1 4*0.0 165.1 15.24 1
REFLECTOR 3 2 6*5.0 6
REFLECTOR 3 8 6*0.48 1
KENO-VI:
.. code-block:: scale
GBL=4 ARA=4 NUX=9 NUY=1 NUZ=1 FILL 5 6 3Q2 5 END FILL
GLOBAL UNIT 7
CUBOID 1 594.36 0.0 1310.64 0.0 185.42 0.0
CUBOID 2 594.36 0.0 1310.64 0.0 350.52 -15.24
CUBOID 3 599.36 -5.00 1315.64 -5.00 355.52 -20.24
CUBOID 4 604.36 -10.00 1320.64 -10.00 360.52 -25.24
CUBOID 5 609.36 -15.00 1325.64 -15.00 365.52 -30.24
CUBOID 6 614.36 -20.00 1330.64 -20.00 370.52 -35.24
CUBOID 7 619.36 -25.00 1335.64 -25.00 375.52 -40.24
CUBOID 8 624.36 -30.00 1340.64 -30.00 380.52 -45.24
CUBOID 9 624.84 -30.48 1341.12 -30.48 381.00 -45.72
ARRAY 4 1 PLACE 1 1 1 3*0.0
MEDIA 0 1 2 -1
MEDIA 3 2 3 -2
MEDIA 3 3 4 -3
MEDIA 3 4 5 -4
MEDIA 3 5 6 -5
MEDIA 3 6 7 -6
MEDIA 3 7 8 -7
MEDIA 3 8 9 -8
BOUNDARY 9
.. figure:: figs/Keno/fig27.png
:align: center
:width: 400
:name: fig8-1-27
Entire storage array in the room.
The complete input for this room is given below: The plots for this
problem must be quite large in order to see all the detail because the
array is sparse and the shelves are thin. Therefore, the plots for this
system are not included as Fig.s. The user can generate the plots if it
is desirable to see them. The nuclide IDs used in this problem are for
the 16-group Hansen-Roach working format library, which is no longer
distributed with SCALE.
KENO V.a:
.. code-block:: scale
=KENO5A
STORAGE ARRAY
READ PARAMETERS FDN=YES LIB=41
END PARAMETERS
READ MIXT SCT=1 MIX=1 92500 4.48006e-2 92800 2.6578e-3 92400 4.827e-4
92600 9.57e-5 MIX=2 200 1.0 MIX=3 301 1 END MIXT
READ GEOMETRY
UNIT 1
COM='METAL BUTTONS'
CYLINDER 1 1 5.08 2.54 0.0
CUBOID 0 1 2P22.86 2P30.48 45.72 0.0
CUBOID 2 1 2P22.86 2P30.48 45.72 -0.635
UNIT 2
COM='SINGLE SHELF (1 X 10 X 1 ARRAY OF METAL BUTTONS ON A SHELF)'
ARRAY 1 3*0.0
UNIT 3
COM='SINGLE RACK (4 SHELVES TALL)'
ARRAY 2 3*0.0
UNIT 4
COM='CENTRAL AISLE UNIT SAME HEIGHT AS 4 SHELVES'
CUBOID 0 1 2P22.86 2P45.72 185.42 0.0
UNIT 5
COM='SET OF TWO RACKS END TO END SEPARATED BY THE CENTRAL AISLE'
ARRAY 3 3*0.0
UNIT 6
COM='AISLE BETWEEN ADJACENT SETS OF TWO RACKS & CENTRAL AISLE (UNITS 5)'
CUBOID 0 1 91.44 0.0 1310.64 0.0 185.42 0.0
GLOBAL
UNIT 7
COM='STORAGE ARRAY IN THE ROOM WITH WALLS, FLOOR AND CEILING'
ARRAY 4 3*0.0
REFLECTOR 0 1 4*0.0 165.1 15.24 1
REFLECTOR 3 2 6*5.0 6
REFLECTOR 3 8 6*0.48 1
END GEOMETRY
READ ARRAY
ARA=1 COM='SINGLE SHELF CONTAINING 10 METAL BUTTONS'
NUX=1 NUY=10 NUZ=1 FILL F1 END FILL
ARA=2 COM='SINGLE RACK OF 4 SHELVES'
NUX=1 NUY=1 NUZ=4 FILL F2 END FILL
ARA=3 COM='TWO RACKS END TO END WITH CENTRAL AISLE'
NUX=1 NUY=3 NUZ=1 FILL 3 4 3 END FILL
ARA=4 COM='ENTIRE STORAGE ARRAY'
NUX=9 NUY=1 NUZ=1 FILL 5 6 3Q2 5 END FILL
END ARRAY
READ BIAS ID=301 2 8 END BIAS
READ START NST=5 NBX=5 END START
READ PLOT TTL='X-Z SLICE AT Y=30.48 WITH Z ACROSS AND X DOWN'
XUL=594.8 YUL=30.48 ZUL=-1.0 XLR=-0.5 YLR=30.48 ZLR=186.0
WAX=1.0 UDN=-1.0 NAX=640 END
TTL='Y-Z SLICE OF LEFT RACKS, X=22.86 WITH Z ACROSS AND Y DOWN'
XUL=22.86 YUL=1311.0 ZUL=-0.5 XLR=22.86 YLR=-3.0 ZLR=186.0
WAX=1.0 VDN=-1.0 NAX=640 END
TTL='X-Y SLICE OF ROOM THROUGH SHELF Z=0.3175 WITH X ACROSS AND Y DOWN'
XUL=-1.0 YUL=1312.0 ZUL=0.3175 XLR=596.0 YLR=-2.5 ZLR=0.3175
UAX=1.0 VDN=-1.0 NAX=320 END
END PLOT
END DATA
END
KENO-VI:
.. code-block:: scale
=KENOVI
STORAGE ARRAY
READ PARAMETERS FDN=YES LIB=41 END PARAMETERS
READ MIXT SCT=1
MIX=1 92500 4.48006e-2 92800 2.6578e-3 92400 4.827e-4 92600 9.57e-5
MIX=2 200 1.0 MIX=3 301 1
END MIXT
READ GEOMETRY
UNIT 1
CYLINDER 1 5.08 2.54 0.0
CUBOID 2 2P22.86 2P30.48 45.72 0.0
CUBOID 3 2P22.86 2P30.48 45.72 -.635
MEDIA 1 1 1
MEDIA 0 1 2 -1
MEDIA 2 1 3 -2
BOUNDARY 3
UNIT 2
CUBOID 1 45.72 0.0 609.60 0.0 46.355 0.0
ARRAY 1 1 PLACE 1 1 1 22.86 30.48 0.635
BOUNDARY 1
UNIT 3
CUBOID 1 45.72 0.0 609.60 0.0 185.42 0.0
ARRAY 2 1 PLACE 1 1 1 3*0.0
BOUNDARY 1
UNIT 4
CUBOID 1 2P22.86 2P45.72 185.42 0.0
MEDIA 0 1 1
BOUNDARY 1
UNIT 5
CUBOID 1 45.72 0.0 1310.64 0.0 185.42 0.0
ARRAY 3 1 PLACE 1 1 1 3*0.0
BOUNDARY 1
UNIT 6
CUBOID 1 91.44 0.0 1310.64 0.0 185.42 0.0
MEDIA 0 1 1
BOUNDARY 1
GLOBAL UNIT 7
CUBOID 1 594.36 0.0 1310.64 0.0 185.42 0.0
CUBOID 2 594.36 0.0 1310.64 0.0 350.52 -15.24
CUBOID 3 599.36 -5.00 1315.64 -5.00 355.52 -20.24
CUBOID 4 604.36 -10.00 1320.64 -10.00 360.52 -25.24
CUBOID 5 609.36 -15.00 1325.64 -15.00 365.52 -30.24
CUBOID 6 614.36 -20.00 1330.64 -20.00 370.52 -35.24
CUBOID 7 619.36 -25.00 1335.64 -25.00 375.52 -40.24
CUBOID 8 624.36 -30.00 1340.64 -30.00 380.52 -45.24
CUBOID 9 624.84 -30.48 1341.12 -30.48 381.00 -45.72
ARRAY 4 1 PLACE 1 1 1 3*0.0
MEDIA 0 1 2 -1
MEDIA 3 2 3 -2
MEDIA 3 3 4 -3
MEDIA 3 4 5 -4
MEDIA 3 5 6 -5
MEDIA 3 6 7 -6
MEDIA 3 7 8 -7
MEDIA 3 8 9 -8
BOUNDARY 9
END GEOMETRY
READ ARRAY
ARA=1 NUX=1 NUY=10 NUZ=1 FILL F1 END FILL
ARA=2 NUX=1 NUY=1 NUZ=4 FILL F2 END FILL
ARA=3 NUX=1 NUY=3 NUZ=1 FILL 3 4 3 END FILL
GBL=4 ARA=4 NUX=9 NUY=1 NUZ=1 FILL 5 6 3Q2 5 END FILL
END ARRAY
READ BIAS ID=301 2 8 END BIAS
READ START NST=5 NBX=5 END START
READ PLOT PLT=YES TTL='X-Z SLICE AT Y=30.48 WITH Z ACROSS AND X DOWN'
XUL=594.8 YUL=30.48 ZUL=-1.0 XLR=-0.5 YLR=30.48 ZLR=186.0
WAX=1.0 UDN=-1.0 NAX=640 END
TTL='Y-Z SLICE OF LEFT RACKS, X=22.86 WITH Z ACROSS AND Y DOWN'
XUL=22.86 YUL=1311.0 ZUL=-0.5 XLR=22.86 YLR=-3.0 ZLR=186.0
WAX=1.0 VDN=-1.0 NAX=640 END
TTL='X-Y SLICE OF ROOM THROUGH SHELF Z=0.3175 WITH X ACROSS AND Y DOWN'
XUL=-1.0 YUL=1312.0 ZUL=0.3175 XLR=596.0 YLR=-2.5 ZLR=0.3175
UAX=1.0 VDN=-1.0 NAX=320 END
END PLOT
END DATA
END
.. _8-1-3-6-4:
Arrays and holes
^^^^^^^^^^^^^^^^
:numref:`sec-module.keno.geom.holes` and :numref:`sec-module.keno.geom.nesting_holes` describe the use of ``HOLE``\ s, and
:numref:`8-1-3-6-3` describes multiple ``ARRAY``\ s and ``ARRAY``\ s of
``ARRAY``\ s. ``HOLE``\ s can be used to place ``ARRAY``\ s at locations
in other ``UNIT``\ s. This section contains examples to illustrate the
combined use of ``ARRAY``\ s and ``HOLE``\ s.
.. centered:: EXAMPLE 19. A SIMPLE CASK
This example consists of cylindrical mild steel container with an inside
radius of 4.15 cm and a radial wall thickness of 0.45 cm. The thickness
of the ends of the container is 1.27 cm, and the inside height is
10.1 cm. Highly enriched uranium rods 1 cm in diameter and 10 cm long
are banded together into square bundles of four. These bundles are then
positioned in the mild steel container as shown in :numref:`fig8-1-28`. The rods
sit on the floor of the container and have a 0.1 cm gap between their
tops and the top of the container.
.. figure:: figs/Keno/fig28.png
:align: center
:width: 400
:name: fig8-1-28
Uranium rods in a cylindrical container.
To generate the geometry description for this system, ``UNIT`` 1 is
defined as one uranium rod and its associated square-pitch close-packed
spacing region.
KENO V.a:
.. code-block:: scale
UNIT 1
CYLINDER 1 1 0.5 2P5.0
CUBOID 0 1 4P0.5 2P5.0
KENO-VI:
.. code-block:: scale
UNIT 1
CYLINDER 1 0.5 2P5.0
CUBOID 2 4P0.5 2P5.0
MEDIA 1 1 1
MEDIA 0 1 2 -1
BOUNDARY 2
From here, the geometry description diverges between KENO V.a and KENO-VI.
KENO V.a:
``ARRAY`` 1 is defined to be the central square ``ARRAY`` consisting of
four bundles of rods.
.. code-block:: scale
ARA=1 NUX=4 NUY=4 NUZ=1 FILL F1 END FILL
``ARRAY`` 2 is defined to be a bundle of four rods.
.. code-block:: scale
ARA=2 NUX=2 NUY=2 NUZ=1 FILL F1 END FILL
``ARRAY`` 2 is placed in ``UNIT`` 2. This defines the outer boundaries
of an imaginary ``CUBOID`` that contains the ``ARRAY``. It is convenient
to have the origin of the ``ARRAY`` at its center, so the most negative
point of the array will be (-1, -1,-5).
.. code-block:: scale
UNIT 2
ARRAY 2 -1.0 -1.0 -5.0
An ``ARRAY`` record is used to place ``ARRAY`` 1 in the ``GLOBAL UNIT``.
Then the cylindrical container is described around it and ``HOLE``\ s
are used to place the four outer bundles around the central ``ARRAY``.
.. code-block:: scale
GLOBAL UNIT 3
ARRAY 1 -2.0 -2.0 -5.0
CYLINDER 0 1 4.15 5.1 -5.0
HOLE 2 0.0 -3.0 0.0
HOLE 2 3.0 0.0 0.0
HOLE 2 0.0 3.0 0.0
HOLE 2 -3.0 0.0 0.0
CYLINDER 2 1 4.6 6.37 -6.27
The first ``HOLE`` places the bottom bundle of four rods, the second
``HOLE`` places the bundle of four rods at the right, the third ``HOLE``
places the top bundle of rods and the fourth ``HOLE`` places the left
bundle of rods.
KENO-VI:
Define ``UNIT`` 2 to be a void ``CUBOID`` with the same square pitch as
the rod square pitch.
``UNIT`` 2
``CUBOID`` 1 4P0.5 2P5.0
``MEDIA`` 0 1 1
``BOUNDARY`` 1
``ARRAY`` 1 is defined to be the central square 10 :math:`\times` 10 ``ARRAY``
consisting of 32 rods and 68 void positions that can be used to
represent the array shown in :numref:`fig8-1-28`.
.. code-block:: scale
ARA=1 NUX=10 NUY=10 NUZ=1
FILL 14*2 1 1 8*2 1 1 7*2 4*1 4*2 8*1 2 2 8*1 4*2 4*1 7*2 1 1 8*2 1 1 14*2
END FILL
``ARRAY`` 1 is placed in ``UNIT`` 3. The first ``CYLINDER`` card defines
the ``ARRAY`` ``BOUNDARY``. Everything external to this boundary is not
considered part of the problem. The positions in the ``ARRAY`` that do
not contain rods are filled with cuboids consisting of void. The
``ARRAY`` boundary must either coincide with the outer boundary of the
``ARRAY`` or be contained within the ``ARRAY``. An exterior void region
is placed around the array boundary to coincide with the size of the
interior radius of the container. The 10 :math:`\times` 10 ``ARRAY`` with the
``ARRAY`` boundary is shown in :numref:`fig8-1-29`.
.. code-block:: scale
UNIT 3
CYLINDER 1 4.15 5.0 -5.0
CYLINDER 2 4.15 5.1 -5.0
ARRAY 1 1 PLACE 5 5 1 -0.5 -0.5 -0.0
MEDIA 0 1 2 -1
BOUNDARY 2
.. figure:: figs/Keno/fig29.png
:align: center
:width: 400
:name: fig8-1-29
The 10 :math:`\times` 10 array of 32 uranium rods and 68 void cuboids with the array boundary.
The ``UNIT`` containing the ``ARRAY`` is now placed within the global
unit using a ``HOLE`` content record. The location of the ``HOLE`` is
determined using ``ORIGIN`` data to match the origin of the ``UNIT`` in
the ``HOLE`` with an X, Y, Z position in the surrounding ``UNIT``. In
this problem, the origin of the ``UNIT`` must be at position (0,0,0).
Since only nonzero data must be entered, ``ORIGIN`` data are not needed
for this problem. The boundary region consists of the steel container.
.. code-block:: scale
GLOBAL UNIT 4
CYLINDER 2 4.6 6.37 -6.27
HOLE 3 ORIGIN X=0.0 Y=0.0 Z=0.0
MEDIA 2 1 2
BOUNDARY 2
The overall problem description is shown below. Two of the color plots
used for verification of this mockup are shown in :numref:`fig8-1-30` and
:numref:`fig8-1-31`. The black outside border of the two color plots indicates
volume outside the global unit. The plot can be extended just outside
the global unit boundary to ensure that the entire problem is included
in the plot. This results in a black area surrounding the actual
problem.
KENO V.a:
.. code-block:: scale
=KENOVA
CASK ARRAY
READ PARAMETERS FDN=YES LIB=41 GEN=10
END PARAMETERS
READ MIXT SCT=1 MIX=1 92500 4.48006e-2 92800 2.6578e-3 92400 4.827e-4
92600 9.57e-5 MIX=2 100 1.0 END MIXT
READ GEOMETRY
UNIT 1
CYLINDER 1 1 0.5 2P5.0
CUBOID 0 1 4P0.5 2P5.0
UNIT 2
ARRAY 2 -1.0 -1.0 -5.0
GLOBAL UNIT 3
ARRAY 1 -2.0 -2.0 -5.0
CYLINDER 0 1 4.15 5.1 -5.0
HOLE 2 0.0 -3.0 0.0
HOLE 2 3.0 0.0 0.0
HOLE 2 0.0 3.0 0.0
HOLE 2 -3.0 0.0 0.0
CYLINDER 2 1 4.6 6.37 -6.27
END GEOM
READ ARRAY
ARA=1 NUX=4 NUY=4 NUZ=1 FILL F1 END FILL
ARA=2 NUX=2 NUY=2 NUZ=1 FILL F1 END FILL
END ARRAY
READ PLOT TTL='X-Z SLICE AT Y=0.25 WITH X ACROSS AND Z DOWN'
XUL=-5.0 YUL=0.25 ZUL=6.5 XLR=5.0 YLR=0.25 ZLR=-6.5
UAX=1.0 WDN=-1.0 NAX=640 END
TTL='X-Y SLICE AT Z=0.0 WITH X ACROSS AND Y DOWN'
XUL=-5.0 YUL=5.0 ZUL=0.0 XLR=5.0 YLR=-5.0 ZLR=0.0
UAX=1.0 VDN=-1.0 NAX=640 END
END PLOT
END DATA
END
KENO-VI:
.. code-block:: scale
KENO VI
CASK ARRAY
READ PARAMETERS TME=1.0 FDN=YES LIB=41 GEN=10 END PARAMETERS
READ MIXT SCT=1
MIX=1 92500 4.48006e-2 92800 2.6578e-3 92400 4.827e-4 92600 9.57e-5
MIX=2 100 1.0 END MIXT
READ GEOMETRY
UNIT 1
CYLINDER 1 0.5 2P5.0
CUBOID 2 4P0.5 2P5.0
MEDIA 1 1 1
MEDIA 0 1 2 -1
BOUNDARY 2
UNIT 2
CUBOID 1 4P0.5 2P5.0
MEDIA 0 1 1
BOUNDARY 1
UNIT 3
CYLINDER 1 4.15 5.0 -5.0
CYLINDER 2 4.15 5.1 -5.0
ARRAY 1 1 PLACE 5 5 1 -0.5 -0.5 -0.0
MEDIA 0 1 2 -1
BOUNDARY 2
GLOBAL UNIT 4
CYLINDER 2 4.6 6.37 -6.27
HOLE 3 ORIGIN X=0.0 Y=0.0 Z=0.0
MEDIA 2 1 2
BOUNDARY 2
END GEOM
READ ARRAY
ARA=1 NUX=10 NUY=10 NUZ=1 FILL 14*2 1 1 8*2 1 1 7*2 4*1 4*2 8*1 2 2 8*1 4*2 4*1 7*2 1 1
8*2 1 1 14*2 END FILL
END ARRAY
READ PLOT TTL='X-Z SLICE AT Y=0.25 WITH X ACROSS AND Z DOWN'
XUL=-5.0 YUL=0.25 ZUL=6.5 XLR=5.0 YLR=0.25 ZLR=-6.5
UAX=1.0 WDN=-1.0 NAX=640 END
TTL='X-Y SLICE AT Z=0.0 WITH X ACROSS AND Y DOWN'
XUL=-5.0 YUL=5.0 ZUL=0.0 XLR=5.0 YLR=-5.0 ZLR=0.0
UAX=1.0 VDN=-1.0 NAX=640 END
END PLOT
END DATA
END
.. figure:: figs/Keno/fig30.png
:align: center
:width: 400
:name: fig8-1-30
X-Y slice of uranium rods in a cylindrical container.
.. figure:: figs/Keno/fig31.png
:align: center
:width: 400
:name: fig8-1-31
X-Z slice of uranium rods in a cylindrical container.
.. centered:: EXAMPLE 20. A TYPICAL PRESSURIZED WATER REACTOR (PWR) SHIPPING CASK
A typical PWR shipping cask is illustrated in :numref:`fig8-1-32`. The interior
and exterior shell of the cask is carbon steel (mixture 7), and a
depleted uranium gamma shield (mixture 6) is present in the annulus
between the steel layers. The shipping cask contains seven PWR fuel
assemblies. Each assembly is a 17 :math:`\times` 17 ``ARRAY`` of fuel rods with water
holes. Each assembly is contained in a stainless steel (mixture 5) box.
Each fuel rod is composed of 4% enriched UO\ :sub:`2` (mixture 1) clad
with Zircaloy (mixture 2). Rods of B\ :sub:`4`\ C clad (mixture 4) with
stainless steel are positioned between the fuel assemblies. The entire
cask is filled with water (mixture 3).
.. figure:: figs/Keno/fig32.png
:align: center
:width: 400
:name: fig8-1-32
Typical PWR shipping cask.
To describe the geometry of the cask, some simple units are defined as
shown in :numref:`fig8-1-33`. ``UNIT`` 1 represents a fuel rod and its
associated square pitch spacing region. ``UNIT`` 2 represents a water
hole in a fuel assembly. ``UNIT``\ s 3, 4, and 6 represent the
B\ :sub:`4`\ C rods with their various spacings, and ``UNIT`` 5 is a
water hole that is used in association with some of the B\ :sub:`4`\ C
rods.
.. figure:: figs/Keno/fig33.png
:align: center
:width: 400
:name: fig8-1-33
Simple units.
KENO V.a:
.. code-block:: scale
UNIT 1
CYLINDER 1 1 .41148 365.76 0.0
CYLINDER 2 1 .48133 365.76 0.0
CUBOID 3 1 .63754 -.63754 .63754 -.63754 365.76 0.0
UNIT 2
CUBOID 3 1 .63754 -.63754 .63754 -.63754 365.76 0.0
UNIT 3
CYLINDER 4 1 .584 365.76 0.0
CYLINDER 5 1 .635 365.76 0.0
CUBOID 3 1 .9912 -.9912 2.2352 -1.27 365.76 0.0
UNIT 4
CYLINDER 4 1 .584 365.76 0.0
CYLINDER 5 1 .635 365.76 0.0
CUBOID 3 1 .9912 -.9912 1.2702 -2.235 365.76 0.0
UNIT 5
CUBOID 3 1 .9912 -.9912 1.7526 -1.7526 365.76 0.0
UNIT 6
CYLINDER 4 1 .584 365.76 0.0
CYLINDER 5 1 .635 365.76 0.0
CUBOID 3 1 1.1875215 -1.1875215 1.883706 -1.883706 365.76 0.0
KENO-VI:
.. code-block:: scale
UNIT 1
CYLINDER 1 .41148 365.76 0.0
CYLINDER 2 .48133 365.76 0.0
CUBOID 3 .63754 -.63754 .63754 -.63754 365.76 0.0
MEDIA 1 1 1
MEDIA 2 1 2 -1
MEDIA 3 1 3 -2
BOUNDARY 3
UNIT 2
CUBOID 1 .63754 -.63754 .63754 -.63754 365.76 0.0
MEDIA 3 1 1
BOUNDARY 1
UNIT 3
CYLINDER 1 .584 365.76 0.0
CYLINDER 2 .635 365.76 0.0
CUBOID 3 .9912 -.9912 2.2352 -1.27 365.76 0.0
MEDIA 4 1 1
MEDIA 5 1 2 -1
MEDIA 3 1 3 -2
BOUNDARY 3
UNIT 4
CYLINDER 1 .584 365.76 0.0
CYLINDER 2 .635 365.76 0.0
CUBOID 3 .9912 -.9912 1.2702 -2.235 365.76 0.0
MEDIA 4 1 1
MEDIA 5 1 2 -1
MEDIA 3 1 3 -2
BOUNDARY 3
UNIT 5
CUBOID 1 .9912 -.9912 1.7526 -1.7526 365.76 0.0
MEDIA 3 1 1
BOUNDARY 1
UNIT 6
CYLINDER 1 .584 365.76 0.0
CYLINDER 2 .635 365.76 0.0
CUBOID 3 1.1875215 -1.1875215 1.883706 -1.883706 365.76 0.0
MEDIA 4 1 1
MEDIA 5 1 2 -1
MEDIA 3 1 3 -2
BOUNDARY 3
``UNIT``\ s 1 and 2 are stacked together into ``ARRAY`` 1 to form the
``ARRAY`` of fuel pins and water holes in a fuel assembly as shown in
:numref:`fig8-1-34`. This ``ARRAY`` is then encompassed with a layer of water
and a layer of stainless steel to complete a fuel assembly in a storage
cell (``UNIT`` 7) as shown in :numref:`fig8-1-35`.
.. figure:: figs/Keno/fig34.png
:align: center
:width: 400
:name: fig8-1-34
Quarter section of fuel pin array.
.. figure:: figs/Keno/fig35.png
:align: center
:width: 400
:name: fig8-1-35
Quarter section of fuel assembly.
KENO V.a:
.. code-block:: scale
ARA=1 NUX=17 NUY=17 NUZ=1 FILL
39R1 2 2Q3 8R1 2 9R1 2 22R1 2 4Q3 38R1 2 4Q3
Q51 22R1 2 Q10 Q9 2Q3 39R1 END FILL
UNIT 7
ARRAY 1 -10.83818 -10.83818 0.0
CUBOID 3 1 11.112495 -11.112495 11.112495 -11.112495 365.76 0.0
CUBOID 8 1 11.302238 -11.302238 11.302238 -11.302238 365.76 0.0
KENO-VI:
.. code-block:: scale
ARA=1 NUX=17 NUY=17 NUZ=1 FILL
39R1 2 2Q3 8R1 2 9R1 2 22R1 2 4Q3 38R1 2 4Q3
Q51 22R1 2 Q10 Q9 2Q3 39R1 END FILL
UNIT 7
CUBOID 1 10.83818 -10.83818 10.83818 -10.83818 365.76 0.0
CUBOID 2 11.112495 -11.112495 11.112495 -11.112495 365.76 0.0
CUBOID 3 11.302238 -11.302238 11.302238 -11.302238 365.76 0.0
ARRAY 1 1 PLACE 9 9 1 3*0.0
MEDIA 3 1 2 -1
MEDIA 5 1 3 -2
BOUNDARY 3
An array of ``UNIT`` 6s is created to represent the array of
B\ :sub:`4`\ C rods that is positioned between the fuel assemblies. In
KENO V.a, the array of B\ :sub:`4`\ C rods shown in :numref:`fig8-1-36` is
contained in ``UNIT`` 8 for further use. KENO-VI geometry description
does not need the placement of ``ARRAY`` 2 in a separate ``UNIT``.
.. figure:: figs/Keno/fig36.png
:align: center
:width: 100
:name: fig8-1-36
2 :math:`\times` 6 array of B\ :sub:`4`\ C rods.
KENO V.a:
.. code-block:: scale
ARA=2 NUX=2 NUY=6 NUZ=1 FILL F6 END FILL
UNIT 8
ARRAY 2 0 0 0
KENO-VI:
.. code-block:: scale
ARA=2 NUX=2 NUY=6 NUZ=1 FILL F6 END FILL
The next step is to create the central array of three fuel assemblies
with B\ :sub:`4`\ C rods between them. In KENO V.a, this is done by
stacking fuel assemblies in storage cells (``UNIT`` 7) and
B\ :sub:`4`\ C rod arrays (``UNIT`` 8) into an array (``ARRAY`` 3) and
placing it in a ``UNIT`` (``UNIT`` 9). In KENO-VI description, ``UNIT``
7 (fuel assembly in storage cell) and the array of B\ :sub:`4`\ C rods
(``ARRAY`` 2) are directly placed into a ``UNIT`` (``UNIT`` 8). The
resultant geometry is shown in :numref:`fig8-1-37`.
.. figure:: figs/Keno/fig37.png
:align: center
:width: 400
:name: fig8-1-37
Central array.
KENO V.a:
.. code-block:: scale
ARA=3 NUX=5 NUY=1 NUZ=1 FILL 7 8 7 8 7 END FILL
UNIT 9 ARRAY 3 0 0 0
KENO-VI:
.. code-block:: scale
UNIT 8
CUBOID 4 -11.302238 -16.052324 11.302238 -11.302238 365.76 0.0
CUBOID 5 16.052324 11.302238 11.302236 -11.302236 365.76 0.0
CUBOID 6 38.052324 -38.052324 11.302236 -11.302236 365.76 0.0
HOLE 7
HOLE 7 ORIGIN X= -27.354562
HOLE 7 ORIGIN X= 27.354562
ARRAY 2 4 PLACE 1 1 1 -14.8648025 -9.418530 0.0
ARRAY 2 5 PLACE 1 1 1 12.4897595 -9.418530 0.0
MEDIA 3 1 6 -5 -4
BOUNDARY 6
``UNIT``\ s 3, 4, and 5 are used to define the arrays of B\ :sub:`4`\ C
rods that fit above and below the central array, as shown in
:numref:`fig8-1-38`.
.. figure:: figs/Keno/fig38.png
:align: center
:width: 400
:name: fig8-1-38
Long B\ :sub:`4`\ C rod arrays.
.. code-block:: scale
ARA=4 NUX=39 NUY=1 NUZ=1 FILL 3 5 2Q2 3 4 2Q2 5 4 3 2Q2 5 3 4 2Q2 5 4 3 2Q2 5 2Q2 3
END FILL
ARA=5 NUX=39 NUY=1 NUZ=1 FILL 4 5 2Q2 4 3 2Q2 5 3 4 2Q2 5 4 3 2Q2 5 3 4 2Q2 5 2Q2 4
END FILL
In KENO V.a these ``ARRAY``\ s are placed in ``UNIT``\ s (``UNIT``\ s 10
and 11) for further use.
KENO V.a:
.. code-block:: scale
UNIT 10 ARRAY 4 0 0 0
UNIT 11 ARRAY 5 0 0 0
``UNIT``\ s 9, 10, and 11 in the KENO V.a description, or ``UNIT`` 8 and
``ARRAY``\ s 3 and 4 in the KENO-VI description, are stacked to form the
central array with B\ :sub:`4`\ C rods as shown in :numref:`fig8-1-39`.
.. figure:: figs/Keno/fig39.png
:align: center
:width: 400
:name: fig8-1-39
Central array with long B\ :sub:`4`\ C arrays.
KENO V.a:
.. code-block:: scale
ARA=6 NUX=1 NUY=3 NUZ=1 FILL 11 9 10 END FILL
KENO-VI:
.. code-block:: scale
CUBOID 2 38.052324 -38.052324 14.807436 11.302236 365.76 0.0
CUBOID 3 38.052324 -38.052324 11.302236 -14.807436 365.76 0.0
HOLE 8
ARRAY 3 2 PLACE 20 1 1 0.0 13.054836 0.0
ARRAY 4 3 PLACE 20 1 1 0.0 13.054836 0.0
This completes the three central fuel assemblies and all the
B\ :sub:`4`\ C rods associated with them. Next, ``UNIT``\ s 7 and 8 in
KENO V.a geometry, ``UNIT`` 7 and ``ARRAY`` 2 in the KENO-VI geometry,
are stacked together to form the array of two fuel assemblies separated
by B\ :sub:`4`\ C rods as shown in :numref:`fig8-1-40`. This is designated as
``ARRAY`` 7 and ``UNIT`` 12 in KENO V.a, and ``UNIT`` 9 in KENO-VI. The
origin of ``UNIT`` 12 for KENO V.a is specified at the center of the
array in the X and Y directions and the bottom of the fuel assemblies
(Z=27.94 cm). The origin of ``UNIT`` 9 in the KENO-VI description is
specified at the center of the B\ :sub:`4`\ C array in the X and
Y directions and the bottom of the array in the Z direction.
.. figure:: figs/Keno/fig40.png
:align: center
:width: 400
:name: fig8-1-40
Two fuel assemblies and B\ :sub:`4`\ C rods.
KENO V.a:
.. code-block:: scale
ARA=7 NUX=3 NUY=1 NUZ=1 FILL 7 8 7 END FILL
UNIT 12 ARRAY 7 -24.979519 -11.302238 27.94
KENO-VI:
.. code-block:: scale
UNIT 9
CUBOID 1 2.375043 -2.375043 11.302236 -11.302236 365.76 0.0
CUBOID 4 24.979519 -23.7919975 11.302238 -11.302238 365.76 0.0
ARRAY 2 1 PLACE 1 1 1 -1.1875215 -9.418530 0.0
HOLE 7 ORIGIN X=-13.67728
HOLE 7 ORIGIN X=13.67728
MEDIA 0 1 4 -1
BOUNDARY 4
In KENO V.a, ``UNIT`` 13 is simply a cylindrical lid that fits on top of
the shipping cask. It is described relative to the origin of the
shipping cask and is made of depleted uranium.
KENO V.a:
::
UNIT 13
CYLINDER 6 1 47.625 457.2 449.58
All necessary subassemblies that make up the shipping cask have been
built. The shipping cask is completed by specifying the origin of the
central section (``ARRAY`` 6 in KENO V.a) (see :numref:`fig8-1-39`) to be at the
center of the array in X and Y and the bottom of the array in the Z
direction. A cylinder of water defining the interior of the shipping
cask is described around the array. In the KENO V.a geometry, a ``HOLE``
is used to place ``UNIT`` 12 (:numref:`fig8-1-40`) below the array, and a second
HOLE is used to place another ``UNIT`` 12 above the array. In the
KENO-VI geometry, ``UNIT`` 9 is placed as a ``HOLE`` above and below the
central array. Then a cylinder of steel is placed around the water,
which is in turn encased by depleted uranium. The depleted uranium is
then contained in the outer steel cylinder of the shipping cask. In KENO
V.a description, a third ``HOLE`` is used to place the depleted uranium
lid (``UNIT`` 13) on the shipping cask. This completes the shipping cask
description of :numref:`fig8-1-32`
The geometry data for this shipping cask are shown below. The plot data
have been included for verification of the geometry description.
However, the plot generated by this data is quite large and is therefore
not included in this document.
KENO V.a:
.. code-block:: scale
READ GEOM
UNIT 1
CYLINDER 1 1 .41148 365.76 0.0
CYLINDER 2 1 .48133 365.76 0.0
CUBOID 3 1 .63754 -.63754 .63754 -.63754 365.76 0.0
UNIT 2
CUBOID 3 1 .63754 -.63754 .63754 -.63754 365.76 0.0
UNIT 3
CYLINDER 4 1 .584 365.76 0.0
CYLINDER 5 1 .635 365.76 0.0
CUBOID 3 1 .9912 -.9912 2.2352 -1.27 365.76 0.0
UNIT 4
CYLINDER 4 1 .584 365.76 0.0
CYLINDER 5 1 .635 365.76 0.0
CUBOID 3 1 .9912 -.9912 1.2702 -2.235 365.76 0.0
UNIT 5
CUBOID 3 1 .9912 -.9912 1.7526 -1.7526 365.76 0.0
UNIT 6
CYLINDER 4 1 .584 365.76 0.0
CYLINDER 5 1 .635 365.76 0.0
CUBOID 3 1 1.1875215 -1.1875215 1.883706 -1.883706 365.76 0.0
UNIT 7 ARRAY 1 -10.83818 -10.83818 0.0
CUBOID 3 1 11.112495 -11.112495 11.112495 -11.112495 365.76 0.0
CUBOID 8 1 11.302238 -11.302238 11.302238 -11.302238 365.76 0.0
UNIT 8 ARRAY 2 0 0 0
UNIT 9 ARRAY 3 0 0 0
UNIT 10 ARRAY 4 0 0 0
UNIT 11 ARRAY 5 0 0 0
UNIT 12 ARRAY 7 -24.979519 -11.302238 27.94
UNIT 13
CYLINDER 6 1 47.625 457.2 449.58
ARRAY 6 -38.6568 -14.807438 27.94
CYLINDER 3 1 47.625 447.04 16.51
HOLE 12 0.0 -26.1097 0.0
HOLE 12 0.0 26.1097 0.0
CYLINDER 7 1 48.895 447.04 13.335
CYLINDER 6 1 59.06 447.04 3.81
CYLINDER 7 1 63.01 462.28 0.0
HOLE 13 0.0 0.0 0.0
END GEOM
READ ARRAY
ARA=1 NUX=17 NUY=17 NUZ=1 FILL
39R1 2 2Q3 8R1 2 9R1 2 22R1 2 4Q3 38R1 2 4Q3
Q51 22R1 2 Q10 Q9 2Q3 39R1 END FILL
ARA=2 NUX=2 NUY=6 NUZ=1 FILL F6 END FILL
ARA=3 NUX=5 NUY=1 NUZ=1 FILL 7 8 7 8 7 END FILL
ARA=4 NUX=39 NUY=1 NUZ=1 FILL 3 5 2Q2 3 4 2Q2 5 4 3 2Q2 5 3 4 2Q2
5 4 3 2Q2 5 2Q2 3 END FILL
ARA=5 NUX=39 NUY=1 NUZ=1 FILL 4 5 2Q2 4 3 2Q2 5 3 4 2Q2 5 4 3 2Q2
5 3 4 2Q2 5 2Q2 4 END FILL
ARA=6 NUX=1 NUY=3 NUZ=1 FILL 11 9 10 END FILL
ARA=7 NUX=3 NUY=1 NUZ=1 FILL 7 8 7 END FILL
END ARRAY
READ PLOT
TTL=? SHIPPING CASK IF-300 X-Y SLICE ?
XUL=-63 YUL=63 ZUL=180 XLR=63 YLR=-63 ZLR=180
UAX=1 VDN=-1 NAX=350
PLT=NO
END PLOT
KENO-VI:
.. code-block:: scale
READ GEOM
UNIT 1
CYLINDER 1 .41148 365.76 0.0
CYLINDER 2 .48133 365.76 0.0
CUBOID 3 .63754 -.63754 .63754 -.63754 365.76 0.0
MEDIA 1 1 1
MEDIA 2 1 2 -1
MEDIA 3 1 3 -2
BOUNDARY 3
UNIT 2
CUBOID 1 .63754 -.63754 .63754 -.63754 365.76 0.0
MEDIA 3 1 1
BOUNDARY 1
UNIT 3
CYLINDER 1 .584 365.76 0.0
CYLINDER 2 .635 365.76 0.0
CUBOID 3 .9912 -.9912 2.2352 -1.27 365.76 0.0
MEDIA 4 1 1
MEDIA 5 1 2 -1
MEDIA 3 1 3 -2
BOUNDARY 3
UNIT 4
CYLINDER 1 .584 365.76 0.0
CYLINDER 2 .635 365.76 0.0
CUBOID 3 .9912 -.9912 1.2702 -2.235 365.76 0.0
MEDIA 4 1 1
MEDIA 5 1 2 -1
MEDIA 3 1 3 -2
BOUNDARY 3
UNIT 5
CUBOID 1 .9912 -.9912 1.7526 -1.7526 365.76 0.0
MEDIA 3 1 1
BOUNDARY 1
UNIT 6
CYLINDER 1 .584 365.76 0.0
CYLINDER 2 .635 365.76 0.0
CUBOID 3 1.1875215 -1.1875215 1.883706 -1.883706 365.76 0.0
MEDIA 4 1 1
MEDIA 5 1 2 -1
MEDIA 3 1 3 -2
BOUNDARY 3
UNIT 7
CUBOID 1 10.83818 -10.83818 10.83818 -10.83818 365.76 0.0
CUBOID 2 11.112495 -11.112495 11.112495 -11.112495 365.76 0.0
CUBOID 3 11.302238 -11.302238 11.302238 -11.302238 365.76 0.0
ARRAY 1 1 PLACE 9 9 1 3*0.0
MEDIA 3 1 2 -1
MEDIA 8 1 3 -2
BOUNDARY 3
UNIT 8
CUBOID 4 -11.302238 -16.052324 11.302238 -11.302238 365.76 0.0
CUBOID 5 16.052324 11.302238 11.302236 -11.302236 365.76 0.0
CUBOID 6 38.052324 -38.052324 11.302236 -11.302236 365.76 0.0
HOLE 7
HOLE 7 ORIGIN X= -27.354562
HOLE 7 ORIGIN X= 27.354562
ARRAY 2 4 PLACE 1 1 1 -14.8648025 -9.418530 0.0
ARRAY 2 5 PLACE 1 1 1 12.4897595 -9.418530 0.0
MEDIA 0 1 6 -5 -4
BOUNDARY 6
UNIT 10
CUBOID 1 1.1875215 -1.1875215 11.302236 -11.302236 365.76 0.0
CUBOID 4 23.7919975 -23.7919975 11.302238 -11.302238 365.76 0.0
ARRAY 2 1 PLACE 1 1 1 3*0.0
HOLE 7 ORIGIN X=-12.4897595
HOLE 7 ORIGIN X=12.4897595
MEDIA 0 1 4 -1
BOUNDARY 4
GLOBAL UNIT 11
CUBOID 2 38.052324 -38.052324 13.284638 11.302236 365.76 0.0
CUBOID 3 38.052324 -38.052324 11.302236 -13.284638 365.76 0.0
CYLINDER 6 47.625 419.10 -11.43
CYLINDER 7 48.895 419.10 -14.605
CYLINDER 8 59.06 419.10 -24.13
CYLINDER 9 47.625 429.26 421.64
CYLINDER 10 63.01 434.34 -27.94
HOLE 8
ARRAY 3 2 PLACE 20 1 1 0.0 12.293438 0.0
ARRAY 4 3 PLACE 20 1 1 0.0 12.293438 0.0
HOLE 9 ORIGIN Y=24.586876
HOLE 9 ORIGIN Y=-24.586876
MEDIA 3 1 6 -3 -2
MEDIA 7 1 7 -6 -3 -2
MEDIA 6 1 8 -7
MEDIA 7 1 9
MEDIA 6 1 10 -9 -8
BOUNDARY 10
END GEOM
READ ARRAY
ARA=1 NUX=17 NUY=17 NUZ=1 FILL
39R1 2 2Q3 8R1 2 9R1 2 22R1 2 4Q3 38R1 2 4Q3
Q51 22R1 2 Q10 Q9 2Q3 39R1 END FILL
ARA=2 NUX=2 NUY=6 NUZ=1 FILL F6 END FILL
ARA=3 NUX=5 NUY=1 NUZ=1 FILL 7 8 7 8 7 END FILL
ARA=4 NUX=39 NUY=1 NUZ=1 FILL 3 5 2Q2 3 4 2Q2 5 4 3 2Q2 5 3 4 2Q2
5 4 3 2Q2 5 2Q2 3 END FILL
ARA=5 NUX=39 NUY=1 NUZ=1 FILL 4 5 2Q2 4 3 2Q2 5 3 4 2Q2 5 4 3 2Q2
5 3 4 2Q2 5 2Q2 4 END FILL
ARA=6 NUX=1 NUY=3 NUZ=1 FILL 11 9 10 END FILL
ARA=7 NUX=3 NUY=1 NUZ=1 FILL 7 8 7 END FILL
END ARRAY
READ PLOT
TTL=? SHIPPING CASK IF-300 X-Y SLICE ?
XUL=-63 YUL=63 ZUL=180 XLR=63 YLR=-63 ZLR=180
UAX=1 VDN=-1 NAX=350
PLT=NO
END PLOT
Triangular pitched arrays in KENO-VI
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.. centered:: EXAMPLE 21.
Triangular pitched ``ARRAY``\ s can be described in KENO-VI
by defining the ``UNIT``\ s that make up the ``ARRAY`` as ``HEXPRISM``
and in the array data block setting ``TYP``\ =TRIANGULAR, HEXAGONAL,
SHEXAGONAL, or RHEXAGONAL. This includes close-packed triangular pitched
arrays. Since the ``ARRAY``\ s are constructed by stacking hexprisms,
care must be taken to ensure that the ``ARRAY`` boundary is completely
enclosed within the stacked ``UNIT``. Below is an example of a
triangular pitched ``ARRAY``.
The first and second ``UNIT``\ s are the ``HEXPRISM``\ s that make up
the ``ARRAY``. ``UNIT`` 1 is the fuel cell stacked in a triangular
pitched or hexagonal lattice. ``UNIT`` 2 is a dummy ``UNIT`` used to
fill in the ``ARRAY`` so the array boundary is contained within the
stacked ``UNIT``\ s. Since the ``ARRAY`` is not moderated, ``UNIT`` 2
contains void. :numref:`fig8-1-41` shows an X-Y cross section schematic of
``UNIT``\ s 1 and 2.
.. figure:: figs/Keno/fig41.png
:align: center
:width: 400
:name: fig8-1-41
Fuel cell and empty cell set up as hexprisms.
.. code-block:: scale
UNIT 1
COM='SINGLE CELL FUEL CAN IN HEXPRISM'
CYLINDER 10 10.16 18.288 0.0
CYLINDER 20 10.312 18.288 -0.152
HEXPRISM 30 10.503 18.288 -0.152
MEDIA 1 1 10
MEDIA 2 1 20 -10
MEDIA 0 1 30 -20
BOUNDARY 30
UNIT 2
COM='EMPTY CELL'
HEXPRISM 10 10.503 18.288 -0.152
MEDIA 0 1 10
BOUNDARY 10
``UNIT`` 3 is the ``GLOBAL UNIT`` that contains the ``ARRAY`` and
``ARRAY BOUNDARY``. The ``ARRAY`` is an unmoderated triangular
pitched assembly of 7 cells. Unrotated triangular or hexagonal pitched
arrays can be set up in two array configurations. The first
configuration, selected using the ``TYP=`` followed by keyword
``HEXAGONAL`` or ``TRIANGULAR``, stacks the ``UNIT``\ s so that the
faces perpendicular to the X axis meet. Each consecutive row in the Y
direction begins :math:`1/2` of the face-to-face dimension farther over in the
positive X direction than in the previous row. The second configuration,
selected using the ``TYP=`` followed by keyword ``SHEXAGONAL``, also
stacks the ``UNIT``\ s so that the faces perpendicular to the X axis
meet. However, for this type of ``ARRAY``, the odd numbered rows in the
Y direction (1, 3, 5, etc.) begin at the left edge of the ``ARRAY``, and
the even numbered rows in the Y direction (2, 4, 6, etc.) begin :math:`1/2` of the
face-to-face dimension to the right of the left edge of the ``ARRAY``.
:numref:`fig8-1-42` and :numref:`fig8-1-43` show X-Y cross section schematics of the
assembly for the two different unrotated hexagonal ``ARRAY`` types.
.. code-block:: scale
GLOBAL UNIT 3
COM='7 CYLINDERS IN A CIRCLE WITH CYLINDRICAL BOUNDARY'
CYLINDER 10 32.000 18.288 -0.152
ARRAY 1 10 PLACE 3 3 1 3*0.0
BOUNDARY 10
READ ARRAY GBL=1 ARA=1 TYP=HEXAGONAL NUX=5 NUY=5 NUZ=1
FILL 7*2 2*1 2*2 3*1 2*2 2*1 7*2 END FILL END ARRAY
.. figure:: figs/Keno/fig42.png
:align: center
:width: 400
:name: fig8-1-42
Seven cylinders stacked in a HEXAGONAL array with cylindrical array boundary.
.. figure:: figs/Keno/fig43.png
:align: center
:width: 400
:name: fig8-1-43
Seven cylinders stacked in a SHEXAGONAL array with a cylindrical array boundary.
The overall problem description is shown below. The cross section
library would be generated in a separate CSAS-MG step. An X-Y cross
section color plot used for verification of this mockup is shown in
:numref:`fig8-1-44`.
.. figure:: figs/Keno/fig44.png
:align: center
:width: 400
:name: fig8-1-44
X-Y slice of 7 cylinders in a triangular pitch array.
Data description of Example 21.
.. code-block:: scale
=KENOVI
TRIANGULAR PITCHED ARRAY 7 PINS IN A CIRCLE
READ PARAMETERS LNG=20000 LIB=4 END PARAMETERS
READ MIXT SCT=2
MIX=1 NCM=8 92235 1.37751E-03 92238 9.92354E-05 8016 3.32049E-02
9019 2.95349E-03 1001 6.05028E-02
MIX=2 NCM=14 13027 6.02374E-02
END MIXT
READ GEOMETRY
UNIT 1
COM='SINGLE CELL FUEL CAN IN HEXPRISM'
CYLINDER 10 10.16 18.288 0.0
CYLINDER 20 10.312 18.288 -0.152
HEXPRISM 30 10.503 18.288 -0.152
MEDIA 1 1 10
MEDIA 2 1 20 -10
MEDIA 0 1 30 -20
BOUNDARY 30
UNIT 2
COM='EMPTY CELL'
HEXPRISM 10 10.503 18.288 -0.152
MEDIA 0 1 10
BOUNDARY 10
GLOBAL UNIT 3
CYLINDER 10 32.000 18.288 -0.152
COM='7 CYLINDERS IN A CIRCLE WITH CYLINDRICAL BOUNDARY'
ARRAY 1 10 PLACE 3 3 1 3*0.0
BOUNDARY 10
END GEOMETRY
READ ARRAY GBL=1 TYP=HEXAGONAL NUX=5 NUY=5 NUZ=1
FILL 7*2 2*1 2*2 3*1 2*2 2*1 7*2 END FILL END ARRAY
READ PLOT
TTL='TRIANGULAR PITCHED ARRAY, 7 PINS IN A CIRCLE'
XUL=-33.0 YUL=33.0 ZUL=0.0
XLR=33.0 YLR=-33.0 ZLR=0.0
UAX=1 VDN=-1 NAX=640 END
END PLOT
END DATA
END
.. centered:: EXAMPLE 21a.
Another hexagonal ``ARRAY`` type involves stacking rotated hexprisms,
which are hexprisms rotated 30\ :math:`^{\circ}`/ 90\ :math:`^{\circ}` so that the flat faces
perpendicular to the Y axis now meet. Rotated hexagonal arrays are
specified by setting ``TYP=RHEXAGONAL`` in the array data block.
Because the ``ARRAY``\ s are constructed by stacking hexprisms, care
must be taken to ensure the array boundary is completely enclosed within
the stacked ``UNIT``. Below is an example of a rotated hexagonal pitched
``ARRAY``.
The first and second ``UNIT``\ s are the rotated hexprisms that make up
the ``ARRAY``. They are specified using the geometry keyword
``RHEXPRISM``. ``UNIT`` 1 is the fuel cell that is stacked in a rotated
hexagonal lattice. ``UNIT`` 2 is a dummy ``UNIT`` used to fill in the
``ARRAY`` so that the ``ARRAY BOUNDARY`` is contained within the stacked
``UNIT``\ s. Since the ``ARRAY`` is not moderated, ``UNIT`` 2 contains
void. :numref:`fig8-1-45` shows an X-Y cross section schematic of ``UNIT``\ s 1
and 2.
.. figure:: figs/Keno/fig45.png
:align: center
:width: 400
:name: fig8-1-45
Fuel cell and empty cell set up as rotated hexprism (RHEXPRISM).
.. code-block:: scale
UNIT 1
COM='SINGLE CELL FUEL CAN IN HEXPRISM'
CYLINDER 10 10.16 18.288 0.0
CYLINDER 20 10.312 18.288 -0.152
RHEXPRISM 30 10.503 18.288 -0.152
MEDIA 1 1 10
MEDIA 2 1 20 -10
MEDIA 0 1 30 -20
BOUNDARY 30
UNIT 2
COM='EMPTY CELL'
RHEXPRISM 10 10.503 18.288 -0.152
MEDIA 0 1 10
BOUNDARY 10
``UNIT`` 3 is the ``GLOBAL UNIT`` that contains the ``ARRAY`` and
``ARRAY BOUNDARY``. The ``ARRAY`` is an unmoderated rotated hexagonal
pitched assembly of 7 cells. The rotated hexagonal array type is
specified in the array data block using ``TYP=`` with the keyword
``RHEXAGONAL``. This ``ARRAY`` type stacks the ``UNIT``\ s so the faces
perpendicular to the Y axis meet. In the odd numbered columns (i.e., 1,
3, 5, etc.), the ``UNIT``\ s are stacked so the columns begin at the
lower edge of the array and in the even numbered columns (i.e., 2, 4, 6,
etc.), the ``UNIT``\ s are stacked so the columns begin :math:`1/2` of the
face-to-face dimension above the lower edge of the ``ARRAY``.
:numref:`fig8-1-46` shows the X-Y cross section schematic of the assembly for
the rotated hexagonal ``ARRAY`` type.
.. figure:: figs/Keno/fig46.png
:align: center
:width: 400
:name: fig8-1-46
Seven cylinders stacked in a RHEXAGONAL array with a cylindrical array boundary.
.. code-block:: scale
GLOBAL UNIT 3
COM='7 CYLINDERS IN A CIRCLE WITH CYLINDRICAL BOUNDARY'
CYLINDER 10 32.000 18.288 -0.152
ARRAY 1 10 PLACE 3 3 1 3*0.0
BOUNDARY 10
READ ARRAY GBL=1 ARA=1 TYP=RHEXAGONAL NUX=5 NUY=5 NUZ=1
FILL 6*2 3*1 2*2 3*1 3*2 1*1 7*2 END FILL END ARRAY
The overall problem description is shown below. The cross section
library would be generated in a separate CSAS-MG step. An X-Y cross
section color plot used for verification of this mockup is shown in
:numref:`fig8-1-47`.
.. figure:: figs/Keno/fig47.png
:align: center
:width: 400
:name: fig8-1-47
X-Y slice of 7 cylinders in a rotated hexagonal pitched array.
Data description of Example 21a.
.. code-block:: scale
=KENOVI
TRIANGULAR PITCHED ARRAY 7 PINS IN A CIRCLE
READ PARAMETERS LNG=20000 LIB=4 END PARAMETERS
READ MIXT SCT=2
MIX=1 NCM=8 92235 1.37751E-03 92238 9.92354E-05 8016 3.32049E-02
9019 2.95349E-03 1001 6.05028E-02
MIX=2 NCM=14 13027 6.02374E-02
END MIXT
READ GEOMETRY
UNIT 1
COM='SINGLE CELL FUEL CAN IN HEXPRISM'
CYLINDER 10 10.16 18.288 0.0
CYLINDER 20 10.312 18.288 -0.152
RHEXPRISM 30 10.503 18.288 -0.152
MEDIA 1 1 10
MEDIA 2 1 20 -10
MEDIA 0 1 30 -20
BOUNDARY 30
UNIT 2
COM='EMPTY CELL'
RHEXPRISM 10 10.503 18.288 -0.152
MEDIA 0 1 10
BOUNDARY 10
GLOBAL UNIT 3
CYLINDER 10 32.000 18.288 -0.152
COM='7 CYLINDERS IN A CIRCLE WITH CYLINDRICAL BOUNDARY'
ARRAY 1 10 PLACE 3 3 1 3*0.0
BOUNDARY 10
END GEOMETRY
READ ARRAY GBL=1 TYP=RHEXAGONAL NUX=5 NUY=5 NUZ=1
FILL 6*2 3*1 2*2 3*1 3*2 1*1 7*2 END FILL END ARRAY
READ PLOT
TTL='ROTATED HEXAGONAL ARRAY, 7 PINS IN A CIRCLE'
XUL=-33.0 YUL=33.0 ZUL=0.0
XLR=33.0 YLR=-33.0 ZLR=0.0
UAX=1 VDN==-1 NAX=640 END
END PLOT
END DATA
END
Triangular pitched Arrays in KENO V.a
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Triangular pitched arrays can be described in KENO V.a geometry by
properly defining the basic unit from which the array can be built. This
includes close-packed triangular pitched arrays. Two geometry
configurations are described below.
.. centered:: EXAMPLE 1. Bare Triangular pitched Array.
:numref:`fig8-1-48` illustrates a small close-packed triangular pitched
``ARRAY``. Each rod in the ``ARRAY`` has a radius of 2.0 cm, and the
pitch of the ``ARRAY`` is 4 cm. To create this ``ARRAY``, describe five
units as defined in :numref:`fig8-1-49`.
Assume the rods described in the ``ARRAY`` are each 2.0 cm in radius and
100 cm tall. The rods are composed of mixture 1. The geometry
descriptions for the first four ``UNIT``\ s are given below.
.. code-block:: scale
UNIT 1
ZHEMICYL-Y 1 1 2.0 50.0 -50.0
UNIT 2
ZHEMICYL+Y 1 1 2.0 50.0 -50.0
UNIT 3
ZHEMICYL-X 1 1 2.0 50.0 -50.0
UNIT 4
ZHEMICYL+X 1 1 2.0 50.0 -50.0
.. figure:: figs/Keno/fig48.png
:align: center
:width: 400
:name: fig8-1-48
Bare triangular pitched ARRAY.
.. figure:: figs/Keno/fig49.png
:align: center
:width: 400
:name: fig8-1-49
Units used to describe a bare triangular pitched ARRAY.
To describe ``UNIT`` 5, the origin of the ``UNIT`` is defined to be at
its center. One of the hemicylinders is built into the box, and the
other three are added as holes. In this example, the +X hemicylinder is
built into the box, and the other hemicylinders are inserted as holes.
(Because the +X hemicylinder is built into ``UNIT`` 5, ``UNIT`` 4 is not
used in the problem.) The half dimension of the box in the X dimension
is equal to the radius, 2.0 cm. The half dimension of the box in the
Y direction is :math:`\frac{\sqrt{3}}{2}` times the pitch (0.866025 \* 4.0) or 3.46411 cm.
``UNIT`` 5 is described below.
.. code-block:: scale
UNIT 5
ZHEMICYL+X 1 1 2.0 50.0 -50.0 ORIGIN -2.0 0.0
CUBOID 0 1 2P2.0 2P3.46411 2P50.0
HOLE 1 0.0 3.46411 0.0
HOLE 2 0.0 -3.46411 0.0
HOLE 3 2.0 0.0
In the description of ``UNIT`` 5, the ``ZHEMICYL+X`` places the
hemicylinder at the left of the box. ``HOLE`` 1 places the top
hemicylinder, ``HOLE`` 2 places the bottom hemicylinder, and ``HOLE`` 3
places the hemicylinder at the right of the box.
Next, a ``UNIT`` 6 is defined that can be used to complete the lower rod
of ``UNIT`` 5. A ``UNIT`` 7 is defined that can be used to complete the
upper rod of ``UNIT`` 5. ``UNIT`` 8 is defined to complete the left rod
of ``UNIT`` 5, and ``UNIT`` 9 is defined to complete the right rod of
``UNIT`` 5. ``UNIT`` 10 is defined to complete the corners of the
overall ``ARRAY``. The input data for these ``UNIT``\ s are given below
and are illustrated in :numref:`fig8-1-50`.
.. figure:: figs/Keno/fig50.png
:align: center
:width: 400
:name: fig8-1-50
UNITs to complete the triangular pitched ARRAY.
.. code-block:: scale
UNIT 6
ZHEMICYL-Y 1 1 2.0 50.0 -50.0
CUBOID 0 1 2P2.0 0.0 -2.0 50.0 -50.0
UNIT 7
ZHEMICYL+Y 1 1 2.0 50.0 -50.0
CUBOID 0 1 2P2.0 2.0 0.0 2P50.0
UNIT 8
ZHEMICYL-X 1 1 2.0 50.0 -50.0
CUBOID 0 1 0.0 -2.0 2P3.46411 2P50.0
UNIT 9
ZHEMICYL+X 1 1 2.0 50.0 -50.0
CUBOID 0 1 2.0 0.0 2P3.46411 2P50.0
UNIT 10
CUBOID 0 1 2.0 0.0 2.0 0.0 2P50.0
:numref:`fig8-1-51` shows the arrangement of the ``UNIT``\ s to complete the
``ARRAY``. The data to describe the ``ARRAY`` are shown below.
.. code-block:: scale
ARA=1 NUX=6 NUY=4 NUZ=1
FILL 10 4R6 10 8 4R5 9 1Q6 10 4R7 10 END FILL
The bottom row of the ``ARRAY`` is described by the data entries
10 4R6 10. The second row of the ``ARRAY`` is described by the data
entries 8 4R5 9. The third row is filled by repeating the previous six
entries (1Q6). It could also have been described by entering 8 4R5 9.
The top row of the ``ARRAY`` is described by the data entries 10 4R7 10.
.. figure:: figs/Keno/fig51.png
:align: center
:width: 400
:name: fig8-1-51
Completed ARRAY.
.. centered:: EXAMPLE 2a. Triangular Pitched ARRAY in a Cylinder
:numref:`fig8-1-52` illustrates a close-packed triangular pitched **ARRAY** in a
cylinder. This array may be described by defining five basic units that
are the same as those of Example 1 shown in :numref:`fig8-1-49`.
.. figure:: figs/Keno/fig52.png
:align: center
:width: 400
:name: fig8-1-52
Triangular pitched ARRAY within a cylinder.
.. code-block:: scale
UNIT 1
ZHEMICYL-Y 1 1 2.0 50.0 -50.0
UNIT 2
ZHEMICYL+Y 1 1 2.0 50.0 -50.0
UNIT 3
ZHEMICYL-X 1 1 2.0 50.0 -50.0
UNIT 4
ZHEMICYL+X 1 1 2.0 50.0 -50.0
To describe ``UNIT`` 5, the origin of the ``UNIT`` to be at its center
is defined. One of the hemicylinders is built into the box, and the
other three are added as ``HOLE``\ s. In this example, the
+X hemicylinder is built into the box, and the other hemicylinders are
inserted as ``HOLE``\ s. The half dimension of the box in the
X dimension is equal to the radius, 2.0 cm. The half dimension of the
box in the Y direction is :math:`\frac{\sqrt{3}}{2}` times the pitch (0.866025 * 4.0) or
3.46411 cm. ``UNIT`` 5 is described below.
.. code-block:: scale
UNIT 5
ZHEMICYL+X 1 1 2.0 50.0 -50.0 ORIGIN -2.0 0.0
CUBOID 0 1 2P2.0 2P3.46411 2P50.0
HOLE 1 0.0 3.46411 0.0
HOLE 2 0.0 -3.46411 0.0
HOLE 3 2.0 0.0 0.0
In the description of ``UNIT`` 5, the ``ZHEMICYL+X`` places the
hemicylinder at the left of the box. ``HOLE`` 1 places the top
hemicylinder, ``HOLE`` 2 places the bottom hemicylinder, and ``HOLE`` 3
places the hemicylinder at the right of the box.
To describe the base ``ARRAY`` of the problem, ``UNIT``\ s 5 is stacked
in a 4 :math:`\times` 2 :math:`\times` 1 array as shown in :numref:`fig8-1-53`. The input data for the
``ARRAY`` are the following:
.. code-block:: scale
ARA=1 NUX=4 NUY=2 NUZ=1 FILL F5 END FILL
.. figure:: figs/Keno/fig53.png
:align: center
:width: 400
:name: fig8-1-53
4 :math:`\times` 2 :math:`\times` 1 array to be placed within a cylinder.
Next, the ``ARRAY`` is placed within the cylinder. This is done by
placing the ``ARRAY`` in a ``UNIT``, defined here to be ``UNIT`` 6. The
origin of the cylinder has been defined to be at the center of the
``ARRAY``. The resulting geometry is shown in :numref:`fig8-1-54`.
.. figure:: figs/Keno/fig54.png
:align: center
:width: 400
:name: fig8-1-54
4 :math:`\times` 2 :math:`\times` 1 ARRAY within a cylinder.
.. code-block:: scale
UNIT 6
ARRAY 1 -8.0 -6.92822 -50.0
CYLINDER 0 1 12.4 2P50.0
CYLINDER 2 1 12.65 2P50.0
Next, the hemicylinders necessary to complete all of the half cylinders
remaining in :numref:`fig8-1-54` are added. This is done by placing four
``UNIT``\ s 1 at the appropriate positions along the bottom of the
``ARRAY``, four ``UNIT``\ s 2 at the top of the ``ARRAY``, two
``UNIT``\ s 3 at the left of the ``ARRAY``, and two ``UNIT``\ s 4 at the
right of the ``ARRAY``. The input data are shown below, and the
resulting configuration is shown in :numref:`fig8-1-55`. In ``UNIT`` 6, the
first ``HOLE`` 1 places a ``UNIT`` 1 under the lower left ``UNIT`` of
the ``ARRAY``. The second ``HOLE`` 1 places a ``UNIT`` 1 under the next
``ARRAY UNIT`` to the right of the first one. This procedure is
repeated for the next two lower ``ARRAY UNIT``\ s, thus completing
the lower row of cylinders. Similarly, the first ``HOLE`` 2 places a
``UNIT`` 2 above the upper left ``UNIT`` of the ``ARRAY``. The second
``HOLE`` 2 places a ``UNIT`` 1 to the right of the first one, etc.,
until the four cylinders at the top of the ``ARRAY`` are completed. The
first ``HOLE`` 3 places a ``UNIT`` 3 at the lower left side of the
``ARRAY`` to complete that rod. The second ``HOLE`` 3 completes the rod
above it. The first ``HOLE`` 4 completes the lower rod on the right side
of the ``ARRAY``. The second ``HOLE`` 4 completes the rod above it. The
geometry data listed below result in the configuration shown in
:numref:`fig8-1-55`.
.. figure:: figs/Keno/fig55.png
:align: center
:width: 400
:name: fig8-1-55
Partially completed triangular pitched ARRAY in a cylinder.
.. code-block:: scale
UNIT 6
ARRAY 1 -8.0 -6.92822 -50.0
CYLINDER 0 1 12.4 2P50.0
HOLE 1 -6.0 -6.92822 0.0
HOLE 1 -2.0 -6.92822 0.0
HOLE 1 2.0 -6.92822 0.0
HOLE 1 6.0 -6.92822 0.0
HOLE 2 -6.0 6.92822 0.0
HOLE 2 -2.0 6.92822 0.0
HOLE 2 2.0 6.92822 0.0
HOLE 2 6.0 6.92822 0.0
HOLE 3 -8.0 -3.46411 0.0
HOLE 3 -8.0 3.46411 0.0
HOLE 4 8.0 -3.46411 0.0
HOLE 4 8.0 3.46411 0.0
CYLINDER 2 1 12.65 2P50.0
To complete the desired configuration, a cylinder is defined, ``UNIT``
7, and it is placed at the four appropriate positions as shown below.
The first ``HOLE`` 7 places the cylinder of ``UNIT`` 7 at the left of
the ``ARRAY``, the second ``HOLE`` 7 places the cylinder at the top of
the ``ARRAY``, the third ``HOLE`` 7 places the cylinder at the right of
the ``ARRAY``, and the fourth ``HOLE`` 7 places the cylinder at the
bottom of the ``ARRAY``. The completed configuration is shown in
:numref:`fig8-1-56`. It is not necessary for ``UNIT`` 7 to precede ``UNIT`` 6.
It is allowable to place ``UNIT`` 7 after ``UNIT`` 6 in the input data.
Because the final configuration is defined in ``UNIT`` 6, it must be
designated as the ``GLOBAL UNIT``. The total geometry input for this
example is listed below.
.. figure:: figs/Keno/fig56.png
:align: center
:width: 400
:name: fig8-1-56
Completed triangular pitched array in a cylinder.
.. code-block:: scale
READ GEOM
UNIT 1
ZHEMICYL-Y 1 1 2.0 50.0 -50.0
UNIT 2
ZHEMICYL+Y 1 1 2.0 50.0 -50.0
UNIT 3
ZHEMICYL-X 1 1 2.0 50.0 -50.0
UNIT 4
ZHEMICYL+X 1 1 2.0 50.0 -50.0
UNIT 5
ZHEMICYL+X 1 1 2.0 50.0 -50.0 ORIGIN -2.0 0.0
CUBOID 0 1 2P2.0 2P3.46411 2P50.0
HOLE 1 0.0 3.46411 0.0
HOLE 2 0.0 -3.46411 0.0
HOLE 3 2.0 0.0 0.0
UNIT 7
CYLINDER 1 1 2.0 2P50.0
GLOBAL UNIT 6
ARRAY 1 -8.0 -6.92822 -50.0
CYLINDER 0 1 12.4 2P50.0
HOLE 1 -6.0 -6.92822 0.0
HOLE 1 -2.0 -6.92822 0.0
HOLE 1 2.0 -6.92822 0.0
HOLE 1 6.0 -6.92822 0.0
HOLE 2 -6.0 6.92822 0.0
HOLE 2 -2.0 6.92822 0.0
HOLE 2 2.0 6.92822 0.0
HOLE 2 6.0 6.92822 0.0
HOLE 3 -8.0 -3.46411 0.0
HOLE 3 -8.0 3.46411 0.0
HOLE 4 8.0 -3.46411 0.0
HOLE 4 8.0 3.46411 0.0
HOLE 7 -10.0 0.0 0.0
HOLE 7 0.0 10.39233 0.0
HOLE 7 10.0 0.0 0.0
HOLE 7 0.0 -10.39233 0.0
CYLINDER 2 1 12.65 2P50.0
END GEOM
READ ARRAY
ARA=1 NUX=4 NUY=2 NUZ=1 FILL F5 END FILL
END ARRAY
.. centered:: EXAMPLE 2b. Alternative Mockup of Triangular Pitched ARRAY in a Cylinder.
Consider the triangular pitched ``ARRAY`` shown in :numref:`fig8-1-52`. Another
method of describing this configuration is given below. Four basic
``UNIT``\ s are defined, as listed below. These are the same ``UNIT``\ s
shown in :numref:`fig8-1-49`.
.. code-block:: scale
UNIT 1
ZHEMICYL-Y 1 1 2.0 50.0 -50.0
UNIT 2
ZHEMICYL+Y 1 1 2.0 50.0 -50.0
UNIT 3
ZHEMICYL-X 1 1 2.0 50.0 -50.0
UNIT 4
ZHEMICYL+X 1 1 2.0 50.0 -50.0
``UNIT`` 5 is the same as previously defined in Example 2a, and pictured
in :numref:`fig8-1-49`.
.. code-block:: scale
UNIT 5
ZHEMICYL+X 1 1 2.0 50.0 -50.0 ORIGIN -2.0 0.0
CUBOID 0 1 2P2.0 2P3.46411 2P50.0
HOLE 1 0.0 3.46411 0.0
HOLE 2 0.0 -3.46411 0.0
HOLE 3 2.0 0.0 0.0
To describe the basic array for the problem, ``UNIT``\ s 5 is stacked in
a 4 :math:`\times` 2 :math:`\times` 1 as shown in :numref:`fig8-1-53`. The input data for the ``ARRAY``
are the following:
.. code-block:: scale
ARA=1 NUX=4 NUY=2 NUZ=1 FILL F5 END FILL
Next, the ``ARRAY`` (``ARRAY 1``) is placed in ``UNIT`` 6, and
``UNIT``\ s 7 and 8 are defined to be placed to the left and right of it
(see :numref:`fig8-1-57`). ``UNIT`` 7 will complete the two rods at the left
boundary of the ``ARRAY`` and will contain half of the far left rod in
the completed configuration. In the description of ``UNIT`` 7, the
``ZHEMICYL+X`` is half of the far right rod and is located with its cut
face at the left boundary of a box that is as tall as the entire
``ARRAY`` of :numref:`fig8-1-53`. The first ``HOLE 3`` in ``UNIT 7`` completes
the lower left rod of that ``ARRAY``, and the second ``HOLE 3``
completes the upper left rod. ``UNIT 8`` is constructed in similar
fashion to complete the two rods at the right of the ``ARRAY`` shown in
:numref:`fig8-1-53`. ``UNIT 8`` is the mirror image of ``UNIT 7``.
``UNIT``\ s 6, 7, and 8 are stacked in an ``ARRAY`` (``ARRAY 2``) to
achieve the configuration shown in :numref:`fig8-1-57`. The data to accomplish
this are listed below.
.. figure:: figs/Keno/fig57.png
:align: center
:width: 400
:name: fig8-1-57
Array to be placed in a cylinder.
.. code-block:: scale
UNIT 6
ARRAY 1 -8.0 -6.92822 -50.0
GLOBAL
UNIT 7
ZHEMICYL+X 1 1 2.0 50.0 -50.0
CUBOID 0 1 2.0 0.0 2P6.92822 2P50.0
HOLE 3 2.0 -3.46411 0.0
HOLE 3 2.0 3.46411 0.0
UNIT 8
ZHEMICYL-X 1 1 2.0 50.0 -50.0
CUBOID 0 1 0.0 -2.0 2P6.92822 2P50.0
HOLE 4 -2.0 -3.46411 0.0
HOLE 4 -2.0 3.46411 0.0
ARA=2 NUX=3 NUY=1 NUZ=1 FILL 7 6 8 END FILL
Next, ``ARRAY 2`` is placed in the cylinder as shown in :numref:`fig8-1-58`. The
data are listed below.
.. figure:: figs/Keno/fig58.png
:align: center
:width: 400
:name: fig8-1-58
Partially completed array in a cylinder.
.. code-block:: scale
UNIT 9
ARRAY 2 -10.0 -6.92822 -50.0
CYLINDER 0 1 12.4 2P50.0
CYLINDER 2 1 12.65 2P50.0
Now ``UNIT``\ s 10 and 11 are described and placed above and below the
``ARRAY``. These ``UNIT``\ s are shown in :numref:`fig8-1-59`. ``UNIT 10`` is
described to complete the two central rods at the top of the ``ARRAY``
of :numref:`fig8-1-58`. :numref:`fig8-1-59` and :numref:`fig8-1-60` illustrate these ``UNIT``\ s.
The ``ZHEMICYL-Y`` is placed at the top of the ``UNIT`` to describe
half of the rod at the very top of the ``ARRAY``. The first ``HOLE 2``
completes the left center rod at the top of the ``ARRAY`` pictured in
:numref:`fig8-1-58`. The second ``HOLE 2`` completes the right center rod at
the top of the ``ARRAY``. ``UNIT 11`` is described in similar fashion.
It is the mirror image of ``UNIT 10`` and is placed below the
``ARRAY`` of :numref:`fig8-1-58`. The resulting configuration is shown in
:numref:`fig8-1-59`.
.. figure:: figs/Keno/fig59.png
:align: center
:width: 400
:name: fig8-1-59
Description of UNITs 10 and 11 for Example 2b.
.. code-block:: scale
UNIT 10
ZHEMICYL-Y 1 1 2.0 2P50.0
CUBOID 0 1 2P4.0 0.0 -3.46411 2P50.0
HOLE 2 -2.0 -3.46411 0.0 2P50.0
HOLE 2 2.0 -3.46411 0.0
UNIT 11
ZHEMICYL+Y 1 1 2.0 2P50.0
CUBOID 0 1 2P4.0 3.46411 0.0 2P50.0
HOLE 1 -2.0 3.46411 0.0
HOLE 1 2.0 3.46411 0.0
Now ``UNIT``\ s 10 and 11 are placed above and below the ``ARRAY`` of
:numref:`fig8-1-58` to obtain the configuration shown in :numref:`fig8-1-60`.
.. figure:: figs/Keno/fig60.png
:align: center
:width: 400
:name: fig8-1-60
Partially completed triangular pitched ARRAY in a cylinder.
.. code-block:: scale
UNIT 9
ARRAY 2 -10.0 -6.92822 -50.0
CYLINDER 0 1 12.4 2P50.0
HOLE 10 0.0 10.39233 0.0
HOLE 11 0.0 -10.39233 0.0
CYLINDER 2 1 12.65 2P50.0
To complete the array, the remaining half cylinders must be entered as
``HOLE``\ s, as shown below. The first ``HOLE 1`` completes the half rod
at the lower left of :numref:`fig8-1-60`. The second ``HOLE 1`` completes the
half rod at the lower center, and the third ``HOLE 1`` completes the
half rod at the lower right of :numref:`fig8-1-60`. Similarly, the first
``HOLE 2`` completes the half rod at the upper left of :numref:`fig8-1-60`.
The second ``HOLE 2`` completes the half rod at the upper center, and
the third ``HOLE 2`` completes the half rod at the upper right.
``HOLE 3`` completes the half rod at the left of :numref:`fig8-1-60`, and
``HOLE 4`` completes the half rod at the right. The final geometry
configuration is shown in :numref:`fig8-1-61`. ``UNIT 9`` must be specified as
the ``GLOBAL UNIT`` because it defines the overall configuration.
.. figure:: figs/Keno/fig61.png
:align: center
:width: 400
:name: fig8-1-61
Final configuration of triangular pitched ARRAY in a cylinder.
.. code-block:: scale
GLOBAL UNIT 9
ARRAY 2 -10.0 -6.92822 -50.0
CYLINDER 0 1 12.4 2P50.0
HOLE 10 0.0 10.39233 0.0
HOLE 11 0.0 -10.39233 0.0
HOLE 1 -6.0 -6.92822 0.0
HOLE 1 0.0 -10.39233 0.0
HOLE 1 6.0 -6.92822 0.0
HOLE 2 -6.0 6.92822 0.0
HOLE 2 0.0 10.39233 0.0
HOLE 2 6.0 6.92822 0.0
HOLE 3 -10.0 0.0 0.0
HOLE 4 10.0 0.0 0.0
CYLINDER 2 1 12.65 2P50.0
The geometry data for Example 2b are given below.
.. code-block:: scale
READ GEOM
UNIT 1
ZHEMICYL-Y 1 1 2.0 50.0 -50.0
UNIT 2
ZHEMICYL+Y 1 1 2.0 50.0 -50.0
UNIT 3
ZHEMICYL-X 1 1 2.0 50.0 -50.0
UNIT 4
ZHEMICYL+X 1 1 2.0 50.0 -50.0
UNIT 5
ZHEMICYL+X 1 1 2.0 50.0 -50.0 ORIGIN -2.0 0.0
CUBOID 0 1 2P2.0 2P3.46411 2P50.0
HOLE 1 0.0 3.46411 0.0
HOLE 2 0.0 -3.46411 0.0
HOLE 3 2.0 0.0 0.0
UNIT 6
ARRAY 1 -8.0 -6.92822 -50.0
UNIT 7
ZHEMICYL+X 1 1 2.0 50.0 -50.0
CUBOID 0 1 2.0 0.0 2P6.92822 2P50.0
HOLE 3 2.0 -3.46411 0.0
HOLE 3 2.0 3.46411 0.0
UNIT 8
ZHEMICYL-X 1 1 2.0 50.0 -50.0
CUBOID 0 1 0.0 -2.0 2P6.92822 2P50.0
HOLE 3 0.0 -3.46411 0.0
HOLE 3 0.0 3.46411 0.0
UNIT 10
YZHEMICYL-Y 1 1 2.0 2P50.0
CUBOID 0 1 2P4.0 0.0 -3.46411 2P50.0
HOLE 2 -2.0 -3.46411 0.0
HOLE 2 2.0 -3.46411 0.0
UNIT 11
YZHEMICYL+Y 1 1 2.0 2P50.0
CUBOID 0 1 2P4.0 3.46411 0.0 2P50.0
HOLE 1 -2.0 3.46411 0.0
HOLE 1 2.0 3.46411 0.0
GLOBAL
UNIT 9
ARRAY 2 -10.0 -6.92822 -50.0
CYLINDER 0 1 12.4 2P50.0
HOLE 10 0.0 10.39233 0.0
HOLE 11 0.0 -10.39233 0.0
HOLE 1 -6.0 -6.92822 0.0
HOLE 1 0.0 -10.39233 0.0
HOLE 1 6.0 -6.92822 0.0
HOLE 2 -6.0 6.92822 0.0
HOLE 2 0.0 10.39233 0.0
HOLE 2 6.0 6.92822 0.0
HOLE 3 -10.0 0.0 0.0
HOLE 4 10.0 0.0 0.0
CYLINDER 2 1 12.65 2P50.0
END GEOM
READ ARRAY
ARA=1 NUX=4 NUY=2 NUZ=1 FILL F5 END FILL
ARA=2 NUX=3 NUY=1 NUZ=1 FILL 7 6 8 END FILL
END ARRAY
Dodecahedral pitched arrays
^^^^^^^^^^^^^^^^^^^^^^^^^^^
.. centered:: EXAMPLE 22.
Dodecahedral pitched **ARRAY**\ s can be described in
KENO-VI by defining the **UNIT**\ s that make up the **ARRAY** as
dodecahedra and in the **ARRAY** data block setting
**TYP**\ =DODECAHEDRAL. Since the **ARRAY**\ s are constructed by
stacking dodecahedra, care must be taken to ensure the **ARRAY**
boundary is completely enclosed within the stacked unit. Below is an
example of a dodecahedral **ARRAY** that represents a close packed
**ARRAY** of spheres.
The first and second **UNIT**\ s are the dodecahedra that make up the
**ARRAY**. **UNIT** 1 is the fuel sphere stacked in a dodecahedral
lattice. **UNIT** 2 is a dummy **UNIT** used to fill in the **ARRAY** so
the **ARRAY** boundary is contained within the stacked **UNIT**\ s.
Since the **ARRAY** is not moderated, **UNIT** 2 contains void.
:numref:`fig8-1-62` shows an isometric, cross section view of **UNIT**\ s 1 and
2.
.. figure:: figs/Keno/fig62.png
:align: center
:width: 400
:name: fig8-1-62
Fuel cell and empty cell set up as dodecahedra.
::
UNIT 1
COM='SINGLE CELL FUEL CAN IN DODECAHDRON'
SPHERE 10 8.0
SPHERE 20 8.5
DODECAHEDRON 30 10.5
MEDIA 1 1 10
MEDIA 2 1 20 -10
MEDIA 0 1 30 -20
BOUNDARY 30
UNIT 2
COM='EMPTY CELL'
DODECAHEDRON 10 10.5
MEDIA 0 1 10
BOUNDARY 10
**UNIT** 3 is the **GLOBAL UNIT** that contains the **ARRAY** and
**ARRAY BOUNDARY**. The **ARRAY** is an unmoderated triangular pitched
assembly of 17 fuel spheres. Dodecahedral **ARRAY**\ s are specified by
using **TYP**\ = followed by keyword dodecahedral in the array data
block. The X and Y coordinates are stacked together as a square pitched
**ARRAY** with the pitch equal to twice the dodecahedron radius. In the
Z dimension, the odd Z planes (Z = 1, 3, 5, etc.) have the X and
Y \ **UNIT**\ s begin at the most negative edge of the **ARRAY**, while
the even Z planes (Z = 2, 4, 6, etc.) have the X and Y \ **UNIT**\ s
begin one dodecahedron inscribed sphere radius in the positive direction
from the most negative edge of the **ARRAY**. Also, the Z distance
between the centers of the **UNIT**\ s in successive Z planes is the
square root of 2.0 times the dodecahedron radius (or the dodecahedron
diameter divided by the square root of 2.0). :numref:`fig8-1-63` and :numref:`fig8-1-64`
show X-Y cross sectional color plots of the assembly at an odd and even
Z plane.
::
GLOBAL UNIT 3
COM='17 CLOSE PACKED FUEL SPHERES IN A CYLINDER'
CYLINDER 10 41.0 44.5 0.0
CYLINDER 20 42.0 44.5 -1.0
ARRAY 1 10 PLACE 3 3 1 3*0.0
MEDIA 3 20 -10
BOUNDARY 20
READ ARRAY GBL=1 ARA=1 TYP=DODECAHEDRAL NUX=5 NUY=5 NUZ=5
FILL 25*2
6*2 2*1 3*2 2*1 12*2
6*2 3*1 2*2 3*1 2*2 3*1 6*2
6*2 2*1 3*2 2*1 12*2
25*2 END FILL END ARRAY
.. figure:: figs/Keno/fig63.png
:align: center
:width: 400
:name: fig8-1-63
X-Y slice of dodecahedral array at even level Z = 2.
.. figure:: figs/Keno/fig64.png
:align: center
:width: 400
:name: fig8-1-64
X-Y slice of dodecahedral array at odd level Z = 3.
The overall problem description is shown below. The cross section
library would be generated in a separate CSAS-MG step.
Data description of Example 22.
::
=KENOVI
CLOSE PACKED DODECAHEDRAL ARRAY 17 FUEL SPHERES IN A CYLINDER
READ PARAMETERS LNG=20000 LIB=4 END PARAMETERS
READ MIXT SCT=2
MIX=1 NCM=8 92235 1.37751E-03 92238 9.92354E-05 8016 3.32049E-02
9019 2.95349E-03 1001 6.05028E-02
MIX=2 NCM=14 13027 6.02374E-02
MIX=3 NCM=14 13027 6.02374E-02
END MIXT
READ GEOMETRY
UNIT 1
COM='SINGLE CELL FUEL CAN IN DODECAHDRON'
SPHERE 10 8.0
SPHERE 20 8.5
DODECAHEDRON 30 10.5
MEDIA 1 1 10
MEDIA 2 1 20 -10
MEDIA 0 1 30 -20
BOUNDARY 30
UNIT 2
COM='EMPTY CELL'
DODECAHEDRON 10 10.5
MEDIA 0 1 10
BOUNDARY 10
GLOBAL UNIT 3
COM='9 CLOSE PACKED FUEL SPHERES IN A CYLINDER'
CYLINDER 10 41.0 44.5 0.0
CYLINDER 20 42.0 44.5 -1.0
ARRAY 1 10 PLACE 3 3 1 3*0.0
MEDIA 3 1 20 -10
BOUNDARY 20
END GEOMETRY
READ ARRAY GBL=1 ARA=1 TYP=DODECAHEDRAL NUX=5 NUY=5 NUZ=5
FILL 25*2
6*2 2*1 3*2 2*1 12*2
6*2 3*1 2*2 3*1 2*2 3*1 6*2
6*2 2*1 3*2 2*1 12*2
25*2 END FILL END ARRAY
READ PLOT
TTL='DODECAHEDRAL ARRAY, 4 SPHERES - Z LEVEL = 2'
XUL=-43.0 YUL=43.0 ZUL=14.85 XLR=43.0 YLR=-43.0 ZLR=14.85
UAX=1 VDN=-1 NAX=640 END PLT0
TTL='DODECAHEDRAL ARRAY, 9 SPHERES - Z LEVEL = 3'
XUL=-43.0 YUL=43.0 ZUL=29.70 XLR=43.0 YLR=-43.0 ZLR=29.70
UAX=1 VDN=-1 NAX=640 END PLT1
END PLOT
END DATA
END
Alternative sample problem mockups
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The geometry data for KENO can often be described correctly in several
ways. Some alternative geometry descriptions are given here for sample
problems C.12 and C.13. (See :numref:`sec-module.keno.examples` of the KENO manual.)
Sample Problem C.12, First Alternative
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
This mockup maintains the same overall unit dimensions that were used in
sample problem C.12. In sample problem C.12, the origin of **UNIT** 1,
the solution cylinder, is at the center of the unit; the origin of
**UNIT**\ s 2, 3, 4, and 5, the metal cylinders, are at the center of
the cylinders. In this mockup, the unit numbers remain the same and the
origin of each unit is at the center of the unit. In each unit the
cylinder is offset by specifying the position of its centerline relative
to the origin of the **UNIT**.
KENO V.a:
::
READ GEOM
UNIT 1
CYLINDER 2 1 9.525 8.89 -8.89
CYLINDER 3 1 10.16 9.525 -9.525
CUBOID 0 1 10.875 -10.875 10.875 -10.875 10.24 -10.24
UNIT 2
CYLINDER 1 1 5.748 9.3975 -1.3975 ORIG 4.285 4.285
CUBOID 0 1 10.875 -10.875 10.875 -10.875 10.24 -10.24
UNIT 3
CYLINDER 1 1 5.748 9.3975 -1.3675 ORIG 4.285 -4.285
CUBOID 0 1 10.875 -10.875 10.875 -10.875 10.24 -10.24
UNIT 4
CYLINDER 1 1 5.748 1.3675 -9.3975 ORIG 4.285 4.285
CUBOID 0 1 10.875 -10.875 10.875 -10.875 10.24 -10.24
UNIT 5
CYLINDER 1 1 5.748 1.3675 -9.3975 ORIG 4.285 -4.285
CUBOID 0 1 10.875 -10.875 10.875 -10.875 10.24 -10.24
END GEOM
READ ARRAY NUX=2 NUY=2 NUZ=2 FILL 2 1 3 1 4 1 5 1 END ARRAY
KENO-VI:
::
READ GEOM
UNIT 1
CYLINDER 1 9.525 8.89 -8.89
CYLINDER 2 10.16 9.525 -9.525
CUBOID 3 10.875 -10.875 10.875 -10.875 10.24 -10.24
MEDIA 2 1 1
MEDIA 3 1 2 -1
MEDIA 0 1 3 -2
BOUNDARY 3
UNIT 2
CYLINDER 1 5.748 9.3975 -1.3675 ORIG X=4.285 Y=4.285
CUBOID 2 10.875 -10.875 10.875 -10.875 10.24 -10.24
MEDIA 1 1 1
MEDIA 0 1 2 -1
BOUNDARY 2
UNIT 3
CYLINDER 1 5.748 9.3975 -1.3675 ORIG X=4.285 Y=-4.285
CUBOID 2 10.875 -10.875 10.875 -10.875 10.24 -10.24
MEDIA 1 1 1
MEDIA 0 1 2 -1
BOUNDARY 2
UNIT 4
CYLINDER 1 5.748 1.3675 -9.3975 ORIG X=4.285 Y=4.285
CUBOID 2 10.875 -10.875 10.875 -10.875 10.24 -10.24
MEDIA 1 1 1
MEDIA 0 1 2 -1
BOUNDARY 2
UNIT 5
CYLINDER 1 5.748 1.3675 -9.3975 ORIG X=4.285 Y=-4.285
CUBOID 2 10.875 -10.875 10.875 -10.875 10.24 -10.24
MEDIA 1 1 1
MEDIA 0 1 2 -1
BOUNDARY 2
GLOBAL UNIT 6
CUBOID 1 21.75 -21.75 21.75 -21.75 20.48 -20.48
ARRAY 1 PLACE 1 1 1 -10.875 -10.875 -10.24
BOUNDARY 1
END GEOM
READ ARRAY ARA=1 NUX=2 NUY=2 NUZ=2 FILL 2 1 3 1 4 1 5 1 END ARRAY
Sample Problem C.12, Second Alternative
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
In this mockup, the outer boundaries of the system are made as close
fitting as possible on all six faces. The origin of each **UNIT** is
located at the center of the cylinder. **UNIT**\ s 1, 3, 5, and 7
contain the metal cylinders. **UNIT**\ s 2, 4, 6, and 8 contain the
solution cylinders.
KENO V.a:
::
READ GEOM
UNIT 1
CYLINDER 1 1 5.748 5.3825 -5.3825
CUBOID 0 1 6.59 -5.748 6.59 -14.445 6.225 -13.54
UNIT 2
CYLINDER 2 1 9.525 8.89 -8.89
CYLINDER 3 1 10.16 9.525 -9.525
CUBOID 0 1 10.16 -10.875 10.875 -10.16 10.24 -9.525
UNIT 3
CYLINDER 1 1 5.748 5.3825 -5.3825
CUBOID 0 1 6.59 -5.748 14.444 -6.59 6.225 -13.54
UNIT 4
CYLINDER 2 1 9.525 8.89 -8.89
CYLINDER 3 1 10.16 9.525 -9.525
CUBOID 0 1 10.16 -10.875 10.16 -10.875 10.24 -9.525
UNIT 5
CYLINDER 1 1 5.748 5.3825 -5.3825
CUBOID 0 1 6.59 -5.748 6.59 -14.445 13.54 -6.225
UNIT 6
CYLINDER 2 1 9.525 8.89 -8.89
CYLINDER 3 1 10.16 9.525 -9.525
CUBOID 0 1 10.16 -10.875 10.875 -10.16 9.525 -10.24
UNIT 7
CYLINDER 1 1 5.748 5.3825 -5.3825
CUBOID 0 1 6.59 -5.748 14.445 -6.59 13.54 -6.225
UNIT 8
CYLINDER 2 1 9.525 8.89 -8.89
CYLINDER 3 1 10.16 9.525 -9.525
CUBOID 0 1 10.16 -10.875 10.16 -10.875 9.525 -10.24
READ ARRAY NUX=2 NUY=2 NUZ=2 FILL 6I1 8 END FILL END ARRAY
KENO-VI:
::
READ GEOM
UNIT 1
CYLINDER 1 5.748 5.3825 -5.3825
CUBOID 2 6.59 -5.748 6.59 -14.445 6.225 -13.54
MEDIA 1 1 1
MEDIA 0 1 2 -1
BOUNDARY 2
UNIT 2
CYLINDER 1 9.525 8.89 -8.89
CYLINDER 2 10.16 9.525 -9.525
CUBOID 3 10.16 -10.875 10.875 -10.16 10.24 -9.525
MEDIA 2 1 1
MEDIA 3 1 2 -1
MEDIA 0 1 3 -2
BOUNDARY 3
UNIT 3
CYLINDER 1 5.748 5.3825 -5.3825
CUBOID 2 6.59 -5.748 14.444 -6.59 6.225 -13.54
MEDIA 1 1 1
MEDIA 0 1 2 -1
BOUNDARY 2
UNIT 4
CYLINDER 1 9.525 8.89 -8.89
CYLINDER 2 10.16 9.525 -9.525
CUBOID 3 10.16 -10.875 10.16 -10.875 10.24 -9.525
MEDIA 2 1 1
MEDIA 3 1 2 -1
MEDIA 0 1 3 -2
BOUNDARY 3
UNIT 5
CYLINDER 1 5.748 5.3825 -5.3825
CUBOID 2 6.59 -5.748 6.59 -14.445 13.54 -6.225
MEDIA 1 1 1
MEDIA 0 1 2 -1
BOUNDARY 2
UNIT 6
CYLINDER 1 9.525 8.89 -8.89
CYLINDER 2 10.16 9.525 -9.525
CUBOID 3 10.16 -10.875 10.875 -10.16 9.525 -10.24
MEDIA 2 1 1
MEDIA 3 1 2 -1
MEDIA 0 1 3 -2
BOUNDARY 3
UNIT 7
CYLINDER 1 5.748 5.3825 -5.3825
CUBOID 2 6.59 -5.748 14.445 -6.59 13.54 -6.225
MEDIA 1 1 1MEDIA 0 1 2 -1
BOUNDARY 2
UNIT 8
CYLINDER 1 9.525 8.89 -8.89
CYLINDER 2 10.16 9.525 -9.525
CUBOID 3 10.16 -10.875 10.16 -10.875 9.525 -10.24
MEDIA 2 1 1
MEDIA 3 1 2 -1
MEDIA 0 1 3 -2
BOUNDARY 3
GLOBAL UNIT 9
CUBOID 1 20.035 -12.748 20.67 -20.67 19.765 -19.765
ARRAY 1 1 PLACE 1 1 1 -7.00 -6.225 -6.225
BOUNDARY 1
END GEOM
READ ARRAY ARA=1 NUX=2 NUY=2 NUZ=2 FILL 6I1 8 END FILL END ARRAY
Sample Problem C.13, Alternative
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
This mockup maintains the same overall **UNIT** dimensions that were
used in sample problem C.13, (KENO Manual, :numref:`sec-module.keno.examples`). In sample
problem C.13, the origin of **UNIT**\ s 1, 2, and 3 is located at the
center of the base of the uranium metal cuboid. In this mockup, the
origin of **UNIT**\ s 1 and 2 is located at the center of the cylinder.
In \ **UNIT** 3, the origin is at the center of the **UNIT**.
KENO V.a:
::
READ GEOM
UNIT 1
CUBOID 1 1 0.2566 -12.4434 6.35 -6.35 3.81 -3.81
CYLINDER 0 1 13.97 3.81 -3.81
CYLINDER 1 1 19.05 3.81 -3.81
CUBOID 0 1 19.05 -19.05 19.05 -19.05 3.81 -3.81
UNIT 2
CUBOID 1 1 12.4434 -0.2566 6.35 -6.35 4.28 -4.28
CYLINDER 0 1 13.97 4.28 -4.28
CYLINDER 1 1 19.05 4.28 -4.28
CUBOID 0 1 19.05 -19.05 19.05 -19.05 4.28 -4.28
UNIT 3
CUBOID 1 1 12.4434 -0.2566 6.35 -6.35 1.308 -1.308
CUBOID 0 1 19.05 -19.05 19.05 -19.05 1.308 -1.308
END GEOM
READ ARRAY NUX=1 NUY=1 NUZ=3 FILL 1 2 3 END ARRAY
KENO-VI:
::
READ GEOM
UNIT 1
CUBOID 1 0.2566 -12.4434 6.35 -6.35 3.81 -3.81
CYLINDER 2 13.97 3.81 -3.81
CYLINDER 3 19.05 3.81 -3.81
CUBOID 4 19.05 -19.05 19.05 -19.05 3.81 -3.81
MEDIA 1 1 1
MEDIA 0 1 2 -1
MEDIA 1 1 3 -2 -1
MEDIA 0 1 4 -3 -2 -1
BOUNDARY 4
UNIT 2
CUBOID 1 12.4434 -0.2566 6.35 -6.35 4.28 -4.28
CYLINDER 2 13.97 4.28 -4.28
CYLINDER 3 19.05 4.28 -4.28
CUBOID 4 19.05 -19.05 19.05 -19.05 4.28 -4.28
MEDIA 1 1 1
MEDIA 0 1 2 -1
MEDIA 1 1 3 -2 -1
MEDIA 0 1 4 -3 -2 -1
BOUNDARY 4
UNIT 3
CUBOID 1 12.4434 -0.2566 6.35 -6.35 1.308 -1.308
CUBOID 2 19.05 -19.05 19.05 -19.05 1.308 -1.308
MEDIA 1 1 1
MEDIA 0 1 2 -1
BOUNDARY 2
GLOBAL UNIT 4
CUBOID 1 19.05 -19.05 19.05 -19.05 6.896 -11.90
ARRAY 1 1 PLACE 1 2 1 0.0 0.0 0.0
BOUNDARY 1
END GEOM
READ ARRAY ARA=1 NUX=1 NUY=1 NUZ=3 FILL 1 2 3 END ARRAY
.. _sec-module.keno.start_dist:
Initial starting distributions with Start data
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
:numref:`sec-module.keno.start_data` discusses the input directions for entering different
starting distributions in the start data input block. The following start type 0
and start type 6 examples demonstrate how KENO codes process
the entered start data parameters.
Example-1:
An 8 cm radius fissile sphere without a start data block is modeled with
both KENO-VI and KENO V.a geometries. Start type 0, which is the default
starting option, is used, and neutrons are started uniformly in the entire
volume defined by the outermost geometry (fissile sphere).
KENO-VI:
::
...
read geometry
global unit 1
sphere 1 8
media 1 1 1
boundary 1
end geometry
end data
end
KENO V.a:
::
' input without global unit
...
read geometry
unit 1
sphere 1 1 8
end geometry
end data
end
' input with global unit
...
read geometry
global unit 1
sphere 1 1 8
end geometry
end data
end
Example-2:
This input models a simple 2 :math:`\times` 2 :math:`\times` 2 array of fissile cylinders
with the default starting option, which is start type 0. In this array problem,
**XSM**, **YSM**, and **ZSM** are defaulted to the minimum X, Y, and Z
coordinates of the global array, and **XSP**, **YSP**, and **ZSP** are
defaulted to the maximum coordinates of the global array. A bounding box is
constructed with these values, and neutrons are started at the points uniformly
sampled inside the fissile cylinders within this cuboid (For KENO V.a model,
the cuboid is defined by +x=27.48, -x=0.0, +y=27.48, -y=0.0, +z= 26.02, -z= 0.0,
and for KENO-VI model, it is defined by
+x=13.74, -x=-13.74, +y=13.74, -y=-13.74, +z= 13.01, -z=-13.01).
::
KENO-VI:
...
read geometry
unit 1
cylinder 1 5.748 2p5.3825
cuboid 2 4p6.87 2p6.505
media 1 1 1
media 0 1 2 -1
boundary 2
global unit 2
cuboid 10 4p13.74 2p13.01
array 1 +10 place 1 1 1 2r-6.87 -6.505
boundary 10
end geometry
read array
gbl=1 ara=1 nux=2 nuy=2 nuz=2 fill f1 end fill
end array
end data
end
KENO V.a:
' input with a global array
...
read geometry
unit 1
cylinder 1 1 5.748 5.3825 -5.3825
cuboid 0 1 6.87 -6.87 6.87 -6.87 6.505 -6.505
end geometry
read array
gbl=1 ara=1 nux=2 nuy=2 nuz=2 fill f1 end fill
end array
end data
end
Example-3:
Neutrons are started uniformly throughout the fissile materials in a
user-defined box that is inside the outermost geometry
(+x=3.0 -x=-3.0 +y= 1.0 -y=-1.0 +z= 2.0 -z=-2.0).
::
KENO-VI:
...
read geometry
global unit 1
sphere 1 8
media 1 1 1
boundary 1
end geometry
READ START
NST=0
XSP=3.0 XSM=-3.0 YSP=1.0 YSM=-1.0 ZSP=2.0 ZSM=-2.0
END START
end data
end
Example-4:
This test case is another example of the start type 0 specification
with a user-defined cuboid, but whole cuboid is not inside the outermost
geometry. KENO V.a immediately terminates the execution with some error
messages since some starting points are sampled outside the outermost
geometry.
Unlike KENO V.a, KENO-VI continues the sampling process by discarding these
points, which are outside the global geometry, until all starting points
have been successfully sampled throughout the fissile regions inside the
global unit.
::
KENO-VI:
...
read geometry
global unit 1
sphere 1 8
media 1 1 1
boundary 1
end geometry
READ START
NST=0
XSP=10.0 XSM=-10.0 YSP=10.0 YSM=-10.0 ZSP=10.0 ZSM=-10.0
END START
end data
end
.. note:: Note that the KENO-VI sampling process for
such a case will be terminated if
- the first starting point has not been sampled in *tbtch* minutes.
*tbtch* is the time per generation in minutes, defaulted to 10
minutes. User can control this with parameter **TBA=** in
parameter input; see :numref:`sec-module.keno.parameters` for details, or
- all points have not been successfully sampled inside the
global units in total *tbtch* :math:`\times` *9.5* minutes.
Example-5:
This test input demonstrates how KENO-VI performs source sampling
with the default starting type (start type 0) if the boundary
definition vector of the global unit has the multiple body labels.
For such cases, KENO-VI starts neutrons at the points that are
uniformly sampled in the first body entered in the boundary
definition vector of the global unit if and only if none of
translation and transformation operations are performed on this
body. For this KENO-VI specific example, all starting points are
sampled throughout the fissile materials inside the *cylinder 3*.
::
KENO-VI:
...
read geometry
global unit 1
sphere 1 8.741
sphere 2 10.0
cylinder 3 8.0 2p8.0
media 1 1 1
media 2 1 2 3 -1
BOUNDARY 3 2
end geometry
end data
end
Example-6:
Start type 0 specification with one or more missing optional parameters;
their default values (0.0) are used to construct a cuboid, and neutrons
are started uniformly throughout the fissile materials in this box
(+x=3.0 -x=0.0 +y= 1.0 -y=0.0 +z=0.0 -z=-2.0).
::
KENO-VI:
...
read geometry
global unit 1
sphere 1 8
media 1 1 1
boundary 1
end geometry
READ START
NST=0
XSP=3.0 YSP=1.0 ZSM=-2.0
END START
end data
end
.. note:: In start data input, user-defined cuboid shape is considered as a deformed
cuboid shape if the minimum and maximum bounds in any dimension are equal entries
(**XSP = XSM** or/and **YSP = YSM** or/and **ZSP = ZSM**). Deformed shape
specification is a legitimate input specification across SCALE sequences
(i.e., a box is deformed into a plane if minimum and maximum bounds in
one dimension are the same, e.g., +x = -x). In such a case, user-defined entries
for **XSM**, **XSP**, **YSM**, **YSP**, **ZSM**, and **ZSP** are ignored,
and source sampling is performed throughout the volume defined by the
outermost geometry card.
The following two examples with start type 0 demonstrate code behavior for the
deformed shapes for start types 0, 1, 2, and 7.
Example-7:
Box defined with missing **ZSM**, and **ZSP** is considered as a deformed
cuboid since these parameters are identical after defaulting their values
to 0.0. Instead of this deformed cuboid box, neutrons are started uniformly
throughout the fissile materials in the global unit.
::
KENO-VI:
...
read geometry
global unit 1
sphere 1 8
media 1 1 1
boundary 1
end geometry
READ START
NST=0
XSP=3.0 XSM=-3.0 YSP=1.0 YSM=-1.0
END START
end data
end
Example-8:
A box defined with identical **XSM** and **XSP** entries is considered as a deformed
cuboid since these parameters are identical after defaulting their values
to 0.0. Instead of this deformed cuboid box, neutrons are started uniformly
throughout the fissile materials in the global unit.
::
KENO-VI:
...
read geometry
global unit 1
sphere 1 8
media 1 1 1
boundary 1
end geometry
READ START
NST=0
XSP=3.0 XSM=3.0 YSP=1.1 YSM=-2.1 ZSP=4.0 ZSM=-4.1
END START
end data
end
In the start type 6 capability, the selection process for the initial fission
source points depends on the values of the last LNU value and number per
generation (parameter NPG= in the parameter input :numref:`sec-module.keno.parameters`).
The following rules are applied when selecting the starting points:
- Start NPG initial fission neutrons at first-NPG starting points defined
by start type 6 data if **NPG** < **LNU**. Remaining starting points beyond
NPG will be discarded.
- Start NPG initial fission neutrons at LNU starting points defined by
start type 6 data if **NPG** = **LNU**.
- Start LNU initial fission neutrons at the starting points defined by
start type 6 data, then randomly select the remaining fission source
points (NPG-LNU) from these starting points if **NPG** > **LNU**.
.. warning:: It is the user's responsibility to enter all arbitrary starting
points consistent with the geometry specified. Both KENO V.a and
KENO-VI terminate the execution with several error messages if any
user-specified starting point entered is outside the outermost
geometry.
Example-9:
In this example, 120 starting points have been defined by start type
6 data, and NPG=100 starting points are selected from the defined
start type 6 data, 25 neutrons are started at the point
(2.0, 3.0, 0.0), 20 neutrons are started at the point (3.0, -2.0, -6.0),
and the remaining 55 neutrons are started at (3.0, 5.2, 1.0). All
selected points are relative to the global coordinate system. Missing
**TFX** entry in the last start type 6 data set is set to the last updated
**TFX** value which is 3.0.
::
KENO-VI:
...
READ PARAMETER
NPG=100
END PARAMETER
read geometry
global unit 1
sphere 1 8
media 1 1 1
boundary 1
end geometry
READ START
NST=6
TFX=2.0 TFY= 3.0 TFZ=0.0 LNU=25
TFX=3.0 TFY=-2.0 TFZ=-6.0 LNU=45
TFY=5.2 TFZ=1.0 LNU=120
END START
end data
end
Example-10:
In this example, only 45 starting points have been defined by start
type 6 data. The first 25 neutrons are started at the point
(2.0, 0.0, 0.0), and 20 neutrons are started at the point
(2.0, 3.0, -6.0). The remaining 55 neutrons are started at the points
randomly selected from these starting points. All selected points are
relative to the global coordinate system. Missing
**TFY** and **TFZ** entries are defaulted to 0.0 in the first start type
6 data set. The missing **TFX** entry in the last start type 6 data set is
set to the last updated **TFX** value, which is 2.0 (from the previous start
type 6 data set).
::
KENO-VI:
...
READ PARAMETER
NPG=100
END PARAMETER
read geometry
global unit 1
sphere 1 8
media 1 1 1
boundary 1
end geometry
READ START
NST=6
TFX=2.0 LNU=25
TFY=3.0 TFZ=-6.0 LNU=45
END START
end data
end
Example-11:
In this example, 35 neutrons are started at the point (0.0, 0.0, 0.0)
relative to the global array element (2,1,1), and the remaining 65
neutrons are started at the point (2.0, 1.0, 3.0) relative to the
global array element (1,2,2). The missing **TFX**, **TFY**, and **TFZ**
entries in each data set are defaulted to 0.0.
::
KENO V.a:
...
READ PARAMETER
NPG=100
END PARAMETER
read geometry
unit 1
cylinder 1 1 5.748 5.3825 -5.3825
cuboid 0 1 6.87 -6.87 6.87 -6.87 6.505 -6.505
end geometry
read array
gbl=1 ara=1 nux=2 nuy=2 nuz=2 fill f1 end fill
end array
READ START
NST=6
NXS=2 NYS=1 NZS=1 LNU=35
TFX=2.0 TFY=1.0 TFZ=3.0 NXS=1 NYS=2 NZS=2 LNU=100
END START
end data
end
Start type 6 is capable of reading starting points from an ASCII start data
file, which could be created by writing starting points from a previous
calculation, defined by RDU in a start type 6 data set. See
:numref:`sec-module.keno.start_data.ascii` for the details about a typical ASCII start data file
currently supported.
Reading starting data from multiple ASCII start data files is also
supported. Similarly, single or multiple start type 6 date sets with RDU
specification can be used together with other start type 6 data sets
discussed above. The following examples demonstrate this capability.
Example-12:
In this example, all starting points stored in the ASCII start data file
`sample.src` are read, and **NPG** neutrons are started at these points.
If the number of starting points (last LNU read from the file) is less
than **NPG**, **LNU** number of neutrons are started at the points read,
and the remaining neutrons (NPG-LNU) are started at the points randomly
sampled from the starting points already read. The starting points beyond
**NPG** are discarded if **NPG** is less than the number of starting points
read.
::
...
READ START
NST=6
RDU=sample.src
END START
Example-13:
The first 32 starting points stored in the ASCII start data file `sample.src`
are read, and **NPG** neutrons are started at these points. If **NPG** >
**LNU** = 32, then 32 neutrons are started at these starting points,
and the remaining neutrons are started at the points randomly sampled from
these 32 starting points. The starting points beyond **NPG** is
discarded if **NPG** < 32.
::
...
READ START
NST=6
RDU=sample.src LNU=32
END START
.. note:: Reading starting data from multiple ASCII start data files is also
supported. Similarly, single or multiple start type 6 date sets with the RDU
specification can be used together with other start type 6 data sets
discussed above. The following examples demonstrates this capability.
Example-14:
A total of 30 starting points are read both from the specified ASCII start
data files and from the start type 6 data set defined with **TFX**,
**TFY**, and **TFZ**. Neutrons are started at these points.
If there is a shortage of starting points (NPG >> last LNU), then the required
number of starting points is randomly sampled from these 30 starting
points.
::
...
READ START
NST=6
RDU=sample1.src LNU=10
RDU=sample2.src LNU=25
TFX=1.0 TFY=3.0 TFZ=4.0 LNU=30
END START
Biasing or weighting data for multigroup mode
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
:numref:`8-1-3-6-3` discusses the basis of weighting or biasing. The use of
biasing data in reflected problems has been illustrated in Examples 9,
10, and 11 of :numref:`sec-module.keno.geom_guide`. :numref:`sec-module.keno.biasing` discusses the input
directions for entering biasing data.
Every **shape** card in KENO V.a, or **MEDIA** card in KENO-VI requires
a bias ID to associate that geometry region with a biasing or weighting
function. A biasing or weighting function is a set of energy-dependent
values of the average weight that are applicable in a given region. The
default function for all bias IDs is constant through all energy groups
and is defined to be the default value of weight average which can be
specified in the parameter data. A bias ID can be associated with a
biasing function (other than default) by specifying it in the biasing
input data. This function can be chosen from the weighting library, or
it can be entered from records. :numref:`tab8-1-20` lists the materials and
energy group structures for biasing functions available from the
weighting library.
.. caution:: In general, the use of biasing should be restricted to external
reflectors unless the user has generated correct biasing functions for
other applications. Improper use of biasing functions can result in
erroneous answers without giving any indication that they are invalid.
Caution should be exercised in the generation and use of biasing
functions.
Biasing functions are most applicable to thick external reflectors.
Their use can significantly reduce the amount of computer time required
to obtain answers in KENO. If the user wishes to use a biasing function
for a concrete reflector, for example, the following steps must be
included in preparing the input data:
1. The geometry region data must define the shape and dimensions of the
reflector using the mixture ID for concrete and a sequence of bias IDs
that associate the geometry region with the appropriate interval of the
concrete weighting function. CAUTION: THE THICKNESS AND SEQUENTIAL
LOCATION OF EACH REGION USING BIASING FUNCTIONS MUST MATCH OR VERY
NEARLY MATCH THE INCREMENT THICKNESS AND ORDER OF THE WEIGHTING DATA. NO
CHECK IS MADE ON THE REQUIREMENT. IT IS THE USER’S RESPONSIBILITY TO
ENSURE CONSISTENCY.
2. Biasing data must be entered. This must include the material ID for
the reflector material (from :numref:`tab8-1-20` or as specified on records)
and a beginning and ending bias ID. The beginning bias ID is used to
select the first set of energy-dependent average weights, and the
subsequent sets of energy-dependent average weights are assigned
consecutive IDs until the ending bias ID is reached.
Small deviations in reflector region thickness are allowed, such as
using three generated regions with a thickness per region of 5.08 cm to
generate a 15.24 cm thick reflector of concrete, or using five generated
regions with a thickness per region of 3.048 cm to generate a 15.24 cm
thick reflector of water. See :numref:`tab8-1-20` for a list of the increment
thicknesses for the materials in the weighting library. It is acceptable
for the thickness of the last reflector region to be significantly
different than the increment thickness. For example, a reflector record
specifying five generated regions with a thickness per region of 3.0 cm
could be followed by a reflector record specifying one region with a
thickness per region of 0.24 cm. Assuming that material 2 is water and a
15.24 cm thick cuboidal reflector of water is desired, the required
reflector description and biasing data could be entered as follows:
KENO V.a:
::
REFLECTOR 2 2 6*3.0 5
REFLECTOR 2 7 6*0.24 1
READ BIAS ID=500 2 7 END BIAS
KENO-VI:
::
GLOBAL UNIT 1
CUBOID 1 6P10.0
CUBOID 2 6P13.0
CUBOID 3 6P16.0
CUBOID 4 6P19.0
CUBOID 5 6P22.0
CUBOID 6 6P25.0
CUBOID 7 6P25.24
MEDIA 1 1 1
MEDIA 2 2 2 -1
MEDIA 2 3 3 -2
MEDIA 2 4 4 -3
MEDIA 2 5 5 -4
MEDIA 2 6 6 -5
MEDIA 2 7 7 -6
BOUNDARY 7
READ BIAS ID=500 2 7 END BIAS
The same 15.24 cm thick reflector can be described by including the
extra 0.24 cm in the last region as shown below:
KENO V.a:
::
REFLECTOR 2 2 6*3.0 4
REFLECTOR 2 6 6*3.24 1
READ BIAS ID=500 2 6 END BIAS
KENO-VI:
::
GLOBAL UNIT 1
CUBOID 1 6P10.0
CUBOID 2 6P13.0
CUBOID 3 6P16.0
CUBOID 4 6P19.0
CUBOID 5 6P22.0
CUBOID 6 6P25.24
MEDIA 1 1 1
MEDIA 2 2 2 -1
MEDIA 2 3 3 -2
MEDIA 2 4 4 -3
MEDIA 2 5 5 -4
MEDIA 2 6 6 -5
BOUNDARY 6
READ BIAS ID=500 2 6 END BIAS
Here the weighting functions associated with bias IDs 2, 3, 4, and 5
each have a thickness of 3.0 cm, corresponding exactly to the increment
thickness for water in :numref:`tab8-1-20` Bias ID 6 is used for the last
generated region which is 3.24 cm thick.
The following examples illustrate the use of biasing data. Suppose the
user wishes to use the weighting function for water from :numref:`tab8-1-20`
for bias IDs 2 through 6. The biasing input data would then be:
::
READ BIAS ID=500 2 6 END BIAS
The energy-dependent values of weight average for the first 3 cm
interval of water will be used for weighting the geometry regions that
specify a bias ID of 2. The energy-dependent values of weight average
for the second 3 cm interval of water will be used for geometry regions
that specify a bias ID of 3, etc. Thus, the energy-dependent values of
weight average for the fifth 3 cm interval of water will be used for
geometry regions that specify a bias ID of 6. Geometry regions that use
bias IDs other than 2, 3, 4, 5, and 6 will use the default value of
weight average that is constant for all energies as a biasing function.
Several sets of biasing data can be entered at once. Assume the user
wishes to use the weighting function for concrete from :numref:`tab8-1-20` for
bias IDs 2 through 4 and the weighting function for water for bias IDs 5
through 7. The appropriate input data block is the following:
::
READ BIAS ID=301 2 4 ID=500 5 7 END BIAS
The energy-dependent values of weight average for the first 5 cm
interval of concrete will be used for the geometry regions that specify
a bias ID of 2, the energy-dependent values of weight average for the
second 5 cm interval of concrete will be used for the geometry regions
that specify a bias ID of 3, and the energy-dependent values of weight
average for the third 5 cm interval of concrete will be used for the
geometry regions that specify a bias ID of 4. The energy-dependent
values of weight average for the first 3 cm interval of water will be
used for geometry regions that specify a bias ID of 5, the values for
the second 3 cm interval of water will be used for geometry regions that
specify a bias ID of 6, and the values for the third 3 cm interval of
water will be used for geometry regions that specify a bias ID of 7. The
default value of weight average will be used for all bias IDs outside
the range of 2--7.
If the biasing data block defines the same bias ID more than once, the
value that is entered last supersedes previous entries. Assuming that
the following data block is entered,
::
READ BIAS ID=400 2 7 ID=500 5 7 END BIAS
the data for paraffin (ID=400) will be used for bias IDs 2, 3, and 4,
and the data for water (ID=500) will be used for bias IDs 5, 6, and 7.
.. centered:: EXAMPLE 1. USE OF BIASING DATA
It is assumed that a 5 cm radius sphere of material 2 is reflected by a
20 cm thickness of material 1 (concrete). The concrete reflector is
spherical and close fitting upon the sphere of material 2. The mixing
table must specify material 1 and material 2. Material 1 must be defined
as concrete. The geometry and biasing data should be entered as follows:
KENO V.a:
::
READ GEOM
SPHERE 2 1 5.0
REPLICATE 1 2 5.0 4
END GEOM
READ BIAS ID=301 2 5 END BIAS
KENO-VI:
::
READ GEOM
GLOBAL UNIT 1
SPHERE 1 5.0
SPHERE 2 10.0
SPHERE 3 15.0
SPHERE 4 20.0
SPHERE 5 25.0
MEDIA 2 1 1
MEDIA 1 2 2 -1
MEDIA 1 3 3 -2
MEDIA 1 4 4 -3
MEDIA 1 5 5 -4
BOUNDARY 5
END GEOM
READ BIAS ID=301 2 5 END BIAS
The bias ID for the first generated region is 2, the second is 3, the
third is 4, and the fourth is 5. The biasing data block specifies that
the biasing function for material ID 301 (concrete) will be used from
the weighting library. The bias ID to which the energy-dependent
weighting function for the first 5.0 cm interval of concrete is applied
is 2; the energy-dependent weighting function for the fourth 5 cm
interval of concrete is applied to the fourth generated geometry region.
This generated region has a bias ID of 5.
In KENO V.a, Example 1 can also be described without using a reflector
record as shown below. The records that are generated by the reflector
record in the previous set of data are identical to the last four
spheres in this mockup.
EXAMPLE 1. Use of biasing without a reflector record.
KENO V.a:
::
READ GEOM
SPHERE 2 1 5.0
SPHERE 1 2 10.0
SPHERE 1 3 15.0
SPHERE 1 4 20.0
SPHERE 1 5 25.0
END GEOM
READ BIAS ID=301 2 5 END BIAS
.. _8-1-3-9:
Color plots
~~~~~~~~~~~
Plots are generated only if a plot data block has been entered for the
problem and **PLT**\ =NO has not been entered in the parameter data or
the plot data. See :numref:`8-1-2-11` for a description of plot data. When a
plot is to be made, the user MUST correctly specify the upper left-hand
corner of the plot with respect to the origin of the plot. The origin of
a plot is defined as the origin of the **GLOBAL UNIT**.
Plots can represent mixture numbers, unit numbers, or bias ID numbers. A
title can be entered for each plot. If plot titles are omitted, the
title of the KENO case will be printed for each plot title until a plot
title is entered. If a plot title is entered and a subsequent plot title
is omitted, the last plot title prior to the omitted one will be used
for the omitted one.
The upper left and lower right coordinates define the area (i.e., the
slice and its location) for which the plot is to be made. The direction
cosines across the plot and the direction cosines down the plot define
the direction of the vector across the plot and the vector down the plot
with respect to the geometry coordinate system. One of the simplest ways
of generating a plot is to specify the desired coordinates of the upper
left and lower right corners of the plot. Then one must determine which
plot axis is to be across the plot and which is to be down. The sign of
the direction cosine should be consistent with the direction of that
component when moving from the upper left to lower right corner. For
example, to draw a plot of an X-Z slice at Y = 5.0 with X across the
plot and Z down the plot for a system whose X coordinates ranges from
0.0 to 10.0 and whose Z coordinates range from 0.0 to 20.0, the upper
left coordinate could be **XUL**\ =0.0 **YUL**\ =5.0 **ZUL**\ =20.0 and
the lower right coordinates could be **XLR**\ =10.0 **YLR**\ =5.0
**ZLR**\ =0.0. Since X is to be plotted across the plot with X = 0.0 at
the left and X = 10.0 at the right, only the X component of the
direction cosines across the plot need be entered. It should be positive
because going from 0.0 to 10.0 is moving in the positive direction.
Thus, **UAX**\ =1.0 would be entered for the direction cosines across
the plot. **VAX** and **WAX** could be omitted. Z is to be plotted down
the plot with Z = 20.0 at the top and Z = 0.0 at the bottom. Therefore,
only the Z component of the direction cosines down the plot needs to be
defined. It should be negative because moving from 20.0 to 0.0 is moving
in the negative direction. Thus, **WDN** = -1.0 would be entered for the
direction cosines down the plot. **UDN** and **VDN** could be omitted.
The sign of the direction cosines should be consistent with the
coordinates of the upper left and lower right corners in order to get a
plot.
It is not necessary that the plot be made for a slice orthogonal to one
of the axes. Plots can be made of slices cut at any desired angle, but
the user should exercise caution and be well aware of the distortion of
shapes that can be introduced. (Nonorthogonal slices through cylinders
plot as ellipses.)
The user can specify the horizontal and vertical spacing between points
on the plot. It is usually advisable to enter one or the other. Entering
both can cause distortion of the plot. **DLX**\ = is used to specify the
horizontal spacing between points and **DLD**\ = is used to specify the
vertical spacing between points. When only one of them is specified, the
code calculates the correct value of the other so the plot will not be
distorted. **DLX** or **DLD** can be specified by the user to be small
enough to show the desirable detail in the plot. The plot is generated
by starting at the upper left corner of the plot and generating a point
every **DLX** across the plot; then moving down **DLD** and repeating
the generation of the points across the plot.
**NAX** specifies the number of intervals (pixels) that will be printed
across the plot. **NDN** specifies the number of intervals (pixels) that
will be printed down the plot. If both **NAX** and **NDN** are entered,
the plot may be distorted. If one of them is entered, the value of the
other will be calculated so the plot will not be distorted.
When a plot is being made, the first pixel represents the coordinates of
the upper left corner. The value of **DELV** is added to the coordinate
that is to be printed across the plot, and the next pixel is printed.
**DELV** is added to that value to determine the location of the next
pixel, that is, a point is determined every **DELV** across the plot and
a pixel is printed for each point. When a line has been completed, a new
line is begun **DELU** from the first line. This procedure is repeated
until the plot is complete.
.. centered:: EXAMPLE 1. SINGLE UNIT WITH CENTERED ORIGIN
Consider two concentric cylinders in a cuboid. The inner cylinder is
5.2 cm in diameter. The outer cylinder has an inside diameter of 7.2 cm
and an outside diameter of 7.6 cm. Both cylinders are 30 cm high. They
are contained in a tight-fitting box with a wall thickness of 0.5 cm and
top and bottom thickness of 1.0 cm. The inner cylinder is composed of
mixture 1, the outer cylinder is made of mixture 4, and the box is made
of mixture 2. The problem can be described with its origin at the center
of the inner cylinder. The problem description for this arrangement is
shown below:
KENO V.a:
::
=KENOVA
SINGLE UNIT CONCENTRIC CYLINDERS IN CUBOID WITH ORIGIN AT CENTER
READ PARAM RUN=NO LIB=41 END PARAM
READ MIXT SCT=1
MIX=1 92500 4.7048e-2
MIX=2 200 1.0
MIX=3 502 0.1
MIX=4 200 1.0
END MIXT
READ GEOM
UNIT 1
CYLINDER 1 1 2.6 2P15.0
CYLINDER 0 1 3.6 2P15.0
CYLINDER 4 1 3.8 2P15.0
CUBOID 0 1 4P3.8 2P15.0
CUBOID 2 1 4P4.3 2P16.0
END GEOM
READ PLOT
TTL='X-Y SLICE AT Z MIDPOINT. SINGLE UNIT CONCENTRIC CYLS'
XUL=-4.6 YUL=4.6 ZUL=0.0 XLR=4.6 YLR=-4.6 ZLR=0.0
UAX=1.0 VDN=-1.0 NAX=640 END
PIC=UNIT END
END PLOT
END DATA
END
KENO-VI:
::
=KENOVI
SINGLE UNIT CONCENTRIC CYLINDERS IN CUBOID WITH ORIGIN AT CENTER
READ PARAM RUN=NO LIB=41 TME=0.5 END PARAM
READ MIXT SCT=1 MIX=1 92500 4.7048-2 MIX=2 200 1.0 MIX=3 502 0.1
MIX=4 200 1.0
END MIXT
READ GEOM
GLOBAL UNIT 1
CYLINDER 1 2.6 2P15.0
CYLINDER 2 3.6 2P15.0
CYLINDER 3 3.8 2P15.0
CUBOID 4 4P3.8 2P15.0
CUBOID 5 4P4.3 2P16.0
MEDIA 1 1 1
MEDIA 0 1 2 -1
MEDIA 4 1 3 -2
MEDIA 0 1 4 -3
MEDIA 2 1 5 -4
BOUNDARY 5
END GEOM
READ PLOT
TTL='X-Y SLICE AT Z MIDPOINT. SINGLE UNIT CONCENTRIC CYLS.'
XUL=-4.6 YUL=4.6 ZUL=0.0 XLR=4.6 YLR=-4.6 ZLR=0.0
UAX=1.0 VDN=-1.0 NAX=640 END
PIC=UNIT END
END PLOT
END DATA
END
The plot data blocks included above are set up to draw a mixture map of
an X-Y slice taken at the half height (Z=0.0) and a unit map for the
same slice. In the above examples, the geometry dimensions extend from X
= -4.3 to X = 4.3, from Y = -4.3, to Y = 4.3, and from Z = -16.0 to Z =
16.0. An X-Y slice is be printed at the half height (Z = 0.0). The
desired plot data sets the upper left-hand corner of the plot to be
X = -4.6 and Y = 4.6. The lower right-hand corner of the plot is
specified as X = 4.6 and Y = -4.6. These data are entered by specifying
the upper left-hand corner as **XUL**\ = -4.6 **YUL**\ =4.6
**ZUL**\ =0.0 and the lower right-hand corner as **XLR**\ =4.6
**YLR**\ = -4.6 **ZLR**\ =0.0. It is desired to print X across the plot
and Y down the plot. Therefore, the X direction cosine is specified
across the plot, in the direction from X = -4.6 to X = 4.6 as
**UAX**\ =1.0. The Y direction cosine is specified down the plot, from
Y = 4.6 to Y = -4.6 as **VDN**\ = -1.0.
A black border will be printed for points outside the range of the
problem geometry description. By setting the plot dimension slightly
larger than the geometry dimension, a black border will be printed
around the specified plot. This verifies that the outer boundaries of
the geometry are contained within the plot dimensions. NAX is the number
of pixels across for a color plot. An initial recommended range for NAX
is between 600 and 800 pixels. The resulting plots are shown in
:numref:`fig8-1-65` and :numref:`fig8-1-66`. The associated data for both plots are
shown in :numref:`list8-1-1` and :numref:`list8-1-2`.
.. figure:: figs/Keno/fig65.png
:align: center
:width: 400
:name: fig8-1-65
Mixture color plot for single unit with centered origin.
.. figure:: figs/Keno/fig66.png
:align: center
:width: 400
:name: fig8-1-66
Unit map color plot for single unit with centered origin.
.. code-block:: scale
:name: list8-1-1
:caption: Associated data for single unit mixture map.
mixture map
mixture 0 1 2 4
symbol 1 2 3
upper left lower right
coordinates coordinates
x -4.6000e+00 4.6000e+00
y 4.6000e+00 -4.6000e+00
z 0.0000e+00 0.0000e+00
u axis v axis
(down) (across)
x 0.00000 1.00000
y -1.00000 0.00000
z 0.00000 0.00000
nu= 640 nv= 640 delu= 1.4375e-02 delv= 1.4375e-02 lpi= 10.000
.. code-block:: scale
:name: list8-1-2
:caption: Associated data for single unit map.
x-y slice at z midpoint. single unit concentric cyls
unit map
unit 1
symbol 1
upper left lower right
coordinates coordinates
x -4.6000e+00 4.6000e+00
y 4.6000e+00 -4.6000e+00
z 0.0000e+00 0.0000e+00
u axis v axis
(down) (across)
x 0.00000 1.00000
y -1.00000 0.00000
z 0.00000 0.00000
nu= 640 nv= 640 delu= 1.4375e-02 delv= 1.4375e-02 lpi= 10.000
.. centered:: EXAMPLE 2. SINGLE UNIT WITH OFFSET ORIGIN.
The physical problem is the same as that described in Example 1: two
concentric cylinders in a cuboid. The dimensions are exactly the same,
and the difference is in the choice of the origin. In this geometry
description, the origin was specified as the most negative point of the
unit. Thus, the cylinders must have an origin specified to center them
in the cuboid, and the cuboid extends from 0.0 to 8.6 in X and Y and
from 0.0 to 32 in Z as shown in the problem description below.
KENO V.a:
::
=KENO5
SINGLE UNIT CONCENTRIC CYLINDERS IN CUBOID WITH ORIGIN AT CORNER
READ PARAM RUN=NO LIB=41 END PARAM
READ MIXT SCT=1 MIX=1 92500 4.7048-2 MIX=2 200 1.0 MIX=3 502 0.1
MIX=4 200 1.0
END MIXT
READ GEOM
UNIT 1
CYLINDER 1 1 2.6 31.0 1.0 ORIGIN 4.3 4.3
CYLINDER 0 1 3.6 31.0 1.0 ORIGIN 4.3 4.3
CYLINDER 4 1 3.8 31.0 1.0 ORIGIN 4.3 4.3
CUBOID 0 1 8.1 0.5 8.1 0.5 31.0 1.0
CUBOID 2 1 8.6 0.0 8.6 0.0 32.0 0.0
END GEOM
READ PLOT
TTL='X-Y SLICE AT Z MIDPOINT. SINGLE UNIT CONCENTRIC CYLS.'
XUL=-0.3 YUL=8.9 ZUL=16.0 XLR=8.9 YLR=-0.3 ZLR=16.0
UAX=1.0 VDN=-1.0 NAX=640 END
PIC=UNIT END
END PLOT
END DATA
END
KENO-VI:
::
=KENOVI
SINGLE UNIT CONCENTRIC CYLINDERS IN CUBOID WITH ORIGIN AT CORNER
READ PARAM RUN=NO LIB=41 TME=0.5 END PARAM
READ MIXT SCT=1 MIX=1 92500 4.7048-2 MIX=2 200 1.0 MIX=3 502 0.1
MIX=4 200 1.0
END MIXT
READ GEOM
GLOBAL UNIT 1
CYLINDER 1 2.6 31.0 1.0 ORIGIN X=4.3 Y=4.3
CYLINDER 2 3.6 31.0 1.0 ORIGIN X=4.3 Y=4.3
CYLINDER 3 3.8 31.0 1.0 ORIGIN X=4.3 Y=4.3
CUBOID 4 8.1 0.5 8.1 0.5 31.0 1.0
CUBOID 5 8.6 0.0 8.6 0.0 32.0 0.0
MEDIA 1 1 1
MEDIA 0 1 2 -1
MEDIA 4 1 3 -2 -1
MEDIA 0 1 4 -3 -2 -1
MEDIA 2 1 5 -4
BOUNDARY 5
END GEOM
READ PLOT
TTL='X-Y SLICE AT Z MIDPOINT. SINGLE UNIT CONCENTRIC CYLS.'
XUL=-0.3 YUL=8.9 ZUL=16.0 XLR=8.9 YLR=-0.3 ZLR=16.0
UAX=1.0 VDN=-1.0 NAX=640 END
PIC=UNIT NCH='01' END
END PLOT
END DATA
END
The plot data included above will draw a mixture map of an X-Y slice
taken at the half height (Z = 16.0). It will also draw a unit map of the
same slice. The plot dimensions extend 0.3 cm beyond the problem
dimensions to provide a black border around the plot. The associated
plot data specification for the mixture map is shown in :numref:`list8-1-3`, the
mixture map is shown in :numref:`fig8-1-70`, and the associated plot data for
the unit map is shown in :numref:`list8-1-4`. The unit map is identical to
:numref:`fig8-1-66` and is not included.
.. code-block:: scale
:name: list8-1-3
:caption: Associated data for mixture map of single unit with offset origin.
x-y slice at z midpoint. single unit concentric cyls.
mixture map
mixture 0 1 2 4
symbol 1 2 3
upper left lower right
coordinates coordinates
x -3.0000e-01 8.9000e+00
y 8.9000e+00 -3.0000e-01
z 1.6000e+01 1.6000e+01
u axis v axis
(down) (across)
x 0.00000 1.00000
y -1.00000 0.00000
z 0.00000 0.00000
nu= 640 nv= 640 delu= 1.4375e-02 delv= 1.4375e-02 lpi= 10.000
.. figure:: figs/Keno/fig70.png
:align: center
:width: 400
:name: fig8-1-70
Mixture map of single unit with offset origin.
.. code-block:: scale
:name: list8-1-4
:caption: Associated data for unit map of single unit with offset origin.
x-y slice at z midpoint. single unit concentric cyls.
unit map
unit 1
symbol 1
upper left lower right
coordinates coordinates
x -3.0000e-01 8.9000e+00
y 8.9000e+00 -3.0000e-01
z 1.6000e+01 1.6000e+01
u axis v axis
(down) (across)
x 0.00000 1.00000
y -1.00000 0.00000
z 0.00000 0.00000
nu= 640 nv= 640 delu= 1.4375e-02 delv= 1.4375e-02 lpi= 10.000
.. centered:: EXAMPLE 3. A 2 :math:`\times` 2 :math:`\times` 2 UNREFLECTED ARRAY OF CONCENTRIC CYLINDERS IN
CUBOIDS
The physical representation of this example is a 2 :math:`\times` 2 :math:`\times` 2 array of the
configuration described in Example 1 of this section. The input data
description for this array is given below:
KENO V.a:
::
=KENOVA
2x2x2 BARE ARRAY OF CONCENTRIC CYLINDERS IN CUBOID
READ PARAM RUN=NO LIB=41 END PARAM
READ MIXT SCT=1 MIX=1 92500 4.7048-2 MIX=2 200 1.0 MIX=3 502 0.1
MIX=4 200 1.0
END MIXT
READ GEOM
UNIT 1
CYLINDER 1 1 2.6 2P15.0
CYLINDER 0 1 3.6 2P15.0
CYLINDER 4 1 3.8 2P15.0
CUBOID 0 1 4P3.8 2P15.0
CUBOID 2 1 4P4.3 2P16.0
END GEOM
READ ARRAY NUX=2 NUY=2 NUZ=2 END ARRAY
READ PLOT
TTL='X-Y SLICE AT HALF HEIGHT OF BOTTOM LAYER.'
XUL=-0.3 YUL=17.5 ZUL=16.0 XLR=17.5 YLR=-0.3 ZLR=16.0
UAX=1.0 VDN=-1.0 NAX=640 END
TTL='X-Z SLICE THROUGH FRONT ROW, Y=12.9.'
XUL=-1.0 YUL=12.9 ZUL=65.0 XLR=18.2 YLR=12.9 ZLR=-1.0
UAX=1.0 WDN=-1.0 NAX=320 END
END PLOT
END DATA
END
KENO-VI:
::
=KENOVI
2x2x2 BARE ARRAY OF CONCENTRIC CYLINDERS IN CUBOID
READ PARAM RUN=NO LIB=41 TME=8.5 END PARAM
READ MIXT SCT=1 MIX=1 92500 4.7048-2 MIX=2 200 1.0 MIX=3 502 0.1
MIX=4 200 1.0
END MIXT
READ GEOM
UNIT 1
CYLINDER 1 2.6 2P15.0
CYLINDER 2 3.6 2P15.0
CYLINDER 3 3.8 2P15.0
CUBOID 4 4P3.8 2P15.0
CUBOID 5 4P4.3 2P16.0
MEDIA 1 1 1
MEDIA 0 1 2 -1
MEDIA 4 1 3 -2 -1
MEDIA 0 1 4 -3 -2 -1
MEDIA 2 1 -5 -4
BOUNDARY 5
GLOBAL UNIT 2
CUBOID 1 17.2 0.0 17.2 0.0 64.0 0.0
ARRAY 1 1 PLACE 1 1 1 4.3 4.3 16.0
BOUNDARY 1
END GEOM
READ ARRAY ARA=1 NUX=2 NUY=2 NUZ=2 FILL F1 END FILL END ARRAY
READ PLOT
TTL='X-Y SLICE AT HALF HEIGHT OF BOTTOM LAYER.'
XUL=-0.3 YUL=17.5 ZUL=16.0 XLR=17.5 YLR=-0.3 ZLR=16.0
UAX=1.0 VDN=-1.0 NAX=640 END
TTL='X-Z SLICE THROUGH FRONT ROW, Y=12.9.'
XUL=-1.0 YUL=12.9 ZUL=65.0 XLR=18.2 YLR=12.9 ZLR=-1.0
UAX=1.0 WDN=-1.0 NAX=320 END
END PLOT
END DATA
END
As stated at the beginning of :numref:`8-1-3-9`, the origin of a plot is
defined as the origin of the **GLOBAL UNIT**. Each individual unit in
the array is 8.6 cm wide in X and Y and 32 cm high in Z. Since the array
has two units stacked in each direction, the array is 17.2 cm wide in X
and Y and is 64 cm high. Therefore, the array exists from X = 0.0 to X =
17.2, from Y = 0.0 to Y = 17.2 and from Z = 0.0 to Z = 64.0.
The first color plot is to generate an X-Y slice through the array at
the half height (Z = 16.0 cm) of the first layer as shown in
:numref:`fig8-1-72`. It is desirable to create an image with a larger extent
than the global unit to ensure that the boundaries are as expected. This
is achieved by setting the boundaries of the plot larger than the array.
In this case, the boundaries were arbitrarily set 0.3 cm larger than the
array, resulting in a black border around the array. If the plot were to
exclude everything external to the array, the following coordinates
could have been entered: **XUL**\ =0.0 **YUL**\ =17.2 **ZUL**\ =16.0
**XLR**\ =17.2 **YLR**\ =0.0 **ZLR**\ =16.0. This would have eliminated
the black border. The existing plot was made using **XUL**\ = -0.3
**YUL**\ =17.5 **ZUL**\ =16.0 **XLR**\ =17.5 **YLR**\ = -0.3
**ZLR**\ =16.0.
.. figure:: figs/Keno/fig72.png
:align: center
:width: 400
:name: fig8-1-72
X-Y plot of 2 :math:`\times` 2 :math:`\times` 2 bare array.
The second color plot is to generate an X-Z slice through the center of
the front row of the array. In order to obtain a black border, the
coordinates of X and Z were arbitrarily set 1.0 cm larger than the
boundaries of the array. The center of the front row occurs at Y = 12.9.
The coordinates of the plot were: **XUL**\ = -1.0 **ZUL**\ =65.0
**YUL**\ =12.9 **XLR**\ =18.2 **ZLR**\ = -1.0 **YLR**\ =12.9. The
resulting mixture map is shown in :numref:`fig8-1-73`.
.. figure:: figs/Keno/fig73.png
:align: center
:width: 400
:name: fig8-1-73
X-Z plot of 2 :math:`\times` 2 :math:`\times` 2 bare array.
.. centered:: EXAMPLE 4. A 2 :math:`\times` 2 :math:`\times` 2 REFLECTED ARRAY WITH THE ORIGIN AT THE MOST
NEGATIVE POINT OF THE ARRAY
The **ARRAY** is described in Example 3 of this section with a 6 in.
concrete reflector on all faces. The input data description for this
array is given below.
KENO V.a:
::
=KENOVA
2x2x2 REFLECTED ARRAY OF CONCENTRIC CYLINDERS IN CUBOID
READ PARAM RUN=NO LIB=41 END PARAM
READ MIXT SCT=1 MIX=1 92500 4.7048-2 MIX=2 200 1.0 MIX=3 301 1.0
MIX=4 200 1.0
END MIXT
READ GEOM
UNIT 1
CYLINDER 1 1 2.6 2P15.0
CYLINDER 0 1 3.6 2P15.0
CYLINDER 4 1 3.8 2P15.0
CUBOID 0 1 4P3.8 2P15.0
CUBOID 2 1 4P4.3 2P16.0
GLOBAL
UNIT 2
ARRAY 1 3*0.0
REFLECTOR 3 2 6*5.0 3
REFLECTOR 3 5 6*0.24 1
END GEOM
READ BIAS ID=301 2 5 END BIAS
READ ARRAY ARA=1 NUX=2 NUY=2 NUZ=2 FILL F1 END FILL END ARRAY
READ PLOT
TTL='X-Y SLICE AT HALF HEIGHT OF BOTTOM LAYER.INCLUDES REFL.'
XUL=-16.24 YUL=33.44 ZUL=16.0 XLR=33.44 YLR=-16.24 ZLR=16.0
UAX=1.0 VDN=-1.0 NAX=640 END
TTL='X-Y SLICE AT HALF HEIGHT OF BOTTOM LAYER, INCLUDE 3 CM OF REFL.'
XUL=-3.0 YUL=20.2 ZUL=16.0 XLR=20.2 YLR=-3.0 ZLR=16.0
UAX=1.0 VDN=-1.0 NAX=640 END
TTL='X-Z SLICE THROUGH FRONT ROW, Y=12.9. INCLUDE REFLECTOR'
XUL=-16.24 YUL=12.9 ZUL=80.24 XLR=33.44 YLR=12.9 ZLR=-16.24
UAX=1.0 WDN=-1.0 NAX=640 END
TTL='X-Z SLICE THROUGH FRONT ROW, Y=12.9. INCLUDE 3 CM OF REFLECTOR'
XUL=-3.0 YUL=12.9 ZUL=67.0 XLR=20.2 YLR=12.9 ZLR=-3.0
UAX=1.0 WDN=-1.0 NAX=640 END
END PLOT
END DATA
END
KENO-VI:
::
=KENOVI
2x2x2 REFLECTED ARRAY OF CONCENTRIC CYLINDERS IN CUBOID
READ PARAM RUN=NO LIB=41 TME=0.5 END PARAM
READ MIXT SCT=1 MIX=1 92500 4.7048-2 MIX=2 200 1.0 MIX=3 301 1.0
MIX=4 200 1.0
END MIXT
READ GEOM
UNIT 1
CYLINDER 1 2.6 2P15.0
CYLINDER 2 3.6 2P15.0
CYLINDER 3 3.8 2P15.0
CUBOID 4 4P3.8 2P15.0
CUBOID 5 4P4.3 2P16.0
MEDIA 1 1 1
MEDIA 0 1 2 -1
MEDIA 4 1 3 -2
MEDIA 0 1 4 -3
MEDIA 2 1 5 -4
BOUNDARY 5
GLOBAL UNIT 2
CUBOID 1 17.2 0.0 17.2 0.0 64.0 0.0
CUBOID 2 22.20 -5.00 22.20 -5.00 69.00 -5.00
CUBOID 3 27.20 -10.00 27.20 -10.00 74.00 -10.00
CUBOID 4 32.20 -15.00 32.20 -15.00 79.00 -15.00
CUBOID 5 32.44 -15.24 32.44 -15.24 79.24 -15.24
ARRAY 1 1 PLACE 1 1 1 4.3 4.3 16.0
MEDIA 3 2 2 -1
MEDIA 3 3 3 -2
MEDIA 3 4 4 -3
MEDIA 3 5 5 -4
BOUNDARY 5
END GEOM
READ BIAS ID=301 2 5 END BIAS
READ ARRAY ARA=1 NUX=2 NUY=2 NUZ=2 FILL F1 END FILL END ARRAY
READ PLOT
TTL='X-Y SLICE AT HALF HEIGHT OF BOTTOM LAYER.INCLUDES REFL.'
XUL=-16.24 YUL=33.44 ZUL=16.0 XLR=33.44 YLR=-16.24 ZLR=16.0
UAX=1.0 VDN=-1.0 NAX=640 END
TTL='X-Y SLICE AT HALF HEIGHT OF BOTTOM LAYER, INCLUDE 3 CM OF REFL.'
XUL=-3.0 YUL=20.2 ZUL=16.0 XLR=20.2 YLR=-3.0 ZLR=16.0
UAX=1.0 VDN=-1.0 NAX=640 END
TTL='X-Z SLICE THROUGH FRONT ROW, Y=12.9. INCLUDE REFLECTOR'
XUL=-16.24 YUL=12.9 ZUL=80.24 XLR=33.44 YLR=12.9 ZLR=-16.24
UAX=1.0 WDN=-1.0 NAX=640 END
TTL='X-Z SLICE THROUGH FRONT ROW, Y=12.9. INCLUDE 3 CM OF REFLECTOR'
XUL=-3.0 YUL=12.9 ZUL=67.0 XLR=20.2 YLR=12.9 ZLR=-3.0
UAX=1.0 WDN=-1.0 NAX=640 END
END PLOT
END DATA
END
The **ARRAY** record specifies the array number and the coordinates of
the most negative point of the array to be (0.0,0.0,0.0) and the
coordinates of the most positive point to be (17.2,17.2,64.0). Thus the
reflected array extends from -15.24 cm to +32.44 cm in X and Y and from
-15.24 to +79.24 in Z.
The first color plot for this example is to show an X-Y slice through
the array and reflector at the half height of the bottom layer. A black
border is used to verify that the entire reflector has been shown. This
is accomplished by arbitrarily setting the plot boundaries 1 cm beyond
the reflector boundaries. The coordinates used for this plot are **XUL**
= -16.24 **YUL** = 33.44 **ZUL** = 16.0 **XLR** = 33.44 **YLR** = 16.24
**ZLR** = 16.0. The plot data description is shown in :numref:`list8-1-5`, and
the plot is shown in :numref:`fig8-1-75`.
.. code-block:: scale
:name: list8-1-5
:caption: Plot data for X-Y slice of Example 4.
x-y slice at half height of bottom layer. includes refl.
mixture map
mixture 0 1 2 3 4
symbol 1 2 3 4
upper left lower right
coordinates coordinates
x -1.6240e+01 3.3440e+01
y 3.3440e+01 -1.6240e+01
z 1.6000e+01 1.6000e+01
u axis v axis
(down) (across)
x 0.00000 1.00000
y -1.00000 0.00000
z 0.00000 0.00000
nu= 640 nv= 640 delu= 7.7625e-02 delv= 7.7625e-02 lpi= 10.000
.. figure:: figs/Keno/fig75.png
:align: center
:width: 400
:name: fig8-1-75
X-Y plot of 2 :math:`\times` 2 :math:`\times` 2 reflected array.
The next color plot is the same as the previous plot, except this plot
includes only the first 3 cm of the reflector in order to show more
detail. The coordinates used for this plot are **XUL**\ = -3.0
**YUL**\ =20.2 **ZUL**\ =16.0 **XLR**\ =20.2 **YLR**\ = -3.0
**ZLR**\ =16.0. This plot data description is given in :numref:`list8-1-6`, and
the plot is shown in :numref:`fig8-1-77`.
.. code-block:: scale
:name: list8-1-6
:caption: Plot data for enlarged X-Y slice of Example 4.
x-y slice at half height of bottom layer, include 3 cm of refl.
mixture map
mixture 0 1 2 3 4
symbol 1 2 3 4
upper left lower right
coordinates coordinates
x -3.0000e+00 2.0200e+01
y 2.0200e+01 -3.0000e+00
z 1.6000e+01 1.6000e+01
u axis v axis
(down) (across)
x 0.00000 1.00000
y -1.00000 0.00000
z 0.00000 0.00000
nu= 640 nv= 640 delu= 3.6250e-02 delv= 3.6250e-02 lpi= 10.000
.. figure:: figs/Keno/fig77.png
:align: center
:width: 400
:name: fig8-1-77
Enlarged X-Y plot of 2 :math:`\times` 2 :math:`\times` 2 reflected array.
The third color plot for this example is an X-Z slice through the center
of the front row. An extra 1 cm is included in the coordinates to
provide a black border around the plot. The coordinates are: **XUL**\ =
-16.24 **YUL**\ =12.9 **ZUL**\ =80.24 **XLR**\ =33.44 **YLR**\ =12.9
**ZLR**\ = -16.24. The resultant plot data and plot are shown in
:numref:`list8-1-7` and :numref:`fig8-1-79`. X-Z plot for 2 :math:`\times` 2 :math:`\times` 2 reflected array.
.. code-block:: scale
:name: list8-1-7
:caption: Plot data for X-Z slice of Example 4.
x-z slice through front row, y=12.9. include reflector
mixture map
mixture 0 1 2 3 4
symbol 1 2 3 4
upper left lower right
coordinates coordinates
x -1.6240e+01 3.3440e+01
y 1.2900e+01 1.2900e+01
z 8.0240e+01 -1.6240e+01
u axis v axis
(down) (across)
x 0.00000 1.00000
y 0.00000 0.00000
z -1.00000 0.00000
nu= 1242 nv= 640 delu= 7.7625e-02 delv= 7.7625e-02 lpi= 10.000
.. figure:: figs/Keno/fig79.png
:align: center
:width: 400
:name: fig8-1-79
X-Z plot for 2 :math:`\times` 2 :math:`\times` 2 reflected array.
The last color plot for this example is the same as the previous one,
except only 3 cm of the reflector is included in the plot. The plot data
and associated plot are shown in :numref:`list8-1-8` and :numref:`fig8-1-81`.
.. code-block:: scale
:name: list8-1-8
:caption: Plot data for enlarged X-Z slice of Example 4.
x-z slice through front row, y=12.9. include 3 cm of reflector
mixture map
mixture 0 1 2 3 4
symbol 1 2 3 4
upper left lower right
coordinates coordinates
x -3.0000e+00 2.0200e+01
y 1.2900e+01 1.2900e+01
z 6.7000e+01 -3.0000e+00
u axis v axis
(down) (across)
x 0.00000 1.00000
y 0.00000 0.00000
z -1.00000 0.00000
nu= 1931 nv= 640 delu= 3.6250e-02 delv= 3.6250e-02 lpi= 10.000
.. figure:: figs/Keno/fig81.png
:align: center
:width: 400
:name: fig8-1-81
Enlarged X-Z plot of 2 :math:`\times` 2 :math:`\times` 2 reflected array.
.. centered:: EXAMPLE 5. A 2 :math:`\times` 2 :math:`\times` 2 REFLECTED ARRAY WITH THE ORIGIN CENTERED IN THE
ARRAY
This example is physically identical to Example 4. The difference is in
the specification of the origin. The bare array is 17.2 cm wide in X and
Y and 64 cm high. The origin (0,0,0) can be placed at the exact center
of the array by specifying the most negative point of the array as X =
-8.6, Y = -8.6 and Z = -32.0. This is done using the **ARRAY**
description in the geometry block. Because the origin is located at a
different position, the coordinates of the plots will also be different.
The input data description for this example is given below.
KENO V.a:
::
=KENOVA
2x2x2 REFLECTED ARRAY OF CONCENTRIC CYLINDERS IN CUBOID
READ PARAM RUN=NO LIB=41 TME=0.5 END PARAM
READ MIXT SCT=1 MIX=1 92500 4.7048-2 MIX=2 200 1.0 MIX=3 301 1.0
MIX=4 200 1.0
END MIXT
READ GEOM
UNIT 1
CYLINDER 1 1 2.6 2P15.0
CYLINDER 0 1 3.6 2P15.0
CYLINDER 4 1 3.8 2P15.0
CUBOID 0 1 4P3.8 2P15.0
CUBOID 2 1 4P4.3 2P16.0
GLOBAL
UNIT 2
ARRAY 1 1 2*-8.6 -32.0
REFLECTOR 3 2 6*5.0 3
REFLECTOR 3 5 6*0.24 1
END GEOM
READ BIAS ID=301 2 5 END BIAS
READ ARRAY ARA=1 NUX=2 NUY=2 NUZ=2 FILL F1 END FILL END ARRAY
READ PLOT
TTL='X-Y SLICE AT HALF HEIGHT OF BOTTOM LAYER.INCLUDES REFL.'
XUL=-24.84 YUL=24.84 ZUL=-8.0 XLR=24.84 YLR=-24.84 ZLR=-8.0
UAX=1.0 VDN=-1.0 NAX=640 END
TTL='X-Y SLICE AT HALF HEIGHT OF BOTTOM LAYER, INCLUDE 3 CM OF REFL.'
XUL=-11.6 YUL=11.6 ZUL=-8.0 XLR=11.6 YLR=-11.6 ZLR=-8.0
UAX=1.0 VDN=-1.0 NAX=640 END
TTL='X-Z SLICE THROUGH FRONT ROW. Y=4.3 INCLUDE REFLECTOR'
XUL=-24.84 YUL=4.3 ZUL=48.24 XLR=24.84 YLR=4.3 ZLR=-48.24
UAX=1.0 WDN=-1.0 NAX=640 END
TTL='X-Z SLICE THROUGH FRONT ROW, Y=4.3 INCLUDE 3 CM OF REFLECTOR'
XUL=-11.6 YUL=4.3 ZUL=35.0 XLR=11.6 YLR=4.3 ZLR=-35.0
UAX=1.0 WDN=-1.0 NAX=640 END
END PLOT
END DATA
END
KENO-VI:
::
=KENOVI
2x2x2 REFLECTED ARRAY OF CONCENTRIC CYLINDERS IN CUBOID
READ PARAM RUN=NO LIB=41 TME=0.5 END PARAM
READ MIXT SCT=1 MIX=1 92500 4.7048-2 MIX=2 200 1.0 MIX=3 301 1.0
MIX=4 200 1.0
END MIXT
READ GEOM
UNIT 1
CYLINDER 1 2.6 2P15.0
CYLINDER 2 3.6 2P15.0
CYLINDER 3 3.8 2P15.0
CUBOID 4 4P3.8 2P15.0
CUBOID 5 4P4.3 2P16.0
MEDIA 1 1
MEDIA 0 1 2 -1
MEDIA 4 1 3 -2
MEDIA 0 1 4 -3
MEDIA 2 1 5 -4
BOUNDARY 5
GLOBAL UNIT 2
CUBOID 1 8.6 -8.6 8.6 -8.6 32.0 -32.0
CUBOID 2 13.6 -13.6 13.6 -13.6 37.0 -37.0
CUBOID 3 18.6 -18.6 18.6 -18.6 42.0 -42.0
CUBOID 4 23.6 -23.6 23.6 -23.6 47.0 -47.0
CUBOID 5 23.84 -23.84 23.84 -23.84 47.24 -47.24
ARRAY 1 1 PLACE 1 1 1 -4.3 -4.3 -16.0
MEDIA 3 2 2 -1
MEDIA 3 3 3 -2
MEDIA 3 4 4 -3
MEDIA 3 5 5 -4
BOUNDARY 5
END GEOM
READ BIAS ID=301 2 5 END BIAS
READ ARRAY ARA=1 NUX=2 NUY=2 NUZ=2I FILL F1 END FILL END ARRAY
READ PLOT
TTL='X-Y SLICE AT HALF HEIGHT OF BOTTOM LAYER INCLUDES REFL.'
XUL=-24.84 YUL=24.84 ZUL=-8.0 XLR=24.84 YLR=-24.84 ZLR=-8.0
UAX=1.0 VDN=-1.0 NAX=130 NCH=' *=.X' END
TTL='X-Y SLICE AT HALF HEIGHT OF BOTTOM LAYER, INCLUDE 3 CM OF REFL.'
XUL=-11.6 YUL=11.6 ZUL=-8.0 XLR=11.6 YLR=-11.6 ZLR=-8.0
UAX=1.0 VDN=-1.0 NAX=640 END
TTL='X-Z SLICE THROUGH FRONT ROW. Y=4.3 INCLUDE REFLECTOR'
XUL=-24.84 YUL=4.3 ZUL=48.24 XLR=24.84 YLR=4.3 ZLR=-48.24
UAX=1.0 WDN=-1.0 NAX=640 END
TTL='X-Z SLICE THROUGH FRONT ROW, Y=4.3 INCLUDE 3 CM OF REFLECTOR'
XUL=-11.6 YUL=4.3 ZUL=35.0 XLR=11.6 YLR=4.3 ZLR=-35.0
UAX=1.0 WDN=-1.0 NAX=640 END
END PLOT
END DATA
END
The first color plot for this example covers exactly the same area as
the first plot for Example 4. The plot data and the plot are given in
:numref:`list8-1-9` and :numref:`fig8-1-83`, respectively.
.. code-block:: scale
:name: list8-1-9
:caption: Plot data for X-Y slice of Example 5.
x-y slice at half height of bottom layer.includes refl.
mixture map
mixture 0 1 2 3 4
symbol 1 2 3 4
upper left lower right
coordinates coordinates
x -2.4840e+01 2.4840e+01
y 2.4840e+01 -2.4840e+01
z -8.0000e+00 -8.0000e+00
u axis v axis
(down) (across)
x 0.00000 1.00000
y -1.00000 0.00000
z 0.00000 0.00000
nu= 640 nv= 640 delu= 7.7625e-02 delv= 7.7625e-02 lpi= 10.000
.. figure:: figs/Keno/fig83.png
:align: center
:width: 400
:name: fig8-1-83
X-Y plot of 2 :math:`\times` 2 :math:`\times` 2 reflected array with centered origin.
The Example 5 plot data and associated plots for an enlarged X-Y plot,
an X-Z plot and an enlarged X-Z plot are given in :numref:`list8-1-10` through :numref:`fig8-1-89`.
.. code-block:: scale
:name: list8-1-10
:caption: Plot data for an enlarged X-Y slice of Example 5.
x-y slice at half height of bottom layer, include 3 cm of refl.
mixture map
mixture 0 1 2 3 4
symbol 1 2 3 4
upper left lower right
coordinates coordinates
x -1.1600e+01 1.1600e+01
y 1.1600e+01 -1.1600e+01
z -8.0000e+00 -8.0000e+00
u axis v axis
(down) (across)
x 0.00000 1.00000
y -1.00000 0.00000
z 0.00000 0.00000
nu= 640 nv= 640 delu= 3.6250e-02 delv= 3.6250e-02 lpi= 10.000
.. figure:: figs/Keno/fig85.png
:align: center
:width: 400
:name: fig8-1-85
Enlarged X-Y plot of 2 :math:`\times` 2 :math:`\times` 2 reflected array with centered origin.
.. code-block:: scale
:name: list8-1-11
:caption: Plot data for X-Z slice of Example 5.
x-z slice through front row. y=4.3 include reflector
mixture map
mixture 0 1 2 3 4
symbol 1 2 3 4
upper left lower right
coordinates coordinates
x -2.4840e+01 2.4840e+01
y 4.3000e+00 4.3000e+00
z 4.8240e+01 -4.8240e+01
u axis v axis
(down) (across)
x 0.00000 1.00000
y 0.00000 0.00000
z -1.00000 0.00000
nu= 1242 nv= 640 delu= 7.7625e-02 delv= 7.7625e-02 lpi= 10.000
.. figure:: figs/Keno/fig87.png
:align: center
:width: 400
:name: fig8-1-87
X-Z plot of reflected 2 :math:`\times` 2 :math:`\times` 2 array with centered origin.
.. code-block:: scale
:name: list8-1-12
:caption: Plot data for enlarged X-Z slice of Example 5.
x-z slice through front row, y=4.3 include 3 cm of reflector
mixture map
mixture 0 1 2 3 4
symbol 1 2 3 4
upper left lower right
coordinates coordinates
x -1.1600e+01 1.1600e+01
y 4.3000e+00 4.3000e+00
z 3.5000e+01 -3.5000e+01
u axis v axis
(down) (across)
x 0.00000 1.00000
y 0.00000 0.00000
z -1.00000 0.00000
nu= 1931 nv= 640 delu= 3.6250e-02 delv= 3.6250e-02 lpi= 10.000
.. figure:: figs/Keno/fig89.png
:align: center
:width: 400
:name: fig8-1-89
Enlarged X-Z plot of reflected 2 :math:`\times` 2 :math:`\times` 2 array with centered origin.
.. centered:: EXAMPLE 6. NESTED HOLES.
The nested hole description is provided in :numref:`sec-module.keno.geom.nesting_holes`. Because this
example involves a complicated placement of units, it is helpful useful
to the user to generate a mixture plot and/or a unit plot for the
problem. The resultant mixture plot for this problem is shown in
:numref:`fig8-1-90`, and the data description for Example 6 follows.
.. figure:: figs/Keno/fig90.png
:align: center
:width: 400
:name: fig8-1-90
Mixture plot of nested holes problem.
.. code-block:: scale
:name: list8-1-13
:caption: Plot data for unit plot of nested holes.
x-y slice at z midpoint. nested holes. unit map
0 unit map
unit 1 2 3 4 5 6 7 8 9
symbol 1 2 3 4 5 6 7 8 9
overall system coordinates:
xmin= 0.00000e+00 xmax= 8.00000e+00 ymin= 0.00000e+00 ymax= 8.00000e+00
zmin= 0.00000e+00 zmax= 3.20000e+01
upper left lower right
coordinates coordinates
x -1.0000e-01 8.1000e+00
y 8.1000e+00 -1.0000e-01
z 1.6000e+01 1.6000e+01
u axis v axis
(down) (across)
x 0.00000 1.00000
y -1.00000 0.00000
z 0.00000 0.00000
nu= 640 nv= 640 delu= 1.2813e-02 delv= 1.2813e-02 lpi= 10.000
.. figure:: figs/Keno/fig92.png
:align: center
:width: 400
:name: fig8-1-92
Unit plot of nested holes problem.
KENO V.a:
::
=KENOVA
NESTED HOLES SAMPLE
READ PARAM RUN=NO LIB=41 END PARAM
READ MIXT SCT=1 MIX=1 92500 4.7048-2 MIX=2 200 1.0 MIX=3 502 0.1
MIX=4 200 1.0
END MIXT
READ GEOM
UNIT 1
CYLINDER 1 1 0.1 2P15.0
UNIT 2
CUBOID 2 1 2P0.1 2P0.05 2P15.0
UNIT 3
CUBOID 2 1 2P0.05 2P0.1 2P15.0
UNIT 4
CYLINDER 1 1 0.1 2P15.0
CYLINDER 3 1 0.5 2P15.0
HOLE 1 0.0 -0.4 0.0
HOLE 1 0.4 0.0 0.0
HOLE 1 0.0 0.4 0.0
HOLE 1 -0.4 0.0 0.0
HOLE 2 -0.2 0.0 0.0
HOLE 2 0.2 0.0 0.0
HOLE 3 0.0 -0.2 0.0
HOLE 3 0.0 0.2 0.0
UNIT 5
CYLINDER 1 1 0.5 2P15.0
UNIT 6
CYLINDER 2 1 0.2 2P15.0
UNIT 7
CYLINDER 2 1 0.2 2P15.0
CYLINDER 0 1 1.3 2P15.0
HOLE 5 0.707107 2*0.0
HOLE 6 0.707107 0.707107 0.0
HOLE 4 0.0 0.707107 0.0
HOLE 6 -0.707107 0.707107 0.0
HOLE 5 -0.707107 0.0 0.0
HOLE 6 -0.707107 -0.707107 0.0
HOLE 4 0.0 -0.707107 0.0
HOLE 6 0.707107 -0.707107 0.0
CYLINDER 4 1 1.4 2P15.0
UNIT 8
CYLINDER 2 1 0.6 2P15.0
UNIT 9
CYLINDER 2 1 0.6 2P15.0
CYLINDER 0 1 3.6 2P15.0
HOLE 7 2.0 0.0 0.0
HOLE 8 2*2.0 0.0
HOLE 7 0.0 2.0 0.0
HOLE 8 -2.0 2.0 0.0
HOLE 7 -2.0 2*0.0
HOLE 8 2*-2.0 0.0
HOLE 7 0.0 -2.0 0.0
HOLE 8 2P2.0 0.0
CYLINDER 4 1 3.8 2P15.0
CUBOID 0 1 4P4.0 2P16.0
END GEOM
READ ARRAY ARA=1 NUX=1 NUY=1 NUZ=1 FILL 9 END ARRAY
READ PLOT
TTL='X-Y SLICE AT Z MIDPOINT. NESTED HOLES'
XUL=-0.1 YUL=8.1 ZUL=16.0 XLR=8.1 YLR=-0.1 ZLR=16
UAX=1.0 VDN=-1.0 NAX=640 END
TTL='X-Y SLICE AT Z MIDPOINT. NESTED HOLES. UNIT MAP'
PIC=UNIT END
END PLOT
END DATA
END
KENO-VI:
::
=KENOVI
NESTED HOLES SAMPLE
READ PARAM RUN=NO LIB=41 TME=0.5 END PARAM
READ MIXT SCT=1 MIX=1 92500 4.7048-2 MIX=2 200 1.0 MIX=3 502 0.1
MIX=4 200 1.0
END MIXT
READ GEOM
UNIT 1
CYLINDER 1 0.1 2P15.0
CYLINDER 2 0.1 2P15.0 ORIGIN Y=-0.4
CYLINDER 3 0.1 2P15.0 ORIGIN X=0.4
CYLINDER 4 0.1 2P15.0 ORIGIN Y=0.4
CYLINDER 5 0.1 2P15.0 ORIGIN X=-0.4
CUBOID 6 2P0.1 2P0.05 2P15.0 ORIGIN X=-0.2
CUBOID 7 2P0.1 2P0.05 2P15.0 ORIGIN X=0.2
CUBOID 8 2P0.05 2P0.1 2P15.0 ORIGIN Y=-0.2
CUBOID 9 2P0.05 2P0.1 2P15.0 ORIGIN Y=0.2
CYLINDER 10 0.5 2P15.0
MEDIA 1 1 1 -6 -7 -8 -9
MEDIA 1 1 2 -8
MEDIA 1 1 3 -7
MEDIA 1 1 4 -9
MEDIA 1 1 5 -6
MEDIA 2 1 6 -1 -5
MEDIA 2 1 7 -1 -3
MEDIA 2 1 8 -1 -2
MEDIA 2 1 9 -1 -4
MEDIA 3 1 -1 -2 -3 -4 -5 -6 -7 -8 -9 10
BOUNDARY 10
UNIT 2
CYLINDER 1 0.2 2P15.0
CYLINDER 2 0.2 2P15.0 ORIGIN X=0.707107 Y=0.707107
CYLINDER 3 0.2 2P15.0 ORIGIN X=-0.707107 Y=0.707107
CYLINDER 4 0.2 2P15.0 ORIGIN X=-0.707107 Y=-0.707107
CYLINDER 5 0.2 2P15.0 ORIGIN X=0.707107 Y=-0.707107
CYLINDER 6 0.5 2P15.0 ORIGIN X=0.707107
CYLINDER 7 0.5 2P15.0 ORIGIN X=-0.707107
CYLINDER 8 0.5 2P15.0 ORIGIN Y=0.707107
CYLINDER 9 0.5 2P15.0 ORIGIN Y=-0.707107
CYLINDER 10 1.3 2P15.0
CYLINDER 11 1.4 2P15.0
MEDIA 2 1 1
MEDIA 2 1 2
MEDIA 2 1 3
MEDIA 2 1 4
MEDIA 2 1 5
MEDIA 1 1 6 -8 -9
MEDIA 1 1 7 -8 -9
HOLE 1 8 -3 -6 ORIGIN Y=0.707107
HOLE 1 9 -6 -7 ORIGIN Y=-0.707107
MEDIA 0 1 10 -1 -2 -3 -4 -5 -6 -7 -8 -9
MEDIA 4 1 11 -10
BOUNDARY 11
GLOBAL UNIT 3
CYLINDER 1 0.6 2P15.0
CYLINDER 2 0.6 2P15.0 ORIGIN X=2.0 Y=2.0
CYLINDER 3 0.6 2P15.0 ORIGIN X=-2.0 Y=2.0
CYLINDER 4 0.6 2P15.0 ORIGIN X=-2.0 Y=-2.0
CYLINDER 5 0.6 2P15.0 ORIGIN X=2.0 Y=-2.0
CYLINDER 6 1.4 2P15.0 ORIGIN X=2.0
CYLINDER 7 1.4 2P15.0 ORIGIN Y=2.0
CYLINDER 8 1.4 2P15.0 ORIGIN X=-2.0
CYLINDER 9 1.4 2P15.0 ORIGIN Y=-2.0
CYLINDER 10 3.6 2P15.0
CYLINDER 11 3.8 2P15.0
CUBOID 12 4P4.0 2P16.0
MEDIA 2 1 1 -6 -7 -8 -9
MEDIA 2 1 2 -6 -7
MEDIA 2 1 3 -7 -8
MEDIA 2 1 4 -8 -9
MEDIA 2 1 5 -9 -6
HOLE 2 6 -1 -5 -2 ORIGIN X=2
HOLE 2 7 -1 -2 -3 ORIGIN Y=2
HOLE 2 8 -1 -3 -4 ORIGIN X=-2
HOLE 2 9 -1 -4 -5 ORIGIN Y=-2
MEDIA 0 1 10 -1 -2 -3 -4 -5 -6 -7 -8 -9
MEDIA 4 1 11 -10
MEDIA 0 1 12 -11
BOUNDARY 12
END GEOM
READ PLOT
TTL='X-Y SLICE AT Z MIDPOINT. NESTED HOLES'
XUL=-4.1 YUL=4.1 ZUL=0.0 XLR=4.1 YLR=-4.1 ZLR=0
UAX=1.0 VDN=-1.0 NAX=640 END
TTL='X-Y SLICE AT Z MIDPOINT. NESTED HOLES, UNIT MAP.'
PIC=UNIT END
END PLOT
END DATA
END
.he plot data description for the **UNIT** plot of nested holes is shown
in :numref:`list8-1-13`. The **UNIT** plot is shown in :numref:`fig8-1-92`. The user can
reference this map to verify the correct placement of the **UNIT**\ s.
Note that the **UNIT** map plots the **UNIT**\ s present at the deepest
nesting level for the 2-D slice. It does not show any detail within a
**UNIT**. The apparent detail within **UNIT** 7 includes
**UNIT**\ s 1--6, which were placed there via the hole option. In the
legend of the plot, the material number actually refers to the **UNIT**
number.
.. centered:: EXAMPLE 7. LARGE STORAGE ARRAY.
The storage array described Example 18 in :numref:`8-1-3-6-3` and
:numref:`fig8-1-27` is such a sparse array that the mixture map had to be very
large in order to show the detail of the shelves and uranium buttons.
The mixture maps for this configuration were not presented in
:numref:`8-1-3-6-3`, but the data description was listed so the user can
generate them. It may be useful to generate a **UNIT** map for this kind
of problem. The input data for generating unit maps for this storage
array is given below.
::
READ PLOT PIC=UNIT
TTL='X-Z SLICE THROUGH STORAGE ARRAY ROOM AT Y=30.48 WITH Z ACROSS AND X DOWN'
XUL=624.84 YUL=30.48 ZUL=-45.72 XLR=-30.48 YLR=30.48 ZLR=381.0
WAX=1.0 UDN=-1.0 NAX=320 END
TTL='X-Y SLICE THROUGH STORAGE ARRAY ROOM AT Z=0.3175 WITH X ACROSS AND Y DOWN'
XUL=-30.48 YUL=1341.1 ZUL=0.3175 XLR=624.84 YLR=-30.48 ZLR=0.3175
UAX=1.0 VDN=-1.0 NAX=320 END
END PLOT
The plot data and **UNIT** map for an X-Z slice through the array at
Y=30.48 cm is given in :numref:`list8-1-14` and :numref:`fig8-1-94`. The Z direction,
which extends from -45.72 cm to 381.0 cm, is plotted in 320 pixels
across the plot. This **UNIT** map was created with Z across the plot
and X down the plot.
.. code-block:: scale
:name: list8-1-14
:caption: Plot data for X-Z slice of storage array.
x-z slice through storage array room at y=30.48 with z across and x down
unit map
unit 1 2 3 4 5 6 7
symbol 1 2 3 4 5 6 7
upper left lower right
coordinates coordinates
x 6.2484e+02 -3.0480e+01
y 3.0480e+01 3.0480e+01
z -4.5720e+01 3.8100e+02
u axis v axis
(down) (across)
x -1.00000 0.00000
y 0.00000 0.00000
z 0.00000 1.00000
nu= 491 nv= 320 delu= 1.3335e+00 delv= 1.3335e+00 lpi= 10.000
.. figure:: figs/Keno/fig94.png
:align: center
:width: 400
:name: fig8-1-94
X-Z plot of storage array.
The plot data and **UNIT** map for an X-Y slice through the shelf are
given in :numref:`list8-1-15` and :numref:`fig8-1-96`. This **UNIT** map was created with
X across the plot and Y down the plot. This shows five rows of shelves
in the X direction.
.. code-block::
:name: list8-1-15
:caption: Plot data for X-Y slice of storage array.
x-y slice through storage array room at z=0.3175 with x across and y down
unit map
unit 1 2 3 4 5 6 7
symbol 1 2 3 4 5 6 7
upper left lower right
coordinates coordinates
x -3.0480e+01 6.2484e+02
y 1.3411e+03 -3.0480e+01
z 3.1750e-01 3.1750e-01
u axis v axis
(down) (across)
x 0.00000 1.00000
y -1.00000 0.00000
z 0.00000 0.00000
nu= 669 nv= 320 delu= 2.0479e+00 delv= 2.0479e+00 lpi= 10.000
.. figure:: figs/Keno/fig96.png
:align: center
:width: 400
:name: fig8-1-96
X-Y plot of storage array.
.. _8-1-3-10:
KENO Multiple Mesh and Mesh-based Quantity Specifications
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
KENO constructs a grid object and stores several mesh definitions in this object.
The following mesh definitions are supported by KENO:
i. Default mesh grid (grid ``ID`` =10001):
KENO generates a 5 :math:`\times` 5 :math:`\times` 5 Cartesian mesh grid which
overlays the entire geometry. This mesh is used only for fission source
convergence diagnostics if the user does not specify any spatial mesh for
this quantity.
.. note:: Currently, users cannot enter grid ``ID``\ s greater than 9999.
ii. A cubic mesh grid (grid ``ID`` = 20001):
KENO generates a cubic mesh with the mesh size specified by ``MSH`` parameter,
which is introduced in :numref:`tab-module.keno.parameters`. This mesh definition can be used
by all mesh-based quantities except the Shannon Entropy tallies used for
fission source convergence diagnostics.
iii. Mesh with ``grid geometry data`` input (grid ``ID`` = NUMBER):
The user can specify either a mesh with a single ``grid data`` input block or
multiple meshes by repeating the ``grid data`` input block with different mesh
definitions. Note that the entire block, including ``READ GRID`` and
``END GRID``, must be repeated each time; this behavior is different
from all other blocks of KENO input.
After processing all grid data and constructing all grid meshes, KENO prints
the specification of each mesh grid in the Grid Definitions output edit;
see :numref:`keno_7-1-4-17` for details.
Before starting the transport process, KENO tries to match the IDs specified in
the parameter block with the keywords ``SCD``, ``MFX``, ``CDS``, ``CGD``,
``FIS``, and ``GFX`` (See :numref:`sec-module.keno.parameters`) to the grid ``ID`` in each
grid definition. Each mesh-based quantity requested
by the user is associated with a grid if the requested grid ``ID`` exists.
.. note:: Parameters ``CDS``, ``CGD``, ``FIS``, ``GFX``, and ``MFX`` with
*YES* entry always require a mesh defined by either parameter ``MSH``
or ``grid data`` input.
Parameters ``CDS``, ``CGD``, ``FIS``, ``GFX``, and ``MFX`` with
*YES* entry always use the mesh defined by the first ``grid data`` input
if there are multiple meshes defined by both ``MSH`` and ``grid data``
input block(s).
The following examples demonstrate the mesh features in KENO:
Example: Source Convergence Diagnostics with Default Mesh
KENO always generates a default mesh for source convergence diagnostics
if the user does not specify any mesh for this quantity. The following
example (only KENO-VI version is shown) with some updates in ``parameter data``
and ``grid data`` input blocks will be used in all examples in
this section to summarize several mesh definition scenarios with several
mesh-based quantity requests.
In this sample problem, a bounding box is
defined to enclose the entire geometry with xmin=-13.74, xmax=13.74,
ymin=-13.74, ymax=13.74, zmin=-13.01, and zmax=13.01. KENO uses this
bounding box and creates a 5 :math:`\times` 5 :math:`\times` 5 grid
for source convergence diagnostics.
KENO-VI:
::
=kenovi
mesh test - scd with default mesh (5x5x5), scd=yes (default)
READ PARAMETER
CEP=ce_v7.1_endf NPG=10000
END PARAMETER
read mixt
mix=1
92234 4.82716E-04 92235 4.47972E-02
92236 9.57234E-05 92238 2.65768E-03
end mixt
read geometry
unit 1
com='single 2c8 unit centered'
cylinder 10 5.748 5.3825 -5.3825
cuboid 20 4p6.87 2p6.505
media 1 1 10 vol=8938.968624
media 0 1 20 -10 vol=10710.044784
boundary 20
global unit 2
cuboid 10 4p13.74 2p13.01
com='2x2x2 2c8 array'
array 1 +10 place 1 1 1 2r-6.87 -6.505
boundary 10
end geometry
read array
ara=1 nux=2 nuy=2 nuz=2 fill f1 end fill
end array
end data
end
In the output, KENO notifies users about the default mesh usage for
source convergence diagnostics with the message *k6-316*. The default
grid definition with some details is shown in :numref:`oedit7-1-3-11-1`.
:numref:`fig7-1-3-11-1` shows the Fulcrum visualized
Shannon Entropy by generations plot for this sample problem.
.. raw:: latex
\begin{landscape}
.. code-block:: scale
:caption: Grid Definitions output edit
:name: oedit7-1-3-11-1
***** warning ***** keno message number k6-316 follows:
No mesh provided for Source Convergence Diagnostics (SCD). Continue with default mesh.
...
********************************************************************************************************************
*** ***
*** grid definitions ***
*** ***
*** Only a single grid geometry is either specified or internally setup for this problem ***
*** ***
********************************************************************************************************************
**** Grid geometries utilized in this problem ****
Grid Geometry: 10001
title: Default 5 x 5 x 5 Cartesian mesh which overlays the entire geometry
Plane Summary
x: 5 cells from -1.37400E+01 to 1.37400E+01
y: 5 cells from -1.37400E+01 to 1.37400E+01
z: 5 cells from -1.30100E+01 to 1.30100E+01
Total number of cells: 125
x-planes y-planes z-planes
----- --------------------- --------------------- ---------------------
1 -1.37400137400000E+01 -1.37400137400000E+01 -1.30100130100000E+01
2 -8.24400824399998E+00 -8.24400824399998E+00 -7.80600780599998E+00
3 -2.74800274799999E+00 -2.74800274799999E+00 -2.60200260199999E+00
4 2.74800274799999E+00 2.74800274799999E+00 2.60200260199999E+00
5 8.24400824399998E+00 8.24400824399998E+00 7.80600780599998E+00
6 1.37400137400000E+01 1.37400137400000E+01 1.30100130100000E+01
----- --------------------- --------------------- ---------------------
.. raw:: latex
\end{landscape}
.. figure:: figs/Keno/keno_shannon_entropy_default.png
:align: center
:name: fig7-1-3-11-1
Shannon entropy tallied on default mesh.
Example: Source Convergence Diagnostics with User-defined Mesh.
The user can request the accumulation of the fission source on a
different grid rather than the default grid for source convergence
diagnostics. In this example, the sample problem specified in previous example
is modified for this purpose. A new 6 :math:`\times` 6 :math:`\times` 6 grid is defined over the
entire geometry in a **grid geometry data** input with grid **ID** 12, and
source convergence diagnostics are requested by setting **SCD**
parameter to *12* in the parameter block that matches the NUMBER
specification in the **grid geometry data** input.
::
=kenovi
mesh test - scd with user-defined grid
READ PARAMETERS
CEP=ce_v7.1_endf NPG=10000 SCD=12
END PARAMETERS
...
READ GRID
12
TITLE "test scd with this mesh"
NUMXCELLS=6 NUMYCELLS=6 NUMZCELLS=6
XMIN=-13.74 XMAX=13.74
YMIN=-13.74 YMAX=13.74
ZMIN=-13.01 ZMAX=13.01
END GRID
...
.. note:: Starting from this example, only a summary of Grid Definiton
output edit will be presented for the remaining examples.
A User-defined grid is printed in Grid Definitons output edit, and
:numref:`oedit7-1-3-11-2` presents only a summary of this output section.
:numref:`fig7-1-3-11-2` shows the variation of Shannon Entropy
(tallied on user-defined mesh) over generations for the same problem given
in the previous example.
.. code-block:: scale
:caption: Grid Definitions output edit
:name: oedit7-1-3-11-2
...
Grid Geometry: 12
title: test scd with this mesh
Plane Summary
x: 6 cells from -1.37400E+01 to 1.37400E+01
y: 6 cells from -1.37400E+01 to 1.37400E+01
z: 6 cells from -1.30100E+01 to 1.30100E+01
Total number of cells: 216
...
.. figure:: figs/Keno/keno_shannon_entropy_scd_12.png
:align: center
:name: fig7-1-3-11-2
Shannon entropy tallied on user-defined mesh.
Example: Source Convergence Diagnostics with Non-Existing Mesh.
This example demonstrates the code behavior if there is a mismatch
between the NUMBER entry in **grid geometry data** input and the **SCD**
parameter in the **parameter data**. The sample input in
the first example was modified as (a) a single mesh is defined with grid
**ID** = 12, and (b) source convergence diagnostics is intended to use a
grid with grid **ID** = 99, which does not exist.
::
=kenovi
mesh test - scd with non-existing grid id
READ PARAMETERS
CEP=ce_v7.1_endf NPG=10000 SCD=99
END PARAMETERS
...
READ GRID
12
TITLE "test scd with this mesh"
NUMXCELLS=6 NUMYCELLS=6 NUMZCELLS=6
XMIN=-13.74 XMAX=13.74
YMIN=-13.74 YMAX=13.74
ZMIN=-13.01 ZMAX=13.01
END GRID
...
In this example, calculation is stopped with an error message since the requested
grid definition for source convergence diagnostics does not exist in the input.
::
...
***** error ***** keno message number k6-315 follows:
Mesh < 99 > specified for Shannon entropy tally and source convergence diagnostics(SCD) is not found in input.
...
***** error ***** keno message number k6-100 follows:
this problem will not be run because errors were encountered in the input data.
...
Example: Fission Rate Mesh Tally with a Cubic Mesh Definition with MSH Parameter.
In this example, the sample problem described in the first example was modified
as (a) a cubic mesh defined with the **MSH** parameter, and (b) fission rate
mesh tally is requested on this cubic mesh. In this case, a default mesh with grid
**ID**\ =10001 is constructed and used only for source convergence diagnostics.
The cubic mesh with grid **ID**\ =20001 is also constructed with the length of
one side as equals to *2.748 cm* and is used for the fission rate mesh tally.
::
=kenovi
mesh test - fis with uniform mesh defined by MSH
READ PARAMETERS
CEP=ce_v7.1_endf NPG=10000 FIS=yes MSH=2.748
END PARAMETERS
...
The output prints the details of mesh grid entries in Grid Definitions
edit, as shown in :numref:`oedit7-1-3-11-3`.
For this sample problem, the cubic mesh grid is
constructed in a box that is larger than the bounding box around the global
unit (+x=13.74, -x=-13.74, +y=13.74, -y=-13.74, +z=13.01 and -z=-13.01).
The extents of the global boundary in each dimension are not
equal; therefore, KENO tries to adjust the box size to place the
cubic meshes properly inside this box. A grid mesh perfectly overlapping
the problem geometry can be defined only by the **grid data** input rather
than using the **MSH** parameter.
.. code-block:: scale
:caption: Grid Definitions output edit
:name: oedit7-1-3-11-3
**** Grid geometries utilized in this problem ****
Grid Geometry: 20001
title: Cubic mesh grid automatically generated with mesh_size = 2.74799991
Plane Summary
x: 12 cells from -1.64880E+01 to 1.64880E+01
y: 12 cells from -1.64880E+01 to 1.64880E+01
z: 12 cells from -1.64880E+01 to 1.64880E+01
Total number of cells: 1728
x-planes y-planes z-planes
----- --------------------- --------------------- ---------------------
1 -1.64879994392395E+01 -1.64879994392395E+01 -1.64879994392395E+01
2 -1.37399995326996E+01 -1.37399995326996E+01 -1.37399995326996E+01
...
Grid Geometry: 10001
title: Default 5 x 5 x 5 Cartesian mesh which overlays the entire geometry
Plane Summary
x: 5 cells from -1.37400E+01 to 1.37400E+01
y: 5 cells from -1.37400E+01 to 1.37400E+01
z: 5 cells from -1.30100E+01 to 1.30100E+01
Total number of cells: 125
...
Specifications of fission rate mesh tally in Mesh Tallies
output edit are listed in :numref:`oedit7-1-3-11-4`.
Fission rate mesh tally is saved in a 3dmap file named
`example4.fission_density.3dmap`, and results from this file
overlayed on the geometry are shown in :numref:`fig7-1-3-11-3`.
.. code-block:: scale
:caption: Mesh tallies output edit
:name: oedit7-1-3-11-4
**** mesh tallies ****
1 mesh tallies computed for this problem
mesh tally (requested with parameter fis)
response : fission_density
grid id : 20001
energy id : Default
memory allocated : 6.645 MB
output : example4.fission_density.3dmap
energy boundaries:
group energy (eV)
------ ------------
1 2.00000E+07
2 1.73300E+07
3 1.56800E+07
. .
250 7.50000E-04
251 5.00000E-04
252 1.00000E-04
1.00000E-05
------ ------------
grid summary:
x: 12 cells from -1.64880E+01 to 1.64880E+01
y: 12 cells from -1.64880E+01 to 1.64880E+01
z: 12 cells from -1.64880E+01 to 1.64880E+01
Total number of cells: 1728
.. figure:: figs/Keno/keno_fis_rate_yes_msh_2.748.png
:align: center
:name: fig7-1-3-11-3
Fission rate mesh tally computed on a uniform mesh defined by **MSH=2.748**
(X-Y view at z=5.0).
Example: Fission Rate Mesh Tally with a NUMBER.
In this example, problem given in the first example was modified to
request a fission rate mesh tally calculation over a mesh defined
in the **grid geometry data** input. A default mesh with grid
**ID**\ =10001 is constructed and used for the source convergence diagnostics.
The user defined mesh (grid **ID**\ =17) is used for the fission rate mesh tally.
::
=kenovi
mesh test - fis with a mesh defined by grid data block
READ PARAMETERS
CEP=ce_v7.1_endf NPG=10000 FIS=17
END PARAMETERS
...
READ GRID
17
TITLE "test fis with this mesh"
NUMXCELLS=20 NUMYCELLS=20 NUMZCELLS=6
XMIN=-13.74 XMAX=13.74
YMIN=-13.74 YMAX=13.74
ZMIN=-13.01 ZMAX=13.01
END GRID
...
A summary of the mesh grids utilized in this sample problem is printed in
Grid Definitions, as shown in :numref:`oedit7_1_3_11_5`.
.. code-block:: scale
:caption: Grid Definitions output edit
:name: oedit7_1_3_11_5
**** Grid geometries utilized in this problem ****
Grid Geometry: 17
title: test fis with this mesh
Plane Summary
x: 20 cells from -1.37400E+01 to 1.37400E+01
y: 20 cells from -1.37400E+01 to 1.37400E+01
z: 6 cells from -1.30100E+01 to 1.30100E+01
Total number of cells: 2400
...
Grid Geometry: 10001
title: Default 5 x 5 x 5 Cartesian mesh which overlays the entire geometry
Plane Summary
x: 5 cells from -1.37400E+01 to 1.37400E+01
y: 5 cells from -1.37400E+01 to 1.37400E+01
z: 5 cells from -1.30100E+01 to 1.30100E+01
Total number of cells: 125
:numref:`oedit7-1-3-11-6` is a snapshot of the Mesh Tallies output edit, which
summarizes the specification of this mesh quantity.
The fission rate mesh tally is saved in a 3dmap file
named *example5.fission_density.3dmap*. Tally results from this file overlayed
over the geometry are shown in :numref:`fig7-1-3-11-4`.
.. code-block:: scale
:caption: Mesh tallies output edit
:name: oedit7-1-3-11-6
**** mesh tallies ****
1 mesh tallies computed for this problem
mesh tally (requested with parameter fis)
response : fission_density
grid id : 17
energy id : Default
memory allocated : 9.229 MB
output : example5.fission_density.3dmap
energy boundaries:
group energy (eV)
------ ------------
1 2.00000E+07
2 1.73300E+07
3 1.56800E+07
. .
250 7.50000E-04
251 5.00000E-04
252 1.00000E-04
1.00000E-05
------ ------------
grid summary:
x: 20 cells from -1.37400E+01 to 1.37400E+01
y: 20 cells from -1.37400E+01 to 1.37400E+01
z: 6 cells from -1.30100E+01 to 1.30100E+01
Total number of cells: 2400
.. figure:: figs/Keno/keno_fis_rate_yes_grid_20x20x6.png
:align: center
:name: fig7-1-3-11-4
Fission rate mesh tally computed on a mesh defined by **grid geometry data** input (X-Y view at z=5.0).
Example: Fission Rate Mesh Tally with Multiple Mesh Definitions.
In this example, the sample input from the previous example is used with the
old-style definition so that fission rate mesh tally is requested by
setting the **FIS** parameter to *YES*.
Additional mesh grids were added to the sample input
to demonstrate how KENO assigns a mesh grid
to a mesh-based quantity when the value of mesh quantity has been
entered as *YES* and multiple mesh grids have already been defined:
(a) two mesh grids with grid **IDs** *118* and *113* are defined in
**grid geometry data** inputs, and
(b) another mesh grid is also defined with the **MSH** parameter.
KENO uses the default mesh grid (grid **ID**\ =10001)
for the source convergence diagnostics, using the mesh with
grid **ID**\ = 118 from the grid data container for the fission
rate mesh tally.
::
=kenovi
mesh test - fis=yes with multiple mesh defined by grid data block
READ PARAMETERS
CEP=ce_v7.1_endf NPG=10000 MSH=2.5 FIS=yes
END PARAMETERS
...
READ GRID
118
TITLE "test fis with this mesh partially covering the geometry"
NUMXCELLS=20 NUMYCELLS=20 NUMZCELLS=18
XMIN=-1.74 XMAX=13.74
YMIN=-1.74 YMAX=13.74
ZMIN=-1.01 ZMAX=13.01
END GRID
READ GRID
113
TITLE "mesh will not be used"
NUMXCELLS=3 NUMYCELLS=3 NUMZCELLS=3
XMIN=-1.74 XMAX=13.74
YMIN=-1.74 YMAX=13.74
ZMIN=-1.01 ZMAX=13.01
END GRID
READ GRID
17
TITLE "test fis with this mesh"
NUMXCELLS=20 NUMYCELLS=20 NUMZCELLS=6
XMIN=-13.74 XMAX=13.74
YMIN=-13.74 YMAX=13.74
ZMIN=-13.01 ZMAX=13.01
END GRID
...
A summary of Grid Definitions output edit is given in :numref:`oedit7-1-3-11-7`.
Note that KENO does
not print anything for the cubic mesh (requested by setting **MSH=2.5**,
grid **ID**\ = 20001) because this mesh was not constructed. KENO ignores
the mesh definition request done with the **MSH** parameter if any mesh grid
is defined by **grid data** input.
.. code-block:: scale
:caption: Grid Definitions output edit
:name: oedit7-1-3-11-7
**** Grid geometries utilized in this problem ****
Grid Geometry: 118
title: test fis with this mesh partially covering the geometry
Plane Summary
x: 20 cells from -1.74001E+00 to 1.37400E+01
y: 20 cells from -1.74001E+00 to 1.37400E+01
z: 18 cells from -1.01001E+00 to 1.30100E+01
Total number of cells: 7200
...
Grid Geometry: 113
title: mesh will not be used
Plane Summary
x: 3 cells from -1.74001E+00 to 1.37400E+01
y: 3 cells from -1.74001E+00 to 1.37400E+01
z: 3 cells from -1.01001E+00 to 1.30100E+01
Total number of cells: 27
...
Grid Geometry: 17
title: test fis with this mesh
Plane Summary
x: 20 cells from -1.37400E+01 to 1.37400E+01
y: 20 cells from -1.37400E+01 to 1.37400E+01
z: 6 cells from -1.30100E+01 to 1.30100E+01
Total number of cells: 2400
...
Grid Geometry: 10001
title: Default 5 x 5 x 5 Cartesian mesh which overlays the entire geometry
Plane Summary
x: 5 cells from -1.37400E+01 to 1.37400E+01
y: 5 cells from -1.37400E+01 to 1.37400E+01
z: 5 cells from -1.30100E+01 to 1.30100E+01
Total number of cells: 125
...
KENO assigns the first grid entry from the grid data container to any
mesh quantity whose value is entered as *YES* in the **parameter data** input.
Each grid defined in the grid data blocks is stored in the grid
data container unit in the order in which it is processed.
In this example, the grid entry *118*, which is processed and stored first,
is assigned to the fission rate mesh tally calculation.
Mesh Tallies output edit shown in :numref:`oedit7-1-3-11-8` reflects this
grid assignment to the fission ate mesh tally.
.. code-block:: scale
:caption: Mesh tallies output edit
:name: oedit7-1-3-11-8
**** mesh tallies ****
1 mesh tallies computed for this problem
mesh tally (requested with parameter fis)
response : fission_density
grid id : 118
energy id : Default
memory allocated : 27.686 MB
output : example6.fission_density.3dmap
energy boundaries:
group energy (eV)
------ ------------
1 2.00000E+07
2 1.73300E+07
3 1.56800E+07
. .
250 7.50000E-04
251 5.00000E-04
252 1.00000E-04
1.00000E-05
------ ------------
grid summary:
x: 20 cells from -1.74001E+00 to 1.37400E+01
y: 20 cells from -1.74001E+00 to 1.37400E+01
z: 18 cells from -1.01001E+00 to 1.30100E+01
Total number of cells: 7200
...
:numref:`fig7-1-3-11-5` illustrates the fission rate mesh tally overlayed on the
geometry. Note that the mesh used in the fission rate mesh tally calculation does not
cover the entire geometry, and this is not a requirement for this tally.
.. note:: The fission rate mesh tally capability as well as fission source and grid
flux tallies (averaged over mesh volumes) do not require that the mesh grid used
in the calculation cover the entire geometry.
However, the mesh flux capability (calculated over the volume of materials in
each mesh voxel) activated by the **MFX** parameter always requires that
the mesh grid used in its calculations cover the entire geometry.
.. figure:: figs/Keno/keno_fis_rate_yes_partial_grid_20x20x18.png
:align: center
:name: fig7-1-3-11-5
Fission rate mesh tally computed over a mesh grid defined by **grid geometry data** input. Defined mesh grid with **ID**\ = 118 partially covers the geometry (X-Y view at z=6.8).
Example: Mesh Flux Tally with Multiple Mesh Definitions.
In this example, the sample problem described in previous example is modified
to request a mesh flux calculation (**MFX**) on a mesh grid which partly
covers the problem geometry. The mesh volume calculation required by the mesh flux
calculation is already requested by adding a volume block to the input.
.. note:: Calculation of mesh fluxes in all regions enclosed by a mesh voxel
requires the volume of each region in this mesh voxel. KENO V.a automatically
activates stochastic volume calculation with RANDOM volume estimate for such
a case. The user can override the parameters in the **volume data** input block.
However, users cannot change the volume calculation method
from RANDOM volume estimate to TRACE volume estimate.
In the KENO-VI case, it is the user's responsibility to add a **volume data** input
block to activate the stochastic mesh volume calculation. Like KENO V.a,
KENO-VI only allows RANDOM volume estimate for mesh volume calculation.
See :numref:`8-1-2-13` and :numref:`8-1-4-15` for more details.
After these updates, KENO with this sample problem uses the default mesh
(grid **ID**\ =10001) for the source convergence diagnostics,
and the user-defined mesh with grid **ID**\ =118 for accumulating the mesh fluxes.
Unlike the fission rate mesh tally case discussed in the previous example,
execution is terminated for this scenario since the mesh flux capability
requested with **MFX** parameter requires a mesh grid covering the entire geometry.
::
=kenovi
mesh test - mfx=yes with a grid mesh covering the part of the geometry
READ PARAMETERS
CEP=ce_v7.1_endf NPG=10000 MFX=yes
END PARAMETERS
...
READ GRID
118
TITLE "test fis with this mesh partially covering the geometry"
NUMXCELLS=20 NUMYCELLS=20 NUMZCELLS=18
XMIN=-1.74 XMAX=13.74
YMIN=-1.74 YMAX=13.74
ZMIN=-1.01 ZMAX=13.01
END GRID
READ GRID
113
TITLE "mesh will not be used"
NUMXCELLS=3 NUMYCELLS=3 NUMZCELLS=3
XMIN=-1.74 XMAX=13.74
YMIN=-1.74 YMAX=13.74
ZMIN=-1.01 ZMAX=13.01
END GRID
READ GRID
17
TITLE "test fis with this mesh"
NUMXCELLS=20 NUMYCELLS=20 NUMZCELLS=6
XMIN=-13.74 XMAX=13.74
YMIN=-13.74 YMAX=13.74
ZMIN=-13.01 ZMAX=13.01
END GRID
...
READ VOLUME
TYPE=RANDOM BATCHES=100 POINTS=1000
XP=+13.01 XM=-13.01
YP=+13.74 YM=-13.74
ZP=+13.74 ZM=-13.74
END VOLUME
...
The code is stopped with the following error message in the output:
::
...
***** warning ***** keno message number k6-316 follows:
No mesh provided for Source Convergence Diagnostics (SCD). Continue with default mesh.
1 mesh test - fis with multiple grid data input
volumes for those units utilized in this problem
Mesh Volume Sampling Parameters
-------------------------------
The number of points per batch was specified as 1000
This gives a sampling density of 5.08931E-02 points per cc per batch.
The number of batches is 100
***** error ***** keno message number k6-305 follows:
Mesh fluxes have been specified, but the mesh does not completely cover the geometry.
The point x= 3.65030E+00 y= 1.90999E+00 z= -1.02504E+01 lies outside the mesh.
The problem will not be run. Fix the mesh and resubmit the case.
...
***** error ***** keno message number k6-100 follows:
this problem will not be run because errors were encountered in the input data.
stop code 129
execution terminated due to errors. completion code 129. cpu time used 3.15388 seconds
***Error: Application failed - see messages file for details.
...
Example: Multiple Mesh Quantity with Multiple Mesh Definitions.
This example demonstrates the multiple mesh definition for multiple
mesh-based quantities. Our sample problem from a previous example is modified
as (a) the source convergence diagnostics and mesh fluxes are requested
with (grid *ID*\ = 17), (b) grid fluxes are requested with (grid *ID*\ = 113), and (c) fission rate mesh tally is requested with *YES*.
The first grid entry (grid *ID*\ =118) in **grid geometry data** input
is assigned to the fission rate mesh tally.
::
=kenovi
mesh test - test mfx, gfx, and fis together
READ PARAMETERS
CEP=ce_v7.1_endf NPG=10000 MFX=17 scd=17 gfx=113 fis=yes pms=yes
END PARAMETERS
...
READ GRID
118
TITLE "test fis with this mesh partially covering the geometry"
NUMXCELLS=20 NUMYCELLS=20 NUMZCELLS=18
XMIN=-1.74 XMAX=13.74
YMIN=-1.74 YMAX=13.74
ZMIN=-1.01 ZMAX=13.01
END GRID
READ GRID
113
TITLE "mesh will not be used"
NUMXCELLS=3 NUMYCELLS=3 NUMZCELLS=3
XMIN=-1.74 XMAX=13.74
YMIN=-1.74 YMAX=13.74
ZMIN=-1.01 ZMAX=13.01
END GRID
READ GRID
17
TITLE "test fis with this mesh"
NUMXCELLS=20 NUMYCELLS=20 NUMZCELLS=6
XMIN=-13.74 XMAX=13.74
YMIN=-13.74 YMAX=13.74
ZMIN=-13.01 ZMAX=13.01
END GRID
...
READ VOLUME
TYPE=RANDOM BATCHES=100 POINTS=1000
XP=+13.01 XM=-13.01
YP=+13.74 YM=-13.74
ZP=+13.74 ZM=-13.74
END VOLUME
...
All three user-defined mesh grids and default mesh grids constructed by KENO are
printed in the Grid Definitions output edit as shown in :numref:`oedit7-1-3-11-9`. In this output edit,
a summary of the volume calculation results performed on the mesh grid *17*
is also printed as part of the grid geometry 17 output edit. Further details
on the mesh volume calculation can be seen in the volume information edit in
the output. All mesh volumes can be printed by setting **PMV=YES** in the
**parameter data** input (see :numref:`tab-module.keno.parameters`).
.. code-block:: scale
:caption: Grid Definitions output edit
:name: oedit7-1-3-11-9
**** Grid geometries utilized in this problem ****
Grid Geometry: 118
title: test fis with this mesh partially covering the geometry
Plane Summary
x: 20 cells from -1.74001E+00 to 1.37400E+01
y: 20 cells from -1.74001E+00 to 1.37400E+01
z: 18 cells from -1.01001E+00 to 1.30100E+01
Total number of cells: 7200
...
Grid Geometry: 113
title: mesh will not be used
Plane Summary
x: 3 cells from -1.74001E+00 to 1.37400E+01
y: 3 cells from -1.74001E+00 to 1.37400E+01
z: 3 cells from -1.01001E+00 to 1.30100E+01
Total number of cells: 27
...
Grid Geometry: 17
title: test fis with this mesh
Plane Summary
x: 20 cells from -1.37400E+01 to 1.37400E+01
y: 20 cells from -1.37400E+01 to 1.37400E+01
z: 6 cells from -1.30100E+01 to 1.30100E+01
Total number of cells: 2400
x-planes y-planes z-planes
----- --------------------- --------------------- ---------------------
1 -1.37400137400000E+01 -1.37400137400000E+01 -1.30100130100000E+01
2 -1.23660000000000E+01 -1.23660000000000E+01 -8.67333333333333E+00
...
20 1.23660000000000E+01 1.23660000000000E+01
21 1.37400137400000E+01 1.37400137400000E+01
----- --------------------- --------------------- ---------------------
...
Region volumes in each mesh voxel have been calculated.
Total number of volume elements : 7468
Number of non-zero volume elements: 3734
Mesh/region pairs indexed together to speed up mesh flux scoring.
KENO prints the summary of the specifications of the mesh quantities
computed in Mesh tallies output edit as shown in :numref:`oedit7-1-3-11-10`.
The code saves the fission rate mesh tally and grid fluxes in two separate 3dmap files
named *example8.fission_density.3dmap* and *example8.flux.3dmap*, respectively. Mesh fluxes
are also saved in an ASCII file since the **PMS** parameter is set to *YES*.
:numref:`fig7-1-3-11-6` presents the fission rate mesh tally, grid fluxes, and Shannon entropy computed on the meshes defined in **grid geometry data** input.
.. code-block:: scale
:caption: Mesh tallies output edit
:name: oedit7-1-3-11-10
...
**** mesh tallies ****
2 mesh tallies computed for this problem
mesh tally (requested with parameter gfx)
response : flux
grid id : 113
energy id : Default
memory allocated : 0.104 MB
output : example8.flux.3dmap
energy boundaries:
group energy (eV)
------ ------------
1 2.00000E+07
2 1.73300E+07
3 1.56800E+07
. .
250 7.50000E-04
251 5.00000E-04
252 1.00000E-04
1.00000E-05
------ ------------
grid summary:
x: 3 cells from -1.74001E+00 to 1.37400E+01
y: 3 cells from -1.74001E+00 to 1.37400E+01
z: 3 cells from -1.01001E+00 to 1.30100E+01
Total number of cells: 27
mesh tally (requested with parameter fis)
response : fission_density
grid id : 118
energy id : Default
memory allocated : 27.686 MB
output : example8.fission_density.3dmap
energy boundaries:
group energy (eV)
------ ------------
1 2.00000E+07
2 1.73300E+07
3 1.56800E+07
. .
250 7.50000E-04
251 5.00000E-04
252 1.00000E-04
1.00000E-05
------ ------------
grid summary:
x: 20 cells from -1.74001E+00 to 1.37400E+01
y: 20 cells from -1.74001E+00 to 1.37400E+01
z: 18 cells from -1.01001E+00 to 1.30100E+01
Total number of cells: 7200
...
.. figure:: figs/Keno/keno_fis_gfx_shannon_entropy_scd_3.png
:align: center
:name: fig7-1-3-11-6
Fission rate mesh tally, grid fluxes, and Shannon entropy computed over the different meshes defined by **grid geometry data** input.
Random sequence
~~~~~~~~~~~~~~~
The random-number package used by KENO always starts with the same seed
and thus always reproduces the same sequence of random numbers. Any
random number except the one printed as the starting random number in
the parameter table can be used to activate a different random sequence.
The user can rerun a problem with a different random sequence by simply
entering a hexadecimal random number other than the starting random
number in the parameter data. For example, by entering RND=A10C1893E6D5
in the parameter data, the problem will be run with a different random
sequence.
.. _8-1-3-12:
Matrix k-effective
~~~~~~~~~~~~~~~~~~
Matrix k-effective calculations provide an alternative method of
calculating the k-effective of the system. Cofactor k-effectives and
source vectors are additional information that can be provided when the
matrix k-effective is calculated. The necessary source and fission
weight data are collected during the neutron tracking procedure. This
information is converted to a FISSION PRODUCTION MATRIX, which is the
number of next generation neutrons produced at J by a neutron born at I.
The principal eigenvalue of the fission probability matrix is the matrix
k-effective. KENO offers four alternatives when calculating matrix
k-effective as discussed below:
(1) If ``MKP``\ =YES is specified in the parameter data, the fission
production matrix is collected by array position or position index in
the GLOBAL ARRAY. The position index is used to reference a given
location in a 3-D lattice. For a 2 :math:`\times` 2 :math:`\times` 2 array, there are nine unique
position indices as shown below. Position zero contains everything
outside the GLOBAL ARRAY.
.. table:: Array index guide for a sample 2 :math:`\times` 2 :math:`\times` 2 array
:align: center
:name: tab8-1-24
+---+----------+---+---+
| | POSITION | | |
+---+----------+---+---+
| | X | Y | Z |
+---+----------+---+---+
| 0 | 0 | 0 | 0 |
+---+----------+---+---+
| 1 | 1 | 1 | 1 |
+---+----------+---+---+
| 2 | 2 | 1 | 1 |
+---+----------+---+---+
| 3 | 1 | 2 | 1 |
+---+----------+---+---+
| 4 | 2 | 2 | 1 |
+---+----------+---+---+
| 5 | 1 | 1 | 2 |
+---+----------+---+---+
| 6 | 2 | 1 | 2 |
+---+----------+---+---+
| 7 | 1 | 2 | 2 |
+---+----------+---+---+
| 8 | 2 | 2 | 2 |
+---+----------+---+---+
The fission production matrix is the number of next generation neutrons
produced at index J by a neutron born at index I. This matrix is used to
calculate the matrix k-effective, cofactor k-effectives and the source
vector by position index. Because the size of the fission probability
matrix is the square of the array size (for a 4 :math:`\times` 4 :math:`\times` 4 array there are
4,096 entries), it can use vast amounts of computer memory.
(2) If ``MKU``\ =YES is specified in the parameter data, the fission
production matrix is collected by ``UNIT``. It is the number of next
generation neutrons produced in ``UNIT`` J by a neutron born in
``UNIT`` I. This matrix is used to calculate the matrix k-effective,
cofactor k-effectives and source vector by ``UNIT``.
(3) If ``MKH``\ =YES is specified in the parameter data, the fission
production matrix is collected by the ``HOLE`` number. Matrix
information can be collected at either the highest ``HOLE`` nesting
level (first level of nesting) or the deepest ``HOLE`` nesting level.
``HHL``\ =YES specifies that the matrix information will be collected at
the first nesting level. By default, the matrix information is collected
at the deepest nesting level. The fission production matrix is the
number of next generation neutrons produced in ``HOLE`` J by a neutron
born in ``HOLE`` I. This matrix is used to calculate the matrix
k-effective, cofactor k-effectives and the source vector by ``HOLE``.
(4) If ``MKA``\ =YES is specified in the parameter data, the fission
production matrix is collected by ``ARRAY`` number. It can be collected
at the highest ``ARRAY`` level (first level of nesting) or at the
deepest ``ARRAY`` level. ``HAL``\ =YES specifies that the matrix
information will be collected at the first nesting level. By default,
the matrix information is collected at the deepest nesting level. The
fission production matrix is the number of next generation neutrons
produced in ``ARRAY`` J by a neutron born in ``ARRAY`` I. This matrix is
used to calculate the matrix k-effective, cofactor k-effectives and the
source vector by ``ARRAY``.
The user can simultaneously implement all methods of calculating the
matrix k-effective. The results are labeled in the printout. Matrix
k-effectives cannot be calculated for a single unit problem. If the user
wishes to do so, the geometry description must have a cube or cuboid as
its outer region, and the problem description should include ``READ
ARRAY END ARRAY``. These two actions convert the single unit problem
into a 1 :math:`\times` 1 :math:`\times` 1 array.
A cofactor k-effective is the eigenvalue of the fission production
matrix reduced by the row and column that references the specified
``UNIT`` or position index. The difference between the k-effective for
the system and the cofactor k-effective for a ``UNIT`` or position index
is an indication of the *in situ* k-effective of that ``UNIT`` or the
contribution that ``UNIT`` makes to the k-effective of the system. The
cofactor k-effective of a ``UNIT`` devoid of fissile material should
approximate the k-effective of the system.
Deviations
~~~~~~~~~~
When a deviation is calculated by KENO, it is the standard deviation of
the mean. This assumes a large sample having a normal distribution.
KENO calculates the real variance using an iterative approach and lag
covariance data between generations as follows :cite:`KENO-demaret_accurate_1999,KENO-ueki_error_1997`
1. The sample variance and covariance estimates are calculated.
2. The apparent variance is set equal to the sample variance and the
apparent covariance is set equal to the sample covariance.
3. The real covariance is set equal to the apparent covariance and the
real variance is calculated.
4. Using the real variance and apparent covariance calculate the real
covariance.
5. The real variance is recalculated.
6. Steps 4 and 5 are repeated until the real variance converges within a
preset tolerance.
The covariance estimates are only calculated for the previous
20 generations. A maximum of 50 iterations are allowed for the real
variance to converge.
Generation time and lifetime
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The generation time and lifetime calculations use the average velocity.
The validity of these calculations is determined by how accurately the
average velocity represents the spectrum over the range of the energy
group. The lifetime and generation time calculated by KENO are not
kinetics parameters. The lifetime is the average life span of a neutron
(in seconds) from the time it is born until it is absorbed or leaks from
the system. The generation time is the average time (in seconds) between
successive neutron generations.
Energy of the Average Lethargy of Fission
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The energy of the average lethargy of neutrons causing fission (*EALF*)
is a parameter calculated in KENO to characterize the neutron energy
spectrum or fastness of a system. The *EALF* is given in units of eV in
the KENO output. An *EALF* value that is high (> 100 keV) indicates that
most fissions in the system are being caused by fast neutrons, and an
*EALF* value that is low (< 1 eV) indicates that most fissions are
induced by thermal neutrons.
The *EALF* is calculated by determining the lethargy, :math:`u`, a
measure of how much neutron energy changes from its initial or birth
energy:
.. math::
:label: eq8-1-1
u = ln\left( \frac{E_{0}}{E} \right),
where :math:`E` is the energy of the neutron colliding with a nucleus
and :math:`E_{0}` is the maximum possible energy of fission neutrons
(assumed in KENO to be 10 MeV). The average lethargy of all fission
events is calculated by weighting the lethargy for each collision by the
probability that the collision will create a fission event, and
averaging this quantity. Using a log-scale parameter like lethargy to
represent the fastness of systems is more convenient than directly
averaging the energy of neutrons causing fission both because of the
wide range of neutrons in a problem (potentially more than seven orders
of magnitude), and because fast neutrons that are slowing down lose
about the same fraction of their energy during each collision.
.. math::
:label: eq8-1-2
EALF = E_{o}e^{- u_{\text{avg}}}
Equation :eq:`eq8-1-2` is then applied again to transform the average lethargy of
neutrons causing fission into a neutron energy that corresponds to the
average lethargy of neutrons causing fission (this is the *EALF*); this
transformation back to units of energy is done because energy has a much
more intuitive meaning than units of lethargy.
.. _sec-module.keno.output:
Description of Output
---------------------
This section contains a brief description and explanation of the KENO
output. Portions of the printout will not be printed for every problem.
Some printout is optional, as noted in this section. This section
provides representative samples of the output format. The actual data
contained in this section are not necessarily consistent with results
computed by the current version of KENO.
KENO offers an HTML output format including a series of files that can
be viewed in a standard web browser. The HTML formatted output offers
interactive output that is easy to read and navigate. Many of the tables
of data can be sorted in ascending or descending order by clicking on
the heading of the column for which sorting is desired.
In this section, the standard
text output description is followed by a description of the optional
HTML formatted output. The HTML formatted output can be deactivated by
entering HTM=NO in the parameter data section.
.. warning:: The HTML-formatted output is no longer actively developed,
and the output files created with it may therefore not include
recently added capabilities or changes. For example, the fission
rate mesh tally and some CE TSUNAMI edits are not included in the HTML output.
Program verification information
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Program verification information :numref:`fig8-1-97` is printed after the
header page. It lists the name of the program, the date the load module
was created, the library that contains the load module, the computer
code name from the configuration control table, and the revision number.
The job name, date, and time of execution are also printed. This
information may be used for quality assurance purposes.
.. figure:: figs/Keno/fig97.png
:align: center
:width: 700
:name: fig8-1-97
Sample program verification table.
The program verification information is the first page shown in the
KENO HTML output, after selecting KENO from the SCALE HTML index page.
This page can also be displayed by selecting the *Program Verification
Information* link under the *General Information* submenu and is shown
in :numref:`fig8-1-97`.
Tables of parameter data
~~~~~~~~~~~~~~~~~~~~~~~~
The first two tables printed by KENO list the numeric parameters and
logical parameters used in the problem. The user should always verify
that the parameter data block was entered as desired. An example of
numeric parameters table is shown in :numref:`fig8-1-98`. An example of the logical parameters table is shown in
:numref:`fig8-1-99`.
.. figure:: figs/Keno/fig98.png
:align: center
:width: 800
:name: fig8-1-98
Sample table of numeric parameter data.
.. figure:: figs/Keno/fig99.png
:align: center
:width: 800
:name: fig8-1-99
Sample table of logical parameter data.
For the logical parameter data table, messages concerning the parameter
data may be printed at the bottom of the table. If the problem is being
restarted, the title of the parent case is printed at the bottom of the
table. If the restart title or messages are not printed, the bottom
section of the table is omitted.
Unprocessed geometry input data
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
This printout is optional and is usually used to locate code
difficulties, to show all the geometry input data when only part of it
is used in the problem, or to show the order in which units were
entered. It is considered debug information and is printed only if
**PGM**\ =YES is specified in the parameter input data. Standard KENO
use does not require printing these data because the processed geometry
that is used in the problem is always printed. See :numref:`8-1-4-52-9` and
:numref:`8-1-4-13` for examples of the standard printed KENO geometry data.
When the unprocessed geometry input is printed, the problem title is
located at the top of the page, followed by the heading "GEOMETRY
DESCRIPTION INPUT." The region-dependent geometry information is then
printed. If the problem contains a unit orientation array, the problem
title is printed again, followed by the unit orientation. This is
followed by a statement affirming the completion of the data input.
.. _8-1-4-4:
Table of data sets used in the problem
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
This table is the third table of data printed by KENO. It should be
carefully scrutinized to verify the desired data set name is associated
with the proper unit number and volume. An example of this table is
shown in :numref:`fig8-1-100`.
.. figure:: figs/Keno/fig100.png
:align: center
:width: 800
:name: fig8-1-100
Sample table of data sets used in the problem.
This table lists unit numbers specified in the parameter data or that
are defaulted in the code, along with the information pertinent to them.
This information is given in the following order, left to right: (1) the
keyword used in the parameter data to define the unit number, (2) the
unit number, (3) the data set name, (4) the name of the volume on which
the data set resides, and (5) the type of data contained on the data
set. This table can be useful for quality assurance purposes.
Information for units for which default values have not been overridden
is printed even though they may not be used in the problem. Information
for every unit specified in the parameter data is also printed. Units 8
and 10 are the direct-access devices, and their unit numbers are fixed
within the code. When this table is printed, Unit 10 has not yet been
defined. This causes its data set names to be listed as FT10F001 or as
"UNKNOWN" on some systems. If KENO is run as part of a CSAS sequence,
this table will include two entries for Unit 35: one for binary input
data, and one for read restart data.
Table of additional information
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The fourth table of data printed by KENO contains additional information
determined from the input data. An example of this table is shown in
:numref:`fig8-1-101`.
This table should be used to verify the problem input. The NUMBER OF
ENERGY GROUPS for a multigroup problem is read either from the
Monte Carlo formatted library, identified by the keyword **XSC** and the
unit function name MIXED CROSS SECTIONS from the Table of Data Sets in
:numref:`8-1-4-4`, or from the restart unit, identified by the keyword
**RST** and the unit function name, READ RESTART DATA. The NO. OF
FISSION SPECTRUM SOURCE GROUP is the number of different energy groups
for which a fission spectrum is defined. In the present version, this
number should always be 1. The NO. OF SCATTERING ANGLES IN XSECS is the
number of scattering angles to be used in processing the cross sections.
The default value is 3, and it may be overridden by specifying the
parameter **SCT**\ = in the mixing table input. One scattering angle
yields P\ :sub:`1` cross sections, two scattering angles yield
P\ :sub:`3` cross sections, three scattering angles yield P\ :sub:`5`
cross sections, etc.
.. figure:: figs/Keno/fig101.png
:align: center
:width: 800
:name: fig8-1-101
Sample table of additional information.
The NUMBER OF MIXTURES USED is the number of different mixtures (media)
used in the geometry data used by the problem. This may be less than the
total number of different mixtures specified in the geometry data if
portions of the geometry data are not used in the problem.
The NUMBER OF BIAS IDS USED is the number of different biasing regions
used in the problem. This will always be one unless a biasing data block
is entered.
The NUMBER OF DIFFERENTIAL ALBEDOS USED is the number of different
differential albedo reflectors used in the problem. This will always be
zero unless the boundary condition data specify the use of differential
albedo reflection on one or more faces of the system as described in
:numref:`8-1-4-7`. The BOUNDARY CONDITION data printed in this table should
also be checked. The number of different differential albedos specified
on the faces should be consistent with the NUMBER OF DIFFERENTIAL
ALBEDOS USED. Specular, mirror, vacuum, and periodic are not
differential albedos. Several different keywords may be used to specify
the same differential albedo.
The TOTAL INPUT GEOMETRY REGIONS is the number of geometry regions
specified in the problem input. This excludes UNIT label and comments
provided using COM=, but it includes the array boundary description.
It excludes the automatic reflector description, but it includes the
geometry regions generated by it. The NUMBER OF GEOMETRY REGIONS USED is
the number of geometry regions used in the problem. It may be less than
or equal to the TOTAL INPUT GEOMETRY REGIONS. The LARGEST GEOMETRY UNIT
NUMBER is the largest unit number defined in the geometry data,
including unused units and implicitly defined units. Implicitly defined
unit numbers are created when a core boundary specification is not
immediately preceded by a specification. The unit number is assigned by
the code by adding one to the largest unit number encountered in the
geometry region data. For example, if two such core boundary
specifications are contained in a problem whose largest explicitly
defined unit number is 7, then a unit number of 8 is assigned to the
first one, and a unit number of 9 is assigned to the second one. A value
of 9 would be printed for the LARGEST GEOMETRY UNIT NUMBER. The LARGEST
ARRAY NUMBER is the largest array number specified in the array data.
USE LATTICE GEOMETRY is determined by the logical flag that indicates
whether or not the problem is a single unit problem. This should be YES
for any problem that is not a single unit problem and NO for a single
unit problem. By definition, a single unit problem does not use array
data in any form. :numref:`8-1-4-12` describes array data. The GLOBAL
ARRAY NUMBER is the number of the array designated as the global,
overall, or universal array. The global array can be thought of as the
array that defines the overall system.
The NUMBER OF UNITS IN THE GLOBAL X/Y/Z DIR. defines the size of the
global array in terms of the number of units that are located along the
edge of the array boundaries in the X/Y/Z directions. For a single unit,
all three of these should be zero. For a simple 1 :math:`\times` 1 :math:`\times` 1 array
consisting of one unit type, all three of these numbers should be 1.
USE NESTED HOLES is set YES if holes are nested deeper than one level.
NUMBER OF HOLES is the number of HOLES that are entered in the geometry
region data.
The MAXIMUM HOLE NESTING LEVEL is the deepest level of hole nesting.
USE NESTED ARRAYS is set YES if arrays are nested deeper than one level.
The NUMBER OF ARRAYS USED is the number of array descriptions actually
used in the problem description.
MAXIMUM ARRAY NESTING LEVEL is the deepest level of array nesting.
BOUNDARY CONDITIONs are printed near the bottom of the table. They
show the type of boundary condition that is applied to each surface of the
system. These should all be VACUUM unless albedo boundary conditions are
applied to one or more faces of the system. One should refer to the
NUMBER OF DIFFERENTIAL ALBEDOS USED, as discussed previously in the
description of this table of information.
The outer boundary of the global unit can consist of multiple shapes in
KENO-VI geometry. For such a case, BOUNDARY CONDITIONS are printed for
all shapes enclosing the global unit as shown in :numref:`fig8-1-101-2`.
.. figure:: figs/Keno/fig101_2.png
:align: center
:width: 800
:name: fig8-1-101-2
Boundary conditions of a KENO-VI model in which combination of multiple shapes encloses the global unit.
.. note:: Boundary condition edit in Table of additional information does
not list the surfaces added to each boundary body by CHORD operations.
.. _keno-7-1-4-6:
Cross section data edits for the continuous energy mode
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Unlike with the multigroup mode, KENO with continuous-energy mode
loads each nuclide data directly from libraries. When loading data,
Doppler broadening temperature correction (controlled by **DBX**
parameter, see :numref:`8-1-6-2-10` for further details) is performed
by default, on all nuclide cross sections, if the requested
temperature is more than 4 K from the library temperature. If the Doppler
broadening temperature correction is not enabled, then the nuclides' data
are loaded from libraries with the closest temperature.
When running KENO standalone, material temperatures can be entered
by the **TEMP** parameter in the *MIXT data block*. When running KENO
as part of a SCALE sequence, all material temperatures can be entered
by each composition data definition in the *COMPOSITION data block*.
Cross sections data edits in KENO output summarize the data setup
in the continuous-energy calculations. Examples of this summary are
given in :numref:`fig-keno-oedit-ce-xs-dbx`
and :numref:`fig-keno-oedit-ce-xs-no-dbx` for a sample continuous-energy
calculation with and without Doppler broadening temperature correction.
This edit starts with printing the thermal energy cutoff utilized in
the problem that, followed by a diagnostic edit, notifies that inverse
velocity calculations have completed. In the next section, nuclide id,
temperature at which data are being processed, and name of temperature-independent and -dependent cross section data files loaded are printed.
When Doppler broadening temperature correction has been enabled (**DBX=** 2),
one of the temperature-dependent data files used in this correction
is printed as shown in :numref:`fig-keno-oedit-ce-xs-dbx`. This is
one of the caveats of this edit since full details of broadening
are not listed here. Some messages from the cross section data loader
related to broadening can be shown in the message file. After this
section, nuclides for which DBRC data loaded are listed if DBRC
has been enabled in the calculations. Finally, elapsed time required
for data processing (loading + broadening) is reported.
.. figure:: figs/Keno/keno_oedit_ce_xs_dbx.png
:align: center
:width: 800
:name: fig-keno-oedit-ce-xs-dbx
Example of cross section data summary for continuous-energy mode (with DBX=2, DBRC=2)
When Doppler broadening temperature correction is turned off (**DBX=** 0), KENO
loads the temperature-dependent data from libraries with the closest
temperature and prints their names as shown in :numref:`fig-keno-oedit-ce-xs-no-dbx`.
KENO always notifies the user with a warning message as shown in
:numref:`fig-keno-oedit-ce-xs-no-dbx` if there is a difference between
the temperature at which data would be loaded and the closest
temperature for which data has been loaded.
.. figure:: figs/Keno/keno_oedit_ce_xs_no_dbx.png
:align: center
:width: 800
:name: fig-keno-oedit-ce-xs-no-dbx
Example of cross section data summary for continuous-energy mode (with DBX=0, DBRC=2)
.. note:: **Mixture temperatures** printed in the mixing table output edit
discussed in the next section are the user-defined temperatures at which
cross section data processing has been requested. On the contrary,
**nuclide temperatures** printed in the mixing table output edit show
the exact temperatures utilized at which nuclide data are processed for
the current calculation.
Mixing table data edits
~~~~~~~~~~~~~~~~~~~~~~~
If **LIB=** is entered in the KENO parameter data and a mixing table
data block is provided to KENO, mixing table data will be printed. This
output edit is not considered optional because it cannot be suppressed
if the necessary data are present. There are some differences between
the mixing table data edits for both multigroup and continuous-energy modes.
Multigroup mode mixing table data edit
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Sample mixing table data for multigroup
mode are shown in :numref:`fig8-1-102`. In the HTML output, the mixing
table data can be accessed with the *Mixing Table* link in the *Input Data*
section.
The data printed in this table include the problem title, the number of
scattering angles, and the cross section message threshold. Data are
then printed for each mixture. First the mixture number, density, and
temperature are printed, followed by a table of the nuclides which make
up the mixture. This table contains the following data: nuclide
ID number, nuclide mixture ID number, atom density, weight fraction of
nuclide in mixture, ZA number, atomic weight, temperature, and nuclide
title. Mixture temperature is the same as the nuclides' temperatures for
the multigroup calculations. After
all mixture data have been printed, a table of nuclides and descriptive
titles is printed for all nuclides included in the mixtures. If extra
1-D cross sections were specified in the problem (see **X1D**\ =,
:numref:`sec-module.keno.parameters`), the extra 1-D cross section IDs will be printed under
the heading "1-D CROSS SECTION ARRAY ID NUMBERS." If :math:`\bar{\nu}` is to be calculated
(parameter **NUB**\ =YES), six MT numbers will be printed. The MT number
for the total cross section (:math:`\Sigma_{\mathrm{T}}`) is 1; the MT number for the sum
of the transfer array normalized by :math:`\Sigma_{\mathrm{T}}` is 2002; the MT number
for the normalized fission-product cross section :math:`\left(v \Sigma_{\mathrm{f}} / \Sigma_{\mathrm{t}}\right)`
is 1452; the MT number for the normalized absorption cross section
:math:`\left(\sum_{\mathrm{abs}} / \Sigma_{\mathrm{T}}\right)` is 27;
the MT number for the normalized fission
cross section :math:`\left(\Sigma_{\mathrm{f}} / \Sigma_{\mathrm{T}}\right)` is 18; and the MT number for the
fission spectrum (:math:`\chi`) is 1018. :math:`\chi` is summed and normalized to 1.0. Other
MT numbers in this list have been specified by the user. If the number
of blocks on the direct access data set are insufficient to hold the
cross section data, a message is printed stating THE NUMBER OF DIRECT
ACCESS BLOCKS ON UNIT____\_ HAS BEEN INCREASED TO \____. If the problem
is to write a restart data set (parameter **RES**\ =), a message is
printed stating that restart information was written, and the restart
I/O unit number is specified. This is followed by a statement of the
number of I/Os used in preparing the cross sections. The user should
examine the mixing table carefully to verify that the proper nuclides
are specified for the proper mixtures and that all the data are correct.
The mixing table is printed in subroutine PRTMIX.
.. figure:: figs/Keno/keno_oedit_mix_table_mg_mode.png
:align: center
:width: 1000
:name: fig8-1-102
Example of mixing table data for multigroup mode.
.. note::
See :numref:`8-1-3-4-4` for the details for the warning message printed
in mixing table edit.
Continuous-energy mode mixing table data edit
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
In continuous energy mode, each mixture data is printed immediately after
the problem title. For a mixture, first the mixture number, density, and
temperature are printed, followed by a table of the nuclides which make
up this mixture. Format of the nuclide edits in this table is same as
the one used for multigroup mode, it contains the following data:
nuclide ID number, nuclide mixture ID number, atom density, weight fraction of
nuclide in mixture, ZA number, atomic weight, temperature, and nuclide
title.
Sample mixing table data for continuous-energy mode are shown in
:numref:`fig-keno-oedit-mix-table-ce-dbx`. The nuclides' titles are
relatively short compared to those for the multigroup mode since
these data are not provided by AMPX, and KENO creates a short
title while loading each nuclide data from the continuous-energy
libraries.
.. figure:: figs/Keno/keno_oedit_mix_table_ce_mode_dbx_2.png
:align: center
:width: 700
:name: fig-keno-oedit-mix-table-ce-dbx
Example of mixing table data for continuous energy mode with **DBX=2**.
Unlike the multigroup calculations, mixture temperature may be different
from the nuclides' temperatures for the continuous-energy calculations
if Doppler broadening temperature correction is not enabled
(setting **DBX=** to 0 disables the temperature correction) because the
nuclides are loaded from libraries with the closest temperature.
:numref:`fig-keno-oedit-mix-table-ce-no-dbx` is a sample mixing table data
edits for such a case.
.. figure:: figs/Keno/keno_oedit_mix_table_ce_mode_dbx_0.png
:align: center
:width: 700
:name: fig-keno-oedit-mix-table-ce-no-dbx
Example of mixing table data for multigroup mode with **DBX=0**.
.. _8-1-4-7:
Albedo cross section correspondence
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Printing the albedo cross section correspondence tables is optional. The
headings for the tables are printed in subroutine CORRE, and then
subroutine RATIO prints the data. These tables are printed only if
**PAX**\ =YES is specified in the parameter data as described in
:numref:`sec-module.keno.parameters`. Examples of these tables are shown in :numref:`fig8-1-103` and
:numref:`fig8-1-104`.
The table shown in :numref:`fig8-1-103` contains, left to right, the cross
section energy group, the lower and upper lethargy bounds, the
corresponding albedo energy groups, and the cumulative probability
associated with each albedo energy group for choosing the albedo energy
group corresponding to the cross section energy group. The table shown
in :numref:`fig8-1-104` is the inverse of the table shown in :numref:`fig8-1-103`. It
provides the cumulative probabilities for choosing the cross section
energy group corresponding to the albedo energy group. The information
in these tables is automatically generated by KENO.
.. figure:: figs/Keno/fig103.png
:align: center
:width: 600
:name: fig8-1-103
Cumulative probabilities for correlating the albedo energy group to the cross section energy group.
.. figure:: figs/Keno/fig104.png
:align: center
:width: 600
:name: fig8-1-104
Cumulative probabilities for correlating the cross section energy group to the albedo energy group.
1-D macroscopic cross sections
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The decision to print the 1-D mixture cross sections is optional. They
are printed only if **XS1**\ =YES is specified in the parameter data.
When the 1-D cross sections are to be printed, they are printed a group
at a time for each mixture. The 1-D mixture cross sections for a mixture
are shown in :numref:`fig8-1-105`.
.. figure:: figs/Keno/fig105.png
:align: center
:width: 600
:name: fig8-1-105
Example of macroscopic 1-D cross sections.
When the 1-D mixture cross sections are printed, the problem title is
printed at the top of the page. The mixture ID, mixture index, and
mixture number are then printed. ID is the mixture number from the
mixing table, and mixture index is the index used to reference it and
mixture number is its identifier. This step is followed by a heading to
identify the different 1-D cross sections. *GROUP* is the energy group,
*sigt* is the total cross section for the mixture, *sigs* is the
nonabsorption probability, *siga* is the absorption probability, *signu*
is the production probability, *chi* is the fission spectrum, *mwa1* is
the pointer for the first position of the cross sections for the energy
group, *mwa2* is the pointer for the last position of the cross sections
for the energy group, and *mwa3* contains the group for the transfer
corresponding to the first position. *SUM* is the sum of the absorption
probability and the nonabsorption probability. The absorption
probability is defined as the absorption cross section divided by the
total cross section. The nonabsorption probability is the sum of the
group-to-group transfers for this group, divided by the total
cross section. The production probability is defined as the fission
production cross section divided by the total cross section
:math:`\left(v \Sigma_{f} / \Sigma_{\mathrm{T}}\right)`. The nonabsorption probability and the production
probability are not true probabilities in that they may be greater than
1. This is because the nonabsorption probability has the (n,2n) transfer
array summed into the total transfer array twice, and the (n,3n) is
summed three times, etc.
Extra 1-d cross sections
~~~~~~~~~~~~~~~~~~~~~~~~
Printing the extra 1-D cross sections is optional. They are printed if
**P1D**\ =YES is specified in the parameter data. Extra 1-D
cross sections are not used in KENO unless **NUB**\ =YES is specified in
the parameter data or the user has altered the code to access and
utilize other 1-D cross sections. If \ **NUB**\ =YES is specified, the
extra 1-D cross section is the fission cross section, which is used to
calculate the average number of neutrons per fission. This is printed
only for fissile mixtures as shown in :numref:`fig8-1-105`. The fission cross
section heading follows the table of 1D cross sections. The fission
cross section heading is XSEC ID 18, and it follows the table of 1-D
cross sections.
2-D macroscopic cross sections
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The decision to print the 2-D mixture cross sections is optional. They
are printed only if **XS2**\ =YES is specified in the parameter data.
They are printed after the 1-D cross sections for the mixture. A
heading is printed, followed by the transfer data. An example of the
2-D mixture cross sections is given in :numref:`fig8-1-106`.
.. figure:: figs/Keno/fig106.png
:align: center
:width: 600
:name: fig8-1-106
Example of 2-D macroscopic cross sections.
Probabilities and angles
~~~~~~~~~~~~~~~~~~~~~~~~
Printing the probabilities and angles is optional. They are printed if
the number of scattering angles is greater than zero and **XAP**\ =YES
is specified in the parameter data. Examples of the probabilities are
shown in :numref:`fig8-1-107`. Examples of the angles are shown in :numref:`fig8-1-108`. If the group-to-group
transfer for a mixture is isotropic, the first angle for that transfer
will be set to -2.0 as a flag to the code.
.. figure:: figs/Keno/fig107.png
:align: center
:width: 600
:name: fig8-1-107
Example of macroscopic probabilities.
.. figure:: figs/Keno/fig108.png
:align: center
:width: 600
:name: fig8-1-108
Example of macroscopic angles.
.. _keno-oedit-energy-bounds-1:
Energy boundaries
~~~~~~~~~~~~~~~~~
KENO codes in the previous SCALE versions supported only single energy
group boundaries used in all tally calculations. The energy group boundaries
were obtained from the multigroup library used by transport process if
the calculation mode is multigroup. These energy bounds may not be overridden
by users in multigroup mode. In continuous-energy mode, energy group
boundaries were defaulted to the library structure read from the SCALE 252-group multigroup library. The user could override the default energy boundaries
either by defining the number of energy groups with **NGP** parameter, or by
entering the energy points in **energy data** input block.
In SCALE 6.3, KENO codes can store multiple energy group boundaries;
each may be used for different tallies. However, this capability is not
enabled for standalone KENO calculations. If KENO is run as part of
a CSAS or a TRITON sequence, then multiple energy boundaries can be entered
in the **definitions data** input block available for these sequences
(see :numref:`sec-csas.def`).
Energy boundaries output edit always prints **DEFAULT** energy boundaries
that are used in all tally calculations if it has not been otherwise requested.
In multigroup mode, **DEFAULT** energy boundaries are always read from
the multigroup library used by transport, and it cannot be overridden by the
users. An example of energy boundaries output edit printed by a standalone
multigroup KENO calculation is given in :numref:`fig-keno-oedit-ebounds-mg-1`.
.. figure:: figs/Keno/keno_oedit_ebounds_mg_1.png
:align: center
:width: 600
:name: fig-keno-oedit-ebounds-mg-1
Example of energy boundaries output edit for multi group mode.
In continuous-energy mode, **DEFAULT** energy boundaries are
defaulted to the library group structure of the SCALE 252-group library
and can be overridden by (1) setting the number of energy groups with **NGP**
parameter as shown in :numref:`energy-set-ngp-11` and :numref:`energy-set-ngp-8`,
(2) entering all energy points in **energy data** block :numref:`energy-set-energy-data`,
or (3) entering energy boundaries in the **definitions data** block (valid when running
KENO codes as part of a sequence, see :numref:`sec-csas.def` for
more details).
.. code-block:: scale
:name: energy-set-ngp-11
:caption: Energy boundaries are set by NGP=11
...
read parameter
...
NGP=11
end parameter
...
.. code-block:: scale
:name: energy-set-ngp-8
:caption: Energy boundaries are set by NGP=8
...
read parameter
...
NGP=8
end parameter
...
.. code-block:: scale
:name: energy-set-energy-data
:caption: Energy boundaries are read from energy data block
...
read energy
2.e7 1.e5 1.e1 0.65 1.e-4
end energy
...
Three examples of energy boundaries output edits for continuous-energy KENO calculations are given in the :numref:`fig-keno-oedit-ebounds-ce-1`,
:numref:`fig-keno-oedit-ebounds-ce-2`, and :numref:`fig-keno-oedit-ebounds-ce-3`.
In the first example, the energy boundaries constructed with having 11
equal lethargy intervals by setting **NGP\ =11** overwrites the **DEFAULT**
energy boundaries. :numref:`fig-keno-oedit-ebounds-ce-2` shows the
energy group output edits for a case in which the **DEFAULT** energy boundaries
are overridden by the energy boundaries read from the SCALE 8 group test library
that was provided by setting **NGP\ =8**. And the **DEFAULT** energy boundaries
are overridden in the last example whose output edit shown in :numref:`fig-keno-oedit-ebounds-ce-3`
by reading the energy boundaries from the **energy data** input block.
.. figure:: figs/Keno/keno_oedit_ebounds_ce_2.png
:align: center
:width: 600
:name: fig-keno-oedit-ebounds-ce-1
Example of energy boundaries output edit for continuous-energy mode (NGP=11).
.. figure:: figs/Keno/keno_oedit_ebounds_ce_1.png
:align: center
:width: 600
:name: fig-keno-oedit-ebounds-ce-2
Example of energy boundaries output edit for continuous-energy mode (NGP=8).
.. figure:: figs/Keno/keno_oedit_ebounds_ce_3.png
:align: center
:width: 600
:name: fig-keno-oedit-ebounds-ce-3
Example of energy boundaries output edit for continuous-energy mode (energy data).
.. _8-1-4-12:
Array summary
~~~~~~~~~~~~~
The arrays that are used in the problem are summarized in the table
shown in :numref:`fig8-1-109`. This table is printed whenever more than one array is used in
the problem.
.. figure:: figs/Keno/fig109.png
:align: center
:width: 600
:name: fig8-1-109
Example of array summary.
The ARRAY NUMBER is the number by which the array is designated in the
input data. The number of units in the X, Y, and Z directions is listed
for each array. The NESTING LEVEL indicates the level of nesting for
each array. The global, overall, or universe array is flagged by the
word GLOBAL. The global array should always appear at the first nesting
level. Arrays that have been placed in the global reflector by using
holes should also appear at the first nesting level. A nesting level of
one is the highest or first nesting levels. The larger the number in the
nesting level column, the deeper the nesting level will be.
.. _8-1-4-13:
Geometry data edits
~~~~~~~~~~~~~~~~~~~
KENO V.a geometry edit
^^^^^^^^^^^^^^^^^^^^^^
The geometry region data used by the problem are always printed and
cannot be suppressed. They should be carefully examined by the user to
verify the mixture number, bias ID, and geometry specifications used in
the problem. If geometry region data are entered but are not referenced
in the unit orientation array data, they will not be printed here. An
example would be to enter geometry region data describing Units 1, 2, 3,
and 4 and to use only Units 1, 3, and 4 in the unit orientation array.
Then the geometry region data for Unit 2 will not be printed. An example
of the KENO V.a geometry region printout for a problem is given in
:numref:`fig8-1-110`.
The problem title and a heading are printed at the top of each page.
REGION is the region number within a unit. Each unit has its regions
numbered sequentially, beginning with one. MEDIA NUM is the mixture
number or mixture ID that occupies the volume defined by the region.
BIAS ID is the bias ID that corresponds to the desired set of weight
average for biasing the region. The unit number is printed at the top of
each unit's geometry region description near the center of the page. The
data printed for each geometry region include (1) the region number
relative to the unit (numbered sequentially within the unit), (2) the
shape of the geometry region, (3) the mixture ID of the material within
the volume defined by the region, (4) the bias ID to define the average
weight of a neutron in the region, and (5) the dimensions defining the
outer boundaries of the geometry region. If additional geometry
surrounds an array, a heading is printed stating: UNIT \___\_ EXTERNAL
TO LATTICE \____. The lattice number is the number of the array that is
surrounded by the specified geometry. The unit number is the unit that
contains the specified geometry. In the case of an external reflector
for the global array, the unit number is assigned by the code.
.. figure:: figs/Keno/keno_oedit_geometry_1.png
:align: center
:width: 600
:name: fig8-1-110
Example of KENO V.a geometry region data
KENO-VI geometry edit
^^^^^^^^^^^^^^^^^^^^^
The geometry region data utilized by the problem are printed
and cannot be suppressed. They should be carefully examined
by the user to verify the mixture number, bias ID, and geometry
specifications used in the problem. If geometry region data
are input but are not referenced in the unit orientation
array data, they will not be printed here. An example would
be to input geometry region data describing Units 1, 2, 3, and 4
and to utilize only Units 1, 3, and 4 in the unit orientation array.
Then the geometry region data for Unit 2 will not be printed.
An example of the geometry region printout for a problem
is given in :numref:`keno-oedit-k6-geom-parameter` and
:numref:`keno-oedit-k6-geom`.
First, a table of geometry parameters for the problem is printed.
This specifies the overall size of the problem, number of
components in the problem, and the size of the array needed
to store the geometry. Next, the quadratic equations by unit
are printed. The problem title and a heading are printed at
the top of each page. The unit number followed by the GEOMETRY
data for that unit is then printed. Each geometry record type
used in the unit, numbered in the order they appear in the
unit, is printed out. Following each geometry record type is
the set of quadratic equations that describe the input geometry
for that geometry record. The CONTENTS data, consisting of
four columns, are then listed in the order they appear in the
problem. The first column contains the content keyword.
The second column contains the media/hole/array number.
The third column labeled IMP contains the bias ID number
if the content keyword is MEDIA. Otherwise, this column
is blank. The fourth column contains the sector definition
array, which describes the region location relative to the
GEOMETRY records listed above for that unit.
The data consisting of the unit number, GEOMETRY data,
and CONTENT data are repeated for each unit used in
the problem. The global unit has a heading printed before
the unit number to identify it as the global unit.
.. figure:: figs/Keno/keno_oedit_k6_geometry_parameter.png
:align: center
:width: 700
:name: keno-oedit-k6-geom-parameter
Example of KENO-VI geometry parameter table.
.. figure:: figs/Keno/keno_oedit_k6_geometry.png
:align: center
:width: 800
:name: keno-oedit-k6-geom
Example of KENO-VI geometry region data.
Unit orientation description
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Each unit orientation description defines the location of units in the
3-D lattice that represent the specified array. The array described is
identified in the heading UNIT ORIENTATION DESCRIPTION FOR ARRAY \____.
The arrays used in the problem are stacked together to represent the
physical problem being analyzed. The unit orientation description is not
printed if only Unit 1 is described in the problem. The user should
carefully examine the unit orientation descriptions to ensure proper
placement of the units in each lattice. A sample unit orientation
description is shown in :numref:`fig8-1-111` .
.. figure:: figs/Keno/keno_oedit_geometry_2.png
:align: center
:width: 600
:name: fig8-1-111
Example of unit orientation description.
If a very large array is used by the problem, its unit orientation
description may be spread over several pages. When checking the
printout, the user should pay careful attention to the headings that
indicate the portion of each lattice being printed. The detailed
printout of an array may be suppressed using the ARRAY parameter **PRT=no**.
.. _8-1-4-15:
Volume information
~~~~~~~~~~~~~~~~~~
The volume information printout differs between KENO V.a and KENO-VI.
Because it does not allow intersections of bodies, KENO V.a is always
able to calculate analytically the volume of any region in the geometry.
KENO-VI, on the other hand, never calculates volumes analytically. In
fact, KENO-VI never calculates volumes unless it is directed to do so,
but it can read volumes off the **MEDIA** cards or off a **VOLUME** file
(:numref:`8-1-2-13`).
KENO V.a volume edit
^^^^^^^^^^^^^^^^^^^^
Three tables of volumes are always printed and cannot be suppressed. The
problem title is printed at the top of the page, followed by the heading
"VOLUMES FOR THOSE UNITS UTILIZED IN THIS PROBLEM." An example of the
volume printout is given in :numref:`fig8-1-112`.
The first table is arranged by ascending unit number. It includes
(1) the unit number, (2) the region number within the unit, (3) the
overall geometry region number, (4) the net volume of each individual
region, and (5) the cumulative volume through each region in the unit.
The cumulative volume of the last region in a unit is the total volume
of the unit. The unit number is printed under the heading UNIT. Data
listed under the heading REGION refer to the number of the geometry
region within the unit. The geometry regions within a unit are numbered
sequentially starting with 1. Data entered under the heading GEOMETRY
REGION refer to the entry number of the individual geometry region.
These are numbered sequentially, starting with 1, through the TOTAL
INPUT GEOMETRY REGIONS defined in :numref:`fig8-1-112`. The net volume of each individual
region is calculated by subtracting the volume of the interior region
from the volume of the region and is listed under the heading VOLUME.
The data listed under the heading CUMULATIVE VOLUME are calculated from
the dimensions of the region. A simple example demonstrating how volumes
are calculated can be given by assuming a unit that is composed of three
concentric cubes. Region 1 is a cube 3 cm on a side, region 2 is a cube
4 cm on a side, and region 3 is a cube 5 cm on a side. The cumulative
volume of region 1 is 27 cm\ :sup:`3` (3\ :sup:`3`); the cumulative volume
of region 2 is 64 cm\ :sup:`3` (4\ :sup:`3`); the cumulative volume of
region 3 is 125 cm\ :sup:`3` (5\ :sup:`3`). The volume of region 1 is
27 cm\ :sup:`3` (3\ :sup:`3`), the volume of region 2 is 37 cm\ :sup:`3`
(64 - 27), and the volume of region 3 is 61 cm\ :sup:`3` (125 - 64).
.. figure:: figs/Keno/keno_oedit_vol.png
:align: center
:width: 800
:name: fig8-1-112
Sample volume information.
The second table contains (1) the unit number, (2) the number of times
the unit is used in the problem, (3) the region number within the unit,
(4) the mixture number present in the region, and (5) the total volume
associated with the region in the whole problem. The unit number is
printed under the heading UNIT, data printed under the heading USES
indicates the number of times the unit is used in the problem. Data
printed under the heading MIXTURE indicates the mixture number used in
the region. The total volume of each region is printed under the heading
TOTAL VOLUME and is determined by multiplying the VOLUME of the region
listed in the first table by the number of times the unit containing
that region is used in the problem.
The third table is printed following the heading "TOTAL MIXTURE
VOLUMES." In this table, the mixtures used in the problem are listed
with their associated total volume and total mass. The mixture numbers
are printed under the heading MIXTURE, the total volume of each mixture
is printed under the heading TOTAL VOLUME, and the mass of each mixture
is printed under the heading MASS(G). All masses will be printed as zero
if the working format cross section library does not contain the data
required to calculate the densities of the mixtures used in the problem.
KENO-VI volume edit
^^^^^^^^^^^^^^^^^^^
Two tables of volumes are printed by subroutine VOLUME and cannot be
suppressed. The first table will list the number of times each unit
is used in the problem and the total volume of each region throughout
the entire problem description. The second table will list the total
volume and mass of each mixture used in the problem.
If a volume calculation type of NONE is specified and no
volumes are read in for the regions, then the volumes will be set to
-1.0, which will result in negative fluxes and fission densities.
A sample volume output edit for such a case is given in :numref:`fig-keno-oedit-no-vol.png`.
Calculations with zero volumes always provide a notification with a warning
message as shown in :numref:`fig-keno-oedit-no-vol.png`.
.. figure:: figs/Keno/keno_oedit_k6_no_vol.png
:align: center
:width: 800
:name: fig-keno-oedit-no-vol.png
Sample volume information (volumes are neither defined nor calculated).
For the calculated volumes, an error estimate is printed after the volumes.
A summary of the parameters used in both **TRACE** and **RANDOM** volume
estimates and some diagnostic information is always printed before the
first table if any region volume is calculated by one of these methods. Two
examples of the KENO-VI volume output edits with these volume calculation
methods are given in :numref:`fig-keno-oedit-vol-random-1`
and :numref:`fig-keno-oedit-vol-trace-1`, respectively.
.. figure:: figs/Keno/keno_oedit_vol_random_1.png
:align: center
:width: 800
:name: fig-keno-oedit-vol-random-1
Sample volume information, undefined volumes are calculated by RANDOM estimate.
.. figure:: figs/Keno/keno_oedit_vol_trace_1.png
:align: center
:width: 800
:name: fig-keno-oedit-vol-TRACE-1
Sample volume information, undefined volumes are calculated by TRACE estimate.
The unit number is printed under the heading **UNIT**. The REGION refers
to the number of the geometry region within the unit determined by the
order of the CONTENT records in the unit. USES indicates the number of
times the unit is used in the problem. MIXTURE is the mixture number
used in the region. A blank indicates an array or unit, placed in a
hole, in that region. TOTAL VOLUME is the total volume of that region
followed by +/- and an error estimate if the volume for the region was
calculated.
If mesh volumes are used, there will be a table listing the cumulative
volumes generated by summing the mesh volumes, the deviations, and the
deltas between the summed volumes and the overall volumes for the
regions. If the overall volume has been calculated, then the delta
should be zero, but if it was entered, then the delta will show the
difference.
In the last table, the mixtures used in the problem are listed along
with their total volumes and masses. Along with the total volumes and
masses, an error estimate is printed for any mixtures having regions
that were calculated using either the **RANDOM** or **TRACE** volume
estimates..
Mesh volumes output edit
~~~~~~~~~~~~~~~~~~~~~~~~
With the mesh flux accumulator, fluxes are tabulated for each region of
each unit in the defined mesh grid. KENO computes the volume of each region in
each mesh interval so that fluxes per unit volume can be determined. For KENO V.a
models where the mesh flux accumulator is activated by setting
**MFX**\ =YES and either (a) the mesh size set to a positive value with **MSH**\ =,
or (b) mesh grid defined by **grid geometry data** input,
a mesh volume sampling summary and the cumulative volume of all mesh intervals for
a given region are printed as shown in :numref:`fig8-1-114`. Details of mesh grid
20001 on which a mesh volume calculation was performed are printed in the *grid
definitions* output edit. An example of grid definitions output edit can be shown
in :numref:`keno_7-1-4-17`.
Note that KENO V.a allows users to alter the default settings for the mesh volume
calculation. However, **TRACE** volume estimate is not available for mesh volume;
therefore, the **RANDOM** volume estimate is always enforced when *type=trace* is entered
in **volume data**. A corresponding warning message (message number k?=370)
is printed in the output to notify the user about this change.
.. figure:: figs/Keno/fig114.png
:align: center
:width: 800
:name: fig8-1-114
Sample sum of mesh volumes edit (KENO V.a with cubic mesh, MSH=20.0).
.. note:: Unlike the KENO V.a implementation, mesh flux accumulation with KENO-VI
always needs a **volume data** input block to activate the mesh volume
calculation; otherwise, calculation is terminated with an error message.
KENO-VI does not support mesh volume calculation with **TRACE** volume
estimation. Just as KENO V.a does, KENO-VI continues by using the **RANDOM**
volume estimation for the mesh volume calculation.
An optional edit of volumes for each mesh interval for each region can
be activated by entering **PMV**\ =YES in the parameter input. This edit
can be very large, especially if a small mesh size is used with a large
model. A sample of the volume by mesh for each region is shown
in :numref:`fig8-1-115`.
.. figure:: figs/Keno/fig115.png
:align: center
:width: 800
:name: fig8-1-115
Sample of volume by mesh for each region (only a small section of the output).
.. _keno_7-1-4-17:
Grid definitions
~~~~~~~~~~~~~~~~
This table specifies the mesh grids to be used in the problem. Each mesh
grid is either defined by the **MSH** parameter and/or **grid geometry data**
input, or constructed internally. An example of
grid information is given in :numref:`fig-oedit-grid-definition-1`.
.. figure:: figs/Keno/keno_oedit_grid_definition_1.png
:align: center
:width: 700
:name: fig-oedit-grid-definition-1
Sample of grid definitions.
Grid definitions output edit lists all user-defined and internally
constructed mesh grids, even some that are not used for any mesh
tally. Only one of the grids is stored in the grid data container
if the multiple grids are defined with identical grid data. This can
be easily seen in the diagnostic messages followed by
*grid definitions* header as well as the messages printed just
before each stored grid entry. The sample grid definitions shown
in :numref:`fig-oedit-grid-definition-1` specify that two mesh
grids with grid **IDs=** 12 and 15 were defined by two **grid geometry data**
inputs, but only one of them was stored since their definitions
were identical. A default mesh grid was also shown in :numref:`fig-oedit-grid-definition-1`
that was constructed for Shannon entropy tallies.
Biasing information
~~~~~~~~~~~~~~~~~~~
This table specifies the weighting or biasing data to be used in the
problem. An example of biasing information is given in :numref:`fig8-1-116`.
.. figure:: figs/Keno/fig116.png
:align: center
:width: 700
:name: fig8-1-116
Biasing information.
The user is responsible for determining from the input data whether the
group-dependent weights (wtavg) for the specified material(s) were
obtained from the weighting library or were entered by the user. The
group-dependent weights can be printed for verification purposes as
shown in :numref:`8-1-4-18`.
.. _8-1-4-18:
Group-dependent weights
~~~~~~~~~~~~~~~~~~~~~~~
Printing the group-dependent weights is optional. They are printed if
**PWT**\ =YES is entered in the parameter data. An example of the
printed group-dependent weights is shown in :numref:`fig8-1-117`.
.. figure:: figs/Keno/fig117.png
:align: center
:width: 600
:name: fig8-1-117
Example of biasing data.
The title is printed at the top of the table. The average weight (wtavg)
is printed for each energy group and each BIAS ID. The BIAS ID number
printed at the top of the column corresponds to the BIAS ID used in the
geometry region description or MEDIA record and printed in the biasing
information.
Plot representation
~~~~~~~~~~~~~~~~~~~
Plots representing 2-D slices through the geometrical description of the
problem are optional. They are created if plot data are entered unless
**PLT**\ =NO is specified either in the plot data or the parameter data.
Plots can be generated and displayed as (1) character plots with
alphanumeric characters representing mixture numbers, unit numbers, or
bias ID numbers or (2) color plots with colors representing mixture
numbers, unit numbers, or bias ID numbers. Color plots generate a PNG
file and require an independent program to be displayed.
An example of the output generated using the character plot method is
given in :numref:`fig8-1-118` and :numref:`fig8-1-119`. An example of the output generated using the color plot
method is given in :numref:`fig8-1-120` and :numref:`fig8-1-121`.
.. figure:: figs/Keno/fig118.png
:align: center
:width: 600
:name: fig8-1-118
Summary of character plot symbols, coordinates, and data.
:numref:`fig8-1-118` summarizes the data used to generate the character plot. :numref:`fig8-1-119` is an example
of a character plot of the 2-D slice specified through the geometrical
description of the problem. In :numref:`fig8-1-118`, the plot title is printed at the top of
the page, followed by a statement that "THE FOLLOWING WILL BE A
CHARACTER PLOT." If a plot title was not entered in the plot data, the
plot title is defaulted to the problem title. The title is followed by a
heading specifying the type of plot (MIXTURE MAP, BIAS ID MAP, or UNIT
MAP). This is followed by a table that correlates the symbols to be used
in the character plot with the mixture numbers, bias ID numbers, or unit
numbers that were used in the problem. If the problem is a bare array,
the overall system coordinates are printed. Then the coordinates of the
upper left corner and lower right corner of the plot are printed. This
is followed by the direction cosines down and across the plot. The
remaining plot parameters (including both input data and calculated
values) are then printed. NU is the number of characters printed in the
U (down) direction, NV is the number of characters printed in the V
(across) direction, DELU is the incremental distance, in cm, represented
by each character in the U (down) direction, DELV is the incremental
distance, in cm, represented by each character in the V (across)
direction, and LPI is the vertical to horizontal scaling factor for plot
proportionality.
.. figure:: figs/Keno/fig119.png
:align: center
:width: 600
:name: fig8-1-119
Sample character plot representation.
:numref:`fig8-1-119` shows a character plot of a 2-D slice specified through the
geometrical description of the problem. These plots aid the user in
verifying that the problem is described correctly. Any number of plots
can be made in one problem.
:numref:`fig8-1-120` summarizes the data used to generate the color plot.
:numref:`fig8-1-121` is an example of a color plot of the 2-D slice specified
through the geometrical description of the problem. This plot does not
appear in the KENO printout. It is generated from a PNG file that is
created when a color plot has been specified in the KENO input data and
requires special processing by the user.
In :numref:`fig8-1-120`, the plot title is printed at the top of the page,
followed by a statement that "THE FOLLOWING WILL BE A COLOR PLOT." If a
plot title was not entered in the plot data, the plot title is defaulted
to the problem title. The title is followed by a heading specifying the
type of plot (MIXTURE MAP, BIAS ID MAP, or UNIT MAP). If the problem is
a bare array, the overall system coordinates are printed. Then the
coordinates of the upper left corner and lower right corner of the plot
are printed. This is followed by the direction cosines down and across
the plot. The remaining plot parameters (including both input data and
calculated values) are then printed. NU is the number of characters
printed in the U (down) direction, NV is the number of characters
printed in the V (across) direction, DELU is the incremental distance,
in cm, represented by each character in the U (down) direction, DELV is
the incremental distance, in cm, represented by each character in the V
(across) direction, and LPI is the vertical to horizontal scaling factor
for plot proportionality.
.. figure:: figs/Keno/fig120.png
:align: center
:width: 600
:name: fig8-1-120
Summary of color plot symbols, coordinates, and data.
:numref:`fig8-1-121` shows an example of a color plot of a 2-D slice specified through the
geometrical description of the problem. Any number of plots can be made
in one problem. The color plots can be valuable tools to assist the user
in verifying that a problem is described correctly.
.. figure:: figs/Keno/fig121.png
:align: center
:width: 500
:name: fig8-1-121
Sample color plot representation.
Initial source and final pretracking edits
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Prior to calculating the *k\ eff* values for each generation, KENO
prints the number of I/Os used before tracking and the number of minutes
used processing the data. If the problem is not a restart problem,
initial source information follows those two lines as shown in
both :numref:`fig8-1-122-1` (KENO V.a example) and :numref:`fig8-1-122-2`
(KENO-VI example).
The VOLUME FRACTION OF FISSILE MATERIAL IN THE SYSTEM is the first line of
data printed for KENO V.a case. This is followed by the start type, other data
used to generate the initial source distribution, and finally, the
amount of time used to generate the initial source distribution and the
total elapsed time. :numref:`fig8-1-122-1` illustrates starting information printed
for start type 0. The cuboid for choosing starting points is (1) the bounding
box around the global array (either bare or reflected) (2) the overall system
if the outermost region is a cuboid, or (2) a cuboid
specified by the user via the keywords **XSM**\ =, **XSP**\ =,
**YSM**\ =, **YSP**\ =, **ZSM**\ =, and **ZSP**\ =.
:numref:`fig8-1-122-1` illustrates typical starting data for start type 0 (a flat start in
fissile material). The parameter used in this example was **NST**\ =0.
.. figure:: figs/Keno/kenova_start_data_output_edit.png
:align: center
:width: 600
:name: fig8-1-122-1
Example of initial source information for start type 0 (KENO V.a).
In KENO-VI case, the first line is a warning message followed by the VOLUME FRACTION OF
FISSILE MATERIAL IN THE SYSTEM line. This warning message notifies users about
the potential issues that might be encountered when the volume fraction of
fissile material in the system is calculated, especially for the cases in which volumes
are partially defined or computed. In such cases, the volume fraction of
fissile could be a negative values since KENO-VI resets the undefined volumes
to -1.0.
This message is followed by the start type, other data
used to generate the initial source distribution, and finally, the
amount of time used to generate the initial source distribution and the
total elapsed time. :numref:`fig8-1-122-2` illustrates the starting information printed
for start type 0.
.. figure:: figs/Keno/kenovi_start_data_output_edit.png
:align: center
:width: 600
:name: fig8-1-122-2
Example of initial source information for start type 0 (KENO-VI).
Reference center for flux moment/angular flux transform
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
When **TFM**\ =YES is entered, the flux moments and angular fluxes are
computed in a transformed coordinate system, relative to a "reference
center" point. The default position for the reference center is the
center of all fueled regions in the model. However, the center can be
specified by the user for each region defined in the system model using
the "center" modifier on a region input card. Edits of the fuel center
and the position of the reference center for each region are shown when
**TFM**\ =YES as shown in :numref:`fig8-1-123`.
.. figure:: figs/Keno/fig123.png
:align: center
:width: 600
:name: fig8-1-123
Example fuel center and reference center edits.
Print starting points
~~~~~~~~~~~~~~~~~~~~~
This printout is optional and is used to verify the initial source
starting points. This option is activated by specifying the parameter
**PSP**\ =YES in **start data** block, and it is valid with all start types available.
Examples of this information are given in :numref:`fig8-1-124`.
The information pertinent to the initial source distribution is printed
three lines at a time and appears under the designated headings. For
example, the coordinates X, Y, and Z are printed on one line, the
direction cosines U, V, and W are printed directly under them, and the
global coordinates XGBL, YGBL, and ZGBL on the last line. The data
printed for each source neutron include the following:
NEUTRON
is the ID number of the neutron.
X, Y, and Z
are the coordinates of the starting point relative to the
coordinate system of the unit.
WT
is the starting weight (WT is always 1.0 for a neutron when it is
started).
K
is the region number that contains the point X, Y, Z.
NOW
is the array number.
NBX, NBY, NBZ
are the coordinates of the unit within the array.
LL
is the unit number located at NBX, NBY, NBZ.
KR
is the mixture number present at the starting point.
KI
is the bias ID number or importance region at the starting point.
KCOR
is the region in the unit that contains the array where the
neutron is located.
U, V, and W
are the direction cosines defining the direction the history
is traveling.
IG
is the energy group.
K1
is the region number of the first region in unit LL.
K2
is the region number of the last region in unit LL.
IGEO
is an integer that defines the geometry shape of the region.
KCOL
is the region number in which the last collision occurred.
RANDOM NUMBER
is the current random number.
XGBL, YGBL, ZGBL
are the coordinates of the starting point relative to the
coordinate system of the **global unit**.
UGBL, VGBL, WGBL
are the direction cosines defining the direction the history
is traveling in the global coordinate system.
.. note::
When starting points are printed, **many of the above named variables have
not been initialized**. For example, RANDOM NUMBER does not reflect the
random number used to sample the starting point whose details are printed.
For starting, the variables of interest are X, Y, Z, NBX, NBY, NBZ, LL,
XGBL, YGBL, and, ZGBL.
.. figure:: figs/Keno/keno_psp_output_edit.png
:align: center
:width: 600
:name: fig8-1-124
Example of initial source points.
.. _8-1-4-23:
K-effectives by generation
~~~~~~~~~~~~~~~~~~~~~~~~~~
At the completion of each generation, KENO prints the *k\ eff* for that
generation and associated information. An example of this printout is
given in :numref:`fig8-1-126`.
.. figure:: figs/Keno/fig126.png
:align: center
:width: 600
:name: fig8-1-126
Example of k-effectives and source entropy by generation.
The data printed include (1) the generation number, (2) the k-effective
calculated for the generation, (3) the average value of k-effective
through the current generation (excluding the *nskip-1* generations),
(4) the deviation associated with the average k-effective, (5) Shannon
entropy for the generation, (6) the matrix k-effective for the
generation, and (7) the deviation associated with the matrix
k-effective. Column 5 is omitted if the user disabled source convergence
diagnostics. The last two columns are filled with zeros if the user did
not specify matrix k-effective calculations. The matrix k-effective is
the largest eigenvalue of the fission production matrix. Matrix
information can be calculated based on (1) position index, (2) unit
number, (3) hole number, and (4) array number. The matrix k-effective
printed in the sixth column is based on this order. If the matrix
k-effective is calculated by position index, it is the one printed in
the sixth column. The matrix k-effective by unit number is given second
preference, followed by hole number and then array number.
After the last generation, a message is printed to indicate why
execution was terminated. If matrix k-effectives were calculated, this
is followed by a message stating the method used to determine the matrix
k-effective.
The user should examine this portion of the printed results to ensure
that the two methods of calculating k-effective are in acceptable
agreement and to verify that the average value of k-effective has become
relatively stable. If the k-effectives appear to be oscillating or
drifting significantly, then the user should consider rerunning the
problem with a larger number of histories per generation.
If a problem is restarted, then the generation numbers and k-effectives
are printed and the words FROM RESTART UNIT are printed in the elapsed
time column. All other columns are blank. When the generation at which
the problem is to be restarted is reached, the print reverts to the
normal format as shown in :numref:`fig8-1-126`.
Problem characterization edit
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The problem characterization edit follows the k-effective by generation
edit. The title is printed at the top of the page, followed by the
lifetime and the generation time and their associated deviations. The
lifetime is the average lifespan of a neutron (in seconds) from the time
it is born until it is absorbed or leaks from the system. The generation
time is the average time (in seconds) between successive neutron
generations. If **NUB**\ =YES is specified in the parameter data,
(:numref:`sec-module.keno.parameters`) the average number of neutrons per fission, NU BAR, and
its associated deviation are printed and the AVERAGE FISSION GROUP
(the average energy group at which fission occurs) and its associated
deviation are printed. Then the ENERGY(EV) OF THE AVERAGE LETHARGY OF
NEUTRONS CAUSING FISSION and its associated deviation are printed,
followed by the system mean free path. If **SMU**\ =YES is specified in
the parameter data, the average self-multiplication of a unit and its
associated deviation is printed. This self-multiplication results from
fissions caused by neutrons born in the unit. Fissions caused by
neutrons that exit the unit and return are not included. The problem
characterization edit is shown in :numref:`fig8-1-127`.
.. figure:: figs/Keno/fig127.png
:align: center
:width: 600
:name: fig8-1-127
Example problem characterization edit.
.. _8-1-4-25:
Final k-effective edit
~~~~~~~~~~~~~~~~~~~~~~
The final k-effective edit prints the average k-effective and its
associated deviation and the limits of
k-effective for the 67, 95, and 99% confidence intervals. The number
of histories used in calculating the average k-effective is also
printed. This is done skipping various numbers of generations. The
user should carefully examine the final k-effective edit to determine
if the average k-effective is relatively stable. If a noticeable drift
is apparent as the number of initial generations skipped increases, it
may indicate a problem in converging the source. If this appears to be
the case, the problem should be rerun with a better initial source
distribution and should be run for a sufficient number of generations
that the average k-effective becomes stable. The final
k-effective edit is printed as shown in :numref:`fig8-1-128`.
.. figure:: figs/Keno/fig128.png
:align: center
:width: 600
:name: fig8-1-128
Example of the final k-effective edit.
.. _8-1-4-26:
Plot of average k-effective by generation run
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
This plot consists of average k-effectives plotted versus the number of
generations run. The limits of one standard deviation are plotted on
either side of each average k-effective. These average k-effectives are
not necessarily the same as the average k-effectives described in
:numref:`8-1-4-23`. The code omits the k-effectives of the first *nskip*
generations when the average k-effectives for this plot are calculated.
Although the k-effective of the *nskip* generation is summed into the
average k-effective, it is not plotted because standard deviations
cannot be calculated for a single point. Thus, if *nskip* is 3 (i.e.,
the first three generations are skipped), the first value plotted is the
average k-effective corresponding to the fifth generation. The dotted
line represents the value of the average k-effective corresponding to
the smallest deviation when the average k-effective and its deviation
are computed for each generation over the range of *nskip* through the
total number of generations.
:numref:`fig8-1-129` is an example of this type of plot in the text output. The
primary use for this plot is to determine if the problem has source
convergence difficulties.
.. figure:: figs/Keno/fig129.png
:align: center
:width: 600
:name: fig8-1-129
Sample plot of average k-effective by generation run.
.. _8-1-4-27:
Plot of average k-effective by generations skipped
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
This plot illustrates the average k-effective versus the number of
generations skipped as shown in :numref:`fig8-1-130`. The limits of one standard
deviation are plotted on either side of the average k-effective. The
dotted line represents the value of the average k-effective
corresponding to the smallest deviation when the average k-effective and
its deviation are computed for the number of generations skipped over
the range of *nskip*\ +1 through :sup:`2`/:sub:`3` the total number of
generations calculated. The plot is essentially a plot of the data
described in :numref:`8-1-4-25`. It is useful for determining if source
convergence has been achieved.
.. figure:: figs/Keno/fig130.png
:align: center
:width: 600
:name: fig8-1-130
Sample plot of average k-effective by generations skipped.
Final edit of fissions, absorptions, and leakage
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The final edit of fissions, absorptions, and leakage follows the final
k-effective edit and includes the fission fraction for each group and
the fission production, absorptions, and leakage, each with its
associated percent deviation. Examples of the final edits of fissions,
absorptions, and leakage are shown in :numref:`fig8-1-131`\ -\ :numref:`fig8-1-133`.
If **FAR**\ =NO is specified, region-dependent fissions and absorptions
are not printed. :numref:`fig8-1-131` demonstrates the printout if **FAR**\ =NO.
.. figure:: figs/Keno/fig131.png
:align: center
:width: 700
:name: fig8-1-131
Sample of the final edit of fissions, absorptions, and leakage with all region-dependent information suppressed (**FAR**\ =NO).
.. figure:: figs/Keno/fig132.png
:align: center
:width: 700
:name: fig8-1-132
Sample of the final edit of region-dependent fissions, absorptions, and leakage and the region-dependent totals (**FAR**\ =YES **GAS**\ =YES).
.. figure:: figs/Keno/fig133.png
:align: center
:width: 700
:name: fig8-1-133
Sample of the final edit of fissions, absorptions, and leakage and the region-dependent totals with print by region suppressed (**FAR**\ =YES **GAS**\ =NO).
If **FAR**\ =YES is specified in the parameter data, the fissions and
absorptions for each geometry region used in the problem are calculated
for each energy group. Leakage is not collected by geometry region, but
rather it represents the leakage from the system. GROUP is the energy
group number; FISSION FRACTION is the fraction of the fissions that
occur in that energy group. The percent deviation for the fission
fraction is the same as that of the fissions in the same group. The
heading **UNIT** refers to the unit, and REGION is the region number
within the specified unit. The geometry regions are numbered
sequentially within each unit, starting with 1. The sum of the fissions
for every region for a given energy group is the total printed for that
energy group. The same is true of absorptions. The fissions,
absorptions, and leakages are given in units of per source neutron. The
SYSTEM TOTAL is the sum over all the energy groups of the fissions,
absorptions, and leakage. The associated percent deviation is printed
for each.
The parameter **GAS** is used to control printing of fission productions
and absorptions for each geometry region by energy group as shown in
:numref:`fig8-1-132`. **GAS**\ =YES causes this data to be printed, provided
**FAR**\ =YES is also specified. **GAS**\ =NO turns off this print by
group as shown in :numref:`fig8-1-133`.
The sum of the leakage and absorptions printed for the system total
should be close to 1. The fissions printed for the system total should
be the same as the first k-effective printed in the final k-effective
edit described in :numref:`8-1-4-25`. If differential albedos are used, the
leakage does not include the weight lost in the albedo reflection. A
message stating the weight lost in the albedo is printed. This is the
weight lost due to absorptions in the albedo reflector and leakage from
the albedo reflector. No leakage is associated with faces having
specular, mirror image, or periodic reflection. Thus there is no leakage
associated with an infinite problem. The total elapsed time and final
random number are printed at the end of this edit.
Matrix k-effective by position index
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The matrix k-effective by unit location (also referred to as array
position or position index) is calculated if **MKP**\ =YES is specified
in the parameter data and a global array is present in the model. It is
the largest eigenvalue of the fission production matrix collected by
position index. :numref:`8-1-3-12` provides a complete discussion of
matrix k-effective. The POSITION INDEX is a number referencing a
position in a 3-D lattice. POSITION is the X, Y, and Z location within
the lattice. **UNIT** is the unit located at the specified location in
the lattice. Thus, in :numref:`fig8-1-139` , **UNIT** 1 is located at the lower left-hand
front corner of the array or 3-D lattice representing the problem (X=1,
Y=1, Z=1) and the corresponding POSITION INDEX is 1. POSITION INDEX 8 is
the top right-hand back corner of the lattice, POSITION X=2, Y=2, Z=2
and the unit located at that position is **UNIT** 8. An example of the
matrix k-effective by position is given in :numref:`fig8-1-136` . The text output is
contained within two rows of asterisks to draw attention to it.
.. figure:: figs/Keno/fig136.png
:align: center
:width: 700
:name: fig8-1-136
Example of matrix k-effective by position index.
Fission production by position index matrix
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
To obtain fission production by position information, the user must
specify **MKP**\ =YES and **FMP**\ =YES in the parameter data. The
number of entries in the fission production matrix by position index is
the square of the array size. Thus for a 2 :math:`\times` 2 :math:`\times` 2 array there are
64 entries, and for a 4 :math:`\times` 4 :math:`\times` 4 array there are 4,096 entries in the
fission production matrix by position index. An example of the fission
production matrix by position index for a 2 :math:`\times` 2 :math:`\times` 2 array is shown in :numref:`fig8-1-137`.
.. figure:: figs/Keno/fig137.png
:align: center
:width: 700
:name: fig8-1-137
Sample fission production matrix by position index.
For each position index in the array, the number of next-generation neutrons
produced at position index J per neutron born at position index I is determined.
The fission production matrix by position index is used to determine the matrix
k-effective, cofactor k-effective and source vector by position index.
.. _8-1-4-33:
Source vector by position index
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Source vector by position index information is printed if **MKP**\ =YES
is specified in the parameter data. The source vector by position index
is the eigenvector of the fission production matrix by position index
and should sum to 1.0. It represents the fission source for the
specified locations in the 3-D lattice representing the physical problem
being analyzed. Position zero contains all material outside the global
array. An example of the source vector by position index is shown in :numref:`fig8-1-138`.
The average self-multiplication by array position is the overall average
of the self-multiplication of all units used in the problem.
.. figure:: figs/Keno/fig138.png
:align: center
:width: 450
:name: fig8-1-138
Example of source vector by position index.
Cofactor k-effective by position index
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The cofactor k-effective by position index edit is printed if
**MKP**\ =YES is specified in the parameter data. This means that the
fission production matrix is collected by position index. Calculating
and printing cofactor k-effectives by position index can be avoided by
specifying **CKP**\ =NO in the parameter data. An example of the
cofactor k-effective by position index is shown in :numref:`fig8-1-139`. See
KENO :numref:`sec-module.keno.examples` for a description of the problem
used for the example.
.. figure:: figs/Keno/fig139.png
:align: center
:width: 500
:name: fig8-1-139
Example of cofactor k-effective by position index.
The cofactor k-effective for a given position index is the largest
eigenvalue of the fission production matrix collected by position index,
reduced by the row and column associated with that position index. Thus
the cofactor k-effective is the value of k-effective for the system
calculated without the fission source of the unit located at the
specified position index.
Matrix k-effective by unit number
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The matrix k-effective by unit number (unit k-effective) is the largest
eigenvalue of the fission production by unit matrix. It is calculated
only if **MKU**\ =YES is specified in the parameter data. An example of
the matrix k-effective by unit is given in :numref:`fig8-1-140`.
.. figure:: figs/Keno/fig140.png
:align: center
:width: 700
:name: fig8-1-140
Example of matrix k-effective by unit number.
Fission production by unit number matrix
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The fission production by unit number matrix is computed and printed if
**MKU**\ =YES and **FMU**\ =YES are specified in the parameter data.
Thus, for each unit in the array, the number of next-generation neutrons
produced in Unit J per neutron born in Unit I is determined. This is the
fission production matrix by unit, and it is used to determine the
matrix k-effective by unit, the cofactor k-effective by unit, and the
source vector by unit. An example of the fission production matrix by
unit is shown in :numref:`fig8-1-141` for text output.
.. figure:: figs/Keno/fig141.png
:align: center
:width: 700
:name: fig8-1-141
An example of the fission probability matrix by unit.
Source vector by unit number
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The source vector by unit is the eigenvector of the fission production
matrix by unit and is printed if **MKU**\ =YES is specified in the
parameter data. It represents the fission source for the units used in
the problem. The components of the source vector should sum to 1.0.
An example of the source vector by unit is given in :numref:`fig8-1-142`.
The average self-multiplication by unit is printed following the source
vector. This value of self-multiplication includes those histories born
in the unit which cause fissions in the same unit regardless of whether
or not it exited and then returned. Therefore, this value will not agree
with the value printed for the self-multiplication of the unit as described
in Sect. :numref:`8-1-4-33` if the problem uses multiple units, if the
system is reflected, or if a differential albedo is used in the problem.
.. figure:: figs/Keno/fig142.png
:align: center
:width: 450
:name: fig8-1-142
Example of the source vector by unit.
Cofactor k-effective by unit number
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The cofactor k-effective for a given unit is the k-effective of the
system calculated without the fission source of that unit. Cofactor
k-effectives are printed if **MKU**\ =YES is specified in the parameter
data. Calculating and printing cofactor k-effectives by unit can be
avoided by specifying **CKU**\ =NO in the parameter data. This step is
accomplished by determining the eigenvalue of the fission production
matrix by unit after it has been reduced by the row and column
associated with that unit. An example of the cofactor k-effective by
unit is given in :numref:`fig8-1-143`.
.. figure:: figs/Keno/fig143.png
:align: center
:width: 500
:name: fig8-1-143
Example of cofactor k-effective by unit number.
Matrix k-effective by hole number
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The matrix k-effective by hole number is the largest eigenvalue of the
fission production matrix collected by hole number and is calculated if
**MKH**\ =YES was specified in the parameter data. An example of the
matrix k-effective by hole number is given in :numref:`fig8-1-144`.
.. figure:: figs/Keno/fig144.png
:align: center
:width: 700
:name: fig8-1-144
Example of matrix k-effective by hole number.
Fission production by hole number matrix
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
This is the fission production matrix collected by hole number. It is
printed only if **MKH**\ =YES and **FMH**\ =YES were specified in the
parameter data. An example of this fission production matrix is given in
:numref:`fig8-1-145`. This matrix indicates the number of next generation neutrons produced
in **HOLE** number J by a neutron born in **HOLE** number I.
.. figure:: figs/Keno/fig145.png
:align: center
:width: 700
:name: fig8-1-145
Example of fission production matrix by hole.
Source vector by hole number
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The source vector by hole is the eigenvalue of the fission production
matrix by hole number and is printed if **MKH**\ =YES is specified in
the parameter data. The source vector should sum to 1.0. An example of
the source vector by hole is shown in :numref:`fig8-1-146`. The average self-multiplication
by hole is the overall average of the self-multiplication of all the
holes in the problem.
.. figure:: figs/Keno/fig146.png
:align: center
:width: 450
:name: fig8-1-146
Example of source vector by hole number.
Cofactor k-effective by hole number
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The cofactor k-effective for a given hole is the k-effective of the
system calculated without the fission source of that hole and is
calculated if **CKH**\ =YES is entered in the parameter data. These
values are computed by determining the eigenvalue of the fission
production matrix by hole after it has been reduced by the row and
column associated with that hole. An example of the cofactor k-effective
by hole number is given in :numref:`fig8-1-147`.
.. figure:: figs/Keno/fig147.png
:align: center
:width: 500
:name: fig8-1-147
Example of cofactor k-effective by hole number.
Matrix k-effective by array number
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The matrix k-effective by array number is the largest eigenvalue of the
fission production matrix collected by array number and is calculated if
**MKA**\ =YES is entered in the parameter data. An example is given in :numref:`fig8-1-148` .
The number of next generation neutrons produced in array number J by a
neutron born in array number I is given in this fission production
matrix.
.. figure:: figs/Keno/fig148.png
:align: center
:width: 700
:name: fig8-1-148
Example of matrix k-effective by array number.
Fission production by array number matrix
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The fission production matrix collected by array number is shown in :numref:`fig8-1-149` . It
is printed only if **MKA**\ =YES and **FMA**\ =YES are specified in the
parameter data.
.. figure:: figs/Keno/fig149.png
:align: center
:width: 700
:name: fig8-1-149
An example of the fission production matrix by array number.
Source vector by array number
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The source vector by array number is the eigenvector of the fission
production matrix by array number and is printed if **MKA**\ =YES is
specified in the parameter data. The source vector should sum to 1.0.
An example of the source vector by array number is shown in :numref:`fig8-1-150`. The
average self-multiplication by array number is the overall
self-multiplication of all the arrays in the problem.
.. figure:: figs/Keno/fig150.png
:align: center
:width: 450
:name: fig8-1-150
Example of source vector by array number.
Cofactor k-effective by array number
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The cofactor k-effective by array number is the k-effective of the
system calculated without the fission source of that array and is
calculated if **CKA**\ =YES is entered in the parameter data. This is
achieved by determining the eigenvector of the fission production matrix
by array after reducing it by the row and column associated with the
specified array. :numref:`fig8-1-151` is an example of the cofactor k-effective by array
number.
.. figure:: figs/Keno/fig151.png
:align: center
:width: 500
:name: fig8-1-151
Example of cofactor k-effective by array number.
.. _keno-oedit-mesh-tallies-1:
Mesh tallies
~~~~~~~~~~~~
The mesh tallies edit is optional. KENO prints the specification
of each mesh tally defined by **CDS=**, **FIS=**, and **GFX=**
parameters. A sample mesh tallies edit is given in :numref:`fig-keno-oedit-mesh-tallies-1`.
This edit does not print any details for both the mesh flux tally
activated by **MFX=** and the :math:`F^{*}(r)` mesh tally controlled
by **CGD=** parameters.
At the top of this output edit, the number of tallies computed for
the given problem is printed. Then, a summary section including the
tally response, spatial and energy grid identifiers, approximate memory
required to compute and write this tally data, and tally 3dmap output
filename is provided. The grid identifier points to the spatial mesh grid
defined either with **MSH=** parameter or **grid geometry data**
input block. Similarly, the energy identifier points to the DEFAULT energy
boundaries (see :numref:`keno-oedit-energy-bounds-1`). A summary of the energy
and spatial grids is presented after this section. Details of both energy
boundaries and grid definitions used for these mesh tallies
can be seen in :numref:`keno-oedit-energy-bounds-1` and :numref:`keno_7-1-4-17`.
.. figure:: figs/Keno/keno_oedit_mesh_tallies_1.png
:align: center
:width: 600
:name: fig-keno-oedit-mesh-tallies-1
Example of mesh tallies output edit.
.. note:: Tally results stored in 3dmap files can be visualized by Fulcrum
mesh tally plotting capability. Similarly, they can be processed by using
the utility tools provided by MAVRIC utilities.
Reaction tally
~~~~~~~~~~~~~~
Reaction tally calculations are performed if the required data are
specified in the reaction data block (:numref:`8-1-2-15`). KENO prints a
table in the output that summarizes the parameter specifications in
reaction tally calculations. An example of the parameter table for the
reaction tally calculations is shown in :numref:`fig8-1-134`.
.. figure:: figs/Keno/fig134.png
:align: center
:width: 600
:name: fig8-1-134
Example of reaction tally summary table.
.. _8-1-4-30:
Source convergence diagnostics edit
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
KENO calculates the Shannon entropy of the fission source distribution
at each generation and reports this in the problem output
(:numref:`8-1-4-23`). At the end of calculation, KENO performs three tests
to check the fission source convergence and reports these test results
in the output. (See :numref:`8-1-6-7` for the definition of these tests.) An
example of the fission source convergence diagnostics is given in
:numref:`fig8-1-135`. The last entry in this output edit is the plot of Shannon entropy
by generations run, and a sample Shannon entropy plot is shown in
:numref:`fig-keno-oedit-shannon-entropy`.
.. figure:: figs/Keno/fig135.png
:align: center
:width: 700
:name: fig8-1-135
Summary of fission source convergence diagnostics.
.. figure:: figs/Keno/keno-oedit-shannon-enropy.png
:align: center
:width: 700
:name: fig-keno-oedit-shannon-entropy
A sample Shannon entropy plot.
Fission density edit
~~~~~~~~~~~~~~~~~~~~
The fission density edit is optional. Subroutine KEDIT prints the
neutron production density and the fission density for each geometry
region if **FDN**\ =YES and **NUB**\ =YES is specified in the parameter
data (these are the default values). If **NUB**\ =NO is specified, but
**FDN**\ =YES, then only the production density will be given. An
example of the fission density edit is shown in :numref:`fig8-1-152`.
.. figure:: figs/Keno/fig152.png
:align: center
:width: 700
:name: fig8-1-152
Example of the fission density edit.
The UNIT is the unit number from the geometry data, the REGION is the
region number relative to the unit, the PRODUCTION DENSITY is the
neutrons produced per cm\ :sup:`3` per source-neutron, and the FISSION
DENSITY is the fissions per cm\ :sup:`3` per source-neutron for that
geometry region, the PERCENT DEVIATION is 100 times the fractional
standard deviation associated with the production density and/or the
fission density, the TOTAL PRODUCTIONS is the total number of neutrons
produced per source neutron, and the TOTAL FISSIONS is the total number
of fissions per source neutron in the geometry region.
Flux edit
~~~~~~~~~
Printing the region fluxes is optional; they are only printed if **FLX**\ =YES
is specified in the parameter data. The fluxes are printed for each unit
and each geometry region in the unit for every energy group. A sample of
a flux edit is given in :numref:`fig8-1-153`.
The title of the problem is printed at the top of the page. The heading
FLUXES FOR UNIT___\_ indicates the geometry unit for which fluxes are
being printed. The region numbers relative to the unit are identified by
the heading REGION____. The geometry regions within each unit are
numbered sequentially, beginning with 1. Then, the volume of each region
is printed. Note that if the region volume is printed as -1.0, it indicates
that either volume is not defined for this region, or that volume is not
calculated, or it is calculated as 0.0. GROUP is the heading for the
energy groups. The headings FLUX and PERCENT DEVIATION are printed for
each geometry region in the unit. The flux and its associated percent
deviation are printed for every energy group and every geometry region.
The last entry printed for the flux edit is the TOTL which is
the total flux integrated over all energy groups for each region.
The flux is in units of neutrons/cm\ :sup:`2` \ /source neutron.
.. figure:: figs/Keno/fig153.png
:align: center
:width: 600
:name: fig8-1-153
An example of a flux edit.
Frequency distributions
~~~~~~~~~~~~~~~~~~~~~~~
A frequency distribution consists of a bar graph indicating the number
of generations having k-effective in a specified interval. The intervals
are determined by the code, based on the upper and lower limits of the
k-effectives calculated for the generations. In this example, one
asterisk is printed for each generation k-effective. Four frequency
distributions are printed as shown in :numref:`fig8-1-154`.
These four plots are: (1) all active generations,
(2) the last 3/4 of active generations,
(3) the last half of active generations, and
(4) the last quarter of active generations.
Note that departures from normal distributions in these plots
and radical shifts among them may be indications of source
convergence issues in the calculation.
.. figure:: figs/Keno/fig154.png
:align: center
:width: 600
:name: fig8-1-154
An example of a frequency distribution.
Summary of parallel performance
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
KENO summarizes parallel performance in the output if parallel execution
is requested by the user. The performance table, shown in :numref:`fig8-1-155`,
can be used to evaluate the code parallel performance with the given
problem parameters. The quantities like speedup, parallel efficiency,
and wall-clock time for each section (serial section, parallel section,
and communication time among the processors) can be used to estimate
resource requirement for similar problems to accomplish a faster
execution.
.. figure:: figs/Keno/fig155.png
:align: center
:width: 600
:name: fig8-1-155
Example of performance analysis table.
Final results table
~~~~~~~~~~~~~~~~~~~
The final results table contains a summary of the most important physics
parameters of the system and the number of error and warning messages
generated during execution. The table contains the best-estimate system
k-effective with one standard deviation, the energy of the average
lethargy of fission, the average system nu-bar, the average mean free
path of a neutron throughout the system, the number of warning and error
messages generated during code execution, and a final statement on the
convergence of the :math:`\chi`\ :sup:`2` test results.
A summary of the Shannon entropy source convergence diagnostics is
printed here. See the details of tests in :numref:`8-1-4-30`
and :numref:`8-1-6-7`. An example of this table is
shown in :numref:`fig8-1-156`. Also shown is the terminal edit of KENO, detailing the time
required to traverse the "perilous path" through KENO.
.. figure:: figs/Keno/fig156.png
:align: center
:width: 700
:name: fig8-1-156
An example of the final results table.
HTML output
~~~~~~~~~~~
The HTML-formatted output is no longer actively developed,
and the output files created with it may therefore not include
recently added capabilities or changes. For example, the fission
rate mesh tally and some CE TSUNAMI edits are not included in the
HTML output.
HTML output: Program verification information
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
The program verification information is the first page shown in the
KENO HTML output, after selecting KENO from the SCALE HTML index page.
This page can also be displayed by selecting the *Program Verification
Information* link under the *General Information* submenu and is shown
in :numref:`fig8-1-157`.
.. figure:: figs/Keno/fig157.png
:align: center
:width: 600
:name: fig8-1-157
Sample program verification information in HTML output.
HTML output: Messages
^^^^^^^^^^^^^^^^^^^^^
In the HTML output, all error and warning messages are consolidated into
the *Messages* section of the output. *Error Messages* and *Warning
Messages* links are available to the user as needed. An example edit
with warning messages is shown in :numref:`fig8-1-158`.
.. figure:: figs/Keno/fig158.png
:align: center
:width: 600
:name: fig8-1-158
Example messages edit in HTML output.
HTML output: Tables of parameter data
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
The first two tables generated by KENO HTML output list the numeric
parameters and logical parameters that are used in the problem. The user
should always verify that the parameter data block was input as desired.
An example of numeric parameters table is shown in :numref:`fig8-1-159`. An
example of the logical parameters table is shown in :numref:`fig8-1-160`. The
HTML output is accessed with the *Numeric Parameters* and *Logical
Parameters* links in the *Input Data* section.
.. figure:: figs/Keno/fig159.png
:align: center
:width: 600
:name: fig8-1-159
Sample numeric parameters in HTML output.
.. figure:: figs/Keno/fig160.png
:align: center
:width: 600
:name: fig8-1-160
Sample logical parameters in HTML output.
HTML output: Table of additional information
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
The fourth table of data printed by KENO contains additional information
determined from the input data. An example of this table is shown in
:numref:`fig8-1-161`. The HTML output is accessed with the *Additional
Information* link in the *Input Data* section.
.. figure:: figs/Keno/fig161.png
:align: center
:width: 600
:name: fig8-1-161
Sample table of additional information in HTML output.
HTML output: Mixing table data
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
If **LIB=** is entered in the KENO parameter data and a mixing table
data block is provided to KENO, then mixing table data will be printed.
Sample mixing table data are shown in :numref:`fig8-1-162`. In the HTML output,
the mixing table data can be accessed with the *Mixing Table* link in
the *Input Data* section.
.. figure:: figs/Keno/fig162.png
:align: center
:width: 600
:name: fig8-1-162
Example of mixing table data in HTML output.
HTML output: 1D macroscopic cross sections
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
The decision to print the 1-D mixture cross sections is optional. They
are printed only if **XS1**\ =YES is specified in the parameter data.
The 1-D mixture cross sections for a mixture are shown in :numref:`fig8-1-163`.
The HTML output is accessed with the *Mixture Cross Sections* link in
the *Derived Data* section. The top menu on the right side of the window
is used to set the mixture displayed in the bottom menu on the right
side of the window. The bottom menu contains hyperlinks to all available
edits for mixture cross sections. The 1-D cross sections are accessed
with the *Neutron Cross Sections* link in the bottom menu for the
desired mixture.
.. figure:: figs/Keno/fig163.png
:align: center
:width: 600
:name: fig8-1-163
Example 1-D macroscopic cross section in HTML output.
When the 1-D mixture cross sections are printed, the problem title is
printed at the top of the page. The mixture ID, mixture index and
mixture number are then printed. ID is the mixture number from the
mixing table and mixture index is the index used to reference it and
mixture number is its identifier. This step is followed by a heading to
identify the different 1-D cross sections. *GROUP* is the energy group,
*sigt* is the total cross section for the mixture, *sigs* is the
nonabsorption probability, *siga* is the absorption probability, *signu*
is the production probability, *chi* is the fission spectrum, *mwa1* is
the pointer for the first position of the cross sections for the energy
group, *mwa2* is the pointer for the last position of the cross sections
for the energy group, and *mwa3* contains the group for the transfer
corresponding to the first position. *SUM* is the sum of the absorption
probability and the nonabsorption probability. The nonabsorption
probability and the production probability are not true probabilities in
that they may be greater than 1. This is because the nonabsorption
probability has the (n,2n) transfer array summed into the total transfer
array twice, and the (n,3n) is summed three times, etc. The absorption
probability is defined as the absorption cross section divided by the
total cross section. The nonabsorption probability is the sum of the
group-to-group transfers for this group divided by the total
cross section. The production probability is defined as the fission
production cross section divided by the total cross section
:math:`\left(\nu \Sigma_{f} / \Sigma_{\mathrm{T}}\right)`.
HTML output: 2-D macroscopic cross sections
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
The decision to print the 2-D mixture cross sections is optional. An
example of the 2-D mixture cross sections is given in :numref:`fig8-1-164`. The
HTML output is accessed with the *Mixture Cross Sections* link in the
*Derived Data* section. The top menu on the right side of the window is
used to set the mixture displayed in the bottom menu on the right side
of the window. The bottom menu contains hyperlinks to all available
edits for mixture cross sections. The 1-D macroscopic cross sections are
accessed with the *primary-to-primary scattering transfer array* link in
the bottom menu for the desired mixture.
.. figure:: figs/Keno/fig164.png
:align: center
:width: 600
:name: fig8-1-164
Example of 2-D macroscopic cross sections in HTML output.
HTML output: Probabilities and angles
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Printing the probabilities and angles is optional. The HTML output,
:numref:`fig8-1-165`, is accessed with the *Mixture Cross Sections* link in the
*Derived Data* section. The top menu on the right side of the window is
used to set the mixture displayed in the bottom menu on the right side
of the window. The bottom menu contains hyperlinks to all available
edits for mixture cross sections. The probabilities and angles edits,
shown in :numref:`fig8-1-166`, are accessed with the *primary-to-primary
probability* link in the bottom menu for the desired mixture.
.. figure:: figs/Keno/fig165.png
:align: center
:width: 600
:name: fig8-1-165
Example of macroscopic probabilities in HTML output.
.. figure:: figs/Keno/fig166.png
:align: center
:width: 600
:name: fig8-1-166
Example of macroscopic angles in HTML output.
.. _8-1-4-52-9:
HTML output: Geometry data
^^^^^^^^^^^^^^^^^^^^^^^^^^
The KENO V.a HTML version of the geometry region printout is shown in :numref:`fig8-1-167`.
The HTML edits of geometry are accessed with the *Geometry* link in the
*Input Data* section\ *.*
.. figure:: figs/Keno/fig167.png
:align: center
:width: 600
:name: fig8-1-167
Example of geometry region data in HTML output.
HTML output: Volume information
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
KENO V.a
''''''''
Three tables of volumes are always printed. An example of the volume
printout is given in :numref:`fig8-1-168`. The HTML edit is accessed with the
*Volumes* link in the *Derived Data* section.
.. figure:: figs/Keno/fig168.png
:align: center
:width: 600
:name: fig8-1-168
Sample volume information in HTML output.
KENO-VI
'''''''
Two tables of volumes are always printed. The first table will list the
number of times each unit is used in the problem and the total volume of
each region throughout the entire problem description. The second table
will list the total volume and mass of each mixture used in the problem.
Mesh volumes
''''''''''''
With the mesh flux accumulator, fluxes are tabulated for each region of
each unit in a cubic mesh. For models in which the mesh flux accumulator
is activated by setting **MFX**\ =YES and the mesh size set to a
positive value with **MSH**\ =, the cumulative volume of all mesh
intervals for a given region and the number of meshes used in each
region are printed as shown in :numref:`fig8-1-169`. The HTML edit is accessed
with the *Mesh Volumes* link in the *Derived Data* section.
.. figure:: figs/Keno/fig169.png
:align: center
:width: 600
:name: fig8-1-169
Sample sum of mesh volumes in HTML output.
An optional edit of volumes for each mesh interval for each region can
be activated by entering **PMV**\ =YES in the parameter input. This edit
can be very large, especially if a small mesh size is used with a large
model. A sample of the volume by mesh for each region is shown in
:numref:`fig8-1-170`. This edit is found under *Derived Data* with the *Mesh
Volumes by Interval* link. For the HTML output, the links on the right
side of the screen control what data are displayed in the center pane.
Clicking on the unit number in the pane labeled **UNIT** places the pane
labeled Region at that unit. Clicking on a region number in the region
pane places the volume by mesh for the selected unit in the center pane.
.. figure:: figs/Keno/fig170.png
:align: center
:width: 600
:name: fig8-1-170
Sample of volume by mesh for each region in HTML output.
HTML output: Biasing information
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
This table specifies the weighting or biasing data to be used in the
problem. An example of biasing information is given in :numref:`fig8-1-171`.
.. figure:: figs/Keno/fig171.png
:align: center
:width: 600
:name: fig8-1-171
Biasing information in HTML output.
HTML output: Group-dependent weights
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Printing the group-dependent weights is optional. They are printed if
**PWT**\ =YES is entered in the parameter data. This edit is available
in the HTML output under *Results* in the *Average Weight* link, as
shown in :numref:`fig8-1-172`.
.. figure:: figs/Keno/fig172.png
:align: center
:width: 600
:name: fig8-1-172
Example of biasing data in HTML output.
HTML output: Plot representation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Plots representing 2-D slices through the geometrical description of the
problem are optional. They are created if plot data are entered unless
**PLT**\ =NO is specified either in the plot data or the parameter data.
Character plots are not available in the HTML output, but the color
plots are easily viewed as shown in :numref:`fig8-1-173`. The user-requested
plots can be viewed under *Derived Data* in the *2-D Geometry Plots*
link.
:numref:`fig8-1-173` shows two color plots in a single HTML page. The color
plots do not appear in the KENO text printout, but they are an integral
part of the HTML output. They are generated from PNG files created when
a color plot has been specified in the KENO input data. Any number of
plots can be made in one problem. The color plots can be valuable tools
to assist the user in verifying that a problem is described correctly.
.. figure:: figs/Keno/fig173.png
:align: center
:width: 600
:name: fig8-1-173
Sample color plots in HTML output.
HTML output: Initial source and final pretracking edits
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Prior to calculating the k-effs for each generation, KENO prints the
final input data edit. The starting information is available in the HTML
output under *Input Data* with the *Starting Information* link. An
example of the HTML edit is shown in :numref:`fig8-1-174`.
.. figure:: figs/Keno/fig174.png
:align: center
:width: 600
:name: fig8-1-174
Example of initial source information for start type 6 in HTML output.
HTML output: Reference center for flux moment/angular flux tranform
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
When **TFM**\ =YES is entered, the flux moments and angular fluxes are
computed in a transformed coordinate system relative to a reference
center point. Edits of the fuel center and the position of the reference
center for each region are shown in :numref:`fig8-1-175`. The
HTML output edit is available under *Derived Data* in the *Reference
Centers* link.
.. figure:: figs/Keno/fig175.png
:align: center
:width: 600
:name: fig8-1-175
Example of fuel center and reference center edits in HTML output.
HTML output: K-effectives by generation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
At the completion of each generation, KENO prints the k-effective for
that generation and associated information. An example of this printout
is given in :numref:`fig8-1-175` for HTML output. This HTML output edit is
available under *Results* in the section of *k\ eff Results* in the
*k\ eff by Generations Run* link.
Example fuel center and reference center edits in HTML output.
.. figure:: figs/Keno/fig176.png
:align: center
:width: 600
:name: fig8-1-176
Example of k-effective by generation in HTML output.
The problem title is printed at the top of the page. A descriptive
heading is printed at the top of each column of data. The data printed
include (1) the generation number, (2) the k-effective calculated for
the generation, (3) the average value of k-effective through the current
generation (excluding the first two generations), (4) the deviation
associated with the average k-effective, and (5) the matrix k-effective
for the generation and the deviation associated with the matrix
k-effective. The last two columns are filled with zeros if the user did
not specify matrix k-effective calculations. The matrix k-effective is
the largest eigenvalue of the fission production matrix. Matrix
information can be calculated based on (1) position index, (2) unit
number, (3) hole number, and (4) array number. The matrix k-effective
printed in the sixth column is based on this order. If the matrix
k-effective is calculated by position index, it is the one printed in
the sixth column. The matrix k-effective by unit number is given second
preference, followed by hole number and then array number. After the
last generation, a message is printed to indicate why execution was
terminated. If matrix k-effectives were calculated, this is followed by
a message stating the method used to determine the matrix k-effective.
The user should examine this portion of the results to ensure that the
two methods of calculating k-effective are in acceptable agreement and
to verify that the average value of k-effective has become relatively
stable. If the k-effectives appear to be oscillating or drifting
significantly, the user should consider rerunning the problem with a
larger number of histories per generation.
If a problem is restarted, the generation numbers and k-effectives are
printed and the words FROM RESTART UNIT are printed in the elapsed time
column. All other columns are blank. When the generation at which the
problem is to be restarted is reached, the print reverts to the normal
format as shown in :numref:`fig8-1-126`.
HTML output: Problem characterization edit
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
The problem characterization edit is shown in :numref:`fig8-1-177` for HTML
output.
.. figure:: figs/Keno/fig177.png
:align: center
:width: 600
:name: fig8-1-177
Example problem characterization edit in HTML output.
HTML output: Final k-effective edit
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
The final k-effective edit prints the average k-effective and its
associated deviation and the limits of
k-effective for the 67, 95, and 99% confidence intervals. The final
k-effective edit is printed as shown in :numref:`fig8-1-178`. This HTML output edit is
available under *Results* in the section of *k\ eff Results* in the
*k\ eff by Generations Skipped* link.
.. figure:: figs/Keno/fig178.png
:align: center
:width: 600
:name: fig8-1-178
Example of the final k-effective edit in HTML output.
HTML output: Final edit of fissions, absorptions, and leakage
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
The final edit of fissions, absorptions, and leakage follows the final
k-effective edit and includes the fission fraction for each group and
the fission production, absorptions, and leakage, each with its
associated percent deviation.
Tables corresponding to those available in the text output are also
available in the HTML output. These data are accessed with the *Fissions
and Absorptions Data* link under *Fissions and Absorptions* in the
*Results* section, as illustrated in :numref:`fig8-1-181`, where the region and group data
(**FAR**\ =YES and **GAS**\ =YES) are present. To allow quicker loading
of the large amounts of data in the HTML output, the data have been
subdivided into several separate tables, which are accessed with the
menu on the right side of the window.
.. figure:: figs/Keno/fig181.png
:align: center
:width: 600
:name: fig8-1-181
Sample fissions, absorptions and leakage data in HTML output.
HTML output: Matrix k-effective by position index
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
The matrix k-effective by unit location (also referred to as array
position or position index) is calculated if **MKP**\ =YES is specified
in the parameter data and a global array is present in the model. An
example of the matrix k-effective by position is given in :numref:`fig8-1-183`.
In the HTML output, the k-effective by position data is available in the
*Matrix by Position* link in the *Results* section.
.. figure:: figs/Keno/fig183.png
:align: center
:width: 600
:name: fig8-1-183
Example of matrix k-effective by position index edit in HMTL output.
HTML output: Fission production by position index matrix
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
To obtain fission production by position information, the user must
specify **MKP**\ =YES and **FMP**\ =YES in the parameter data. An
example of the fission production matrix by position index for a
2 :math:`\times` 2 :math:`\times` 2 array is shown in :numref:`fig8-1-184`.
.. figure:: figs/Keno/fig184.png
:align: center
:width: 600
:name: fig8-1-184
Sample fission production matrix by position index edit in HMTL output.
For each position index in the array, the number of next-generation
neutrons produced at position index J per neutron born at position
index I is determined. The fission production matrix by position index
is used to determine the matrix k-effective, cofactor k-effective and
source vector by position index.
HTML output: Source vector by position index
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Source vector by position index information is printed if **MKP**\ =YES
is specified in the parameter data. An example of the source vector by
position index is shown in :numref:`fig8-1-185`. The average self-multiplication
by array position is the overall average of the self-multiplication of
all units used in the problem.
.. figure:: figs/Keno/fig185.png
:align: center
:width: 600
:name: fig8-1-185
Example of source vector by position index edit in HTML output.
HTML output: Cofactor k-effective by position index
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
The cofactor k-effective by position index edit is printed if
**MKP**\ =YES is specified in the parameter data. An example of the
cofactor k-effective by position index is shown in :numref:`fig8-1-186` and an
example of the source vector by position index is shown in :numref:`fig8-1-187`.
.. figure:: figs/Keno/fig186.png
:align: center
:width: 600
:name: fig8-1-186
Example cofactor k-effective by position index edit in HTML output.
.. figure:: figs/Keno/fig187.png
:align: center
:width: 600
:name: fig8-1-187
Example of source vector by position index edit in HTML output.
HTML output: Matrix k-effective, fission production, source vector and cofactor k-effective by unit number
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
The matrix k-effective by **UNIT** number (unit k-effective) is the
largest eigenvalue of the fission production by unit matrix. It is
calculated only if **MKU**\ =YES is specified in the parameter data. An
example of the matrix k-effective by **UNIT** is given in :numref:`fig8-1-188`.
Fission production, source vector and average self-multiplication by
**UNIT** are all printed on the same page as the matrix k-effective by
**UNIT**. The matrix k-effective HTML data by unit is available in the
*Matrix by Unit* link in the *Results* section.
.. figure:: figs/Keno/fig188.png
:align: center
:width: 600
:name: fig8-1-188
Example matrix by unit edit in HTML output.
HTML output: Matrix k-effective, fission production, source vector and cofactor k-effective by hole number
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
The matrix k-effective by **HOLE** number is the largest eigenvalue of
the fission production matrix collected by **HOLE** number and is
calculated if **MKH**\ =YES was specified in the parameter data. An
example of the matrix k-effective by **HOLE** number is given in :numref:`fig8-1-189`.
Fission production, source vector and average self-multiplication by
**HOLE** are all printed on the same page as the matrix k-effective by
**HOLE**. The matrix k-effective HTML data by **HOLE** is available in
the *Matrix by Hole* link in the *Results* section.
.. figure:: figs/Keno/fig189.png
:align: center
:width: 600
:name: fig8-1-189
Example matrix k-effective by hole edit in HTML output.
HTML output: Matrix k-effective, fission production, source vector and cofactor k-effective by array number
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
The matrix k-effective by array number is the largest eigenvalue of the
fission production matrix collected by array number and is calculated if
**MKA**\ =YES is entered in the parameter data. The number of next
generation neutrons produced in array number J by a neutron born in
array number I is given in this fission production matrix.
The matrix k-effective HTML data by array is available in the *Matrix by
Array* link in the *Results* section, with an example shown in
:numref:`fig8-1-190`. Fission production, source vector and average
self-multiplication by **ARRAY** number are all printed on the same page
as the matrix k-effective by **ARRAY** number.
.. figure:: figs/Keno/fig190.png
:align: center
:width: 600
:name: fig8-1-190
Example matrix by array edit in HTML output.
HTML output: Fission density edit
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
The fission density edit is optional. In the HTML output, the fission
density edit is available in the *Fission Density* link of *Fissions and
Absorptions* under the *Results* section, as shown in :numref:`fig8-1-191`.
.. figure:: figs/Keno/fig191.png
:align: center
:width: 600
:name: fig8-1-191
Example fission density edit in HTML output.
HTML output: Flux edit
^^^^^^^^^^^^^^^^^^^^^^
Printing the fluxes is optional; they are only printed if **FLX**\ =YES
is specified in the parameter data. The fluxes are printed for each unit
and each geometry region in the unit for every energy group.
In the HTML output, a table of flux data can be accessed with the
*Scalar* *Fluxes* under *Fluxes* in the *Results* section, as shown in :numref:`fig8-1-192`.
The fluxes for each unit in the problem are accessed from links on the
right side of the page. Separate links are presented for *Angular
Fluxes* and *Flux Moments* if they are requested in the problem.
.. figure:: figs/Keno/fig192.png
:align: center
:width: 600
:name: fig8-1-192
Example scalar flux edit in HTML output.
HTML output: Final results table
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
The final results table contains a summary of the most important physics
parameters of the system and the number of error and warning messages
generated during execution.
In the HTML output, the final results table is accessed with the *Final
Results* link in the *Results* section, as shown in :numref:`fig8-1-195`.
.. figure:: figs/Keno/fig195.png
:align: center
:width: 600
:name: fig8-1-195
An example of the final results table in HTML output.
.. _sec-module.keno.warn:
Warning messages and error messages
-----------------------------------
KENO prints warning and error messages that are identified by K5- or K6-
for KENO V.a and KENO-VI, respectively, followed by a unique number
(i.e., K5-001 is the identifier of the first message for KENO V.a). The
generic symbol for messages originating in KENO V.a and KENO-VI is K?,
where the question mark stands for 5 or 6. For additional information
concerning the message, refer to the identifier number in this section.
Warning messages appear when a possible error is encountered. If the
code alters data, that fact is stated in the message. It is the
responsibility of the user to verify correct usage when a warning
message is printed.
When an error is encountered, a global error flag (MFLAG) is set true and an
error message is printed. The code immediately stops or execution is
terminated with an error code
if the error is too severe to
continue. The warning and error messages in this section may show an
underscore ___\_ or a numbered underscore (1) where data will be printed
by the code. The explanation of the message will show an underscore or a
numbered underscore to indicate the corresponding data.
Messages
~~~~~~~~
KMSG001
******* WARNING ******* K?-001 FOLLOWS:
|br| READ FLAG NOT FOUND. ASSUME PARAMETER DATA FOLLOWS.
This message occurs in subroutine INITAL. It indicates that the word
``READ`` was not the first word of data encountered after the title
card. If a parameter data block is to be entered, the code expects the
words ``READ PARAMETERS`` to precede the parameter input data. If the
word ``READ`` is not the first word, the code expects parameter input
data immediately.
KMSG002
****** ERROR ****** K?-002 FOLLOWS:
|br| THE NUMBER OF ENERGY GROUPS IS
OUT OF RANGE FOR THE CROSS SECTION LIBRARY ON UNIT ___
THE INPUT MAY NOT SPECIFY A VALID DATA SET ON THIS UNIT
OR THE MODULE THAT WAS TO CREATE
THE CROSS SECTION LIBRARY ON THIS UNIT MAY HAVE FAILED
This message occurs in subroutine INITAL after subroutine PARAM has been
executed. Unit number \___\_ should be checked to ensure that it was
properly specified in the job control language. The data set name
associated with this unit number should also be verified. This
information is given in the printout in the third table. The module that
generated the cross sections should be verified as having executed
properly and that the data were saved or passed correctly. When this
message is printed for an AMPX working format library, a STOP 108 is
executed. When this message is printed for a mixed cross section format
library, a STOP 109 is executed.
KMSG003
******* WARNING ******* K?-003 FOLLOWS:
|br| MAT ID=___ WAS NOT FOUND IN THE WEIGHTS LIBRARY FOR THE SPECIFIED ENERGY GROUP STRUCTURE.
This message is printed in subroutine LODWTS when loading biasing
factors from the direct access scratch file. It indicates that weights
library did not contain biasing factors for this ID for the group
structure that corresponds to the cross sections (multigroup), or to the
binning structure (continuous energy). Default biasing factors will be
substituted. The location of this set of biasing parameters should be
checked to verify that the substitution does not cause a problem.
KMSG004
******* ERROR ******* K?-004 FOLLOWS:
|br| INVALID INPUT PARAMETER NAME ___
This message comes from subroutine PARAM and indicates that the keyword
for entering parameter data was misspelled or in error in some other
way. A list of allowed keywords is given in :numref:`tab-module.keno.parameters` in the KENO
input outline.
KMSG005
******* ERROR ******* K?-005 FOLLOWS:
|br| AN ERROR WAS ENCOUNTERED IN THE ALPHANUMERIC PARAMETER DATA. THE DATA WAS ___
This message comes from subroutine PARAM and indicates that the keyword
for the alphanumeric parameter data was entered correctly, but the data
associated with it were not YES or NO as is required. The___\_ \___\_ in
the error message could be something like ``FLX``\ =YEX instead of
``FLX``\ =YES.
KMSG006
****** WARNING ****** K?-006 FOLLOWS:
|br| READ FLAG FOUND WHEN LOOKING FOR END FLAG. PARAMETER INPUT ASSUMED COMPLETE
This message occurs in subroutine PARAM. It indicates that the keywords
``END PARAMETERS`` were not found. The keywords ``READ``\ \___\_ were
found instead. The code assumes the parameter data are complete and
proceeds normally.
KMSG007
****** ERROR ****** K?-007 FOLLOWS:
|br| ATTEMPT TO FIND END PARAMETER FLAG WAS UNSUCCESSFUL.
This message from subroutine PARAM occurs during the reading of the
parameter data if the word ``END`` is found and it is not followed by
the word ``PARAMETERS``. A STOP 118 may be executed when this message is
printed.
KMSG008
****** ERROR ****** K?-008 FOLLOWS:
|br| AN END OF FILE WAS ENCOUNTERED WHILE ATTEMPTING TO READ PARAMETER DATA
This message is from subroutine PARAM. A STOP 118 may be executed when
this message is printed.
KMSG009
****** WARNING ****** K?-009 FOLLOWS:
|br| DUE TO INCONSISTENCIES BETWEEN INPUT AND RESTART DATA,
FISSIONS AND ABSORPTIONS BY REGION WILL BE CALCULATED BUT NOT PRINTED.
INPUT DATA SET FAR=NO, BUT DATA FROM THE RESTART UNIT SPECIFIED YES.
This message occurs in subroutine PARTBL and is mostly self-explanatory.
The original problem (parent case) that wrote the restart data specified
data inconsistent with the parameter data input to the restarted
problem. The title of the parent case is given at the end of the
parameter tables. The specification of the restart unit RST is given in
the third table of the KENO output.
KMSG010
******* WARNING ******* K?-010 FOLLOWS:
|br| DUE TO INCONSISTENCIES BETWEEN INPUT AND RESTART DATA, FLUXES WILL BE
CALCULATED BUT NOT PRINTED.
INPUT DATA SET FLX=NO, BUT DATA FROM THE RESTART UNIT SPECIFIED YES.
This message occurs in subroutine PARAM. The original problem (parent
case) that wrote the restart data specified data did not agree with the
parameter data input to the restarted problem. The title of the parent
case is given at the end of the parameter tables. The specification of
the restart unit RST is given in the third table of the KENO output.
KMSG011
****** ERROR ****** K6-011 FOLLOWS:
|br| A BOUNDARY GEOMETRY WORD WAS NOT SPECIFIED FOR UNIT ___
This KENO-VI message is from subroutine SGGM_KENOG. A ``BOUNDARY`` card must
be associated with each unit identifying the outermost region of the
unit.
KMSG012
****** WARNING ****** K?-012 FOLLOWS:
|br| INPUT PARAMETER NBK WAS ENTERED AS ___. IT WAS CHANGED TO ___.
AT LEAST ___ POSITIONS ARE NECESSARY TO ACCOMMODATE THE NEUTRON BANK DATA.
This self-explanatory message is from subroutine PARTBL. ``NBK`` should
not be entered as input data unless it is known that the default value
is inadequate.
KMSG013
****** ERROR ****** K6-013 FOLLOWS:
|br| MEDIA DATA MUST BE ENTERED FOR UNIT ___
This KENO-VI message is from subroutine SGGM_KENOG. Either another ``UNIT``
card or an ``END GEOM`` card was encountered prior to inputting
``MEDIA`` data for the current unit.
KMSG014
****** ERROR ****** K?-014 FOLLOWS:
|br| ERROR - KEYWORD ___ ___ IS NOT A VALID MIXING TABLE KEYWORD.
This message is from subroutine MIXING_TABLE. It can only be encountered if a
mixing table is expected (i.e., ``READ MIX`` or ``READ MIXT`` has been
entered as data). At this point the only valid keywords are ``MIX``\ =,
``EPS``\ =, ``SCT``\ = or ``NCM``\ =. The keyword that was entered is
printed in the message. See :numref:`sec-module.keno.mixing_table` for assistance in setting up
the mixing table data.
KMSG015
****** ERROR ****** K5-015 FOLLOWS:
|br| AN ERROR WAS FOUND IN THE HEMISPHERE DESIGNATION
This KENO V.a message was printed by subroutine K5GM_KENOG. It signifies that
the geometry keyword has been destroyed after it was read. This
indicates a code bug.
KMSG016
******* ERROR ******* K?-016 FOLLOWS:
|br| ****** ERROR ****** A VALUE MUST BE ENTERED FOR LIB IN THE PARAMETER
INPUT SO CROSS SECTIONS CAN BE MIXED.
This message is from subroutine DATAIN. It occurs when a mixing table
has been read but the unit number for the AMPXS working library is
undefined. This is corrected by entering ``LIB``\ =___\_ in the
parameter input data and making sure the desired AMPXS working library
is properly defined as being on that unit in the job control language.
KMSG017
******* ERROR ******* K?-017 FOLLOWS:
|br| UNRECOGNIZABLE GEOMETRY WORD ___
This message is from subroutines K5GM_KENOG, SGGM_KENOG, K5GM_CENTER or
SGGM_CENTER. In the process of reading the
geometry data, the word ___\_ was encountered when a geometry word was
expected. Several of these messages may be generated. A message is
generated for each word of data that is read, until a valid geometry
word is found. The data are out of phase or the geometry word is
misspelled. The previous geometry word should be checked to ensure that
it has the correct entries. See :numref:`sec-scale.keno5.shapes` and
:numref:`sec-scale.keno6.shapes` for lists of accepted geometry words.
KMSG018
\****\* ERROR \****\* K6-018 FOLLOWS:
|br| INVALID INDEX INTO KEYWRD ARRAY. INP=___
CHECK SUBROUTINE KENOG FOR A CODE ERROR.
This KENO-VI message is from subroutine SGGM_KENOG. This message usually means that a
code error was introduced when changes were made to the program.
Subroutine KENOG, function LCOMPR, and KEYWRD data block should be
checked.
KMSG019
\****\* ERROR \*******\* ERROR \*******\* ERROR \*******\* ERROR \*******\* ERROR \*******\* ERROR \*******\* ERROR \*******\* ERROR \*******\* ERROR \*******\* ERROR \***\*
|br| K6-019 FOLLOWS:
A GLOBAL UNIT HAS NOT BEEN SPECIFIED.
|br| \***\* ERROR \*******\* ERROR \*******\* ERROR \*******\* ERROR \*******\* ERROR \*******\* ERROR \*******\* ERROR \*******\* ERROR \*******\* ERROR \*******\* ERROR \***\*
This KENO-VI message from subroutine SGGM_KENOG indicates that a ``GLOBAL UNIT`` has
not been specified. The outermost unit in the problem must be specified
as the ``GLOBAL UNIT``. See :numref:`sec-module.keno.geom` to determine the correct
specification.
KMSG020
******* ERROR ******* K6-020 FOLLOWS:
|br| GEOMETRY WORD INDEX OUT OF RANGE ON SCRATCH UNIT ___ FOR GEOMETRY
WORD NUMBER ___ INP=___ GWRD=___
This KENO-VI message from subroutine SGGM_READGM means that INP
is negative or larger
than NP when the geometry data are read from the scratch unit, SKRT.
This usually means that a code error was introduced when changes were
made to the program. True geometry errors should be detected when the
scratch unit, SKRT, is written. A STOP 125 is executed when this message
is printed.
KMSG021
******* ERROR ******* K?-021 FOLLOWS:
|br| ___ IS AN INVALID PARAMETER NAME FOR BIASING DATA.
ID= OR WT= OR WTS= SHOULD HAVE BEEN ENTERED.
This message is from subroutine RDBIAS. See :numref:`sec-module.keno.biasing` for assistance
in determining the proper procedure for entering biasing data.
KMSG022
******* ERROR ******* K?-022 FOLLOWS:
|br| PROBLEM IN READGM, IGEO=___ IS AN INVALID GEOMETRY TYPE
If this message has not been preceded by other geometry error messages,
it indicates a code bug.
KMSG023
******* ERROR ******* K5-023 FOLLOWS:
|br| REFLECTION OR PERIODIC BOUNDARY CONDITIONS ARE ILLEGAL ON A CURVED BOUNDARY.
This self-explanatory KENO V.a message from K5GM_JOMCHK indicates
that only a vacuum or a white boundary condition is allowed on a
curvilinear surface.
KMSG024
K?-024 FOLLOWS:
|br| INCORRECT FLAG RETURNED FROM AREAD. IRET=___
This message from subroutine RDBIAS indicates that an error was
encountered while reading the biasing data. The biasing data were not
entered properly. See :numref:`sec-module.keno.biasing` for assistance.
KMSG025
******* ERROR ******* K5-025 FOLLOWS:
|br| WHITE BOUNDARY CONDITION IS ALLOWED ONLY ON CUBOIDS, CYLINDERS, OR SPHERES
This self-explanatory KENO V.a message from K5GM_JOMCHK
indicates that WHITE albedo
boundary conditions cannot be applied to the outermost geometry if it
is a hemisphere or a hemicylinder.
KMSG026
K?-026 - ARRAY DESCRIPTION ERROR MESSAGES
|br| K?-026 FOLLOWS:
|br| SET NUMBER ___ OF THE UNIT ORIENTATION DATA CONTAINS ___ ERROR(S).
This message from subroutine RDBOX is triggered when input errors are
recognized in the unit orientation data. A set of unit orientation data
consists of 10 numbers as shown in the companion message KMSG027. The
number of errors printed in this message is a lower bound. More errors
may actually exist. This message often means that a number was omitted
or a blank was omitted when entering the unit orientation data.
KMSG027
K?-027 FOLLOWS:
|br| LTYPE=___ IX1=___ IX2=___ INCX=___ IY1=___ IY2=___ INCY=___ IZ1=___ IZ2=___ INCZ=___
This message is a companion to KMSG026. It indicates how the unit
orientation data description for the set named in KMSG026 was entered.
See :numref:`sec-module.keno.array_orient` for information pertaining to unit orientation data.
KMSG028
K?-028 FOLLOWS:
|br| THE ABOVE UNIT ORIENTATION CARD(S) CONTAIN(S) AT LEAST ONE
OF THE FOLLOWING ERRORS.
|br| 1. IX1, IY1, IZ1, INCX, INCY, OR INCZ IS LESS THAN OR EQUAL TO ZERO
|br| 2. IX2 IS LESS THAN IX1, IY2 IS LESS THAN IY1, OR IZ2 IS LESS THAN IZ1
|br| 3. IX2 IS GREATER THAN NBXMAX, IY2 IS LARGER THAN NBYMAX, OR IZ2 IS LARGER THAN NBZMAX
|br| 4. LTYPE IS LESS THAN 1 OR GREATER THAN NBOX
This self-explanatory message is from subroutine RDBOX. It pertains to
the input orientation data for LOOP. See :numref:`sec-module.keno.geom.array_data` for input
instructions.
KMSG029
******* ERROR ******* K?-029 FOLLOWS:
|br| THE ARRAY SIZE HAS BEEN SPECIFIED INCORRECTLY. NBXMAX=___ NBYMAX=___ NBZMAX=___
UNIT ORIENTATION DATA CANNOT BE READ UNLESS NBXMAX, NBYMAX AND NBZMAX ARE GREATER THAN ZERO.
This message from subroutine ARAYIN indicates that the array definition
data were incorrectly specified. It occurs only if one or more of
NBXMAX, NBYMAX, or NBZMAX is less than 1. In the array information data
these are entered in the form ``NUX=``\ ____ ``NUY=``\ ____
``NUZ=``\ ____. See :numref:`sec-module.keno.geom.array_data`. If a unit orientation data
description is to be entered, NBXMAX, NBYMAX, and NBZMAX must all be
greater than zero.
KMSG030
******* ERROR ******* K?-030 FOLLOWS:
|br| END ___ FLAG WAS NOT FOUND. ___ ___ WAS READ INSTEAD.
This message from subroutine ARAYIN occurs if the unit orientation data
description is terminated with the incorrect ``END`` flag.
KMSG031
******* ERROR ******* K?-031 FOLLOWS:
|br| ___ IS AN INVALID PARAMETER NAME IN THE ARRAY DATA.
This message is written from subroutine ARAYIN if the array data block
contains an incorrect keyword. The allowed keywords include ``NUX=``,
``NUY=``, ``NUZ=``, ``FILL,`` ``LOOP``, ``ARA``* =, ``TYP`` =. See
:numref:`sec-module.keno.geom.array_data` for additional assistance. A STOP 101 is executed when
this message is printed.
KMSG032
`````` ERROR `````` K?-032 FOLLOWS:
|br| AN ERROR EXISTS IN UNIT ORIENTATION ARRAY NUMBER ___
This message from subroutines K5_SORTA or K6_SORTA
is printed when an error is
recognized in the array description. The type of error that will trigger
the message is for a position in the unit orientation array to be
undefined, zero, negative or greater than NBOX, the largest unit number.
KMSG033 is a companion message.
KMSG033
******* ERROR ******* K?-033 FOLLOWS:
|br| UNIT ___ IS INVALID AT X INDEX =___ Y INDEX =___ Z INDEX =___
This message comes from subroutines K5_SORTA or K6_SORTA.
It is printed for each
position in the unit orientation array that is in error. The message is
printed a maximum of 10 times. Refer to :numref:`sec-module.keno.geom.array_data` for assistance in
correcting the error(s).
KMSG034
******* ERROR ******* K?-034 FOLLOWS:
|br| THE NUMBER OF MIXTURES REQUESTED IN THE GEOMETRY IS ___ THE NUMBER OF MIXTURE CROSS SECTIONS IS ___
This message from subroutines K5_FLDATA, K6_FLDATA or MFLDATA occurs
if the number of mixture
cross sections from the restart unit, RSTRT, does not equal the number
of mixtures requested in the geometry for a restarted problem.
KMSG035
******* ERROR ******* K?-035 FOLLOWS:
|br| IN THE ALBEDO INPUT DATA ___ IS AN INVALID FACE CODE NAME.
This message is from subroutine RDREF. It occurs if an invalid face code
name was entered in the albedo data. See :numref:`tab8-1-18` in :numref:`sec-module.keno.albedo`
for a list of acceptable face code names.
KMSG036
******* ERROR ******* K6-036 FOLLOWS:
|br| A BOUNDARY BODY ___ WAS SPECIFIED THAT IS NOT
ONE OF THE BODIES IN THE GLOBAL UNIT BOUNDARY.
This message is from subroutines K6_RDBNDS or LOADGEOM1. It indicates that a boundary
body was specified to assign boundary conditions that do not exist in
the global unit. The bodies specified for boundary conditions should be
carefully matched with those specified in the boundary definition
vector of the global unit.
KMSG037
******** ERROR ********* K?-037 FOLLOWS:
|br| AVERAGE NU-BAR AND AVG. FISSION GROUP WAS SPECIFIED, BUT THE FISSION XSEC ID (18)
WAS NOT FOUND IN THE EXTRA 1-D ARRAY (MT).
This message is from subroutine IDX1D. It indicates that the parameter
data contained ``NUB=`` YES, but the corresponding necessary type of
data was absent from the extra 1-D array. This can be due to a code
error or an error concerning the extra 1-D data (``X1D=`` in the
parameter data).
KMSG038
******** ERROR ******* K?-038 FOLLOWS:
|br| INPUT DATA INDICATED NO EXTRA 1-D XSEC IDS TO BE READ, BUT A READ FLAG WAS ENCOUNTERED.
This message from subroutine DATAIN is printed when the parameter data
did not specify ``X1D=`` and the words ``READ X1DS`` were encountered
later in the data. If extra 1-D data are to be used, ``X1D=`` must be
entered in the parameter data and appropriate code modifications must be
made to properly use the extra 1-D data.
KMSG039
******* ERROR ******* K?-039 FOLLOWS:
|br| INVALID START PARAMETER NAME ___
This message is from subroutine RDSTRT. It indicates that an invalid
start parameter name was encountered when the start data block was being
read. A list of allowed start parameter names is contained in
:numref:`sec-module.keno.start_data`.
KMSG040
******* WARNING ******* K?-040 FOLLOWS:
|br| LNU FOR START TYPE 6 WAS ENTERED AS ___.
THE LARGEST VALUE NEEDED FOR LNU IS NPG; ENTRIES BEYOND NPG WILL BE IGNORED.
This self-explanatory message is from subroutine RDSTRT. See
:numref:`sec-module.keno.start_data` and :numref:`sec-module.keno.start_dist` for assistance in
determining a valid value for ``LNU``.
``NPG``, the number of histories per generation, starting
neutrons are needed to fill the initial neutron bank. KENO
discards the starting points beyond ``NPG`` and notifies user
with this message about this action.
KMSG041
******* ERROR ******* K?-041 FOLLOWS:
|br| ALPHANUMERIC START DATA MUST BE ENTERED AS YES OR NO. THE DATA READ WAS ___ ___
This self-explanatory message is from subroutine RDSTRT. See
:numref:`sec-module.keno.start_data` for assistance concerning start data.
KMSG042
******* WARNING ******* K?-042 FOLLOWS:
|br| END ___ FLAG WAS NOT FOUND.___ ___ WAS READ INSTEAD
This message occurs when the ``READ`` ____ and ``END`` ____ do not
match. When entering data blocks, each block must start with ``READ``
____ and end with ``END`` ____.
KMSG043
******* ERROR ******* K?-043 FOLLOWS:
|br| AN END OF FILE WAS ENCOUNTERED BEFORE AN END DATA WAS FOUND. THE PROBLEM WILL NOT RUN.
This message is from subroutine DATAIN. It occurs when an end of file is
encountered while reading data.
KMSG044
******* ERROR ******* K?-044 FOLLOWS:
|br| A PLOT OF ZERO HEIGHT AND/OR WIDTH HAS BEEN SPECIFIED.
|br| THE HEIGHT IS ___ AND THE WIDTH IS ___
|br| THE DELTA X IS ___, THE DELTA Y IS ___, AND THE DELTA Z IS ___
|br| THE DIRECTION COSINES DOWN THE PAGE ARE ___ ___ ___
|br| THE DIRECTION COSINES ACROSS THE PAGE ARE ___ ___ ___
This message is from subroutine RDPLOT. At least one of the X, Y, or
Z components that make up the upper left corner and lower right corner
is inconsistent or one of the direction cosines ``UAX``, ``VAX``,
``WAX``, ``UDN``, ``VDN``, or ``WDN`` have the wrong sign. Check the
plot data for consistency.
KMSG045
******* ERROR ******* K?-045 FOLLOWS:
|br| ILLEGAL DATA BLOCK IDENTIFIER, ___ ___
This message from subroutine DATAIN is printed whenever an invalid data
block identifier is encountered. This can be caused by having the data
out of order, by omitting data or by misspelling data. A block
identifier consists of the words ``READ XXXX`` where ``XXXX`` is a keyword
identifying the type of data to be read. Acceptable keywords when
running KENO stand-alone are listed in :numref:`sec-module.keno.input_outline`.
KMSG046
******* ERROR ******* K?-046 FOLLOWS:
|br| IPT=___ IS OUTSIDE THE ALLOWABLE LIMIT OF ___
This message is from subroutine DATAIN. It is indicative of a code
error. IPT is the index into the LPOINT array, which contains the direct
access pointers for the various types of data.
|br| LPOINT(1) is the pointer for the geometry region data.
|br| LPOINT(2) is the pointer for the array description (unit orientation) data.
|br| LPOINT(3) is the pointer for the mixing table data.
|br| LPOINT(4) is the pointer for volume data.
|br| LPOINT(5) is the pointer for the biasing or weighting data.
|br| LPOINT(6) is the pointer for the start data.
|br| LPOINT(7) is the pointer for the albedo data.
|br| LPOINT(8) is the pointer for the mixed cross section data.
|br| LPOINT(9) is the pointer for the energy and inverse velocity data.
|br| LPOINT(10) is the pointer for the plot data.
|br| LPOINT(11) is the pointer for the biasing input data.
|br| LPOINT(12) is the pointer for the grid data for fluxes.
|br| LPOINT(13) is the pointer for importance mapping data.
|br| LPOINT(14) is the pointer for reactions data.
|br| LPOINT(15) is the pointer for definitions data.
|br| LPOINT(16) is the pointer for system responses data.
|br| LPOINT(17) is the pointer for tallies data.
|br| LPOINT(18) is the pointer for the albedo-xsec energy correspondence data.
A STOP 152 is executed when this message is printed.
KMSG047
\****\* ERROR \****\* K6-047 FOLLOWS:
|br| SECTOR DATA WAS NOT FOUND FOR ARRAY ___
This KENO-VI message is from subroutine SGGM_ARRAY. This message usually
means that sector data was left off the ``ARRAY`` contents record. See
:numref:`sec-module.keno.geom` for assistance in specifying an ``ARRAY``.
KMSG048
******* ERROR ******* K?-048 FOLLOWS:
|br| UNABLE TO ALLOCATE ___ DUE TO ERROR STATUS CODE ___ IN SUBROUTINE ___
This message is associated with allocating memory used to store problem
dependent data. The message states the type of data memory was allocated
for the error type returned when memory could not be allocated and the
current subroutine. This message could be caused by insufficient system
memory or a code problem.
KMSG050
******* ERROR ******* K6-050 FOLLOWS:
|br| THE ___ POSITION OF ARRAY ___ IN UNIT ___ WAS SPECIFIED AS ___ WHICH IS LESS THAN 1 OR GREATER THAN ___, THE NUMBER OF UNITS IN THAT DIRECTION.
This self-explanatory KENO-VI message from subroutine
SGGM_CORSIZ indicates that an array was not properly
placed in a unit. This is usually due to the incorrect
definition of one of the array indices in one dimension
(X, Y, or Z) such that it was specified outside the
array bounds in that dimension.
KMSG051
******* ERROR ******* K?-051 FOLLOWS:
|br| SURFACE ___ OF BOUNDARY LABEL ___ REQUESTED A DIFFERENTIAL ALBEDO THAT IS NOT ON THE ALBEDO DATA SET.
THE REQUESTED ALBEDO NAME IS ___
This message is from subroutine ALBRD. A list of the albedos that are on
the standard albedo data set is given in :numref:`tab8-1-19` (:numref:`sec-module.keno.albedo`).
KMSG052
******* ERROR ******* K?-052 FOLLOWS:
|br| INTERPOLATION CODE SHOULD BE IN THE RANGE 1 TO 5
|br| INT: ___
This message is from subroutine XSEC_INTERP. This indicates an error in
the continuous energy point data. INT is the interpolation code from the
data. A STOP 104 is executed in conjunction with this message, and a
traceback may be printed from subroutine STOP.
KMSG053
******* ERROR ******* K?-053 FOLLOWS:
|br| LOG INTERPOLATION SHOULD NOT BE USED WITH NEG OR ZERO ARGUMENT
|br| XP: ___
This message is from subroutine XSEC_INTERP and indicates that
a LIN-LOG interpolation was requested with a non-positive
value. A STOP 104 is executed in conjunction with this message, and a
traceback may be printed from subroutine STOP.
KMSG054
******* ERROR ******* K?-054 FOLLOWS:
|br| A SURFACE NUMBER ___ WAS SPECIFIED THAT IS LARGER THAN NUMBER OF SURFACES IN THE INDICATED GLOBAL BODY.
THE PROBLEM WILL NOT BE RUN.
This message is from subroutines K5_RDBNDS or K6_RDBNDS. It indicates that an
incorrect surface was specified to which a boundary condition was to be
assigned. The surfaces of the bodies specified for boundary conditions
should be carefully matched with those specified in the bounds of the
global unit. Corresponding albedo surface numbers for all geometric
shapes supported by KENO V.a and KENO-VI are listed in
:numref:`kenova-surf-enum` and :numref:`kenovi-surf-enum`, respectively.
KMSG056
******* ERROR ******* K?-056 FOLLOWS:
|br| MIXTURE ___ LACKS EITHER NU*FISSION OR CHI DATA
This message from subroutines NORM1D or XSEC1D indicates that a mixture
that contains fissile material is missing the nu-fission cross section
or the fission spectrum. A STOP 115 is executed when this message is
printed.
KMSG057
******* ERROR ******* K5-057 FOLLOWS:
|br| INVALID BIAS ID ___ IN REGION ___ ABOVE.
This KENO V.a message is from subroutines K5GM_PRTJOM or K5GM_READGM. It is printed if a
negative or zero bias ID is entered for the specified geometry region.
Review :numref:`sec-module.keno.geom` for correct geometry data specification
information.
KMSG058
******* ERROR ******* K6-058 FOLLOWS:
|br| INVALID BIAS ID IN REGION ABOVE.
This KENO-VI message is from subroutine SGGM_PRTJOM. It is printed if a negative or
zero bias ID is entered for the specified geometry region. Review
:numref:`sec-module.keno.geom` for correct geometry data specification information.
KMSG059
******* ERROR ******* K?-059 FOLLOWS:
|br| THE CALCULATION WAS TERMINATED BECAUSE OF EXCESSIVE SPLITTING.
This message from subroutines K5_GUIDE or K6_GUIDE is printed only if message K?-128 is
printed 50 or more times for a given generation. This indicates that the
problem and/or the code is incapable of achieving a reasonable solution.
If changes have been made in the code, they should be carefully
scrutinized. If a biasing data block has been entered (:numref:`sec-module.keno.biasing`),
it should be checked carefully.
KMSG060
******* WARNING ******* K?-060 FOLLOWS:
|br| THE ANGULAR SCATTERING DISTRIBUTION FOR MIXTURE ___ HAS BAD MOMENTS FOR THE TRANSFER FROM GROUP ___ TO GROUP ___
|br| ___ MOMENTS WERE ACCEPTED
This message from subroutine BADMOM indicates that the moments from the
cross section data are incorrect for the group transfer shown. The code
replaces the incorrect moments with acceptable moments and proceeds
normally. The moments printed in the last line of the message should
match those printed in the eighth line. The user can suppress these
messages by entering an appropriate value for the cross section message
cutoff parameter, ``EPS=`` in the mixing table data, :numref:`sec-module.keno.mixing_table`.
See :numref:`8-1-3-4-4` for assistance in determining an appropriate value.
KMSG061
******* ERROR ******* K6-061 FOLLOWS:
|br| ___ IS NOT A VALID UNIT NUMBER, A UNIT NUMBER MUST BE A POSITIVE INTEGER.
This KENO-VI message is from subroutine SGGM_KENOG. A unit number must be an integer
greater than 0.
KMSG062
******* ERROR ******* K6-062 FOLLOWS:
|br| INSUFFICIENT DATA FOLLOWED THE KEYWORD ARRAY.
This KENO-VI message is from subroutine SGGM_ARRAY. The data following the keyword
ARRAY are misspelled or incomplete. See :numref:`sec-module.keno.geom.array_data` for assistance in
determining the correct method for inputting array data.
KMSG063
******* WARNING ******* K?-063 FOLLOWS:
|br| NUCLIDE ___ ___
|br| HAS NO GAMMA PRODUCTION DATA.
|br| ******* WARNING *******
This message from subroutine MIXMIX indicates that somehow KENO has been
told to run a coupled neutron-gamma problem, and the indicated nuclide
has no neutron to gamma transfer data. This means this nuclide cannot
produce any gammas. This message should never occur in KENO, as it
should have ignored all gamma data from a coupled library.
KMSG064
******* WARNING ******* K?-064 FOLLOWS:
|br| THE ANGULAR SCATTERING DISTRIBUTION FOR MIXTURE ___ HAS BAD MOMENTS FOR THE TRANSFER FROM GROUP ___ TO GROUP ___
|br| ___ MOMENTS WERE ACCEPTED. THE P0 COEFFICIENT IS ___
This message from subroutine BADMOM is printed to inform the user that
the cross sections were altered by the code because the moments from the
cross section data were incorrect for the group transfer shown. The
P\ :sub:`0` coefficient was larger than the cross section message cutoff
parameter ``EPS``, but the relative change in the moments was smaller
than ``EPS``.
KMSG065
******* WARNING ******* K?-065 FOLLOWS:
|br| AN AMPX WORKING LIBRARY WAS SPECIFIED ON UNIT ___ BUT NO MIXING DATA WAS READ.
|br| MIXED CROSS SECTIONS FROM UNIT ___ WILL BE USED.
This message from subroutine ICEMIX occurs if the parameter data
specified ``LIB``\ =___\_ but no cross section mixing data block was
entered. The cross section mixing data block begins with ``READ MIXT``.
See :numref:`sec-module.keno.parameters` for parameter data and :numref:`sec-module.keno.mixing_table` for mixing table
information.
KMSG066
******* WARNING ******* K?-066 FOLLOWS:
|br| ___ MIXTURES WERE REQUESTED IN THE GEOMETRY, BUT ONLY ___ MIXTURES ARE ON THE MIXED CROSS SECTION LIBRARY.
This message from subroutine ICEMIX indicates that more mixtures were
requested in the geometry region data than were available on the mixed
cross section library. See :numref:`sec-module.keno.parameters` for the specification of the
unit number of the mixed cross section library (**XSC**\ =),
:numref:`sec-module.keno.mixing_table` for the specification of the mixing table, and
:numref:`sec-module.keno.geom` to determine the mixtures used in the geometry region
data.
KMSG067
******* ERROR ******* K?-067 FOLLOWS:
|br| THE ADJOINT INPUT PARAMETER WAS _ BUT THE ADJOINT INDICATOR FROM THE MIXTURE CROSS SECTION LIBRARY WAS _. KENO WILL NOT EXECUTE.
This message from subroutine ICEMIX occurs if the adjoint input
parameter ``ADJ``\ = specified a forward calculation and the
cross sections were adjointed, or the adjoint input parameter specified
an adjoint calculation and the cross sections were not adjointed. T
indicates true, F indicates false.
KMSG069
___ IS AN INVALID GEOMETRY TYPE INDEX
This KENO V.a message from K5GM_HOLEXT
is a companion message to KMSG091, and will follow it.
KMSG070
******* ERROR ******* K?-070 FOLLOWS:
|br| ERROR IN SUBROUTINE WRTRST. NDX=___
This message from subroutines K5_WRTRST or K6_WRTRST
occurs only if the type of data to
be written on the restart (``WSTRT``) unit is undefined (i.e., ``NDX`` is
greater than 15). ``NDX`` is the index in the LPOINT array as described in
messages KMSG046 and KMSG058. This error is usually caused by code
errors that were introduced when changes were made to the code. A STOP
133 is executed when this message is printed.
KMSG071
THIS INTERSECTION MAY BE DUE TO ROUNDOFF IN CALCULATING THE ARRAY BOUNDARY DIMENSIONS.
|br| FOR ROUNDOFF ERRORS, INCREASE THE DIMENSIONS OF ALL SUBSEQUENT REGIONS SHARING THAT BOUNDARY.
|br| +X -X +Y -Y +Z -Z
|br| ARRAY ___ ___ ___ ___ ___ ___
This KENO V.a message from K5GM_JOMCHK is a companion message to KMSG092 and will follow it.
KMSG072
CUBOID ___ ___ ___ ___ ___ ___
This KENO V.a message from K5GM_JOMCHK is a companion message to KMSG092 and will follow it.
KMSG073
******* ERROR ******* K?-073 FOLLOWS:
|br| ___ MIXTURES WERE REQUESTED IN THE GEOMETRY DATA, BUT ONLY ___ OF THESE WERE FOUND IN THE MIXED CROSS SECTIONS.
This message from subroutines K5_MASTER or K6_MASTER
indicates a mixture number used in the KENO model was not
included in the cross sections defined in the READ MIXT block.
KMSG074
******* ERROR ******* K6-074 FOLLOWS:
|br| INVALID GEOMETRY TYPE IN VOLCUB. IGEO =___
This KENO-VI message from subroutine SGGM_VOLCUB is probably the result of a code error.
KMSG075
******* ERROR ******* THE PROBLEM WILL NOT RUN
This KENO V.a message from subroutines K5GM_HOLE or K5GM_HOLCHK
is a companion message to KMSG188.
KMSG076
******* ERROR ******* K5-076 FOLLOWS:
|br| POSIT ERROR --- ILLEGAL GEOMETRY TYPE
|br| X =___ Y =___ Z =___ K1 =___ K2 =___ K =___ IGEO =___
This KENO V.a message from subroutine K5GM_POSIT indicates
that the history at X,Y,Z in region K in the unit
with regions K1 to K2 has a geometry type IGEO which is not valid
geometry type. This is caused by a code error.
KMSG077
******* INFORMATION WARNING ******* K5-077 FOLLOWS:
|br| POSIT WARNING --- POINT NOT IN GEOMETRY
|br| X =___ Y =___ Z =___ K1 =___ K2 =___
This KENO V.a message from subroutine K5GM_POSIT indicates that
point X,Y,Z is not within any region between K1 and K2. This is
usually caused from specifying start data that tries to start
histories outside the geometry.
KMSG078
******* ERROR ******* K5-078 FOLLOWS:
|br| INVALID GEOMETRY ENCOUNTERED FOR THE LAST GEOMETRY REGION. IGEO=___
This KENO V.a message from subroutine K5GM_CORSIZ says the geometry
type of the last geometry region of the
global unit is invalid. This indicates a code bug.
KMSG079
******* ERROR ******* K6-079 FOLLOWS:
|br| UNABLE TO DETERMINE IF QUADRATIC IS CONVEX OR CONCAVE. CHECK FUNCTION VEXCAV CALLED FROM QUAD.
This self-explanatory KENO-VI message is from function SGGM_VEXCAV. It
indicates a problem with an arbitrary quadratic. KENO-VI is missing the
data indicating whether a surface is convex or concave and so was unable
to determine this for the current arbitrary quadratic.
KMSG080
******* ERROR ******* K5-080 FOLLOWS:
|br| UNRECOGNIZED GEOMETRY TYPE. IGEOM =___ IN SUBROUTINE PRTJOM
This KENO V.a message from subroutine K5GM_PRTJOM indicates a code bug.
This error should be reported to scalehelp@ornl.gov.
KMSG081
******* ERROR ******* K5-081 FOLLOWS:
|br| ERROR IN HEMISPHERE DESIGNATION. ISET =___ IN SUBROUTINE PRTJOM
This KENO V.a message from subroutine K5GM_PRTJOM indicates a code bug.
This error should be reported to scalehelp@ornl.gov.
KMSG082
******* ERROR ******* K5-082 FOLLOWS:
|br| ERROR IN PRTJOM WITH HEMICYLINDER DESIGNATION. NHCYL =___
This KENO V.a message from subroutine K5GM_PRTJOM indicates a code bug.
This error should be reported to scalehelp@ornl.gov.
KMSG083
******* ERROR ******* K5-083 FOLLOWS:
|br| FOR ARRAY ___, THE _ DIMENSIONS OF UNIT ___ AT (___ ___ ___) DO NOT MATCH THOSE OF UNIT ___ AT (___ ___ ___)
|br| FOR UNIT ___ +_ =___ AND -_ =___ WHILE FOR UNIT ___ +_ =___ AND -_ =___
This KENO V.a message is from subroutine K5GM_ARASIZ. The common faces of adjacent
units must be the same size and shape. This message occurs whenever this
requirement is not met. One or more of the dimensions of the units
specified in the message may be incorrect, or the array definition data
may be incorrect. Carefully check the input data relating to the
geometry region data and the array definition data as described in
:numref:`sec-module.keno.geom` and :numref:`sec-module.keno.geom.array_data`.
KMSG084
******* ERROR ******* K?-084 FOLLOWS:
|br| UNIT ___, IN UNIT ORIENTATION ARRAY NUMBER ___ IS UNDEFINED IN THE INPUT DATA.
This message from subroutines K5GM_ARASIZ or SGGM_ARASIZ
occurs when the array description
data block specifies a unit that was not defined in the geometry region
data. Verify the array definition data and the geometry region data as
described in :numref:`sec-module.keno.geom` and :numref:`sec-module.keno.geom.array_data`.
KMSG085
******* ERROR ******* K?-085 FOLLOWS:
|br| UNIT ___ AT POSITION X=___ Y=___ Z=___ IN UNIT ORIENTATION ARRAY NUMBER ___
|br| IS INVALID BECAUSE IT IS LESS THAN ZERO OR LARGER THAN THE LARGEST UNIT NUMBER IN THE INPUT DATA.
This message from subroutines K5GM_ARASIZ or SGGM_ARASIZ
occurs if the unit number named in
the message is less than or equal to zero or greater than NBOX (the
number of different units). The position of the offending unit is also
given. This error usually results from leaving some positions undefined
in the unit orientation array or from erroneous data in the unit
orientation data. (This includes extra data, mistyped data and omitted
data.) See :numref:`sec-module.keno.geom.array_data` for additional information.
KMSG086
******* ERROR ******* K6-086 FOLLOWS:
|br| GEOMETRY WORD INDEX OUT OF RANGE. IGEOM =___ IN SUBROUTINE PRTJOM
This KENO-VI message from subroutine K6_PRTJOM is self-explanatory. The printed
value of IGEOM must be greater than zero and less than 24 in KENO V.a or
less than 27 in KENO-VI to be valid. If the geometry words (see
:numref:`sec-module.keno.geom`) are correct, this message is due to a code error that has
been introduced when changes were made to the code.
KMSG087
******* ERROR ******* K6-087 FOLLOWS:
|br| INSUFFICIENT DATA FOLLOWED THE KEYWORD MEDIA.
This KENO-VI message from subroutine K6_MEDIA. Either the material, bias
ID, or sector data were not included on the media card, or non-integer
data were inadvertently entered. See :numref:`sec-module.keno.geom` for additional
information on the type of data required on a MEDIA card.
KMSG088
******* ERROR ******* K6-088 FOLLOWS:
|br| SECTOR DATA WAS NOT FOUND FOR MEDIA ___
This KENO-VI message from subroutine K6_MEDIA. Either the material, bias
ID, or sector data were not included on media card \____\_ or
non-integer data were inadvertently entered. See :numref:`sec-module.keno.geom` for
additional information on the type of data required on a MEDIA card.
KMSG089
******* ERROR ******* K6-089 FOLLOWS:
|br| VOLUME HAS BEEN MULTIPLY DEFINED.
|br| GENERATION = ___ NEUTRON = ___ UNIT =___
|br| PARTICLE AT POSITION X=___ Y=___ Z=___
|br| IS LOCATED INSIDE THE FOLLOWING REGIONS IN THE UNIT:
This KENO-VI message from subroutine K6_PRTPOS out of either subroutine
SGGM_TRACE or K6_TRACK. It is caused by incorrectly specifying the region
definition vector in the media cards of a unit. It may be caused by a
volume defined as part of more than one media record or incorrectly
specifying regions that share a common boundary so the boundary between
regions is contained in more than one region. See :numref:`sec-module.keno.geom` for more
information concerning vector definition arrays on MEDIA records.
KMSG090
******* ERROR ******* K?-090 FOLLOWS:
|br| THE PROBLEM HAS TERMINATED BECAUSE THE PARTICLE HAS ENTERED AN INFINITE LOOP.
|br| THIS IS POSSIBLY DUE TO A PROBLEM WITH THE CODE.
|br| UNIT ___ ARRAY ___ HOLE ___
This self-explanatory message indicates that a history has become
totally lost, and this message prevents the code from wasting time in an
infinite loop. This message should never occur.
This error should be reported to scalehelp@ornl.gov.
KMSG091
******* ERROR ******* K5-091 FOLLOWS:
|br| UNIT ___ CONTAINS THE FOLLOWING GEOMETRY INCONSISTENCIES:
This message from subroutines K5GM_JOMCHK, K5GM_HOLEXT or K5GM_HOLHOL
indicates that
one or more intersecting geometry regions were encountered in unit____.
KMSG092 is the companion message from subroutine JOMCHK and specifies
the regions that intersect. KMSG069 is the companion message from
subroutine HOLEXT. KMSG163 and KMSG179 are the companion messages from
subroutine HOLHOL. The geometry region data should be corrected and the
problem resubmitted. :numref:`sec-module.keno.geom` may provide assistance in correctly
specifying the data.
KMSG092
******* ERROR ******* K5-092 FOLLOWS:
|br| REGION NUMBER ___ INTERSECTS REGION NUMBER ___.
This KENO V.a message from subroutine K5GM_JOMCHK is a companion message to
K5-91 and K5-94. It specifies the intersecting regions. The user must
determine which region is incorrectly specified or if the data are out
of order. KENO V.a REQUIRES THAT EACH SUCCESSIVE GEOMETRY REGION MUST
COMPLETELY ENCLOSE THE PREVIOUS REGION. THIS DOES ALLOW COMMON FACES AND
TANGENCY.
KMSG093
******* ERROR ******* K5-093 FOLLOWS:
|br| INVALID GEOMETRY TYPE. IGEO=___
This KENO V.a message is from subroutine K5GM_JOMCHK. IGEO must be greater than zero
and less than 20. If it does not fall in this range, a code error is the
probable cause. K5GM_KENOG or K5GM_READGM are the subroutines likely to have the
code error. Verify that all the geometry words (``fgeom``, :numref:`sec-module.keno.geom`)
are correct.
KMSG094
******* ERROR ******* K5-094 FOLLOWS:
|br| THE REFLECTOR DIMENSIONS ARE INCONSISTENT.
This KENO V.a message is from subroutine K5GM_JOMCHK. It is a companion to
message K?-095 and is printed whenever one or more intersecting geometry
regions are encountered in the external reflector.
KMSG095
******* ERROR ******* K5-095 FOLLOWS:
|br| REGION NUMBER ___ IN UNIT NUMBER ___ CONTAINS AN ERROR IN THE DIMENSIONS.
This KENO V.a message from subroutine K5GM_VOLUME indicates an error in the geometry
input data such that the negative dimension specification for a cube or
cuboid is larger than the positive dimension specification (i.e., the
-X dimension is greater than the +X dimension, or the -Y dimension is
greater than the +Y dimension or the -Z dimension is greater than the +Z
dimension). This message is also printed if the magnitude of the chord
for a hemicylinder or hemisphere is larger than the radius. See
:numref:`sec-module.keno.geom` for assistance in specifying the geometry correctly.
KMSG096
******* ERROR ******* K5-096 FOLLOWS:
|br| THE VOLUME DEFINED BY REGION ___ IN UNIT ___ IS NEGATIVE.
This KENO V.a message from subroutine K5GM_VOLUME is printed whenever a negative
volume is calculated. This can be caused by the positive dimension being
smaller than the negative dimension on a face of a geometry region. It
can also be caused by having intersecting regions, or it may be the
result of round-off when the volumes are calculated. Either the geometry
regions are incorrectly specified, the data are out of order, or the
dimensions are so tight fitting that round-off causes the net volume of
the region to be negative. If the error is caused by round-off, adjust
the appropriate dimensions slightly. See :numref:`sec-module.keno.geom`.
KMSG097
******* ERROR ******* K5-097 FOLLOWS:
|br| THE VOLUME FOR UNIT ___ IS NEGATIVE.
This KENO V.a message is from subroutine K5GM_VOLUME.
A negative volume for a unit can
be caused by having intersecting regions within the unit, or by having a
unit consisting of one region and having a positive dimension smaller
than the negative dimension on one or more faces. Message K5-95 or K5-96
may accompany this message. See :numref:`sec-module.keno.geom` for assistance in
specifying the geometry data correctly.
KMSG098
******* ERROR ******* K6-098 FOLLOWS:
|br| PROBLEM IN UNIT ___
|br| THE ARRAY TYPE SPECIFIED IN THIS UNIT IS UNDEFINED. SPECIFY IF THE ARRAY TYPE IS CUBOID, HEXPRISM, OR DODECAHEDRON.
This KENO-VI message is from subroutine K6_ARASIZ. The array type specified in this
unit in an unknown type. See :numref:`sec-module.keno.geom.array_data` for how to enter array definitions.
KMSG099
******* ERROR ******* K?-099 FOLLOWS:
|br| PROBLEM WITH UNIT ___
|br| THE OUTERMOST GEOMETRY REGION OF A UNIT UTILIZED IN THE UNIT ORIENTATION DESCRIPTION OF THE ARRAY DATA MUST BE A ___
This message is from subroutines K5_ARASIZ or K6_ARASIZ.
It can occur when the boundary
region of a unit in an array is not consistent with the array type. The
unit specified should be corrected so that the outer boundary is of the
type required, or it should be replaced in the unit orientation data
with a unit that has the correct outer boundary.
KMSG100
******* ERROR ******* K?-100 FOLLOWS:
|br| THIS PROBLEM WILL NOT BE RUN BECAUSE ERRORS WERE ENCOUNTERED IN THE INPUT DATA.
This message is from subroutines K5_MASTER or K6_MASTER, and indicates that other error
messages were printed in the problem output. These messages should be
located and the data corrected accordingly. Execution is terminated
with error code 129.
KMSG101
******* ERROR ******* K?-101 FOLLOWS:
|br| NO FISSILE MATERIAL WAS FOUND IN SUBROUTINE START
This message is from subroutine START. It indicates that none of the
mixtures used in this problem has an associated fission spectrum. Either
the geometry data did not specify a fissionable mixture number, the
mixing table is incorrect, the wrong mixed cross section data set was
mounted, or the mixed cross section data set was incorrectly or
incompletely made.
KMSG102
******* ERROR ******* K?-102 FOLLOWS:
|br| THE START DATA SPECIFIES THAT NEUTRONS CAN BE STARTED IN THE REFLECTOR.
HOWEVER, NEUTRONS WILL NOT BE STARTED BECAUSE THE OUTER REGION OF THE REFLECTOR IS NOT A CUBE OR CUBOID.
NEUTRONS CAN BE STARTED FOR THE EXISTING GEOMETRY IF XSM,XSP,YSM,YSP,ZSM AND ZSP ARE ENTERED AS START DATA.
|br| XSM,XSP,YSM,YSP,ZSM AND ZSP MUST FIT WITHIN THE OUTER REGION OF THE REFLECTOR.
This message is from subroutine START. Start type 0 allows starting
points throughout noncuboidal regions. If a start type other than 0 or 6
is desired and the outermost region of the reflector is not a cube or
cuboid, then data must be entered to specify an imaginary cube or cuboid
within this outer region. See :numref:`sec-module.keno.start_data` for assistance in specifying
this data.
KMSG103
******* ERROR ******* K?-103 FOLLOWS:
|br| START TYPE ___ IS OUT OF RANGE.
This message from subroutines K5_START or K6_START
indicates that the start type was
less than zero or greater than 9. The start type is defined by entering
the keyword ``NST=`` followed by the desired start type in the start
data. The available starting options are given in :numref:`tab8-1-21`,
:numref:`sec-module.keno.start_data`.
KMSG104
******* ERROR ******* K?-104 FOLLOWS:
|br| A POSIT ERROR INDICATES THAT THE POINT X=___ Y=___ Z=___ DOES NOT OCCUR WITHIN UNIT ___
|br| IF XSM, XSP, YSM, YSP, ZSM, ZSP WERE ENTERED IN THE START DATA, VERIFY THAT THEY FIT WITHIN THE OVERALL COORDINATES OF THE SYSTEM.
|br| THE OVERALL COORDINATES MAY NOT BE PRINTED FOR A BARE ARRAY.
If ``XSM``, ``XSP``, ``YSM``, ``YSP``, ``ZSM``, ``ZSP`` were entered in the
start data, they should fit within the overall coordinates of the system.
The overall coordinates may not be printed for a bare array. This message
from subroutines K5_START or K6_START may result from precision difficulties.
It is allowed to occur a maximum of five times before being considered fatal.
A code error may be the cause of this message if it becomes fatal.
KMSG105
K?-105
|br| ******* WARNING, ONLY ___ INDEPENDENT STARTING POSITIONS WERE GENERATED. *******
This message is from subroutines K5_START or K6_START.
KENO must have *npb* (``NPG=``,
see parameter data, :numref:`sec-module.keno.parameters`) starting positions. This message is
to inform the user that fewer than *npb* starting positions were
generated. The remaining starting positions are randomly selected from
those that were generated, thus giving duplicate starting positions. If
the number of independent starting positions is nearly *npb*, the
starting distribution is probably acceptable. If it is much smaller than
*npb*, a different start type should be used to give a better starting
distribution (see :numref:`sec-module.keno.start_data`). The amount of time allowed to generate
the starting positions is controlled by parameter ``TBA=`` (see
:numref:`sec-module.keno.parameters`). If the start data are appropriate, it may be necessary
to increase the value of ``TBA`` to ensure generating *npb* starting
positions.
KMSG106
******* ERROR ******* K6-106 FOLLOWS:
|br| POSIT ERROR --- UNIT ___ HAS MULTIPLY DEFINED SPACE AT
|br| X = ___ Y = ___ Z = ___
|br| SECTOR INSIDE
This KENO-VI message from subroutine SGGM_POSIT is usually the result of an
incorrectly specified starting point for the initial source distribution
when ``NST=``\ 3, 4 or 6 is specified in the start data. The starting
point may not be consistent with the unit's position in the global
array. The message can also be caused by improperly specifying media
records. ``MEDIA`` records in the specified units should be checked for
multiply defined volumes. X, Y, Z is the location of the neutron, and
SECTOR INSIDE is the sectors which contain that point. See :numref:`sec-module.keno.geom`
for correct geometry words.
KMSG107
******* ERROR ******* K7-107 FOLLOWS:
|br| POSIT ERROR --- UNIT ___ HAS AN UNDEFINED SPACE AT
|br| X = ___ Y = ___ Z = ___
|br| SECTOR INSIDE
This KENO-VI message from subroutine SGGM_POSIT may result from not specifying all
volumes in the unit using media records. It could also occur from start
data if a particle is attempting to start outside the global unit or in
an undefined space. Geometry should be checked for the specified unit.
KMSG108
******* ERROR ******* K?-108 FOLLOWS:
|br| POSITION (___,___,___) IS NOT VALID FOR THE POSITION OF THE SPIKE FOR START TYPE 2.
This message from subroutine START2 indicates that ``NXS``, ``NYS`` or
``NZS`` was entered as zero. See :numref:`sec-module.keno.start_data` for the correct start
data specification.
KMSG109
******* ERROR ******* K?-109 FOLLOWS:
|br| INVALID GEOMETRY TYPE IN START. IGEO =___
This message from subroutines K5_STRTSU or K6_STRTSU is likely the result of a code
error. This error should be reported to scalehelp@ornl.gov.
KMSG110
******* ERROR ******* K?-110 FOLLOWS:
|br| THE PROBLEM WILL NOT BE EXECUTED BECAUSE NO FISSILE MATERIAL WAS FOUND.
This message from subroutines K5_VOLFIS or K6_VOLFIS occurs when the volume of fissile
material is found to be zero. It should be verified that the fissile
material was correctly specified in the geometry data, and the volume of
the fissile material in the printout should be nonzero. The mixing table
should be verified as being correct or that the correct Monte Carlo
mixed cross section data set has been used if a mixing table is not
used. If the fissile region is small compared to the rest of the problem
and the region volumes are calculated using TRACE or RANDOM types with
default number of traces or particles, the fissile region volumes may be
incorrect (even zero). If the volumes calculate to be zero, this message
may be issued. In this case, the volume calculation (see :numref:`8-1-2-13`)
should be corrected. A STOP 131 is executed when this message is
printed.
KMSG111
\******\* WARNING \******\* K?-111 FOLLOWS:
|br| RESTART DATA IS NOT AVAILABLE FOR RESTARTING WITH GENERATION ___ AS SPECIFIED IN THE INPUT DATA. \***\*
|br| \***\* HOWEVER, AVAILABLE RESTART DATA HAS ALLOWED RESTARTING WITH GENERATION ___
This message from subroutine RDCALC indicates that *nbas* (``BEG=`` in
:numref:`sec-module.keno.parameters`) was not consistent with the set of restart data that was
to be used. A set of restart data is written every *nrstrt* (``RES=``
in :numref:`sec-module.keno.parameters`). The value of *nbas* should be 1 greater than one of
these generations.
KMSG112
\******\* ERROR \******\* K?-112 FOLLOWS:
|br| ERROR IN RESTART. PARAMETER DATA AND RESTART DATA DO NOT AGREE
|br| NUMBER PER GENERATION FROM RESTART, NPBT=___NUMBER PER GENERATION FROM INPUT DATA, NPB=___
|br| NUMBER OF ENERGY GROUPS FROM RESTART, NGPT=___ NUMBER OF ENERGY GROUPS FROM INPUT DATA, NGP=___
This message is from subroutine RDCALC. A restarted problem MUST use the
same number per generation and the same number of energy groups as the
parent problem that wrote the restart data. It should be verified that
the correct data set is mounted on unit *rstrt*. (``RST=`` in
:numref:`sec-module.keno.parameters`). This message can also be caused by a code error.
KMSG113
******* ERROR ******* K?-113 FOLLOWS:
|br| ERROR IN RESTART. PARAMETER DATA AND RESTART DATA DO NOT AGREE.
|br| FISSION DENSITIES, FLUXES, OR REGION DEPENDENT FISSIONS AND ABSORPTIONS WERE REQUESTED, BUT THE GEOMETRY DATA IS INCONSISTENT.
|br| NUMBER OF GEOMETRY REGIONS FROM RESTART, KMAXT=___ NUMBER OF GEOMETRY REGIONS FROM INPUT DATA, KMAX=___
This message is from subroutine RDCALC. It should be verified that the
correct data set is mounted on unit *rstrt* (``RST``\ = in
:numref:`sec-module.keno.parameters`). A code error can also cause this message.
KMSG114
******* ERROR ******* K?-114 FOLLOWS:
|br| PARAMETER DATA SPECIFIED FLUXES BUT THE RESTART DATA DID NOT INCLUDE FLUXES.
This message is from subroutine RDCALC. The restarted problem can turn
off fluxes if the parent case that wrote the restart data set calculated
fluxes. However, if the parent case did not calculate fluxes, the
restarted problem cannot calculate fluxes either. If the correct restart
data set was mounted on *rstrt* (``RST=`` in :numref:`sec-module.keno.parameters`), the
parameter data ``FLX=YES`` must be removed from the input data or
``FLX=NO`` must be entered later in the parameter data of the
restarted problem.
KMSG115
******* ERROR ******* K?-115 FOLLOWS:
|br| PARAMETER DATA SPECIFIED REGION DEPENDENT FISSIONS AND ABSORPTIONS,
BUT THEY WERE NOT INCLUDED ON RESTART
This message is from subroutine RDCALC. The restarted problem specified
``FAR=YES`` in the parameter data block but the parent case that wrote
the restart data set did not calculate region-dependent fissions and
absorptions. The restarted problem can turn off region-dependent data if
the parent case calculated them, but cannot turn them on if they were
not calculated by the parent case. It should be verified that the
correct restart data set is mounted on *rstrt* (``RST``\ = in
:numref:`sec-module.keno.parameters`). ``FAR``\ =YES should be removed from the parameter data
of the restarted problem, or ``FAR``\ =NO should be added later in the
parameter data. :numref:`sec-module.keno.parameters` illustrates methods of changing the
parameter input data.
KMSG116
******* ERROR ******* K?-116 FOLLOWS:
|br| EXECUTION IS TERMINATED.
This message from subroutine RDCALC is a companion to messages K?-112
through K?-115. A STOP 121 is executed when this message is printed.
KMSG117
******* ERROR ******* K?-117 FOLLOWS:
|br| THE CALCULATION WAS TERMINATED BECAUSE ERRORS WERE ENCOUNTERED IN THE START DATA.
This message is from subroutines K5_GUIDE or K6_GUIDE.
It will be accompanied by one or more of messages K?-101
through K?-104 or K?-106 through K?-110. A STOP 130 is executed when this message is printed.
KMSG118
******* ERROR ******* K?-118 FOLLOWS:
|br| EXECUTION TERMINATED. RAKBAR HAS BECOME ZERO OR NEGATIVE.
This message is from subroutines K5_GUIDE or K6_GUIDE.
If this message appears without other error messages,
a code error is the probable cause. For such a case,
this error should be reported to scalehelp@ornl.gov.
KMSG119
k?-119 JOB PULLED GENERATION= ___ NEUTRON = ___
This message from subroutine REPORTIT indicates that the problem is
looping, or the time allotted for each generation, *tbtch* (``TBA=``
in :numref:`sec-module.keno.parameters`) is too small. If *tbtch* (``TBA=``) is increased
significantly and the message occurs again for the same generation and
the same neutron, it is due to a code error. Without a functional
system-dependent routine (PULL) to interrupt execution, the problem will
loop indefinitely, and this message will not be printed.
KMSG121
******* ERROR ******* K?-121 FOLLOWS:
|br| EXECUTION TERMINATED DUE TO INSUFFICIENT TIME IN THE JOB STEP.
|br| ___ SECONDS ARE NEEDED PER GENERATION, BUT ONLY ___ REMAIN IN THE JOB STEP.
This message is from subroutines K5_GUIDE or K6_GUIDE. If more histories are desired,
the job control language should be changed to allow adequate time and
resubmit the problem. This message is inaccessible on computers lacking
job control language to specify the maximum execution time.
KMSG122
******* ERROR ******* K?-122 FOLLOWS:
|br| EXECUTION TERMINATED DUE TO EXCEEDING THE TIME SPECIFIED FOR THE PROBLEM.
This message is from subroutines K5_GUIDE or K6_GUIDE. If more histories are desired,
*tmax* (``TME``\ = in :numref:`sec-module.keno.parameters`) should be increased to allow
computation of the desired number of histories.
KMSG123
K?-123 EXECUTION TERMINATED DUE TO COMPLETION OF THE SPECIFIED NUMBER OF GENERATIONS.
This message from subroutines K5_GUIDE or K6_GUIDE states that the requested number of
histories has been completed. If more histories are desired, the number
of generations (``GEN=`` in :numref:`sec-module.keno.parameters`) should be increased.
KMSG124
******* ERROR ******* K?-124 FOLLOWS:
|br| THE OPTION TO USE EXTRA 1-DS WAS SPECIFIED, BUT ID NO.___ WAS NOT FOUND IN THE EXTRA 1-D ARRAY.
This self-explanatory message is from function INDX. If extra 1-Ds are
specified in the parameter data (``X1D=``, :numref:`sec-module.keno.parameters`), extra 1-D
IDs must be entered as data. See :numref:`sec-module.keno.xs1d`. A STOP 107 is executed
when this message is printed.
KMSG126
******* ERROR ******* K5-126 FOLLOWS:
|br| CROSS ERROR ___ ___ ___ ___ ___ ___ ___ ___
This KENO V.a message from subroutine K5GM_CROS indicates a code error. The printed
data, left to right, are as follows: IGEO,K,X,Y,Z,X1,Y1,Z1. IGEO is the
geometry type, K is the region number, X,Y,Z is the current position,
and X1,Y1,Z1 is the end point of the path. A STOP 103 is executed when
this message is printed.
KMSG127
******* ERROR ******* K5-127 FOLLOWS:
|br| NHCYL=___
This KENO V.a message from subroutines K5GM_CROS or K5GM_KENOG indicates invalid hemicylinder
information as the result of a code error. A STOP 104 is executed when
this message is printed.
KMSG128
******* ERROR ******* K?-128 FOLLOWS:
|br| NEUTRON BANK IS FULL. SPLITTING NOT ALLOWED
This message from subroutine TALLYONGRID indicates that the neutron bank is
too small to allow additional splitting. This can occur if the bank
size, *nbank* (``NBK=`` in :numref:`sec-module.keno.parameters` is too small, if the biasing
or weighting data are incorrect (:numref:`sec-module.keno.biasing`), or if the biasing data
are incorrectly utilized in the geometry description (:numref:`sec-module.keno.geom`).
KMSG129
******* ERROR ******* K?-129 FOLLOWS:
|br| ****** ERROR IN SUBROUTINE ALBEDO ****** FACE NUMBER ___ USES ___ ALBEDO NUMBER=___
|br| INCIDENT XSEC ENERGY GROUP=___ INCIDENT ALBEDO ENERGY GROUP=___ INCIDENT ANGLE INDEX=___
|br| RANDOM NUMBER=___
This message from subroutines K5GM_ALBEDO or SGGM_ALBEDO indicates that a code error was
encountered when determining the output energy group during the albedo
treatment.
KMSG130
******* ERROR ******* K?-130 FOLLOWS:
|br| PROBLEM IN SUBROUTINE ALBEDO: FACE NUMBER ___ USES ___ ALBEDO NUMBER=___
|br| RETURNING XSEC ENERGY GROUP=___ INCIDENT ALBEDO ENERGY GROUP=___ INCIDENT ANGLE INDEX=___
|br| RETURNING ALBEDO ENERGY GROUP=___ RANDOM NUMBER=___
This message from subroutines K5GM_ALBEDO or SGGM_ALBEDO indicates that a code error was
encountered while computing the returning angle in the albedo treatment.
KMSG131
******* ERROR ******* K?-131 FOLLOWS:
|br| NO FISSIONS WERE GENERATED
This message from subroutine NSTART indicates that none of the histories
in the generation encountered a fissile material, so no fission points were
generated.
KMSG132
K?-132 FOLLOWS:
|br| ONLY ___ INDEPENDENT FISSION POINTS WERE GENERATED FOR GENERATION ___
This message from subroutine NSTART indicates that fewer than *npb*
(``NPG``\ = in :numref:`sec-module.keno.parameters`) fission points were generated during the
previous generation. Because *npb* fission points are required by the
code, the remaining fission points are randomly selected from those that
were generated, thus using duplicate fission points. If the k-effective
of the system is significantly less than 1.0, several of these messages
should be expected in the first few generations. The code attempts to
set RAKBAR so the message can be expected to occur about once every 100
generations. The message may occur more frequently in a correctly
modeled problem. However, if the number of fission points is
considerably less than *npb* for most of the generations, the answer can
be affected.
KMSG133
******* WARNING ******* K?-133 FOLLOWS:
|br| THE CALCULATION CONCLUDED WITHOUT PRODUCING RESULTS BECAUSE NO ACTIVE GENERATIONS WERE RUN.
|br| THE NUMBER OF GENERATIONS RUN WAS NOT GREATER THAN THE NUMBER OF GENERATIONS SKIPPED.
This message from subroutine KEDIT occurs if the number of generations
completed is less than *nskip*\ +1 (``NSK=``, :numref:`sec-module.keno.parameters`). In this
instance, the summaries for the problem cannot be printed.
KMSG136
******* ERROR ******* K5-136 FOLLOWS:
|br| GEOMETRY TYPE - IGEO = ___ - OUT OF RANGE IN ___
This message from subroutines K5GM_SRMAX, K5GM_CRMIN or K5GM_CRMAX
occurs if the geometry indicator is
invalid as the result of a code error. A STOP 127 is executed in
conjunction with this message and a traceback may be printed from
subroutine STOP.
KMSG137
******* ERROR ******* K?-137 FOLLOWS:
|br| THERE ARE MISSING CROSS SECTIONS. CHECK THE OUTPUT FOR OTHER ERROR MESSAGES.
This message from subroutine FILLSG says that not all the cross sections
requested have been found. There should be other previous messages
giving more detail on what cross sections are missing.
KMSG138
******* WARNING ******* K?-138 FOLLOWS:
|br| A WEIGHT OF 0.0 INDICATES THAT WEIGHTS WERE NOT READ OR GENERATED
FOR THE BIAS ID.
|br| WEIGHTS OF 0.0 WILL BE DEFAULTED TO 0.5 PRIOR TO EXECUTION.
This message is from subroutine PRTWTS. It is printed to alert the user that
weights were not entered, defaulted, or generated. This message may appear as
the result of a code error.
KMSG139
******* ERROR ******* K?-139 FOLLOWS:
|br| NO VALID MIXTURES WERE FOUND IN THE GEOMETRY DESCRIPTION.
This message from subroutine ICEMIX indicates that the geometry data did
not specify any valid mixtures. The geometry data (:numref:`sec-module.keno.geom`) should
be checked and any errors that are found should be corrected. This
message can also be triggered if the unit orientation data description
is not properly entered for geometry having more than one unit.
KMSG140
******* WARNING ******* THE UNIT THE HOLE IS IN IS NOT USED IN THE MODEL, SO THE
PROBLEM WILL NOT BE TERMINATED BECAUSE OF THIS ERROR.
This KENO V.a message from subroutine K5GM_HOLCHK is companion message to KMSG188.
KMSG141
******* ERROR ******* K?-141 FOLLOWS:
|br| DATA CANNOT BE CHANGED WHEN A PROBLEM IS RESTARTED AT A GENERATION
GREATER THAN ONE.
This message from subroutine DATAIN is printed if data other than
parameter data are entered for a problem being restarted at a generation
greater than 1. If data other than certain parameter data are to be
changed, the problem must be restarted with the first generation. The
error flag is set so the problem will not execute.
KMSG142
******* ERROR ******* K?-142 FOLLOWS:
|br| NO GEOMETRY DATA HAS BEEN SPECIFIED IN THE INPUT DATA.
This message from subroutine DATAIN indicates that a geometry data block
was not entered for the problem either as input data or from the restart
unit. The data needs to be corrected and the problem resubmitted.
KMSG143
******* ERROR ******* K?-143 FOLLOWS:
|br| UNIT ORIENTATION DATA IS REQUIRED IF MORE THAN ONE UNIT TYPE IS
SPECIFIED IN THE GEOMETRY DATA.
This self-explanatory message is from subroutine DATAIN. Enter an array
i or unit orientation data block as described in :numref:`sec-module.keno.geom.array_data` and
:numref:`sec-module.keno.geom_guide`.
KMSG144
******* WARNING ******* K?-144 FOLLOWS:
|br| DUE TO INCONSISTENCIES BETWEEN INPUT AND RESTART DATA,
|br| MATRIX INFORMATION BY UNIT TYPE WILL BE CALCULATED BUT NOT PRINTED.
|br| INPUT DATA SET MKU=NO, BUT DATA FROM THE RESTART UNIT SPECIFIED YES.
This self-explanatory warning message is from subroutine PARTBL. The
matrix information by unit type cannot be eliminated if it was
calculated by the original problem (parent case) that wrote the restart
data. However, printing it can be avoided. It should be verified that
the correct problem is being used for restarting the problem (the title
is printed at the bottom of the parameter tables). The specification of
the restart unit, ``RST``, in the third table of the output should also
be verified.
KMSG145
******* WARNING ******* K?-145 FOLLOWS:
|br| DUE TO INCONSISTENCIES BETWEEN INPUT AND RESTART DATA,
|br| MATRIX INFORMATION BY UNIT LOCATION WILL BE CALCULATED BUT NOT PRINTED.
|br| INPUT DATA SET MKP=NO, BUT DATA FROM THE RESTART UNIT SPECIFIED YES.
This self-explanatory warning message is from subroutine PARTBL. The
matrix information by unit location (also called array position or
position index) cannot be eliminated if it was calculated by the
original problem (parent case) that wrote the restart data. However,
printing it can be avoided. It should be verified that the correct
problem is being used for restarting the problem (the title is printed
at the bottom of the parameter tables). The specification of the restart
unit, RST, in the third table of the output should also be verified.
KMSG146
******* ERROR ******* K?-146 FOLLOWS:
|br| PARAMETER DATA SPECIFIED MATRIX INFORMATION BY UNIT TYPE BUT IT WAS NOT FOUND ON THE RESTART UNIT.
This message from subroutine RDCALC is printed if a restarted problem
requests matrix information by unit type when it was not requested and
calculated by the original problem (parent case) that wrote the restart
data. It should be verified that the correct restart data are being used
and that the restart unit (``RST``) is correctly specified. The request
for matrix information by unit type (``MKU=``, in the parameter data)
should be eliminated if it is not necessary. The problem must be
restarted with the first generation (``BEG=1``, in the parameter data)
if matrix information by unit type is required and was not calculated by
the parent case. A STOP 121 is executed in conjunction with this
message.
KMSG147
******* ERROR ******* K?-147 FOLLOWS:
|br| PARAMETER DATA SPECIFIED MATRIX INFORMATION BY UNIT LOCATION BUT IT WAS NOT FOUND ON THE RESTART UNIT.
This message from subroutine RDCALC is printed if a restarted problem
requests matrix information by unit location (also called array position
or position index) when it was not requested and calculated by the
original problem (parent case) that wrote the restart data. It should be
verified that the correct restart data are being used and that the
restart unit (``RST``) is correctly specified in the first table
following the parameter table. The request for matrix information by
unit location (``MKP=``, in the parameter data) should be eliminated
if it is not necessary. If matrix information by unit location is
required and it was not calculated by the parent case, the problem must
be restarted with the first generation (``BEG=1``, in the parameter
data). A STOP 121 is executed in conjunction with this message.
KMSG148
******* ERROR ******* K?-148 FOLLOWS:
|br| AN ERROR WAS ENCOUNTERED WHILE ATTEMPTING TO READ RESTART DATA FROM UNIT ___
NDX =___ NREC =___
This message from subroutines RDRST or RDRST_ERROR is printed if a problem is
encountered while reading restart data from the restart file. This may
be caused by the specified section of the restart file not being present
or the file section being the wrong length. The restart file is
corrupted. It should be verified that the problem ran to completion and
a restart file was generated. Problems in the input should be corrected,
and the problem should be run again. If the problem persists, contact
the SCALE helpline.
KMSG149
******* ERROR ******* K?-149 FOLLOWS:
|br| A CROSS SECTION LIBRARY WAS SPECIFIED FOR A RESTARTED PROBLEM, BUT
|br| MIXING TABLE DATA WAS NOT AVAILABLE. THE PROBLEM WILL NOT EXECUTE.
This message from subroutine READ_MIXED_XSECS means that ``LIB=`` was entered in
the parameter data block and a mixing table data block was not
available. A flag is set to terminate execution when the data reading
has been completed. If cross sections are to be used from the restart
unit (``RST=``), the ``LIB=`` or ``XSC=`` should be eliminated
from the parameter data. If new cross sections are to be mixed,
``LIB=`` must be specified in the parameter data. The IDs in the
mixing table must be available on the cross section library specified by
``LIB=`` . A problem can be restarted using a new mixed cross section
library by specifying ``XSC=`` in the parameter data.
KMSG150
******* ERROR ******* K5-150 FOLLOWS:
|br| TOO FEW ENTRIES WERE SUPPLIED IN THE REFLECTOR GEOMETRY DESCRIPTION.
This KENO V.a message from subroutine K5GM_KENOG indicates that too few data
entries were supplied for the geometry word ``REFLECTOR``. The mixture
ID, bias ID, one of the thickness/region specifications or the number of
regions to be generated was omitted or incorrectly specified. Each
``REFLECTOR`` entry requires (1) a mixture ID, (2) a bias ID, (3) N
entries for the thickness/region specifications, and (4) the number of
regions to be generated. The thickness/region can be obtained from the
Increment Thickness column of :numref:`tab8-1-20` for the material to be used
in the regions generated by the ``REFLECTOR`` specification. N is the
number of thickness/region specifications required by the geometry
shape: N=1 for spheres or hemispheres, N=3 for cylinders and
hemicylinders, and N=6 for cubes, cuboids, and cores. A flag is set to
terminate the problem when the input data reading is completed.
KMSG151
******* ERROR ******* K?-151 FOLLOWS:
|br| ___ IS AN INVALID ARRAY TYPE IN THE ARRAY DEFINITION DATA.
This message from subroutine ARAYIN indicates that a parameter name was
misspelled or the data were out of order. See :numref:`sec-module.keno.geom.array_data` for a list
of the array parameter names. A stop 137 is executed in conjunction with
this message.
KMSG152
******* ERROR ******* K?-152 FOLLOWS:
|br| IRET=___ A PREMATURE TERMINATION WAS ENCOUNTERED WHILE READING ARRAY DATA.
IRET=1 INDICATES AN END WAS FOUND. IRET=2 INDICATES AN END OF FILE.
This message from subroutine ARAYIN indicates that an array number was
specified without entering the corresponding UNIT ORIENTATION
DESCRIPTION. See :numref:`sec-module.keno.geom.array_data` and :numref:`sec-module.keno.geom_guide` for assistance.
KMSG153
******* ERROR ******* IF THE UNIT THIS HOLE IS IN IS USED IN THE MODEL, THE PROBLEM WILL NOT BE RUN.
This KENO V.a message from subroutine K5GM_READGM is a companion message to KMSG188.
KMSG154
******* ERROR ******* K?-154 FOLLOWS:
|br| ARRAY LEVEL ___ IS LARGER THAN ___, THE NUMBER OF ARRAYS.
|br| CHECK THE ARRAY AND GEOMETRY INPUT FOR AN ARRAY OR UNIT THAT IS RECURSIVELY NESTED.
This message from subroutines K5GM_SORTA or SGGM_SORTA indicates that the array data specified in
the problem are recursively nested. An example of this follows:
array 1 contains array 3
|br| array 2 contains array 1
|br| array 3 contains array 2
Thus, the definition of array 1 and array 3 are intertwined in a never-ending loop.
The array data (:numref:`sec-module.keno.geom.array_data`) should be corrected and the problem resubmitted.
If the input data did not specify recursive nesting, a code error has occurred.
A STOP 139 is executed in conjunction with this message.
KMSG155
******* ERROR ******* K?-155 FOLLOWS:
|br| THE NESTING FLAG OR NUMBER OF ARRAY LEVELS HAS BEEN DESTROYED BY A CODE ERROR.
|br| THE ORIGINAL NESTING FLAG WAS SET _ IT IS NOW SET _. THE ORIGINAL NESTING LEVEL WAS ___, IT IS NOW ___
This self-explanatory message is from subroutines K5GM_LODARA or SGGM_LOADARA. A STOP 140 is
executed in conjunction with this message.
KMSG156
******* ERROR ******* K?-156 FOLLOWS:
|br| MIXTURE ___ CONTAINS AT LEAST ONE ZERO VALUE FOR THE TOTAL CROSS SECTION.
This message is from subroutine XSEC1D. All the total cross sections
must be positive. Zero total cross sections can occur if all the
components of a mixture are mixed with a zero-number density. Correct
the mixing table for the specified mixture and resubmit the problem.
KMSG157
******* ERROR ******* K5-157 FOLLOWS:
|br| THE FIRST HOLE IN A UNIT MUST FOLLOW A VALID GEOMETRY REGION.
A STOP 141 accompanies this KENO V.a message from subroutine K5GM_READGM. If
holes are to be used in the geometry region data (:numref:`sec-module.keno.geom`), they
must follow the region in which they are to be placed. This message
indicates that HOLE was the first geometry description in a unit or was
placed inside an ARRAY description. Correct the geometry region data and
resubmit the problem.
KMSG158
******* ERROR ******* K5-158 FOLLOWS:
|br| THE NUMBER OF HOLES IS INCORRECT. IHOL=___ NUMHOL=___
This KENO V.a message is from subroutine K5GM_READGM. A code error is the probable cause of this error.
KMSG159
******* ERROR ******* K?-159 FOLLOWS:
|br| ARRAY NUMBER ___ SPECIFIED IN THE GEOMETRY REGION DATA WAS NOT ENTERED IN THE ARRAY DATA.
This message from subroutines K5GM_SORTA or K5GM_HOLE or
subroutine SGGM_SORTA occurs if the
array number specified for an ARRAY region description of the EXTENDED
GEOMETRY data (:numref:`sec-module.keno.geom`) did not have the corresponding UNIT
ORIENTATION DATA entered in the ARRAY DATA (:numref:`sec-module.keno.geom.array_data`). A STOP 142
is executed in conjunction with this message when it is printed from
subroutine SORTA. The data should be corrected and the problem
resubmitted.
KMSG160
******* ERROR ******* K?-160 FOLLOWS:
|br| THE HOLES ARE RECURSIVELY NESTED.
This message from subroutines K5GM_HOLE or SGHM_HOLE indicates that the geometry region data
description (:numref:`sec-module.keno.geom`) specifies holes that are recursively nested.
This can occur if a unit contains a hole whose definition traces back to
the same unit or are defined in terms of each other. A simple example of
recursive nesting is
KENO V.a:
.. code-block:: scale
UNIT 1 CUBE 0 1 2P10.0 HOLE 2 3*0.0
UNIT 2 CUBE 0 1 2P10.0 HOLE 1 3*0.0
KENO-VI:
.. code-block:: scale
UNIT 1 CUBOID 10 6P10.0 BOUNDARY 10 HOLE 2 1 3*0.0
UNIT 2 CUBOID 10 6P10.0 BOUNDARY 10 HOLE 1 1 3*0.0
Thus ``UNIT`` 1 contains ``UNIT`` 2 and ``UNIT`` 2 contains ``UNIT`` 1.
The geometry region data should be checked for recursive nesting. In the
absence of recursive nesting, a code error is the probable cause of this
message. A STOP 143 is executed when this message occurs and a traceback
is printed.
KMSG161
******* ERROR ******* K5-161 FOLLOWS:
|br| THE GLOBAL ARRAY SPECIFIED IN THE GEOMETRY REGION DATA IS ___
|br| BUT THE GLOBAL ARRAY SPECIFIED IN THE ARRAY DATA IS ___. EXECUTION IS TERMINATED.
This KENO V.a message is from subroutine K5_FLDATA. A STOP 144 is executed in
conjunction with it. The global array specified in the array data
(:numref:`sec-module.keno.geom.array_data`) was entered using the keyword ``GBL=``. It was not
consistent with the implied global array from the geometry region data
(:numref:`sec-module.keno.geom`). The global array number in the geometry region data is
defined to be the array number in the global unit or of the last
``ARRAY`` description that does not immediately follow a ``UNIT``
definition (i.e., other geometry definitions occur between ``UNIT`` and
``ARRAY``). The data should be corrected, and the problem resubmitted.
KMSG162
******* ERROR ******* K5-162 FOLLOWS:
|br| THE GLOBAL ARRAY WAS NOT CONSISTENTLY SPECIFIED.
|br| THE ARRAY DATA SPECIFIED ARRAY NUMBER ___ AND THE GEOMETRY DATA SPECIFIED ARRAY NUMBER ___.
This KENO V.a message from subroutine K5GM_SORTA occurs if ``GBL=`` in the array
data (:numref:`sec-module.keno.geom.array_data`) does not agree with the global array number
implicitly set in the geometry region data (:numref:`sec-module.keno.geom`). The geometry
region data define the global array number in the global unit or to be
the array number of the last ``ARRAY`` description that does not
immediately follow a ``UNIT`` definition (i.e., other geometry
definitions occur between ``UNIT`` and ``ARRAY``). A flag is set to
terminate execution when the data reading is completed.
KMSG163
******* ERROR ******* K5-163 FOLLOWS:
|br| HOLE NUMBER ___ (UNIT NUMBER ___) INTERSECTS REGION NUMBER ___
This self-explanatory KENO V.a message is from subroutine K5GM_HOLHOL.
KMSG164
******* ERROR ******* K5-164 FOLLOWS:
|br| HOLE NUMBER ___ (UNIT NUMBER ___) INTERSECTS REGION NUMBER ___.
This self-explanatory KENO V.a message is from subroutine K5GM_HOLEXT.
KMSG165
******* ERROR ******* K5-165 FOLLOWS:
|br| ****** ERROR ****** GEOMETRY TYPE OUT OF RANGE IN SUBROUTINE ADJUST. IGEOH = ___
This KENO V.a message from subroutine K5GM_ADJUST indicates that the geometry type,
IGEO, falls outside the allowable range of 1 through 19. This can occur
if a ``HOLE`` references an undefined unit number. If all the unit
numbers referenced by the holes are valid, a code error is the probable
cause.
KMSG166
******* ERROR ******* K5-166 FOLLOWS:
|br| THE PLUS CUBE FACE IS NOT GREATER THAN THE MINUS CUBE FACE
|br| PLUS FACE = ___ MINUS FACE = ___
This self-explanatory KENO V.a message is from subroutine K5GM_KENOG.
KMSG167
******* ERROR ******* K5-167 FOLLOWS:
|br| ONE OR MORE PLUS FACES OF A CUBOID ARE NOT GREATER THAN THE CORRESPONDING MINUS FACES
|br| +X = ___ -X = ___ +Y = ___ -Y = ___ +Z = ___ -Z = ___
This self-explanatory KENO V.a message is from subroutine K5GM_KENOG.
KMSG168
******* ERROR ******* K5-168 FOLLOWS:
|br| THE CYLINDER RADIUS IS NOT GREATER THAN ZERO, OR THE + HEIGHT IS NOT GREATER THAN THE - HEIGHT
|br| RADIUS = ___ +H = ___ -H = ___
This self-explanatory KENO V.a message is from subroutine K5GM_KENOG.
KMSG169
******* ERROR ******* K5-169 FOLLOWS:
|br| THE SPHERE RADIUS IS NOT GREATER THAN ZERO - RADIUS = ___
This self-explanatory KENO V.a message is from subroutine K5GM_KENOG.
KMSG170
******* ERROR ******* K5-170 FOLLOWS:
|br| A REPLICATE THICKNESS IS LESS THAN ZERO
SURFACE NUMBER = ___ THICKNESS = ___
This KENO V.a message from subroutine K5GM_KENOG specifies that a thickness on a replicate
was specified as a negative number. This is not allowed, as it would lead to
an intersection.
KMSG171
******* ERROR ******* K?-171 FOLLOWS:
|br| DIRECTION COSINES DOWN THE PAGE WERE ALL INPUT AS ZERO.
This message from subroutine RDPLOT indicates that the values for
``UDN=``, ``VDN-`` and ``WDN=`` were all zero. A zero value vector
does not define a direction, so an error has occurred. See
:numref:`8-1-2-11` for information concerning direction cosines down the
page.
KMSG172
******* ERROR ******* K?-172 FOLLOWS:
|br| DIRECTION COSINES ACROSS THE PAGE WERE ALL INPUT AS ZERO.
This message from subroutine RDPLOT indicates that the values for
``UAX=``, ``VAX=`` and ``WAX=`` were all zero. This is an error
because a zero-value vector does not define a direction. See
:numref:`8-1-2-11` for assistance in defining direction cosines across the
page.
KMSG173
******* ERROR ******* K?-173 FOLLOWS:
|br| ERRORS WERE DETECTED IN THE INPUT DATA FOR PLOT ___. IT WILL NOT BE DRAWN
This message from subroutine RDPLOT is a companion to messages
K?-171, K?-172, K?-174, and K?-180. The error that triggered the companion
message should be corrected, and the problem resubmitted.
KMSG174
******* ERROR ******* K?-174 FOLLOWS:
|br| ERROR IN KENO PLOT DATA- ___ ___ SHOULD BE ENTERED AS ___YES, OR ___NO
This self-explanatory message is from subroutine RDPLOT.
The error should be corrected, and the problem resubmitted.
See :numref:`8-1-2-11` for assistance.
KMSG175
******* WARNING ******* K?-175 FOLLOWS:
|br| DUE TO INCONSISTENCIES BETWEEN INPUT AND RESTART DATA,
|br| MATRIX INFORMATION BY HOLE WILL BE CALCULATED BUT NOT PRINTED.
|br| INPUT DATA SET MKH=NO, BUT DATA FROM THE RESTART UNIT SPECIFIED YES.
This self-explanatory warning message is from subroutine PARTBL. The
matrix information by hole cannot be eliminated if it was calculated by
the original problem (parent case) that wrote the restart data. However,
printing it can be avoided. It should be verified that the correct
problem is being used for restarting the problem (the title is printed
at the bottom of the parameter tables). The specification of the restart
unit, ``RST``, in the third table of the computer output should be
verified.
KMSG176
******* WARNING ******* K?-176 FOLLOWS:
|br| DUE TO INCONSISTENCIES BETWEEN INPUT AND RESTART DATA,
|br| MATRIX INFORMATION BY ARRAY WILL BE CALCULATED BUT NOT PRINTED.
|br| INPUT DATA SET MKA=NO BUT DATA FROM THE RESTART UNIT SPECIFIED YES.
This self-explanatory warning message is from subroutine PARTBL. The
matrix information by array cannot be eliminated if it was calculated by
the original problem (parent case) that wrote the restart data. However,
printing it can be avoided. It should be verified that the correct
problem is being used for restarting the problem (the title is printed
at the bottom of the parameter tables). Specification of the restart
unit, RST, in the third table in the computer output should also be
verified.
KMSG177
******* ERROR ******* K?-177 FOLLOWS:
|br| PARAMETER DATA SPECIFIED MATRIX INFORMATION BY HOLE BUT IT WAS NOT FOUND ON THE RESTART UNIT.
This message from subroutine RDCALC is printed if a restarted problem
requests matrix information by hole when it was not requested and
calculated by the original problem (parent case) that wrote the restart
data. It should be verified that the correct restart data file is being
used and that the restart unit (``RST``) is correctly specified. The
request for matrix information by hole (``MKH=``, in the parameter
data) should be eliminated if it is not necessary. The problem must be
restarted with the first generation (``BEG=1``, in the parameter data)
if matrix information by hole is required and was not calculated by the
parent case. A STOP 121 is executed in conjunction with this message.
KMSG178
******* ERROR ******* K?-178 FOLLOWS:
|br| PARAMETER DATA SPECIFIED MATRIX INFORMATION BY ARRAY BUT IT WAS NOT FOUND ON THE RESTART UNIT.
This message from subroutine RDCALC is printed if a restarted problem
requests matrix information by array (also called array position or
position index) when it was not requested and calculated by the original
problem (parent case) that wrote the restart data. It should be verified
that the correct restart data are being used and that the restart unit
(``RST``) is correctly specified in the first table following the
parameter tables. The request for matrix information by array (MKA=, in
the parameter data) should be eliminated if it is not necessary. If
matrix information by array is required and it was not calculated by the
parent case, the problem must be restarted with the first generation
(``BEG=1``, in the parameter data). A STOP 121 is executed in
conjunction with this message.
KMSG179
******* ERROR ******* K5-179 FOLLOWS:
|br| HOLE NUMBER ___ (UNIT NUMBER ___) INTERSECTS HOLE NUMBER ___ (UNIT NUMBER ___) IN REGION NUMBER ___.
This KENO V.a message from subroutine K5GM_HOLHOL indicates that the specified holes
intersect. Check the dimensions and origins of the units being placed in
the region.
KMSG180
******* ERROR ******* K?-180 FOLLOWS:
|br| PROBLEM IN KENO PLOT DATA - KEYWORD ___ IS NOT VALID
This message from subroutine RDPLOT indicates that the plot data are out
of order or a keyword is incorrectly spelled. See :numref:`8-1-2-11` for a
list of correct keywords.
KMSG181
******* ERROR ******* K?-181 FOLLOWS:
|br| LPIC IS OUT OF RANGE. LPIC=___
This message from subroutines K5GM_PRTPLT or K6GM_PRTPLT indicates that a code error has
occurred or the type of plot (``PIC=``) was not properly specified.
*lpic*\ =l for a mixture map, *lpic*\ =2 for a unit map, and *lpic*\ =3
for a bias ID map. Any other values of *lpic* are invalid.
KMSG182
******* ERROR ******* K5-182 FOLLOWS:
|br| AN ARRAY WAS SPECIFIED IN THE GLOBAL UNIT, BUT ARRAY DATA WAS NOT ENTERED.
This KENO V.a message from subroutine K5GM_SORTA indicates that the global unit
contains an array specification, but the array was not entered in the
array data block. A typo may need to be corrected in the ``GLOBAL UNIT``
or in the ``ARRAY`` data block.
KMSG183
******* WARNING ******* K5-183 FOLLOWS:
|br| UNIT ___ WAS NOT CHECKED FOR GEOMETRIC CONSISTENCY.
|br| IT CONTAINS ARRAY ___ BUT WAS NOT USED IN THE PROBLEM.
This KENO V.a warning message is from subroutine K5GM_JOMCHK. It indicates that a unit
whose first region is an array was described in the extended geometry
data, but that unit was not referenced in the unit orientation data (see
:numref:`sec-module.keno.geom` and :numref:`sec-module.keno.geom.array_data`). KENO usually checks all the geometry region
data to be sure it is correct, even when the unit is not used in the
problem. The code is unable to make these checks when a unit containing
an array is not used in the problem. It is not necessarily an error, but
the user should double check to be sure that unit was intentionally
omitted from all the arrays.
KMSG184
******* ERROR ******* K5-184 FOLLOWS:
|br| ALBEDOS WERE SPECIFIED FOR A PROBLEM WHOSE OUTER BOUNDARY IS NOT A CUBE OR CUBOID.
|br| THE PROBLEM WILL NOT EXECUTE.
This KENO V.a message from subroutine K5GM_JOMCHK indicates that a
non-vacuum albedo boundary condition was entered for a
curvilinear outer surface. This is not allowed, and the problem will not be run.
KMSG185
******* ERROR ******* K?-185 FOLLOWS:
|br| ****** ERROR ****** THE NUMBER OF SETS OF BIASING CORRELATION DATA EXCEEDS THE NUMBER THAT WAS WRITTEN WHEN THE BIASING DATA WAS
|br| READ. ___ WERE WRITTEN, BUT AN ATTEMPT WAS MADE TO READ ___.
This message from subroutine WAITIN is accompanied by a STOP 148.
It indicates a code error unless it is accompanied by error messages
related to the biasing input data.
KMSG186
******* ERROR ******* K?-186 FOLLOWS:
|br| THE NUMBER OF SETS OF BIASING AUXILIARY DATA EXCEEDS THE NUMBER THAT WAS WRITTEN WHEN THE BIASING DATA WAS
|br| READ. ___ WERE WRITTEN, BUT AN ATTEMPT WAS MADE TO READ ___.
This message from subroutine WAITIN is accompanied by a STOP 149.
It indicates a code error unless it is accompanied by error messages related
to the biasing input data.
KMSG187
******* WARNING ******* K?-187 FOLLOWS:
|br| INTERVALS IN THE ABOVE RANGE WERE NOT USED.
|br| THIS COULD LEAD TO IMPROPER BIASING.
This message from subroutine LODWTS is printed to remind the user that
at least one of the specified intervals was not used in the problem.
This can result in improper biasing. Biasing should not be used between
fissile units. When biasing is used, it should be flat or increasing as
distance from the fissile material increases and flat or decreasing as a
history moves toward fissile material. See :numref:`sec-module.keno.biasing` for additional
assistance.
KMSG188
******* ERROR ******* K?-188 FOLLOWS:
|br| HOLE NUMBER ___ REFERENCES UNDEFINED UNIT NUMBER ___
This message is printed by subroutines K5GM_HOLCHK, K5GM_HOLE,
K5GM_READGM, or SGGM_HOLE if the unit number
referenced by the hole is less than 1 or greater than the largest unit
number in the geometry data. The message is printed by subroutine HOLE
if the unit number referenced by the hole is larger than zero and not
greater than the largest unit number in the geometry data but is a unit
number for which all data are missing. The message is printed by
subroutine HOLCHK if the unit number referenced by the hole is
undefined. Message K?-165 may accompany this message. Specify a valid
unit number (*lhole* --- see EXTENDED GEOMETRY DESCRIPTION, :numref:`sec-module.keno.geom`)
and resubmit the problem.
KMSG189
******* ERROR ******* K6-189 FOLLOWS:
|br| HOLE NUMBER ___ REFERENCES UNDEFINED UNIT NUMBER ___
This self-explanatory KENO-VI message is from subroutine SSGM_READGM.
KMSG190
******* ERROR ******* K?-190 ERROR IN PLOT DATA - OPTION ___ IS NOT VALID FOR KEYWORD PIC=.
This message from subroutine RDPLOT indicates an incorrect option
associated with the keyword ``PIC=``. See :numref:`8-1-2-11`. Acceptable
options include MAT, MIX, MIXT, MEDI, UNT, UNIT, IMP, BIAS, WTS, WGT,
WGTS, or WEIGH.
KMSG191
******* ERROR ******* K?-191 FOLLOWS:
|br| START TYPE ___ IS INVALID FOR A PROBLEM THAT DOES NOT HAVE A GLOBAL ARRAY.
This message from subroutine DATAIN occurs if the start type (``NST=``
in the start data, :numref:`sec-module.keno.start_data`) is 2, 3, 4, or 5. A global array is
required to use the specified start type.
KMSG192
******* WARNING ******* K?-192 FOLLOWS:
|br| MATRIX INFORMATION BY ARRAY WAS SPECIFIED AS YES IN THE PARAMETER DATA (MKA=),
|br| BUT IS NOT OF USE UNLESS ARRAYS ARE SPECIFIED.
This warning message from subroutine DATAIN is self-explanatory. The
code redefines the problem so matrix information will not be collected
by array number.
KMSG193
******* WARNING ******* K?-193 FOLLOWS:
|br| MATRIX INFORMATION BY HOLE WAS SPECIFIED AS YES IN THE PARAMETER, DATA (MKH=),
|br| BUT IS NOT OF USE UNLESS HOLES ARE SPECIFIED.
This warning message from subroutine DATAIN is self-explanatory.
The code redefines the problem so matrix information will not be
collected by hole number.
KMSG194
******* WARNING ******* K?-194 FOLLOWS:
|br| MATRIX INFORMATION BY UNIT LOCATION WAS SPECIFIED AS YES IN THE PARAMETER DATA (MKP=),
|br| BUT IS NOT ALLOWED BECAUSE A GLOBAL ARRAY WAS NOT SPECIFIED.
This warning message from subroutine DATAIN is self-explanatory.
The code redefines the problem so matrix information will not be
collected by unit location.
KMSG195
******* ERROR ******* K?-195 FOLLOWS:
|br| CHARACTER STRING EXCEEDS THE SPECIFIED LENGTH. CHECK FOR ENDING DELIMITER.
This error message is from subroutine RCHRS. It indicates that either
the character string exceeds 132 characters or the ending delimiter was
omitted for ``TTL=`` (plot title, :numref:`8-1-2-11`) or for ``COM=``
(unit comment, :numref:`sec-module.keno.geom`, or array comment, :numref:`sec-module.keno.geom.array_data`). A
STOP 153 is executed when this message is printed.
KMSG196
******* ERROR ******* K?-196 FOLLOWS:
|br| A PROBLEM CANNOT BE RESTARTED WHEN RESTART DATA DO NOT EXIST FOR THE SPECIFIED GENERATION AND THE
|br| NEXT GENERATION FOR WHICH RESTART DATA ARE AVAILABLE IS LARGER THAN THE REQUESTED NUMBER OF GENERATIONS. \*\*
|br| \*\* EXECUTION IS TERMINATED.
This message from subroutine RDCALC indicates that a problem was to be
restarted but the requested number of generations (``GEN=`` in
:numref:`sec-module.keno.parameters`) was smaller than the beginning generation number
(``BEG=`` in :numref:`sec-module.keno.parameters`). The beginning generation number for a
restarted problem is the generation at which the calculation of
k-effectives and associated information is resumed. Therefore, the
number of generations to be run must be larger than the beginning
generation number. The data should be corrected and the problem
resubmitted. A STOP 154 is executed when this message is printed.
KMSG197
******* ERROR ******* K5-197 FOLLOWS:
|br| A VALID GEOMETRY REGION MUST PRECEDE A REPLICATE REGION.
This KENO V.a message from subroutine K5GM_KENOG indicates that a replicate
specification follows an invalid geometry specification (for example,
REPLICATE immediately follows a UNIT specification).
KMSG198
******* ERROR ******* K?-198 FOLLOWS:
|br| ARRAY ___ CONTAINS AN ERROR IN THE INPUT DATA.
This message from subroutine ARAYIN is printed as the result of an error in
the FILL input data for the specified array. One or more messages from the
library routine YREAD should immediately precede this message and indicate
the nature of the error. The data should be corrected and the problem resubmitted.
Messages K?-32, K?-33, and/or K?-85 may also print as a result of this error.
KMSG199
******* ERROR ******* K?-199 FOLLOWS:
|br| THERE IS NO MIXING TABLE
This self-explanatory message comes from subroutine PREMIX-SETUP.
A continuous energy problem requires a mixing table, but none was entered.
KMSG200
******* ERROR ******* K?-200 FOLLOWS:
|br| START TYPE 6 WAS SPECIFIED IN THE START DATA, BUT THE STARTING
|br| POINTS WERE NOT SPECIFIED.
This message from subroutine RDSTRT indicates that start type 6 was
specified but the corresponding starting points were not included in the
START data block. The corresponding starting points must be entered or
the start type must be changed. See :numref:`sec-module.keno.start_data`.
KMSG201
******* WARNING ******* K?-201 FOLLOWS:
|br| NEUTRON ___ SPECIFIED A POSITION IN THE GLOBAL ARRAY.
|br| THE GLOBAL UNIT DID NOT CONTAIN AN ARRAY SO THE POSITION WAS IGNORED
|br| ****** WARNING ************ WARNING ********* WARNING ************ WARNING ************ WARNING ************ WARNING ************ WARNING ************ WARNING ************ WARNING ************ WARNING ******
This warning message from subroutine K_STDATA indicates that extraneous
data were specified in the start type 6 data. It should be verified that
the correct global unit is specified.
KMSG202
******* ERROR ******* K?-202 FOLLOWS:
|br| ONLY START TYPES 0,1,6 OR 7 ARE VALID FOR A PROBLEM WITHOUT AN ARRAY IN THE GLOBAL UNIT.
This message from subroutines K5_START or K6_START indicates that the specified
start type is not valid for the problem. An appropriate start type must be chosen.
KMSG203
******* ERROR ******* K?-203 FOLLOWS:
|br| UNIDENTIFIED KEYWORD ___ IN MIXING TABLE
This message from subroutine MIXING_TABLE indicates that when reading the mixing table,
an unrecognized keyword was found. See :numref:`sec-module.keno.mixing_table` for the acceptable keywords.
KMSG204
K?-204 EXECUTION TERMINATED DUE TO ACHIEVING THE STANDARD DEVIATION SPECIFIED FOR THE PROBLEM.
|br| NOTE THAT AT LEAST 50 OR NSK*2 ACTIVE GENERATIONS ARE ALWAYS RUN.
This message from subroutines K5_GUIDE or K6_GUIDE indicates that the
specified standard
deviation has been achieved and the problem will therefore terminate at
the current generation. If a lower standard deviation is desired the
requested standard deviation (``SIG=``, :numref:`sec-module.keno.parameters`) must be
decreased.
KMSG205
******* ERROR ******* K5-205 FOLLOWS:
|br| A GLOBAL UNIT MUST BE SPECIFIED FOR A SINGLE UNIT PROBLEM.
This message from subroutine K5_FLDATA is printed if a global unit is not
specified for a single unit problem. A STOP 164 is executed when the
message is printed. If the input data do not specify the global unit, it
is defaulted to Unit 1.
KMSG206
******* ERROR ******* K?-206 FOLLOWS:
|br| THE UNIT SPECIFIED FOR STARTING IS NOT USED IN THE PROBLEM OR IS UNDEFINED.
This message from subroutines K5_START or K6_START indicates that the unit in which
neutrons are to be started is undefined. It should be verified that the
global unit or array is correctly specified. The start data should be
checked for start types 4 and 5 (:numref:`sec-module.keno.start_data`) to be sure that
``NBX=`` is correctly specified.
KMSG207
******* ERROR ******* K?-207 FOLLOWS:
|br| THE STARTING ARRAY POSITION IS INVALID.
This message from subroutines K5_START or K6_START indicates that the array position
``NXS``, ``NYS``, or ``NZS`` is not valid for start types 3 or 6.
``NXS``, ``NYS``, and ``NZS`` must be larger than zero and no larger
than NBXMAX, NBYMAX, and NBZMAX of the global array, respectively. It
should be verified that the ``GLOBAL UNIT`` or ``ARRAY`` is correctly
specified. The start data (:numref:`sec-module.keno.start_data`) should be corrected and the
problem resubmitted.
KMSG208
******* WARNING ******* K?-208 FOLLOWS:
|br| THE FRACTION OF NEUTRONS STARTED AS A SPIKE WAS LESS THAN ZERO. IT HAS BEEN RESET TO ZERO.
This message from subroutines K5_START or K6_START indicates that ``FCT=`` was
incorrectly specified in the start data for start type 2. The resultant
starting distribution is a cosine distribution throughout the volume of
a cuboid defined by ``XSM``, ``XSP``, ``YSM``, ``YSP``, ``ZSM``, and
``ZSP`` (see :numref:`sec-module.keno.start_data`). If a spike was desired, ``FCT=`` should
be set to a positive number between 0.0 and 1.0. If ``FCT =0.0`` is
specified, a cosine distribution without a spike is used as the starting
distribution. If ``FCT=1.0`` is specified, all the neutrons are
started as a spike (i.e., they are started uniformly in the unit located
at position ``NXS``, ``NYS``, ``NZS`` in the global array) as noted in
:numref:`sec-module.keno.start_data`
KMSG209
******* WARNING ******* K?-209 FOLLOWS:
|br| THE FRACTION OF NEUTRONS STARTED AS A SPIKE WAS GREATER THAN ONE. IT HAS BEEN RESET TO ONE.
This message from subroutines K5_START or K6_START indicates that ``FCT=`` was
incorrectly specified in the start type 2 data. The code reset
``FCT=1``, so all the neutrons are started as a spike (i.e., they
are started uniformly in the unit located at ``NXS``, ``NYS``, ``NZS``
in the global array) as noted in :numref:`sec-module.keno.start_data`
KMSG210
******* ERROR ******* K?-210 FOLLOWS:
|br| THE UNIT SPECIFIED FOR STARTING IS NOT IN THE GLOBAL ARRAY.
This message from subroutines K5_START or K6_START indicates that the unit specified by
``NBX=`` does not occur in the global array. It should be verified
that the global array is correctly specified and that the unit specified
by ``NBX=`` is correct (see :numref:`sec-module.keno.start_data`).
KMSG211
******* ERROR ******* K?-211 FOLLOWS:
|br| THE NUMBER OF SETS OF BIAS FACTORS FROM CARDS EXCEEDS THE NUMBER THAT WAS WRITTEN WHEN THE BIASING DATA WAS
|br| READ. ___ WERE WRITTEN, BUT AN ATTEMPT WAS MADE TO READ ___.
This message from subroutine WAITIN indicates a code error.
A STOP 161 is executed when this message is printed.
KMSG212
******* ERROR ******* K?-212 FOLLOWS:
|br| THE BIASING DATA SPECIFIED IBGN=___ AND IEND=___.
|br| IBGN MUST BE LARGER THAN ZERO AND IEND MUST BE AT LEAST AS LARGE AS IBGN.
|br| THE PROBLEM WILL NOT BE RUN.
This message from subroutine RDBIAS indicates an error in the biasing
data. The biasing correlation data is order dependent. The order of data
entry is ID=\ *nn ibgn iend*, where *nn* is an ID number from
:numref:`tab8-1-20` and *ibgn* is the beginning BIAS ID and *iend* is the
ending BIAS ID (see :numref:`sec-module.keno.biasing` and :numref:`sec-module.keno.biasing`). To continue
checking the input data, if *ibgn* is less than or equal to zero, it is
set to 1. Similarly, if *iend* is less than *ibgn*, it is set to *ibgn*.
KMSG214
\****\* ERROR \****\* K6-214 FOLLOWS:
|br| THE BASE OF A TRIANGULAR FACE OF A WEDGE CANNOT BE ZERO.
This KENO-VI message is from subroutine SGGM_WEDGE.
The input data for the wedge following the keyword WEDGE are incorrect.
See :numref:`sec-scale.keno6.shapes`.
KMSG215
\****\* ERROR \****\* K6-215 FOLLOWS:
|br| THE Y COORDINATE OF A TRIANGULAR FACE OF A WEDGE CANNOT BE ZERO.
This KENO-VI message is from subroutine SGGM_WEDGE.
The input data for the wedge following the keyword WEDGE are incorrect. See :numref:`sec-scale.keno6.shapes`.
KMSG216
\****\* ERROR \****\* K5-216 FOLLOWS:
|br| UNIT ___ CONTAINS ARRAY ___ WHICH WAS NOT DEFINED IN THE INPUT DATA.
This message from subroutine K5GM_JOMCHK indicates that the unit specified an array,
but the array number was not entered in the array data block.
The array number specified in the unit should be checked to verify that it is correct,
or the unit orientation data should be entered in the array data block.
KMSG217
\****\* ERROR \****\* K?-217 FOLLOWS:
|br| \*\*\* ERROR \*\*\* DIFFERENTIAL ALBEDOS CANNOT BE USED IN AN ADJOINT PROBLEM.
This self-explanatory message is from subroutines MFLDATA, K5_FLDATA or K6_FLDATA.
Reflector material in the mixing table and the geometry
should be described instead of using differential albedos, or
the problem should be run in the forward mode.
KMSG218
\****\* ERROR \****\* K?-218 FOLLOWS:
|br| AN INPUT DATA ERROR HAS BEEN ENCOUNTERED IN THE ___ DATA ENTERED FOR THIS PROBLEM.
This message is from subroutines INITAL, DATAIN, or KENOBUILDER.
Additional error messages should be
found and corrected, and the data in the named data block should be checked.
KMSG219
\****\* ERROR \****\* K?-219 FOLLOWS:
|br| THE START DATA SPECIFIED ___ STARTING POINTS CHOSEN FROM A COSINE DISTRIBUTION BUT NONE WERE FOUND.
This message from subroutines K5_START or K6_START is
printed if start type 2 was
specified and the code was unable to start any neutrons in the cuboid
defined by ``XSM``, ``XSP``, ``YSM``, ``YSP``, ``ZSM``, ``ZSP``. It
should be verified that fissile material exists within that cuboid. If
it does not, the starting cuboid should be respecified to contain
fissile material, or a different start type should be chosen. If message
KMSG105 states that only 0 independent starting points were generated,
it indicates that the code was unable to start any neutrons in the spike
specified by start type 2. It should be verified that the unit specified
for the spike contains fissile material. If only a very small fraction
of the volume of this unit is fissile, it may be necessary to enter a
larger value for the KENO parameter **TBA**\ = or a different start type
may need to be selected. The problem will not be run if message KMSG219
is printed.
KMSG220
\****\* ERROR \****\* K?-220 FOLLOWS:
|br| ERROR IN PLOT DATA.
|br| IF THE COORDINATE OF THE LOWER RIGHT-HAND CORNER IS ENTERED, ONE OF THE PLOT PARAMETERS DLX, DLD, NAX OR NDN MUST BE ENTERED.
|br| CURRENT VALUES ARE LISTED BELOW. TITLE:
|br| _____
|br| UPPER LEFT LOWER RIGHT
|br| COORDINATES COORDINATES
|br| X _________ _________
|br| Y _________ _________
|br| Z _________ _________
|br| U AXIS V AXIS
|br| (DOWN) (ACROSS)
|br| X ________ ________
|br| Y ________ ________
|br| Z ________ ________
|br| NDN=___ NAX=___ DLD=___ DLX=___
This message from subroutine RDPLOT indicates that the coordinates of
the lower right-hand corner of the plot were specified in the input data
without specifying one of the following plot parameters: (1) ``NDN``,
the number of characters down the page, (2) ``NAX``, the number of
characters across the page, (3) ``DLD``, the vertical spacing between
points, or (4) ``DLX``, the horizontal spacing between points. The
problem will not be run. To correct the error, ``NDN``, ``NAX``,
``DLD``, or ``DLX`` should be specified in the plot data and the problem
resubmitted. See :numref:`8-1-2-11` and :numref:`8-1-3-9` for assistance.
KMSG221
\****\* ERROR \****\* K6-221 FOLLOWS:
|br| THE LENGTH OF THE EDGE ALONG THE BASE OF THE X AXIS FOR A RHOMBOID
|br| MUST BE GREATER THAN 0.0. CHECK GEOMETRY WORD ___
This KENO-VI message is from subroutine SGGM_RHOMB. The data following the
keyword RHOMB should be checked. See :numref:`sec-scale.keno6.shapes`.
KMSG222
\****\* WARNING \****\* K?-222 FOLLOWS:
|br| ___ TRANSFERS FOR MIXTURE ___ WERE CORRECTED FOR BAD MOMENTS.
This message from subroutine MAKANG indicates moments were corrected to
eliminate negative probabilities for calculated angles. If the moment
was changed by more than ``EPS`` times the moment, a K?-60 or K?-64
message is printed. If ``EPS`` is very small, any change without an
accompanying message is trivial. The K?-60 or K?-64 messages can be used
to determine if the affected transfer and correction are significant.
Most messages are caused by the cross sections being in single precision
and the moments calculations being done in double precision. Generally,
as the number of energy groups increase, so does the number of corrected
transfers for a given mixture.
KMSG224
\****\* ERROR \****\* K6-224 FOLLOWS:
|br| THE HEIGHT OF A WEDGE CANNOT BE ZERO.
This KENO-VI message is from subroutine SGGM_WEDGE. The input data for the wedge
following the keyword WEDGE are incorrect. See :numref:`sec-scale.keno6.shapes`.
KMSG225
\****\* ERROR \****\* K6-225 FOLLOWS:
|br| TO START IN A GLOBAL PLANE GEOMETRY, IGEO =___
|br| VALUES FOR XSM, XSP, YSM, YSP, ZSM, AND ZSP MUST BE ENTERED AS START DATA.
This error message is from subroutine K6_STRTSU. A GLOBAL PLANE GEOMETRY implies
an infinite media. The boundary of the starting points must be entered.
See :numref:`sec-module.keno.start_data`.
KMSG226
\****\* ERROR \****\* K6-226 FOLLOWS:
|br| XDIST, YDIST, AND ZDIST SPECIFIED FOR A PPIPED MUST BE GREATER THAN 0.0.
|br| CHECK GEOMETRY WORD ___
This KENO-VI message is from subroutine SGGM_PPIPED.
The data must be checked following the keyword PPIPED. See :numref:`sec-scale.keno6.shapes`.
KMSG227
\****\* ERROR \****\* K6-227 FOLLOWS:
|br| PSI, THETA, AND PHI SPECIFIED FOR A PARALLELEPIPED MUST BE GREATER THAN OR EQUAL TO 0.0 AND LESS THAN 90.0.
|br| CHECK GEOMETRY WORD ___
This KENO-VI message is from subroutine SGGM_PPIPED.
The data following the keyword PPIPED should be checked. See :numref:`sec-scale.keno6.shapes`.
KMSG228
\****\* ERROR \****\* K5-228 FOLLOWS:
|br| ___ ___ IS INVALID. UNITS MUST BE GREATER THAN 0.
|br| THE PREVIOUS UNIT NUMBER IS ___. PRINTING THE GEOMETRY AS READ WILL BE TURNED ON
This message from subroutine K5GM_KENOG is printed if a unit number, *nn*, is
read which is not greater than 0. This unit followed unit *mm* in the
input (if *mm* is 1, the unit *nn* may be the first unit in the
geometry). The geometry following this will be printed as read as an aid
in locating the error. The error must be corrected, and all unit numbers
must be greater than 0.
KMSG229
\****\* WARNING \****\* K?-229 FOLLOWS:
|br| THE NUMBER OF START TYPE 6 STARTING POINTS (LNU=___) SPECIFIED IN START DATA DOES NOT MATCH THE NUMBER
|br| OF NEUTRONS PER GENERATION (NPG=___). SPECIFIED STARTING POINTS WILL BE USED FOR FIRST ___ NEUTRONS, AND
|br| THE STARTING POINTS FOR THE REMAINING NEUTRONS WILL BE RANDOMLY SELECTED FROM THESE (LNU=___) POINTS.
This message from subroutine START6 is printed if the number of starting
points specified (``LNU``) is less than the number of histories per
generation (``NPG``). The remaining unspecified starting points will be
randomly selected from the already specified starting points.
KMSG230
\****\* ERROR \****\* K?-230 FOLLOWS:
|br| MATRIX K-EFFECTIVE WAS NOT CONVERGED. K-EFFECTIVE IS ___ CONVERGENCE ERROR IS ___
This message is printed by subroutines K5_GUIDE, K6_GUIDE, or MATK
if the matrix eigenvalue equation did not converge to
0.1 % after a maximum number of iterations. This is likely a code error,
but it might be caused by too much variance in the matrix terms.
KMSG231
\****\* ERROR \****\* K6-231 FOLLOWS:
|br| THE CALCULATION WAS TERMINATED BECAUSE ARRAY ___ IS NOT PROPERLY POSITIONED IN REGION ___ OF UNIT ___.
|br| THE ARRAY BOUNDARY IS OUTSIDE POSITION ___ ___ ___ ON THE ___ ARRAY FACE.
This KENO-VI message from subroutine SGGM_PNTCHK is printed only
if an array is placed in a region so that there is space in the
region not occupied by the array. The array needs to be repositioned.
KMSG233
\****\* ERROR \****\* K?-233 FOLLOWS:
|br| MIXTURE ___ HAS A NEGATIVE CROSS SECTION FOR REACTION ___ - GROUP ___ THE VALUE IS ___
This error message from subroutine NORM1D is printed if an MT number for a
specified mixture has a negative cross section value in any group. This is a
library or cross section processing problem. This error should be reported to
scalehelp@ornl.gov.
KMSG234
\****\* ERROR \****\* K?-234 FOLLOWS:
|br| MIXTURE ___ HAS NEGATIVE CROSS SECTIONS FOR REACTION ___
|br| SET XS1=YES AND P1D=YES IN THE PARAMETERS TO SEE THE VALUE(S).
This error message from subroutine FILLSG is printed if an MT number for
a specified mixture has a negative cross section value in any group.
This is a library or cross section processing problem.
This error should be reported to scalehelp@ornl.gov.
KMSG236
\****\* ERROR \****\* K?-236 FOLLOWS:
|br| EITHER NEUTRON OR GAMMA SHOULD HAVE BEEN ENTERED TO SELECT THE TYPE OF 1-D CROSS SECTIONS, BUT ___ WAS ENTERED INSTEAD.
This error message from subroutine IDX1D indicates the user specified
extra 1-D cross sections but specified an invalid type. Valid types are
either neutron or gamma. The data must be corrected in the ``READ X1DS``
data block.
KMSG237
\****\* ERROR \****\* K?-237 FOLLOWS:
|br| NUMBER OF SCATTERING ANGLES ASKED FOR, ___, DO NOT MATCH THE NUMBER ON THE MIXED CROSS SECTION LIBRARY ,___.
|br| UNABLE TO PROCESS FURTHER.
This error message from subroutine ICEMIX indicates the user requested a
number of angles to be used in the problem, NSCT, that is inconsistent
with the premixed cross section library specified for this problem.
Either ``SCT=`` should not be specified, or it should be specified by
creating a new mixed library.
KMSG238
\****\* ERROR \****\* K?-238 FOLLOWS:
|br| DELTA ___-COORDINATE ___
|br| DIRECTION COSINE ACROSS ___
|br| DIRECTION COSINE DOWN ___
|br| ARE INCONSISTENT. IF DELTA IS ZERO, THEN BOTH DIRECTION COSINES SHOULD BE ZERO.
|br| IF DELTA IS NOT ZERO, THEN AT LEAST ONE DIRECTION COSINE SHOULD BE NONZERO, AND THE NONZERO VALUES SHOULD ALL HAVE THE SAME SIGN.
The error message from subroutine RDPLOT indicates an error in the
``READ PLOT`` input data. The direction cosines entered using ``UAX``,
``VAX``, ``WAX``, ``UDN``, ``VDN``, and ``WDN`` are inconsistent with
one of the following: (1) the lower right-hand corner and upper
left-hand corner specified; (2) the delta across (``DLX``) and delta
down (``DLD``); or (3) the number of points across (``NAX``) and the
number of points down (``NDN``).
KMSG239
\****\* WARNING \****\* K6-239 FOLLOWS:
|br| THE VOLUMES FOR ALL REGIONS ARE NOT SET.
|br| SOME REGION VOLUMES ARE NOT SET BY INPUT, NOT IN THE SPACE FOR WHICH VOLUMES ARE CALCULATED,
|br| MISSED BY THE VOLUME CALCULATION, OR ACTUALLY 0.0. FOR THESE REGIONS, VOLUMES ARE SET TO -1.0
|br| AND THE FLUXES AND FISSION DENSITIES ARE DIVIDED BY -1.0 INSTEAD OF THE REAL VOLUME.
This error message is from subroutine SGGM_VOLUME. If fluxes or other densities are needed,
the real volumes are required. These can be calculated, with some error,
or entered with as much precision as needed and the user knows.
KMSG240
\****\** ERROR \****\*K6-240 FOLLOWS:
|br| GEOMETRY WORD UNIT IS REQUIRED BUT ___ WAS READ INSTEAD.
This error message is from subroutine SGGM_KENOG. Prior to specifying geometry or
media data in the GEOMETRY DATA BLOCK, a unit must be specified.
KMSG241
\****\** ERROR \****\*K6-241 FOLLOWS:
|br| NEUTRON ___ OF GENERATION ___ HAS LEAKED WITHOUT BEING ON THE
|br| SURFACE OF THE BOUNDARY REGION OF UNIT ___ AT
|br| X = ___ Y = ___ Z = ___
|br| U = ___ V = ___ W = ___
This message from subroutine K6_TRACK indicates a history exited the system from
somewhere internal to the geometry. The geometry of the unit at the specified
point should be checked to ensure that it is correctly defined.
KMSG242
\****\** ERROR \****\*K6-242 FOLLOWS:
|br| NEUTRON ___ IN GENERATION ___ HAS LEAKED FROM UNIT ___
|br| AT X = ___ Y = ___ Z = ___
|br| BUT IS STILL WITHIN THE VOLUME DEFINED BY THE UNIT BOUNDARY RECORD.
This error message from subroutines K6_TRACK or ADVANCETRACKTONEXTBOUNDARY
indicates that the specified particle
is inside the volume defined by the unit’s boundary record but is not in any region.
The media record descriptions should be checked for the specified unit.
Also, specifying a screen plot of the problem may help identify the problem.
KMSG243
\****\* ERROR \****\* K6-243 FOLLOWS:
|br| IN UNIT ___ THE BOUNDARY RECORD CONTAINS LABEL ___ WHICH DOES NOT CORRESPOND TO A GEOMETRY RECORD.
This KENO-VI error message from subroutine SGGM_KLANGA indicates that in the
specified unit the boundary record contains a geometry record label that is
not linked to a geometry record in the unit.
KMSG244
\****\* ERROR \****\* K?-244 FOLLOWS:
|br| UNRECOGNIZABLE VOLUME CALCULATION TYPE ___ SPECIFIED
This error message from subroutine RDVOL indicates an invalid input.
TYPE = parameter was encountered in the READ volume data block.
KMSG245
\****\* ERROR \****\* K?-245 FOLLOWS:
|br| UNIT ___ REGION ___ REFERENCES UNIT ___.
|br| AN INSTANCE OF THIS REGION HAS OCCURRED WITHOUT FINDING THE REFERENCED UNIT AT ANY NESTING LEVEL.
This error message from subroutines K5_GEOMETRY or K6_GEOMETRY indicates that the fuel center for
the unit and region printed is specified with respect to the referenced unit,
but the referenced unit could not be found in the geometry. A STOP 245 is
executed in conjunction with this message.
KMSG246
\****\* ERROR \****\* K?-246 FOLLOWS:
|br| THE RESTART FILE WAS A ___ PROBLEM, BUT THE CURRENT PROBLEM IS ___.
|br| THE CURRENT PROBLEM WILL NOT BE RUN
This error message from subroutine PARAM indicates that a restart file to be read
for this problem was either forward or adjoint, which conflicted with what was
specified in the input. Only a forward restart file can be used for a forward
problem, and only an adjoint restart file can be used for an adjoint problem.
KMSG247
\****\* ERROR \****\* K?-247 FOLLOWS:
|br| INVALID KEYWORD ___ IN THE VOLUME INPUT DATA \****\* ERROR \****\*
This error message from subroutine RDVOL indicates the keyword printed
is not valid in the ``READ VOLUME`` data block. See :numref:`8-1-2-13` for
guidance on ``VOLUME`` inputs.
KMSG249
\****\* ERROR \****\* K6-249 FOLLOWS:
|br| UNDEFINED SPACE IN THE REGION CONTAINING HOLE ___.
This error message from subroutine SGGM_TRACE is caused by a unit improperly being
placed in a hole, leaving a gap between crossing into a hole and entering the
unit in the hole. The hole geometry must be checked.
KMSG250
K?-250 EXECUTION TERMINATED ON USER SIGNAL.
This message from subroutines K5_GUIDE or K6_GUIDE indicates that the
user has set the flag to
KENO so that it will not run further generations and wrap up execution.
The flag is set by creating a file named stop_keno in the working directory.
KMSG251
\****\* ERROR \****\* K6-251 FOLLOWS:
|br| INVALID VOLUME CALCULATION TYPE ___
This error message from subroutine SGGM_VOLUME indicates that the variable VCALC
has been overwritten. This indicates a code error.
KMSG253
\****\* ERROR \****\* K6-253 FOLLOWS:
|br| CANNOT SELECT A FACE FOR VOLUME INTEGRATION.
This error message from subroutine SGGM_PATHVOLS indicates an invalid face was
selected for the volume integration. This indicates a code error.
KMSG254
\****\* ERROR \****\* K6-254 FOLLOWS:
|br| THE ANGLE BETWEEN THE Y AXIS AND THE Y EDGE OF THE BASE MUST BE BETWEEN 0 AND 90 DEGREES. CHECK GEOMETRY WORD ___
This KENO-VI error message from subroutine SGGM_RHOMB indicates an invalid angle
has been entered. The angle must be between 0 and 90 degrees.
KMSG256
\****\* ERROR \****\* K6-256 FOLLOWS:
|br| RAY TRACE NUMBER ___ HAS LEAKED FROM UNIT ___
|br| AT X= ___ Y= ___ Z= ___
|br| BUT IS STILL WITHIN THE VOLUME DEFINED BY THE UNIT BOUNDARY RECORD.
This KENO-VI message from subroutine SGGM_TRACE occurs when volumes are calculated
using ray tracing and an undefined region was encountered by a ray.
KMSG257
\****\* ERROR \****\* K6-257 FOLLOWS:
|br| \****\* ERROR \****\* KEYWORD PLACE NOT FOUND FOR ARRAY ___
This KENO-VI error message from subroutine SGGM_ARRAY means an array was
improperly placed within a unit. The keyword ``PLACE``, which should
immediately follow the array's vector definition array, is missing from
the array data. See :numref:`sec-module.keno.geom.array_data` for more information about array
placement.
KMSG258
\****\* ERROR \****\* K6-258 FOLLOWS:
|br| THE CALCULATION WAS TERMINATED BECAUSE A GEOMETRY WORD IN REGION ___ OF UNIT ___ PRODUCES AN IMAGINARY BOUNDARY.
This KENO-VI message from subroutine SGGM_PNTCHK should only be produced by the
geometry word QUADRATIC when used as part of an array boundary. The boundary
produces imaginary results. The coefficients of the geometry word should be
checked.
KMSG259
\****\* ERROR \****\* K6-259 FOLLOWS:
|br| NEUTRON ___ FROM GENERATION ___ LOCATED IN UNIT ___
|br| AT POSITION X = ___ Y = ___ Z = ___
|br| IN ARRAY ___ BOUNDARY UNIT ___ GLOBAL REGION ___
|br| AT BOUNDARY POSITION XARY = ___ YARY = ___ ZARY = ___
|br| HAS A NEGATIVE DISTANCE TO CROSS THE ARRAY BOUNDARY
|br| THIS COULD BE DUE TO AN ARRAY BOUNDARY OVERLAPPING A HOLE.
This message from subroutines K6_TRACK, SGGM_TRACE, or NEWUNITINTERSECTIONTABLE
occurs when a history computes a negative
distance to cross an array boundary when it is inside the array. This can be
caused by the array boundary intersecting a hole, of by round off in computing
the coordinates of the point in the unit containing the array boundary for large
dodecahedral arrays. For the latter case, KENO-VI will silently allow up to
5 such events per generation before giving this message and terminating.
KMSG260
\****\* ERROR \****\* K6-260 FOLLOWS:
|br| NEUTRON ___ FROM GENERATION ___ LOCATED IN UNIT ___
|br| A PARTICLE AT POSITION X = ___ Y = ___ Z = ___
|br| TRAVELING IN DIRECTION U = ___ V = ___ W = ___
|br| TRAVELED___ CM INSIDE HOLE ___ BEFORE CROSSING THE BOUNDARY.
|br| THIS COULD BE DUE TO THE HOLE OVERLAPPING ANOTHER HOLE, UNIT, OR ARRAY BOUNDARY.
This message from subroutines K6_TRACK, SGGM_TRACE, and CROSSINTOAHOLE
occurs when a history checks whether it
is crossing into a hole and finds it is already inside the hole.
KMSG261
\****\* ERROR \****\* K6-261 FOLLOWS:
|br| NEUTRON ___ FROM GENERATION ___ LOCATED IN UNIT ___
|br| A PARTICLE AT POSITION X = ___ Y = ___ Z = ___
|br| TRAVELING IN DIRECTION U = ___ V = ___ W = ___
|br| TRAVELED___ CM OUTSIDE THE UNIT BEFORE CROSSING THE BOUNDARY.
|br| THIS COULD BE DUE TO A HOLE OVERLAPPING THE UNIT BOUNDARY.
This message from subroutines K6_TRACK, SGGM_TRACE, or ADVANCETRACKTONEXTBOUNDARY
occurs when a history goes to check crossing
out of a unit and finds that it does not occur at the unit boundary.
KMSG262
\****\* ERROR \****\* K6-262 FOLLOWS:
|br| NEUTRON ___ FROM GENERATION ___ LOCATED IN UNIT ___
|br| A PARTICLE AT POSITION X = ___ Y = ___ Z = ___
|br| TRAVELING IN DIRECTION U = ___ V = ___ W = ___
|br| IS OUTSIDE THE ARRAY BOUNDARY WITHOUT CROSSING OUT OF THE ARRAY
|br| THIS COULD BE DUE TO A HOLE OVERLAPPING THE ARRAY BOUNDARY.
This message from subroutine SGGM_CRSARA occurs when a history computes a negative
distance to cross an array boundary when it is inside the array. This can be
caused by the array boundary intersecting a hole.
KMSG263
\****\* ERROR \****\* K6-263 FOLLOWS:
|br| MULTIPLY DEFINED POINT - LL = ___ X = ___ Y = ___ Z = ___
This KENO-VI message from subroutine SGGM_TRACE indicates incorrect sector definitions in unit LL at point X, Y, Z.
KMSG264
\****\* ERROR \****\* K6-264 FOLLOWS:
|br| HOLE ___ NOT DEFINED IN REGION ___
This message from subroutine SGGM_TRACE indicates incorrect geometry
specification of holes. See :numref:`sec-module.keno.geom.holes` for more information on
the correction specification of ``HOLE``\ s.
KMSG265
\****\* ERROR \****\* K6-265 FOLLOWS:
|br| BOUNDARY SECTOR DATA WAS NOT FOUND FOR UNIT ___
This KENO-VI message from subroutine SGGM_BNDRY indicates that the region
definition vector for the unit is missing in the input.
KMSG266
\****\* ERROR \****\* K6-266 FOLLOWS:
|br| A VECTOR DEFINITION ARRAY IN UNIT ___ REFERENCES GEOMETRY RECORD ___ WHICH HAS NOT BEEN SPECIFIED.
This KENO-VI message from subroutine SGGM_KLANGA indicates that a region definition
vector in the unit references an undefined geometry input record.
KMSG267
\****\* ERROR \****\* K6-267 FOLLOWS:
|br| IN UNIT ___ THE USE OF GEOMETRY LABEL ___ IN THE BOUNDARY DEFINITION VECTOR
|br| CONFLICTS WITH VECTOR DEFINITON GEOMETRY LABEL ___
This KENO-VI message from subroutine SGGM_KLANGA indicates that a geometry word
referenced in a region definition vector in the unit defines the region to
be on the wrong side of the unit boundary (the same geometry record is
referenced with opposite signs).
KMSG268
\****\* ERROR \****\* K6-268 FOLLOWS:
|br| INVALID KEYWORD ___ IN THE VOLUME INPUT FILE
This self-explanatory message is from subroutine SGGM_GTVOLS, and it occurs
when reading a separate volume file. See :numref:`8-1-2-13` for more information
regarding the volume input file.
KMSG269
\****\* ERROR \****\* K6-269 FOLLOWS:
|br| FOR UNIT NUMBER ___ TOO MANY MEDIA ENTRIES WERE SPECIFIED.
This KENO-VI error message results from subroutine SGGM_GTVOLS, and it indicates
that the separate volume file is inconsistent with the geometry input.
KMSG270
\****\* ERROR \****\* K6-270 FOLLOWS:
|br| CYLINDERS/ECYLINDERS/CONES IN THE GLOBAL UNIT BOUNDARY DEFINITION VECTOR
|br| NEED TO BE ORIENTED ALONG A MAJOR AXIS.
This KENO-VI message from subroutine SGGM_VOLCUB indicates that a bounding cuboid
for the global unit cannot be calculated because one of the referenced bodies
has been rotated off axis. The user can bypass this message by specifying a
bounding cuboid in the input in the VOLUME data block.
KMSG271
\****\* ERROR \****\* K6-271 FOLLOWS:
|br| THE FIRST NON-NEGATIVE BODY SPECIFIED IN THE BOUNDARY DEFINITION VECTOR OF THE
|br| GLOBAL UNIT MUST SPECIFY FINITE VOLUME BODY.
This KENO-VI message from subroutine SGGM_VOLCUB indicates that a bounding cuboid
for the global unit cannot be calculated because the first body in the boundary
definition vector does not define a finite volume body. The user can
bypass this message by specifying a bounding cuboid in the input in the
VOLUME data block.
KMSG273
\****\* ERROR \****\* K?-273 FOLLOWS:
|br| THE NUMBER OF GROUPS ON THE RESTART LIBRARY DOES NOT MATCH WHAT WAS SET PREVIOUSLY.
|br| THE NUMBER OF GROUPS SET PREVIOUSLY ___
|br| THE NUMBER OF GROUPS FROM THE RESTART UNIT ___
This self-explanatory message from subroutine READ_MIXED_XSECS indicates
an inconsistency between the number of groups for cross sections on the
restart unit and the number of groups specified elsewhere.
KMSG274
\****\* ERROR \****\* K?-274 FOLLOWS:
|br| ___ ERROR(S) OCCURED WHILE READING ___. THE MESSAGES RECEIVED FROM ___ INPUT PROCESSOR ARE AS FOLLOWS:
This error message comes from subroutines READ_DEFINITIONS_INPUT,
READ_STARMESH_INPUT, or MGRID type's CHECKGRIDDATA procedure, and it
indicates an error in specifying the mesh grid for the problem.
See :numref:`8-1-2-14` for more information about the specification
of the mesh grid geometry.
KMSG275
\****\* ERROR \****\* K?-275 FOLLOWS:
|br| ADJOINT SOLUTIONS ARE CURRENTLY NOT AVAILABLE IN CONTINUOUS ENERGY PROBLEMS.
|br| IF ADJOINT SOLUTION IS DESIRED, THE USER SHOULD CHOOSE THE MULTIGROUP ENERGY TREATMENT
This message from subroutine DATAIN indicates the user turned on adjoint
calculation (see parameter ``ADJ`` in :numref:`sec-module.keno.parameters`) for a continuous
energy problem. The current version of KENO does not have adjoint
continuous energy cross sections. If adjoint solution is desired, the
user should choose the multigroup energy treatment.
KMSG276
\****\* ERROR \****\* K?-276 FOLLOWS:
|br| DIFFERENTIAL ALBEDOS ARE CURRENTLY NOT AVAILABLE IN CONTINUOUS ENERGY PROBLEMS.
This message from subroutine DATAIN indicates the user entered
differential albedos for a continuous energy problem. The current
version of KENO does not have differential albedos for continuous
energy treatment. The user should replace the albedo data with appropriate materials.
KMSG277
\****\* ERROR \****\* K6-277 FOLLOWS:
|br| THE UNIT ___ BOUNDARY RECORD CONTAINS MORE THAN ONE POSITIVE GEOMETRY RECORD LABEL
This KENO-VI message from subroutine SGGM_JOMCHK indicates that the
unit reported has multiple geometry records defining the boundary.
This unit is used in an array, so it is only allowed one boundary
geometry record.
KMSG278
\****\* ERROR \****\* K6-278 FOLLOWS:
|br| TOO MANY ERRORS TRACING THROUGH THE GEOMETRY WHILE INTEGRATING VOLUMES.
This self-explanatory message is from subroutine SGGM_PATHVOLS, and it
indicates that the problem is terminated because of errors. There
should be error messages before this indicating what the problems are.
Errors should be corrected and the problem resubmitted.
KMSG280
\****\* ERROR \****\* K6-280 FOLLOWS:
|br| ERROR IN PERIODIC BOUNDARY CONDITION - DENOMINATOR 0
|br| A = ___ B = ___ C = ___ D = ___ E = ___
|br| F = ___ G = ___ H = ___ I = ___ J = ___
|br| U = ___ V = ___ W = ___
|br| X = ___ Y = ___ Z = ___
This KENO-VI error message comes from subroutine PERIOD, and it
indicates the problem with periodic boundary conditions. A-J are the
coefficients of the relevant quadratic equation, U-W are the direction
cosines, and X-Z is the point on the boundary. The denominator is
AU\ :sup:`2`\ +BV\ :sup:`2`\ +CW\ :sup:`2`\ +DUV+EUW+FVW.
KMSG283
\****\* ERROR \****\* K?-283 FOLLOWS:
|br| USER DID NOT PROVIDE A CROSS SECTION DIRECTORY FILE (CE_XXXX).
|br| A DIRECTORY FILE THAT CONTAINS THE DATA PATH AND THE CROSS SECTION ID RECORDS MUST BE PROVIDED.
This message from subroutines NUCLIDE_SETUP or PREMIX_SETUP indicates that the
filename specified in the library name record is not valid (i.e., the file does
not exist in the working directory) for calculations in the continuous energy mode.
Links to SCALE-provided libraries are automatically created in the working directory.
If one of the default files is being used, the file may not be accessible
due to network problems, or access permissions. If it is a user-supplied
directory file, it should be verified to exist in the SCALE temporary
working directory.
KMSG287
\****\* ERROR \****\* K?-287 FOLLOWS:
|br| OUTGOING ANGLE COSINE ___ IS GREATER THAN 1
This message from subroutine ROTASZ indicates a problem with the angle
cosine when calculating the particle velocity in the continuous energy
mode. This error usually indicates a coding error. Please contact
scalehelp@ornl.gov.
KMSG288
\****\* ERROR \****\* K?-288 FOLLOWS:
|br| SAMPLING PROBABILITY TABLE FOR NUCLIDE:___
|br| ENERGY (EV): ___
This message from subroutine CETRANSPORT_TOTAL_XS_FROM_PTABLE is issued
if the energy of the
particle that is being tracked is higher than the maximum energy of the
probabilities available in the probability table that is being sampled.
This error may be due to data problems. Please contact scalehelp@ornl.gov.
KMSG290
\****\* WARNING \****\* K?-290 FOLLOWS:
|br| COULD NOT FIND TEMP:___ ON CROSS SECTION FILE. USING CLOSEST TEMPERATURE:___
This warning message from subroutine READ_XSEC is issued to indicate
that the temperature selected was not found for the current nuclide and
the continuous energy cross sections that are at the closest temperature
will be used. This should only be issued with ``DBX=0``, so the user
has disabled problem-dependent Doppler broadening. See :numref:`sec-module.keno.parameters` or
:numref:`8-1-6-2-10` for more information.
KMSG292
\****\* ERROR \****\* K?-292 FOLLOWS:
|br| PROBLEM IN SUBROUTINE SAMPLE_COLLISION AT:
|br| NEUTRON: ___
|br| IZA: ___
|br| MT: ___
|br| EIN: ___
|br| MINIMUM ENERGY:___
|br| MAXIMUM ENERGY:___
|br| LOCATION:___
This message from subroutine SAMPLE_COLLISION indicates the energy of the
particle being tracked is outside the energy range of the selected reaction
for the selected nuclide. The code will reset the particle's energy to
correspond to one of the boundaries and will continue tracking. If this
message is issued, it usually indicates a problem with the continuous
energy cross sections. The problem is usually not severe and may be the
result of round off. Please contact scalehelp@ornl.gov.
KMSG293
\****\* ERROR \****\* K?-293 FOLLOWS:
|br| PROBLEM IN SUBROUTINE SAMPLE_ENERGY AT:
|br| MT: ___
|br| EIN: ___
|br| EOUT: ___
|br| LOCATION:___
This message from subroutines SAMPLE_COLLISION or SAMPLE_BETA indicates the energy of
the particle being tracked is outside the energy range of the selected
reaction for the selected nuclide. If this message is issued, it usually
indicates a problem with the continuous energy cross sections. Please
contact scalehelp@ornl.gov.
KMSG294
\****\* WARNING \****\* K?-294 FOLLOWS:
|br| UNIT ___ REGION ___ CONTAINS FISSIONABLE MATERIAL, BUT NO FISSIONS OCCURRED IN IT.
|br| THIS MAY MEAN THE PROBLEM WAS INADEQUATELY SAMPLED.
This message from subroutine KEDIT indicates some of the fissile regions are
not adequately sampled. Depending on the problem, the calculated keff value
may be too small. The problem should be run again with enough histories or
start data to ensure that all regions are sampled adequately.
KMSG295
\****\* WARNING \****\* K?-295 FOLLOWS:
|br| THERE WERE ___ COLLISIONS THAT PRODUCED A NEUTRON WITH AN ENERGY OUTSIDE THE GROUP STRUCTURE YOU SELECTED.
|br| THESE WERE TALLIED INTO THE APPROPRIATE END GROUP.
|br| IF YOU WISH TO SEPARATE THESE NEUTRONS, ADD A GROUP ON EACH END WITH LIMITS CORRESPONDING TO THE CROSS SECTIONS.
This warning message from subroutine SAMPLE_ENERGY indicates the energy
boundaries of the groups specified for tallying in the continuous energy
mode does not cover the possible energy ranges of all reactions for all
nuclides in the problem. Group energy boundaries must be adjusted.
KMSG296
\****\* ERROR \****\* K?-296 FOLLOWS:
|br| IT IS NOT POSSIBLE TO TURN OFF WRITING ARRAYS TO DIRECT ACCESS IN WRTICE.
This error message from subroutine WRITE_ICE indicates that the arrays must be
saved in the direct access file.
KMSG297
\****\* ERROR \****\* K?-297 FOLLOWS:
|br| ENERGY BOUNDARIES MUST BE IN DESCENDING ORDER (EV). EB (___) = ___ IS GREATER THAN EB (___) = ___.
This error message from subroutine RDENER indicates the upper energy boundaries
specified in the ENERGY data block are not in descending order. The upper
energy boundary of the highest energy group (i.e., group 1) must be
specified first and then successive energy groups with descending upper
energy group boundaries must be specified until all groups are specified.
KMSG298
\****\* ERROR \****\* K?-298 FOLLOWS:
|br| CROSS SECTION FILE FOR NUCLIDE ___ HAS NO 2-D KINEMATICS DATA FOR THERMAL RANGE. THIS IS OK IF FREEGAS TREATMENT IS NOT TURNED OFF.
|br| FOR THIS PROBLEM, FREEGAS TREATMENT HAS BEEN TURNED OFF (FRE=NO IN PARAMETER DATA BLOCK).
|br| EITHER PROVIDE DATA THAT CONTAINS 2-D KINEMATICS FOR THERMAL RANGE OR TURN ON FREEGAS TREATMENT.
This message from subroutine READ_KINEMATICS indicates that no thermal
scattering has been specified for the given nuclide. Data must be provided or
free-gas scattering must be allowed.
KMSG299
\****\* ERROR \****\* K?-299 FOLLOWS:
|br| INVALID KEYWORD ___ IN THE ENERGY BOUNDARIES INPUT DATA.
This message from subroutine RDENER says that an invalid keyword was read
while reading the energy boundaries for a continuous energy problem. The
energy data block must be checked to correct the error. See :numref:`8-1-2-12`
for more information.
KMSG300
\****\* ERROR \****\* K?-300 FOLLOWS:
|br| INVALID THERMAL CUTOFF VALUE ___ IN THE PARAMETERS BLOCK. THE CUTOFF VALUE MUST BE GREATER THAN ZERO.
The thermal cutoff value for a continuous energy problem must be greater than
zero. The data must be corrected, and the problem rerun.
KMSG304
K?-304 ALTHOUGH THE STANDARD DEVIATION SPECIFIED FOR THE PROBLEM IS ACHIEVED,
AT LEAST 50 OR NSK*2=___ ACTIVE GENERATIONS HAVE NOT BEEN RUN. EXECUTION WILL CONTINUE.
This message from GUIDE indicates that although the standard deviation
asked for in the input has been achieved, too few generations have been
run to get a fair value for the standard deviation, and more generations
will be run.
KMSG305
\****\* ERROR \****\* K6-305 FOLLOWS:
|br| MESH FLUXES HAVE BEEN SPECIFIED, BUT THE MESH DOES NOT COMPLETELY COVER THE GEOMETRY.
|br| THE POINT X=___ Y=___ Z=___ LIES OUTSIDE THE MESH.
|br| THE PROBLEM WILL NOT BE RUN. FIX THE MESH AND RESUBMIT THE CASE.
This self-explanatory message comes from subroutines ACCUMULATETEMPVOLUMES and
from PNTVOLS.
KMSG306
\****\* ERROR \****\* K?-306 FOLLOWS:
|br| UNIT ___ HAS BEEN DEFINED ___ TIMES.
|br| THIS BEHAVIOR IS NO LONGER ALLOWED AS IT COULD POTENTIALLY MISLEAD THE USERS.
|br| NOTE THAT DEFINING UNITS THAT ARE NOT USED IN THE PROBLEM IS STILL ALLOWED.
|br| IF DUPLICATE UNITS ARE KEPT FOR CONVENIENCE (E.G., SCOPING CALCULATIONS), THEN
|br| SIMPLY USE A UNIT NUMBER THAT IS UNIQUE AND IS NOT UTILIZED IN THE PROBLEM.
|br| THE PROBLEM WILL NOT BE RUN. REMOVE DUPLICATE DEFINITIONS AND RESUBMIT.
This self-explanatory message comes from subroutines K5GM_READGM and SGGM_READGM.
KMSG307
\****\* ERROR \****\* K?-307 FOLLOWS:
|br| INVALID KEYWORD ___ IN THE REACTIONS INPUT DATA.
This message comes from subroutine READ_REACTIONS_INPUT, and indicates that an
invalid keyword was entered in the input. See :numref:`8-1-2-15` for valid
reaction block input. The data must be corrected, and the problem resubmitted.
KMSG308
\****\* ERROR \****\* K?-308 FOLLOWS:
|br| THE USER ENTERED ___ FOR THE ___ NUMBER.
|br| ONLY LEGAL NUMBERS (>0) AND * (WILDCARD) ARE ALLOWED. THE PROBLEM WILL NOT BE RUN.
This message results from subroutine READENTRY, and it indicates invalid
reaction input. See :numref:`8-1-2-15` for valid reaction block input;
data must be corrected and resubmitted.
KMSG309
\****\* ERROR \****\* K?-309 FOLLOWS:
|br| REACTION TALLY CALCULATIONS ARE CURRENTLY ALLOWED FOR ONLY CE TRANSPORT.
This self-explanatory message printed by subroutine
READ_REACTIONS_INPUT indicates that reaction tally
calculations were requested when running KENO with
multigroup transport mode. Currently, this
capability is only available with continuous-energy
transport mode.
KMSG312
\****\* ERROR \****\* K?-312 FOLLOWS:
|br| OBSOLETE PARAMETER (CXM). USE REACTION DATA BLOCK TO SPECIFY PARAMETERS FOR REACTION TALLY CALCULATIONS.
This self-explanatory message printed by subroutine
PARAM indicates that ``CXM`` is no longer supported
as a *user parameter*.
KMSG313
\****\* ERROR \****\* K?-313 FOLLOWS:
|br| INVALID COMPUTATIONAL MODE (CXM=___) FOR TALLYING REACTION CROSS SECTIONS FOR CE-DEPLETION.
|br| AVAILABLE MODES ARE:
|br| (1) ALL REACITONS, NGP GROUP,
|br| (2) TRANSMUATION REACTIONS, NGP GROUP,
|br| (3) ALL REACTIONS, 1 GROUP,
|br| (4) TRANSMUTATION REACTIONS, 1 GROUP.
This self-explanatory message printed by subroutine
TESTREACTIONFLAGS indicates that invalid ``CXM`` parameter
was provided by the sequence that runs KENO. This rare case
might be encountered if the KENO restart file is corrupted.
This error should be reported to scalehelp@ornl.gov.
KMSG314
\****\* ERROR \****\* K?-314 FOLLOWS:
|br| NO MESH FOUND FOR ___. A MESH GRID MUST BE DEFINED EITHER WITH THE PARAMETER MSH IN PARAMETER INPUT
|br| OR WITH A GRID SPECIFIED IN GRIDGEOMETRY DATA INPUT.
This self-explanatory message printed by subroutine
ASSIGNGRIDTOMESHQUANTITY indicates that no mesh
was entered with any input methods. The
mesh quantity was activated with either
``CDS=yes``, ``GFX=yes``, ``FIS=yes``, or
``MFX=yes`` parameters, but a mesh was not defined
either with parameter ``MSH`` in the ``parameter data``
block or in the ``gridgeometry data`` block.
The user should define a mesh using either input method
for the tally requested and rerun the calculation.
KMSG315
\****\* ERROR \****\* K?-315 FOLLOWS:
|br| MESH < ___ > SPECIFIED FOR ___ IS NOT FOUND IN INPUT.
This self-explanatory message is printed by subroutine
ASSIGNGRIDTOMESHQUANTITY. It indicates that the mesh
assigned to the mesh quantity activated with either
``CDS``, ``GFX``, ``FIS``, or ``MFX`` parameters was
not entered in the ``gridgeometry data`` block.
The user should either correct the mesh assignment or
define a mesh for the tally requested, and then rerun
the calculation.
KMSG316
\****\* WARNING \****\* K?-316 FOLLOWS:
|br| NO MESH PROVIDED FOR SOURCE CONVERGENCE DIAGNOSTICS (SCD). CONTINUE WITH DEFAULT MESH.
This self-explanatory message is printed by subroutine
SETUPMESHPOINTERS if no mesh was assigned to Shannon
entropy tally used for fission source convergence
diagnostics tests with parameter ``SCD`` in the
``parameter data`` input block. KENO constructs
a DEFAULT mesh and tally fission points on this mesh
for Shannon entropy calculations.
KMSG319
\****\* WARNING \****\* K?-319 FOLLOWS:
|br| CFP WAS EITHER NOT SPECIFIED OR A NON-POSITIVE VALUE WAS ENTERED!
|br| THE CE TSUNAMI IFP METHOD REQUIRES A POSITIVE NUMBER OF LATENT GENERATIONS.
|br| CFP=5 WILL BE USED FOR THIS CALCULATION.
KMSG320
\****\* WARNING \****\* K?-320 FOLLOWS:
|br| CFP>10 DETECTED! THIS CE TSUNAMI IFP RUN MAY PRODUCE A LARGE MEMORY FOOTPRINT!
KMSG321
\****\* WARNING \****\* K?-321 FOLLOWS:
|br| CFP<0 DETECTED! AN F*(R) MESH WILL NOT BE USED FOR THIS CALCULATION.
|br| THIS CE TSUNAMI CLUTCH CALCULATION MAY NOT PRODUCE ACCURATE SENSITIVITIES.
KMSG322
\****\* ERROR \****\* K?-322 FOLLOWS:
|br| CFP IS GREATER THAN THE NUMBER OF ACTIVE GENERATIONS! CE TSUNAMI IFP SENSITIVITY
|br| TALLIES WILL NOT BE PERFORMED. CFP SHOULD BE << THE NUMBER OF ACTIVE GENERATIONS.
KMSG323
\****\* ERROR \****\* K?-323 FOLLOWS:
|br| CFP IS GREATER THAN THE NUMBER OF INACTIVE GENERATIONS!
|br| CE TSUNAMI F*(R) TALLIES CANNOT BE PERFORMED. CFP SHOULD BE << THE NUMBER OF INACTIVE GENERATIONS.
KMSG324
\****\* ERROR \****\* K?-324 FOLLOWS:
|br| NO F*(R) MESH GRID WAS SPECIFIED!
KMSG325
\****\* WARNING \****\* K?-325 FOLLOWS:
|br| ONLY ___ PARTICLE HISTORIES ARE BEING USED TO POPULATE F*(R) TALLIES
|br| PER F*(R) MESH INTERVAL. THIS MAY LEAD TO POORLY-CONVERGED F*(R) ESTIMATES
|br| AND INACCURATE SENSITIVITY COEFFICIENTS! AT LEAST 10-100 INACTIVE PARTICLE
|br| HISTORIES SHOULD BE SIMULATED PER MESH INTERVAL TO OBTAIN ACCURATE F*(R) SCORES.
KMSG326
\****\* ERROR \****\* K?-326 FOLLOWS:
|br| THE CE TSUNAMI IFP METHOD CANNOT BE EXECUTED IN PARALLEL.
This self-explanatory message is printed by subroutine
INITIALIZE_SENSITIVITIES if CE TSUNAMI calculation
with IFP sensitivity method was run in parallel. Execution
is immediately terminated since MPI parallelism is
not available with IFP sensitivity method.
KMSG327
\****\* WARNING \****\* K?-327 FOLLOWS:
|br| USER SET MAP-TO-UNION (M2U) TO ON.
|br| DOPPLER BROADENING IS ON BY DEFAULT (DBX=2), BUT CANNOT FUNCTION WITH MAP-TO-UNION.
|br| DOPPLER BROADENING HAS BEEN DISABLED.
This self-explanatory message is printed by subroutine
PARAM if ``M2U=yes`` and ``DBX=2`` were set together.
Note that ``DBX`` parameter is defaulted to 2; therefore,
entering only ``M2U=yes`` also satisfies the condition
that controls emitting this message. For such a case,
KENO disables the Doppler Broadening temperature
correction calculations when loading the nuclide
cross section data in continuous-energy mode and
continues the calculation. If data at the actual
problem temperature are required in the calculations
for a more realistic modeling, then it is recommended
that the map-to-union capability be disabled by entering
``M2U=no``.
KMSG328
\****\* ERROR \****\* K?-328 FOLLOWS:
|br| NO SOURCE ENTROPY CALCULATIONS! ALL FISSION SOURCE POINTS ARE OUTSIDE THE USER-DEFINED MESH.
This self-explanatory message is printed by subroutine
MESHSRCTEST if no fission points were tallied on the
user-defined mesh for three consecutive generations.
This results in 0.0 entropy values for these generations.
These results indicate that user-defined mesh covers only
a part of geometry; i.e., the fissile regions are not
covered properly with the user-defined mesh. Therefore,
execution is terminated with this error message. To obtain
better diagnostics information for the fission source
convergence, it is highly recommended to define a mesh
grid for Shannon entropy tally, and to be sure that
defined mesh grid covers all fissile regions.
KMSG329
\****\* ERROR \****\* K?-329 FOLLOWS:
|br| NO SOURCE ENTROPY CALCULATIONS! ALL FISSION SOURCE POINTS ARE SCORED IN THE SAME MESH VOXEL.
|br| USER-DEFINED MESH FOR SOURCE CONVERGENCE DIAGNOSTICS DOES NOT ENCLOSE THE FISSILE REGIONS PROPERLY.
This self-explanatory message is printed by subroutine
MESHSRCTEST if all fission points were tallied in a
single mesh voxel for three consecutive generations.
This results in 0.0 entropy values for these generations.
These results indicate that the user-defined mesh does not
enclose the fissile regions properly. Therefore,
execution is terminated with this error message. To obtain
better diagnostics information for the fission source
convergence, it is highly recommended to define a mesh
grid for Shannon entropy tally, and to be sure that
defined mesh grid covers all fissile regions.
KMSG330
\****\* WARNING \****\* K?-330 FOLLOWS:
|br| DISABLING SOURCE ENTROPY CALCULATIONS. ALL FISSION SOURCE POINTS ARE SCORED IN THE SAME MESH VOXEL.
|br| THE DEFAULT MESH FOR SOURCE CONVERGENCE DIAGNOSTICS DOES NOT ENCLOSE THE FISSILE REGIONS PROPERLY.
This self-explanatory message from subroutine MESHSRCTEST
indicates that for three consecutive generations, all fission
points were tallied in a single mesh voxel; therefore, entropy
for these three generations was calculated as 0.0. For such
a case, KENO disables the Shannon entropy calculations and
source convergence diagnostics tests and continues calculation.
The default mesh constructed by KENO ideally covers the
geometry completely. This result implies that either all
fissile regions are confined in a single mesh voxel
(i.e., fissile regions are relatively small compared
with the entire problem geometry), or fissile regions
are weakly coupled, and source neutrons have been started
in one side. To obtain better diagnostics information for
the fission source convergence, it is highly recommended
to define a mesh grid for Shannon entropy tally, and to
be sure that defined mesh grid covers the entire fissile
regions.
KMSG331
\****\* WARNING \****\* K?-331 FOLLOWS:
|br| ALL FISSION SOURCE POINTS ARE OUTSIDE OF THE USER-DEFINED MESH.
This self-explanatory message is printed by subroutine MESHSRCTEST
if none of the fission points have been tallied on
the user-defined mesh for the current generation. This indicates
that user-defined mesh does not cover the problem geometry
completely (especially all fissile regions), and Shannon entropy
for the current generation is calculated as 0.0. Although the
same message may not be printed for other generations if there
are some fission points scored on this mesh, this does
not change the fact that the mesh was not defined properly for
Shannon entropy calculations. This will result in incorrect
interpretation of the fission source convergence tests.
KMSG332
\****\* WARNING \****\* K?-332 FOLLOWS:
|br| MESH FLUXES HAVE BEEN SPECIFIED, BUT CE TSUNAMI DOES NOT ALLOW MESH FLUX USAGE.
|br| CONTINUE CALCULATIONS WITH DISABLING MESH FLUXES.
KMSG333
\****\* ERROR \****\* K?-333 FOLLOWS:
|br| THE NUMBER OF GENERATIONS SKIPPED MUST BE LESS THAN THE NUMBER OF GENERATIONS TO BE RUN.
|br| NSK=___ - GEN=___.
|br| THE CASE WILL NOT BE RUN.
This self-explanatory message from subroutine PARAM
indicates that the number of generations to be run (``GEN``)
is always greater than the number of generations skipped
(``NSK``). If only ``GEN`` is entered in the parameter data
block, then its value must be greater than the default
``NSK`` value, which is 3. If only ``NSK`` is entered in the
parameter data block, then its value must be less than the
default ``GEN`` value, which is 203.
KMSG334
\****\* ERROR \****\* K?-334 FOLLOWS:
|br| UNABLE TO CREATE A WEIGHTED LIBRARY. CODE COULD NOT INITIALIZE AMPX WORKING LIBRARY
|br| TO WRITE REACTION CROSS SECTIONS IN CE DEPLETION CALCULATIONS.
CE DEPLETION CALCULATIONS WILL BE TERMINATED.
Internal code error when running KENO as part of TRITON sequence.
This error should be reported to scalehelp@ornl.gov.
KMSG335
\****\* ERROR \****\* K?-335 FOLLOWS:
|br| UNABLE TO ADD NUCLIDE ___ TO THE WEIGHTED LIBRARY.
CE DEPLETION CALCULATIONS WILL BE TERMINATED.
Internal code error when running KENO as part of TRITON sequence.
This error should be reported to scalehelp@ornl.gov.
KMSG336
\****\* ERROR \****\* K?-336 FOLLOWS:
|br| UNABLE TO GET NEUTRON 1D CROSS SECTION FOR THE REACTION, MT=___.
CE DEPLETION CALCULATIONS WILL BE TERMINATED.
Internal code error when running KENO as part of TRITON sequence.
This error should be reported to scalehelp@ornl.gov.
KMSG337
\****\* ERROR \****\* K?-337 FOLLOWS:
|br| UNABLE TO CREATE A NEUTRON 1D CROSS SECTION FOR THE WEIGHTING LIBRARY.
CE DEPLETION CALCULATIONS WILL BE TERMINATED.
Internal code error when running KENO as part of TRITON sequence.
This error should be reported to scalehelp@ornl.gov.
KMSG338
\****\* ERROR \****\* K?-338 FOLLOWS:
|br| ERROR OCCURED WHILE WRITING WEIGHTED LIBRARY, RETURN CODE=___.
CE DEPLETION CALCULATIONS WILL BE TERMINATED.
Internal code error when running KENO as part of TRITON sequence.
This error should be reported to scalehelp@ornl.gov.
KMSG339
\****\* ERROR \****\* K?-339 FOLLOWS:
|br| UNABLE TO INITIALIZE OBJECT FOR ENERGY BOUNDS FOR THE WEIGHTING LIBRARY.
CE DEPLETION CALCULATIONS WILL BE TERMINATED.
Internal code error when running KENO as part of TRITON sequence.
This error should be reported to scalehelp@ornl.gov.
KMSG340
\****\* ERROR \****\* K?-340 FOLLOWS:
|br| UNABLE TO INITIALIZE HEADER OBJECT FOR THE WEIGHTING LIBRARY.
CE DEPLETION CALCULATIONS WILL BE TERMINATED.
Internal code error when running KENO as part of TRITON sequence.
This error should be reported to scalehelp@ornl.gov.
KMSG341
\****\* ERROR \****\* K?-341 FOLLOWS:
|br| DATA ENTERED TO THE REACTION BLOCK WITHOUT CALCULATION MODE.
CALCULATION MODE SHOULD BE ENTERED
|br| IN REACTION BLOCK WITH ONE OF THE FOLLOWING KEYWORDS:
(1) XS/XSTALLY=YES, (2) RX/RRTALLY=YES, (3) CEDEPL=YES, AND/OR, (4) MIXFLX=YES.
This continuous-energy--specific self-explanatory message
is printed by subroutine
READ_REACTIOS_INPUT if the data entered in
``reaction data`` block do not include any information
for the calculation mode. The valid keywords to set
the calculations modes are ``XS`` or ``XSTALLY`` for
micro reaction cross section calculations, ``RX`` or
``RRTALLY`` for reaction tally calculations, ``CEDEPL``
for both mixture flux and reaction cross section
calculations, and ``MIXFLX`` for mixture flux calculations.
At least one of the listed calculation modes above must be
entered for a successful calculation.
KMSG342
\****\* WARNING \****\* K?-342 FOLLOWS:
|br| REACTION BLOCK IS CURRENTLY ALLOWED FOR ONLY CE TRANSPORT.
SKIP READING DATA FROM REACTION BLOCK.
This self-explanatory message is printed by subroutine
READ_REACTIOS_INPUT if a ``reaction data`` block was
entered in a multigroup problem. The ``reaction data``
block will not function when KENO is run in multigroup
mode. Use KMART5 or KMART6 to generate reaction
rates when running KENO in multigroup mode.
KMSG346
\****\* ERROR \****\* K?-346 FOLLOWS:
|br| ERROR IN MIXTURE ENTRY IN REACTION BLOCK. MIXTURE NUMBER (MIX=___)
SPECIFIED IN REACTION BLOCK IS NOT USED IN THE PROBLEM.
This self-explanatory message is printed by CHECKDATA procedure of
REACTIONFILTERS type if the user set up a reaction filter for a non-existing MIXTURE
in the problem.
KMSG347
\****\* ERROR \****\* K?-347 FOLLOWS:
|br| ERROR IN NUCLIDE ENTRY IN REACTION BLOCK. NUCLIDE ___[MIXTURE = ___] SPECIFIED IN REACTION BLOCK
|br| IS NOT FOUND IN THE MIXING TABLE.
This self-explanatory message is printed by CHECKDATA procedure of
REACTIONFILTERS if the user set up a reaction filter with a NUCLIDE and MIXTURE
pair where the MIXTURE does not contain this NUCLIDE. Defining
a reaction filter with non-existing nuclide results in a code
termination.
KMSG348
\****\* WARNING \****\* K?-348 FOLLOWS:
|br| SPECIFIED REACTION IS NOT AVAILABLE IN CE DATA LIBRARY FOR THE GIVEN NUCLIDE.
|br| PERFORM REACTION TALLY CALCULATIONS BY SKIPPING THIS REACTION MT=___ FOR THE GIVEN NUCLIDE, ___.
This message is printed by CHECKDATA procedure of
REACTIONFILTERS if the nuclide reaction data requested by the NUCLIDE and MT pairs
have not been found in the continuous-energy data library. Note that
KENO loads 1D neutron reaction data for all nuclides defined in
the problem (MT < 150). This message implies that these reaction
data are not a valid reaction for the given nuclide; therefore,
it is not provided as part of ENDF data, and it is also not included
in the AMPX processed continuous-energy data libraries.
If data for this nuclide reaction exist in ENDF and the nuclide
cross section file being used is a standard file that is part of
an official and current SCALE system, then potentially please contact
scalehelp@ornl.gov.
KMSG349
\****\* WARNING \****\* K?-349 FOLLOWS:
|br| A CE TSUNAMI F*(R) MESH PRINT (FST=YES) WAS REQUESTED BUT AN F*(R) MESH IS NOT BEING USED.
KMSG350
\****\* ERROR \****\* K?-350 FOLLOWS:
|br| A FISSION NEUTRON WAS BORN OUTSIDE OF THE F*(R) MESH AT POSITION:
|br| X =___ Y =___ Z =___
|br| THE F*(R) MESH MUST ENCOMPASS ALL FISSILE MATERIAL IN THE SYSTEM.
KMSG351
\****\* ERROR \****\* K?-351 FOLLOWS:
|br| MISSING REACTION MT SPECIFICATION IN REACTION BLOCK (MT).
This message is printed by subroutine READ_REACTIONS_INPUT for only continuous-energy
calculations. It indicates that reaction MT was not defined in one of the reactions
filter entries. See :numref:`8-1-2-15` for valid reaction block input.
The data must be corrected, and the problem resubmitted.
KMSG352
\****\* ERROR \****\* K?-352 FOLLOWS:
|br| MISSING NUCLIDE SPECIFICATION IN REACTION BLOCK (NUC).
This message is printed by subroutine READ_REACTIONS_INPUT for only continuous-energy
calculations. It indicates that nuclide(s) were not defined in one of the reactions
filter entries. See :numref:`8-1-2-15` for valid reaction block input.
The data must be corrected, and the problem resubmitted.
KMSG353
\****\* ERROR \****\* K?-353 FOLLOWS:
|br| MISSING MIXTURE SPECIFICATION IN REACTION BLOCK (MIX).
This message is printed by subroutine READ_REACTIONS_INPUT for only continuous-energy
calculations. It indicates that mixture(s) were not defined in one of the reactions
filter entries. See :numref:`8-1-2-15` for valid reaction block input.
The data must be corrected, and the problem resubmitted.
KMSG354
\****\* ERROR \****\* K?-354 FOLLOWS:
|br| ERROR IN REACTION BLOCK. NUMBER OF ENERGY GROUPS (___) AND ENERGY BOUNDS (___) DO NOT AGREE.
|br| NUMBER OF ENERGY GROUPS ____ = ___, NUMBER OF ENERGY INTERVAL = ___.
This continuous-energy mode--specific message from subroutine READ_REACTIONS_INPUT
indicates that either ``ngp_xs`` and entries in ``ener_xs``, or ``ngp_flx`` and entries
in ``ener_flx`` are not consistent.
KMSG355
\****\* ERROR \****\* K?-355 FOLLOWS:
|br| CE TSUNAMI GPT SYSTEMRESPONSES MAY ONLY CONTAIN ONE NUMERATOR RESPONSE.
KMSG356
\****\* ERROR \****\* K?-356 FOLLOWS:
|br| CE TSUNAMI GPT SYSTEMRESPONSES MAY ONLY CONTAIN ONE DENOMINATOR RESPONSE.
KMSG357
\****\* ERROR \****\* K?-357 FOLLOWS:
|br| DEFINITION NUMBER ___ IN SYSTEMRESPONSE ___ WAS NOT FOUND.
KMSG358
\****\* ERROR \****\* K?-358 FOLLOWS:
|br| NO GPT DEFINITIONS WERE READ FOR THIS CE TSUNAMI GPT CALCULATION.
KMSG359
\****\* ERROR \****\* K?-359 FOLLOWS:
|br| NO GPT SYSTEMRESPONSES WERE READ FOR THIS CE TSUNAMI GPT CALCULATION.
KMSG360
\****\* ERROR \****\* K?-360 FOLLOWS:
|br| DEFINITION NUMBER ___ CONTAINS AN EHIGH THAT IS NOT LESS THAN ITS ELOW.
KMSG361
\****\* WARNING \****\* K?-361 FOLLOWS:
|br| CFP WAS NOT SPECIFIED! FOR THE BEST RESULTS, THE CE TSUNAMI
|br| CLUTCH F*(R) METHOD REQUIRES A POSITIVE NUMBER OF LATENT GENERATIONS.
|br| CFP=5 WILL BE USED FOR THIS CALCULATION.
KMSG362
\****\* WARNING \****\* K?-362 FOLLOWS:
|br| TEMPERATURE:___ IS WITHIN 4 K OF CLOSEST LIBRARY TEMPERATURE. USING REFERENCE TEMPERATURE: ___.
This message from subroutine READ_XSEC indicates that
when Doppler Broadening temperature correction is applied,
the nuclide cross section data are loaded at the library
reference temperature, which is within 4 K of the given
temperature.
KMSG363
\****\* WARNING \****\* K?-363 FOLLOWS:
|br| TEMPERATURE:___ IS ___ REFERENCE LIBRARY TEMPERATURE. USING REFERENCE TEMPERATURE:___.
This message from subroutine READ_XSEC indicates that
when Doppler Broadening temperature correction is applied,
(1) minimum library temperature is always used if the given
temperature is less than this minimum, or
(2) maximum library temperature is used if the given
temperature is greater than this maximum.
KMSG364
\****\* WARNING \****\* K?-364 FOLLOWS:
|br| AN ENERGY GRID WAS ENTERED THAT DOES NOT COVER ALL POSSIBLE NEUTRON ENERGIES, AS IS REQUIRED BY CE TSUNAMI-3D.
|br| THE MIN AND MAX BOUNDS OF THIS ENERGY GRID WERE AUTOMATICALLY EXTENDED TO ___ EV AND ___ EV.
KMSG365
\****\* WARNING \****\* K?-365 FOLLOWS:
|br| DEFINITION NUMBER ___ REFERENCES A REACTION THAT IS NOT SUPPORTED BY EHIGHTRANSFER OR ELOWTRANSFER.
KMSG366
\****\* ERROR \****\* K?-366 FOLLOWS:
|br| DEFINITION NUMBER ___ CONTAINS AN EHIGHTRANSFER THAT IS NOT LESS THAN ITS ELOWTRANSFER.
KMSG367
\****\* ERROR \****\* K?-367 FOLLOWS:
|br| DBRC PARAMETER (DBR=___) IS NONZERO BUT COULD NOT FIND DBRC DATA IN CE DATA LIBRARY FOR ANY NUCLIDE.
This message is printed by subroutine NUCLIDE_SETUP if
no DBRC data are available in the given continuous-energy data library.
Access permissions, network problems, and typographical errors in the
input file should be verified. If the nuclide cross section file being
used is a standard file that is part of an official and current SCALE
system, then please contact scalehelp@ornl.gov.
KMSG368
\****\* ERROR \****\* K?-368 FOLLOWS:
|br| PARAMETER, THC, IS NO LONGER SUPPORTED IN THE ENERGY DATA BLOCK. PLEASE MOVE THIS PARAMETER TO THE PARAMETERS BLOCK.
This self-explanatory message is printed by subroutine RDENER if
``THC`` parameter was entered in the energy data
block. This parameter is no longer supported as part of the energy
data block. This issue must be corrected by defining ``THC``
parameter in the parameter block rather than in the energy block,
and then rerun the problem.
KMSG369
\****\* WARNING \****\* K?-369 FOLLOWS:
|br| PARAMETER THC SPECIFIED BUT WILL BE IGNORED SINCE THIS IS NOT A CE CALCULATION.
This self-explanatory message is from subroutine KENOBUILDER,
and it notifies that the defined ``THC`` parameter is not a valid multigroup
parameter; therefore, it will be ignored in the multigroup calculations.
KMSG370
\****\* WARNING \****\* K?-370 FOLLOWS:
|br| MESH VOLUME CALCULATION TYPE=___ IS NOT YET AVAILABLE.
THE TYPE IS CHANGED TO RANDOM. BE SURE TO VERIFY THAT THE VOLUMES HAVE BEEN CALCULATED ADEQUATELY.
This self-explanatory message is from subroutine RDVOL, and
it indicates that mesh volume calculation is always performed with
``RANDOM`` estimates. Methods other than ``RANDOM`` estimates
defined in input are always ignored by KENO codes, and
the volume calculation method is defaulted to ``RANDOM`` estimates.
KMSG371
\****\* ERROR \****\* K6-371 FOLLOWS:
|br| KENO-VI GEOMETRY PROCESSOR ALLOWS MAXIMUM SIX CHORD MODIFIER OF ANY TYPE WHEN TRUNCATING A PRE-DEFINED SHAPE.
|br| THERE ARE MORE THAN SIX CHORD MODIFIERS ON THE SHAPE, ___ ___, IN UNIT ___.
This self-explanatory KENO-VI message is printed by subroutine
SGGM_KENOG if more than the supported number of
``CHORD`` modifiers were defined on the given shape in the
specified unit.
KMSG372
\****\* WARNING \****\* K?-372 FOLLOWS:
|br| ___ POSITIONS HAVE F*(R) MESH TALLIES OF 0.0; A VALUE OF 1.0 WILL BE USED IN THE SENSITIVITY CALCULATIONS.
KMSG373
\****\* ERROR \****\* K?-373 FOLLOWS:
|br| INVALID NGP PARAMETER, (NGP=___). NGP MUST BE A POSITIVE INTEGER.
This self-explanatory continuous-energy mode--specific message from subroutine
DATAIN is caused by an invalid **NGP** entry in the parameter data block.
The number of energy groups is always a positive integer number.
KMSG374
\****\* WARNING \****\* K?-374 FOLLOWS:
|br| NO ENERGY BOUNDARIES SPECIFIED. DEFAULT ENERGY GROUP BOUNDARIES USED FOR TALLYING
WILL BE OBTAINED FROM ___-GROUP SCALE
|br| MULTI GROUP LIBRARY.
This self-explanatory message from subroutine DATAIN indicates
no energy boundaries were specified with any input method in the
continuous-energy calculations. KENO codes always need a set of
energy boundaries for tallying. For such a case, KENO codes
acquire the energy group boundaries from the 252-group SCALE
multigroup library and continue calculation.
KMSG375
\****\* WARNING \****\* K?-375 FOLLOWS:
|br| NGP PARAMETER WILL BE IGNORED SINCE THE ENERGY GROUP BOUNDARIES HAS ALREADY BEEN
READ FROM ENERGY DATA BLOCK. NGP VALUE PRINTED IN
|br| NUMERIC PARAMETERS EDIT IN THE OUTPUT REFLECTS THIS UPDATE.
This self-explanatory message from subroutine DATAIN indicates that
data provided by another input method (energy data block) will
override the number of energy group value entered by ``NGP``
parameter.
KMSG376
\****\* WARNING \****\* K?-376 FOLLOWS:
|br| NGP PARAMETER WILL BE IGNORED SINCE IT IS NOT A VALID PARAMETER FOR MULTI GROUP TRANSPORT.
This self-explanatory message coming from subroutine DATAIN indicates
that the multigroup calculation does not process ``NGP`` parameter
that is dedicated for continuous-energy calculations.
KMSG377
\****\* WARNING \****\* K?-377 FOLLOWS:
|br| ENERGY DATA BLOCK IS CURRENTLY ALLOWED FOR ONLY CONTINUOUS ENERGY TRANSPORT. SKIP READING DATA FROM ENERGY DATA BLOCK.
This self-explanatory message from RDENER indicates that
the multigroup calculation does not process data in
the energy data input block since it is dedicated for
continuous-energy calculations.
KMSG378
\****\* WARNING \****\* K?-378 FOLLOWS:
|br| IN MULTI GROUP MODE, DEFAULT ENERGY BOUNDARIES USED FOR TALLYING ARE ALWAYS OBTAINED FROM THE MULTI GROUP LIBRARY USED BY
|br| TRANSPORT.
This self-explanatory message from subroutine UPDATE_EBOUNDS_MG_MODE
reminds that multigroup mode acquires the energy group structure from
the multigroup library used by transport process, and it uses these
energy boundaries in all tallies if not otherwise requested.
KMSG379
\****\* WARNING \****\* K?-379 FOLLOWS:
|br| NGP PARAMETER WILL BE IGNORED SINCE ENERGY GROUP BOUNDARIES HAS ALREADY BEEN READ FROM ENERGY DATA BLOCK. NGP VALUE PRINTED
|br| IN NUMERIC PARAMETERS EDIT IN THE OUTPUT MAY NOT REFLECT THIS UPDATE. FINAL NGP VALUE IS CORRECTLY PRINTED IN ADDITIONAL
|br| INFORMATION EDIT (SHOWN AS NUMBER OF ENERGY GROUPS).
This self-explanatory message from subroutine DATAIN reminds that
energy boundaries were read from the energy data block and **NGP**
value printed in different output edits might not be updated
accordingly. Update methods for data used in the output edits,
and/or order of output editing might show some minor differences
depending on how KENO is run (e.g., running KENO as stand-alone,
running KENO through a SCALE sequence, running KENO through a
SCALE sequence with parm=check).
KMSG380
\****\* WARNING \****\* K6-380 FOLLOWS:
|br| CALCULATED VOLUME FRACTION OF FISSILE MATERIAL IN THE SYSTEM REPORTED BELOW MAY NOT REFLECT
|br| THE ACTUAL VALUE SINCE SOME REGION VOLUMES WERE NEITHER SPECIFIED NOR CALCULATED. EVEN NEGATIVE
|br| VOLUME FRACTION FOR FISSILE MATERIAL MAY BE REPORTED SINCE ALL UNDEFINED VOLUMES WERE SET TO -1.0.
This self-explanatory KENO-VI message is printed by subroutine K6_VOLFIS. It
notifies that the fraction of the fissile material might be calculated as
negative numbers if there is a missing region volume data. When volumes
are not entered, not calculated, or calculated as zero, KENO resets their
values to -1.0. Therefore, missing volumes might result in incorrect
volume fraction calculation for the fissile materials.
KMSG381
\****\* WARNING \****\* K?-381 FOLLOWS:
|br| IN MULTI GROUP MODE, DEFAULT ENERGY BOUNDARIES USED FOR TALLYING ARE
ALWAYS OBTAINED FROM THE MULTI GROUP LIBRARY USED BY
|br| TRANSPORT. NGP VALUE PRINTED IN NUMERIC PARAMETERS EDIT IN THE OUTPUT
MAY NOT REFLECT THIS. FINAL NGP VALUE IS CORRECTLY
|br| PRINTED IN ADDITIONAL INFORMATION EDIT (SHOWN AS NUMBER OF ENERGY GROUPS).
This self-explanatory message is multigroup mode--specific and comes
from subroutine DATAIN. It indicates that the default energy
group structure used for all tallies are always acquired from the
library used by transport process in multigroup calculations.
The ``NGP`` value printed in different output edits might not be
updated accordingly. Update methods for data used in the output edits,
and/or order of output editing, might show some minor differences
depending on how KENO is run (e.g., running KENO as standalone,
running KENO through a SCALE sequence, running KENO through a
SCALE sequence with parm=check).
KMSG383
\****\* WARNING \****\* K?-383 FOLLOWS:
|br| ENERGY GROUP BOUNDARIES READ FROM ENERGY DATA BLOCK OVERRIDE
THE DEFAULT NGP VALUE (252). NGP VALUE PRINTED IN NUMERIC
|br| PARAMETERS EDIT IN THE OUTPUT MAY NOT REFLECT THIS UPDATE.
THE FINAL NGP VALUE IS CORRECTLY PRINTED IN ADDITIONAL
|br| INFORMATION EDIT (SHOWN AS NUMBER OF ENERGY GROUPS).
This self-explanatory message is specific to continuous-energy mode,
and it is printed by subroutine DATAIN when running KENO standalone or
through a sequence with PARM=CHECK. The ``NGP`` value printed in
different output edits might not be updated accordingly.
KMSG384
\****\* ERROR \****\* K?-384 FOLLOWS:
|br| SPECIFICATION OF ENERGY BOUNDARIES WITH BOTH ENERGY DATA BLOCK AND DEFINITIONS DATA BLOCK IS NOT ALLOWED.
This self-explanatory message is printed by subroutine
READ_DEFINITIONS_INPUT
when running KENO as part of a SCALE sequence (CSAS, TRITON).
It indicates that energy boundaries were specified
with both ``CSAS definitions data`` and ``KENO energy data``
blocks, and this is illegal.
KMSG385
\****\* ERROR \****\* K?-385 FOLLOWS:
|br| ___ IS NOT ALLOWED TO BE USED TOGETHER WITH THE DATA SPECIFIED IN ___ BLOCK.
This message from subroutine READ_DEFINITIONS_INPUT is caused
by using both old and new input definition methods when running
KENO as part of either CSAS or TRITON sequence to activate some
of the KENO capabilities. For example, specifying the fission rate
mesh tally with ``FIS`` parameter in KENO parameter data block
(old method, activate capability with a single parameter) together
with specifying fission source accumulation in ``CSAS tallies data``
block is not allowed.
KMSG386
\****\* ERROR \****\* K?-386 FOLLOWS:
|br| INCONSISTENT ENERGY BOUNDARIES. THE SIZE OF ENERGY BOUNDARIES
SPECIFIED IN DEFINITIONS DATA WITH THE IDENTIFICATION NUMBER, ___,
|br| MUST BE LESS THAN THE SIZE OF THE DEFAULT ENERGY BOUNDARIES
ACQUIRED FROM THE MULTI GROUP LIBRARY USED BY TRANSPORT, (___ > ___).
This message is specific to multigroup mode and emitted from
subroutine VALIDATE_ENERGY_INTERVALS to explain that energy
boundaries specified in ``CSAS definitions data`` block are
not consistent with the DEFAULT energy group structure (or
energy boundaries) obtained from the library used by transport
process. Multiple energy group structures for tallying are
supported in KENO, even for multigroup mode. However, in
multigroup mode, each group structure must be a subset of
the DEAFAULT energy boundaries acquired from the multigroup
library used in the neutron transport. Therefore, the size
of a group structure defined in ``CSAS definition data`` block
cannot be larger than the DEFAULT energy boundaries.
KMSG387
\****\* ERROR \****\* K?-387 FOLLOWS:
|br| INCONSISTENT ENERGY INTERVALS. ALTHOUGH THEIR SIZE MATCH,
ENERGY BOUNDARIES SPECIFIED IN DEFINITIONS DATA WITH IDENTIFICATION
|br| NUMBER, ___, DEFINE DIFFERENT ENERGY INTERVALS COMPARED TO THE
DEFAULT ENERGY BOUNDARIES ACQUIRED FROM MULTI GROUP LIBRARY USED BY TRANSPORT.
This message is specific to multigroup mode and emitted from
subroutine VALIDATE_ENERGY_INTERVALS to explain that energy
boundaries specified in ``CSAS definitions data`` block are
not consistent with the DEFAULT energy group structure (or
energy boundaries) obtained from the library used by transport
process. Multiple energy group structures for tallying are
supported in KENO, even for multigroup mode. However, in
multigroup mode, each group structure must be a subset of
the DEFAULT energy boundaries acquired from the multigroup
library used in the neutron transport. Therefore, the energy
intervals defined in ``CSAS definition data`` block
must be the same as the DEFAULT energy boundaries if their sizes
are equal.
KMSG388
\****\* ERROR \****\* K?-388 FOLLOWS:
|br| INCONSISTENT ENERGY INTERVALS. ENERGY BOUNDARIES SPECIFIED IN
DEFINITIONS DATA WITH THE IDENTIFICATION NUMBER ___
|br| MUST BE A SUBSET OF THE DEFAULT ENERGY BOUNDARIES ACQUIRED FROM
THE MULTI GROUP LIBRARY USED BY TRANSPORT.
This message is specific to multigroup mode and emitted from
subroutine VALIDATE_ENERGY_INTERVALS to indicate that energy
boundaries specified in ``CSAS definitions data`` block are
not consistent with the DEFAULT energy group structure (or
energy boundaries) obtained from the library used by transport
process. Multiple energy group structures for tallying are
supported in KENO. However, in multigroup mode, each group
structure must be a subset of the DEFAULT energy boundaries
acquired from the multigroup library used in the neutron
transport.
KMSG389
\****\* ERROR \****\* K?-389 FOLLOWS:
|br| ENERGY BOUNDARIES SPECIFIED IN DEFINITIONS DATA WITH THE
IDENTIFICATION NUMBER ___ MUST BE IN DESCENDING ORDER (EV).
EB (___) = ___ IS GREATER THAN OR EQUAL TO EB(___) = ___.
This message is emitted from subroutine VALIDATE_ENERGY_INTERVALS
to indicate that energy boundaries defined either with
**KENO energy data** or **CSAS definitions data** blocks
were not in descending order. KENO always expects the
energy points entered in descending order.
KMSG390
\****\* ERROR \****\* K?-390 FOLLOWS:
|br| IDENTIFICATION NUMBER ___ WAS USED MORE THAN ONCE WHEN SPECIFYING ENERGY BOUNDARIES IN DEFINITIONS DATA.
This self-explanatory message is printed by eBounds_type's ADD
procedure when running KENO as part of CSAS or TRITON
sequences. It indicates that identification numbers must be unique
entries, and using the same identification number multiple times
for different energy boundaries definitions is an illegal operation.
KMSG391
\****\* ERROR \****\* K?-391 FOLLOWS:
|br| MESH TALLY IDENTIFICATION NUMBER ___ WAS USED MORE THAN ONCE WHEN SPECIFYING MESH TALLY IN TALLIES BLOCK.
This self-explanatory message is printed by subroutine
TALLIES_TYPE_ADD_MESH_TALLY when running KENO as part of CSAS or
TRITON sequences. It indicates that identification numbers must
be unique entries and using the same identification number
multiple times for different
mesh tallies is an illegal operation.
KMSG392
\****\* ERROR \****\* K?-392 FOLLOWS:
|br| MESH TALLIES ___ AND ___ SPECIFIED IN TALLIES BLOCK HAVE IDENTICAL DEFINITIONS.
This self-explanatory message is printed by subroutine
TALLIES_TYPE_ADD_MESH_TALLY when running KENO as part of CSAS or
TRITON sequences. It indicates that the same mesh tally was defined
two times in the tallies data block. This is considered a potential
user error: therefore, calculation is terminated.
KMSG393
\****\* ERROR \****\* K?-393 FOLLOWS:
|br| BAD VALUE FOR KEYWORD MESH TALLY, NEEDS AN IDENTIFICATION NUMBER.
This message from subroutine READ_MESH_TALLY_INPUT
when running KENO as part of CSAS or TRITON sequences indicates that
the mesh tally identification number either was not entered
or was defined as a non-integer number.
KMSG394
\****\* ERROR \****\* K?-394 FOLLOWS:
|br| INVALID MESHTALLY IDENTIFIER, ___, IN TALLIES BLOCK. IDENTIFICATION NUMBER MUST BE A POSITIVE INTEGER.
This message from subroutine READ_MESH_TALLY_INPUT
when running KENO as part of CSAS or TRITON sequences indicates that
mesh tally identification number is not a positive integer number.
KMSG395
\****\* ERROR \****\* K?-395 FOLLOWS:
|br| ___ -- ENDED WITH -- END ___ --.
This message is printed by subroutine READ_MESH_TALLY_INPUT when running
KENO as part of CSAS or TRITON sequences if
``READ TALLIES`` is not ended with ``END TALLIES``,
or ``READ MESH`` is not ended with ``END MESH``.
KMSG396
\****\* ERROR \****\* K?-396 FOLLOWS:
|br| INVALID RESPONSE TYPE, ___. ONLY [FLUX, FISSION_DENSITY, FISSION_SOURCE] ARE THE VALID RESPONSE TYPES.
This message printed by subroutine READ_MESH_TALLY_INPUT when running
KENO as part of CSAS or TRITON sequences if the mesh
tally calculation was requested with an invalid response type.
KMSG397
\****\* ERROR \****\* K?-397 FOLLOWS:
|br| INVALID ENERGY IDENTIFICATION NUMBER (ENERGY= ___) IN MESH TALLY ___
IN TALLIES BLOCK. IDENTIFICATION NUMBER MUST BE A POSITIVE INTEGER OR DEFAULT.
This message printed by subroutine READ_MESH_TALLY_INPUT when running
KENO as part of CSAS or TRITON sequences is caused by an invalid
identification number that was entered as the energy identifier
in tallies data block.
KMSG398
\****\* ERROR \****\* K?-398 FOLLOWS:
|br| SPECIFICATION OF ENERGY BOUNDARIES WITH BOTH NGP PARAMETER AND
DEFINITIONS DATA IS NOT ALLOWED.
This self-explanatory message printed by subroutine READ_DEFINITIONS_INPUT
when running KENO as part of CSAS or TRITON sequences indicates that
energy boundaries cannot be specified by using the old input
specification method (``NGP`` parameter) and new input specification
methods (``energybounds`` in CSAS definition data block) together.
KMSG399
\****\* ERROR \****\* K?-399 FOLLOWS:
|br| INVALID ENERGY BOUNDS SPECIFICATIONS WITH IDENTIFICATION NUMBER ___;
ALL ENERGY POINTS ARE IDENTICAL.
This self-explanatory message is printed by eBounds_type's ADD
procedure when running KENO as part of CSAS or TRITON
sequences. It indicates that defined energy boundaries cannot
be used for tallying since all energy points were entered as the same.
KMSG400
\****\* WARNING \****\* K?-400 FOLLOWS:
|br| IGNORE READING ENERGY GROUP BOUNDARIES FROM DEFINITIONS DATA THAT
ARE MARKED AS DEFAULT SINCE THIS IS A MULTI GROUP CALCULATION.
This self-explanatory message is printed by eBounds_type's ADD
procedure when running KENO as part of CSAS or TRITON
sequences. It notifies that DEFAULT energy group structure
acquired from the library used in the neutron transport
cannot be overridden by the energy boundaries data in
**CSAS definitions data** block.
KMSG401
\****\* WARNING \****\* K?-401 FOLLOWS:
|br| IDENTICAL ENERGY BOUNDARIES WERE SPECIFIED IN DEFINITIONS DATA
WITH IDENTIFICATION NUMBERS ___ AND ___. ONLY ONE OF
|br| THEM WILL BE PROCESSED AND STORED FOR THE CALCULATIONS.
This self-explanatory message is printed by eBounds_type's ADD
procedure when running KENO as part of CSAS or TRITON
sequences. It notifies that two sets of energy boundaries
defined in **CSAS definitions data** block have the identical
specifications. KENO only processes one of them and
stores it in energy data container for tallying. It updates
energy bound pointers for the tallies if they are defined to
use the energy bounds not stored.
KMSG403
\****\* ERROR \****\* K?-403 FOLLOWS:
|br| ENERGY BOUNDARIES (ENERGY=___) SPECIFIED IN ___ ___ IN TALLIES
BLOCK IS NOT FOUND IN THE DEFINITIONS DATA INPUT BLOCK.
This self-explanatory message is printed by VALIDATE_ENERGY_BOUNDS_ID
procedure when running KENO as part of CSAS or TRITON
sequences. It indicates that the energy boundaries were
not entered in **CSAS definitions data** block even though
it was intended to be used with a mesh tally calculation
defined in **CSAS tallies data** block.
KMSG404
\****\* ERROR \****\* K?-404 FOLLOWS:
|br| SPECIFICATION OF MESH GRIDS WITH BOTH GRIDGEOMETRY DATA INPUT
AND GRIDGEOMETRY IN DEFINITIONS DATA IS NOT ALLOWED.
This self-explanatory message is emitted by subroutine
READ_DEFINITIONS_INPUT when running KENO as part of a
SCALE sequence (CSAS, TRITON). It indicates that mesh grids
were specified with both **CSAS definitions data** and
**KENO gridgeometry data** blocks, and this is not allowed.
KMSG405
\****\* WARNING \****\* K?-405 FOLLOWS:
|br| WARNING MESSAGES EMITTED BY ___ INPUT PROCESSOR ARE AS FOLLOWS:
KENO and MONACO use the same legacy input parser to process
the data entered in **definitions data** block. This common
utility has its own messaging method, which accumulates all
user error and warning messages encountered while processing
data, then forwards them to the caller who runs this
utility. Warning messages from this utility are filtered and
printed with this message by READ_DEFINITIONS_INPUT to notify
user about the
possible issues in the input. Note that this message is only
emitted when running KENO as part of a SCALE sequence
(CSAS, TRITON).
KMSG406
\****\* ERROR \****\* K?-406 FOLLOWS:
|br| GRID IDENTIFICATION NUMBER ___ WAS USED MORE THAN ONCE WHEN
SPECIFYING GRIDGEOMETRY.
This self-explanatory message is printed by CHECKGRIDDATA procedure of
MGRID type procedure, and it indicates that identification numbers must be unique
entries and using the same identification number multiple times
for different
mesh grid definitions is an illegal operation.
KMSG407
\****\* WARNING \****\* K?-407 FOLLOWS:
|br| IDENTICAL GRIDGEOMETRIES WERE SPECIFIED WITH IDENTIFICATION NUMBERS
___ AND ___. ONLY ONE OF THEM WILL BE PROCESSED AND
|br| STORED FOR THE CALCULATIONS.
This self-explanatory message is printed by REMOVEDUPLICATES
procedure of MGRID type, and it notifies that two sets of grid geometry
either defined in **CSAS definitions data** or in **KENO gridgeometry data**
blocks have the identical specifications. KENO only processes
one of them and stores it in grid data container for tallying.
It updates the grid data pointers for the tallies if they are
defined to use the mesh grids not stored.
KMSG408
\****\* ERROR \****\* K?-408 FOLLOWS:
|br| GRIDGEOMETRY (GRID=___) SPECIFIED IN ___, ___ IN TALLIES BLOCK
IS NOT FOUND IN THE DEFINITIONS DATA INPUT BLOCK.
This self-explanatory message is printed by VALIDATE_GRID_ID
procedure when running KENO as part of CSAS or TRITON
sequences. It indicates that the mesh grid was
not entered in **CSAS definitions data** block even though
it was intended to be used with a mesh tally calculation
defined in **CSAS tallies data** block.
KMSG409
\****\* ERROR \****\* K?-409 FOLLOWS:
|br| INVALID GRID IDENTIFICATION NUMBER (GRID= ___) IN MESH TALLY ___ IN
TALLIES BLOCK. IDENTIFICATION NUMBER MUST BE A POSITIVE INTEGER.
This message comes from subroutine READ_MESH_TALLY_INPUT
when running KENO as part of CSAS or TRITON sequences. It indicates that the
mesh grid identification number defined in **CSAS tallies data** block
is not a positive integer number.
KMSG410
\****\* WARNING \****\* K?-410 FOLLOWS:
|br| ENERGY BOUNDARIES MARKED AS DEFAULT WILL BE USED IN ALL TALLY
CALCULATIONS IF OTHERWISE NOT REQUESTED.
This message is printed immediately after the energy boundaries
output edit to indicate that the DEFAULT energy boundaries
listed in this edit will be used in all tally calculations,
unless otherwise requested. Note that the default energy boundaries
can be defined with different input data or can be read by the code
from the relevant SCALE library depending on the computation mode.
KMSG411
\****\* WARNING \****\* K?-411 FOLLOWS:
|br| ENERGY GROUP BOUNDARIES READ FROM ENERGY BLOCK OVERRIDE THE DEFAULT NGP VALUE.
This self-explanatory message printed by subroutine DATAIN
indicates that data read from energy data block will
override the default ``NGP`` value.
KMSG412
\****\* WARNING \****\* K?-412 FOLLOWS:
|br| NO ENERGY BOUNDARIES SPECIFIED AS DEFAULT IN DEFINITIONS DATA.
THE DEFAULT ENERGY GROUP BOUNDARIES USED FOR TALLYING ARE OBTAINED FROM ___-GROUP SCALE MULTI GROUP LIBRARY.
This self-explanatory message printed by subroutine DATAIN
when running KENO as part of CSAS or TRITON sequences indicates
that **CSAS definition data** block does not have a definition
for the DEFAULT energy boundaries. For this continuous-energy--specific case, KENO obtains the DEFAULT energy boundaries
from the SCALE 252-group multigroup library and utilizes it
for tallying.
KMSG413
\****\* WARNING \****\* K?-413 FOLLOWS:
|br| DEFAULT ENERGY GROUP BOUNDARIES READ FROM DEFINITIONS DATA OVERRIDE
THE DEFAULT NGP VALUE. NGP VALUE PRINTED IN NUMERIC
|br| PARAMETERS EDIT IN THE OUTPUT MAY NOT REFLECT THIS UPDATE.
THE FINAL NGP VALUE IS CORRECTLY PRINTED IN ADDITIONAL INFORMATION
|br| EDIT (SHOWN AS NUMBER OF ENERGY GROUPS).
This self-explanatory message is specific to continuous-energy mode,
and it is printed by subroutine DATAIN when running KENO through a
sequence with PARM=CHECK. This message
reminds that the DEFAULT NGP value will be overridden by this data
read from the definitions data block, and the updated NGP value
can be shown in Additional information output edit.
KMSG414
\****\* WARNING \****\* K?-414 FOLLOWS:
|br| DEFAULT ENERGY GROUP BOUNDARIES READ FROM DEFINITIONS DATA OVERRIDE THE DEFAULT NGP VALUE. NGP VALUE PRINTED IN
|br| NUMERIC PARAMETERS EDIT IN THIS OUTPUT REFLECTS THIS UPDATE.
This self-explanatory message is specific to continuous-energy mode,
and it is printed by subroutine DATAIN when running KENO through a
sequence. This message indicates that the DEFAULT NGP value printed
in numeric parameters output edit was also updated accordingly.
KMSG415
\****\* WARNING \****\* K?-415 FOLLOWS:
|br| SPECIFIED NGP VALUE (NGP=___) DOES NOT CORRESPOND TO ONE OF THE
STANDARD ENERGY GROUP STRUCTURES AVAILABLE.
|br| CONSTRUCT ___ EQUAL LETHARGY BINS AND SET THEM AS DEFAULT ENERGY GROUP BOUNDARIES WHICH WILL BE USED FOR TALLYING.
This self-explanatory message is specific to continuous-energy mode,
and it is printed by subroutine SETUP_DEFAULT_EBOUNDS_CE_MODE.
It indicates that specified ``NGP`` parameter does not match
any SCALE group structure; therefore, KENO constructs the
DEFAULT energy boundaries with ``NGP`` equal
lethargy bins and stores this in the ebounds data container.
The DEFAULT energy boundaries will be used for all tallies.
KMSG416
\****\* ERROR \****\* K6-416 FOLLOWS:
|br| BOUNDARY CONDITIONS OTHER THAN VACUUM IS NOT ALLOWED ON THE
BOUNDARIES WHEN THE BOUNDARY DEFINITION VECTOR OF THE GLOBAL UNIT HAS NEGATIVE BODY LABEL(S).
This self-explanatory KENO-VI message from subroutine K6_RDBNDS
indicates that a non-vacuum albedo boundary condition was defined
illegally. KENO-VI allows constructing global unit with combinations
of multiple bodies whose labels listed in the boundary definition
vector of the global unit. However, only VACUUM albedo boundary
condition is to be applied to the global boundaries if the boundary
definition vector of the global unit has negative body label(s).
Therefore, execution is terminated with this error message.
See :numref:`sec-module.keno.albedo` for specific examples for
albedo boundary condition specifications for KENO-VI geometry.
KMSG417
\****\* ERROR \****\* K6-417 FOLLOWS:
|br| BOUNDARY CONDITION SPECIFICATION WITH SURFACE AND FACE CODES
WITHOUT CORRESPONDING BODY IS NOT ALLOWED WHEN MULTIPLE BODIES USED TO DEFINE THE GLOBAL UNIT BOUNDARY.
This self-explanatory KENO-VI message from subroutine K6_RDBNDS
is caused by a missing ``BODY`` parameter in the boundary
condition specification. When multiple bodies define the
global boundaries, boundary conditions of each body should
be defined with ``BODY`` parameter following by the corresponding
face codes. Therefore, the execution is terminated with this
error message. See :numref:`sec-module.keno.albedo` for specific examples for
albedo boundary condition specifications for KENO-VI geometry.
KMSG418
\****\* ERROR \****\* K?-418 FOLLOWS:
|br| FACE CODES AND SURFACE KEYWORDS ARE NOT ALLOWED TO BE USED TOGETHER
IN BOUNDARY DATA SPECIFICATION FOR THE SAME BODY (BODY=___).
This self-explanatory message from subroutines K6_RDBNDS or K5_RBNDS
indicate that there is illegal input data in bounds data block. KENO
does not allow using ``SURFACE`` and cuboidal ``FACE CODE`` s together
for albedo boundary condition specifications.
KMSG419
\****\* ERROR \****\* K5-419 FOLLOWS:
|br| FACE CODES ARE NOT ALLOWED TO BE USED WITH NON-CUBOIDAL BOUNDING SHAPE WHICH IS A ___.
This self-explanatory message from subroutine K5_JOMCHK
indicates that ``FACE CODE`` s were used illegally when
specifying albedo boundary conditions. Cuboidal
``FACE CODE`` s cannot be used for non-cuboidal
boundary shape when defining boundary conditions.
KMSG420
\****\* ERROR \****\* K5-420 FOLLOWS:
|br| ___ BOUNDARY CONDITION IS NOT ALLOWED ON HEMISPHERES AND HEMICYLINDERS.
This message from subroutine K5GM_JOMCHK indicates that
non-vacuum boundary conditions were applied to the
outermost geometry region, which is a hemisphere or a
hemicylinder. KENO V.a geometry does not allow boundary conditions other
than VACUUM on these boundary shapes.
Execution is terminated.
KMSG421
\****\* ERROR \****\* K5-421 FOLLOWS:
|br| BODY IS AN INVALID PARAMETER NAME IN BOUNDARY CONDITION DATA SPECIFICATION.
This message emitted from subroutine K5GM_RDBNS indicates that
an invalid bounds data parameter was used when defining
albedo boundary conditions. ``BODY`` parameter is a
KENO-VI specific parameter used to define albedo
boundary conditions to the boundary shape(s)
which constructs the global unit. Therefore, execution
is terminated.
KMSG422
\****\* ERROR \****\* K6-422 FOLLOWS:
|br| FACE CODES ARE NOT ALLOWED TO BE USED WITH NON-CUBOIDAL BOUNDING SHAPE
(BOUNDARY BODY ___ IN THE GLOBAL UNIT BOUNDARY IS A ___).
This self-explanatory message emitted from subroutine K6_RDBNDS
indicates that ``FACE CODE``\ s were used illegally when
specifying albedo boundary conditions on the non-cuboidal
boundary shape(s). Cuboidal ``FACE CODE`` s cannot be
used with non-cuboidal boundary shape(s) when defining
the boundary conditions. Therefore, execution
is terminated.
KMSG430
\****\* ERROR \****\* K?-430 FOLLOWS:
|br| ILLEGAL PARAMETER VALUE (___ , ___), IT MUST BE A POSITIVE NUMBER.
This message printed by subroutine RDSTRT is caused by an illegal
parameter value in ``START data`` block. START data
parameters ``LNU``, ``NXS``, ``NYS``, and ``NZS`` must be
a positive integer value; otherwise, execution is
terminated with this error message.
KMSG431
\****\* ERROR \****\* K?-431 FOLLOWS:
|br| LNU IN EACH SUCCESSIVE DATA SET SHOULD BE LARGER THAN THE PREVIOUS VALUE OF LNU (CURRENT LNU=___, PREVIOUS LNU=___).
This message printed by subroutine RDSTRT if an illegal
``LNU`` parameter value is in ``START data`` block. ``LNU``
parameter is used in START type 6 data. This start type
allows neutrons to be started at the arbitrary starting
points defined by a set of data. The last entry for each
start 6 data set must be ``LNU``, and the ``LNU`` value
of each successive set of data must be larger than the last.
Otherwise, execution is terminated with this error message.
KMSG432
\****\* WARNING \****\* K?-432 FOLLOWS:
|br| ONLY ___ STARTING POINT WILL BE READ FROM THE ASCII START DATA FILE (RDU=___).
This message emitted by subroutine RDSTRT indicates that
starting points read from the ASCII start data file
is less than the number of neutrons per generations.
If there are no other start data sets defined in the
``START data`` block, KENO uniformly samples the remaining
starting points from the set of these arbitrary starting
points already read from the ascii start data file.
See :numref:`sec-module.keno.start_dist` for specific examples for
start type 6.
KMSG433
\****\* ERROR \****\* K?-433 FOLLOWS:
|br| START TYPE 6 PARAMETER ___ HAS BEEN USED MORE THAN ONCE IN THE SAME DATA SET.
This self-explanatory message from subroutine RDSTRT
indicates that one of the START type 6 parameter was
defined more than once in the same start type 6 data
set. Starting parameters ``NXS``, ``NYS``, ``NZS``, ``TFX``,
``TFY``, and ``TFZ`` should be used once in the same
start type 6 data set ended by ``LNU`` parameter.
KMSG434
\****\* ERROR \****\* K?-434 FOLLOWS:
|br| NO LNU HAS BEEN SPECIFIED WITH THE ___ SET IN START TYPE 6.
This self-explanatory message printed by subroutine RDSTRT
is caused by a missing ``LNU`` parameter in one of
the start type 6 data set which may include either
``NXS``, ``NYS``, and ``NZS``, or ``TFX``,
``TFY``, and ``TFZ`` parameters.
KMSG435
\****\* ERROR \****\* K?-435 FOLLOWS:
|br| RDU (RDU=___) CANNOT BE USED TOGETHER WITH ___ IN THE SAME START TYPE 6 DATA SET ENDED WITH (___ , ___).
This self-explanatory message from subroutine RDSTRT
is caused by using ``RDU`` parameter together with any
``NXS``, ``NYS``, ``NZS``, ``TFX``,
``TFY``, and ``TFZ`` options in the same start type 6
data set. ``RDU`` cannot be used together with these
start type 6 options in the same data set; therefore,
execution is terminated.
KMSG436
\****\* ERROR \****\* K?-436 FOLLOWS:
|br| SPECIFIED ASCII START DATA FILE (RDU=___) DOES NOT EXIST.
This self-explanatory message is printed by subroutine RDSTRT
if the defined ASCII start data file could
not be found. Execution is terminated with this error
message for such a case.
KMSG437
\****\* ERROR \****\* K?-437 FOLLOWS:
|br| INSUFFICIENT NUMBER OF START DATA POINTS (SPECIFIED LNU=___ >> MAX. LNU READ FROM RDU FILE, LNU=___) FOUND IN
|br| SPECIFIED ASCII START DATA FILE (RDU=___).
This self-explanatory message is printed by subroutine RDSTRT
if the ASCII start data file contains
starting points less than the defined ``LNU`` value.
There must be at least ``LNU`` number of starting points
in the ASCII start data file for a successful operation.
See :numref:`sec-module.keno.start_dist` for specific examples for
start type 6.
KMSG438
\****\* WARNING \****\* K?-438 FOLLOWS:
|br| ___ SEQUENCE DOES NOT SUPPORT PARAMETER (___) SPECIFIED IN THE PARAMETER DATA.
THIS PARAMETER WILL BE IGNORED IN THIS CALCULATION.
This self-explanatory message is printed by subroutine PARAM
if an unsupported parameter is entered in
the **parameter data** input block. KENO by design
has several parameters, some of them dedicated to
the sequence running KENO. For example,
parameters ``CET``, ``CFP``, etc. are allocated for
sensitivity calculations performed by KENO when
running KENO as part of a TSUNAMI sequence. These
parameters are not valid for other sequences
running KENO such as CSAS and TRITON. If there is
an inconsistency between such sequence-specific
parameters and the sequence, which is running KENO,
then execution is terminated with this error message to
prevent excess resource allocation for the
sequence-specific capabilities activated by these
parameters.
KMSG439
\****\* ERROR \****\* K?-439 FOLLOWS:
|br| ILLEGAL VALUE FOR START TYPE 6 PARAMETER (___=___). ___ CANNOT BE GREATER
THAN THE NUMBER OF UNITS IN THE ___-DIRECTION OF THE GLOBAL ARRAY (___=___).
This message from subroutine K_STDATA indicates that
the values entered with the ``NXS``, ``NYS``, and ``NZS``
start type 6 parameters are not consistent with the
definition of the global array. Valid ``NXS``, ``NYS``,
and ``NZS`` values must be less than or equal to the
``NUX``, ``NUY``, and ``NUZ`` entries in the
global array definitions in the ``array data`` block.
Otherwise, execution is terminated with this error message.
KMSG440
\****\* WARNING \****\* K?-440 FOLLOWS:
|br| ___ IS NOT A VALID DATA FOR START TYPE ___. THIS PARAMETER WILL BE IGNORED IN THIS CALCULATION.
This self-explanatory message is printed by subroutine RDSTRT
if a start type parameter is defined
with another start type which does not support this
parameter. For example, ``LNU`` parameter is a start
type 6-specific parameter, and it is not allowed with
start type 0. For such a case, execution is terminated
with this error message.
KMSG441
\****\* WARNING \****\* K?-441 FOLLOWS:
|br| ___ IS NO LONGER SUPPORTED BY START DATA (OBSOLETE PARAMETER). THIS PARAMETER WILL BE IGNORED IN THIS CALCULATION.
This self-explanatory message from subroutine RDSTRT
indicates that an obsolete parameter
was used in the **start data** input block. KENO development
is an evolving process; sometimes due to new
limitations as part of modernization or other needs,
some legacy parameters are no longer supported. KENO
ignores processing this parameter and continues the
calculation by emitting this warning message.
KMSG442
\****\* INFORMATION WARNING \****\* K6-442 FOLLOWS:
|br| POSIT WARNING --- POINT MAY NOT BE IN GEOMETRY X = ___ Y = ___ Z = ___
This message from subroutine K6_START indicates
that starting point sampled/entered might be outside
the geometry. Usually, this warning message is followed
by an error message if the starting point is verified
that it is not located inside the geometry by subroutine
SGGM_POSIT. If the number of points outside the
geometry is less than 5, then calculation will continue
by resampling these points from the set of successful
starting points (which are inside the geometry).
Otherwise, execution is terminated. For such a case,
the user should ensure that all starting points are
located inside the geometry that are either defined
with start type 6 data or defined in ASCII start
data file(s).
Theory and Techniques
---------------------
The transport equation
~~~~~~~~~~~~~~~~~~~~~~
The equation KENO solves may be derived in the following manner,
starting with the Boltzmann neutron transport equation which may be
written as
.. math::
:label: eq8-1-3
& \frac{1}{\mathrm{v}}\frac{\partial\Phi}{\partial t}\left( X,E,\Omega,t \right) + \Omega \bullet \nabla\Phi\left( X,E,\Omega,t \right) + \Sigma_{t}\left( X,E,\Omega,t \right)\Phi\left( X,E,\Omega,t \right)
& \ \ \ \ \ \ \ \ = S\left( X,E,\Omega,t \right)
& \ \ \ \ \ \ \ \ + \int_{E^{'}}^{}{\int_{\Omega^{'}}^{}{\Sigma_{s}\left( X,E^{'} \rightarrow E,\Omega^{'} \rightarrow \Omega,t \right)\Phi\left( X,E^{'},\Omega^{'},t \right)}}d\Omega^{'}dE^{'}\ ,
where
:math:`\Phi(\mathrm{X}, \mathrm{E}, \Omega, \mathrm{t})` = neutron flux (neutrons/cm\ :sup:`2`\ /s) per unit energy at
energy E per steradian about direction :math:`\Omega` at position X at time t
moving at speed v corresponding to E;
:math:`\Sigma_{t}(\mathrm{X}, \mathrm{E}, \Omega, \mathrm{t})` = macroscopic total cross section of the media
(cm\ :sup:`-1`) at position X, energy E, direction :math:`\Omega` and time t;
:math:`\Sigma_{\mathrm{s}}\left(\mathrm{X}, \mathrm{E}^{\prime} \rightarrow \mathrm{E}, \Omega^{\prime} \rightarrow \Omega, \mathrm{t}\right)` = macroscopic differential cross section
of the media (cm\ :sup:`-1`) per unit energy at energy E' per steradian
about direction :math:`\Omega^{\prime}` at position X, and time t, for scattering to
energy E and direction :math:`\Omega`;
:math:`\mathrm{S}(\mathrm{X}, \mathrm{E}, \Omega, \mathrm{t})` = neutrons/cm\ :sup:`3`/s born at position X and time t
per unit energy at energy E per steradian about direction :math:`\Omega` (excludes
scatter source).
Defining :math:`\mathrm{q}(\mathrm{X}, \mathrm{E}, \Omega, \mathrm{t})` as the total source resulting from the external
source, scattering, fission, and all other contributions, the following
relationship can be written.
.. math::
:label: eq8-1-4
q(X,E,\Omega, t) =
& S(X,E,\Omega, t) + \int_{E^{'}}^{}{\int_{\Omega^{'}}^{}{\Sigma_{s}\left( X,E^{'} \rightarrow E,\Omega^{'} \rightarrow \Omega,t \right)\Phi\left( X,E^{'},\Omega^{'},t \right)}}d\Omega^{'}dE^{'}\ .
Combining :eq:`eq8-1-3` and :eq:`eq8-1-4`, assuming media to be stationary and ignoring time-dependence, yields
.. math::
:label: eq8-1-5
\ \Omega \bullet \nabla\Phi\left( X,E,\Omega \right)+ \Sigma_{t}\left( X,E,\Omega \right)\Phi\left( X,E,\Omega \right) = q\left( X,E,\Omega \right)
Continuous energy mode solution procedure
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Using the relationship :math:`X' = X - R \Omega`, using an integrating factor on both
sides of :eq:`eq8-1-5`, and defining
.. math::
T(R) = \int_{0}^{R} \Sigma_{t}(X - R^{'}\Omega, E)dR ,
the following equation can be written.
At this point, the problem becomes an eigenvalue problem. If there is no
external source, the source may be defined as
.. math::
:label: eq8-1-6
\Phi(X,E,\Omega) = \int_{O}^{\infty}q(X - R\Omega,E,\Omega)e^{-T(R)}dR
At this point, the problem becomes an eigenvalue problem. If there is no external source, the source may be defined as
.. math::
:label: eq8-1-7
q\left( X,E,\Omega \right) = & \int_{}^{}{\int_{}^{}{{dE^{'}d\Omega^{'}\ \Phi\left( X,E^{'},\Omega^{'} \right)\ \Sigma}_{s}\left( X,E^{'} \rightarrow E,\Omega^{'} \cdot \Omega \right)}}
& + \ \frac{1}{k}Q^{'}(X,E,\Omega) ,
where
k
is the largest eigenvalue of the integral equation,
:math:`\mathrm{Q}^{\prime}(\mathrm{X}, \mathrm{E}, \Omega)`
is the fission source at position X for energy E and
direction :math:`\Omega` (all fission contributions to point E from all energy
points in the previous generation),
:math:`\Sigma_{\mathrm{s}}\left(\mathrm{X}, \mathrm{E}^{\prime} \rightarrow \mathrm{E}, \Omega^{\prime} \bullet \Omega\right)`
is the scattering cross section for
scattering at position X from energy point E' and direction :math:`\Omega^{\prime}` to
energy point E and direction :math:`\Omega`.
Assuming the fission neutrons to be isotropic, the fission source
:math:`\mathrm{Q}^{\prime}(\mathrm{X}, \mathrm{E}, \Omega)` can be written as
.. math::
:label: eq8-1-8
Q^{'}(X,E,\Omega) = \frac{1}{4\pi}\int_{E^{'}}^{}\int_{\Omega^{'}}^{}dE^{'}d\Omega^{'}\Phi(X,E^{'},\Omega^{'})\chi(X,E^{'}\rightarrow E)\nu(X,E^{'})\Sigma_{f}(X,E^{'}) ,
where
- :math:`\chi\left( X,E^{\prime}\rightarrow E \right)` is the fraction of neutrons born at energy point E from
fission at energy point :math:`E^{\prime}` in the media at position X,
- :math:`\nu\left( X,E^{\prime}\right)` is the number of neutrons resulting from a fission at energy
point :math:`E^{\prime}` at position X,
- :math:`\Sigma_f \left(X, E^{\prime} \right)` is the macroscopic fission cross section of the
material at position X for a neutron at energy point :math:`E^{\prime}`.
Substituting :eq:`eq8-1-7` into :eq:`eq8-1-6` yields the following equation:
.. _ first equation says chapter 9
.. math::
:label: eq8-1-9
\ {\Phi\left( X,E,\Omega \right) = \int_{0}^{\infty}{\text{dR }e^{- T\left( R \right)}\left\{ \frac{1}{k}Q^{'}\left( X - R\Omega,E,\Omega \right) \right.\ }}
{+ \left. \ \int_{E^{'}}^{}{\int_{\Omega^{'}}^{}{{dE^{'}d\Omega^{'}\Phi\left( X - R\Omega,E^{'},\Omega^{'} \right)\Sigma}_{s}\left( X - R\Omega,E^{'} \rightarrow E,\Omega^{'} \cdot \Omega \right)}} \right\}}
The definition of k may be given as the ratio of the number of neutrons
produced in the (n + 1)\ *th* generation to the number of neutrons
produced in the n\ *th* generation or the largest eigenvalue of the
integral equation. Using :eq:`eq8-1-8`, :eq:`eq8-1-6` can be written as
.. math::
:label: eq8-1-10
\begin{gathered}
\Phi(X, E, \Omega)=\int_{0}^{\infty} d R e^{-T(R)}\left\{\frac{1}{k} \int_{E^{\prime}} \int_{\Omega^{\prime}} \nu \left(X-R \Omega, E^{\prime}\right) \Sigma_{f}\left(X-R \Omega, E^{\prime}\right) \chi\left(X-R \Omega, E^{\prime} \rightarrow E\right) \Phi\left(X-R \Omega, E^{\prime}, \Omega^{\prime}\right) d \mathrm{E}^{\prime} \frac{d \Omega^{\prime}}{4 \pi}\right. \\
\left.+\int_{E^{\prime}} \int_{\Omega^{\prime}} d \mathrm{E}^{\prime} d \Omega^{\prime} \Phi\left(X-R \Omega, E^{\prime}, \Omega^{\prime}\right) \Sigma_{s}\left(X-R \Omega, E^{\prime} \rightarrow E, \Omega^{\prime} \cdot \Omega\right)\right\}
\end{gathered}
Writing :eq:`eq8-1-10` in generation notation, multiplying and dividing
certain terms by :math:`\Sigma_t \left(X,E \right)` and multiplying both sides of the
equation by :math:`\nu \left(X,E \right) \Sigma_f \left(X,E \right)`,
yields the following equation, which is solved by KENO V in the continuous energy mode:
.. _ first equation says chapter 9
.. math::
:label: eq8-1-11
\begin{gathered}
\frac{v(X, E) \Sigma_{f}(X, E)}{\Sigma_{t}(X, E)} \Sigma_{t}(X, E) \Phi_{n}(X, E, \Omega)=\frac{v(X, E) \Sigma_{f}(X, E)}{\Sigma_{t}(X, E)} \Sigma_{t}(X, E) \int_{0}^{\infty} d R e^{-T(R)} \\
\left\{\frac{1}{k} \int_{E^{\prime}} \int_{\Omega^{\prime}} \frac{v\left(X-R \Omega, E^{\prime}\right) \Sigma_{f}\left(X-R \Omega, E^{\prime}\right)}{\Sigma_{t}\left(X-R \Omega, E^{\prime}\right)} \chi\left(X-R \Omega, E^{\prime} \rightarrow E\right) \Sigma_{t}\left(X-R \Omega, E^{\prime}\right) \Phi_{n-1}\left(X-R \Omega, E^{\prime}, \Omega^{\prime}\right) d \mathrm{E}^{\prime} \frac{d \Omega^{\prime}}{4 \pi}\right. \\
\left.+\int_{E^{\prime}} \int_{\Omega} \frac{\Sigma_{S}\left(X-R \Omega, E^{\prime} \rightarrow E, \Omega^{\prime} \cdot \Omega\right)}{\Sigma_{t}\left(X-R \Omega, E^{\prime}\right)} \Sigma_{t}\left(X-R \Omega, E^{\prime}\right) \Phi_{n}\left(X-R \Omega, E^{\prime}, \Omega^{\prime}\right) d E^{\prime} d \Omega^{\prime}\right\}
\end{gathered}
where n indicates the n\ *th* generation and n - 1 is the (n - 1)\ *th*
generation. Note that the left-hand side of the equation,
:math:`\nu\left(X,E \right) \Sigma_f \left(X,E \right) \phi_n \left(X,E,\Omega \right)`
is the fission production for the n\ *th* generation.
The solution strategy used by KENO solves :eq:`eq8-1-11` by using an
iterative procedure. The fission production at point X at energy point E
due to neutrons in the (n - 1)\ *th* generation, normalized to the
system multiplication, is
.. math::
\frac{1}{k}\int_{E^{'}}{}\int_{\Omega^{'}}{}\frac{\nu(X,E^{'})\Sigma_{f}(X,E^{'})}{\Sigma_{t}(X,E^{'})}\chi(X,E^{'}\rightarrow E)\Sigma_{t}(X,E)\Phi_{n-1}(X,E^{'}\Omega^{'})dE^{'}\frac{d\Omega^{'}}{4\pi}
The collision points used in KENO are chosen by selecting path lengths
from the distribution
e\ :sup:`-T(R)` ,
which is the probability of transport from any position :math:`X-R\Omega` to
position X.
The first collision density of neutrons at energy E per unit solid angle
about :math:`\Omega` resulting from the fission source produced by the (n - 1)
generation, normalized to the system multiplication, is
.. math::
\Sigma_{t}(X,E)\int_{0}^{\infty}dRe^{-T(R)}\frac{1}{k}\int_{\Omega^{'}}^{}\int_{E^{'}}^{}\frac{\nu(X-R\Omega,E^{'})\Sigma_{f}(X-R\Omega,E^{'})}{\Sigma_{t}(X-R\Omega,E^{'})}
\chi(X - R\Omega, E^{'}\rightarrow E)\Sigma_{t}(X - R\Omega,E^{'})\Phi_{n-1}(X-R\Omega,E^{'},\Omega^{'})dE^{'}\frac{d\Omega^{'}}{4\pi}
The scattering source at position X emerging at energy E and direction :math:`\Omega` resulting from previous collisions in the same generation, is
.. math::
\int_{E^{'}}^{}{\int_{\Omega^{'}}^{}{\frac{\Sigma_{s}\left( X,E^{'} \rightarrow E,\Omega^{'} \cdot \Omega \right)}{\Sigma_{t}\left( X,E^{'} \right)}\Sigma_{t}\left( X,E^{'} \right)\Phi_{n}\left( X,E^{'},\Omega^{'} \right)}}d\Omega^{'}dE^{'}
The collision density at energy E, per solid angle about :math:`\Omega` is
.. math::
\Sigma_{t}\left( X,E \right)\int_{0}^{\infty}{\text{dR }e^{- T\left( R \right)}}\int_{E^{'}}^{}{\int_{\Omega^{'}}^{}{\frac{\Sigma_{s}\left( X - R\Omega,E^{'} \rightarrow E,\Omega^{'} \cdot \Omega \right)}{\Sigma_{t}\left( X - R\Omega,E^{'} \right)}\Sigma_{t}\left( X - R\Omega,E^{'}\right)\Phi_{n}\left( X - R\Omega,E^{'},\Omega^{'} \right)}}d\Omega^{'}dE^{'}
The total collision density times :math:`\frac{\nu_{g}(X)\Sigma_{fg}(X)}{\Sigma_{tg}(X)}` is the relationship from which KENO picks the source points for the next generation.
.. _8-1-6-2-1:
Problem initialization
^^^^^^^^^^^^^^^^^^^^^^
In order to use continuous energy cross sections in the random walk,
various initialization tasks must be addressed for each problem. Based
on the mixture specifications for a problem, KENO reads the microscopic
cross section data for each nuclide and dynamically allocates storage
for the particular problem. For continuous energy problems, if
**UUM=**\ no then KENO will not allocate macroscopic cross sections for
each material, and will instead use the master set of microscopic cross
section data (on a non-unionized energy grid). This is the default
behavior. Storing cross sections on a material-based unionized energy
grid (**UUM=**\ yes) results in smaller cross section lookup times and
faster KENO runtimes; however, storing unionized cross section data for
every material can require a prohibitively large amount of memory for
problems with a large number of materials. Users should therefore only
set **UUM**\ =yes for relatively small models; experience is the best
guide as to what "small" means with respect to available system
resources. After finishing the cross section processing, KENO reads the
user-specified KENO data (See :numref:`sec-module.keno.output`) and stores the problem-dependent
data for retrieval during the random walk. After the data initialization
tasks are complete, the Monte Carlo random walk can be performed
according to the procedures that are documented in the subsequent
sections.
.. _8-1-6-2-2:
Initial source distribution
^^^^^^^^^^^^^^^^^^^^^^^^^^^
Before the Monte Carlo simulation can be performed, the initial source
distribution of neutrons must be sampled. Typically, each mixture in a
problem is composed of multiple isotopes, and each mixture must be
checked for the presence of fissionable material. For each fissionable
mixture, the volume fraction of fissionable material must be calculated
on a per isotope basis.
The first source distribution is comprised of the initial spatial
coordinates, direction cosines and energy for each neutron within the
problem. Regarding the coordinate values, both continuous energy and
multigroup KENO use the same start types, and the initial angular
distribution is sampled from an isotropic distribution. For the initial
energy distribution, the energy of each neutron must be sampled from the
continuous energy fission spectrum, :math:`\chi\left( E \right)`, of a fissionable isotope
within the mixture. If more than one fissionable isotope is present, the
*i*\ :sup:`th` isotope can be selected using the following relation:
.. math::
:label: eq8-1-12
\sum^{i-1}_{j=1}\Sigma^{j}_{f} < R\sum^{N}_{j=1}\Sigma^{j}_{f} \leq \sum^{i}_{j=1}\Sigma^{j}_{f}
where
:math:`\sum^{j}_f` = macroscopic fission cross section for the *j*\ :sup:`th`
isotope,
*R* = random number [0, 1),
*N* = total number of fissionable isotopes in the mixture.
Note that the relation in :eq:`eq8-1-12` requires the knowledge of the fission
cross section at a particular energy. Therefore, an initial energy of
0.025 eV is assumed for selecting the appropriate isotope to sample.
Once the *i*\ :sup:`th` isotope is selected, the initial energy is
sampled from the corresponding :math:`\chi`\ :sub:`i`\ (*E*).
.. _8-1-6-2-3:
Collision site selection
^^^^^^^^^^^^^^^^^^^^^^^^
Each neutron must be tracked until the history is terminated via leakage
from the system or the particle is "killed" via roulette. The selection
of the next collision site is governed by the following probability
density function (PDF):
.. math::
:label: eq8-1-13
f(x)dx = \Sigma^{m}_{t}(E)e^{-\Sigma^{m}_{t}(E)x}dx ,
where
:math:`\Sigma^{m}_{t}(E)` = macroscopic total cross section for mixture *m* at
energy *E*,
*x* = spatial variable.
The PDF in :eq:`eq8-1-13` describes the probability that a neutron will have an
interaction between *x* and *x* + *dx* along its flight path.
Integrating :eq:`eq8-1-13` over the spatial variable yields the following
cumulative distribution function (CDF):
.. math::
:label: eq8-1-14
F(x) = \int^{x}_{0}\Sigma^{m}_{t}(E)e^{-\Sigma^{m}_{t}(E)x^{'}}dx^{'} = 1 - e^{-\Sigma^{m}_{t}(E)x} ,
and the next collision site is determined by setting the CDF in :eq:`eq8-1-14`
equal to a random number on the interval [0, 1) and solving for *x*.
Note that :eq:`eq8-1-14` requires the total cross section for mixture *m* at
energy *E* in order to calculate the next collision site. As mentioned
in the :numref:`8-1-6-2-1`, KENO has two approaches to calculate the
macroscopic total cross section for each mixture; (1) use a unionized
energy grid (**UUM=**\ yes) --- once KENO reads the microscopic data for
each isotope/nuclide in a mixture, KENO calculates and stores the
macroscopic total cross sections for the nuclides in each mixture (2)
on-the-fly mixture macroscopic cross section calculation (**UUM=**\ no)
--- KENO does not store macroscopic cross sections and instead calculates
mixture cross sections upon request during particle tracking. Selecting
**UUM**\ =yes results in substantially increased memory usage for
problems with a large number of materials, making it impossible to
perform CE calculations for some detailed problems. Thus, it is highly
recommended to use **UUM**\ =no, the default setting, for the large
problems with multiple mixture definitions. For most cases selecting
**UUM**\ =no increases the runtime for KENO CE calculations by
approximately 17 %, but this feature also expands the code's capability
to simulate very large problems with multiple mixture configurations.
Just as the ``UUM`` option allows the user to prevent KENO from storing
mixture cross sections on a unionized energy grid, the ``M2U`` option
toggles whether or not KENO stores cross sections on a unionized energy
grid for each individual nuclide. The default for this option is
``M2U=no``, which prevents the storage of all the transport cross
sections (i.e. inelastic scattering levels) for each nuclide in addition
to the major reactions that are already on the unionized energy grid
(i.e. total, fission, capture, and scatter) on an energy grid that is
unionized for that nuclide, and setting ``M2U=``\ yes activates this
unionization and storage. ``M2U=``\ no reduces the nuclear data memory
footprint of large models by several gigabytes, but it also increases
the runtime of these problems by several percent. It is encouraged to
investigate both ``UUM`` and ``M2U`` options in continuous energy
problems to optimize the runtime and memory depending on the user's
models and applications. In the continuous energy depletion
calculations, ``UUM`` parameter is intentionally forced to "no" to
minimize the memory requirement of internal data storage. The cross
section storage and treatment options should be used consistently in
both validation and analysis calculations.
If any of the isotopes in the mixture have unresolved-resonance data and
corresponding probability-table data, KENO must determine if the neutron
energy is in the unresolved resonance range (URR) for each isotope
during the random walk. If the neutron energy is in the URR for an
isotope, the appropriate probability table must be sampled to obtain the
total cross section for each isotope (refer to :numref:`8-1-6-2-1` for sampling
probability tables). Subsequently, the macroscopic total cross section
for mixture *m* is adjusted to account for sampling the probability
tables. Once the revised :math:`\Sigma_{\mathrm{t}}^{\mathrm{m}}(E)` is determined,
:eq:`eq8-1-14` can be used to select the next collision site within mixture *m* at
energy *E*.
Collision treatment
^^^^^^^^^^^^^^^^^^^
Once the collision site is determined, the collision can be modeled, and
the post collision parameters can be calculated. In the continuous
energy approach, each collision is modeled with an individual
isotope/nuclide. If a mixture is defined by multiple isotopes and/or
nuclides, the target must be selected at each collision site. If there
are *N* different isotopes/nuclides present in a mixture, the following
equation can be used to select the *i*\ :sup:`th` target for
interaction:
.. math::
:label: eq8-1-15
\sum^{i-1}_{j=1}\Sigma^{j}_{t} < R \sum^{N}_{j=1}\Sigma^{j}_{t} \leq \sum^{i}_{j=1}\Sigma^{j}_{t} ,
where,
:math:`\Sigma_{t}^{j}` = macroscopic total cross section for the *j*\ :sup:`th`
isotope/nuclide.
As noted in :numref:`8-1-6-2-2` and :numref:`8-1-6-2-3`, the collision energy may be in the
URR of one or more isotopes within the mixture. Consequently, the total
cross section for each isotope that has unresolved-resonance data is
sampled from the probability table information prior to selecting the
next collision site (see discussion in :numref:`8-1-6-2-1`). Subsequently, the
sampled values for the total and partial reactions are stored for
retrieval. Therefore, the macroscopic total cross section values that
are used in :eq:`eq8-1-15` are adjusted to account for sampling the probability
table data by retrieving the appropriate microscopic total cross section
value at energy *E*. Once the corrected values for :math:`\Sigma_{t}^{j}(E)` are
determined, :eq:`eq8-1-15` can be used to select the target for interaction.
After selecting the collision target, the neutron's weight is reduced by the nonabsorption probability:
.. math::
:label: eq8-1-16
w = \frac{\sigma^{i}_{s}(E)}{\sigma^{i}_{t}(E)}w_{b} = P_{nabs}(E)w_{b} ,
where
:math:`\sigma^{i}_{s}(E)` = microscopic scattering cross section for the
*i*\ :sup:`th` isotope/nuclide at energy *E*,
:math:`\sigma^{i}_{t}(E)` = microscopic total cross section for the
*i*\ :sup:`th` isotope/nuclide at energy E,
*w\ b* = weight before collision.
The absorption and fission weights are calculated using the following relations, respectively:
.. math::
:label: eq8-1-17
w_{a} = \frac{\sigma^{i}_{a}(E)}{\sigma^{i}_{t}(E)}w_b ,
where
:math:`\sigma^{i}_{a}(E)` = microscopic absorption cross section for the *i*\ :sup:`th` isotope/nuclide at energy *E*,
and
.. math::
:label: eq8-1-18
w_f = \frac{\bar{\nu}^{i}(E)\sigma^{i}_{f}(E)}{\sigma^{i}_{t}(E)}w_b ,
:math:`\bar{\nu}^i` = average number of neutrons released per fission at energy *E*,
:math:`\sigma^{i}_{f}(E)` = microscopic fission cross section for the *i*\ :sup:`th` isotope/nuclide at energy *E*.
If the collision isotope is in the URR at energy *E* and probability
table data are available, the collision probabilities must be adjusted
for sampling the partial reactions from the appropriate probability
table. In particular, the revised or sampled values for scattering,
absorption and fission must be used to calculate the collision weights
as defined by :eq:`eq8-1-16` through :eq:`eq8-1-18`. Depending on the neutron's weight, splitting
and/or Roulette are performed as necessary. Once the appropriate weights
are calculated, the collision can be processed to determine the type of
interaction and the corresponding exiting energy and angle if secondary
neutrons are generated.
Because an explicit collision treatment is dictated by the point cross
section data, the type of reaction must be modeled explicitly in the
continuous energy version of KENO. :numref:`fig8-1-196` summarizes the cross section
hierarchy and can be used as an aide to understanding the collision
treatment in KENO in continuous energy mode. After selecting the
isotope/nuclide for interaction according to :eq:`eq8-1-15` and calculating the
weights using :eq:`eq8-1-16` through :eq:`eq8-1-18`, the collision is modeled using the following
procedures:
1. At each collision site, ensure that the type of collision is
selected based on the cross section data. Moreover, the
*k*\ :sup:`th` reaction can be randomly selected using the following
relation:
.. math::
:label: eq8-1-19
\sum^{k-1}_{j=1}\sigma_{j} < R\sum^{NI}_{j=1}\sigma_{j} < \sum^{k}_{j=1}\sigma_{j}
where
:math:`\sigma_{j}(E)` = cross section for the *j*\ :sup:`th` reaction,
*NI* = number of elastic and nonelastic reactions (i.e., excludes
neutron disappearance reactions).
Note that the fission reactions (e.g., first chance fission, second
chance fission, etc.) are excluded from :eq:`eq8-1-19` because an implicit
approach is used to treat fission. The details of the fission
treatment are provided in :numref:`8-1-6-2-5`. If a neutron production reaction
with multiple exit neutrons such as (n, 2n), (n, 3n) is selected and
the reaction is not a fission reaction, then the weight of the
neutron is adjusted by the multiplicity to account for the additional
neutrons, such as *w* = 2\ *w* for (n, 2n), *w* = 3\ *w* for (n, 3n).
.. figure:: figs/Keno/fig196.png
:align: center
:width: 600
:name: fig8-1-196
Cross section hierarchy for particle interactions.
2. Select the exiting angle for the collision. The cross section
library provides a kinematics data block that provides the angle and
energy distributions of secondary particles for a specified reaction.
Each record for each section of a reaction provides a flag (NPU)
indicating the number of secondary angles for that energy. If the NPU
flag is 1 and the corresponding cosine value is -2 (set as a
programming flag), then the reaction is isotropic. The exiting angle
for the collision can be obtained as follows:
i. Isotropic Emission
If the LAND flag is 0 for the secondary angular distribution, the
exiting angle cosine is sampled uniformly between -1 and +1:
.. math::
:label: eq8-1-20
\mu = 2R - 1
If the LAND flag is 1 for the secondary angular distribution, the
exiting angle cosine must be sampled from an anisotropic distribution
provided in the cross section library for the specified reaction.
Details for sampling the exiting angle from the angular distribution
data are provided in :numref:`sec-module.keno.sampling`.
The secondary angular distribution data are provided as a function of
incident energy. The initial record of each section for a reaction
provides the number of incident energies (*NE*) for the secondary
angular and energy distributions. Corresponding to each incident
energy is a secondary angular distribution. Therefore, there will be
*NE* records used to describe the secondary angular data for each
section.
For each angular distribution record, there is an *LMU* flag and a
*NPU* flag that describes the format of the data. The *LMU* flag
designates whether the secondary distribution is provided in
equiprobable cosine bins or in nonequiprobable cosine bins. The
procedures for sampling the two types of data are provided in :numref:`sec-module.keno.kinematics`.
The *LMU* flag must be the same for all *NE* records within a
section. The *NPU* flag specifies the number of cosine values in the
distribution.
Based on the incident energy of the neutron, the angular distribution
data are sampled according to the procedures of :numref:`sec-module.keno.kinematics` to obtain the
exiting angle cosine, :math:`\mu`, in the lab system.
3. Select the exiting energy for the collision. In addition to the
angular distributions of the kinematics data, the cross section
library provides the energy distributions of secondary particles for
a specified reaction.
The secondary energy distributions are provided as a function of
incident energy and secondary angle cosine in each section. Once the
exiting angle cosine is selected, the exiting energy is selected from
the energy distribution that corresponds to the (*E*, \ :math:`\mu`) pair.
The exit energy is determined using the procedures of :numref:`sec-module.keno.kinematics`.
For each energy distribution record, there is an *LE* flag and an
*NPE* flag describing the format of the data. The *LE* flag
designates whether the secondary distribution is provided in
equiprobable energy bins or in nonequiprobable energy bins. The
procedures for sampling the two types of data are provided in :numref:`sec-module.keno.kinematics`.
Note that the *LE* flag must be the same for all *NE* records within
a section for the secondary energy distribution data. The *NPE* flag
specifies the number of secondary energy values in the distribution.
For elastic scattering and discrete-level inelastic scattering, the
*NPE* flag will equal the *NPU* flag due to the one-to-one
correspondence between angle and energy.
4. Select the azimuthal angle :math:`\eta` uniformly between 0. and :math:`2 \pi` (i.e., :math:`\eta=2 R \pi`.
5. Calculate the new direction cosines in the lab system using the
following equations:
.. math::
:label: eq8-1-21
u^{'} = u\mu - \sqrt{\nu^{2}+w^{2}} \sqrt{1-\mu^{2}}\text{cos}(\eta)
.. math::
:label: eq8-1-22
\nu^{'} = \nu \mu + \frac{u\nu}{\sqrt{\nu^{2}+w^{2}}}\text{cos}(\eta)\sqrt{1-\mu^{2}} - \frac{w}{\sqrt{\nu^{2}+w^{2}}}\sqrt{1-\mu^{2}}\text{sin}(\eta)
.. math::
:label: eq8-1-23
w^{'} = w\mu + \frac{uw}{\sqrt{\nu^{2}+w^{2}}}\text{cos}(\eta)\sqrt{1-\mu^{2}} + \frac{v}{\sqrt{\nu^{2}+w^{2}}}\sqrt{1-\mu^{2}}\text{sin}(\eta)
where
*u*, :math:`\nu`, and *w* = initial direction cosines,
:math:`u^{\prime}, \nu^{\prime}, \text { and } w^{\prime}` = exiting direction cosines,
:math:`\mu` = cosine of the scattering angle, and
:math:`\eta` = cosine of the azimuthal angle.
.. _8-1-6-2-5:
Fission treatment
^^^^^^^^^^^^^^^^^
As noted in the previous section, an implicit approach is used to treat
a fission event. During the collision treatment, the fission weight is
calculated using :eq:`eq8-1-18`. After processing the collision, the fission
weight is evaluated to determine if the fission treatment should be
applied. If the fission weight is greater than zero, the collision
occurred in fissile material. During the random walk, several fission
source points must be generated to provide an adequate representation of
the true source distribution. A minimum production factor is defined at
the beginning of each generation to ensure that enough fission points
are generated:
.. math::
:label: eq8-1-24
mpf = \frac{3.0\bar{k}}{\sqrt{FG}} ,
where
:math:`\bar{k}` = running average of :math:`k_{eff}` through the current generation, and
*FG* = number of histories per generation.
:eq:`eq8-1-24` represents an estimate of the 99% lower confidence interval for the distribution of the generation k-effective.
If the fission weight is greater than zero, a pseudo-fission weight is calculated as follows:
.. math::
:label: eq8-1-25
pfw = \frac{w_{f}}{R} = \frac{\nu^{-i}(E)\sigma^{i}_{f}(E)}{R\sigma^{i}_{t}(E)}w_{b} .
If the pseudo-fission weight is less than the minimum production factor
given by :eq:`eq8-1-24` fission points are not generated and tracking of the
particle continues. However, if the pseudo-fission weight is greater
than the minimum production factor, *pfw* is redefined to be the minimum
production factor divided by a random number:
.. math::
:label: eq8-1-26
pfw = \frac{mpf}{R}
Once the pseudo-fission weight is redefined, a fission point can be
generated. Each time a fission point is generated, the pseudo-fission
weight is stored with the point in the fission bank. When a new point is
stored in the fission bank, the energy and angular cosine must be
selected from the kinematics data. Once the kinematics data are sampled
for the new fission point, the fission weight of the history is
decremented by the minimum production factor. If the remaining fission
weight is greater than zero, the fission treatment procedures are
repeated until the fission weight of the history has been exhausted
(i.e., :math:`w_f \leq 0`).
.. _sec-module.keno.sampling:
Sampling details
^^^^^^^^^^^^^^^^
The preceding sections describe the procedures for the continuous energy
random walk for KENO. During the random walk, KENO must sample various
tables of data that may include probability tables and angle-energy distributions
for secondary particles.
Probability tables
''''''''''''''''''
For each isotope with unresolved resonance data, multiple probability
tables may be used to describe the URR. The header block for each
isotope has an LPTAB flag that provides the number of probability tables
for an isotope. Each table is defined for a range of incident energies
between :math:`E_i` and :math:`E_{i+1}`, and the energy range for a table should not
overlap with another table for the isotope. For a particle with energy
*E*, a search must be performed to find the probability table with
energy bounds that bracket the particle energy, :math:`E_{i} \leq E < E_{i+1}`.
Once the appropriate table is identified, the table can be
sampled to obtain the total, elastic scattering, fission and capture
cross section values in the URR.
The probability table block provides four separate records that
correspond to each reaction within a table; however, the probability
table construction is based on the total cross section. Therefore, the
probabilities in each table refer to the total cross section band
values, and the bands should be sampled based on the total cross
section. Once the band is sampled, the corresponding partial reaction
cross section values are selected from the same band as the total
cross section. The cross section format permits the probability table to
be expressed in equiprobable or nonequiprobable cross section bands
(i.e., LBND = 0 or 1, respectively). The procedures for sampling both
types of tables are provided in the subsequent subsections.
Equiprobable cross section bands
''''''''''''''''''''''''''''''''
Each probability record has an NB parameter that designates the number
of cross section bands for a table. If the table is constructed with
equiprobable cross section bands, the *k*\ :sup:`th` band can be
selected as follows:
.. math::
:label: eq8-1-27
k = NB \ ^{\ast} R + 1
where
*R* = random number [0., 1).
Based on the sampled cross section band, the total cross section
corresponding to *k*\ :sup:`th` band is extracted from the table.
Likewise, the elastic scattering, fission and capture cross section
values that correspond to the *k*\ :sup:`th` band are also extracted
from their respective records in the probability-table block.
Nonequiprobable cross section bands
'''''''''''''''''''''''''''''''''''
If the LBND flag is 1, the cross section bands in the table are not
equiprobable, and a different procedure must be used to sample the
appropriate cross section band. For this case, the probability values in
the table must be constructed as a cumulative distribution function. As
noted previously, each probability record has an NB parameter that
designates the number of cross section bands for a table, and the
*k*\ :sup:`th` band can be selected as follows:
.. math::
:label: eq8-1-28
\sum^{k-1}_{j=1}P_{j} < R\sum^{NB}_{j=1}P_{j} \leq \sum^{k}_{j=1}P_{j} ,
where
*P*\ :math:`j` = probability corresponding to the j\ :sup:`th` cross section
band.
Based on the sampled cross section band, the total cross section
corresponding to the *k*\ :sup:`th` band is extracted from the table.
Likewise, the elastic scattering, fission and capture cross section
values that correspond to the *k*\ :sup:`th` band are also extracted
from their respective records in the probability-table block.
.. _sec-module.keno.kinematics:
Kinematics data
^^^^^^^^^^^^^^^
The kinematics data in the KENO library are provided in the lab or
target-at-rest system as opposed to the center-of-mass system. By
adhering to the lab coordinate system, KENO does not have to transform
between different coordinate systems during the random walk; however,
the energy and angle representations for elastic and discrete-level
inelastic scattering become more complex in the lab system. For example,
an angular distribution that is isotropic in the center-of-mass system
is anisotropic in the lab system. Moreover, the secondary energy
distribution as a function of exit angle in the lab system can be double
valued (i.e., two possible exit energies with respect to a single angle)
for energies above the threshold for the reaction. Likewise, a similar
double valued distribution is observed for elastic scattering with
hydrogen in the lab system if the actual mass ratio is used (i.e.,
*A* = 0.99928 as opposed to *A* = 1.0). Consequently, special care must
be exercised in the construction of the secondary angle and energy
distributions in the lab system.
The subsequent sections address the general procedures for sampling the
kinematics data with emphasis on the special cases that must be
addressed during the random walk. In :numref:`sec-module.keno.kinematics.gen`, the general
procedures for sampling the kinematics data are provided,
:numref:`8-1-6-2-7-4` discusses isotropic angular data with energy coupling,
while :numref:`8-1-6-2-7-5` discusses coherent and incoherent elastic
scattering. A discussion is also provided in :numref:`8-1-6-2-7-6` to
describe the elastic and discrete-level inelastic treatment.
.. _sec-module.keno.kinematics.gen:
General procedures
''''''''''''''''''
The kinematics data format is designed to accommodate coupled angle
energy distributions of secondary particles. The following discussion
provides the procedures for sampling the coupled distributions. Special
cases such as elastic and discrete level inelastic scattering are
discussed after the "General Procedures" section.
The sampling procedures in the following sections assume that the angle
and energy distributions are continuous in nature. As a result,
interpolation procedures can be used to obtain intermediate angle or
energy values between the tabulated angle or energy values. During the
course of KENO development, there may be a need to provide an average
angle or energy value for a bin. The kinematics format can be modified
as needed to accommodate additional angle and energy representations.
Therefore, the following procedures represent the anticipated approach
for sampling the current form of the kinematics data.
.. _sec-module.keno.kinematics.exit_angle:
Exit angle cosine
'''''''''''''''''
The first record for each reaction provides the number of sections
(NSECT) used to describe the kinematics for the reaction. Within each
section, the first record defines the incident energy range for the
section. After the first record for a section, the first block of data
provides the secondary angular distributions for *NE* different incident
energies within the energy range of the section. Consequently, there
will be *NE* different angular distribution records in the secondary
angle cosine block. The kinematics format permits the anisotropic
angular distributions to be expressed in either equiprobable or
nonequiprobable cosine bins (i.e., LMU = 0 or 1, respectively).
Moreover, the formats permit the number of cosine bins to vary as a
function of incident energy. In particular, each cosine distribution
record can have *NPU* secondary angles that correspond to *NPU* - 1
cosine bins.
**Equiprobable Cosine Bins.** If the incident energy, *E*, is between
*E*\ :sub:`i` and *E*\ :sub:`i+1`, the angle cosine is sampled in both
tables, and the exit angle cosine is obtained by interpolating between
the two tables. If the angular distribution is provided in equiprobable
cosine bins, the *a*\ :sup:`th` bin is selected from the *i*\ :sup:`th`
table as follows:
.. math::
:label: eq8-1-29
a = (NPU_{i} - 1) \ ^{\ast} R_{1} + 1 = NA_{i} \ast R_{1} + 1 .
In :eq:`eq8-1-29` *a* denotes an integer quantity, and *NA*\ :sub:`i` is the number of
cosine bins for the *i*\ :sup:`th` table. Using a similar procedure, the
*b*\ :sup:`th` bin is selected from the *i*\ +1\ :sup:`st` table:
.. math::
:label: eq8-1-30
b = NA_{i+1} \ ^{\ast} R_{1} + 1
As noted for the *i*\ :sup:`th` table, *b* is an integer quantity in
Eq. :eq:`eq8-1-30` and *NA*\ :sub:`i+1` is the number of cosine bins for the
*i*\ +1\ :sup:`st` table. Once the cosine bins are selected, the cosine
of the exiting angle from the *i*\ :sup:`th` and *i*\ +1\ :sup:`st`
tables is calculated with :eq:`eq8-1-31` and :eq:`eq8-1-32`, respectively:
.. math::
:label: eq8-1-31
{\dot{\mu}}_{i} = \mu_{ia} + \left( a - NA_{i}*R_{1} \right)\left( \mu_{ia + 1} - \mu_{ia} \right) ,
.. math::
:label: eq8-1-32
{\dot{\mu}}_{i + 1} = \mu_{i + 1b} + \left( b - NA_{i + 1}*R_{1} \right)\left( \mu_{i + 1b + 1} - \mu_{i + 1b} \right) .
The exiting angle cosine is obtained by interpolating between *i* and
*i*\ +1 based on the incident energy grid:
.. math::
:label: eq8-1-33
\ \mu = {\dot{\mu}}_{i} + \left( \frac{E - E_{i}}{E_{i + 1} - E_{i}} \right)\left( {\dot{\mu}}_{i + 1} - {\dot{\mu}}_{i} \right).
**Nonequiprobable Cosine Bins.** If the angular distribution is in the
form of nonequiprobable cosine bins, the *a*\ :sup:`th` bin is selected
from the cumulative distribution function for the *i*\ :sup:`th` table:
.. math::
:label: eq8-1-34
C_{ia - 1} < R_{1} \leq C_{ia}\ ,
where
*C*\ :math:`_{ia-1}` = cumulative probability corresponding to the :math:`a-1^{st}` cosine bin,
*C*\ :math:`_{ia}` = cumulative probability corresponding to the :math:`a^{th}` cosine bin,
Using a similar procedure, the *b*\ :sup:`th` bin is selected from the
*i*\ +1\ :sup:`st` table:
.. math::
:label: eq8-1-35
C_{i + 1b - 1} < R_{1} \leq C_{i + 1b}\ ,
where
:math:`C_{ib-1}` = cumulative probability corresponding to the :math:`b - 1^{st}` cosine bin,
:math:`C_{ib}` = cumulative probability corresponding to the :math:`b^{th}` cosine bin.
If the cosine bins are not equiprobable and the PDF is represented by a
continuous distribution, the bins are selected so that linear
interpolation can be performed in the PDF. Because the CDF is obtained
by integrating the PDF, the interpolation procedure for the CDF has a
quadratic form. The value for :math:`{\dot{\mu}}_{i}` is obtained with
the following equation:
.. math::
:label: eq8-1-36
{\dot{\mu}}_{i} = \mu_{ia} + \frac{\sqrt{P_{ia}^{2} + 2s_{i}(R_{1} - C_{ia - 1})} - P_{ia}}{s_{i}}\ ,
and
.. math::
:label: eq8-1-37
s_{i} = \frac{P_{ia + 1} - P_{ia}}{\mu_{ia + 1} - \mu_{ia}}\ ,
where
:math:`P_{ia}` = value of the PDF corresponding to the lower boundary of the :math:`a^{th}` cosine bin in the distribution for :math:`E_{i}`, and
:math:`P_{ia+1}` = value of the PDF corresponding to the upper boundary of the :math:`a^{th}` cosine bin in the distribution for :math:`E_{i}`.
Likewise, the equation for :math:`{\dot{\mu}}_{i + 1}` is obtained using
an equation that is similar to :eq:`eq8-1-36`
.. math::
:label: eq8-1-38
{\dot{\mu}}_{i + 1} = \mu_{i + 1b} + \frac{\sqrt{P_{i + 1b}^{2} + 2s_{i + 1}(R_{1} - C_{i + 1b - 1})} - P_{i + 1b}}{s_{i + 1}},
and
.. math::
:label: eq8-1-39
s_{i + 1} = \frac{P_{i + 1b + 1} - P_{i + 1b}}{\mu_{i + 1b + 1} - \mu_{i + 1b}} ,
where
:math:`P_{i + 1b}` = value of the PDF corresponding to the lower value of the :math:`b^{th}` cosine bin in the distribution for :math:`E_{i+1}`, and
:math:`P_{i + 1b + 1}` = value of the PDF corresponding to the upper value of the :math:`b^{th}` cosine bin in the distribution for :math:`E_{i+1}`.
The exiting angle cosine is obtained by interpolating between
:math:`{\dot{\mu}}_{i}` and :math:`{\dot{\mu}}_{i + 1}` based on the
incident energy using :eq:`eq8-1-33`.
.. _sec-module.keno.kinematics.exit_energy:
Exit energy
'''''''''''
In the kinematics data block, each incident energy has a secondary
distribution of *NPU* angle cosines. Therefore, there are *NPU*
(*E*, \ :math:`\mu`) pairs associated with each incident energy. For each
(*E*, \ :math:`\mu`) pair, there is a corresponding exit energy distribution
that can have *NPE* exit energies. Because the kinematics data are
tabulated in a coupled angle-energy format, the exit energy is obtained
by a 2-D interpolation as shown in :numref:`fig8-1-197`.
The objective of the sampling procedure is to sample the exit energy
*E'* in conjunction with the sampled angle cosine. Therefore, the
interpolation for the exit energy is performed with an equation that is
analogous to :eq:`eq8-1-33`:
.. math::
:label: eq8-1-40
E^{'} = E^{'}_{i} + \bigg(\frac{E - E_{i}}{E_{i+1} - E_{i}}\bigg) (E^{'}_{i + 1} - E^{'}_{i})
Based on :eq:`eq8-1-40`, the values of :math:`E^{\prime}_{i}` and :math:`E^{\prime}{ }_{i+1}` must
be obtained in order to calculate the exit energy for the collision. The
*a*\ :sup:`th` and *b*\ :sup:`th` cosine bins are selected according to
the procedures in :numref:`sec-module.keno.kinematics.gen` from tables
*i* and *i*\ +1, respectively. As a result, the secondary energy
distributions corresponding to the *a*\ :sup:`th` and *b*\ :sup:`th`
cosine bins must be used to sample the exit energies from tables *i* and
*i*\ +1. The details for sampling the energy bins are deferred for the
moment. Once the appropriate energy bins are sampled from the two
tables, the interpolation for :math:`E^{'}_{i}` and :math:`{E_{i+1}}` is obtained
with the following equations:
.. math::
:label: eq8-1-41
E_{i}^{'} = E_{ia}^{'} + \left( \frac{{\dot{\mu}}_{i} - \mu_{ia}}{\mu_{ia + 1} - \mu_{ia}} \right)\left( E_{ia + 1}^{'} - E^{'}_{ia} \right)\ ,
.. math::
:label: eq8-1-42
E_{i + 1}^{'} = E_{i + 1b}^{'} + \left( \frac{{\dot{\mu}}_{i + 1} - \mu_{i + 1b}}{\mu_{i + 1b + 1} - \mu_{i + 1b}} \right)\left( E_{i + 1b + 1}^{'} - E_{i + 1b}^{'} \right) .
.. figure:: figs/Keno/fig197.png
:align: center
:width: 600
:name: fig8-1-197
Interpolation diagram for secondary angle-energy data.
Based on :eq:`eq8-1-41` and :eq:`eq8-1-42` the values for :math:`E^{'}_{ia}`, :math:`E^{'}_{ia + 1}`, and
:math:`E^{'}_{ia + 1 b+1}`are needed to
calculate :math:`E^{'}_{i}` and :math:`E^{'}_{i+1}`. The values for :math:`E^{'}_{ia}`
and :math:`E^{'}_{ia + 1}` correspond to secondary energies that are coupled
with the *a*\ :sup:`th` and :math:`a+1^{st}` angle cosines in Table
*i*. Likewise, the values for :math:`E^{'}_{i+1 b}` :math:`E^{'}_{i+1 b+1}`
correspond to the secondary energies that are coupled with the
*b*\ :sup:`th` and :math:`b+1^{st}` angle cosines in Table *i*\ +1.
Therefore, the exit energies from Table *i* are sampled from the
secondary energy distributions that correspond to :math:`\left(E, \mu_{i a}\right)` and
:math:`\left(E, \mu_{i a+1}\right)`, and the energies from Table *i*\ +1 are
sampled from the energy distributions for :math:`\left(E, \mu_{i+1} b\right)`
and :math:`\left(E, \mu_{i+1 b+1}\right)`.
As with the angular data, the secondary energy distributions may be
provided in equiprobable or nonequiprobable energy bins. The following
discussion provides the procedures for sampling the different
distributions.
**Equiprobable Energy Bins.** In Table *i*, the *k*\ :sup:`th` and
*m*\ :sup:`th` energy bins are sampled from the energy distributions for
(*E*, :math:`\mu_{i \ a}`) and (*E*, :math:`\mu_{i \ a+1}`), respectively. The
number of energy bins in a distribution is one less than the number of
energies in the table (i.e., *NPE* - 1). If the energy distributions are
provided in equiprobable bins, the *k*\ :sup:`th` and *m*\ :sup:`th`
bins are selected as follows:
.. math::
:label: eq8-1-43
k = (NPE_{ia} - 1)\ast R_{2} + 1 ,
.. math::
:label: eq8-1-44
m = (NPE_{ia+1} - 1)\ast R_{2} + 1 .
The exiting energy values for :math:`E^{'}_{i \ a}` :math:`E^{'}_{i \ a+1}` are interpolated as follows:
.. math::
:label: eq8-1-45
E^{'}_{ia} = E^{'}_{iak} + \bigg[k - (NPE_{ia} - 1)\ast R_{2}\bigg] \bigg(E^{'}_{iak+1} - E^{'}_{iak}\bigg) ,
.. math::
:label: eq8-1-46
E^{'}_{ia+1} = E^{'}_{ia + 1m} + \bigg[m - (NPE_{ia+1} - 1)\ast R_{2}\bigg] \bigg(E^{'}_{ia+1m+1} - E^{'}_{ia+1m}\bigg) .
In Table *i*\ +1, the *n*\ :sup:`th` and *q*\ :sup:`th` energy bins
are sampled from the energy distributions for :math:`\left(E, \mu_{i} b\right)` and
:math:`\left(E, \mu_{i b+1}\right)`, respectively. As presented for the
*i*\ :sup:`th` table, the *n*\ :sup:`th` and *q*\ :sup:`th` bins are
selected from an equiprobable distribution in a manner analogous with
:eq:`eq8-1-43` and :eq:`eq8-1-44`:
.. math::
:label: eq8-1-47
n = (NPE_{i+1b} - 1)\ast R_{2} + 1 ,
.. math::
:label: eq8-1-48
q = (NPE_{i+1b+1} - 1)\ast R_{2} + 1 .
The exiting energy values for :math:`E_{i+1 \ b}` and :math:`E_{i+1 b+1}` are interpolated as follows:
.. math::
:label: eq8-1-49
E^{'}_{i+1b} = E^{'}_{i+1bn} + \bigg[n - (NPE_{i+1b} - 1)\ast R_{2}\bigg] \bigg(E^{'}_{i+1bn+1} - E^{'}_{i+1bn}\bigg) ,
.. math::
:label: eq8-1-50
E^{'}_{i+1b+1} = E^{'}_{i+1b+1q} + \bigg[q - (NPE_{i+1b+1} - 1)\ast R_{2}\bigg] \bigg(E^{'}_{i+1b+1q+1} - E^{'}_{i+1b+1q}\bigg) .
The exit energy from the *i*\ :sup:`th` table (i.e., :math:`E^{'}`) is
obtained by substituting the values for :math:`E^{'}_{ia}` and :math:`E^{'}_{ia+1}`
into :eq:`eq8-1-41`, and the exit energy from the *i*\ +1\ :sup:`st` table (i.e.,
:math:`E^{'}_{i+1}`) is calculated by substituting the values for
:math:`E^{'}_{ib}` and :math:`E^{'}_{ib+1}` into :eq:`eq8-1-42`. Finally, the exit energy for
the collision is obtained by inserting the calculated values for :math:`E^{'}_{i}`
and :math:`E^{'}_{i+1}` into :eq:`eq8-1-40`.
.. _ last equation in this paragraph says chapter 9
**Nonequiprobable Energy Bins.** If the energy distributions are
provided in nonequiprobable bins, the *k*\ :sup:`th` and *m*\ :sup:`th`
bins are sampled according to the cumulative distribution values:
.. math::
:label: eq8-1-51
C_{iak - 1} < R_2 \leq C_{iak} ,
.. math::
:label: eq8-1-52
C_{ia + 1m - 1} < R_2 \leq C_{ia+1m} ,
where
:math:`C_{iak - 1}` = cumulative probability corresponding to the *k*\ -1\ :sup:`st` energy bin in the :math:`\left(E, \mu_{i a}\right)` distribution,
:math:`C_{iak}` = cumulative probability corresponding to the *k*\ :sup:`th` energy bin in the :math:`\left(E, \mu_{i a}\right)` distribution,
:math:`C_{ia + 1m - 1}` = cumulative probability corresponding to the m-1\ :sup:`st` energy bin in the :math:`\left(E, \mu_{i} a+1\right)` distribution, and
:math:`C_{ia+1m}` = cumulative probability corresponding to the m\ :sup:`th` energy bin in the :math:`\left(E, \mu_{i a+1}\right)` distribution.
For the nonequiprobable bins, the bins for the secondary energy are selected
so that linear interpolation can be performed in the PDF. Since the CDF is
obtained by integrating the PDF, the interpolation procedure for the CDF is
quadratic in form. As a result, the value for :math:`E^{'}_{i \ a}` is obtained with the following equation:
.. math::
:label: eq8-1-53
E^{'}_{ia} = E^{'}_{iak} + \frac{\sqrt{P^{2}_{iak} + 2s_{ia}(R_{2}-C_{iak-1})} - P_{iak}}{s_{ia}} ,
and
.. math::
:label: eq8-1-54
s_{ia} = \frac{\sqrt{P_{iak+1} - P_{iak}}}{E^{'}_{iak+1} - E^{'}_{iak}} ,
where
:math:`P_{iak}` = value of the PDF corresponding to the lower boundary of the *k*\ :sup:`th` energy bin in the (E, :math:`\mu_{i \ a}`) distribution, and
:math:`P_{iak+1}` = value of the PDF corresponding to the upper boundary of the *k*\ :sup:`th` energy bin in the (E, :math:`\mu_{i \ a}`) distribution.
Likewise, the value for :math:`E_{i \ a+1}` is obtained with the following equation:
.. math::
:label: eq8-1-55
E^{'}_{ia+1} = E^{'}_{ia+1m} + \frac{\sqrt{P^{2}_{ia+1m} + 2s_{ia+1}(R_{2} - C_{ia+1m-1})} - P_{ia+1m}}{s_{ia+1}} ,
and
.. math::
:label: eq8-1-56
s_{ia+1} = \frac{P_{ia+1m+1} - P_{ia+1m}}{E^{'}_{ia+1m+1} - E^{'}_{ia+1m}}
where
:math:`P_{ia+1m}` = value of the PDF corresponding to the lower boundary of the *m*\ :sup:`th` energy bin in the (E, :math:`\mu_{i a+1}`) distribution, and
:math:`P_{ia+1m+1}` = value of the PDF corresponding to the upper boundary of the *m*\ :sup:`th` energy bin in the (E, :math:`\mu_{i a+1}`) distribution.
For nonequiprobable distributions in the *i*\ +1\ :sup:`st` table, the
*n*\ :sup:`th` and *q*\ :sup:`th` bins are sampled according to the
cumulative distribution values:
.. math::
:label: eq8-1-57
C_{i+1bn-1} < R_{2} \leq C_{i+1bn} ,
.. math::
:label: eq8-1-58
C_{i+1b+1q-1} < R_{2} \leq C_{i+1b+1q} ,
where
:math:`C_{i+1bn-1}` = cumulative probability corresponding to the n-1\ :sup:`st` energy bin in the (E, :math:`\mu_{i+1 \ b}`) distribution,
:math:`C_{i+1bn}` = cumulative probability corresponding to the *n*\ :sup:`th` energy bin in the (E, :math:`\mu_{i+1 \ b}`) distribution,
:math:`C_{i+1b+1q-1}` = cumulative probability corresponding to the q-1\ :sup:`st` energy bin in the (E, :math:`\mu_{i+1 \ b+1}`) distribution, and
:math:`C_{i+1b+1q}` = cumulative probability corresponding to the *q*\ :sup:`th` energy bin in the (E, :math:`\mu_{i+1 \ b+1}`) distribution.
As observed for the i\ :sup:`th` table, the interpolation procedure for the CDF is
quadratic in form, and the value for :math:`E^{'}_{i+1 \ b}` is obtained as follows:
.. math::
:label: eq8-1-59
E^{'}_{i+1b} = E^{'}_{i+1bn} + \frac{\sqrt{P^{2}_{i+1bn} + 2s_{i+1b}(R_{2} - C_{i+1bn-1})} - P_{i+1bn}} {s_{i+1b}} ,
and
.. math::
:label: eq8-1-60
s_{i+1b} = \frac{P_{i+1bn+1} - P_{i+1bn}}{E^{'}_{i+1bn+1} - E^{'}_{i+1bn}} ,
where
:math:`P_{i+1bn}` = value of the PDF corresponding to the lower boundary of the *n*\ :sup:`th` energy bin in the (E, :math:`\mu_{i+1 b}`) distribution, and
:math:`P_{i+1bn+1}` = value of the PDF corresponding to the upper boundary of the *n*\ :sup:`th` energy bin in the (E, :math:`\mu_{i+1 b}`) distribution.
Likewise, the value for :math:`E^{'}_{i+1 b+1}` is obtained with the following equation:
.. math::
:label: eq8-1-61
E^{'}_{i+1b+1} = E^{'}_{i+1b+1q} + \frac{\sqrt{P^{2}_{i+1b+1q} + 2s_{i+1b+1}(R_{2} - C_{i+1b+1q-1})} - P_{i+1b+1q}}{s_{i+1b+1}} ,
and
.. math::
:label: eq8-1-62
s_{i+1b+1} = \frac{P_{i+1b+1q+1} - P_{i+1b+1q}}{E^{'}_{i+1b+1q+1} - E^{'}_{i+1b+1q}} ,
where
:math:`P_{i+1b+1q}` = value of the PDF corresponding to the lower boundary of the *q*\ :sup:`th` energy bin in the (E, :math:`\mu_{i+1 b+1}`) distribution, and
:math:`P_{i+1b+1q+1}` = value of the PDF corresponding to the upper boundary of the *q*\ :sup:`th` energy bin in the (E, :math:`\mu_{i+1 b+1}`) distribution.
To obtain the exit energy for the collision, the energy from the i\ :sup:`th`
table (i.e., :math:`E^{'}_{i}`) is calculated by substituting the values for
:math:`E^{'}_{ia}` and :math:`E^{'}_{ia+1}` into :eq:`eq8-1-41`, and the exit
energy from the i+1\ :sup:`st` table (i.e., :math:`E^{'}_{i+1}`)
is calculated by substituting the values for :math:`E^{'}_{ib}` and :math:`E^{'}_{ib+1}`
into :eq:`eq8-1-42`.
Finally, the exit energy for the collision is obtained by inserting the
calculated values for :math:`E^{'}_{i}` and :math:`E^{'}_{i+1}` into :eq:`eq8-1-40`.
.. _ last ref says chapter 9
.. _8-1-6-2-7-4:
Isotropic Angular Distributions With Energy Coupling
''''''''''''''''''''''''''''''''''''''''''''''''''''
The kinematics format can accommodate isotropic angular distributions in
the coupled angle energy format. The following discussion describes the
special case with the appropriate sampling procedures. If the secondary
angular distribution is isotropic at an incident energy *E*, a single
exit cosine with a value of -2.0 is specified in the (*E*, \ :math:`\mu`) block.
Therefore, the exit angle cosine is sampled uniformly between -1.0 and
1.0:
.. math::
:label: eq8-1-63
\mu = 2R_{1} - 1 .
Because there is only one exit cosine specified in the (*E*, \ :math:`\mu`)
block, there is a single energy distribution record specified for the
(*E*, \ :math:`\mu`) pair. The general structure (i.e., material identifiers and
data flags are omitted for clarity) of the kinematics data within a
section for a reaction is presented in :numref:`tab8-1-25`. As a result, the
sampling procedure for the exit energy is based on the incident energy.
.. list-table:: Kinematics data structure for isotropic angular distributions
:name: tab8-1-25
:align: center
* - .. image:: figs/Keno/tab25.svg
:align: center
:width: 600
Once the angle is sampled according to :eq:`eq8-1-63`, the exit energy is sampled
in a manner that is analogous to the procedures of :numref:`sec-module.keno.kinematics.exit_energy`. If
the incident energy, *E*, is between *E*\ :sub:`i` and
*E*\ :sub:`i+1`, the *k*\ :sup:`th` energy bin is sampled from the
distribution corresponding to *E*\ :sub:`i` using :eq:`eq8-1-64` or :eq:`eq8-1-65` for
equiprobable or nonequiprobable distributions, respectively.
.. math::
:label: eq8-1-64
k = \big(NPE_{i} - 1\big)\ast R_{2} + 1 ,
or
.. math::
:label: eq8-1-65
C_{ik-1} < R_{2} \leq C_{ik} ,
where
:math:`NPE_{i}` = number of exit energies corresponding to :math:`E_{i}`,
:math:`C_{ik-1}` = cumulative probability corresponding to the k-1\ :sup:`st` energy bin in the distribution for :math:`E_{i}`, and
:math:`C_{ik}` = cumulative probability corresponding to the k\ :sup:`th` energy bin in the distribution for :math:`E_{i}`.
For equiprobable energy bins, the exit energy corresponding to :math:`E_{i}` is calculated as follows:
.. math::
:label: eq8-1-66
E^{'}_i = E^{'}_{ik} + \bigg[k - \big(NPE_{i} - 1\big)\ast R_{2}\bigg] \bigg(E^{'}_{ik+1} - E^{'}_{ik} \bigg) .
If the secondary energy distributions are provided in nonequiprobable bins the exit energy is calculated using the following equation:
.. math::
:label: eq8-1-67
E^{'}_{i} = E^{'}_{ik} + \frac{P^{2}_{ik} +2s_{i}\big(R_{2}-C_{ik-1}\big) - P_{ik}}{s_{i}} ,
and
.. math::
:label: eq8-1-68
s_{i} = \frac{P_{ik+1} - P_{ik}}{E^{'}_{ik+1} - E^{'}_{ik}} ,
where
:math:`P_{ik}` = value of the PDF corresponding to the lower boundary of the *k*\ :sup:`th` energy bin in the distribution for :math:`E_{i}`, and
:math:`P_{ik+1}` = value of the PDF corresponding to the upper boundary of the *k*\ :sup:`th` energy bin in the distribution for :math:`E_{i}`.
By replacing *i* with *i*\ +1 in :eq:`eq8-1-64` through :eq:`eq8-1-68`, the exit energy :math:`E^{'}_{i+1}` can be
calculated from the secondary energy distribution corresponding to the
incident energy :math:`E_{i+1}`. Subsequently, :eq:`eq8-1-40` can be used to calculate the
exit energy.
.. _ last equation says chapter 9.
.. _8-1-6-2-7-5:
Coherent and incoherent elastic scattering
''''''''''''''''''''''''''''''''''''''''''
If thermal scattering law data are available for a material, the elastic
scattering mechanism may be specified as either coherent or incoherent
elastic scattering. Consequently, there is no change in energy resulting
from either collision. The secondary energy distribution block for each
(*E*, \ :math:`\mu`) pair only has one exit energy with a value equal to the
incident energy *E*. Therefore, the procedure for coherent or incoherent
elastic scattering reduces to sampling the exit angle cosine. The
procedures detailed in :numref:`sec-module.keno.kinematics.exit_angle` are used to sample the exit
angle cosine. The general structure of the kinematics data within a
section for coherent or incoherent elastic scattering is presented in
:numref:`tab8-1-26` with the material identifiers and data flags omitted for
clarity. Once the angle cosine is selected, the exit energy is set equal
to the incident energy.
.. list-table:: Kinematics data structure for coherent and incoherent elastic scattering
:name: tab8-1-26
:align: center
* - .. image:: figs/Keno/tab26.svg
:align: center
:width: 600
.. _8-1-6-2-7-6:
Elastic and discrete-level inelastic scattering
'''''''''''''''''''''''''''''''''''''''''''''''
There is a one-to-one correspondence between the exiting angle and
energy for elastic and discrete level inelastic scattering . Once the
exiting angle is selected, the exiting energy is already determined
based on the kinematics equations documented in most conventional
reactor theory text books. However, an obscure fact is that the exiting
energy distributions for discrete-level inelastic reactions and hydrogen
elastic scattering can be double valued in the lab system. For discrete
level inelastic scattering in the lab system, the range of incident
energies that can have a double valued exit energy is given by the
following expression:
.. math::
:label: eq8-1-69
\Delta E_{double} = \frac{Q}{A(1-A)} ,
where
*Q* = the excess of the kinetic energy of the product particles over
that of the original particles, and
*A* = atomic mass ratio of the target mass to the mass of a neutron.
:eq:`eq8-1-69` provides the size in energy of the double valued region above the
threshold energy for the reaction. As indicated by :eq:`eq8-1-69`, the range of
energies for a double valued region is inversely proportional to the
target mass. Using :eq:`eq8-1-69` and ENDF/B data, the values of :math:`\Delta E_{\text {double }}`
can be calculated for all discrete level inelastic scattering reactions
for all isotopes. A plot of :math:`\Delta E_{\text {double }}` as a function of atomic mass
ratio is provided in :numref:`fig8-1-198` for all possible discrete level
inelastic scattering collisions for all isotopes. As shown in Fig.
:numref:`fig8-1-198`, the size of the double valued region approaches 1 MeV as the
mass ratio decreases. Because :math:`\Delta E_{\text {double }}` can be relatively large,
the double valued anomaly cannot be ignored in the collision treatment.
The following discussion outlines the properties of the kinematics data
and the procedures for treating elastic and discrete level inelastic
scattering.
.. figure:: figs/Keno/fig198.png
:align: center
:width: 600
:name: fig8-1-198
Range of incident energies (:math:`\Delta`\ *E*\ :sub:`double`) for double valued region as a function of mass ratio.
As noted previously, *NPU* secondary angle cosines are provided for each
incident energy for a reaction, and the cosine distribution can be
represented with either equiprobable or nonequiprobable distributions.
Depending on the type of distribution, procedures similar to those of
:numref:`sec-module.keno.kinematics.exit_energy` are used to sample an equiprobable or nonequiprobable
angular distribution for the exit cosine in the lab system.
The angular data blocks for discrete level inelastic scattering and
hydrogen elastic scattering are similar in form to other reactions;
however, the exit lab cosines for discrete level inelastic scattering
are greater than zero in the double-valued region, and an exit lab
cosine may appear twice in the distribution with different
probabilities. As an example, discrete level inelastic scattering for
:sup:`7`\ Li is characterized by a double valued exit energy
distribution as a function of exit cosine in the lab system.
:numref:`fig8-1-190` provides the exit energy distribution for an inelastic
collision that leaves the :sup:`7`\ Li nucleus in the first excited
state (i.e., MT = 51) in the lab system. For :sup:`7`\ Li, the threshold
for MT = 51 is 5.4672 :math:`\times` 10\ :sup:`5` eV, and the double valued region
extends from the threshold energy up to 5.58259 :math:`\times` 10\ :sup:`5` eV;
therefore, the incident energy range of the double valued region is
~1.15 :math:`\times`\ 10\ :sup:`4` eV. As shown in :numref:`fig8-1-190`, the exit energy
distributions are provided for different incident energies within the
double valued region and an incident energy above the double valued
region. As the incident energy exceeds the maximum energy for which two
exiting energies can be produced, the secondary energy distribution
becomes single valued (i.e., one exit energy for an exit cosine).
Note that the double valued anomaly does not occur in the center-of-mass
system. Therefore, the two exit energies possible for the lab system
actually correspond to two different center-of-mass exit cosines. During
the preparation of the KENO library, the angular distribution tables for
discrete level inelastic scattering and elastic scattering for hydrogen
can be constructed in the center-of-mass system and subsequently
converted to the lab system. In order to properly construct the angular
distribution tables in the lab system, the minimum lab cosine,
:math:`\mu`\ :sup:`min`\ :sub:`lab`, must be determined because exit angles
below the minimum lab cosine are not possible.
For discrete level inelastic scattering and elastic scattering, the exit
cosine in the lab system can be expressed as a function of the
center-of-mass scattering angle, :math:`\mu`\ :sub:`cm`:
.. math::
:label: eq8-1-70
\mu = \frac{\gamma + \mu_{cm}}{\big(1+2\gamma\mu_{cm}+\gamma^{2}\big)^{1/2}} ,
where
.. math::
:label: eq8-1-71
\frac{1}{\gamma} = \bigg[A^{2} + \frac{A\big(A+1\big)Q}{E}\bigg]^{1/2}
Physically, the quantity 1/:math:`\gamma` represents the ratio of the exit velocity
of the neutron in the lab system to the center-of-mass velocity.
Moreover, the quantity 1/:math:`\gamma` reduces to *A* for elastic scattering
(i.e., *Q* = 0). The minimum value for :math:`\mu` can be obtained by taking the
derivative of :eq:`eq8-1-72` with respect to :math:`\mu`\ :sub:`cm` which yields the following
expression:
.. math::
:label: eq8-1-72
\frac{d\mu}{d\mu_{cm}} = \frac{1+ \gamma\mu_{cm}}{\big(1+2\gamma\mu_{cm}+\gamma^{2}\big)^{3/2}} .
Setting :eq:`eq8-1-72` equal to 0 reveals that the minimum lab cosine
(:math:`\mu`\ :sup:`min`\ :sub:`lab`) occurs when :math:`\mu`\ :sub:`cm` = -1/:math:`\gamma`. For elastic
scattering, the minimum lab cosine occurs when :math:`\mu`\ :sub:`cm` = -\ *A*. Because
hydrogen is the only nuclide with a mass ratio below 1, hydrogen is the
only nuclide that has a double valued exit energy distribution in the
lab system for elastic scattering.
During the preparation of the KENO library, the lab distributions for
discrete level inelastic scattering and hydrogen elastic scattering will
be constructed so that :math:`\mu`\ :sup:`min`\ :sub:`lab` is a boundary for an
angular bin, and no angular cosines in the lab system will be permitted
below :math:`\mu`\ :sup:`min`\ :sub:`lab`. As shown in :numref:`fig8-1-199` for
:sup:`7`\ Li, the exit cosines greater than :math:`\mu`\ :sup:`min`\ :sub:`lab`
will have two possible exit energies in the double valued region. As a
result, the angular distribution table in the library will have angles
that appear twice with different probabilities. For example, an angle
cosine :math:`\mu` may be present in the table with probabilities *P*\ :sub:`m` and
*P*\ :sub:`n`. Although the value of the angle cosine is the same for both
probabilities, the corresponding exit energy will be different for each
(:math:`\mu`, *P)* pair. In other words, the probability for an exit cosine
determines the location in the exit energy distribution table for
selecting the outgoing energy.
.. figure:: figs/Keno/fig199.png
:align: center
:width: 600
:name: fig8-1-199
:sup:`7`\ Li exit energy distribution for the first discrete
level inelastic scattering reaction (MT=51). *E*\ :sub:`threshold` =
5.4672 :math:`\times` 10\ :sup:`5` eV; :math:`\Delta`\ *E*\ :sub:`double` = 1.1539 :math:`\times` 10\ :sup:`4` eV.
Based on the format of the kinematics data, angle cosine distributions
are provided as a function of incident energy. If the incident energy,
*E*, is between *E*\ :sub:`i` and *E*\ :sub:`i+1`, then the *i*\ :sup:`th`
table is selected with probability *P*\ :sub:`i` and the *i*\ +1 table is
selected with probability *P*\ :sub:`i+1`:
.. math::
:label: eq8-1-73
P_{i} = \frac{E_{i+1} - E}{E_{i+1}-E_{i}} ,
.. math::
:label: eq8-1-74
P_{i+1} = \frac{E - E_{i}}{E_{i+1} - E_{i}} .
Once the angular distribution corresponding to the incident energy is
selected, the exit angle cosine can be selected using procedures like
those in :numref:`sec-module.keno.kinematics.exit_angle` For example, if the *i*\ :sup:`th`
incident energy is selected, either :eq:`eq8-1-29` is used to select the
*a*\ :sup:`th` cosine bin for equiprobable bins, or :eq:`eq8-1-34` is used for
nonequiprobable bins. Subsequently, either :eq:`eq8-1-31` or :eq:`eq8-1-36` is used
to calculate the exit angle cosine, depending on the type of angular
distribution provided.
.. _ last equation said chapter 9
The coupled secondary angle-energy data blocks (*E*, :math:`\mu`, *E'* ) follow
the angular data block in the kinematics data. For elastic scattering
and discrete level inelastic scattering, there is one possible exit
energy. Therefore, in the exit energy distribution block, a single exit
energy (*NPE* = 1) is provided for each (*E*, \ :math:`\mu`) pair, and the
general structure (i.e., material identifiers and data flags are omitted
for clarity) of the secondary energy distribution data block is
presented in :numref:`tab8-1-27`. Because only one exit energy is provided for
each (*E*, \ :math:`\mu`) pair, the probability for the exit energy is 1.0. As
indicated in :numref:`tab8-1-27`, a cumulative probability of 1.0 is stored for
each exit energy; however, the parameters stored in the PDF location are
the power-interpolation parameters needed to interpolate the exit
energy.
.. list-table:: Secondary energy distribution format for elastic and discrete-level inelastic scattering
:name: tab8-1-27
:align: center
* - .. image:: figs/Keno/tab27.svg
:width: 600
:align: center
When an exiting angle :math:`{\dot{\mu}}_{i}` is sampled between :math:`\mu`\ :sub:`a`
and :math:`\mu`\ :sub:`a+1`, the exiting energy values that correspond to
:math:`\mu`\ :sub:`a` and :math:`\mu`\ :sub:`a+1` for the incident energy *E*\ :sub:`i` can be used
to interpolate the exiting energy *E*\ ' that corresponds
to\ :math:`{\dot{\mu}}_{i}`. Physically, the interpolation procedures
correspond to an interpolation along one of the incident energy curves
as depicted in :numref:`fig8-1-197`. In order to perform the interpolation, the
*a*\ :sup:`th` and *a*\ +1\ :sup:`st` (*E*, \ :math:`\mu`) pairs are located in
the secondary energy distribution block corresponding to *E*\ :sub:`i`.
Subsequently, the corresponding *a*\ :sup:`th` and *a*\ +1 exit energy
values (i.e., :math:`E^{'}_a` and :math:`E^{'}_{a+1}`) are read from the secondary energy distribution
record.
The exiting energy is interpolated with the following relation:
.. math::
:label: eq8-1-75
E^{'}\left( {\dot{\mu}}_{i} \right) = E_{a}^{'} + \left( \frac{{\dot{\mu}}_{i}^{P_{a}} - \mu_{a}^{P_{a}}}{\mu_{a + 1}^{P_{a}} - \mu_{a}^{P_{a}}} \right)\left( E_{a + 1}^{'} - E_{a}^{'} \right)\ ,
where
*P* = is a "power-interpolation" factor for the *a*\ :sup:`th` cosine
bin that is obtained from a fit to the *E'* distribution as a
function of :math:`\mu`.
The interpolation procedure in :eq:`eq8-1-75` is analogous to the interpolation
scheme that has been used successfully to interpolate Bondarenko factors
as a function of temperature in the BONAMI module. If the curve is
monotonic in nature, the power-interpolation scheme can be used to
represent the curvature with a minimum number of points. For elastic and
discrete level inelastic scattering, the *E'*\ (:math:`\mu`) distribution is
monotonic and is suited for the power interpolation scheme. Note that if
*p* is 1, :eq:`eq8-1-75` reduces to a linear interpolation in :math:`\mu`-*E'* space.
.. _sec-module.keno.ce_physics.tsl:
Thermal scattering effects
^^^^^^^^^^^^^^^^^^^^^^^^^^
A collision between a neutron and nucleus can be affected by the thermal
motion of the target nucleus. Moreover, ENDF provides thermal scattering
law data to account for the thermal effects of scattering with a
material below 10 eV; however, the scattering law data are only available
for a select number materials as shown in :numref:`tab8-1-28`. If thermal
scattering law data are not available, elastic scattering is treated
with the free gas approximation in the KENO library. For heavy nuclides
with 0 K scattering libraries available, the Doppler Broadening
Rejection Correction (DBRC) method is used instead. For DBRC-enabled
nuclides, thermal scattering effects are taken into account up to 210 eV
(although this parameter can be controlled by the user). More
information on DBRC is given in :numref:`8-1-6-2-9`.
.. list-table:: ENDF/B thermal scattering law data.
:align: center
:name: tab8-1-28
* - .. image:: figs/Keno/tab28.svg
:align: center
:width: 600
The continuous energy cross section library is processed to account for
the appropriate scattering effects. As a result, the KENO cross section
library inherently accounts for thermal scattering using either the
thermal scattering law data or the free gas approximation. In other
words, the kinematics data based on thermal effects are combined with
the fast data to represent the collision kinematics for the material.
As noted previously, the kinematics data block for a reaction is divided
into sections that describe the collision kinematics for a range of
incident energies. As a result, the kinematics data structure has a
modular format that is beneficial for data library production. Because
of the kinematics data structure, the thermal scattering law data, which
are typically applied up to 10 eV, can be processed independently with
AMPX to obtain the angle energy probability distributions. Subsequently,
one or more sections in the kinematics data block can be used to
represent the thermal angle -energy distributions for energies up to
10 eV. Moreover, the fast kinematics data can be represented with one or
more sections for energies above 10 eV. As part of the library
preparation, the thermal kinematics data are combined with the fast
kinematics data block to complete the collision representation for the
entire range of incident energies. Because the thermal scattering
effects are treated during the processing of the cross section data for
a material, the thermal effects are inherently treated in KENO. The 10 eV
cutoff energy for thermal scattering can be input by the parameter
**THC** in the parameter input. Using a cutoff value above 10 eV increases
the energy range of free gas approximation because AMPX processed thermal
scattering law data are available up to 10 eV, and this may increase the
runtime in the sampling process while improving the accuracy in the
results for some casees. During
the Monte Carlo random walk, the procedures provided in :numref:`sec-module.keno.kinematics.exit_angle`
and :numref:`sec-module.keno.kinematics.exit_energy` are used to sample the exit angle and energy
for the collision.
.. _8-1-6-2-9:
Doppler broadening rejection correction method
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
When colliding with a heavy nuclide, the thermal motion of the target
nuclide can significantly affect the exit angle and energy of the
neutron. The thermal motion of the target nuclide was previously
ignored, but this assumption has been proven inadequate by Dagan and
Becker :cite:`KENO-becker_proof_2009`.
A new sampling equation has been implemented to allow for Doppler
broadening of the scattering kernel. Removing this approximation can
have a significant impact on the critical eigenvalue of systems by
allowing neutrons to be upscattered into absorption resonances.
Currently, DBRC is enabled in KENO only for :sup:`238`\ U, and this
feature can be activated by setting the parameter **DBR**\ =1.
.. _8-1-6-2-10:
Doppler broadening methods
^^^^^^^^^^^^^^^^^^^^^^^^^^
CE KENO calculations will perform temperature adjustment of neutron
cross sections by default. The cross sections provided with SCALE are
typically supplied in 300 K intervals, and additional cross section
temperature resolution may be desired to model non-room temperature
systems or systems with significant temperature effects.
The capability to perform problem-dependent Doppler broadening of
nuclear cross sections has been implemented in KENO. This feature is
controlled by the **DBX** parameter, which causes KENO to perform
Doppler broadening on the cross sections in all compositions in a
problem before simulating particle histories. When this occurs, the
cross sections for each material are broadened to the temperature
assigned to that material in the ``READ COMP`` block, as long as the
requested temperature is more than 4 K from the library temperature.
Within this :math:`\pm` 4 K band, the library temperature is used to avoid
difficulties with numerical instabilities in small cross section
adjustments. The default for this feature is ``DBX=2``, which performs
Doppler broadening for both the 1-D and 2-D cross sections. Current
options available are as follows:
- ``DBX`` = 0 -- Doppler broadening is not performed. KENO selects the
library at the closest temperature. If desired, the user can use the
``TTL`` parameter to force a job abort if the library temperature is
too far from the requested temperature. By default, ``TTL=-1``, so
the closest library will be used regardless of the temperature
difference.
- ``DBX=1`` -- Doppler broadening is performed using a finite
difference method on the one-dimensional cross sections that are
temperature dependent. Logarithmic interpolation is also used to
broaden the probability table data. When this option is used, the
collision probabilities are recalculated after the Doppler broadening
is complete to ensure consistency.
- ``DBX=2`` -- The same actions as ``DBX=1`` are performed, and
Doppler broadening is also performed on the thermal moderator data by
conducting interpolation on the double differential probability data
present on the cross section library.
Nuclide level energy unionization is automatically disabled
(``M2U=NO``) when Doppler broadening is enabled in order to
reduce the memory usage. At this writing, research is in progress to
allow KENO to perform on-the-fly cross section Doppler broadening as
particle histories are being simulated.
Multigroup mode solution procedure
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
.. math::
:label: eq8-1-76
\frac{1}{v_{g}}\frac{\partial\Phi_{g}}{\partial t}\left( X,\Omega,t \right) + \Omega \bullet \nabla\Phi_{g}\left( X,\Omega,t \right) + \Sigma_{\text{tg}}\left( X \right)\ \Phi_{g}\left( X,\Omega,t \right) = \mathrm{q}_{\mathrm{g}}\left( X,\Omega,t \right),
where
- :math:`g` is the energy group of interest,
- :math:`v_g` is the average velocity of the neutrons in group g,
- :math:`\Phi_g \left(X,\Omega,t \right)` is the angular flux of neutrons having their
energies in group g, at position X and time t, and
- :math:`\Sigma_{tg} \left( X \right)` is the macroscopic total cross section of the
media at position X for group g, corresponding to
.. math::
\Sigma_{tg}(X) = \frac{\int^{}_{\Delta E_{g}}\Sigma_{t}(X,E)\Phi(X,E,\Omega,t)dE} {\int^{}_{\Delta E_{g}}\Phi(X,E,\Omega,t)dE} ,
where
- :math:`\Delta E_g` defines group g, and
- :math:`q_g \left(X,\Omega,t \right)` is the total source contributing to energy group g
at position X, and time t in direction :math:`\Omega`.
Using the relationship :math:`X^{\prime} = X - R\Omega`, defining the problem to be time
independent using an integrating factor on both sides of :eq:`eq8-1-76`,
and defining
.. _ last equation says chapter 9
.. math::
T(R) = \int^{R}_{0}\Sigma_{tg}(X - R^{'}\Omega)dR^{'} ,
the following equation can be written:
.. math::
:label: eq8-1-77
\Phi_{g}(X,\Omega) = \int^{\infty}_{O}q_{g}(X - R\Omega,\Omega)e^{-T(R)}dR .
At this point, the problem becomes an eigenvalue problem. If there is no
external source, the source may be defined as
.. math::
:label: eq8-1-78
q_{g}\left( X,\Omega \right) = \sum_{g^{'}}^{}{\int_{}^{}{{d\Omega^{'}}\Phi_{g^{'}}\left( X,\Omega^{'} \right)\ \Sigma_{s}\left( X,g^{'} \rightarrow g,\Omega^{'} \cdot \Omega \right)} + \frac{1}{k}Q_{g}^{'}\left( X,\Omega \right)},
where
- k is the largest eigenvalue of the integral equation,
- :math:`Q^{\prime}_{g}\left(X,\Omega \right)` is the fission source
at position X for energy group g and direction :math:`\Omega`
(all fission contributions to group g from all energy groups in the
previous generation), and
- :math:`\Sigma_s \left(X,g^{\prime}\rightarrow g,\Omega^{\prime} \rightarrow \Omega \right)`
is the scattering cross section for scattering at position X from group
:math:`g^{\prime}` and direction :math:`\Omega^{\prime}`
to group g and direction :math:`\Omega`.
In terms of energy, the scatter can be defined as
.. math::
:label: eq8-1-79
\Sigma_{s}\left( X,g^{'} \rightarrow g,\Omega^{'} \cdot \Omega \right) = \frac{\int_{\mathrm{\Delta}E_{g}}^{}{\int_{\mathrm{\Delta}E_{g^{'}}}^{}{\Sigma_{s}\left( X,E^{'} \rightarrow E,\Omega^{'} \cdot \Omega \right)\ \Phi\left(X,E^{'},\Omega^{'} \right)\text{d}E^{'}\text{dE}}}}{\int_{\mathrm{\Delta}E_{g^{'}}}^{}{\Phi\left( X,E^{'},\Omega^{'} \right)\text{dE}^{'}}\ }\ \ ,
where
:math:`\Delta E_g` is the energy-range-defining energy group g, and
:math:`\Delta E_g'` is the energy-range-defining energy group g'.
Assuming the fission neutrons to be isotropic, the fission source
:math:`Q_{g^{\prime}}\left(X,\Omega \right)` can be written as
.. math::
:label: eq8-1-80
Q^{'}_{g}(X,\Omega) = \frac{1}{4\pi}\sum_{g^{'}}\int_{\Omega^{'}}^{}{d\Omega^{'}\Phi_{g^{'}}(X,\Omega^{'})\chi(X,g^{'}\rightarrow g)\nu_{g^{'}}(X)\Sigma_{fg^{'}}(X)} ,
.. _ correct?
where
- :math:`\chi \left(X,g^{\prime} \rightarrow g \right)` is the fraction of neutrons born in energy group g from
fission in energy group g in the media at position X,
- :math:`\nu_{g^{\prime}}\left(X \right)` is the number of neutrons resulting from a fission
in group :math:`g^{\prime}` at position X, and
- :math:`\Sigma_{fg^{\prime}} \left( X \right)` is the macroscopic fission cross section of the
material at position X for a neutron in energy group :math:`g^{\prime}`.
Substituting :eq:`eq8-1-78` into :eq:`eq8-1-77` yields the following equation:
.. _ first equation says chapter 9
.. math::
:label: eq8-1-81
\begin{gathered}
\Phi_{g}(X, \Omega)=\int_{0}^{\infty} d R e^{-T(R)}\left\{\frac{1}{k} \mathrm{Q}_{g}^{\prime}(X-R \Omega, \Omega)\right. \\
\left.+\sum_{g^{\prime}}\left[\int_{\Omega^{\prime}} d \Omega^{\prime} \Phi_{g^{\prime}}\left(X-R \Omega, \Omega^{\prime}\right) \Sigma_{s}\left(X-R \Omega, g^{\prime} \rightarrow g, \Omega^{\prime} \cdot \Omega\right)\right]\right\}
\end{gathered}
.. _ correct?
The definition of k may be given as the ratio of the number of neutrons
in the (n + 1)\ *th* generation to the number of neutrons in the n\ *th*
generation or the largest eigenvalue of the integral equation. Using
:eq:`eq8-1-80`, :eq:`eq8-1-81` can be written as
.. _ last equation says chapter 9
.. math::
:label: eq8-1-82
\begin{gathered}
\Phi_{g}(X, \Omega)=\int_{0}^{\infty} d R e^{-T(R)}\left\{\sum_{g^{\prime}} \frac{1}{k} \int_{\Omega^{\prime}} v_{g^{\prime}}(X-R \Omega) \Sigma_{f g^{\prime}}(X-R \Omega) \chi\left(X-R \Omega, g^{\prime} \rightarrow g\right) \Phi_{g}\left(X-R \Omega, \Omega^{\prime}\right) \frac{d \Omega^{\prime}}{4 \pi}\right. \\
\left.+\sum_{g^{\prime}}\left[\int_{\Omega^{\prime}} d \Omega^{\prime} \Sigma_{t g^{\prime}}\left(X-R \Omega, \Omega^{\prime}\right) \Sigma_{s}\left(X-R \Omega, g^{\prime} \rightarrow g, \Omega^{\prime} \cdot \Omega\right)\right]\right\}
\end{gathered}
Writing :eq:`eq8-1-82` in generation notation, multiplying and dividing
certain terms by :math:`\Sigma_{\mathrm{t}}(\mathrm{X})`, and multiplying both sides of the
equation by :math:`\nu_{\mathrm{g}}(\mathrm{X}) \Sigma_{\mathrm{fg}}(\mathrm{X})` yields the following
equation, which is solved by KENO:
.. _ equation says chapter 9
.. math::
:label: eq8-1-83
\begin{gathered}
\frac{v_{g}(X) \Sigma_{f g}(X)}{\Sigma_{t g}(X)} \Sigma_{t g}(X) \Phi_{g, n}(X, \Omega)=\frac{v_{g}(X) \Sigma_{f g}(X)}{\Sigma_{t g}(X)} \Sigma_{t g}(X) \int_{0}^{\infty} d R e^{-T(R)} \\
\left\{\frac{1}{k} \sum_{g^{\prime}}\left[\int_{\Omega^{\prime}} \frac{v_{g^{\prime}}(X-R \Omega) \Sigma_{f s^{\prime}}(X-R \Omega)}{\Sigma_{t g^{\prime}}(X-R \Omega)} \chi\left(X-R \Omega, g^{\prime} \rightarrow g\right) \Sigma_{t g^{\prime}}(X-R \Omega) \Phi_{g^{\prime}, n-1}\left(X-R \Omega, \Omega^{\prime}\right) \frac{d \Omega^{\prime}}{4 \pi}\right]\right. \\
\left.+\sum_{g^{\prime}}\left[\int_{\Omega^{\prime}} \frac{\sum_{s}\left(X-R \Omega, g^{\prime} \rightarrow g, \Omega^{\prime} \cdot \Omega\right)}{\Sigma_{t g^{\prime}}(X-R \Omega)} \Sigma_{t g^{\prime}}(X-R \Omega) \Phi_{g^{\prime}, n}\left(X-R \Omega, \Omega^{\prime}\right) d \Omega^{\prime}\right]\right\}
\end{gathered}
.. _ correct?
where n indicates the n\ *th* generation and n - 1 is the (n - 1)\ *th*
generation. Note that the left-hand side of the
equation --- :math:`v_{\mathrm{g}}(\mathrm{X}) \sum_{\mathrm{fg}}(\mathrm{X}) \Phi_{\mathrm{g}, \mathrm{n}}(\mathrm{X}, \Omega)` --- is the
fission production for the n\ *th* generation.
The solution strategy used by KENO solves :eq:`eq8-1-83` by using an iterative
procedure. The fission production at point X in energy group g due to
neutrons in the (n - 1)\ *th* generation, normalized to the system
multiplication, is
.. math::
\frac{1}{k}\sum_{g^{'}}\int_{\Omega^{'}}\frac{\nu_{g^{'}}(X)\Sigma_{fg^{'}}(X)}{\Sigma_{tg^{'}}(X)}\chi \big(X,g^{'} \rightarrow g\big)\Sigma_{tg^{'}}\big(X\big)\Phi_{g^{'},n-1}\big(X,\Omega^{'}\big)\frac{d\Omega^{'}}{4\pi} .
The collision points used in KENO are chosen by selecting path lengths
from the distribution
e\ :sup:`-T(R)` ,
which is the probability of transport from any position X - R\ :math:`\Omega` to
position X.
The first collision density of neutrons in group g per unit solid angle
about :math:`\Omega` resulting from the fission source produced by the (n - 1)
generation, normalized to the system multiplication, is
.. math::
\frac{\Sigma_{tg}\big(X\big)\int^{\infty}_{0}dRe^{-T(R)}\frac{1}{k}\int_{\Omega^{'}}\sum_{g^{'}}\frac{\nu_{g^{'}}\big(X-R\Omega\big)\Sigma_{fg^{'}}\big(X-R\Omega\big)}{E_{tg^{'}}\big(X-R\Omega\big)}}{\chi\big(X-R\Omega,g^{'}\rightarrow g\big)\Sigma_{tg^{'}}\big(X-R\Omega\big)\Phi_{g^{'},n-1}\big(X-R\Omega,\Omega^{'}\big)\frac{\text{d}\Omega^{'}}{4\pi}} .
.. _ correct?
The scattering source at position X emerging in group g and direction :math:`\Omega`
resulting from previous collisions in the same generation, is
.. math::
\sum_{g^{\prime}} \int_{\Omega^{\prime}} \frac{\Sigma_{s}\left(X, g^{\prime} \rightarrow g, \Omega^{\prime} \cdot \Omega\right)}{\Sigma_{t g^{\prime}}(X)} \Sigma_{t g}^{\prime}(X) \Phi_{g^{\prime}, n}(X, \Omega) d \Omega^{\prime}
The collision density in group g, per solid angle about :math:`\Omega` is
.. math::
\Sigma_{t g} \int_{0}^{\infty} d R e^{-T(R)} \sum_{g^{\prime}} \int_{\Omega^{\prime}} \frac{\Sigma_{s}\left(X-R \Omega, g^{\prime} \rightarrow g, \Omega^{\prime} \cdot \Omega\right)}{\Sigma_{t g^{\prime}}(X-R \Omega)} \Sigma_{t g^{\prime}}(X-R \Omega) \Phi_{g^{\prime}, n}\left(X-R \Omega, \Omega^{\prime}\right) d \Omega^{\prime}
The total collision density times :math:`\frac{\nu_g(X)\Sigma_{fg}(X)}{\Sigma_{tg}(X)}` is the relationship from
which KENO picks the source points for the next generation.
Collision treatment in KENO
^^^^^^^^^^^^^^^^^^^^^^^^^^^
A collision occurs in a geometrical region when a history exhausts its
mean-free-path length within the boundaries of the region. For each
collision, the absorbed weight and the fission weight are tabulated,
then the weight is modified by the nonabsorption probability. This new
weight is checked for splitting and Russian roulette, and if it
survives, the history is scattered. A new energy group is selected from
the cumulative transfer probability distribution. This group-to-group
transfer determines an angular scattering distribution, usually
expressed as a Legendre expansion of the cross section transfer array.
A set of discrete angles and probabilities are generated by a
generalized Gaussian quadrature procedure, preserving the moments of the
Legendre expansion of the angular scattering distribution. KENO treats
P\ :sub:`0` and P\ :sub:`1` Legendre expansions as special cases. If the
scattering distribution is isotropic, a flag is set to randomly select
new direction cosines from an isotropic distribution, instead of using
discrete scattering angles. If the distribution is a P\ :sub:`1`
expansion, KENO randomly selects the cosine of the scattering angle
according to
(1) :math:`|\bar{\mu}| < \frac{10^{-10}}{3}`: scattering distribution is isotropic,
(2) :math:`|\bar{\mu}| \leq 1/3: \mu = \bigg(\sqrt{1+6\zeta\bar{\mu}+\big(3\bar{\mu}\big)^{2}} - 1\bigg)/ 3\bar{\mu}`,
or
(3) :math:`|\bar{\mu}| > 1/3: \mu = \zeta\big(1-|\bar{\mu}|\big) + \bar{\mu}`
where :math:`\zeta` is a uniform random variable between -1 and +1 and
:math:`\bar{\mu}` is the mean cosine of the scattering angle.
Otherwise, KENO randomly selects one of the discrete scattering angles
(:math:`\mu`). New direction cosines are then calculated according to the
following relationships where u, v, and w are the initial direction
cosines and u', v', and w' are the direction cosines after the
collision:
u' = ucos\ :math:`\Psi - \sqrt{\text{v}^{2} + \text{w}^{2}}`\ sin\ :math:`\Psi`\ cos\ :math:`\eta`
v' = vcos\ :math:`\Psi + \frac{\text{uv}}{\sqrt{\text{v}^{2} + \text{w}^{2}}}\text{cos}\eta\text{sin}\Psi - \frac{\text{w}}{\sqrt{\text{v}^{2} + \text{w}^{2}}}\text{sin}\Psi\text{sin}\eta`
w' = wcos\ :math:`\Psi + \frac{\text{uw}}{\sqrt{\text{v}^{2} + \text{w}^{2}}}\text{cos}\eta\text{sin}\Psi + \frac{\text{v}}{\sqrt{\text{v}^{2} + \text{w}^{2}}}\text{sin}\Psi\text{sin}\eta`
where
:math:`\sin \psi` = :math:`\sqrt{1-\mu^{2}}`,
:math:`\cos \psi` = :math:`\mu` = cosine of the scattering angle,
:math:`\eta` = a random azimuthal angle between 0 and :math:`2 \pi`.
Fission point selection
^^^^^^^^^^^^^^^^^^^^^^^
In order for a fission to occur, a neutron must first have a collision.
The fission weight, :math:`\text{fisw}`, is defined as the neutron
weight, :math:`\text{wt}`, times the :math:`\nu`\ -fission probability,
:math:`\text{fnfp}`:
.. math::
:label: eq8-1-84
fisw = wt\ \times \ fnfp
Two important variables used in the processing of fission points are (1)
FWR, which is defined as the fission weight, :math:`\text{fisw}`,
divided by a random number, and (2) RAKBAR, which is defined as a factor
times the running average value of k-effective, AKBAR. This factor is a
function of the square root of the number of neutrons per generation and
was chosen because it usually produces an adequate number of independent
fission points and does not produce so many that an excessive amount of
time is spent choosing from the fission points produced.
The following procedure for generating fission points is repeated until
FWR is less than RAKBAR. A fission point is generated only if FWR is
greater than RAKBAR. Multiple fissions at the same point are allowed
only if :math:`\text{fisw}` is greater than RAKBAR. If
:math:`\text{fisw}` is greater than RAKBAR, a fission point is stored
with FWR set equal to RAKBAR divided by a random number and
:math:`\text{fisw}` is decremented by RAKBAR. Then the energy group of
fission is chosen randomly from the fission spectrum of the mixture in
which the fission occurred. The energy group of fission, the X, Y, and
Z position, the location of the unit within the array, the region
number, the value of FWR, the region number of the array boundary, and
the nesting data for holes and/or arrays are stored in the fission bank.
The quantity of fission points kept to be used as fission positions for
the next generation is limited to the number of positions in the fission
bank (input parameter ``NFB=``). Typically ``NFB`` is equal to the
input parameter ``NPG``, the number of neutrons per generation. If a
fission occurs and the fission counter is less than ``NFB``, the fission
point information is stored in the fission bank. If a fission occurs and
the fission counter is greater than or equal to the number per
generation, a search is made to find the smallest stored value of FWR.
If FWR of the newly fissioned neutron is less than the smallest FWR in
the table, it is discarded. Otherwise, the information from the newly
fissioned neutron replaces that associated with the smallest value of
FWR found in the table.
When the next generation is ready to be processed, data are transferred
from the fission bank into the neutron bank to be used as starting
positions for the fission neutrons. If more than NPG neutrons are saved
in the fission bank, ``NPG`` of those having the highest values of FWR
will be used. If too few fission positions were stored (less than the
number per generation), a warning message to that effect (K?-132) is
printed, and additional fission points are randomly chosen from those
that were stored until the number of fission points available to start
the next generation is equal to the number of neutrons per generation.
Biasing or weighting
^^^^^^^^^^^^^^^^^^^^
In order to minimize the statistical deviation of k-effective per unit
computer time, KENO uses weighted tracking rather than analog tracking.
Weighted tracking accounts for absorption by reducing the neutron weight
rather than allowing the neutron history to be terminated by absorption.
To prevent expending excessive computer time tracking low-weight
neutrons, Russian roulette is played when the weight of the neutron
drops below a preset weight, WTLOW. Neutrons that survive Russian
roulette are assigned a weight, WTAVG. The value of WTLOW and WTAVG can
be assigned as a function of position and energy. The values used by
KENO are
DWTAV = 0.5, the default value of WTAVG,
WTAVG = DWTAV, the weight given a neutron that survives Russian
roulette, and
WTLOW = WTAVG/3.0, the value of weight at which Russian roulette is
played.
A study :cite:`KENO-hoffman_optimization_1982` by Hoffman shows these default values to be reasonable for
bare critical assemblies. :numref:`fig8-1-200` from this study shows the
analytic relationship between the variance and WTLOW when WTAVG is 0.5.
Note that the default value of 0.167 for WTLOW is very close to the
minimum point on the curve. Experimental results of actual Monte Carlo
calculations\ :sup:`7` provide further assurance that 0.167 is an
optimum choice for WTLOW when WTAVG is 0.5.
.. figure:: figs/Keno/fig200.png
:align: center
:width: 600
:name: fig8-1-200
Analytic estimate of the relationship between WTLOW and the variance, :math:`\sigma^{2}_{k}`, when WTAVG is 0.5.
:numref:`fig8-1-201`, also from the Hoffman study, shows the analytic
relationship between the variance and the value chosen for WTAVG for a
value of WTLOW = 0.167. Although the KENO default value for WTAVG is not
the optimum, a close examination of the data shows that the variance was
changing relatively slowly as a function of WTAVG. Even though this
study shows a value near 0.26 to be optimum for this system, further
studies of other systems are needed before changing the default value of
WTAVG from 0.5 as it has been used in previous versions of KENO.
.. figure:: figs/Keno/fig201.png
:align: center
:width: 600
:name: fig8-1-201
Analytic estimate of the relationship between WTAVG and the
variance, :math:`\sigma^{2}_{k}`, when WTLOW is :sup:`1`/:sub:`6`.
Inside a fissile core, the importance of a neutron is a slowly varying
function in terms of energy and position. Hence, for many systems, the
standard defaults for WTLOW and WTAVG are good values to use. For
reflectors, however, the worth of a neutron varies as a function of
distance from the fissile material and as a function of energy. As a
neutron in the reflector becomes less important relative to a neutron in
the fissile region, it becomes desirable to spend less time tracking it.
Therefore a space- and energy-dependent weighting or biasing function is
used in KENO to allow the user to minimize the variance in k-effective
per unit of tracking time. When a biasing function is used in a
reflector, it becomes possible for a neutron to move from one importance
region into another in which the WTLOW is greater than the weight of the
neutron. When this occurs, Russian roulette is played to reduce the
number of neutrons tracked. When the reverse occurs, that is, when the
neutron moves to a region of higher importance, its weight may be much
higher than WTAVG for that region. When the weight of the neutron is
greater than a preset value, WTHI, the neutron is split into two
neutrons, each having a weight equal to one-half the weight of the
original neutron. This procedure is repeated until the weight of the
split neutron is less than WTHI. The default value for WTHI is
WTAVG*3.0. WTHI is the weight at which splitting occurs.
The weighting or biasing function for a given core material and
reflector material can be obtained by using the adjoint solution from
S\ :sub:`n` type programs for a similar (usually simplified) problem.
This adjoint flux gives the relative contribution of a neutron at a
given energy and position to the total fissions in the system. The
weighting function for KENO is thus proportional to the reciprocal of
the adjoint flux. Although such a function can be difficult to obtain,
the savings gained makes the effort worthwhile for many of the materials
that are frequently used as reflectors. Biasing functions :cite:`KENO-odell_transport_1987` have been
prepared for several reflector materials commonly used in KENO
calculations. The use of biasing to minimize the variance in k-effective
per unit of computer time will usually increase the variance in other
parameters such as leakage or absorption in the reflector.
Differential albedos
^^^^^^^^^^^^^^^^^^^^
Arrays reflected by thick layers of material having a small absorption
to the scattering ratio may require large amounts of computer time to
determine k-effective\ :cite:`KENO-demaret_accurate_1999` because of the relatively long time a
history may spend in the reflector. A differential albedo technique was
developed for use with the KENO codes to eliminate tracking in the
reflector. This involves returning a history at the point it impinges on
the reflector and selecting an emergent energy and polar angle from a
joint density function dependent upon the incident energy and polar
angle. The weight of the history is adjusted by the functional return
from the reflector, which is also based on the incident energy and
angle.
The characteristics of a differential albedo emulate the attributes of
the reflector material and are independent of the material or materials
adjacent to the reflector. Thus, a differential albedo that is generated
for a given reflector material can be used with any array, regardless of
the type of fuel or fissile material contained within the array.
For many calculations involving reflected arrays of fissile material,
the differential albedo treatment is a powerful tool that can
significantly reduce the computing time required to determine
k-effective. The savings will vary depending on the importance of the
reflector to the system. A substantial effort is required to generate a
differential albedo, but the savings gained were well worth the effort
for commonly used reflector materials. The savings are not worth the
applicability questions on modern computing platforms; the differential
albedo capability is maintained only for backwards compatibility.
To generate the differential albedo information for a material, a
fixed-source calculation must be made for each incident energy and
angle. The data presently available for use with KENO were generated by
1-D discrete ordinates calculations for slab geometry representing
infinite slabs. Consequently, for a finite reflector, these data will
not correctly treat histories that enter the reflector near an edge.
Past experience with differential albedo reflectors indicates that
k-effective appears to be conservative for small faces and will tend
toward the correct result as the face becomes large relative to the area
near the corners. Care must be taken to ensure that any surface to which
a differential albedo is applied is large enough that the errors at the
edges can be ignored.
Because differential albedos are expensive and time consuming to
generate, those corresponding to the Hansen-Roach 16-energy-group
structure are the only differential albedos available for use with KENO
at this writing. In the past, their use was limited to problems using
cross sections having the Hansen--Roach 16-energy-group structure. KENO
extends the use of differential albedos to other energy-group structures
by allowing appropriate energy transfers. This is accomplished by
creating lethargy boundary tables for the albedo group structure and the
cross section group structure and determining the lethargy interval
corresponding to the desired transfer (cross section group structure to
albedo group structure or vice versa) based on a uniform lethargy
distribution over the interval. When the energy-group boundaries of the
cross sections and albedos are different, the results should be
scrutinized by the user to evaluate the effects of the approximations.
KENO Geometries
~~~~~~~~~~~~~~~
KENO V.a geometry is restricted to the use of specific shapes. These
shapes are called geometry regions or regions. Allowed shapes in KENO
V.a are cubes, cuboids (rectangular parallelepipeds), spheres,
cylinders, hemispheres, and hemicylinders. These shapes must be oriented
along orthogonal axes and cannot be rotated in KENO V.a. They can be
translated. Hemispheres and hemicylinders are not limited to half
spheres and half cylinders; the definitive plane can be positioned by
entering a chord. The value of this chord can range from the positive
magnitude of the radius (giving a complete sphere or cylinder) to the
negative magnitude of the radius (giving a zero volume, nonexistent
sphere or cylinder).
KENO-VI geometry can model any geometric shape that can be described
using quadratic equations. These geometric shapes are stacked together
forming regions. The set of regions is then used to build units. A set
of predefined shapes that include cones, cuboids (rectangular
parallelepipeds), cylinders, dodecahedrons, ecylinders (extruded
elliptical cylinders), ellipsoids, hexprisms, hoppers, parallelepipeds,
planes, rhombohedrons, spheres, wedges (triangular prisms), as well as
others is used to construct regions. In addition, the keyword
``QUADRATIC`` is provided which allows additional shapes to be
constructed by specifying the quadratic equations that describe the
shape. These shapes can be rotated and translated to any orientation and
position within their respective units. Hemispheres and hemicylinders
can be constructed using spheres and cylinders with a chord. Regions are
rotated by providing the nonzero angles associated with the Euler
X-convention.
A major restriction applied to KENO V.a geometry is that intersections
are not allowed. Furthermore, each successive geometry region must
completely enclose the preceding region. Tangency and shared faces are
allowed. The volume of a region is the volume of the specified shape
minus the volume of the preceding region shape and any holes contained
in the region. To alleviate the complete enclosure restriction, KENO V.a
allows multiple sets of geometry regions, with each set independently
governed by this restriction. Each set of these multiple geometry
regions is called a *unit*. Units can be stacked together in a 3-D
rectangular parallelepiped called an *array* or *lattice*, just as
children's blocks can be stacked. Units that are to be stacked together
in this manner must have a rectangular parallelepiped outer region, and
the adjacent faces of adjacent units must be the same size and shape. An
array can be treated as a building block and used as a unit within
another array.
A major improvement in KENO-VI is the ability to intersect regions.
Region volumes are no longer calculated due to the complexity involved
with intersecting regions. Each set of multiple geometry regions is
called a unit. KENO-VI allows multiple sets of geometry regions (i.e.,
units), and each set has an independent coordinate system. A global unit
must be specified for every problem, including single-unit problems.
Units with cuboidal outer boundaries where the adjoining faces have the
same dimensions can be stacked together in a 3-D rectangular
parallelepiped called an *array* or *lattice*, just as children's blocks
can be stacked. Unlike KENO V.a, units having hexagonal or dodecahedral
outer boundaries where the adjoining faces have the same dimensions can
also be stacked together in an array. An array boundary must be
specified that either coexists with the outermost edge of the array or
that is entirely within the array. The array boundary can be any shape
that is definable using quadratic equations. An array can be treated as
a building block and used as a unit within another array.
The use of holes in KENO allows a unit to be emplaced within another
unit. This feature allows the addition of a complex structure,
previously defined as a unit, to be directly placed within another unit.
In KENO V.a a hole is not allowed to intersect other holes or regions,
but holes may intersect multiple regions in KENO-VI.
Multiple arrays can be described in KENO. The global array in an
unreflected problem is the outermost array in the problem geometry
description. The global array in a reflected problem is the array
referenced by surrounding geometry regions following the last array
placement description that does not immediately follow a unit number
description. In KENO-VI, the outermost boundary is always specified as
the global unit boundary. If the outermost boundary is to be the array
boundary, a global unit must still be specified with the global unit
boundary coinciding with the array boundary. Unlike past versions of
KENO, KENO-VI cannot run a single unit problem without specifying a
global unit.
Fluxes
~~~~~~
Fluxes are computed in KENO with a track length estimator. The scalar
flux in region \ *z* for energy group *g* for a single generation is
computed as
.. math::
:label: eq8-1-85
\Phi_{g,z} = \frac{\sum^{K}_{k=1}W_{k,z}l_{k,z}}{V_{z}\sum^{K}_{k=1}W_{k,0}} ,
where
*l*\ :math:`_{k,z}` = distance traversed by particle *k* while within region z
and energy group *g*,
*W*\ :math:`_{k,z}` = weight of particle *k* while traversing region *z*,
*V*\ :math:`_z` = volume of region *z*,
*W*\ :math:`_{k,0}` = initial weight of particle *k*, and
*K* = total number of histories in the generation.
The average fluxes for all active generations and the standard deviation
in the averages are also computed. Scalar fluxes computed by KENO are
reported in units of neutrons per cm\ :sup:`2` per initial source
neutron.
KENO is also capable of computing the angular flux for a level symmetric
quadrature set. The angular flux for energy group g in region z for
quadrature direction \ *n* is computed as
.. math::
:label: eq8-1-86
\Phi^{n}_{g,z} = \frac{\sum_{k=1}^{K}W_{k,z}l_{k,z,n}}{V_{z}\sum^{K}_{k=1}W_{k,0}} ,
where
*l*\ :sub:`k,z,n` = the distance traversed by particle \ *k* while within
region \ *z* and energy group \ *g* within the quadrature
direction \ *n*.
The angular flux can be expanded to flux moments using an appropriate
spherical harmonics expansion. KENO has even number symmetric level
quadrature sets S\ :sub:`2`\ -S\ :sub:`16`.
Flux moments can also be computed directly in KENO. The *j\ th* moment,
which corresponds to real valued spherical harmonics functions :cite:`KENO-demaret_accurate_1999-1` for
a single generation for energy group \ *g* in region \ *z,* is computed
as
.. math::
:label: eq8-1-87
\phi^{j}_{g,z} = \frac{\sum_{k=1}^{K}R^{j}_{k}W_{k,z}l_{k,z}}{V_{z}\sum^{K}_{k=1}W_{k,0}} ,
where
:math:`R^{j}_{k}` = real valued spherical harmonics function for moment index \ *j*
corresponding to the direction of particle \ *k*.
KENO offers the option of computing the angular fluxes and flux moments
using a transformed coordinate system so that the moments are based on a
polar rather than a Cartesian position vector. This is a 3-D extension
of the 1-D method for calculating the flux moments in terms of Legendre
polynomials based only on the direction cosine with respect to the
spatial coordinate.
Here,
:math:`\hat{i}`, :math:`\hat{j}`, and :math:`\hat{k}`
represent the directional coordinate system axes, :math:`\mu`, :math:`\eta`, :math:`\xi` represent the
direction cosines, and :math:`\theta` and :math:`rho`\ represent the polar and
azimuthal angles of the "normal" coordinate system. The same symbols
primed represent the transformed coordinate system. The transformed
polar or :math:`\hat{k}^{'}` axis is co-linear, with the position vector :math:`\vec{r}`
directed from the
center of the region for which moments are desired to the point at which
the flux tally occurs. By using the center of the region as a reference
point, consistency of the moment calculation is assured with differing
models of the same system. The :math:`\hat{i}^{'}` and :math:`\hat{j}^{'}`
axes are chosen to form an
orthogonal coordinate system, with :math:`\hat{i}^{'}` held in the plane formed
by :math:`\hat{i}` and :math:`\hat{j}`. The
use of constraints other than the restriction of :math:`\hat{i}^{'}` to this plane may be
explored in future studies. If an additional constraint is not placed on
either :math:`\hat{i}^{'}` or :math:`\hat{j}^{'}`, the transform would be able to
rotate about :math:`\hat{k}^{'}`, and the
consistency of consecutive transformations of the same direction could
not be assured. With the transform computed, the position and direction
of travel of the particle remain unchanged, but the quadrature
directions and/or spherical harmonics terms are calculated using the
transformed coordinate system. With the direction cosines consistently
transformed for each history, the new polar and azimuthal angles can be
computed and the spherical harmonics functions can be calculated for
each history.
KENO offers a mesh flux tally in which the fluxes are computed in a
user-defined cubic mesh superimposed on the geometry model. The mesh is
defined from the origin of the global unit and is oriented with the
Cartesian axes. At the end of each particle track, appropriate track
lengths are assigned to the mesh intervals that were crossed for the
region in which the track occurred. The length of the actual particle
track is equal to the sum of the lengths assigned to the meshes
encountered by the particle track. Because the coordinates of the mesh
are defined in terms of the global unit, fluxes for regions in repeated
units (i.e., units in arrays or holes) may be stored separately for each
occurrence of the unit. The volumes of each region in each mesh interval
are computed so that the fluxes are appropriately normalized on a per
unit volume basis, consistent with :eq:`eq8-1-85`. When the mesh flux option is
activated, all requested fluxes, scalar, angular and/or moment, are
computed for each mesh interval.
.. figure:: figs/Keno/fig202.png
:align: center
:width: 600
:name: fig8-1-202
Coordinate transform used for quadrature direction and spherical harmonics terms.
.. _8-1-6-6:
Reaction Rate and Few Group Micro Cross Section Calculations
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
A few-group microscopic reaction cross section calculation capability is
included in the KENO codes to provide this data especially for the CE
depletion calculations in SCALE. This new method produces multigroup
cross sections and reaction rates directly in CE mode calculations
rather than using a post-processing approach. In each generation, KENO
uses track length estimators for the reaction rate tallies for all
isotopes in each specified regions. At the end of each generation, a
subsequent calculation is performed to compute few group microscopic
reaction cross sections for all isotopes in a region as the ratio of the
computed reaction rates to the flux averaged over this cell. Finally,
KENO computes mean values and statistical uncertainties for all these
quantities, and saves them in a file, which could be used by the
depletion modules in SCALE.
Reaction tally calculations can be enabled by entering the required data
in the **reaction data** block described in :numref:`8-1-2-15`.
.. _8-1-6-7:
Source Convergence Diagnostics
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Fission source convergence detection techniques are implemented in KENO
to provide improved confidence in the computed *k*\ :sub:`eff` and tally
results. The dominance ratio of a system is equal to the ratio of the
eigenvalue of the first nonfundamental mode to that of the fundamental
mode, *k*\ :sub:`1`\/\ *k*\ :sub:`0`. The dominance ratio is strongly related to the
convergence rate of the fission source for systems, and problems with
larger dominance ratios will require more inactive generations to
produce reliable *k*\ :sub:`eff` and reaction rate estimates. A converged
*k*\ :sub:`eff` estimate does not necessarily guarantee a converged fission
source distribution, and the fission source and flux distribution may
continue to evolve well after *k*\ :sub:`eff` convergence is reached.
Convergence of the fission source distribution is necessary to ensure
that all regions containing fissile material in a model are adequately
represented in the final *k*\ :sub:`eff` estimate. Typically, the *k*\ :sub:`eff`
estimate converges much faster than the fission source and neutron flux
distributions, and simulations may undersample important regions and
produce inaccurate flux and reaction rate estimates if the user includes
only enough inactive generations for the eigenvalue to converge. This is
particularly important in models where one region is physically small
but substantially more reactive than others (i.e. the k-effective of the
World problem :cite:`KENO-whitesides_difficulty_1971`). The highly reactive region may not be adequately
sampled, which may result in an underprediction of *k*\ :sub:`eff`. Thus, it is
essential to monitor the convergence of both the fission source
distribution and *k*\ :sub:`eff`; versions of KENO included in SCALE versions
prior to SCALE 6.2 only monitored the convergence of *k*\ :sub:`eff`, but
diagnostic tools to identify unconverged fission source distributions
are included in SCALE 6.2 and beyond.
.. note:: Due to limited experience with these tests in KENO, the
Shannon entropy test results should be used as a supplement to guarantee
that a problem's fission source is converged. Failure of Shannon entropy
tests typically indicates insufficient convergence of fission site
source distributions. Whenever Shannon entropy tests report failure,
users should review the plots of *k*\ :sub:`eff` as a function of generation
skipped and *k*\ :sub:`eff` as a function of generation completed
(:numref:`8-1-4-26` and :numref:`8-1-4-27`) to ensure that the *k*\ :sub:`eff` value is adequately
converged. If it is not clear that the *k*\ :sub:`eff` value is converged,
users should rerun the calculation using a different number of neutrons
per generation (using the ``NPG`` parameter) or using a different random
number seed value (using the ``RND`` parameter) or a different starting
source term distribution (using the ``READ START`` block).
It may also be possible to pass the Shannon entropy tests by changing
the source convergence mesh (using the ``SCD`` parameter and the ``READ
GRID`` block) or changing the number skipped generations (using the
``NSK`` parameter).
For KENO calculations that are used for other purposes (such as
producing neutron flux and reaction rate distributions, fuel depletion
calculations, or fission distributions for radiation transport
calculations) in which the spatial dependence of the neutron flux and
fission source may be more important, KENO calculations with failed
Shannon entropy tests should be rerun because these spatially dependent
distributions may not be adequately converged.
Shannon Entropy Statistics
^^^^^^^^^^^^^^^^^^^^^^^^^^
The fission source distribution, *S*, is measured at the beginning of
each generation using given spatial meshes. The state of source
distribution at the *j*\ :sup:`th` generation can then be characterized by
Shannon entropy:
.. math::
:label: eq8-1-88
H(S^{j}) = - \sum^{M}_{i}[S^{j}_{i}\text{log}_{2}(S^{j}_{i})] ,
where :math:`{S}_{i}^{j}` is the fraction of the fission source
distribution from the *j*\ :sup:`th'` generation tallied in the spatial bin
*i*, and *M* is the total number of spatial bins (typically represented
using a spatial mesh). The value of *H* ranges from a maximum value of
log\ :sub:`2`\ *M* when the source distribution is uniform, and to a minimum value of zero
when the whole source is located in a single bin. By computing *H* for
each generation, the distribution of the fission source is used to
generate a score for *H* for each generation, and the convergence of the
fission source can be assessed by tracking the convergence and
randomness of the values of *H* over each successive generation. Random
fluctuations in the generation-to-generation Shannon entropy tallies
make it difficult to determine if and when the Shannon entropy of a
system has converged, so several metrics and tests are typically applied
to examine the Shannon entropy and identify convergence in a
system :cite:`KENO-ueki_information_2005`.
The first test for fission source convergence is a comparison between
the mean square of posterior relative entropy, and the centered mean
square Shannon entropy. The posterior relative entropy, :math:`D(S^{j}\parallel T)` , is defined as
the statistical distance between the binned fission source
:math:`{S}^{j}_i`\ and the average fission source over the second half of
the active generations, *T*, and is given by
.. math::
:label: eq8-1-89
D(S^{j}\parallel T) = \sum^{M}_{i}[S^{j}_{i}\text{log}_{2}(S^{j}_{i} / T_{i})] ,
where *T* is defined by
.. math::
:label: eq8-1-90
T_{i} = \frac{2}{N}\sum^{N}_{j=N / 2+1}S^{j}_{i} ,
where *N* is the number of active generations. The posterior relative
entropy is non-negative and becomes zero only when :math:`{S}^{j}`\ = *T*
and achieves its maximum value when :math:`S^{j}` is uniform.
The mean square posterior relative entropy is defined as
.. math::
:label: eq8-1-91
msq(D) = \frac{2}{N}\sum^{N}_{j=N / 2+1}D(S^{j}_{i}\parallel T_{i})^{2} ,
and the centered mean square Shannon entropy is defined as
.. math::
:label: eq8-1-92
cmsq(H) = \frac{2}{N-2}\sum^{N}_{j=N / 2+1}[H(S^{j}_{i}) - \bar{H}]^{2} ,
where :math:`\bar{H}` is defined as
.. math::
:label: eq8-1-93
\bar{H} = \frac{2}{N}\sum^{N}_{j=N / 2+1}H(S^{j}_{i}) .
This test compares the measure of fluctuations of Shannon entropy (*cmsq(H)*)
with the measure of the magnitude of the penalty incurred by assuming *T*
(*msq(D)*) and states that the fission source is converged if *msq(D)* < *cmsq(H)*.
This test is
useful to determine whether the source is converged by the end of the
calculation. Failure of this test indicates that the fission source was
still moving during the active generations, which indicates that the
number of skipped generations was not sufficient to converge the fission
source.
The second test is given by
.. math::
:label: eq8-1-94
D(S^{j}\parallel T) - [H(T-H(S^{j}))] \leq \varepsilon
where :math:`\mathcal{E}` has been set to 0.1. This test verifies that the Shannon entropy
of each active generation does not vary significantly from the average
Shannon entropy of the system and should be valid over all active
generations. For example, this test could detect an unconverged fission
source for a problem with an undersampled, highly fissile fuel region,
as any neutrons that reached this region would produce an outlier in the
Shannon entropy tally for that generation. This test is especially
useful for reporting the generation at which the source converged. Once
the converged generation is determined, the user can repeat the
calculation with the number of inactive generations (skipped
generations) set to be the identified generation or greater to ensure
that only contributions from generations with a converged source
contribute to flux and reaction rate tallies. This test complements the
first test since it will not be affected by whether or not the binned
source is uniform.
The last test calculates whether
.. math::
:label: eq8-1-95
H_{\eta} = H(S^{j}) - H_{b} \leq \eta ,
where *H*\ :sub:`b` is the average Shannon Entropy over the second half of
active generations, and :math:`\eta` has been set to 0.1. This test verifies that
the average Shannon entropy of all active generations does not differ
significantly from the Shannon entropy of the last half of the active
generations. This test is useful for detecting fission source
convergence in problems where an inadequate number of inactive
generations was sampled, as the Shannon entropy would continue to change
during the active generations until it eventually converges.
Source Convergence Diagnostic Input
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Because the processing of the source tallies for fission source
convergence calculations is quite fast and produces small memory
requirements, these source convergence diagnostics have been permanently
enabled in KENO and require no additional input parameters. However, the
KENO input specifications were updated to allow users to specify the
spatial mesh data for the source convergence tests via the ``SCD``
parameter and ``READ GRID`` data block.
Appendices
----------
.. toctree::
KenoA
KenoB
KenoC
.. only:: html
.. rubric:: References
.. bibliography:: zSCALE.bib
:cited:
:keyprefix: KENO-