# 7.8. MCDancoff: Monte-Carlo based Dancoff Factor Calculation

*L. M. Petrie, B. T. Rearden, A. M. Holcomb, and K. S. Kim*

ABSTRACT

The MCDancoff program is used to calculate Dancoff factors in complicated, three-dimensional (3-D) geometries using Monte Carlo integrations. The geometries are standard SCALE geometry descriptions, with the current restriction that Dancoff factors can only be calculated for regions bounded by cuboids, spheres, or cylinders. Multiple Dancoff factors can be calculated with one input file. New AMPX one group library for MCDancoff was developed for SCALE 6.3 based on ENDF/B-VII.1.

ACKNOWLEDGMENT

This work was sponsored in part by Atomic Energy of Canada, Ltd. Development of new ENDF/B-VII.1 based AMPX one group library for SCALE 6.3 was sponsored by the US Nuclear Regulatory Commision (NRC). The contribution of S. J. Poarch in preparing this document is gratefully acknowledged.

## 7.8.1. Introduction

MCDancoff (Monte Carlo Dancoff) is a program that calculates Dancoff factors for complicated, three-dimensional geometries. Its input is a slight modification of a CSAS6 input file which uses the standard SCALE geometry as detailed for KENO-VI. The modifications to the input involve different input in the START data block describing which Dancoff factors are to be calculated. The calculation involves starting histories isotropically on the surface of the region for which the Dancoff factor is to be calculated and following the path of each history until it has encountered all the elements of the material in the region, or until it has exited the system. A one group cross-section library is used to determine the total cross sections of the mixtures in the problem. The one group library has been developed based on ENDF/B-VII.1 for SCALE 6.3 for which various reaction cross sections were obtained by energy group collapsing and elastic cross sections (MT=2) were replaced by potential cross sections.

A current restriction of MCDancoff is that it can only calculate Dancoff factors for regions bounded by cylinders, spheres, or cuboids. Other simple bodies could be added in the future, but a general bounding surface would be impractical.

The Dancoff factors are used in SCALE to correctly self-shield multigroup cross sections for a given problem; either as input to BONAMI or to determine an equivalent cell for CENTRM. This is most typically accomplished through the MORE DATA and CENTRM DATA blocks.

The Dancoff factors are actually calculated by a modified version of the
KENO-VI code called KENO_Dancoff. All printed output from these
calculations is suppressed by default. If there is a need to see this
output (for example, to find an error message), it can be turned on by
setting an environment variable **print_dancoff=yes**.

## 7.8.2. Input data description

MCDancoff input data is the same as CSAS6 input data with the following
exceptions. A special one group cross-section library will be used. It
can be specified as **xn01** in the input but will be set to this if
anything else is entered for the library. Because MCDancoff is running a
fixed source problem, and the Dancoff factor doesn’t need to be
calculated with the same accuracy as an eigenvalue, there are useful
changes that can be made to the parameters in the PARAMETER data block.
Sect. 7.8.3 discusses this in more detail. Finally, the START data
block is used to define which Dancoff factors will be calculated. This
data block is defined below.

```
READ START Begins the data block
1. dancoff
begins defining a new Dancoff factor. Always start
relative to the global unit in the geometry.
2. array
step into an array contained in the current unit – followed
by karray, nbx, nby, nbz where karray is the
region containing the array in the current unit, nbx is the x
position in the array of the next unit, nby is the y position
in the array of the next unit, and **nbz** is the z position in
the array of the next unit.
3. hole
step into a hole contained in the current unit – followed by
nhole, the hole number relative to the current unit.
4. unit
final unit in the nesting chain – followed by **nn**, the
unit number
5. region
region to calculate the Dancoff factor for – followed by
k, the relative geometry word in unit nn defining the
outer bound of the region.
6. nst
if input, must be 0 (defaults to 0).
Repeat 2 and 3 to get from the global unit to the final unit nn.
Repeat 1–5 for each Dancoff factor to be calculated.
END START Ends the data block
```

## 7.8.3. Calculation and use of 3D Dancoff factors

The 3-D Dancoff factors are computed with KENO-VI geometry. If beginning with CSAS5 model, use C5TOC6 to convert to CSAS6.

Change sequence name from CSAS6 to MCDancoff and change cross-section library to

**xn01**.Input appropriate parameter data.

Since the Dancoff calculation is fixed source integration, there is no need to skip generations, and

nskshould be set to 0. Since small changes to the Dancoff have very minor effects on the cross sections, fewer histories are probably needed for calculating the Dancoff than for calculatingkeff. Thirty thousand histories divided as 100 generations of 300 histories per generation has produced Dancoff factors with deviations of less than 1 percent. It may be advantageous to turn off plots at this point. Since the same parameters can be entered more than once, with the final entry being the one used, adding a separate record with these values immediately before theend parameterkeywords would override the original KENO-VI parameters.Example:

```
read param
.........
nsk=0 npg=300 gen=100 nub=no fdn=no flx=yes plt=no
end param
```

Identify the region for which Dancoff factors are desired in START data.

The start type needs to be set to

0for the Dancoff calculation (this is the default). All KENO-VI START data should be removed or commented out by placing an apostrophe in column 1. Each region for which a Dancoff calculation is desired then starts with the keyworddancoff. This is followed by data that specify the relationship of the global unit to the specific geometry description of the region. If the region is nested inside an array, then the keyword,array, is specified, followed by four integers. The first integer is the indices of the media record specifying the array relative to the current unit. The next 3 integers are the X, Y, and Z indexes of the position of the next unit in the array. If the region is nested in a hole, then the keyword,hole, is specified, followed by the relative count of the correct hole in the unit. The preceding data are repeated (in the correct nesting order starting with the global unit) until reaching the unit where the region is located. Then the keyword,unit, followed by the unit number is given, followed by the keyword,region, followed by the relative index of the geometry keyword describing the desired region with respect to that unit. Currently, only cylinders, spheres, and cuboids are programmed for calculating Dancoff factors.Examples:

read start nst=0 dancoff hole 1 unit=1 reg=1 end start read start dancoff array 1 1 1 1 array 1 17 17 2 unit 10 region 1 end start

Execute MCDANCOFF

*filename.*input file like any other SCALE input file.Examine

*filename*.dancoff file, which will contain Dancoff factors for each nuclide in the specified region

```
index nuclide dancoff deviation
1 92234 3.36340E-01 1.81134E-03
2 92235 3.36340E-01 1.81134E-03
3 92236 3.36340E-01 1.81134E-03
4 92238 3.36340E-01 1.81134E-03
5 8016 1.00000E+00 0.00000E+00
```

Once all desired Dancoff factors are obtained, return to original model and enter CENTRM DATA for each cell with dan2pitch(mix) specified.

```
read celldata
latticecell triangpitch fuelr=0.633 1 gapr=0.637 0 cladr=0.675 10 hpitch=0.867 14 end
centrm data
dan2pitch(1)=0.336
end centrm
```

If executing TSUNAMI-3D, additional steps are necessary because TSUNAMI-3D does not treat the dan2pitch input parameter.

Return to the original TSUNAMI-3D input file and replace the sequence name to “CSAS-MG PARM=CHECK” and delete all data after the unit cell data to quickly obtain revised pitch values. (Note: CSAS will not modify cell dimensions to more than 20 cm, so a revised moderator density may need to be entered to obtain the desired Dancoff factor.) Search for the word “

desired”in output file to find new pitch values for each cell.unit cell = 1 original pitch = 1.7340E+00 Dancoff for orig pitch = 2.9728E-01 desired Dancoff = 3.3600E-01 pitch to produce desired Dancoff= 1.6845E+00

Enter revised pitch and revised moderator density (for cell calculation only, not for geometry model) in TSUNAMI model.

## 7.8.4. Example Case

The following is a contrived case to illustrate an input file using both holes, arrays, and multiple sets of Dancoff factors (although both factors apply to the same pin, so only one set can be used). The case represents two fuel assemblies in a cylindrical tank, each assembly having a poisoned central pin, and four water holes. The Dancoff factors are calculated for each central pin. The input file is listed in Example 7.8.1.

```
=mcdancoff
sample case demonstrating calculating Dancoff factors
xn01
read composition
uo2 1 den=10.38 1 294 92234 .0303 92235 4.7378 92236 .1364 92238 95.0955 end uo2
zirc4 2 1 294 end zirc4
h2o 3 1 294 end h2o
uo2 4 den=10.08 1 294 92234 .0303 92235 4.7378 92236 .1364 92238 95.0955 end uo2
gd 4 den= 0.3 1 294 end gd
end composition
read param
nsk=0 gen=100 npg=300
end param
read geometry
unit 1
com=!fuel pin!
cylinder 10 0.395 40.0 -40.0
cylinder 20 0.410 40.0 -40.0
cylinder 30 0.470 40.0 -40.0
cuboid 40 4p0.65 2p40.0
media 1 1 10
media 0 1 20 -10
media 2 1 30 -20
media 3 1 40 -30
boundary 40
unit 2
com=!water hole!
cuboid 40 4p0.65 2p40.0
media 3 1 40
boundary 40
unit 3
com=!unit containing a 2x2 array of fuel pins!
cuboid 10 4p1.30 2p40.0
array 1 10 place 1 1 1 -0.65 -0.65 0.0
boundary 10
unit 4
com=!unit containing a 1x2 array of fuel pins!
cuboid 10 2p0.65 2p1.30 2p40.0
array 2 10 place 1 1 1 0.0 -0.65 0.0
boundary 10
unit 5
com=!unit containing a 2x1 array of fuel pins!
cuboid 10 2p1.30 2p0.65 2p40.0
array 3 10 place 1 1 1 -0.65 0.0 0.0
boundary 10
unit 6
com=!unit containing a 5x5 array of fuel pins!
cuboid 10 4p3.25 2p40.0
array 4 10 place 2 2 1 0.0 0.0 0.0
boundary 10
unit 7
com=!unit containing a 5x5 array of fuel pins - water hole in the middle!
cuboid 10 4p3.25 2p40.0
array 5 10 place 2 2 1 0.0 0.0 0.0
boundary 10
unit 8
com=!unit containing a 5x5 array of fuel pins - poisoned pin in the middle!
cuboid 10 4p3.25 2p40.0
array 6 10 place 2 2 1 0.0 0.0 0.0
boundary 10
unit 9
com=!poisoned fuel pin!
cylinder 10 0.395 40.0 -40.0
cylinder 20 0.410 40.0 -40.0
cylinder 30 0.470 40.0 -40.0
cuboid 40 4p0.65 2p40.0
media 4 1 10
media 0 1 20 -10
media 2 1 30 -20
media 3 1 40 -30
boundary 40
unit 10
com=!unit containing a 15x15 fuel assembly!
cuboid 10 4p9.75 2p40.0
array 7 10 place 2 2 1 0.0 0.0 0.0
boundary 10
global
unit 11
com=!global unit with 2 fuel assemblies!
cylinder 10 25.0 60.0 -60.0
hole 10 origin x=-10.0
hole 10 origin x= 10.0
media 3 1 10
boundary 10
end geometry
read array
ara=1 typ=square nux=2 nuy=2 nuz=1 fill f1 end fill
ara=2 typ=square nux=1 nuy=2 nuz=1 fill f1 end fill
ara=3 typ=square nux=2 nuy=1 nuz=1 fill f1 end fill
ara=4 typ=square nux=3 nuy=3 nuz=1 fill 3 4 3 5 1 5 3 4 3 end fill
ara=5 typ=square nux=3 nuy=3 nuz=1 fill 3 4 3 5 2 5 3 4 3 end fill
ara=6 typ=square nux=3 nuy=3 nuz=1 fill 3 4 3 5 9 5 3 4 3 end fill
ara=7 typ=square nux=3 nuy=3 nuz=1 fill 7 6 7 6 8 6 7 6 7 end fill
end array
read start
' first Dancoff - calculate for the poisoned fuel pin in unit 9 for the x=-10 assembly
dancoff
' hole 1 is unit 10 at x=-10
hole 1
' array in first region of unit 10 is array 7 - 2 2 1 position is unit 8
array 1 2 2 1
' array in first region of unit 8 is array 6 - 2 2 1 position is unit 9
array 1 2 2 1
' cylinder labeled 10 in unit 9 is the first region
unit 9 region 1
' second Dancoff - calculate for the poisoned fuel pin in unit 9 for the x=+10 assembly
dancoff
' hole 2 is unit 10 at x=+10
hole 2
' array in first region of unit 10 is array 7 - 2 2 1 position is unit 8
array 1 2 2 1
' array in first region of unit 8 is array 6 - 2 2 1 position is unit 9
array 1 2 2 1
' cylinder labeled 10 in unit 9 is the first region
unit 9 region 1
end start
end data
end
```

This input file creates two files of Dancoff factors. The first such file is listed in Example 7.8.2.

```
Unit 9 at global x -1.00000E+01 y 0.00000E+00 z 0.00000E+00
index nuclide dancoff deviation
1 92234 2.20873E-01 1.03436E-03
2 92235 2.20873E-01 1.03436E-03
3 92236 2.20873E-01 1.03436E-03
4 92238 2.20873E-01 1.03436E-03
5 8016 9.64748E-01 4.28121E-04
6 64000 2.82254E-10 3.61320E-11
```

The second file is statistically the same, as it solved for the mirror image Dancoff factor.