.. |keff| replace:: *k*\ :sub:`eff` .. _sec-csas: CSAS: Control Module For Enhanced Criticality Safety Analysis Sequences With KENO ================================================================================= *K. B. Bekar*, *L. M. Petrie* :sup:`1`, *S. Goluoglu* :sup:`1`, *D. F. Hollenbach* :sup:`1` and *N. F. Landers* :sup:`1` The **C**\ riticality **S**\ afety **A**\ nalysis **S**\ equences with KENO codes provide reliable and efficient means of performing |keff| calculations for systems that are routinely encountered in engineering practice. Two CSAS sequence implementations, CSAS5 and CSAS6, with two variants of KENO codes, KENO V.a and KENO-VI, provide identical solution capabilities with different geometry packages. In the multigroup calculation mode, CSAS uses XSProc to process the cross sections for temperature corrections and problem-dependent resonance self-shielding and calculates the |keff| of a three-dimensional (3D) system model. If the continuous-energy calculation mode is selected no resonance processing is needed and the continuous-energy cross sections are used directly in KENO codes, with temperature corrections provided as the cross sections are loaded. The geometric modeling capabilities available in KENO codes coupled with the automated cross-section processing within the control sequences allow complex, 3D systems to be easily analyzed. The CSAS5 search capability available in previous SCALE versions is no longer supported by the CSAS5 sequence in SCALE 6.3. In SCALE 6.3, CSAS5 and CSAS6 support two new sequence data blocks, definitions and tallies data, to allow flexible definition and output control of mesh tallies. The mesh responses neutron flux, fission rate, and fission source can now be requested multiple times on different spatial and energy grids in the same calculation. :sup:`1` Formerly with Oak Ridge National Laboratory. Acknowledgments --------------- CSAS5 and its related Criticality Safety Analysis sequences are based on the old CSAS2 control module (no longer in SCALE) and the KENO V.a functional module described in :numref:`sec-module.keno`. Therefore, special acknowledgment is made to J. A. Bucholz, R. M. Westfall, and J. R. Knight who developed CSAS2. G. E. Whitesides is acknowledged for his contributions through early versions of KENO. Appreciation is expressed to C. V. Parks and S. M. Bowman for their guidance in developing CSAS5. Introduction ------------ Criticality Safety Analysis Sequence with KENO V.a (CSAS5) and KENO-VI (CSAS6) provide reliable and efficient means of performing |keff| calculations for systems that are routinely encountered in engineering practice, especially in the calculation of |keff| of three-dimensional (3D) system models. CSAS5 and CSAS6 implement XSProc to process material input and provide a temperature and resonance-corrected cross-section library based on the physical characteristics of the problem being analyzed. If a continuous energy cross-section library is specified, no resonance processing is needed and the continuous energy cross sections are used directly in KENO codes, with temperature corrections provided as the cross sections are loaded. The search capability available in the CSAS5S in previous SCALE versions is no longer supported by the CSAS5 in SCALE 6.3. This capability was excluded when doing modernization work for CSAS sequences in SCALE 6.2 and permanently disabled in SCALE 6.3 due to the inconsistencies between the legacy code implementation and the modern CSAS framework. Research is being continued to support equivalent search capabilities in a more robust modernized code framework for the next SCALE release. In SCALE 6.3, CSAS5 and CSAS6 support two new sequence data blocks, definitions and tallies data, to allow flexible definition and output control of mesh tallies. The mesh responses neutron flux, fission rate, and fission source can now be requested multiple times on different spatial and energy grids in the same calculation. This capability helps users efficiently manage computational resources when collecting detailed information, depending on their requirements. For example, fission density can be tallied in a very fine spatial mesh in a few energy groups while performing calculations in high resolution with SCALE's very fine group multigroup library (1597 energy groups), or fission density can be tallied on multiple spatial fine meshes rather than using a large global fine mesh to keep the runtime and memory footprint of the calculation at reasonable levels. Sequence Capabilities --------------------- In the CSAS sequence framework, SCALE data handling is automated as much as possible. CSAS and many other SCALE sequences apply a standardized procedure to provide appropriate number densities and cross sections for the calculation. XSProc is responsible for reading the standard composition data and other engineering-type specifications, including volume fraction or percent theoretical density, temperature, and isotopic distribution as well as the unit cell data. XSProc then generates number densities and related information, prepares geometry data for resonance self-shielding and flux-weighting cell calculations, if needed, and (if needed) provides problem-dependent multigroup cross-section processing. Sequences that execute KENO codes include a KENO Data Processor to read and check the KENO data. When the data checking has been completed, the control sequence executes XSProc to prepare a resonance-corrected microscopic cross-section library in the AMPX working library format if a multigroup library has been selected. For each unit cell specified as being cell-weighted, XSProc performs the necessary calculations and produces a cell-weighted microscopic cross-section library. KENO codes may be executed to calculate the |keff| or neutron multiplication factor using the cross-section library that was prepared by the control sequence. Computational capabilities available in KENO codes---including 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---are also provided by the CSAS5 sequence. Details of each capability, their input methods, and output edits are provided in :numref:`sec-module.keno` of this document and will not be repeated here. Multigroup limitations ~~~~~~~~~~~~~~~~~~~~~~ The CSAS control module was developed to use simple input data and prepare problem-dependent cross sections for use in calculating the effective neutron multiplication factor of a 3D system using KENO codes, KENO V.a and KENO-VI. An attempt was made to make the system as general as possible within the constraints of the standardized methods chosen to be used in SCALE. Standardized methods of data input were adopted to allow easy data entry and for quality assurance purposes. Some of the limitations of the CSAS multigroup sequences are a result of using preprocessed multigroup cross sections. Inherent limitations in multigroup CSAS calculations are as follows: 1. Two-dimensional (2D) effects such as fuel rods in assemblies where some positions are filled with control rod guide tubes, burnable poison rods and/or fuel rods of different enrichments. The cross sections are processed as if the rods are in an infinite lattice of identical rods. If the user inputs a Dancoff factor for the cell (such as one computed by MCDancoff), XSProc can produce an infinite lattice cell, which reproduces that Dancoff. This can mitigate some two dimensional lattice effects Continuous energy limitations ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ When continuous energy KENO calculations are desired, none of the resonance processing capabilities of XSProc are applicable or needed. The continuous energy cross sections are directly used in KENO. An existing multigroup input file can easily be converted to a continuous energy input file by simply specifying the continuous energy library. In this case, all cell data is ignored. However, the following limitations exist: 1. If CELLMIX is defined in the cell data, the problem will not run in the continuous energy mode. CELLMIX implies new mixture cross sections are generated using XSDRNPM-calculated cell fluxes and therefore is not applicable in the continuous energy mode. 2. Only VACUUM, MIRROR, PERIODIC, and WHITE boundary conditions are allowed. Material-specific albedos, e.g., WATER, CARBON, POLY, etc., are for multigroup only. 3. Problems with DOUBLEHET cell data are not allowed as they inherently utilize CELLMIX feature. .. _sec-csas.input: Input Data Guide ---------------- This section describes the input data required for the CSAS with KENO transport codes. A typical CSAS input, shown in :numref:`csas5-input-layout`, starts with the sequence identifier always preceded by the ``=`` sign (``=CSAS5`` and ``=CSAS6``), and it is followed by the problem title. Then, a cross section library name is specified, and all these entries are followed by several data blocks each starting with ``READ data_block`` and ending with ``END data_block``. .. code-block:: scale :name: csas5-input-layout :caption: A typical CSAS sequence input =sequence_identifier parm=(parm_options) problem title ' ----- XSProc data ' cross section library name (REQUIRED) ce_v7.1 ' List of material specifications in standard SCALE format (REQUIRED) read composition ... end composition ' Specify data for resonance processing (OPTIONAL) read celldata ... end celldata ' ---- New CSAS sequence data blocks ' Used to define energy bounds and grid geometries for ' the tallies defined in tallies data block ' (REQUIRED if tallies data block exists) read definitions ... end definitions ' Used to define tallies in a more robust way (OPTIONAL) read tallies ... end tallies ' ---- KENO transport data ' Specify the problem geometry (REQUIRED) read geometry ... end geometry ' Other input data blocks (OPTIONAL) The input data for the CSAS sequence are composed of three broad categories of data, as shown in :numref:`csas5-input-layout`. The first is XSProc data, including Standard Composition Specification Data and Unit Cell Geometry Specification Data. This first category specifies the cross section library and then defines the composition of each mixture and optionally unit cell geometry that may be used to process the cross sections. This data block is necessary for the CSAS sequence. .. note:: Sequence implementation determines the calculation (transport) mode automatically, either as multigroup or continuous-energy, by testing the cross section library whose name has been entered. .. warning:: Continuous-energy mode does not process data entered in `celldata data` block(s). The second category of data, the CSAS sequence input data, includes two new data blocks, **definitions data** and **tallies data**, for flexible tally definitions. These new blocks available in all CSAS sequences in SCALE 6.3 currently provide only accumulation of neutron flux, fission rate, and neutrons produced from fission on **different** energy and spatial grids. Although similar to capabilities activated with old-style KENO parameter input methods (with ``GFX``, ``CDS``, and ``FIS`` as described in :numref:`sec-module.keno.parameters`), these input methods do not allow tallying the requested quantities on different energy and spatial grids. This limitation is relaxed with the new CSAS input blocks. The third category of data, the KENO input data, is used to specify the geometric and boundary conditions that represent the physical 3D configuration of a KENO problem. CSAS ensures data consistency among these three category of data. For example, it verifies that mixture numbers used in the KENO **geometry data** block must correspond to those defined either in the **composition data** or **celldata data** blocks. Note that in multigroup mode, a unique mixture number can be specified in the **celldata data** block by ``CELLMIX=`` if the cell is cell-weighted. .. note:: As depicted in :numref:`csas5-input-layout`, a successful CSAS calculation requires at least a problem title and cross section library definitions, followed by **composition data** and **geometry data**. Depending on the requirements of the problem, other optional data blocks can be activated. Following CSAS5 input demonstrates this minimal requirement. .. code-block:: scale =csas5 sample problem 14 u metal cylinder in an annulus ce_v7.1 read comp uranium 1 den=18.69 1 300 92235 93.2 92238 5.6 92234 1.0 92236 0.2 end end comp read geom global unit 1 cylinder 1 1 8.89 10.109 0.0 orig 5.0799 0.0 cylinder 0 1 13.97 10.109 0.0 cylinder 1 1 19.05 10.109 0.0 end geom end data end Unlike the CSAS5 and CSAS6 versions in previous SCALE releases, in SCALE 6.3, user can enter all data blocks in any order in both CSAS5 and CSAS6 inputs. Following CSAS5 input illustrates this input flexibility. .. code-block:: scale =csas5 sample problem 14 u metal cylinder in an annulus ce_v7.1 read geom global unit 1 cylinder 1 1 8.89 10.109 0.0 orig 5.0799 0.0 cylinder 0 1 13.97 10.109 0.0 cylinder 1 1 19.05 10.109 0.0 end geom read comp uranium 1 den=18.69 1 300 92235 93.2 92238 5.6 92234 1.0 92236 0.2 end end comp end data end All data are entered in free form, allowing alphanumeric data, floating-point data, and integer data to be entered in an unstructured manner. Up to 252 columns of data entry per line are allowed. Data can usually start or end in any column with a few exceptions. As an example, the word END beginning in column 1 and followed by two blank spaces or a new line will end the problem and any data following will be ignored. Each data entry must be followed by one or more blanks to terminate the data entry. For numeric data, either a comma or a blank can be used to terminate each data entry. Integers may be entered for floating-point values. For example, 10 will be interpreted as 10.0. Imbedded blanks are not allowed within a data entry unless an E precedes a single blank as in an unsigned exponent in a floating-point number. For example, 1.0E 4 would be correctly interpreted as 1.0 :math:`\times` 10\ :sup:`4`. The word "END" is a special data item. An "END" may have a name or label associated with it (e.g., "END DATA"). The name or label associated with an "END" is separated from the "END" by a single blank and is a maximum of 12 characters long. *At least two blanks or a new line MUST follow every labeled and unlabeled ``END``. It is the user's responsibility to ensure compliance with this restriction. Failure to observe this restriction can result in the use of incorrect or incomplete data without the benefit of warning or error messages.* Multiple entries of the same data value can be achieved by specifying the number of times the data value is to be entered, followed by either ``R``, ``\*``, or ``$``, followed by the data value to be repeated. Imbedded blanks are not allowed between the number of repeats and the repeat flag. For example, ``5R12``, ``5*12``, ``5$12``, or ``5R 12``, etc., will enter five successive 12's in the input data. Multiple zeros can be specified as nZ where n is the number of zeroes to be entered. The purpose of this section is to define the input data in discrete subsections relating to a particular type of data. Tables of the input data are included in each subsection, and the entries are described in more detail in the appropriate sections. Resonance-corrected cross sections are generated using the appropriate boundary conditions for the unit cell description (i.e., void for the outer surface of a single unit, white for the outer surface of an infinite array of cylinders). As many unit cells as needed may be specified in a problem. A unit cell is cell-weighted by using the keyword "CELLMIX=" followed by a unique user specified mixture number in the unit cell data. To check the input data without actually processing the cross sections and without performing transport calculations, the sequence parameter options ``PARM=CHECK`` or ``PARM=CHK`` should be entered, as shown below. :: =CSAS5 PARM=CHK =CSAS6 PARM=CHK This will cause the input data for CSAS to be checked and appropriate error messages to be printed. If plots are specified in the data, they will be printed. This feature allows the user to debug and verify the input data while using a minimum of computer time. .. _sec-csas.xsproc_data: XSProc data ~~~~~~~~~~~ The XSProc reads the standard composition specification data and the unit cell geometry specifications. It then produces the mixing table and unit cell information necessary for processing the cross sections if needed. :numref:`sec-scale.mat_xs` of this manual provides a detailed description of the input data and processing options. CSAS sequences are responsible for passing data such that mixing table and problem-dependent cross sections from XSProc calculations are conveyed to the transport calculations. Note that reported elapsed time in each transport calculation does not include the time required to process and prepare multigroup cross section data. When running the transport module concurrently on multiple cores, these data are broadcasted to all instances of the transport module running on each computational node. In contrast, in continuous-energy mode, only mixing table data generated from XSProc utilities are passed to the transport module. In addition to this, the defined continuous-energy data library is first verified by the utilities that exist in XSProc, and then temperature correction is applied to each nuclide data using the defined temperatures when loading these data from disk by each instance of the transport module. Therefore, elapsed time reported at the end of each transport module calculation also includes the time spent on temperature correction and data loading. In multigroup mode, the XSProc calculation path for each unit cell is always determined with the following hierarchy to prepare the problem-dependent multigroup cross section data: - All non-fissionable cells are processed with BONAMI by default, and this cannot be changed. - All fissionable cells are processed with CENTRM by default, and this can be overridden by defining a cross section processing option with the sequence parameter option (PARM=BONAMI or PARM=2REGION). - Double-het cells defined in the **celldata data** block are **always** processed with CENTRM, and this cannot be changed. CSAS sequences always print a cross section processing summary of the cells used/defined in the problem. This can be seen in :numref:`sec-csas.xs_summary`. See :numref:`sec-scale.mat_xs` of this manual for detailed description of these unit cell processing options. .. sec-csas.input: CSAS input data ~~~~~~~~~~~~~~~ Two new data blocks, **definitions data** and **tallies data**, are currently supported by CSAS sequences to provide flexible tally definitions. These new data blocks are currently available to define the mesh responses flux, fission_density, and fission_source on different spatial and energy grids. This section introduces these two new data blocks and discusses the limitations with some details. .. _sec-csas.def: Definitions data ^^^^^^^^^^^^^^^^ The **definitions data** input block allows (1) multiple spatial grids to be defined using the **gridGeometry data** blocks inside the definitions data block, and (2) multiple energy grids to be defined using the **energyBounds data** inside the **definitions data** block. The syntax for defining a **gridGeometry** inside a definitions block is the same as defining a standalone grid at the root level of input (i.e., KENO's **gridgeometry data** block). The syntax for defining energyBounds is already used for defining energy grids in the MAVRIC sequence. See :numref:`sec-module.monaco` for further details. The energy grid definition permits specification of individual energy boundaries, equal-width energy bins and equal-width lethargy bins within a specified energy, and SCALE energy group structures (such as the 56-group structure). The SCALE energy group structure can be any group structures that is used by a SCALE multigroup library that is available in the DATA directory. The syntax is *n* for neutron libraries and *p* for photon (gamma) libraries. A combination of the different options is also supported (see :numref:`csas5-definitions-data-example`). .. note:: As shown in example given :numref:`csas5-definitions-data-example` ``READ`` keyword is not required when defining energy boundaries with **energyBounds** data block. This may show differences from one CSAS sequence to another. .. code-block:: scale :caption: Typical spatial and energy grid specifications in the **definitions data** block :name: csas5-definitions-data-example READ DEFINITIONS read grid 1 xlinear 30 -10 70 ylinear 10 -20 60 zlinear 50 -30 40 end grid read grid 2 numxcells=10 xmin=-18.5 xmax=+68.5 numycells=25 ymin=-28.5 ymax=+58.5 numzcells=10 zmin=-38.5 zmax=+48.5 end grid 'user specified energy grid read energyBounds 1 bounds 2e7 0.625 1e-5 end end energyBounds 'user specified energy grid using equal-energy bins' energyBounds 2 linear=10 1e-5 2e7 end energyBounds 'user specified energy grid using equal-lethargy bins' energyBounds 3 logarithmic=10 1e-5 2e7 end energyBounds 'SCALE 56-group neutron structure with additional energy points' energyBounds 10 56n bounds 1.1 0.11 0.011 0.0011 end energyBounds END DEFINITIONS In continuous-energy mode, a special ``DEFAULT`` keyword allows modification of the default energy group structure that was previously defined with the ``NGP`` parameter and/or the KENO **energy data** block. .. note:: The default energy group structure is currently acquired from the SCALE 252-group neutron library. This may be overridden by defining data with the ``NGP`` parameter, data in the KENO **energy data** block, or data in the **definitions data** block entered with ``DEFAULT`` keyword. .. caution:: CSAS does not allow using **definitions data** block together with KENO ``NGP`` parameter and/or KENO **energy data** block. .. caution:: CSAS does not allow using **definitions data** block together with KENO ``FIS``, ``GFX``, ``CDS``, and ``MSH`` parameters. In multigroup mode, **DEFAULT** energy boundaries are always obtained from the multigroup library used by KENO codes in the neutron transport calculation, and this cannot be overriden by a **DEFAULT** energy boundaries specification in the definitions data block. In other words, an energyBounds **DEFAULT** is not permitted in multigroup mode. .. warning:: In multigroup mode, **DEFAULT** energy boundaries are always acquired from the library used by the KENO V.a transport, and it cannot be changed. .. caution:: In multigroup calculations, energy points of the user-defined energy boundaries must be a subset of the energy points of the energy structure obtained from the multigroup library used by KENO transport. Otherwise, execution will be terminated and an appropriate error message is displayed. The sample definitions data block given in :numref:`example-energybounds-default` defines an energy grid labeled 1 and an energy grid labeled ``DEFAULT`` in the definitions data block. .. code-block:: scale :name: example-energybounds-default :caption: Definitions data block with DEFAULT energyBounds specification READ DEFINITIONS 'user defined energy grid 1 read energyBounds 1 bounds 2e7 0.625 1e-5 end end energyBounds 'user defined default energy grid energyBounds DEFAULT bounds 2e7 8.2e5 2.0e4 1.05e2 5.0 0.65 0.15 0.04 1.e-5 end end energyBounds END DEFINITIONS When using this definitions block in continuous-energy mode, KENO codes read DEFAULT energy boundaries from the definitions data and utilizes these data in all tally calculations (``energyBounds DEFAULT`` overrides the current default that is acquired from the SCALE 252-group library) if requested otherwise in the tallies block for the supported mesh responses. The two energy boundaries read from definitions data are printed in KENO's energy boundaries edit in the output as shown in :numref:`fig-oedit-csas5-default-ebounds-ce`. .. figure:: figs/CSAS/csas5_definitions_ebounds_1.png :align: center :width: 800 :name: fig-oedit-csas5-default-ebounds-ce Sample energy boundaries output edit when running CSAS with the above definitions data in the continuous-energy mode. Unlike continuous-energy mode, when the data defined in the sample definition block given above are processed in mutigroup mode, reading the energy boundaries ``DEFAULT`` from the definitions data is ignored, and the user is notified with a warning message, as shown in :numref:`fig-oedit-csas5-default-ebounds-mg`. However, the calculation is terminated because the energy boundaries given with energy identifier 1 does not conform to the default energy boundaries acquired from the library used by KENO transport (in this test case, the SCALE 28-group neutron and 19-group gamma library was used). The corresponding error message is also shown in :numref:`fig-oedit-csas5-default-ebounds-mg` printed to the output just before the code termination. .. figure:: figs/CSAS/csas5_definitions_ebounds_2.png :align: center :width: 800 :name: fig-oedit-csas5-default-ebounds-mg CSAS terminates execution with an error message when the definitions data given above are used in multigroup mode. Tallies data ^^^^^^^^^^^^ The new tallies data input allows mesh responses to be requested using any energy grid and/or spatial grid from the definitions block. Three response types shown in :numref:`tab-csas5-tallies-responses` were added as mesh tally options for CSAS. Note that the same responses can also be activated by ``GFX``, ``FIS``, and ``CDS``, but only using the default energy boundaries. .. tabularcolumns:: |m{3.5cm}|m{3.5cm}|m{4cm}| .. table:: Mesh tallies available with **tallies data** block. :name: tab-csas5-tallies-responses +--------------------------------------------+----------------------------+----------------------------+ | Description | Old KENO input method to | New response name | | | activate the same tally | in tallies implementation | +--------------------------------------------+----------------------------+----------------------------+ | Neutron flux averaged over mesh volumes | ``GFX`` | ``flux`` | +--------------------------------------------+----------------------------+----------------------------+ | Fission rates per voxel volume | ``FIS`` | ``fission_density`` | +--------------------------------------------+----------------------------+----------------------------+ | Neutron production per voxel volume | ``CDS`` | ``fission_source`` | +--------------------------------------------+----------------------------+----------------------------+ .. note:: Either input method (parameter input or tallies data) can be used to request the mesh tallies described in :numref:`tab-csas5-tallies-responses`. It is recommended to request mesh tallies using the new response names (``flux``, ``fission_density``, ``fission_source``) with the tallies data block rather than the old-style parameter inputs (``GFX``, ``FIS``, ``CDS``) with the limited energy and spatial grid options. A typical mesh tally input block is given in :numref:`csas5-tallies-data-example`. Each spatial and energy grid used by each mesh tally must be defined in the definitions data block. Note that, as shown in :numref:`csas5-tallies-data-example`, the same mesh response can be defined multiple times using different spatial and energy grids. .. code-block:: scale :caption: Typical mesh tally specifications in tallies data :name: csas5-tallies-data-example READ TALLIES read mesh 1 response=FLUX grid=1 energy= 1 end mesh read mesh 2 response=FISSION_DENSITY grid=2 energy=2 end mesh read mesh 3 response=FISSION_SOURCE grid=3 energy=default end mesh read mesh 13 response=FISSION_SOURCE grid=3 energy=2 end mesh END TALLIES The KENO codes in SCALE 6.3 support multiple sets of energy group boundaries for tallying purposes. A data container was designed to store all energy boundaries that are either set up by KENO for some internal use or specified by the user. Note that multiple sets of energy boundaries can be defined only by using the new definitions data block available in CSAS and TRITON sequences. In continuous-energy mode, KENO with the ``NGP`` parameter or data in energy data block provides only a single set of energy boundaries, and these always override KENO's default energy group boundaries used in all tallies. After processing data entered in the definitions and tallies data blocks, KENO codes print the summary of all corresponding definitions in energy boundaries, grid definitions, and tally definitions output edits. The following sample input can be used to demonstrate the new output edits in KENO codes with continuous-energy mode: .. code-block:: scale read definitions read gridgeometry 11 numxcells=2 numycells=2 numzcells=2 xmin=-0.73 xmax=0.73 ymin=-0.73 ymax=0.73 zmin=0 zmax=10.0 end gridgeometry read gridgeometry 12 numxcells=2 numycells=2 numzcells=8 xmin=-0.73 xmax=0.73 ymin=-0.73 ymax=0.73 zmin=0 zmax=10.0 end gridgeometry read gridgeometry 13 numxcells=4 numycells=2 numzcells=4 xmin=-0.73 xmax=0.73 ymin=-0.73 ymax=0.73 zmin=0 zmax=10.0 end gridgeometry read energyBounds 12 title "ebounds is a sub-set of 8 group MG test library" bounds 2.00000E+07 1.05000E+02 5.00000E+00 1.00000E-05 end end energyBounds read energyBounds DEFAULT title "SCALE 8 group test library structure" bounds 2.00000E+07 8.20000E+05 2.00000E+04 1.05000E+02 5.00000E+00 6.50000E-01 1.50000E-01 4.00000E-02 1.00000E-05 end end energyBounds end definitions read tallies read mesh 1 energy=DEFAULT grid=11 response=FLUX end mesh read mesh 2 energy=DEFAULT grid=12 response=FLUX end mesh read mesh 3 energy=12 grid=13 response=FLUX end mesh read mesh 100 energy=12 grid=12 response=FISSION_DENSITY end mesh read mesh 200 energy=DEFAULT grid=13 response=FISSION_DENSITY end mesh read mesh 1000 energy=12 grid=11 response=FISSION_SOURCE end mesh read mesh 1080 energy=DEFAULT grid=13 response=FISSION_SOURCE end mesh end tallies The energy boundaries output edit depicted in :numref:`fig-oedit-csas5-tallies-ebounds-ce` summarizes the data stored in the energy boundaries data container. For the above sample problem, two sets of energy group boundaries are read from the definitions data and stored in the data container. .. figure:: figs/CSAS/csas5_oedit_ebounds_1.png :align: center :width: 800 :name: fig-oedit-csas5-tallies-ebounds-ce Energy boundaries edit in KENO output Another edit that was added to KENO's output is the grid definitions edit, which summarizes the mesh grids that were either defined by the user or automatically constructed by KENO for Shannon entropy tallies. The grid definitions output edit corresponds to the above provided sample input and is shown in :numref:`fig-oedit-csas5-tallies-grids-ce`. Note that :numref:`fig-oedit-csas5-tallies-grids-ce` shows only a part of the mesh tallies output edit. .. figure:: figs/CSAS/csas5_oedit_grids_1.png :align: center :width: 800 :name: fig-oedit-csas5-tallies-grids-ce Grid definitions edit in KENO output The tally definitions output edit summarizes the specifications of tallies defined in tallies block. Currently, only mesh tally edits are supported, and this is shown in :numref:`fig-oedit-csas5-tallies-definitions-ce` for the above sample input. .. figure:: figs/CSAS/csas5_oedit_tallies_1.png :align: center :width: 800 :name: fig-oedit-csas5-tallies-definitions-ce Tally definitions edit in KENO output After the calculations have been completed for all the requested tallies, KENO also prints another output table that summarizes the mesh tallies, as shown in :numref:`fig-oedit-csas5-mesh-tallies-ce`. Other than the mesh tally input specifications, the mesh tallies output edit also summarizes the intervals of the energy and spatial grids used in tally calculations and approximate memory allocation required to compute and write this tally to 3dmap output file. Note that :numref:`fig-oedit-csas5-mesh-tallies-ce` shows only a part of the mesh tallies output edit. .. figure:: figs/CSAS/csas5_oedit_mesh_tallies_1.png :align: center :width: 800 :name: fig-oedit-csas5-mesh-tallies-ce Mesh tallies edit in KENO output See the relevant subsections in :numref:`sec-module.keno.output` for further details for all these output edits. Mesh tally output files ^^^^^^^^^^^^^^^^^^^^^^^ Depending on the user input specifications, the naming of the mesh tally 3dmap output files show some variations. :numref:`tab-csas5-mesh-tally-naming-1` lists the 3dmap output filenames for each response type if only a single tally was requested for each response type. And, :numref:`tab-csas5-mesh-tally-naming-2` lists the 3dmap output filenames for each response type if multiple mesh tallies are requested with the same response type. In such a case, the output filenames are updated with the keyword meshtally followed by the mesh id (mesh identifier used to define each mesh in tallies data). .. table:: Mesh tally 3dmap file naming when a single response is requested :class: longtable :name: tab-csas5-mesh-tally-naming-1 +----------------------+---------------------------------------+ | response | 3dmap file name | +----------------------+---------------------------------------+ | ``flux`` | ``${BASENAME}.flux.3dmap`` | +----------------------+---------------------------------------+ | ``fission_density`` | ``${BASENAME}.fission_density.3dmap`` | +----------------------+---------------------------------------+ | ``fission_source`` | ``${BASENAME}.fission_source.3dmap`` | +----------------------+---------------------------------------+ .. note:: Mesh tallies activated with old-style input method (using the ``GFX``, ``CDS``, and ``FIS`` parameters) also use the definitions for 3dmap file naming given in :numref:`tab-csas5-mesh-tally-naming-1`. .. table:: Mesh tally 3dmap file naming when a response is requested multiple times :class: longtable :name: tab-csas5-mesh-tally-naming-2 +---------------------+-----------------------------------------------------------+ | response | 3dmap file name | +---------------------+-----------------------------------------------------------+ | ``flux`` | ``${BASENAME}.meshtally_${MESHID}_flux.3dmap`` | +---------------------+-----------------------------------------------------------+ | ``fission_density`` | ``${BASENAME}.meshtally_${MESHID}_fission_density.3dmap`` | +---------------------+-----------------------------------------------------------+ | ``fission_source`` | ``${BASENAME}.meshtally_${MESHID}_fission_source.3dmap`` | +---------------------+-----------------------------------------------------------+ .. _sec-csas.keno.data: KENO data ~~~~~~~~~ :numref:`tab-module.keno.input` contains the outline for the KENO input. A typical KENO input is divided into 13 data blocks. A brief outline of commonly used data blocks is shown in :numref:`tab-module.keno.input`. Note that parameter data must precede all other KENO data blocks when running standalone KENO codes; however, this is not applied to the KENO calculations performed as part of each CSAS sequence. As described in above sections, a minimal CSAS input always requires **geometry data**, and KENO data blocks listed in :numref:`tab-module.keno.input` can be defined in any order. Information on all KENO input is provided in :numref:`sec-module.keno` of this document and will not be repeated here. .. tabularcolumns:: |\Y{0.20}|\Y{0.20}|\Y{0.40}|\Y{0.20}| .. table:: Outline of KENO data :class: longtable :name: tab-module.keno.input +-----------------+-----------------+-----------------+-----------------+ | **Type of** | **Starting** | **Comments** | **Termination** | | **data** | **flag** | | **flag** | +=================+=================+=================+=================+ | Parameters | READ PARAMETER | Enter | END PARAMETER | | | | desired | | | | | parameter | | | | | data | | +-----------------+-----------------+-----------------+-----------------+ | Geometry | READ GEOMETRY | Enter | END GEOMETRY | | | :sup:`1` | desired | | | | | geometry | | | | | data | | | | | | | | | | Always | | | | | required | | | | | by CSAS | | +-----------------+-----------------+-----------------+-----------------+ | Array data | READ ARRAY | Enter | END ARRAY | | | :sup:`1` | desired | | | | | array data | | +-----------------+-----------------+-----------------+-----------------+ | Boundary | READ BOUNDS | Enter | END BOUNDS | | conditions | | desired | | | | | boundary | | | | | conditions | | +-----------------+-----------------+-----------------+-----------------+ | Volume data | READ VOLUME | Enter | END VOLUME | | | | desired | | | | | volume data | | | | | (KENO-VI only) | | +-----------------+-----------------+-----------------+-----------------+ | Energy group | READ ENERGY | Enter | END ENERGY | | boundaries | | desired | | | | | neutron | | | | | energy group | | | | | boundaries | | +-----------------+-----------------+-----------------+-----------------+ | Start data | READ START | Enter | END START | | or initial | | desired | | | source | | start data | | +-----------------+-----------------+-----------------+-----------------+ | Plot data | READ PLOT | Enter | END PLOT | | | | desired plot | | | | | data | | +-----------------+-----------------+-----------------+-----------------+ | Grid | READ GRID | Enter | END GRID | | geometry | | desired mesh | | | data | | data | | +-----------------+-----------------+-----------------+-----------------+ | Reaction | READ REACTION | Enter desire | END REACTION | | | | reaction | | | | | tallies (CE | | | | | mode only) | | +-----------------+-----------------+-----------------+-----------------+ | KENO | END DATA | Enter to | | | data | | signal the | | | terminus | | end of all | | | | | KENO. | | | | | data | | +-----------------+-----------------+-----------------+-----------------+ | :sup:`1` Geometry input is different for both KENO V.a and KENO-VI | | See :numref:`sec-module.keno.geom` for further details. | +-----------------------------------------------------------------------+ .. note:: Unlike standalone KENO calculations, each KENO data block can be entered in any order when running KENO codes as part of CSAS sequence. .. _sec-csas.output: Description of Output --------------------- This section contains a brief description and explanation of the CSAS sequence. As CSAS was designed as a SCALE control module/sequence its own output is minimal. To avoid duplicate output edits, it suppresses the output from KENO Data processor except a few diagnostic and warning messages while processing the KENO data blocks. Because the KENO Data processor and KENO codes produce the same output edits for some input data, capturing both output sections and keeping printing them may result in duplicate information in the output sections for those input data. CSAS always captures the XSProc and KENO outputs and prints them in the code output. Because these output sections are described and their details are discussed in :numref:`sec-module.keno.output` and :numref:`sec-xsproc.intro` and relevant XSProc sections, they will not be described in this section. When CSAS is run with PARM=CHECK, only outputs from KENO Data processor and XSProc input processor are shown in the code output. The sample output sections presented in this section were from one of the calculations performed by CSAS5. Here, only CSAS5 examples are given to prevent repetition because CSAS6 prints the same tables in the same format with the same content. Program verification information ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ After the header page, program verification information is printed that lists the name of the program and the revision number. The job name, date, and time of execution are also printed as shown in :numref:`fig-oedit-csas5-1`. This information may be used for quality assurance purposes. .. figure:: figs/CSAS/csas5_oedit_program_verification.png :align: center :width: 800 :name: fig-oedit-csas5-1 Sample program verification table. Mixture table ~~~~~~~~~~~~~ The first table printed by CSAS codes lists the compositions read and processed from the data entered in the **composition data** block. Basically, this table echos what user defined in the **composition data** block; data for each mixture are printed. 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: mixture ID number, nuclide ZA number, atom density and temperature. A sample mixture table is shown in :numref:`fig-oedit-csas5-2`. .. figure:: figs/CSAS/csas5_oedit_mixture_table.png :align: center :width: 600 :name: fig-oedit-csas5-2 An example of a mixture table. .. note:: This output table prints only all mixtures read and processed from the composition data block. Any mixture defined with ``CELLMIX`` in celldata block is not printed here. .. note:: The mixing table printed in KENO output may not reflect the mixture properties listed in this output table. Any mixture which is defined in composition data block but not used in KENO transport process will not be printed in KENO mixing table data edits. KENO also prints the mixture data defined with ``CELLMIX`` or defined in **Double-het** cell treatment in KENO mixing table data edits in the output. See :numref:`sec-module.keno.mixing_table` for further details about the KENO mixing data. .. _sec-csas.xs_summary: Cross section processing summary ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ In multigroup mode, cross section processing calculation path with XSProc show some differences depending on the type of the unit cells being processed and/or desired calculation methodology defined by user as discussed in :numref:`sec-csas.xsproc_data`. CSAS sequences summarize which of the XSProc calculation path is used when processing the unit cells in XSProc in the output. A typical cross section processing summary table printed by a CSAS sequence in the code output is shown in :numref:`fig-oedit-csas-xs-proc-summary`. The first record printed in this table is the multigroup cross section library which will be used in the calculations. This is followed by the cross section processing summary of the unit cells for this problem. This table includes the total number of unit cells being processed, and the number of unit cells processed with CENTRM and BONAMI calculations path. The last record printed in this table is the total elapsed time to process the XSProc data and build all the unit cells for the subsequent XSProc calculations. .. figure:: figs/CSAS/csas5_oedit_xs_proc_summary.png :align: center :width: 800 :name: fig-oedit-csas-xs-proc-summary Summary of cross section processing. .. caution:: CSAS sequence always creates a unit cell for all the mixtures defined in the composition data block and stores them in a cell container. Then, XSProc cross section processing is applied to all the unit cells stored in the cell container regardless of whether they are used in KENO transport calculation. Performing cross section processing for the unused mixtures, especially fissile mixtures, might waste the allocated computational resources for this calculation. Warning and error messages -------------------------- CSAS sequence contains two types of warning and error messages. The first type of messages are from XSProc and SCALE sequence implementation which are common to many of the SCALE sequences. The second type of messages are mainly from the KENO Data processor as part of CSAS sequence implementation, and identified by CS- followed by a number. The details of the messages from KENO Data processor can be seen in :numref:`sec-module.keno.warn`. Warning messages appear when a possible error is encountered. It is the responsibility of the user to verify whether the data are correct when a warning message is encountered. The functional modules, XSProc and KENO, activated by CSAS sequences will be executed if no error messages are generated and a warning message has been generated. When an error is recognized, an error message is written and an error flag is set so the functional modules will not be activated. the code stops immediately if the error is too severe to allow continuation of input. However, it will continue to read and check the data if it is able. When the data reading is completed, execution is terminated if an error flag was set when the data were being processed. If the error flag has not been set, execution continues. When error messages are present in the output, the user should focus on the first error message, because subsequent messages may have been caused by the error that generated the first message. The messages listed below complement the messages, which are from KENO Data processor, listed in KENO manual section, :numref:`sec-module.keno.warn`. .. CS-21 A UNIT NUMBER WAS ENTERED FOR THE CROSS-SECTION LIBRARY. (LIB= IN PARAMETER DATA.) THE DEFAULT VALUE SHOULD BE USED IN ORDER TO UTILIZE THE CROSS SECTIONS GENERATED BY CSAS. MAKE CERTAIN THE CORRECT CROSS-SECTION LIBRARY IS BEING USED. This message is from subroutine CPARAM. It indicates that a value has been entered for the cross-section library in the KENO V.a parameter data. The cross-section library created by the analytical sequence should be used. *MAKE CERTAIN THAT THE CORRECT CROSS SECTIONS ARE BEING USED.* .. CS-55 \**\* ERRORS WERE ENCOUNTERED IN PROCESSING THE KENO DATA. EXECUTION IS IMPOSSIBLE. \**\* This message from subroutine SASSY is printed if errors were found in the KENO input data for CSAS. When the data reading and checking have been completed, the problem will terminate without executing. Check the printout to locate the errors responsible for this message. .. CS-62 \**\* ERROR \**\* MIXTURE ______ IN THE GEOMETRY WAS NOT CREATED IN THE STANDARD COMPOSITIONS SPECIFICATION DATA. This message from subroutine MIXCHK indicates that a mixture specified in the KENO geometry was not created in the standard composition data. .. CS-68 \**\* ERROR \**\* AN INPUT DATA ERROR HAS BEEN ENCOUNTERED IN THE ______ DATA ENTERED FOR THIS PROBLEM. This message from the main program, CSAS, is printed if the subroutine library routine LRDERR returns a value of "TRUE," indicating that a reading error has been encountered in the "KENO PARAMETER" data. The appropriate data type is printed in the message. Locate the unnumbered message stating "ERROR IN INPUT. CARD IMAGE PRINTED ON NEXT LINE". Correct the data and resubmit the problem. .. CS-69 \**\*ERROR\**\* MIXTURE ______ IS AN INAPPROPRIATE MIXTURE NUMBER FOR USE IN THE KENO GEOMETRY DATA BECAUSE IT IS A COMPONENT OF THE CELL-WEIGHTED MIXTURE CREATED BY XSDRNPM. This message from subroutine CMXCHK indicates that a mixture that is a component of a cell-weighted mixture has been used in the KENO geometry data. .. CS-100 \**\* ERROR \**\* THIS PROBLEM WILL NOT BE RUN BECAUSE ERRORS WERE ENCOUNTERED IN THE INPUT DATA. This self-explanatory message indicates that an error occurred in input processing. User should examine the printout to locate the error or errors in the input data. Correct them and resubmit the problem. Sample problems ---------------- This section contains example problems to demonstrate some of capabilities available in CSAS with KENO codes. A brief problem description and the associated input data for multigroup mode of calculation are included for each problem. The same sample problems may be executed in the continuous energy mode by changing the library name from ``v7.1-252`` to ``ce_v7.1``. The complete list of libraries distributed with SCALE is provided in the :ref:`Nuclear Data Libraries chapter `. CSAS5 sample problems ~~~~~~~~~~~~~~~~~~~~~ This section contains sample problems to demonstrate some of the options available in CSAS5. Note that sample problem 8 does not run in continuous-energy mode because they use CELLMIX or DOUBLEHET cell type. CSAS5 sample problem 1: *k*\ :sub:`eff` calculation ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The purpose of this problem is to calculate the k-effective of a system. This problem is the same as the KENO V.a sample problem 12 in Appendix B except the cross-section library and KENO V.a mixing table are prepared by CSAS. The problem represents a critical experiment consisting of a composite array :cite:`C56-thomas_critical_1973,C56-thomas_critical_1964` of four highly-enriched (93.2%) uranium metal cylinders having a density of 18.76 g/cc and four 5.0677-L Plexiglas containers filled with uranyl nitrate solution. The uranium metal cylinders have a radius of 5.748 cm and a height of 10.765 cm. The uranyl nitrate solution has a specific gravity of 1.555 and contains 415 g of uranium per liter. The ID of the Plexiglas bottle is 19.05 cm and the inside height is 17.78 cm. The Plexiglas is 0.635 cm thick. The center-to-center spacing between the metal units is 13.18 cm in the Y direction and 13.45 cm in the Z direction. The center-to-center spacing between the solution units is 21.75 cm in the Y direction and 20.48 cm in the Z direction. The spacing between the Y-Z plane that passes through the centers of the metal units and the Y-Z plane that passes through the centers of the solution units is 17.465 cm in the X direction. The metal units in this experiment are designated in Table II of :cite:`C56-thomas_critical_1964` as cylinder index 11 and reflector index 1. A photograph of the experiment, Fig. 9 in :cite:`C56-thomas_critical_1973`, is given in :numref:`fig-csas5-sample-problem-1`. .. code-block:: scale =csas5 parm=(centrm) sample problem set up 4aqueous 4 metal in csas5 v7.1-252 read composition uranium 1 0.985 300. 92235 93.2 92238 5.6 92234 1.0 92236 0.2 end solution mix=2 rho[uo2(no3)2]= 415. 92235 92.6 92238 5.9 92234 1.0 92236 0.5 molar[hno3]=9.783-3 temperature=300 end solution plexiglass 3 end end composition read param flx=yes fdn=yes nub=yes htm=no end param read geom unit 1 com='uranyl nitrate solution in a plexiglas container' cylinder 2 1 9.525 2p8.89 cylinder 3 1 10.16 2p9.525 cuboid 0 1 4p10.875 2p10.24 unit 2 com='uranium metal cylinder' cylinder 1 1 5.748 2p5.3825 cuboid 0 1 4p6.59 2p6.225 unit 3 com='1x2x2 array of solution units' array 1 3*0.0 unit 4 com='1x2x2 array of metal units padded to match solution array' array 2 3*0.0 replicate 0 1 2*0.0 2*8.57 2*8.03 1 global unit 5 array 3 3*0.0 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 com='composite array of solution and metal units' fill 4 3 end fill end array end data end .. figure:: figs/CSAS/csas5_sample_problem_fig1.png :align: center :width: 400 :name: fig-csas5-sample-problem-1 Critical assembly of four solution units and four metal units. CSAS5 Sample problem 8: k\ :math:`_{\infty}` for a pebble bed fuel ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ This problem demonstrates setting up a fuel pebble from a pebble bed reactor, and calculating its :math:`k_{\boldsymbol{\infty}}`. The pebble consists of a fuel grain of UO\ :sub:`2` 0.025 cm in radius, coated with 0.003 cm of pyrolytic carbon, a further coat of 0.0035 cm thick silicon carbide, with a final coat of 0.004 cm thick pyrolytic carbon. 15000 grains are packed with graphite into an internal fuel sphere of 2.5 cm radius clad with a 0.5 cm thick covering of carbon and surrounded by helium. The fuel is 8.2% enriched :sup:`235`\ U. The pebbles are stacked into an infinite square pitched array with a pitch of 6 cm. This problem uses ``DOUBLEHET`` cell type, which is applicable only in the multigroup mode of KENO calculations. Therefore, the continuous energy version of this problem will end with an error message. .. code-block:: scale =csas5 parm=(centrm) infinite array of pebbles on a square pitch v7.1-252 read composition ' fuel kernel u-238 1 0 2.12877e-2 293.6 end u-235 1 0 1.92585e-3 293.6 end o 1 0 4.64272e-2 293.6 end ' inner pyro carbon c 3 0 9.52621e-2 293.6 end ' silicon carbide c 4 0 4.77240e-2 293.6 end si 4 0 4.77240e-2 293.6 end ' outer pyro carbon c 5 0 9.52621e-2 293.6 end ' graphite matrix c 6 0 8.77414e-2 293.6 end ' carbon pebble outer coating c 7 0 8.77414e-2 293.6 end he-3 8 0 3.71220e-11 293.6 end he-4 8 0 2.65156e-5 293.6 end end composition read celldata doublehet fuelmix=10 end gfr=0.025 1 coatt=0.004 3 coatt=0.0035 4 coatt=0.004 5 matrix=6 numpar=15000 end grain centrm data ixprt=1 isn=8 nprt=2 end centrm pebble sphsquarep right_bdy=white hpitch=3.0 8 fuelr=2.5 cladr=3.0 7 end centrm data ixprt=1 isn=8 nprt=2 end centrm end celldata read param gen=210 npg=1000 htm=no end param read bounds all=mirror end bounds read geom global unit 1 sphere 10 1 2.5 sphere 7 1 3.0 cuboid 8 1 6p3.0 end geom end data end CSAS6 sample problems ~~~~~~~~~~~~~~~~~~~~~ This section contains sample problems to demonstrate some of the options available in CSAS6. A brief problem description and the associated input data for multigroup mode of calculation are included for each problem. The same sample problems may be executed in continuous-energy mode by changing the library name to an continuous-energy library. See Appendix A (:numref:`sec-scale.csas6_examples`) for additional examples. CSAS6 Sample problem 1: Aluminum 30 Degree Pipe Angle Intersection ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The purpose of this problem is to calculate the k-effective of a system composed of intersecting aluminum pipes, in the shape of a Y, filled with a 5% enriched UO\ :sub:`2`\ F\ :sub:`2` solution. The UO\ :sub:`2`\ F\ :sub:`2` solution at 299 K contains 907.0 gm/l of uranium, no excess acid, and has a specific gravity of 2.0289 gm/cm\ :sup:`3`. The assembly is composed of a 212.1 cm long vertical pipe and a second pipe that intersects the vertical pipe 76.7 cm from the outside bottom at an angle of 29.26 degrees with the upper vertical pipe. Both pipes have 13.95 cm inner diameters and 14.11 cm outer diameters. The vertical pipe is open on the top and 1.3 cm thick on the bottom. The Y-leg pipe, in the YZ-plane, is 126.04 cm in length with the sealed end 0.64 cm thick. The assembly is filled with solution to a height 129.5 cm above the outside bottom of the vertical pipe. From the point where the pipes intersect, the assembly is surrounded by water 37.0 cm in the :math:`\pm`\ X directions, 100 cm in the +Y direction, -37 cm in the -Y direction, to the top of the assembly in the +Z direction, and -99.6 cm in the -Z direction. .. figure:: figs/CSAS/csas6_sample_problem_fig1.png :align: center :width: 400 :name: fig-csas6-sample-problem-1 Critical assembly of UO\ :sub:`2`\ F\ :sub:`2` solution in a 30\ :math:`^{\circ}`\ -Y aluminum pipe. .. code-block:: scale =csas6 sample problem 1 Y-30, 5%uo2f2, 907.0g/l, 128.2, soln. ht. v7.1-252 read comp solution mix=1 rho[uo2f2]=907.0 92235 5.0 92238 95.0 density=? temperature=299.0 end solution al 2 1.0 end h2o 3 1.0 end end comp read parameters flx=yes fdn=yes far=yes pgm=yes plt=yes end parameters read start nst=6 tfx=0.0 tfy=0.0 tfz=0.0 lnu=1000 end start read geometry global unit 1 com='30 deg y' cylinder 10 13.95 135.4 -75.4 cylinder 20 14.11 135.4 -76.7 cylinder 30 13.95 125.4 0.0 rotate a2=-29.26 cylinder 40 14.11 126.04 0.0 rotate a2=-29.26 cuboid 50 2p37.0 100. -37.0 52.8 -75.4 cuboid 60 2p37.0 100. -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 -10 boundary 60 end geometry read volume type=random batches=1000 end volume read plot scr=yes lpi=10 ttl='y-z slice at x=0.0 through centerline of both pipes' xul=0.0 yul=-39.0 zul=137.0 xlr=0.0 ylr=105.0 zlr=-105.0 vax=1 wdn=-1 nax=400 end plt0 ttl='x-y slice at z=26.0 slightly above point of separation' xul=-40.0 yul=105.0 zul=26.0 xlr=+40.0 ylr=-40.0 zlr=26.0 uax=1 vdn=-1 nax=400 end plt1 ttl='x-y slice at z=75.0 well above point of separation' xul=-40.0 yul=105.0 zul=75.0 xlr=+40.0 ylr=-40.0 zlr=75.0 uax=1 vdn=-1 nax=400 end plt2 end plot end data end CSAS6 Sample problem 2: Plexiglas Cross ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The purpose of this problem is to calculate the k-effective of a system composed of intersecting Plexiglas pipes, in the shape of a cross, filled with a 5% enriched UO\ :sub:`2`\ F\ :sub:`2` solution. The room temperature UO\ :sub:`2`\ F\ :sub:`2` solution contains 896.1 gm/l of uranium, no excess acid, and has a specific gravity of 2.015 gm/cm\ :sup:`3`. The pipes have a 13.335 cm inner diameter and 16.19 cm outer diameter. The vertical pipe is open on the top and 3.17 cm thick on the bottom. The horizontal pipe ends are 3.17 thick. The vertical pipe is 210.19 cm in length and filled with solution to a height of 117.2 cm. The two horizontal legs, positioned in the XZ-plane, intersect the vertical pipe 91.44 cm from the outside bottom at an 89 degree angle with the upper section of the pipe. Each horizontal is 91.44 cm in length and filled with the above specified UO\ :sub:`2`\ F\ :sub:`2` solution. A water reflector surrounding the solution filled pipes extends out from the point where the pipes intersect 111.76 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. .. figure:: figs/CSAS/csas6_sample_problem_fig2.png :align: center :width: 400 :name: fig-csas6-sample-problem-2 Critical assembly of UO\ :sub:`2`\ F\ :sub:`2` solution in a Plexiglas cross. .. code-block:: scale =csas6 sample problem 2 89-cross, 5% uo2f2 soln, plexiglass pipes, h2o refl. v7.1-252 read comp solution mix=1 rho[uo2f2]=896.1 92235 5.0 92238 95.0 density=? temperature=298.0 end solution plexiglass 3 1.0 end h2o 2 1.0 end end comp read param plt=yes end param read geom 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 cylinder 40 13.335 88.27 0.0 rotate a1=90. a2=89. cylinder 50 16.19 91.44 0.0 rotate a1=90. a2=89. cylinder 60 13.335 88.27 0.0 rotate a1=-90. a2=89. cylinder 70 16.19 91.44 0.0 rotate a1=-90. a2=89. cuboid 80 2p111.74 2p20.64 29.03 -118.428 cuboid 90 2p111.74 2p40.64 121.92 -118.428 media 1 1 10 media 0 1 20 -10 media 3 1 30 -10 -20 -50 -70 media 1 1 40 -10 -20 media 3 1 50 -40 -10 -20 media 1 1 60 -10 -20 media 3 1 70 -60 -10 -20 -50 media 2 1 80 -10 -20 -30 -40 -50 -60 -70 media 0 1 90 -20 -30 -80 boundary 90 end geom read volume type=trace end volume read start nst=6 tfx=0. tfy=0. tfz=0. lnu=1000 end start read plot scr=yes lpi=10 ttl=' x-z slice at y=0.0 ' xul=-113. yul=0. zul= 48. xlr= 113. ylr=0. zlr=-120. uax=1.0 wdn=-1.0 nax=400 end plt0 ttl=' y-z slce at x=0.0 ' xul=0. yul=-42. zul= 122. xlr=0. ylr= 42. zlr=-120. vax=1.0 wdn=-1.0 nax=400 end plt1 ttl=' x-y slice at z=0.0 ' xul=-113.0 yul= 42. zul=0. xlr= 113.0 ylr=-42. zlr=0. uax=1.0 vdn=-1.0 nax=400 end plt2 end plot end data end CSAS6 Sample problem 3: Sphere ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ This problem models an assembly consisting of a 93.2% enriched bare uranium sphere, 8.741 cm in radius, having a density of 18.76 gm/cm\ :sup:`3`. Problem 3 models the assembly as a single bare sphere. The second problem models the assembly as a hemisphere with mirror reflection on the flat surface. The next three problems model the sphere using chords. This set of four problems is designed to illustrate the use of multiple chords in a problem. .. code-block:: scale =csas6 sample problem 3 bare 93.2% enriched uranium sphere v7.1-252 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 global unit 1 sphere 10 8.741 cuboid 20 6p8.741 media 1 1 10 vol=2797.5121 media 0 1 20 -10 vol=2545.3424 boundary 20 end geometry end data end CSAS6 Sample problem 4: Sphere Models Using Chords and Mirror Albedos ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ This problem models an assembly consisting of a 93.2% enriched bare uranium sphere, 8.741 cm in radius, having a density of 18.76 gm/cm\ :sup:`3`. The problem models the assembly as a hemisphere with mirror reflection on the flat surface. .. code-block:: scale =csas6 sample problem 4 bare 93.2% U sphere, hemisphere w/ mirror albedo v7.1-252 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 global unit 1 sphere 10 8.741 chord +x=0.0 cuboid 20 8.741 0.0 8.741 -8.741 8.741 -8.741 media 1 1 10 vol=2797.5121 media 0 1 20 -10 vol=2545.3424 boundary 20 end geometry read bounds -xb=mirror end bounds end data end CSAS6 Sample problem 5: Sphere Models Using Chords and Mirror Albedos ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ This problem models an assembly consisting of a 93.2% enriched bare uranium sphere, 8.741 cm in radius, having a density of 18.76 gm/cm\ :sup:`3`. The problem models the assembly as a quarter sphere with mirror reflection on the two flat surfaces. .. code-block:: scale =csas6 sample problem 5 bare 93.2% U sphere, quarter sphere w/ mirror albedo v7.1-252 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 global unit 1 sphere 10 8.741 chord +x=0.0 chord +y=0.0 cuboid 20 8.741 0.0 8.741 0.0 8.741 -8.741 media 1 1 10 vol=2797.5121 media 0 1 20 -10 vol=2545.3424 boundary 20 end geometry read bounds -xy=mirror end bounds end data end CSAS6 Sample problem 6: Sphere Models Using Chords and Mirror Albedos (Eighth Sphere) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ This problem models an assembly consisting of a 93.2% enriched bare uranium sphere, 8.741 cm in radius, having a density of 18.76 gm/cm\ :sup:`3`. The problem models the assembly as an eighth sphere with mirror reflection on the three flat surfaces. :: =csas6 sample problem 6 bare 93.2% U sphere, eighth sphere w/ mirror albedo v7.1-252 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 global unit 1 sphere 10 8.741 chord +x=0.0 chord +y=0.0 chord +z=0.0 cuboid 20 8.741 0.0 8.741 0.0 8.741 0.0 media 1 1 10 vol=2797.5121 media 0 1 20 -10 vol=2545.3424 boundary 20 end geometry read bounds -fc=mirror end bounds end data end CSAS6 Sample problem 7: Grotesque without the Diaphragm ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The purpose of this problem is to calculate the |keff| of a system composed of eight enriched uranium units placed on a diaphragm, with an irregularly shaped centerpiece positioned in the center hole of the diaphragm :cite:`C56-mihalczo_brief_1999`. The assembly and centerpiece are shown in :numref:`fig-csas6-sample-problem-3`, which is Fig. 4 from :cite:`C56-mihalczo_brief_1999`. The eight units consist of an approximate parallelepiped with an irregular top, a parallelepiped, and six cylinders of various sizes. The centerpiece, which penetrates the hole in the diaphragm, consists of a cylinder topped by a parallelepiped topped by a hemisphere. The diaphragm is not modeled in this example. .. figure:: figs/CSAS/csas6_sample_problem_fig3.png :align: center :width: 400 :name: fig-csas6-sample-problem-3 Grotesque experimental setup. .. code-block:: scale =csas6 sample problem 7 keno-vi grotesque w/o diaphragm, ornl/csd/tm-220 v7.1-252 read comp uranium 1 den=18.76 1 293 92235 93.2 92238 5.6 92234 1.0 92236 0.2 end uranium 2 den=18.76 1 293 92235 93.2 92238 5.6 92234 1.0 92236 0.2 end uranium 3 den=18.76 1 293 92235 93.2 92238 5.6 92234 1.0 92236 0.2 end uranium 4 den=18.76 1 293 92235 93.2 92238 5.6 92234 1.0 92236 0.2 end uranium 5 den=18.76 1 293 92235 93.2 92238 5.6 92234 1.0 92236 0.2 end uranium 6 den=18.76 1 293 92235 93.2 92238 5.6 92234 1.0 92236 0.2 end uranium 7 den=18.76 1 293 92235 93.2 92238 5.6 92234 1.0 92236 0.2 end uranium 8 den=18.76 1 293 92235 93.2 92238 5.6 92234 1.0 92236 0.2 end uranium 9 den=18.76 1 293 92235 93.2 92238 5.6 92234 1.0 92236 0.2 end uranium 10 den=18.76 1 293 92235 93.2 92238 5.6 92234 1.0 92236 0.2 end uranium 11 den=18.76 1 293 92235 93.2 92238 5.6 92234 1.0 92236 0.2 end uranium 12 den=18.76 1 293 92235 93.2 92238 5.6 92234 1.0 92236 0.2 end uranium 13 den=18.76 1 293 92235 93.2 92238 5.6 92234 1.0 92236 0.2 end uranium 14 den=18.76 1 293 92235 93.2 92238 5.6 92234 1.0 92236 0.2 end end comp read param pgm=yes plt=yes end param read geom global unit 1 '*** one through three is item 1 in drawing 84-10649 ornl/csd/tm-220 *** 'one top piece of item 1 cuboid 10 2p6.3515 1.2685 -3.8115 13.377 13.058 origin y=-17.464 z=0.15 rotate a2=-1.35 'two middle piece of item 1 cuboid 20 2p6.3515 6.3515 -3.8115 13.058 11.155 origin y=-17.464 z=0.15 rotate a2=-1.35 'three bottom piece of item 1 cuboid 30 4p6.3515 11.155 0. origin y=-17.464 z=0.15 rotate a2=-1.35 '*** four is item 2 in drawing 84-10649 ornl/csd/tm-220 *** cylinder 40 4.555 12.918 0. origin x=-12.176 y=-9.343 z=0.111 rotate a1=-52.5 a2=-1.400 '*** five is item 3 in drawing 84-10649 ornl/csd/tm-220 *** cylinder 50 5.761 13.475 0. origin x=-16.333 y=1.681 z=0.174 rotate a1=83.5 a2=+1.173 '*** six is item 4 in drawing 84-10649 ornl/csd/tm-220 *** cylinder 60 4.5525 12.969 0. origin x=-9.539 y=11.168 z=0.156 rotate a1=40.5 a2=+1.970 '*** seven and eight are item 5 in drawing 84-10649 ornl/csd/tm-220 *** 'seven cuboid 70 2p3.81 8.13 -4.573 8.91 0. origin y=15.698 z=0.290 rotate a2=+2.58 'eight cylinder 80 4.573 13.229 8.91 origin y=15.698 z=0.290 rotate a2=+2.58 '*** nine is item 6 in drawing 84-10649 ornl/csd/tm-220 *** cylinder 90 4.5545 12.974 0. origin x=9.854 y=10.964 z=0.134 rotate a1=-42.0 a2=+1.680 '*** ten is item 7 in drawing 84-10649 ornl/csd/tm-220 *** cylinder 100 5.7495 13.475 0. origin x=16.388 y=1.434 z=0.140 rotate a1=-86.0 a2=+1.400 '*** eleven is item 8 in drawing 84-10649 ornl/csd/tm-220 *** cylinder 110 4.5565 12.954 0. origin x=12.029 y=-9.398 z=0.087 rotate a1=38.0 a2=-1.100 '*12 through 14 is the centerpiece in drawing 84-10649 ornl/csd/tm-220 'twelve cylinder 120 5.757 2.690 0. origin x=-0.593 y=-0.593 z=-1.753 'thirteen cuboid 130 4p6.35 5.718 0. origin z=0.937 'fourteen sphere 140 6.082 chord +z=0. origin x=-0.268 y=0.268 z=6.655 '*** fifteen is the system boundary *** 'fifteen cuboid 150 4p25.0 15.0 -2.0 media 1 1 +10 vol=20.58546556 media 2 1 +20 -10 vol=245.678420867 media 3 1 +30 -20 vol=1800.040061395 media 4 1 +40 vol=842.019046637 media 5 1 +50 vol=1404.99376489 media 6 1 +60 vol=844.415646269 media 7 1 +70 vol=862.4600226 media 8 1 +80 -70 vol=283.749744681 media 9 1 +90 vol=845.483582679 media 10 1 +100 vol=1399.390119093 media 11 1 +110 vol=844.921798001 media 12 1 +120 -130 vol=280.088070346 media 13 1 +130 vol=922.25622 media 14 1 +140 -130 vol=471.191948666 media 0 1 150 -10 -20 -30 -40 -50 -60 -70 -80 -90 -100 -110 -120 -130 -140 vol=31432.726088316 boundary 150 end geom read plot scr=yes lpi=10 clr= 1 255 0 0 2 0 0 205 3 0 229 238 4 0 238 0 5 205 205 0 6 255 121 121 7 145 44 238 8 150 150 150 9 240 200 220 10 0 191 255 11 224 255 255 12 0 128 64 13 255 202 149 14 255 0 128 end color ttl='grotesque x-y slice at z=0.5' xul=-25.5 yul= 25.5 zul=0.5 xlr= 25.5 ylr=-25.5 zlr=.5 uax=1 vdn=-1 nax=800 end ttl='grotesque x-y slice at z=2.0' xul=-25.5 yul= 25.5 zul=2 xlr= 25.5 ylr=-25.5 zlr=2 end ttl='grotesque x-y slice at z=9.5' xul=-25.5 yul= 25.5 zul=9.5 xlr= 25.5 ylr=-25.5 zlr=9.5 end ttl='grotesque y-z slice at x=-0.593' xul=-.593 yul=-25.5 zul=15.5 xlr=-.593 ylr= 25.5 zlr=-3.5 uax=0 vax=1 vdn=0 wdn=-1 nax=800 end ttl='grotesque x-z slice at y=0.0' xul=-25.5 yul=0.0 zul=15.5 xlr= 25.5 ylr=0.0 zlr=-3.5 uax=1 vax=0 wax=0 udn=0 vdn=0 wdn=-1 nax=800 end ttl='grotesque x-z slice at y=12.125' xul=-25.5 yul=12.125 zul=15.5 xlr= 25.5 ylr=12.125 zlr=-3.5 uax=1 vax=0 wax=0 udn=0 vdn=0 wdn=-1 nax=800 end ttl='grotesque x-z slice at y=-12.000' xul=-25.5 yul=-12.000 zul=15.5 xlr= 25.5 ylr=-12.000 zlr=-3.5 uax=1 vax=0 wax=0 udn=0 vdn=0 wdn=-1 nax=800 end end plot end data end CSAS6 Sample problem 8 Infinite Array of MOX and UO2 Assemblies ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The purpose of this problem is to calculate the |keff| of a system composed of an infinite array of MOX assemblies interspersed between UO\ :sub:`2` assemblies. Both assembly types contain 331 pins in a hexagonal lattice with a pin pitch of 1.275 cm and an assembly pitch of 23.60 cm as shown in :numref:`fig-csas6-sample-problem-4`. The moderator is borated water at 306\ :math:`^{\circ}`\ C having a density of 0.71533 gm/cc and composed of 99.94 wt % H\ :sub:`2`\ O and 0.06 wt % natural boron. Each fuel rod is 355 cm in length, has a radius of 0.3860 cm, 0.722-cm-thick Zr cladding with no gap, and is at a temperature of 754\ :math:`^{\circ}`\ C. The UO\ :sub:`2` fuel consists of 4.4 wt % :sup:`235`\ U and 95.6 wt % :sup:`238`\ U at a density of 8.7922 gm/cc. The UO\ :sub:`2` fuel also contains 9.4581E-9 atoms/b-cm of :sup:`135`\ Xe and 7.3667E-8 atoms/b-cm of :sup:`149`\ Sm. The MOX fuel consists of 96.38 wt % UO\ :sub:`2` and 3.62 wt % PuO\ :sub:`2` at a density of 8.8182 gm/cc. The UO\ :sub:`2` fuel is composed of 2.0 wt % \ :sup:`235`\ U and 98.0 wt % \ :sup:`238`\ U. The PuO\ :sub:`2` fuel is composed of 93.0 wt % :sup:`239`\ Pu, 6.0 wt % \ :sup:`240`\ Pu- and 1.0 wt % \ :sup:`241`\ Pu. The MOX fuel also contains 9.4581E-9 atoms/b-cm of :sup:`135`\ Xe and 7.3667E-8 atoms/b-cm of :sup:`149`\ Sm. These two assemblies are placed so they represent an infinite array in the X and Y dimensions as shown in :numref:`fig-csas6-sample-problem-5`. There is 20 cm of water above and below fuel assemblies. This problem uses CENTRM/PMC as the resolved resonance processor cross section. Since an infinite array cannot be explicitly modeled, a section of the array is modeled and the X and Y sides have mirror reflection. .. code-block:: scale =csas6 parm=(centrm) sample problem 8 - VVER inf. array - MOX & UO2 Assemblies v7.1-252 read comp ' UO2 Fuel uo2 1 den=8.7922 1.0 1027 92235 4.4 92238 95.6 end xe-135 1 0 9.4581E-09 1027 end sm-149 1 0 7.3667E-08 1027 end ' MOX Fuel uo2 2 den=8.8182 0.9638 1027 92235 2.0 92238 98.0 end puo2 2 den=8.8182 0.0362 1027 94239 93.0 94240 6.0 94241 1.0 end xe-135 2 0 9.4581E-09 1027 end sm-149 2 0 7.3667E-08 1027 end ' Cladding for UO2 fuel zr 3 den=6.4073 1.0 579 end ' Moderator for UO2 fuel h2o 4 den=0.71533 0.9994 579 end boron 4 den=0.71533 0.0006 579 end ' Cladding for MOX fuel zr 5 den=6.4073 1.0 579 end ' Moderator for MOX fuel h2o 6 den=0.71533 0.9994 579 end boron 6 den=0.71533 0.0006 579 end ' Moderator for vacant units h2o 7 den=0.71533 0.9994 579 end boron 7 den=0.71533 0.0006 579 end end comp read celldata latticecell triangpitch pitch=1.2750 4 fueld=0.7720 1 cladd=0.9164 3 end latticecell triangpitch pitch=1.2750 6 fueld=0.7720 2 cladd=0.9164 5 end ' more data dab=500 end more end celldata read param gen=203 npg=1000 end param read bounds all=mirror zfc=void end bounds read geom unit 1 com='UO2 Fuel Rod' cylinder 10 0.3860 355.0 0.0 cylinder 20 0.4582 355.0 0.0 hexprism 30 0.6375 355.0 0.0 media 1 1 10 media 3 1 20 -10 media 4 1 30 -20 boundary 30 unit 2 com='Vacant(water filled) hex' hexprism 10 0.6375 355.0 0.0 media 7 1 10 boundary 10 unit 3 com='Vacant(water filled) hex' hexprism 10 0.6375 355.0 0.0 media 7 1 10 boundary 10 unit 4 com='MOX Fuel Rod' cylinder 10 0.3860 355.0 0.0 cylinder 20 0.4582 355.0 0.0 hexprism 30 0.6375 355.0 0.0 media 2 1 10 media 5 1 20 -10 media 6 1 30 -20 boundary 30 global unit 5 rhexprism 10 11.800 355.0 0.0 rhexprism 20 11.800 355.0 0.0 origin y=23.6 rhexprism 30 11.800 355.0 0.0 origin x=20.4382 y=11.8 rhexprism 40 11.800 355.0 0.0 origin x=20.4382 y=35.4 cuboid 50 20.4382 0.0 35.4 0.0 375.0 -20.0 array 1 10 -20 -30 -40 place 12 12 1 0.0 0.0 0.0 array 2 20 -10 -30 -40 place 12 12 1 0.0 23.6 0.0 array 2 30 -10 -20 -40 place 12 12 1 20.4382 11.8 0.0 array 1 40 -10 -20 -30 place 12 12 1 20.4382 35.4 0.0 media 4 1 50 -10 -20 -30 -40 boundary 50 end geom read array ara=1 typ=shexagonal nux=23 nuy=23 nuz=1 fill 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 end fill ara=2 typ=shexagonal nux=23 nuy=23 nuz=1 fill 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 end fill end array read plot lpi=10 scr=yes ttl='VVER assembly x-y x-section' xul=-0.1 yul=35.5 zul=10 xlr=20.6 ylr=-0.1 zlr=10 uax=1 vdn=-1.0 nax=640 pic=mat end plt1 end plot read volume type=random batches=1000 end volume end data end .. figure:: figs/CSAS/csas6_sample_problem_fig4.png :align: center :width: 400 :name: fig-csas6-sample-problem-4 MOX or UO\ :sub:`2` hexagonal assembly. .. figure:: figs/CSAS/csas6_sample_problem_fig5.png :align: center :width: 400 :name: fig-csas6-sample-problem-5 Infinite array of MOX assemblies interspersed between UO\ :sub:`2` assemblies. .. only:: html .. rubric:: References .. bibliography:: zSCALE.bib :cited: :keyprefix: C56- :labelprefix: CSAS5