Several example uses of CSAS6 are shown in this section for a variety of applications.

Run KENO-VI using CSAS6

CSAS6 creates a microscopic working format library and a mixing table that is passed to KENO-VI. The library is created using CENTRM/PMC/WORKER to process the cross section data in the resolved resonance regions of the isotopes contained in the library. CSAS6 then executes KENO-VI, which calculates keff for the problem. The following examples are for using the multigroup mode of calculation for KENO-VI. Using the continuous energy mode can be accomplished by simply changing the library name to one of the continuous energy libraries.

EXAMPLE 1. CSAS6 – Determine the keff of a system.

Consider a problem consisting of eight uranium metal cylinders that are 93.2% wt enriched, having a density of 18.76 g/cm3. The cylinders are arranged in a 2 × 2 × 2 array. Each has a radius of 5.748 cm and a height of 10.765 cm. The center-to-center spacing in the horizontal (X-Y) plane is 13.74 cm and the vertical center-to-center spacing is 13.01 cm. Because the cross section processing will be done assuming an infinite homogeneous medium and no cell mixtures are used, there is no unit cell data. The input data for this problem follow.

=CSAS6 SET UP 2C8 IN CSAS6 V7-238 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 PARAMETERS  FLX=YES FDN=YES FAR=YES  END PARAMETERS READ GEOMETRY UNIT 1 CYLINDER 10  5.748 5.3825 -5.3825 CUBOID   20  6.87 -6.87 6.87 -6.87 6.505 -6.505 MEDIA 1 1 10 MEDIA 0 1 20 -10 BOUNDARY 20 GLOBAL UNIT 2 CUBOID 10 4P13.74   2P13.010 ARRAY  1  10  PLACE 1 1 1 -6.87 -6.87 -6.505 BOUNDARY 10 END GEOMETRY READ ARRAY GBL=1 ARA=1 NUX=2 NUY=2 NUZ=2  FILL  F1 END FILL END ARRAY END DATA END

EXAMPLE 2. CSAS6 – Determine the keff of an array of fuel pellets in a UO2F2 solution.

Consider a 60 cm inside diameter cylindrical tank filled with 5.0%-enriched UO2 fuel rods and 5.0%‑enriched UO2F2 solution at 295 gm/liter. A 51 × 51 × 1 array of fuel rods is centered on the bottom of the tank. The fuel rods are 366 cm long, 0.45 cm in radius, clad with 0.01-cm-thick Al, and at a pitch of 1.5 cm. The fuel rods sit on the bottom of the container and the container and solution rise 5.0 cm above the top of the rods. The container is 10 cm thick in the side and bottom and open at the top. Determine the keff of the system. Input data for this problem follow.

=CSAS6 UO2 pins in a UO2F2 solution V7-238 READ COMP UO2       1 0.95 300 92235 5.0 92238 95.0 END AL        2 1.0  300 END SOLNUO2F2 3 295 0.0 1.0 300 92235 5.0 92238 95.0 END AL        4 1.0  300 END SOLNUO2F2 5 295 0.0 1.0 300 92235 5.0 92238 95.0 END END COMP READ CELLDATA LATTICECELL SQUAREPITCH PITCH=1.50 3 FUELD=0.9  1 CLADD=0.94 2 END END CELLDATA READ GEOM UNIT  1 COM='FUEL PIN' CYLINDER 10  0.45  2P183.0 CYLINDER 20  0.47 2P183.1 CUBOID     30  4P0.75 2P183.1 MEDIA 1 1 10 MEDIA 2 1 20 -10 MEDIA 3 1 30 -20 -10 BOUNDARY 30 GLOBAL UNIT  2 COM='FUEL PINS AND SOLUTION IN TANK' CUBOID    10  4p38.25  2P183.1 CYLINDER  20  60.0  188.1 -183.1 CYLINDER  30  70.0  188.1 -193.1 ARRAY  1  10  PLACE 26 26 1 3*0.0 MEDIA  5  1  20 -10 MEDIA  4  1  30 -20 BOUNDARY  30 END GEOM READ ARRAY ARA=1 NUX=51 NUY=51 NUZ=1 FILL F1 END FILL END ARRAY END DATA END

Run KENO-VI containing cell-weighted mixtures

CSAS6 creates a microscopic working format library and a mixing table that is passed to KENO-VI. The microscopic cross sections of the nuclides used in the unit cell geometry description are cell‑weighted by specifying CELLMIX= followed by a unique mixture number. This mixture number utilizes the cell-weighted cross sections that represent the heterogeneous system. CSAS6 executes KENO-VI and calculates keff for the problem.

EXAMPLE 1. CSAS6 – Calculate the keff of an array of fuel assemblies using cell-weighted cross sections.

Consider the 4 × 4 × 1 array of fuel assemblies in a square aluminum cask described in Sect. 2.2.A.1.1, Example 2. Calculate the keff of the system by using the cell-weighted mixture 200 to represent the fuel pins in the fuel assembly. Note that mixtures 1, 2, and 3, representing UO2, zirconium, and water, respectively, are used in the unit cell description. Cell-weighting is applied to the microscopic cross sections that are used in the cell, making them incorrect for use elsewhere. Because water is used both inside the cell and between the fuel assemblies, an additional mixture, mixture 6, has been added to represent the water between the fuel assemblies. The input data for this problem follow.

=CSAS6 SQUARE FUEL CASK EXAMPLE USING HOMOGENEOUS MOCKUP V7-238 READ COMP UO2  1 DEN=9.21 1.0 293. 92235 2.35 92238 97.65 END ZR   2 1 END H2O  3 1 END B4C  4 0.367 END AL   4 0.636 END AL   5 1 END H2O  6 1 END END COMP READ CELLDATA LATTICECELL SQUAREPITCH PITCH=1.3 3 FUELD=0.8 1 CLADD=0.94 2 CELLMIX=200 END END CELLDATA READ PARAM  FAR=YES GEN=253 END PARAM READ GEOM UNIT  2 COM='FUEL ASSEMBLY' CUBOID  10 4P11.05  2P183.07 CUBOID  20 4P11.70  2P183.72 CUBOID  30 4P12.20  2P184.22 MEDIA  200  1  10 MEDIA  4  1  20  -10 MEDIA  6  1  30  -20  -10 BOUNDARY  30 GLOBAL  UNIT 3 COM='FUEL CASK CONTAINING 4X4 ARRAY OF ASSEMBLIES' CUBOID  10  4P48.8  2P184.22 CUBOID  20  4P58.8  2P194.22 ARRAY  1 10  PLACE 1 1 1 -36.6 -36.6 0.0 MEDIA  5  1  20 -10 BOUNDARY  20 END GEOM READ ARRAY ARA=1 NUX=4 NUY=4 NUZ=1 FILL F2 END FILL END ARRAY END DATA END

EXAMPLE 2. CSAS6 – Determine the keff of an array of fuel pellets in a UO2F2 solution using cell‑weighted cross sections.

This is the same problem as described in Run KENO-VI using CSAS6 Example 2. However, the rods and solutions have been replaced with a cell-weighted mixture 50. Determine the keff of the container. Input data for this problem follow.

=CSAS6 UO2 pins in a UO2F2 solution, cell-weighted mixture V7-238 READ COMP UO2       1 0.95 300 92235 5.0 92238 95.0 END AL        2 1.0  300 END SOLNUO2F2 3 295 0.0 1.0 300 92235 5.0 92238 95.0 END AL        4 1.0  300 END SOLNUO2F2 5 295 0.0 1.0 300 92235 5.0 92238 95.0 END END COMP READ CELLDATA LATTICECELL SQUAREPITCH PITCH=1.50 3 FUELD=0.9 1 CLADD=0.94 2 CELLMIX=50 END END CELLDATA READ GEOM GLOBAL UNIT  2 COM='FUEL PINS AND SOLUTION IN TANK' CUBOID    10  4p38.25  2P183.1 CYLINDER  20  60.0  188.1 -183.1 CYLINDER  30  70.0  188.1 -193.1 MEDIA 50  1  10 MEDIA  5  1  20 -10 MEDIA  4  1  30 -20 BOUNDARY  30 END GEOM END DATA END

Run KENO-VI containing multiple unit cells

CSAS6 can create a microscopic working format library and a mixing table that contains more than one unit cell. Each unit cell is explicitly defined in the CELLDATA section of the standard composition data. Materials may appear in only one unit cell. All materials in the standard composition that are not contained in a unit cell are processed assuming infinite homogeneous media. CSAS6 passes the created working library to KENO-VI which calculates keff for the problem.

EXAMPLE 1. CSAS6 – Calculate the keff of a system using two unit cell descriptions.

Consider an infinite XY-array composed of two types of fuel assemblies in a checkerboard pattern moderated by water. Each assembly consists of a 17 × 17 × 1 array of zirconium-clad, enriched UO2 fuel pins in a square pitched array. In one array the uranium is 3.5%-enriched and in the other array the uranium is 2.9%-enriched. The UO2 has a density of 9.21 g/cm3. The pin diameter is 0.8 cm and is 366 cm long. The clad is 0.07 cm thick, and the pitch is 1.3 cm. Each fuel bundle is contained in a 0.65-cm-thick Boral sheath. The bundles are separated by an edge-to-edge spacing of 1.0 cm. The water and zirconium is input in the standard composition data once for every unit cell in which it appears because a material may appear in only one unit cell. Determine the keff of the infinite array. Note that periodic boundary conditions are required to obtain an infinite checkerboard array. Input data for this problem follow.

=CSAS6 2 SQUARE FUEL ASSEMBLIES EXAMPLE IN AN INFINITE LATTICE OF ASSEMBLIES V7-238 READ COMP UO2  1  DEN=9.21 1.0 293. 92235 3.5 92238 96.5 END ZR   2  1 END H2O  3  1 END UO2  4  DEN=9.21 1.0 293. 92235 2.9 92238 97.1 END ZR   5  1 END H2O  6  1 END B4C  7  0.367 END AL   7  0.636 END END COMP READ CELLDATA LATTICECELL SQUAREPITCH PITCH=1.3 3 FUELD=0.8 1 CLADD=0.94 2 END LATTICECELL SQUAREPITCH PITCH=1.3 6 FUELD=0.8 4 CLADD=0.94 5 END END CELLDATA READ PARAM FAR=YES GEN=253 END PARAM READ GEOM UNIT  1 COM='3.5 W% FUEL PIN' CYLINDER 10  0.4  2P183.0 CYLINDER 20  0.47 2P183.07 CUBOID   30  4P0.65 2P183.07 MEDIA 1 1 10 MEDIA 2 1 20 -10 MEDIA 3 1 30 -20 -10 BOUNDARY 30 UNIT  2 COM='3.5 W% FUEL ASSEMBLY' CUBOID  10  4P11.05  2P183.07 CUBOID  20  4P11.7   2P183.72 CUBOID  30  4P12.2   2P184.22 ARRAY  1 10  PLACE 9 9 1 3*0.0 MEDIA  7  1  20 -10 MEDIA  3  1  20 -20 -20 BOUNDARY  30 UNIT  3 COM='2.9 W% FUEL PIN' CYLINDER 10  0.4  2P183.0 CYLINDER 20  0.47 2P183.07 CUBOID   30  4P0.65 2P183.07 MEDIA 4 1 10 MEDIA 5 1 20 -10 MEDIA 6 1 30 -20 -10 BOUNDARY 30 UNIT   4 COM='2.9 W% FUEL ASSEMBLY' CUBOID  10  4P11.05  2P183.07 CUBOID  20  4P11.7   2P183.72 CUBOID  30  4P12.2   2P184.22 ARRAY  2 10  PLACE 9 9 1 3*0.0 MEDIA  7  1  20 -10 MEDIA  6  1  20 -20 -20 BOUNDARY  30 GLOBAL  UNIT 5 COM='FUEL CASK CONTAINING 4X4 ARRAY OF ASSEMBLIES' CUBOID   10  4P24.4  2P184.22 ARRAY  3 10  PLACE  1 1 1 -12.2  -12.2  0.0 BOUNDARY 10 END GEOM READ ARRAY ARA=1 NUX=17 NUY=17 NUZ=1 FILL F1 END FILL ARA=2 NUX=17 NUY=17 NUZ=1 FILL F3 END FILL GBL=3 ARA=3 NUX=2 NUY=2 NUZ=1 FILL 2 4 4 2 END FILL END ARRAY READ BOUNDS XYF=PERIODIC END BOUNDS END DATA END

EXAMPLE 2. CSAS6 – Calculate the keff of a system using two unit cell descriptions and cell-weighted mixtures.

Consider a problem in which a stainless steel cylinder with an inner diameter of 56 cm and an inside height of 91 cm is filled with pellets of UO2 in borated water. The steel is 0.125 cm thick. The spherical 2.57%-enriched UO2 pellets have a diameter of 1.07 cm and are arranged in a triangular pitch array with a pitch of 1.13 cm. The spherical 2.96%-enriched UO2 pellets have a diameter of 1.07 cm and are arranged in a triangular pitch array with a pitch of 1.12 cm. The cylindrical tank is filled half full of the 2.96% pellets in borated water, and the remainder is filled with the 2.57%-enriched pellets in borated water.

Mixture 100 is the cell-weighted mixture containing the 2.57%-enriched uranium pellets and mixture 200 is the cell-weighted mixture containing the 2.96%-enriched uranium pellets. Determine the keff of this system. Input data for this problem follow.

=CSAS6 2.57% AND 2.96% ENR UO2 PELLETS IN 3500 PPM BORATED WATER V7-238 READ COMP UO2    1 0.925  283 92235 2.57 92238 97.43 END H2O    2 1.0 283 END ATOMBACID 2 2.0017-2 3 5000 1 1001 3 8016 3 1.0 283 END UO2    3 0.925  283 92235 2.96 92238 97.04 END H2O    4 1.0 283 END ATOMBACID 4 2.0017-2 3 5000 1 1001 3 8016 3 1.0 283 END SS304 5 1.0 283 END END COMP READ CELLDATA LATTICECELL CELLMIX=100 SPHTRIANGP PITCH=1.13 2 FUELD=1.07 1 END LATTICECELL CELLMIX=200 SPHTRIANGP PITCH=1.13 4 FUELD=1.07 3 END END CELLDATA READ PARAM  FLX=YES   END PARAM READ GEOM GLOBAL UNIT 1 CYLINDER 10 38.0 45.5 0.0 CYLINDER 20 38.0 91.0 0.0 CYLINDER 30 38.125 91.0 -0.125 MEDIA 100 1 10 MEDIA 200 1 20 -10 MEDIA   5 1 30 -20 BOUNDARY 30 END GEOM END DATA END