CSAS5: Control Module For Enhanced Criticality Safety Analysis Sequences With KENO V.a¶
L. M. Petrie, K. B. Bekar, S. Goluoglu,^{*} D. F. Hollenbach,^{*} N. F. Landers
The Criticality Safety Analysis Sequences with KENO V.a (CSAS5) provides reliable and efficient means of performing k_{eff} calculations for systems that are routinely encountered in engineering practice. In the multigroup calculation mode, CSAS5 uses XSProc to process the cross sections for temperature corrections and problemdependent resonance selfshielding and calculates the k_{eff} of a threedimensional (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 V.a, with temperature corrections provided as the cross sections are loaded. The geometric modeling capabilities available in KENO V.a coupled with the automated crosssection processing within the control sequences allow complex, 3D systems to be easily analyzed. A search capability is achieved by repeatedly activating the control module MODIFY, to alter either the system dimensions or densities, and the functional module KENO V.a to calculate the k_{eff} for the modified dimensions or densities.
*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 the KENO V.a chapter. 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.
Special appreciation is expressed to S. J. Poarch and S. Y. Walker for their efforts in formatting this document.
Introduction¶
Criticality Safety Analysis Sequence with KENO V.a (CSAS5) provides reliable and efficient means of performing k_{eff} calculations for systems that are routinely encountered in engineering practice, especially in the calculation of k_{eff} of threedimensional (3D) system models. CSAS5 implements XSProc to process material input and provide a temperature and resonancecorrected crosssection library based on the physical characteristics of the problem being analyzed. If a continuous energy crosssection library is specified, no resonance processing is needed and the continuous energy cross sections are used directly in KENO V.a, with temperature corrections provided as the cross sections are loaded. A search capability is available to find a desired values of k_{eff} as a function of dimensions or densities. The two basic search options offered are (1) an optimum search seeking a maximum or minimum value of k_{eff} and (2) a critical search seeking a fixed value of k_{eff}.
All the control sequences in the CSAS5 control module are listed in Table 4 with the modules they invoke. The first four sequences are subsets of the CSAS5 sequence.
Control sequence 
Function 
Functional modules executed by the control sequence for multigroup libraries 


CSAS5 
\(k_{eff}\) (3D) 
XSProc 
KENO V.a 

CSAS5S 
\(k_{eff}\) (3D) search 
XSProc 
KENO V.a 
MODIFY 
Sequence Capabilities¶
In order to minimize human error, the SCALE data handling is automated as much as possible. CSAS5 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 engineeringtype 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 selfshielding and fluxweighting cell calculations, if needed, and (if needed) provides problemdependent multigroup crosssection processing. Sequences that execute KENO V.a include a KENO V.a Data Processor to read and check the KENO V.a data. Sequences that execute a search use a Search Data Processor to read and check the search data. When the data checking has been completed, the control sequence executes XSProc to prepare a resonancecorrected microscopic crosssection library in the AMPX working library format if a multigroup library has been selected.
For each unit cell specified as being cellweighted, XSProc performs the necessary calculations and produces a cellweighted microscopic crosssection library. KENO V.a may be executed to calculate the k_{eff} or neutron multiplication factor using the crosssection library that was prepared by the control sequence. MODIFY may be invoked to perform a search [LDPW79] by repeatedly altering the unit cell (multigroup mode only) and KENO V.a data prior to executing the next pass through the calculation. Cross sections are updated at the beginning of each search pass with the modified data. If unit cell data is altered as part of the search, i.e., pitch or material search, the crosssections are correctly processed with the updated data.
The search capability is implemented by the control module MODIFY. It performs operations according to the specified search data to determine (1) the maximum or minimum value of \(k_{eff}\) as a function of pitch, dimensions or densities or (2) the pitch, dimensions, or densities corresponding to a specified value of \(k_{eff}\). An iterative procedure is used, making use of all previous information to modify the dimensions or densities to achieve the desired result. The procedures for conducting optimum and critical searches are summarized in the following sections.
Optimum (minimum/maximum) search¶
Because only an initial value of \(k_{eff}\) and a set of boundary constraints are available, four initial points are generated spanning the range defined by the constraints. The search package identifies the type of cubic equation [i.e., a cubic with no local extrema (type A) or a cubic with two local extrema (type B)] and utilizes this knowledge in determining the pitch, dimensions, or material densities corresponding to the maximum (or minimum) value of \(k_{eff}\). The optimum search procedure is summarized as follows:
Calculate \(k_{eff}\) for the specified problem.
Calculate \(k_{eff}\) for the minimum constraint.
Calculate \(k_{eff}\) for the maximum constraint.
Calculate \(k_{eff}\) for a fourth point that lies approximately equidistant between the initial guess and the constraint that is farthest from it.
Utilize a weighted leastsquares fit to a cubic polynomial on the data points.
Determine the type of cubic. For a type A cubic, go to step 11.
Take the first derivative of the leastsquares cubic.
Solve the quadratic for its roots.
Take the second derivative of the leastsquares cubic to determine which root is the maximum (or minimum), and if it falls within the constraints, use this root as the next guess. Otherwise, convergence has been defined as occurring at the constraint with the maximum (or minimum) \(k_{eff}\).
Calculate the \(k_{eff}\) corresponding to the next guess. Go to step 5. Repeat this procedure until convergence is achieved.
If the cubic equation is a type A cubic, the optimum lies on one of the boundaries. If the fit shows that the cubic is actually a type B cubic, go to step 7 and continue.
Convergence is defined as occurring when a k_{eff} has been calculated for a point on the curve where the value of the curve is within epsilon of the maximum (or minimum) of the curve. Additionally, the calculated k_{eff} must be within two standard deviations of the value of the curve at that point. The search is terminated when convergence is achieved, when the code determines there is no local maximum within the constraints, or the maximum number of search iterations is reached.
Note
At the beginning of each search pass, the cross sections are updated using the updated values of pitch, dimensions, or material densities. Also, the unit or material being modified can be directly tied to a unit cell, so that unit cell is updated during the search. Therefore, the final result should be consistent with the results obtained by running a nonsearch problem using the data from the last pass.
Critical search¶
The critical search option searches for the pitch, dimensions, or material densities corresponding to a specified value of k_{eff}. If the calculated value of k_{eff} is within the specified search tolerance (EPS) of the desired k_{eff}, the search is considered to be complete. The critical search procedure is summarized as follows:
1. Calculate k_{eff} for the specified problem. If it is within EPS of the specified k_{eff}, convergence has been achieved.
2. Calculate k_{eff} for one of the constraints. If the specified k_{eff} of the system does not fall between the initial value and the k_{eff} of the constraint, calculate the k_{eff} of the other constraint. If the calculated k_{eff} is within EPS of the specified k_{eff}, convergence has been achieved.
3. Calculate k_{eff} for a point chosen from a linear fit of the two existing points closest to the specified k_{eff}.
4. Repeat step 3 until convergence has been achieved, the program determines that the specified value lies outside the constraints, or the maximum number of search iterations is reached. Convergence has been achieved when the calculated **k*_{eff} is within EPS of the specified k_{eff}.
5. If convergence is achieved, calculate k_{eff} for a point determined from fitting the previous points to a cubic and solving the cubic for the point closest to the desired k_{eff}. If all roots lie outside the constraints, the problem is terminated and an appropriate message is written. If the maximum number of iterations is reached without the problem converging, the problem is terminated and an appropriate message is written.
Note
At the beginning of each search pass, the cross sections are updated using the updated values of pitch, dimensions, or material densities. Also, the unit or material being modified can be directly tied to a unit cell, so that unit cell is updated during the search. Therefore, the final result should be consistent with the results obtained by running a nonsearch problem using the data from the last pass.
Multigroup CSAS5 limitations¶
The CSAS5 control module was developed to use simple input data and prepare problemdependent cross sections for use in calculating the effective neutron multiplication factor of a 3D system using KENO V.a. 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 CSAS5 multigroup sequences are a result of using preprocessed multigroup cross sections. Inherent limitations in multigroup CSAS5 calculations are as follows:
1. Twodimensional (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 CSAS5 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:
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 XSDRNPMcalculated cell fluxes and therefore is not applicable in the continuous energy mode.
Only VACUUM, MIRROR, PERIODIC, and WHITE boundary conditions are allowed. Other albedos, e.g., WATER, CARBON, POLY, etc. are for multigroup only.
Problems with DOUBLEHET cell data are not allowed as they inherently utilize CELLMIX feature.
Input Data Guide¶
This section describes the input data required for CSAS5. Several subsets of the CSAS5 sequences listed in Table 4 are available to achieve several different levels of processing.
The input data for these CSAS5 sequences are composed of three broad categories of data. The first is XSProc, including Standard Composition Specification Data and Unit Cell Geometry Specification. This first category specifies the crosssection library and 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 all CSAS5 sequences. The second category of data, the KENO V.a input data, is used to specify the geometric and boundary conditions that represent the physical 3D configuration of a KENO V.a problem. Both data blocks are necessary for CSAS5 and CSAS5S. The last category of data is the search data and is required only for CSAS5S.
All data are entered in free form, allowing alphanumeric data, floatingpoint 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 floatingpoint 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 floatingpoint number. For example, 1.0E 4 would be correctly interpreted as 1.0 × 10^{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 12s 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.
Resonancecorrected 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 cellweighted 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, the words “PARM=CHECK” or “PARM=CHK” should be entered, as shown below.
=CSAS5 PARM=CHKor#CSAS5 PARM=CHK
This will cause the input data for CSAS5 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.
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. The XSProc section of this manual provides a detailed description of the input data and processing options.
KENO V.a data¶
If the problem utilizes a sequence that contains KENO V.a as a functional module, the input to KENO V.a comes after the XSProc input. Table 5 contains the outline for the KENO V.a input and the SEARCH input, which is required for a search case (i.e., CSAS5S). The KENO V.a input is divided into 13 data blocks and CSAS5S includes an additional block of search data. A brief outline of commonly used data blocks is shown in Table 5. Note that parameter data must precede all other KENO data blocks. Information on all KENO V.a input is provided in the KENO chapter of this document and will not be repeated here.
Type of data 
Starting flag 
Comments 
Termination flag 
Parameters* 
READ PARAMETER 
Enter desired parameter data 
END PARAMETER 
Geometry 
READ GEOMETRY 
Enter desired geometry data 
END GEOMETRY 
Array data 
READ ARRAY 
Enter desired array data 
END ARRAY 
Boundary conditions 
READ BOUNDS 
Enter desired boundary conditions 
END BOUNDS 
Energy group boundaries 
READ ENERGY 
Enter desired neutron energy group boundaries 
END ENERGY 
Start data or initial source 
READ START 
Enter desired start data 
END START 
Plot data 
READ PLOT 
Enter desired plot data 
END PLOT 
Grid geometry data 
READ GRID 
Enter desired mesh data 
END GRID 
Reaction 
READ REACTION 
Enter desire reaction tallies (CE mode only) 
END REACTION 
KENO V.a data terminus 
END DATA 
Enter to
signal the
end of all
KENO V.a
data


Search data 
READ SEARCH 
Enter for CSAS5 
END SEARCH 
*Must precede all other data blocks in this table. 
Search data¶
Search data must be entered for CSAS5S. The search data enable the code to perform a search according to the instructions specified by the user. The code begins reading search data when it encounters the words READ SEARCH and continues reading search data until it encounters the words END SEARCH. Search data consist of the search type specification and auxiliary search commands.
Search type specification¶
These data are used to define the type of search and to set the parameters that provide limits for the search. The search type specification data consist of (a) a search descriptor, (b) the search type, and (c) optional search parameters as described below.
SEARCH DESCRIPTOR is used to define the search mode.
Use OPTIMUM if the maximum value of k_{eff} is to be determined.
Use CRITICAL if a specified value of k_{eff} is to be obtained.
Use MINIMUM if the minimum value of k_{eff} is to be determined.
SEARCH TYPE is used to specify the variable that is to be changed during the search procedure.
Use PITCH to alter the centertocenter spacing between the units at the lowest array level. By default only the spacing in the X and Y directions will be altered. Use DIMENSION to alter the dimensions of one or more geometry regions in one or more units. Use CONCENTRATION to alter the concentration of one or more standard compositions in one or more mixtures.
The combination of the search descriptor and the search type defines the search method. Each search type has a set of predefined defaults and the ability to change the default settings and expand the scope of the search. Only one SEARCH DESCRIPTOR and one SEARCH TYPE are allowed in a problem.
An OPTIMUM PITCH search determines the pitch that gives the maximum value of k_{eff}.* By default the X spacing will be altered for slab arrays, the X and Y spacing will be altered for arrays of cylinders, and the X, Y, and Z spacing will be altered for spherical arrays. Auxiliary search commands can be used to instruct the code to change any of these defaults.
An OPTIMUM DIMENSION search determines the maximum value of k_{eff} by altering the dimensions of one or more geometry regions in one or more units in accordance with the specified auxiliary search commands. Only the dimensions specified in the search commands will be modified. The relative variations in dimensions are determined by the search constants specified for each dimension.
An OPTIMUM CONCENTRATION search determines the maximum value of k_{eff} by altering the concentration of standard compositions in mixtures in accordance with specified search commands. Only the standard compositions in the materials specified are altered. The relative variations in concentrations are determined by the search constants specified for each composition.
A CRITICAL PITCH search alters the spacing between units in the same manner as an optimum pitch search to achieve the specified value of k_{eff}. By default the X spacing will be altered for slab arrays, the X and Y spacing will be altered for arrays of cylinders, and the X, Y, and Z spacing will be altered for spherical arrays. Auxiliary search commands can be used to instruct the code to change any of these defaults.
A CRITICAL DIMENSION search alters the dimensions of one or more geometry regions in accordance with the specified auxiliary search commands to achieve the specified value of k_{eff}.* Only the dimensions specified in the search commands will be modified. The relative variations in dimensions are determined by the search constants specified for each dimension.
A CRITICAL CONCENTRATION search alters the concentration of standard compositions in mixtures in accordance with the specified auxiliary search commands to achieve the specified value of k_{eff}. Only the standard compositions in the materials specified are altered. The relative variations in concentrations are determined by the search constants specified for each composition.
A MINIMUM PITCH search determines the pitch that gives the minimum value of k_{eff}. By default the X spacing will be altered for slab arrays, the X and Y spacing will be altered for arrays of cylinders, and the X, Y, and Z spacing will be altered for spherical arrays. Auxiliary search commands can be used to instruct the code to change any of these defaults.
A MINIMUM DIMENSION search determines the minimum value of k_{eff} by altering the dimensions of one or more geometry regions in one or more units in accordance with the specified auxiliary search commands. Only the dimensions specified in the search commands will be modified. The relative variations in dimensions are determined by the search constants specified for each dimension.
A MINIMUM CONCENTRATION search determines the minimum value of k_{eff} by altering the concentration of standard compositions in mixtures in accordance with specified search commands. Only the standard compositions in the materials specified are altered. The relative variations in concentrations are determined by the search constants specified for each composition.
OPTIONAL SEARCH PARAMETERS are entered after the SEARCH DESCRIPTOR AND SEARCH TYPE and are used to alter the default values of the optional search parameters. Only one set of optional search parameters can be entered for a problem. The optional search parameters are listed below.
 PAS=nn
is used to set the maximum number of times the search will calculate k_{eff}.* The first pass calculates the k_{eff} corresponding to the initial geometry dimensions. The second pass calculates the k_{eff} corresponding to one of the constraints, and the third pass often corresponds to the other constraint. After the third pass, the search dimensions or concentrations are changed based on a fit to a quadratic or cubic equation. The default value of nn is 10.
 NPM=nn
is used to set the number of search parameters. The default value of nn is 1 and should not be overridden.
 EPS=ff
is used to set the search convergence tolerance (the amount by which k_{eff} is allowed to vary from the desired k_{eff}). An optimum or minimum search is terminated when the calculated k_{eff} is within EPS of the optimum or minimum value as indicated by the mathematical fit to the calculated points. A critical search is terminated when the calculated k_{eff} is within EPS of the specified k_{eff}. The default value of ff is 0.005.
 KEF=ff
is used only for a CRITICAL search. The default value of ff is 1.000.
 MINPITCH=ff
is allowed ONLY for a PITCH search. It is used to specify the minimum allowed pitch (centertocenter spacing in the X; X,Y; or X,Y,Z directions depending on array type) between the units in an array. The search will terminate if the pitch becomes smaller than the specified minimum pitch. The default value of ff is the pitch at which the region immediately inside the outer most region of the unit touches the same region in an adjacent unit. It is much easier to specify the minimum allowed pitch than to calculate the appropriate value of the minimum constraint.
 MAXPITCH=ff
is allowed ONLY for a PITCH search. It is used to specify the maximum allowed pitch (centertocenter spacing in the X; X, Y; or X, Y, Z directions depending on array type) between units in an array. The search will terminate if the specified pitch is exceeded. The default value of ff is the pitch corresponding to −5 times the parameter that corresponds to the minimum pitch. It is much easier to specify a maximum allowed pitch than to calculate the appropriate value of the maximum constraint.
 MORE
is used to terminate the optional search parameters and initiate the auxiliary search commands. Do not enter MORE unless auxiliary search commands are to be entered. This command may only be entered once, immediately prior to the auxiliary search commands.
Entry No. 
Type of data 
Data entry 
Comments 
1 
Search descriptor 
OPTIMUM 
Initiates a search for the maximum value of keff. 
CRITICAL 
Initiates a search for a specified value of keff. 

MINIMUM 
Initiates a search for the minimum value of keff. 

2 
Search type 
PITCH 
Vary the pitch of an array. 
DIMENSION 
Vary one or more dimensions in one or more regions of one or more units. 

CONCENTRATION 
Vary the concentration of one or more standard compositions in one or more mixtures. 

3 
Optional search parameters 
Optional search parameters allow changing default values. Any or all may be entered in any order. 

3a 
No. of search passes 
PAS= 
Enter the keyword PAS= followed by the desired number of search passes. Default=10. 
3b 
No. of search parameters 
NPM= 
Enter the keyword NPM= followed by the number of search parameters. Present capability is limited to 1. 
3c 
Search convergence tolerance 
EPS= 
Enter the keyword EPS= followed by the desired convergence tolerance. Default=0.005. 
3d 
Desired value of keff 
KEF= 
Enter the keyword KEF= followed by the desired value of keff. The default value is 1.000. DO NOT ENTER FOR OPTIMUM OR MINIMUM SEARCHES. 
3e 
Maximum allowed pitch 
MAXPITCH= 
Enter the keyword MAXPITCH= followed by the maximum allowed pitch for a search whose search type, entry 2 above, is PITCH. The default value is the pitch corresponding to −5.0 times the parameter at the minimum possible pitch. 
3f 
Minimum allowed pitch 
MINPITCH= 
Enter the keyword MINPITCH= followed by the minimum allowed pitch for a search whose search type, entry 2 above, is PITCH. The default value is the minimum possible pitch (i.e., the pitch at which the shapes in the array touch). 
4 
Additional search data 
MORE 
Enter the delimiter MORE. This delimiter ends the optional search commands and initiates the auxiliary search commands found in Table 2.1.4. 
Auxiliary search commands and constraints¶
Auxiliary search commands are entered only if MORE, item 4, of the search type specification data is entered (see :numref`tab23`). Individual search commands are used to specify search constraints and to communicate to the search program. Searches can alter geometric dimensions (PITCH or DIMENSION Search) or alter standard composition number densities (CONCENTRATION Search).
A PITCH or DIMENSION search may require the user to specify the units that will be altered, the regions that will be altered within those units, and the faces or surfaces of those regions that will be altered. For a PITCH search, the program automatically assigns the units in the arrays to a unit cell if possible. If multiple units are contained in the array, each unit could be assigned a unit cell if the data in the unit cells match the geometry data of the units in the array. This data may be overridden in the MORE section of the search data. For a DIMENSION search, if the user wishes to tie a unit to unit cell this must be explicitly done in the MORE section of the search data. Several examples of search problems are provided in Introduction.
A CONCENTRATION search requires the user to specify the mixture, standard composition name, and the search constant for the component being altered. For a CONCENTRATION search, the program automatically assigns the material being changed to a unit cell. This data may be overridden in the MORE section of the search data. Several examples of search problems are provided in Introduction.
The data comprising the auxiliary search commands are listed in Table 7. All data except items 1a, 1b, and 1c are keyworded (i.e., the data are entered by specifying a keyword, followed by a value). An explanation of each individual search command follows the table.
 1 Command Definition
A command definition tells the code what action is to be taken. A new search command is initiated whenever an item 1a through 1c is encountered. The code will vary the geometry according to subsequent commands.
 1a. ALTER CHANGE MODIFY
Alter geometry regions. These words specify that modifications will be made to the geometry according to subsequent commands.
 1b. MAINTAIN
Maintain the thickness. The thickness of the specified geometry region(s) will be maintained when the interior regions grow or shrink (i.e., the specified region will grow or shrink in conjunction with the interior region in such a way as to maintain the original distance between the two regions). This means that the original thickness of the region is preserved. For instance, the inner radius of a pipe can be altered and the wall thickness can be preserved by applying the MAINTAIN command to the region defining the outer radius of the pipe.
 1c. KEEP HOLD
Keep the original specification. This command causes the specified geometry region(s) to be reset to their original input value for every search pass. Therefore they go through the entire search process unchanged.
 2 PAR=
Parameter number. The search parameter number is not functional. The default number is 1 and should not be overridden.
 3 +CON=
Maximum constraint. Enter the maximum value you wish to allow the search parameter to obtain. The maximum constraint must be larger than the minimum constraint. For a DIMENSION or PITCH search the default value of the maximum constraint is 1011. For a CONCENTRATION search the default value of the maximum constraint is as follows:
+CON= min(−1/FACTOR ), if any FACTOR < 0
+CON= −5*(−CON ), if all FACTOR > 0
Note
For a PITCH search, the maximum constraint is redefined and is calculated from the data entered for MAXPITCH. +CON should not be entered if a value was entered for MAXPITCH. If constraints, +CON= and/or −CON= are not entered as data, the code computes the minimum constraint corresponding to the pins touching, and the maximum constraint is then negative five times the magnitude of the minimum constraint.
 4 −CON=
Minimum constraint. Enter the minimum value you wish to allow the search parameter to obtain. The minimum constraint must be smaller than the maximum constraint but need not be a negative number. The default value of the minimum constraint for a dimension search is −1011. The default value of the minimum constraint for a pitch search is redefined to correspond to the pins in the lattice touching. For a CONCENTRATION search the default value of the minimum constraint is as follows:
−CON= −5(+CON ), if all FACTOR < 0
−CON= max(−1/FACTOR ), if any FACTOR > 0
 5 CELL=
Unit Cell Number. This is the unit cell to which the unit or mixture will be tied. It needs to follow either the UNIT= or MIX= keyword data. Tying a unit cell to a unit or mixture ensures the unit cell data gets changed as the geometry or mixture data gets changed thus ensuring the cross sections are properly processed.
 6 UNIT=
Geometry unit number. This is the geometry unit to which the previously entered command definition (item 1a, 1b, or 1c) is applied. Items 7, 8, and 9 specify the region(s) within the unit and the surfaces of the region(s) to be altered.
 7 REGION=
First region to be altered. This is used to specify the first or only region in the unit (specified by item 6) that is to be altered according to the search command (item 1a, 1b, or 1c). The region(s) are altered according to the search constants (items 9a, 9b, 9c, and/or 9d).
 8 TO
Last region to be altered. This item is entered to specify the last region to be altered, starting with the region specified by REG=. For example, assume unit 3 contains eight regions and you wish to make changes to regions 4, 5, 6, 7, and 8. These regions are identified by entering the following data. UNIT=3 REG=4 TO 8.
Geometric search constants. A search constant is the proportionality factor utilized to alter a geometry region. A search constant must be entered for each surface of a region that is to be altered. A nonzero search constant will cause the region dimension for that surface to be changed. A search constant of 0.0 will cause the region dimension to remain unchanged. The default value of the search constant is 0.0.
 9 ALL=
Search constant for all surfaces. All of the surfaces in a region are altered simultaneously by using this search command.
 9a. +X=
Search constant for +X face. This parameter is used to specify the value of the search constant for the +X face of a cuboid.
 9a. X=
Search constant for −X face. This parameter is used to specify the value of the search constant for the −X face of a cuboid.
 9a. +Y=
Search constant for +Y face. This parameter is used to specify the value of the search constant for the +Y face of a cuboid.
 9a. Y=
Search constant for −Y face. This parameter is used to specify the value of the search constant for the −Y face of a cuboid.
 9a. +Z=
Search constant for +Z face. This parameter is used to specify the value of the search constant for the +Z face of a cuboid.
 9a. Z=
Search constant for −Z face. This parameter is used to specify the value of the search constant for the −Z face of a cuboid.
Note
If it is desirable to change all the faces of a cuboid except the −Z face by some amount (search constant of 1.0), items 9a and 9b can be used together as follows: ALL=1.0 −Z=0.0. This is the same as entering +X=1.0 −X=1.0 +Y=1.0 −Y=1.0 +Z=1.0. If both Z faces are to remain unchanged, items 8a and 8b can be entered as: ALL=1.0 +Z=0.0 −Z=0.0 or as +X=1.0 −X=1.0 +Y=1.0 −Y=1.0.
 9b. RADIUS=
Search constant for radius. This parameter is used to specify the value of the search constant for the radius of a sphere, hemisphere, cylinder, or hemicylinder.
 9c. +HEIGHT=
Search constant for +height. This parameter is used to specify the value of the search constant for the +height of a cylinder or hemicylinder.
 9c. HEIGHT=
Search constant for −height. This parameter is used to specify the value of the search constant for the −height of a cylinder or hemicylinder.
 9d. CHORD=
Search constant for chord. This parameter is used to specify the value of the search constant for the chord of a hemisphere or hemicylinder.
 10 MIX=
Search constant for mixture. This parameter is the mixture number containing the standard composition that is to be changed during the search.
 11 SCNAME=
Search constant for the standard composition name. This parameter is the standard composition name associated with the material that is to be changed during the search. Only compositions listed in the Standard Composition Library section of the Standard Composition Library chapter are allowed (SECTIONREFERENCE). Standard compositions beginning with SOLN cannot be altered directly.
Note
If the standard composition name specified in the Material Information Data begins with SOLN and the Concentration Search Data specifies SCNAME=UO2(NO3)2, the amount of UO2(NO3)2 in the solution is altered but the amount of H2O and nitric acid is not altered during the search. The resulting mixture, when the search is finished, may no longer meet the criteria associated with the SOLN specification.
 12 FACTOR=
Concentration search factor used to specify the value of the search constant used in the concentration search. It is a proportionality factor used to alter the specified mixture standard composition. A search constant must be entered for each standard composition that is altered. A nonzero search constant will cause the concentration of the associated standard composition to be altered. The default value of the search constant is 1.0. A set of concentration search data consists of the mixture to be altered, the standard composition to be altered in the mixture, and the search factor. Keywords are used to enter the data. Each set of data consists of items 10, 11, and 12. The keywords used in this data may be entered using terse notation.
Entry no. 
Keyword name 
Type of data 
Comments 
GENERIC SEARCH DATA — May be used with all Search Types — 

1a 
ALTER CHANGE MODIFY 
Begin a new search command 
These words are used to specify that modifications will be made to the geometry or concentration according to subsequent commands (entries 3 through 12 as required to specify the desired changes). 
1b 
MAINTAIN 
Begin a new search command 
The spacing (thickness) of the specified geometry regions will be maintained when the interior regions grow or shrink. 
1c 
KEEP HOLD 
Begin a new search command 
This command resets the specified geometry to the original input specifications. 
2 
PAR= 
Parameter number 
Enter the parameter number that the current command (ALTER, MAINTAIN, KEEP) applies to. Default=1 and should not be changed. 
3 
+CON= 
Maximum constraint 
Enter the maximum constraint for the current parameter. Default = +10E10. 
4 
−CON= 
Minimum constraint 
Enter the minimum constraint for the current parameter. Default = −10E10. 
5 
CELL= 
Unit Cell Associated with search data 
Default values are assigned for PITCH and CONCENTRATION searches. Associated Unit Cells must be entered for a DIMENSION search if desired. 
PITCH & DIMENSION SEARCH DATA — Defines Geometric Changes — 

6 
UNIT= 
Unit to which the current command applies 
Enter the unit in which regions are to be altered. 
7 
REGION= 
First region to be altered in the unit 
Enter the first or only region in the unit that the search constants (entry 9a, b, c and/or d) apply to. Default is the first region. 
8 
TO 
Last region to be altered in the unit 
Enter the last region in the unit to which the search constants apply (entry 9a, b, c and/or d).

NOTE: Entry 7 must be entered in order to alter a single region in a unit. Entries 7 and 8 must both be entered in order to alter more than one region in a unit. 
Table 2.1.4. Outline of auxiliary search commands and constraints (continued) 

Entry no. 
Keyword name 
Type of data 
Comments 
9 
ALL= 
Search constant for all surfaces (faces) of the region(s) 
Enter a value for the search constants for the specified regions. This value will be applied to all surfaces of the region(s). 
9a 
+X= 
Search constant for +X face of cuboid 
Enter a value for the search constant for the +X face of a cuboid. 
−X= 
Search constant for −X face of cuboid 
Enter a value for the search constant for the −X face of a cuboid. 

+Y= 
Search constant for +Y face of cuboid 
Enter a value for the search constant for the +Y face of a cuboid. 

−Y= 
Search constant for −Y face of cuboid 
Enter a value for the search constant for the −Y face of a cuboid. 

+Z= 
Search constant for +Z face of cuboid 
Enter a value for the search constant for the +Z face of a cuboid. 

−Z= 
Search constant for −Z face of cuboid 
Enter a value for the search constant for the −Z face of a cuboid. 

9b 
RADIUS= 
Search constant for radius 
Enter a value for the search constant for the radius of a sphere or a cylinder. 
9c 
+HEIGHT= 
Search constant for +height 
Enter a value for the search constant for the +height of a cylinder. 
−HEIGHT= 
Search constant for −height 
Enter a value for the search constant for the −height of a cylinder. 

9d 
CHORD= 
Search constant for chord 
Enter a value for the search constant for the chord face of a hemisphere or hemicylinder. 
CONCENTRATION SEARCH DATA — Defines concentration changes — 

10 
MIX= 
Search constant for mixture 
Enter the mixture number containing the standard composition to be changed. 
11 
SCNAME= 
Search constant for Standard Composition 
Enter the standard composition name whose density is to be changed. 
12 
FACTOR= 
Search proportionality constant 
Enter the value of the search constant for the concentration search. 
Example problems¶
This section contains example problems to demonstrate some of the options available in CSAS5 and its associated sequences. 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 “v7238” to “ce_v7”. The sample problems can also be executed with the multigroup or continuous energy libraries based on ENDF/BVII.1. The complete list of libraries distributed with SCALE is provided in the Nuclear Data Libraries (SECTIONREFERENCE) section of the SCALE manual. Note that sample problems 3, 7, and 8 do not run in the continuous energy mode because they use CELLMIX or DOUBLEHET cell type. See Appendix A (CSAS5App) for additional and historical examples.
Sample problem 1: k_{eff} calculation¶
The purpose of this problem is to calculate the keffective of a system. This problem is the same as the KENO V.a sample problem 12 in Appendix B (SECTIONREFERENCE) except the crosssection library and KENO V.a mixing table are prepared by CSAS. The problem represents a critical experiment consisting of a composite array [Tho73][Tho64] of four highlyenriched (93.2%) uranium metal cylinders having a density of 18.76 g/cc and four 5.0677L 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 centertocenter spacing between the metal units is 13.18 cm in the Y direction and 13.45 cm in the Z direction. The centertocenter 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 YZ plane that passes through the centers of the metal units and the YZ 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 Ref. 2 as cylinder index 11 and reflector index 1. A photograph of the experiment, Fig. 9 in Ref. 3, is given in Fig. 11.
=csas5 parm=(centrm)
sample problem 1 set up 4aqueous 4 metal in csas5
v7238
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]=9.7833
temperature=300
end solution
plexiglass 3 end
end composition
read param
flx=yes fdn=yes nub=yes
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
Sample problem 2: optimum pitch search using detailed geometry¶
This problem represents an attempt to optimize the reactivity of PWRlike fuel bundles in a storage pool. The storage array is an infinite planar array of flooded fuel bundles. Each bundle consists of a 17 × 17 × 1 array of 2.35%enriched UO_{2} pins, density 9.21 g/cc, clad with Zircaloy2. The fuel is 0.823 cm in diameter, the clad diameter is 0.9627 cm, and the length of each pin is 366 cm. Each fuel bundle is encased in a Boral sheath. There is a 1/4in. gap flooded with water between the bundle and the sheath. The Boral sheath is 3/8 in. thick. One inch of water separates the fuel bundle sheaths in the horizontal plane, and 15 cm of water is present on the top and bottom of the array.
The KENO V.a geometry represents each fuel pin in the bundle discretely. The search should determine the optimum pitch within the fuel bundle. The gap between the bundle and the Boral remains fixed, as does the thickness of the sheath and the spacing between sheaths.
=csas5s
sample problem 2 storage array of pwrlike fuel bundles in poison sheaths
v7238
read composition
uo2 1 .84 300.. 92235 2.35 92238 97.65 end
zirc2 2 1 end
h2o 3 1 end
b4c 4 den=2.65 0.3517 end
al 4 den=2.65 0.6483 end
h2o 5 1 end
end composition
read celldata
latticecell squarepitch pitch=1.2751 3 fueld=.823 1 cladd=.9627 2 end
end celldata
read param
nub=yes far=yes gen=103 npg=500 gas=no fdn=yes
end param
read geom
unit 1
cylinder 1 1 .4115 183.0 183.0
cylinder 2 1 .48135 183.1 183.1
cuboid 3 1 .63755 .63755 .63755 .63755 183.1 183.1
global unit 2
array 1 3*0.0
reflector 5 1 4*0.635 2z 1
reflector 4 1 4*0.9525 2z 1
reflector 5 1 4*1.27 2z 1
reflector 5 2 4z 2*3.0 5
end geom
read array
ara=1 nux=17 nuy=17 nuz=1 fill f1 end fill
end array
read bounds
xyf=mirror
end bounds
read bias
id=500 2 6
end bias
end data
read search
optimum pitch
end search
end
Sample problem 3: optimum pitch search using homogenized geometry¶
This problem illustrates the use of a cellweighted mixture to represent a PWRlike fuel bundle. The cask contains a 2 × 2 × 1 array of fuel bundles. Each fuel bundle consists of a 17 × 17 × 1 array of Zircaloy2 clad, 2.35%enriched UO_{2} fuel pins with a density of 9.21 g/cc arranged in a square pitch. The pin diameter is 0.823 cm, and its length is 366 cm. The clad is 0.06985 cm thick, and the pitch is 1.275 cm. Each fuel bundle is contained in a 0.6625cmthick Boral sheath. The bundles are separated by 1 cm of water, representing a flooded cask. The square aluminum cask is 10cm thick on all faces and is reflected by 15 cm of water.
By using CELLMIX=, a cellweighted cross section is created to represent the fuel bundle. The KENO V.a geometry utilizes the cellweighted mixture (500) and the overall dimensions of the fuel bundle to represent the entire fuel bundle as a single homogeneous region. The first reflector entry represents the fuel cask, and the second reflector entry represents the 15cm reflector. Because this problem utilizes a cellweighted mixture, which is not applicable in the continuous energy mode, the problem will end with an error message in the continuous energy mode.
=csas5s
sample problem 3 sample square fuel cask
v7238
read composition
uo2 1 .84 300. 92235 2.35 92238 97.65 end
zirc2 2 1 end
h2o 3 1 end
b4c 4 den=2.65 0.3517 end
al 4 den=2.65 0.6483 end
h2o 5 1 end
al 6 1 end
end composition
read celldata
latticecell
squarepitch pitch=1.275 3 fueld=.823 1 cladd=.9627 2 cellmix=500 end
end celldata
read param
nub=yes far=yes gen=103 npg=500 gas=no fdn=yes
end param
read geom
unit 1
cuboid 500 1 4p10.8375 2p183.0
cuboid 4 1 4p11.5 2p183.0
cuboid 5 1 4p12.0 2p183.0
global unit 2
array 1 3*0
reflector 6 1 6*10.0 1
reflector 5 2 6*3 5
end geom
read array
ara=1 nux=2 nuy=2 nuz=1 fill f1 end fill
end array
read bias
id=500 2 6
end bias
end data
read search
optimum pitch
end search
end
Sample problem 4: search for a specified value of k_{eff}¶
Find the pitch at which a 2 × 2 × 2 array of cylinders of highly enriched (93.2%) uranium metal with a density of 18.76 g/cc are critical. Each cylinder has a radius of 5.748 cm and a height of 10.765 cm. The surfacetosurface spacing between the units is the same in all directions. The initial guess for the critical surfacetosurface spacing was 3.0 cm. The experimentally critical surfacetosurface separation for this system is 2.248 cm. The input data for this problem are given below.
=csas5s
sample problem 4 critical pitch search for case 2c8 bare
v7238
read comp
uranium 1 0.985 300. 92235 93.2 92238 5.6 92234 1.0 92236 0.2 end
end comp
read parameters flx=yes fdn=yes far=yes gas=no rnd=656651ed24de
end parameters
read geometry
unit 1
cylinder 1 1 5.748 5.3825 5.3825
cuboid 0 1 4p7.248 2p6.8825
end geometry
read array
com='single unit problem with 1 array is filled with unit 1'
ara=1 gbl=1 nux=2 nuy=2 nuz=2 fill f1 end fill
end array
end data
read search critical pitch maxpitch=15.5 more
alter unit=1 reg=2 +z=1.0531 z=1.0531
end search
end
Sample problem 5: solution conc. search for a specified k_{eff}¶
Consider a large spherical tank partially filled with UO_{2}F_{2} solution. The tank has a radius of 34.6 cm and is filled with solution to a height of 30.0 cm above the midpoint. The tank is composed of a 0.759 cm thick Al shell. The UO_{2}F_{2} solution is composed of three standard compositions: UO2F2, HF acid, and H2O. The code combines these using a set algorithm. This may or may not produce a solution at the desired density. If the density of the solution is known it should be entered. Also, extra acid can be added to the solution by specifying a nonzero acid molarity.
A critical concentration search is performed on the solution yielding system k_{eff} = 1.0 for various densities of UO_{2}F_{2} in the solution. In the MORE search data, MIX=1 and SCNAME=UO2F2 specify that the UO_{2}F_{2} component of the mixture 1 solution is to be altered during the search. The code calculates the density of the solution. The initial uranium fuel density is 300 gm/liter. The maximum allowed uranium density is 600 gm/liter. The minimum allowed uranium density is 150 gm/liter.
=csas5s
sample problem 5 soln tank  crit. conc. search
v7238
read composition
solution
mix=1
rho[uo2f2]= 300 92235 80 92238 19.98 92234 0.02
temp= 300
end solution
al 2 1.0 300.0 end
end composition
read geom
global unit 1
hemisphez 1 1 16 chord 15.5
sphere 0 1 16
sphere 2 1 16.1
end geom
end data
read search
critical concentration kef=1.0
more
alter mix=1 scname=uo2f2 factor=1.0
con=0.5 +con=1.0
end search
end
Sample problem 6: dimension chord search for a specified k_{eff}¶
Consider a large spherical tank partially filled with UO_{2}F_{2} solution. The tank has a radius of 34.6 cm and is filled with solution to an initial height of 10.0 cm above the midpoint. The tank is composed of a 0.759 cm thick Al shell. The UO_{2}F_{2} solution is composed of three standard compositions: UO2F2, HF acid, and H2O. The code combines these using a set algorithm. This may or may not produce a solution at the desired density. If the density of the solution is known it should be entered. Also, extra acid can be added to the solution by specifying a nonzero acid molarity.
A critical dimension search is performed on the chord length yielding system keff = 0.98. In the MORE search data, UNIT=1 REG=1 CHORD=1.0 specify that the chord length in region 1 of unit 1 is to be altered during the search. The constraints are set so the chord length varies from −10.0 cm to just under 34.6 cm.
=csas5s
sample problem 6 soln tank  crit. dim. search on chord
v7238
read comp
solution
mix=1
rho[uo2f2]= 300 92235 80 92238 19.98 92234 0.02
temp= 300
end solution
al 2 1.0 300.0 end
end comp
read geom
global unit 1
hemisphez 1 1 16 chord 10.
sphere 0 1 16
sphere 2 1 16.1
end geom
end data
read search
critical dimension kef=0.98
more
alter unit=1 reg=1 chord=1.0
con=0.23 +con=0.23
end search
end
Sample problem 7 two material conc. search for a specified k_{eff}¶
The fuel bundles in this problem represent 17 × 17 PWR fuel assemblies. The fuel pin lattice is homogenized, making a cellweighted mixture 100. Because this problem utilizes a cellweighted mixture, which is not applicable in the continuous energy mode, the problem will end with an error message in the continuous energy mode. The fuel pins consist of 4.35 wt % ^{235}U having a diameter of 0.823 cm, zirconium cladding having an outer diameter of 0.9627 cm, and a pitch of 1.275 cm. The fuel bundle is represented as a 10.8375 cm × 10.8375 cm × 366 cm cuboid of mixture 100 surrounded by Boral and then water. The Boral has a density of 2.61 g/cm^{3} and has an initial composed of 50.0 wt % B_{4}C and 50.0 wt % Al. The fuel bundles are at a fixed pitch of 13.0 cm. Boral plates surrounding the X and Y sides of each fuel assembly are 0.1625 cm thick. Full density water is between the Boral plates.
A critical concentration search is performed on the Boral plates searching for a system keff = 0.95. The Boral plates are at a fixed density of 2.61 gm/cc. As the density of the B_{4}C changes, the density of the Al changes in the opposite direction maintaining a constant Boral density. There are two entries in the MORE search data. The first entry, MIX=4 SCNAME=b4c factor=1.0 specifies that the B_{4}C of mixture 4 is to be altered during the search. The second entry, MIX=4 SCNAME=al factor=−1.0 specifies that aluminum is to be changed in the opposite direction and proportionally to B_{4}C during the search. Both B_{4}C and Al have the same initial density of 0.5 * 2.61 = 1.305 gm/cc.
=csas5s
sample problem 7 flux trap between fuel bundles  crit. conc. srch
v7238
read composition
uo2 1 .84 300. 92235 4.35 92238 95.65 end
zr 2 1 end
h2o 3 1 end
arbmb4c 2.61 2 0 1 0 5000 4 6000 1 4 0.5 300.0 end
al 4 den=2.61 0.5 end
h2o 5 1.0 end
end composition
read celldata
latticecell squarepitch pitch=1.275 3 fueld=.823 1
cladd=.9627 2 cellmix=100 end
more data
bal=none
end more
end celldata
read param
far=no gen=203 npg=1000
end param
read geom
global unit 1
cuboid 100 1 4p10.8375 2p183.0
cuboid 4 1 4p11.0 2p183.0
cuboid 5 1 4p13.0 2p183.0
end geom
read bounds
xfc=mirror yfc=mirror
end bounds
end data
read search
critical concentration kef=0.95
more
alter mix=4 scname=arbmb4c factor=1.0
alter mix=4 scname=al factor=1.0
con=0.9 +con=0.99
end search
end
Sample problem 8: k_{∞} for a pebble bed fuel¶
This problem demonstrates setting up a fuel pebble from a pebble bed reactor, and calculating its k∞. The pebble consists of a fuel grain of UO_{2} 0.025 cm in radius, coated with 0.003 cm of pyrolitic carbon, a further coat of 0.0035 cm thick silicon carbide, with a final coat of 0.004 cm thick pyrolitic 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 ^{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.
=csas5 parm=(centrm)
infinite array of pebbles on a square pitch
v7238
read composition
' fuel kernel
u238 1 0 2.12877e2 293.6 end
u235 1 0 1.92585e3 293.6 end
o 1 0 4.64272e2 293.6 end
' inner pyro carbon
c 3 0 9.52621e2 293.6 end
' silicon carbide
c 4 0 4.77240e2 293.6 end
si 4 0 4.77240e2 293.6 end
' outer pyro carbon
c 5 0 9.52621e2 293.6 end
' graphite matrix
c 6 0 8.77414e2 293.6 end
' carbon pebble outer coating
c 7 0 8.77414e2 293.6 end
he3 8 0 3.71220e11 293.6 end
he4 8 0 2.65156e5 293.6 end
end composition
read celldata
doublehet right_bdy=white 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
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
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
Warning and error messages¶
CSAS5 contains two types of warning and error messages. 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 activated by CSAS5 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 following messages originate in the part of CSAS5 that reads, checks, and prepares data for KENO V.a and the search module MODIFY.
 CS10 *** ERROR *** CONCENTRATION SEARCH MATERIAL WAS NOT SPECIFIED IN THE STANDARD COMPOSITION.
This selfexplanatory message from subroutine CNCN indicates that the indicated material is not in the standard composition data. Recheck the standard composition data and the search data, correct the input, and resubmit the problem.
 CS11 *** ERROR *** CONCENTRATION SEARCH DATA HAS BEEN DESTROYED. I= ______ ICMND= ______ IPNUM= ______ MIXUR= ______ SCNAME= ______
This message from subroutine CNCSRH indicates that the search data could not be read properly. This usually indicates either: search data that is required for the specified search type is missing or search data inappropriate for the specified search type is present. Recheck the search data, correct the input, and resubmit the problem.
 CS16 ***WARNING*** READ FLAG NOT FOUND. ASSUME KENO V PARAMETER DATA FOLLOWS.
This message from subroutine CPARAM indicates that the word READ is not the first word of KENO V.a data following the Material Information Processor input data. If parameter data 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 assumes the data are parameter input data.
 CS21 A UNIT NUMBER WAS ENTERED FOR THE CROSSSECTION LIBRARY. (LIB= IN PARAMETER DATA.) THE DEFAULT VALUE SHOULD BE USED IN ORDER TO UTILIZE THE CROSS SECTIONS GENERATED BY CSAS5. MAKE CERTAIN THE CORRECT CROSSSECTION LIBRARY IS BEING USED.
This message is from subroutine CPARAM. It indicates that a value has been entered for the crosssection library in the KENO V.a parameter data. The crosssection library created by the analytical sequence should be used. MAKE CERTAIN THAT THE CORRECT CROSS SECTIONS ARE BEING USED.
 CS50 *** ERROR *** SEARCH COMMAND NUMBER ______ IS UNABLE TO PERFORM A PITCH SEARCH BECAUSE THE DIMENSIONS OF REGION ______ OF UNIT ______ ARE NOT EXPLICITLY DEFINED.
This message from subroutine PCHSRH indicates that the specified search command is not valid for the specified region. An ARRAY or CORE region cannot be altered; nor can a REPLICATE or REFLECTOR region immediately following an ARRAY or CORE region.
 CS55 *** ERRORS WERE ENCOUNTERED IN PROCESSING THE CSASKENO5 DATA. EXECUTION IS IMPOSSIBLE. ***
This message from subroutine SASSY is printed if errors were found in the KENO V.a input data for CSAS5. If a search is being made, data reading will continue until all the data have been entered or a fatal error terminates the data reading. 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.
 CS62 *** 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 V.a geometry was not created in the standard composition data.
 CS68 *** ERROR *** AN INPUT DATA ERROR HAS BEEN ENCOUNTERED IN THE ______ DATA ENTERED FOR THIS PROBLEM.
This message from the main program, CSAS5, 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 or the CSAS5 “SEARCH” 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.
 CS69 ***ERROR*** MIXTURE ______ IS AN INAPPROPRIATE MIXTURE NUMBER FOR USE IN THE KENO GEOMETRY DATA BECAUSE IT IS A COMPONENT OF THE CELLWEIGHTED MIXTURE CREATED BY XSDRNPM.
This message from subroutine CMXCHK indicates that a mixture that is a component of a cellweighted mixture has been used in the KENO V.a geometry data.
 CS70 ***** ERROR ***** SEARCH OR OPTIMIZATION DATA MUST BE ENTERED FOR CSAS5. NO SEARCH DATA WAS ENTERED.
This message from subroutine RDOPT is selfexplanatory. If the user does not desire to run a search, another sequence such as CSAS5 should be chosen.
 CS71 *** ERROR *** ______ IS NOT A VALID SEARCH TYPE.
This message is from subroutine RDOPT. The allowed search types include PITCH, DIMENSION, and CONCENTRATION. The first four characters of the search data after the words READ SEARCH must be PIT, PITC, DIM, DIME, DMSN, CON, or CONC. The data may be misspelled or out of order.
 CS72 *** ERROR *** THE SEARCH TYPE IS INVALID. I= ______.
This message is from subroutine RDOPT. The numerical index, I, should be 1 for an optimum pitch search, 2 for a dimension search, and 3 for a concentration search. If it is none of these, the search type has been incorrectly specified or a code error has been introduced.
 CS73 ***** AN END OF FILE WAS ENCOUNTERED BEFORE ALL THE SEARCH DATA WAS READ.
This selfexplanatory message is from subroutine RDOPT. Check the input data to be sure nothing was omitted or misspelled.
 CS74 ***** AN END SEARCH FLAG WAS READ BEFORE ALL THE SEARCH DATA WAS READ.
This selfexplanatory message is from subroutine RDOPT. Check the input data for omissions and correct order.
 CS75 *** ERROR *** READ SEARCH FLAG WAS NOT FOUND. ______ WAS READ INSTEAD.
This selfexplanatory message is from subroutine RDOPT. READ SEARCH was expected but was not found. Check the input data for omissions and correct order.
 CS76 *** ERROR *** END SEARCH FLAG WAS NOT FOUND. ______ WAS READ INSTEAD.
This selfexplanatory message from subroutine RDOPT indicates that an end of file was encountered when looking for READ SEARCH. Check the input data for omissions, correct order, and spelling.
 CS77 *** ERROR *** AN END OF FILE WAS FOUND WHEN THE READ SEARCH FLAG WAS EXPECTED.
This selfexplanatory message is from subroutine RDOPT. Check the input data for omissions, correct order, and spelling.
 CS78 *** ERROR *** ______ IS NOT A VALID SEARCH TYPE.
This message is from subroutines SRCHTYP. It indicates that an invalid search type was read. The valid search names include PITCH, CONCENTRATION, and DIMENSION. Either the data was entered improperly or a code error has been introduced. A STOP 215 is executed when this message is printed.
 CS80 *** ERROR *** SEARCH DATA HAS BEEN DESTROYED. I= ______ ICMND= ______ IPNUM= ______ II= ______ IGEOM= ______
This message from subroutines DIMSRH indicates that the search data cannot be interpreted. This usually indicates either: search data that is required for the specified search type is missing or search data inappropriate for the specified search type is present. Recheck the search data, correct the input, and resubmit the problem.
 CS82 *** AN ERROR WAS ENCOUNTERED IN ONE OF THE FUNCTIONAL MODULES.
This message from CSAS5 or MODIFY indicates that an error was encountered during execution of one of the functional modules such as CRAWDAD, BONAMI, CENTRM, PMC, XSDRNPM, or KENO V.a. Check the printout to locate and correct the error.
 CS83 ***** NO FEASIBLE SOLUTION WAS FOUND IN THE SEARCH PACKAGE. EXECUTION IS TERMINATED.
This message comes from the MODIFY search package, and indicates that it is unable to find a solution to the problem as presented. This usually occurs when a solution is not within the range specified. For this case the user must decide what to change to improve the possibility of a solution. Fairly rarely, for an optimum problem, there may be 2 maximums within the range specified, and the package has found the wrong one. For this case, the user would tighten the range to be searched to eliminate the unwanted peak. The package uses least mean square fitted cubic polynomials to make guesses as to where a solution is. If the Keffectives have too much variance, the polynomials may not be a good representation of the actual behavior of the system. For this case the user could rerun the problem using more histories per pass to reduce the variance.
 CS85 *** ERROR *** ALL OF THE ROOTS FOR K=_____ LIE OUTSIDE THE PARAMETER CONSTRAINTS
This message from MODIFY indicates that the polynomial fit to the Keffectives already calculated only has solutions for the Keffective asked for outside the parameter constraints specified. Keffectives with large variances can lead to polynomials which fit the actual behavior of a system poorly. The user could rerun the case with more histories to reduce the variance, if this is the problem. If the variance is not the problem, then extending the parameter range, or making some other change to the problem definition to change the Keffective range will be necessary.
 CS89 *** ERROR *** ______ IS AN INVALID DIMENSION SEARCH COMMAND.
This message from subroutine DMSN indicates that the dimension search data are out of order, a search command is spelled incorrectly, or the search data are specified incorrectly.
 CS90 *** ERROR *** ______ IS AN INVALID SEARCH PARAMETER.
This message printed from subroutines CNCTYP, DIMTYP, and PCHTYP indicates that a parameter entered in the search type specification data is not valid. The data could be misspelled or out of order. Omission of the keyword MORE before entering the individual search commands can cause this error.
 CS91 *** ERROR *** ______ IS AN INVALID CONCENTRATION SEARCH COMMAND.
This message from subroutine CNCN is caused by a misspelled or illegal search command when attempting to do a concentration search.
 CS94 *** ERROR *** REG= ______ IS AN INVALID SEARCH DATA ENTRY. THE REGION NUMBER MUST BE GREATER THAN ZERO AND NO LARGER THAN THE NUMBER OF REGIONS IN THE UNIT.
This message from subroutine DMSN indicates that the region to be altered is incorrectly specified. For example, if the unit being altered contains five geometry regions, the value specified for REG= can be as small as 1 and as large as 5.
 CS95 *** ERROR *** AN ERROR WAS ENCOUNTERED IN THE SEARCH DATA. THE LAST REGION NUMBER MUST BE AT LEAST AS LARGE AS THE FIRST REGION NUMBER. CHECK THE SEARCH DATA PRINTED BELOW. keyword UNIT ______ REGIONS ______ TO ______ PARAMETER= SEARCH CONSTANTS ARE ______
This message from subroutine DMSN indicates that the search data specified an invalid region number for the final region to be altered. Check the printed data and correct as appropriate.
 CS96 *** ERROR *** AN ERROR WAS ENCOUNTERED IN THE SEARCH DATA. THE REGION NUMBERS MUST BE GREATER THAN ZERO AND NO LARGER THAN THE NUMBER OF REGIONS IN THE UNIT. CHECK THE SEARCH DATA PRINTED BELOW. keyword UNIT ______ REGIONS ______ TO ______ PARAMETER= ______ SEARCH CONSTANTS ARE ______
This message from subroutine DMSN indicates that one of the specified region numbers is incorrect. Check the printed data and correct as appropriate.
 CS97 *** ERROR *** NO VALID SEARCH COMMANDS WERE FOUND IN THE DATA.
This message is accompanied by a STOP 235 and is printed from subroutines PCHSRH, CNCSRH, and DIMSRH. A common cause of this error is the omission of the MORE command before the individual search commands are entered.
 CS99 *** ERROR *** THIS PROBLEM WILL NOT BE RUN BECAUSE PARM=CHECK WAS ENTERED IN THE ANALYTICAL SEQUENCE SPECIFICATION.
This message from subroutine CSAS5 indicates that the problem data were read and checked and no errors were found. To execute the problem, remove the PARM=CHECK or PARM=CHK from the analytical sequence indicator data entry.
 CS100 *** ERROR *** THIS PROBLEM WILL NOT BE RUN BECAUSE ERRORS WERE ENCOUNTERED IN THE INPUT DATA.
This message from subroutine CSAS5 is selfexplanatory. Examine the printout to locate the error or errors in the input data. Correct them and resubmit the problem.
 CS101 *** ERROR *** THE CONSTRAINTS ARE NOT VALID FOR PARAMETER SET. −CON= ______ +CON= ______
This message is printed from either subroutine CNCN or DMSN if the parameter set is invalid. For a parameter set to be valid, −CON must be less than 0.0 and +CON must be greater than 0.0. They can be explicitly set or calculated using default or provided data.
 CS102 *** ERROR *** THE UNIT CELL SPECIFICATION FOR UNIT ______ IS OUT OF BOUNDS. CELL NUMBER ______ WAS SPECIFIED. THE SPECIFIED CELL MUST BE BETWEEN 1 AND THE NUMBER OF CELLS ______.
This selfexplanatory message from subroutine DMSN indicates that the unit cell specified is not between 1 and the number of unit cells present in the problem. Recheck the unit cell number specified in the search data, correct the input, and resubmit the problem.
 CS103 *** ERROR *** THE UNIT CELL SPECIFICATION FOR MIXTURE ______ IS OUT OF BOUNDS. CELL NUMBER ______ WAS SPECIFIED. THE SPECIFIED CELL MUST BE BETWEEN 1 AND THE NUMBER OF UNIT CELLS ______ .
This selfexplanatory message from subroutine CNCN indicates that the unit cell specified for the indicated mixture is not between 1 and the number of unit cells present in the problem. Recheck the unit cell number specified in the search data, correct the input, and resubmit the problem.
 LDPW79
M. J. Lorek, H. L. Dodds, L. M. Petrie, and R. M. Westfall. Improved criticality search techniques for low and high enriched systems. Technical Report, Tennessee Univ., 1979.
 Tho64
J. T. Thomas. CRITICAL THREEDIMENSIONAL ARRAYS OF NEUTRONINTERACTING UNITS. PART II. U (93.2) METAL. Technical Report, Oak Ridge National Lab., Tenn., 1964.
 Tho73
Joseph T. Thomas. Critical threedimensional arrays of U (93.2)metal cylinders. Nuclear Science and Engineering, 52(3):350–359, 1973. Publisher: Taylor & Francis.