Keno Appendix C: Sample problems

This section contains sample problems to demonstrate some of the options available in KENO in stand-alone mode. Because stand-alone KENO has no means to read standard composition information and process for use, the problem-dependent cross section library must be prepared before executing KENO in the multigroup mode. The MIXTURE data block (See 9-1-2-1) is used to provide the mixing table. In the continuous energy mode, the cross sections are directly used and therefore no problem-dependent library is needed. The mixing table is required in the continuous energy mode as well. If KENO is executed as part of CSAS5 or CSAS6 sequence, generation of the problem-dependent library (for the multigroup mode) and the mixing table is automatically performed by the sequence.

A total of 33 KENO V.a different case inputs and 27 KENO-VI inputs are provided as multigroup mode KENO sample problems in a single input file “kenova.input” and “kenovi.input” for KENO V.a and KENO-VI, respectively. This input file contains an initial CSAS-MG input to create the problem-dependent cross section library to be used in the sample problems in the input file. Although KENO does not run stacked cases, when KENO is run as part of SCALE, the driver allows KENO to be executed each time it encounters an “=KENO5” or “=KENOVA”, respectively “=KENO6” or “=KENOVI.” The “.input” file contains all 33/27 problems one after the other. A similar input file “cekenova.input”, respectively “cekenovi.input” is also provided for continuous energy mode of calculations. The changes required to create the continuous energy mode input file from the multigroup mode input file are simple. The continuous energy mode file does not have (or need) the CSAS-MG input at the beginning. In addition, all “lib=4” entries in the PARAMETER data block are changed to “cep=ce_v7_endf” to indicate the mode of calculation is continuous energy and the continuous energy cross section directory file is “ce_v7_endf” indicating ENDF/B-VII-based cross sections. The mixing table entry SCT is not applicable in the continuous energy mode, so it has been deleted from the continuous energy input file. Finally, the nuclide IDs in the mixing table are modified to remove the mixture number prefix because the continuous energy mode cross section file for a nuclide or isotope is the same regardless of where that nuclide is used.

The same 33/27 problems are also executed as individual cases with filenames “k5smp??.input”, respectively “k6smp??.input”, where ?? stands for sample problem number (01 through 33 or 27). Since each one of these sample problems needs a problem-dependent cross section library (multigroup mode only) and a mixing table, these problems have been converted to run as CSAS5/6 problems. Similar input files are also provided to be run in the continuous energy mode and the files are named “cek5smp??.input”, respectively “cek6smp??.input”, where ?? again stands for sample problem number (01 through 33 or 27). The change required to create the continuous energy mode inputs from the multigroup mode inputs is very simple: the cross-section library name is changed from “v7-238” to “ce_v7”.

In the following section the input for each case is listed assuming the multigroup mode of calculation in KENO. The KENO input is also listed in the file corresponding “.input” file. The CSAS-MG input file for these cases is in the next section.

CSAS-MG data

The multigroup mode KENO sample problems use nuclide IDs that are consistent with the SCALE CSAS5/6 nuclide ID naming convention. Nuclides are identified by the ZA number plus 1000000 times the mixture number. CSAS-MG can be used to create a problem-dependent working format cross-section library suitable for use with the sample problems. CSAS-MG can (1) be run alone with problem-dependent working library on logical Unit 4 saved for later use with the KENO sample problems, or (2) be placed in front of the KENO sample problems.

The CSAS-MG SCALE control module calculates the necessary resonance data required to create the problem-dependent AMPX working format library using SCALE standard composition input.

The multigroup mode KENO sample problem input data are independent of energy group structure. To use a different energy group structure, simply supply the desired master cross-section library name in the CSAS-MG or CSAS5/6 data. See XSProc, Standard Composition and CSAS5/6 chapters for additional information and examples. See the XSLib chapter for information about the master format cross-section libraries that are available in SCALE.

Data for CSAS-MG are provided to create a problem-dependent AMPX working format cross-section library suitable for use with the multigroup mode KENO sample problems. These data include all of the mixtures used in the KENO sample problems and will create an AMPX working format cross-section library with nuclide IDs matching those in the KENO sample problem mixing tables. This cross-section library is problem-specific and is not appropriate for use with other problems.

The CSAS-MG input data to produce an AMPX working format cross-section library for the multigroup mode KENO V.a sample problems are given below.

=CSAS-MG
csasn to prepare 238 group working format xsec lib for kenova smp prbs
v7-238
READ COMP
' uranium metal for smp prbs 1,2,3,4,5,6,7,8,9,10,11,12,19,22,23,24,25,26,27,28
  uranium  1 den=18.76 1 300 92235 93.2 92238 5.6 92234 1.0 92236 0.2 end
' uranyl nitrate solution for smp prbs 12,18,19   spg=1.555
  solution  mix=2  rho[uo2(no3)2]=415 92235 92.6 92238 5.9 92234 1.0  92236 0.5
            molar[hno3]=9.783-3  temp=300 density=?   end solution
' uranium metal for smp prbs 13,14
  uranium  3 den=18.69 1 300  92235 93.2 92238 5.6 92234 1.0 92236 0.2 end
' uranium metal for smp prb 15
  uranium  4 den=18.794 1 300 92235 97.67 92238 1.03
                             92234 1.09  92236 0.21 end
' uranyl fluoride solution for smp prb 16
  solution  mix=5  rho[uo2f2]=578.7 92235 93.2 92238 6.8 temp=300 end solution
' borated uranyl fluoride solution for smp prb 16
  solution  mix=6  rho[uo2f2]=578.7 92235 93.2 92238 6.8 temp=300 end solution
  boron          6 den=.0266 end
' uranyl fluoride solution for smp prb 17
  solution  mix=7  rho[uo2f2]=133  92235 93.0  92238 7.0  temp=300 end solution
' uranyl fluoride solution for smp prb 20
  solution  mix=8  rho[uo2f2]=576.87 92235 93.2 92238 6.8 temp=300 end solution
' uranyl fluoride solution for smp prb 21     spg= 1.56
  solution  mix=9  rho[uo2f2]=494 92235 4.89 92238 95.09 92234 0.02
            temp=300  end solution
' paraffin for smp prbs 3,4,18
  paraffin 10 end
' plexiglas for smp prbs 12,15,18,19
  plexiglas 11 end
' water for smp prbs 15
  h2o 12 end
' pyrex glass for smp prb 16
  pyrex 13 end
' aluminum for smp prb 20,21
  al 14 end
' low density water for smp prb 18
  h2o 15 1-9 end
' uranium metal for smp prbs 29 - 32
  uranium  16 den=18.747 1 300  92235 93.21 92238 5.7697 92234 0.9844
                                92236  0.0359 end
' uranium metal for water moderated portion of smp prb 33
  uranium  17 den=19.0 1 300  92235 1.95 92238 98.042 92234 0.002 92236 0.006  end
' internal (2nd) moderator water for smp prb 33
  h2o      18 end
' external moderator water and reflector for smp prb 33
  h2o      19 end
' uranium metal for bare portion of smp prb 33
  uranium  20 den=19.0 1 300  92235 1.95 92238 98.042 92234 0.002 92236 0.006  end
END COMP
READ CELLDATA
'latticecell data for samp prb 33
  latticecell atriangpitch  pitch=20.828 19 fueld=18.288 17 imodd=6.604 18 end
  latticecell atriangpitch  pitch=20.828  0 fueld=18.288 20 imodd=6.604  0 end
END CELLDATA
END

KENO V.a sample problem data

A brief problem description and the associated input data are included for each multigroup mode KENO sample problem. Different options may be easily activated by making changes in the data. These problems are set up using an AMPX working format library which was created by a CSAS-MG case just prior to the KENO V.a cases. The nuclide identifiers for this library are consistent with the SCALE identifiers created by CSAS-MG. Input data to create this library are given in CSAS-MG data. The unit number is defined by the parameter LIB= in the parameter data.

Sample Problem 1 2C8 BARE

This is a simple 2 × 2 × 2 array of uranium metal cylinders as described in the article “Critical Three-Dimensional Arrays of U(93.2)-Metal Cylinders,” [Tho73] by J. T. Thomas. This critical experiment is designated in Table II of that article as cylinder index 11 and reflector index 1. Fig. 260 shows the critical experiment.

Input Data

KENO V.a

=KENOVA
sample problem 1  case 2c8 bare
READ PARAMETERS
  flx=yes fdn=yes far=yes gas=no lib=4
END PARAMETERS
READ MIXT
  sct=2
  mix=1
    1092234 4.82717e-04 1092235 4.47971e-02 1092236 9.57233e-05 1092238 2.65767e-03
END MIXT
READ GEOMETRY
  unit 1
    cylinder 1 1 5.748 5.3825 -5.3825
    cuboid  0 1 6.87 -6.87 6.87 -6.87 6.505 -6.505
END GEOMETRY
READ ARRAY
  nux=2 nuy=2 nuz=2
END ARRAY
END DATA
END

KENO-VI

=KENOVI
kenovi  sample problem 1  case 2c8 bare
READ PARAMETERS
  flx=yes fdn=yes far=yes gas=no lib=4
END PARAMETERS
READ MIXT
  sct=2
  mix=1 1092234 4.82717e-04 1092235 4.47971e-02 1092236 9.57233e-05
        1092238 2.65767e-03
END MIXT
READ GEOMETRY
  unit 1
    com='single 2c8 unit centered'
    cylinder 10  5.748 5.3825 -5.3825
    cuboid   20  4p6.87 2p6.505
    media  1 1 10      vol=8938.968624
    media  0 1 20 -10  vol=10710.044784
    boundary 20
  global unit 2
    cuboid 10  4p13.74 2p13.01
    com='2x2x2  2c8 array'
    array 1 +10 place 1 1 1 2r-6.87 -6.505
    boundary  10
END GEOMETRY
READ ARRAY
  ara=1 nux=2 nuy=2 nuz=2  fill f1  end fill
END ARRAY
END DATA
END
_images/fig1101.png

Fig. 260 Critical 2C8 bare assembly.

Sample Problem 2 CASE 2C8 BARE WITH 8 UNIT TYPES MATRIX CALCULATION

This problem is the same as sample problem 1 except it is set up as a mixed unit problem with each unit of the array defined as a different unit type. Matrix k-effectives will be calculated for this problem by both unit type and array position. The print flags are set to print all matrix data.

Input Data

KENO V.a

=KENOVA
sample problem 2  2c8 bare with 8 unit types matrix calculation
READ PARAM
  lib=4  flx=yes fdn=yes
  mku=yes fmu=yes mkp=yes fmp=yes
END PARAM
READ GEOMETRY
  unit 1
    cylinder  1 1 5.748 5.3825 -5.3825
    cuboid  0 1 6.87 -6.87 6.87 -6.87 6.505 -6.505
  unit 2
    cylinder  1 1 5.748 5.3825 -5.3825
    cuboid  0 1 6.87 -6.87 6.87 -6.87 6.505 -6.505
  unit 3
    cylinder  1 1 5.748 5.3825 -5.3825
    cuboid  0 1 6.87 -6.87 6.87 -6.87 6.505 -6.505
  unit 4
    cylinder  1 1 5.748 5.3825 -5.3825
    cuboid  0 1 6.87 -6.87 6.87 -6.87 6.505 -6.505
  unit  5
    cylinder  1 1 5.748 5.3825 -5.3825
    cuboid  0 1 6.87 -6.87 6.87 -6.87 6.505 -6.505
  unit 6
    cylinder  1 1 5.748 5.3825 -5.3825
    cuboid  0 1 6.87 -6.87 6.87 -6.87 6.505 -6.505
  unit 7
    cylinder  1 1 5.748 5.3825 -5.3825
    cuboid  0 1 6.87 -6.87 6.87 -6.87 6.505 -6.505
  unit 8
    cylinder  1 1 5.748 5.3825 -5.3825
    cuboid  0 1 6.87 -6.87 6.87 -6.87 6.505 -6.505
END GEOM
READ MIXT
  sct=2
  mix=1
    1092234 4.82717e-04 1092235 4.47971e-02 1092236 9.57233e-05 1092238 2.65767e-03
END MIXT
READ ARRAY
  nux=2 nuy=2 nuz=2  loop
    10*1
    3*2 7*1
    3 1 1 1 2 2 1 1 1 1
    4 2 2 1 2 2 1 1 1 1
    5 6*1 2 2 1
    6 2 2 1 1 1 1 2 2 1
    7  1 1 1 2 2 1 2 2 1
    8 2 2 1 2 2 1 2 2 1    end loop
END ARRAY
END DATA
END

KENO-VI

=KENOVI
kenovi sample problem 2  case 2c8 bare with 8 unit types matrix cal
READ PARAM
  lib=4 flx=yes fdn=yes mku=yes cku=yes fmu=yes mkp=yes ckp=yes fmp=yes
END PARAMETERS
READ MIXT
  sct=2
  mix=1 1092234 4.82717e-04 1092235 4.47971e-02 1092236 9.57233e-05
        1092238 2.65767e-03
END MIXT
READ GEOMETRY
  unit 1
    cylinder 10 5.748 5.3825 -5.3825
    cuboid   20 4p6.87 2p6.505
    media  1 1 10     vol=1117.371078
    media  0 1 20 -10 vol=1338.755598
    boundary   20
  unit 2
    cylinder 10  5.748 5.3825 -5.3825
    cuboid   20  4p6.87 2p6.505
    media  1 1 10     vol=1117.371078
    media  0 1 20 -10 vol=1338.755598
    boundary   20
  unit 3
    cylinder 10  5.748 5.3825 -5.3825
    cuboid   20  4p6.87 2p6.505
    media  1 1 10     vol=1117.371078
    media  0 1 20 -10 vol=1338.755598
    boundary  20
  unit 4
    cylinder 10  5.748 5.3825 -5.3825
    cuboid   20  4p6.87 2p6.505
    media  1 1 10     vol=1117.371078
    media  0 1 20 -10 vol=1338.755598
    boundary 20
  unit 5
    cylinder 10  5.748 5.3825 -5.3825
    cuboid   20  4p6.87 2p6.505
    media  1 1 10     vol=1117.371078
    media  0 1 20 -10 vol=1338.755598
    boundary  20
  unit 6
    cylinder 10  5.748 5.3825 -5.3825
    cuboid   20 4p6.87 2p6.505
    media  1 1 10     vol=1117.371078
    media  0 1 20 -10 vol=1338.755598
    boundary  20
  unit 7
    cylinder 10  5.748 5.3825 -5.3825
    cuboid   20 4p6.87 2p6.505
    media  1 1 10     vol=1117.371078
    media  0 1 20 -10 vol=1338.755598
    boundary 20
  unit 8
    cylinder 10  5.748 5.3825 -5.3825
    cuboid   20 4p6.87 2p6.505
    media  1 1 10     vol=1117.371078
    media  0 1 20 -10 vol=1338.755598
    boundary  20
  global unit 9
    cuboid  10 4p13.74 2p13.01
    com='2x2x2  2c8 array'
    array 1 +10 place 1 1 1 2r-6.87 -6.505
    boundary  10
END GEOMETRY
READ ARRAY
 ara=1 nux=2 nuy=2 nuz=2  gbl=1
 loop  10*1
       3*2 7*1
       3 1 1 1 2 2 1 1 1 1
       4 2 2 1 2 2 1 1 1 1
       5 6*1 2 2 1
       6 2 2 1 1 1 1 2 2 1
       7  1 1 1 2 2 1 2 2 1
       8 2 2 1 2 2 1 2 2 1 end loop
END ARRAY
END DATA
END

Sample Problem 3 2C8 15.24-CM PARAFFIN REFL

A 2 × 2 × 2 array of uranium metal cylinders is reflected by 6 in. of paraffin on all faces (Fig. 260). This critical experiment1 is designated as cylinder index 11 and reflector index 5 in Table II of Ref. 1. Fig. 261 shows half of the critical experiment, which consisted of the half shown and the mirror image of it. These two assemblies were moved together to achieve criticality. The top reflector is missing in Fig. 261, but was present when criticality was achieved.

_images/fig213.png

Fig. 261 Half of the paraffin reflected 2C8 assembly before the top reflector was added.

Input Data

KENO V.a

=KENOVA
sample problem 3  2c8  15.24 cm paraffin refl
READ PARAM
  lib=4  flx=yes fdn=yes pwt=yes
END PARAM
READ ARRAY
  nux=2 nuy=2 nuz=2
END ARRAY
READ MIXT
  mix=1
    1092234 4.82717e-04 1092235 4.47971e-02 1092236 9.57233e-05 1092238 2.65767e-03
  mix=2
    10006000 3.84193e-02 10001901 7.99120e-02
  sct=2
END MIXT
READ GEOM
  unit 1
    cylinder  1 1 5.748 5.3825 -5.3825
    cuboid  0 1 11.74 -11.74 11.74 -11.74 11.375 -11.375
  global unit 2
    array   1 -23.48 -23.48 -22.75
    cuboid  2 2 26.48 -26.48 26.48 -26.48 25.75 -25.75
    cuboid  2 3 29.48 -29.48 29.48 -29.48 28.75 -28.75
    cuboid  2 4 32.48 -32.48 32.48 -32.48 31.75 -31.75
    cuboid  2 5 35.48 -35.48 35.48 -35.48 34.75 -34.75
    cuboid  2 6 38.72 -38.72 38.72 -38.72 37.99 -37.99
END GEOM
READ BIAS
  id=400 2 6
END BIAS
END DATA
END

KENO-VI

=KENOVI
keno-vi sample problem 3  2c8  15.24 cm paraffin refl
READ PARAM
  lib=4 flx=yes fdn=yes pwt=yes
END PARAM
READ MIXT
  sct=2
  mix=1 1092234 4.82717e-04 1092235 4.47971e-02 1092236 9.57233e-05
        1092238 2.65767e-03
  mix=2 10006000 3.84193e-02 10001901 7.99120e-02
END MIXT
READ GEOMETRY
  unit 1
    com='single 2c8 unit centered'
    cylinder 10  5.748 5.3825 -5.3825
    cuboid   20  4p11.74 2p11.375
    media  1 1 10      vol=8938.968624
    media  0 1 20 -10  vol=10710.044784
    boundary  20
  global unit 2
    com='2x2x2  2c8 array with reflector'
    cuboid 10 4p23.48 2p22.75
    cuboid 20   26.48 -26.48 26.48 -26.48 25.75 -25.75
    cuboid 30   29.48 -29.48 29.48 -29.48 28.75 -28.75
    cuboid 40   32.48 -32.48 32.48 -32.48 31.75 -31.75
    cuboid 50   35.48 -35.48 35.48 -35.48 34.75 -34.75
    cuboid 60   38.72 -38.72 38.72 -38.72 37.99 -37.99
    array 1 +10 place 1 1 1 2r-11.74 -11.375
    media  2 2 -10 +20  vol=4.41067E+04
    media  2 3 -20 +30  vol=5.54410E+04
    media  2 4 -30 +40  vol=6.80712E+04
    media  2 5 -40 +50  vol=8.19974E+04
    media  2 6 60 -50   vol=1.05694E+05
    boundary  60
END GEOMETRY
READ BIAS
  id=400 2 6
END BIAS
READ ARRAY
  ara=1 nux=2 nuy=2 nuz=2 fill f1 end fill
END ARRAY
END DATA
END

Sample Problem 4 2C8 15.24-CM PARAFFIN REFL AUTOMATIC REFL

This problem is the same as sample problem 3 except it is set up using more reflector regions.

Input Data

KENO V.a

=KENOVA
sample problem 4  2c8 15.24 cm paraffin refl automatic refl
READ PARAM
  pwt=yes lib=4  flx=yes fdn=yes
END PARAM
READ GEOMETRY
  unit 1
    cylinder  1 1 5.748 5.3825 -5.3825
    cuboid  0 1 11.74 -11.74 11.74 -11.74 11.375 -11.375
  global unit 2
    array      1 -23.48 -23.48 -22.75
    reflector  2 2 6*3.0 5
    reflector  2 7 6*.24 1
END GEOM
READ MIXT
  sct=2
  mix=1
    1092234 4.82717e-04 1092235 4.47971e-02 1092236 9.57233e-05 1092238 2.65767e-03
  mix=2
    10006000 3.84193e-02 10001901 7.99120e-02
END MIXT
READ ARRA
  nux=2 nuy=2 nuz=2
END ARRAY
READ BIAS
  id=400 2 7
END BIAS
END DATA
END

KENO-VI

=KENOVI
keno-vi sample problem 4  2c8  15.24 cm paraffin refl
READ PARAM
  lib=4 flx=yes fdn=yes pwt=yes
END PARAM
READ MIXT
  sct=2
  mix=1 1092234 4.82717e-04 1092235 4.47971e-02 1092236 9.57233e-05
        1092238 2.65767e-03
  mix=2 10006000 3.84193e-02 10001901 7.99120e-02
END MIXT
READ GEOMETRY
  unit 1
    com='single 2c8 unit centered'
    cylinder 10  5.748 5.3825 -5.3825
    cuboid   20  4p11.74 2p11.375
    media  1 1 10
    media  0 1 20 -10
    boundary  20
  global unit 2
    com='2x2x2  2c8 array with reflector'
    cuboid 10 4p23.48 2p22.75
    cuboid 20   26.48 -26.48 26.48 -26.48 25.75 -25.75
    cuboid 30   29.48 -29.48 29.48 -29.48 28.75 -28.75
    cuboid 40   32.48 -32.48 32.48 -32.48 31.75 -31.75
    cuboid 50   35.48 -35.48 35.48 -35.48 34.75 -34.75
    cuboid 60   38.48 -38.48 38.48 -38.48 37.75 -37.75
    cuboid 70   38.72 -38.72 38.72 -38.72 37.99 -37.99
    array 1 +10 place 1 1 1 2r-11.74 -11.375
    media  2 2 -10 +20
    media  2 3 -20 +30
    media  2 4 -30 +40
    media  2 5 -40 +50
    media  2 6  60 -50
    media  2 7  70 -60
    boundary 70
END GEOMETRY
READ VOLUME
   type=trace
END VOLUME
READ BIAS
  id=400 2 7
END BIAS
READ ARRAY
  ara=1 nux=2 nuy=2 nuz=2 fill f1 end fill
END ARRAY
END DATA
END

Sample Problem 5 2C8 12-INCH PARAFFIN ALBEDO REFLECTOR

This problem is the same as samples problems 3 and 4 except the reflector is represented by a 12‑in. paraffin albedo. Note the decrease in execution time when using an albedo reflector instead of doing actual tracking. Note also that k-effective is somewhat higher for this system, probably due to the small edge size of the system [WT69].

Input Data

KENO V.a

=KENOVA
sample problem 5  2c8 12 inch paraffin albedo reflector
READ PARA
  flx=yes far=yes gas=no fdn=yes lib=4
END PARA
READ ARRAY
  nux=2 nuy=2 nuz=2
END ARRAY
READ MIXT
  mix=1
    1092234 4.82717e-04 1092235 4.47971e-02 1092236 9.57233e-05 1092238 2.65767e-03
  sct=2
END MIXT
READ BOUNDS
  all=paraffin
END BOUNDS
READ GEOM
  unit 1
    cylinder  1 1 5.748 5.3825 -5.3825
    cuboid  0 1 11.74 -11.74 11.74 -11.74 11.375 -11.375
END GEOM
END DATA
END

KENO-VI

=KENOVI
kenovi sample problem 5  2c8 12 inch paraffin albedo reflector
READ PARA
  flx=yes far=yes gas=no fdn=yes lib=4
END PARA
READ MIXT
  sct=2
  mix=1 1092234 4.82717e-04 1092235 4.47971e-02 1092236 9.57233e-05
        1092238 2.65767e-03
END MIXT
READ BOUNDS
  all=paraffin
END BOUNDS
READ GEOMETRY
  unit 1
    com='single 2c8 unit centered'
    cylinder 10  5.748 5.3825 -5.3825
    cuboid   20 4p11.74 2p11.375
    media  1 1 10
    media  0 1 20 -10
    boundary  20
  global unit 2
    cuboid 10  4p23.48 2p22.75
    com='2x2x2  2c8 array'
    array 1 +10 place 1 1 1 2r-11.74 -11.375
    boundary 10
END GEOMETRY
READ ARRAY
  ara=1 nux=2 nuy=2 nuz=2  fill f1 end fill
END ARRAY
READ VOLUME
  type=random
END VOLUME
END DATA
END

Sample Problem 6 ONE 2C8 UNIT (SINGLE UNIT)

One of the 2C units1 is described and run as a single-unit problem, and its k-effective is calculated.

Input Data

KENO V.a

=KENOVA
sample problem 6  one 2c8 unit (single unit)
READ PARA
  lib=4  flx=yes fdn=yes far=yes gas=no
END PARA
READ MIXT
  sct=2
  mix=1
    1092234 4.82717e-04 1092235 4.47971e-02 1092236 9.57233e-05 1092238 2.65767e-03
END MIXT
READ GEOMETRY
  unit 1
    cylinder  1 1 5.748 5.3825 -5.3825
END GEOMETRY
END DATA
END

KENO-VI

=KENOVI
kenovi sample problem 6  one 2c8 unit (single unit)
READ PARA
  lib=4 flx=yes fdn=yes far=yes gas=no
END PARA
READ MIXT
  sct=2
  mix=1 1092234 4.82717e-04 1092235 4.47971e-02 1092236 9.57233e-05
        1092238 2.65767e-03
END MIXT
READ GEOMETRY
  global unit 1
    com='single 2c8 unit centered'
    cylinder 10  5.748 5.3825 -5.3825
    media  1 1 10  vol=1117.3710776
    boundary  10
END GEOMETRY
END DATA
END

Sample Problem 7 BARE 2C8 USING SPECULAR REFLECTION

One of the 2C units1 is described and the 2 × 2 × 2 array is simulated by using specular reflection on the positive X, Y, and Z faces of the unit. This is a simulation of sample problem 1.

Input Data

KENO V.a

=KENOVA
sample problem 7  bare 2c8 using specular reflection
READ PARA
  lib=4  flx=yes fdn=yes far=yes gas=no
END PARAMETERS
READ MIXT
  sct=2
  mix=1
    1092234 4.82717e-04 1092235 4.47971e-02 1092236 9.57233e-05 1092238 2.65767e-03
END MIXT
READ GEOM
  unit 1
    cylinder  1 1 5.748 5.3825 -5.3825
    cuboid  0 1 6.87 -6.87 6.87 -6.87 6.505 -6.505
END GEOM
READ BOUNDS
  +fc=specular
END BOUNDS
END DATA
END

KENO-VI

=KENOVI
keno-vi  sample problem 7  bare 2c8 using specular reflection
READ PARA
  flx=yes fdn=yes far=yes gas=no lib=4
END PARAMETERS
READ MIXT
  sct=2
  mix=1 1092234 4.82717e-04 1092235 4.47971e-02 1092236 9.57233e-05
        1092238 2.65767e-03
END MIXT
READ GEOMETRY
  global unit 1
    com='single 2c8 unit centered'
    cylinder 10  5.748 5.3825 -5.3825
    cuboid   20  4p6.87 2p6.505
    media  1 1 10      vol=1117.371078
    media  0 1 20 -10  vol=1338.755598
    boundary  20
END GEOMETRY
READ BOUNDS
  +fc=specular
END BOUNDS
END DATA
END

Sample Problem 8 INFINITELY LONG CYLINDER FROM 2C8 UNIT

The fuel and cylinder radius from sample problem 1 is used. The length of the cylinder is arbitrarily chosen to be 20 cm, and the unit is specularly reflected on the top and bottom to create an infinitely long cylinder.

Input Data

KENO V.a

=KENOVA
sample problem 8  infinitely long cylinder from 2c8 unit
READ PARAM
  lib=4
END PARAM
READ MIXT
  sct=2
  mix=1
    1092234 4.82717e-04 1092235 4.47971e-02 1092236 9.57233e-05 1092238 2.65767e-03
END MIXT
READ GEOMETRY
  unit 1
    cylinder  1 1 5.748 10.0 -10.0
    cuboid  0 1 6.87 -6.87 6.87 -6.87 10.0 -10.0
END GEOMETRY
READ BOUNDS
  zfc=mirror
END BOUNDS
END DATA
END

KENO-VI

=KENOVI
keno-vi  sample problem 8 infinitely long cylinder from 2c8 unit
READ PARAMETERS
  lib=4
END PARAMETERS
READ MIXT
  sct=2
  mix=1 1092234 4.82717e-04 1092235 4.47971e-02 1092236 9.57233e-05
        1092238 2.65767e-03
END MIXTURES
READ GEOMETRY
  global unit 1
    com='single 2c8 unit centered'
    cylinder 10  5.748 2p10.0
    cuboid   20  4p6.87 2p10.0
    media  1 1 10
    media  0 1 20 -10
    boundary  20
END GEOMETRY
READ BOUNDS
  zfc=mirror
END BOUNDS
READ VOLUME
  type=trace  iface=zface
END VOLUME
END DATA
END

Sample Problem 9 INFINITE ARRAY OF 2C8 UNITS

Input Data

KENO V.a

=KENOVA
sample problem 9  infinite array of 2c8 units
READ PARAM
  lib=4  gen=103
END PARAM
READ MIXT
  sct=2
  mix=1
    1092234 4.82717e-04 1092235 4.47971e-02 1092236 9.57233e-05 1092238 2.65767e-03
END MIXT
READ BOUN
  all=mir
END BOUN
READ GEOM
  unit 1
    cylinder  1 1 5.748 5.3825 -5.3825
    cuboid  0 1 6.87 -6.87 6.87 -6.87 6.505 -6.505
END GEOM
END DATA
END

KENO-VI

=KENOVI
keno-vi  sample problem 9  infinite array of 2c8 units
READ PARAMETERS
  lib=4
END PARAMETERS
READ MIXTURES
  sct=2
  mix=1 1092234 4.82717e-04 1092235 4.47971e-02 1092236 9.57233e-05
        1092238 2.65767e-03
END MIXT
READ GEOMETRY
  global unit 1
    com='single 2c8 unit centered'
    cylinder 10  5.748 5.3825 -5.3825
    cuboid   20  4p6.87 2p6.505
    media  1 1 10      vol=1117.371078
    media  0 1 20 -10  vol=1338.755598
    boundary  20
END GEOMETRY
READ BOUNDS
  all=mirror
END BOUNDS
END DATA
END

Sample Problem 10 2C8 BARE WRITE RESTART

The geometry description from sample problem 1 is used, and the cuboid is specularly reflected on all faces to create an infinite array of 2C8 units having an edge-to-edge spacing of 2.244 cm in the X and Y directions and 2.245 cm in the Z direction.

Input Data

KENO V.a

=KENOVA
sample problem 10  case 2c8 bare  write restart
READ PARAMETERS
  flx=yes fdn=yes far=yes gas=no lib=4  res=5 wrs=94
  app=yes
END PARAMETERS
READ MIXT
  sct=2
  mix=1
    1092234 4.82717e-04 1092235 4.47971e-02 1092236 9.57233e-05 1092238 2.65767e-03
END MIXT
READ GEOMETRY
  unit 1
    cylinder 1 1 5.748 5.3825 -5.3825
    cuboid  0 1 6.87 -6.87 6.87 -6.87 6.505 -6.505
END GEOMETRY
READ ARRAY
  nux=2 nuy=2 nuz=2
END ARRAY
END DATA
END

KENO-VI

=KENOVI
sample problem 10  case 2c8 bare  write restart
READ PARAMETERS
  flx=yes fdn=yes far=yes gas=no lib=4 res=5 wrs=94 app=yes
END PARAMETERS
READ MIXT
  sct=2
  mix=1 1092234 4.82717e-04 1092235 4.47971e-02 1092236 9.57233e-05
        1092238 2.65767e-03
END MIXTURES
READ GEOMETRY
  unit 1
    com='single 2c8 unit centered'
    cylinder 10  5.748 5.3825 -5.3825
    cuboid   20  4p6.87 2p6.505
    media  1 1 10      vol=8938.968624
    media  0 1 20 -10  vol=10710.044784
    boundary  20
  global unit 2
    cuboid 10  4p13.74 2p13.01
    com='2x2x2  2c8 array'
    array 1 +10 place 1 1 1 2r-6.87 -6.505
    boundary  10
END GEOMETRY
READ ARRAY
  ara=1 nux=2 nuy=2 nuz=2  fill f1  end fill
END ARRAY
END DATA
END

Sample Problem 11 2C8 BARE READ RESTART DATA

This problem is a restart of sample problem 10. The problem is restarted from the tenth set of restart data that was written by sample problem 10 (i.e., it restarts with the fifty-first generation).

Input Data

KENO V.a

=KENOVA
sample problem 11  2c8 bare  read restart data
READ PARAM
  beg=51  rst=94 res=0
END PARAM
END DATA
END

KENO-VI

=KENOVI
sample problem 11  2c8 bare  read restart data
READ PARAM
  beg=51 rst=94 res=0
END PARAM
END DATA
END

Sample Problem 12 4 AQUEOUS 4 METAL

This problem is a critical experiment consisting of a composite array1 of four highly enriched uranium metal cylinders and four cylindrical Plexiglas containers filled with uranyl nitrate solution. The metal units in this experiment are designated in Table II of Ref. 1 as cylinder index 11 and reflector index 1. A photograph of the experiment is given in Fig. 262.

_images/fig312.png

Fig. 262 Critical assembly of 4 solution units and 4 metal units.

Input Data

KENO V.a

=KENOVA
sample problem 12 4 aqueous 4 metal mixed units
READ PARAM
  lib=4 fdn=yes nub=yes smu=yes mkp=yes
  mku=yes fmp=yes fmu=yes
END PARAM
READ MIXT
  sct=2
  mix=1
    1092234 4.82717e-04 1092235 4.47971e-02 1092236 9.57233e-05 1092238 2.65767e-03
  mix=2
    2001001 5.77931e-02   2007014 2.13092e-03   2008016 3.74114e-02
    2092234 1.06784e-05   2092235 9.84602e-04   2092236 5.29386e-06
    2092238 6.19414e-05
  mix=3
   11001001 5.67873e-02  11006000 3.54921e-02  11008016 1.41968e-02
END MIXT
READ GEOM
  unit 1
    cylinder  2 1 9.525 8.89 -8.89
    cylinder  3 1 10.16 9.525 -9.525
    cuboid  0 1 10.875 -10.875 10.875 -10.875 10.24 -10.24
  unit  2
    cylinder  1 1 5.748 5.3825 -5.3825
    cuboid  0 1 6.59 -15.16 6.59 -15.16 6.225 -14.255
  unit  3
    cylinder  1 1 5.748 5.3825 -5.3825
    cuboid  0 1 6.59 -15.16 15.16 -6.59 6.225 -14.255
  unit  4
    cylinder  1 1 5.748 5.3825 -5.3825
    cuboid  0 1 6.59 -15.16 6.59 -15.16 14.255 -6.225
  unit  5
    cylinder  1 1 5.748 5.3825 -5.3825
    cuboid  0 1 6.59 -15.16 15.16 -6.59 14.255 -6.225
END GEOM
READ ARRAY
  gbl=1 ara=1 nux=2 nuy=2 nuz=2  loop
    1 3r2 1 2 1 1 2 1
    2 9r1
    3 3r1 2 2 1 3r1
    4 6r1 2 2 1
    5 3r1 2 2 1 2 2 1  end loop
END ARRAY
END DATA
END

KENO-VI

=KENOVI
sample problem 12 4 aqueous 4 metal mixed units
READ PARAM
  lib=4  flx=yes fdn=yes nub=yes smu=yes mku=yes fmp=yes fmu=yes
END PARAM
READ MIXT
  sct=2
  mix=1  1092234 4.82717e-04 1092235 4.47971e-02 1092236 9.57233e-05
         1092238 2.65767e-03
  mix=2  2001001 5.77931e-02   2007014 2.13092e-03   2008016 3.74114e-02
         2092234 1.06784e-05   2092235 9.84602e-04   2092236 5.29386e-06
         2092238 6.19414e-05
  mix=3 11001001 5.67873e-02  11006000 3.54921e-02  11008016 1.41968e-02
END MIXT
READ GEOM
  unit 1
    cylinder 10  9.525 8.89 -8.89
    cylinder 20  10.16 9.525 -9.525
    cuboid   30  10.875 -10.875 10.875 -10.875 10.24 -10.24
    media 2 1 10      vol=20270.8327
    media 3 1 -10 20  vol=4440.27764
    media 0 1 30 -20  vol=14042.16966
    boundary  30
  unit      2
    cylinder 10  5.748 5.3825 -5.3825
    cuboid   20  6.59 -15.16 6.59 -15.16 6.225 -14.255
    media 1 1 10      vol=1117.371078
    media 0 1 20 -10  vol=8570.948922
    boundary  20
  unit      3
    cylinder 10  5.748 5.3825 -5.3825
    cuboid   20  6.59 -15.16 15.16 -6.59 6.225 -14.255
    media 1 1 10      vol=1117.371078
    media 0 1 20 -10  vol=8570.948922
    boundary  20
  unit      4
    cylinder 10  5.748 5.3825 -5.3825
    cuboid   20  6.59 -15.16 6.59 -15.16 14.255 -6.225
    media 1 1 10      vol=1117.371078
    media 0 1 20 -10  vol=8570.948922
    boundary  20
  unit      5
    cylinder 10  5.748 5.3825 -5.3825
    cuboid   20  6.59 -15.16 15.16 -6.59 14.255 -6.225
    media 1 1 10      vol=1117.371078
    media 0 1 20 -10  vol=8570.948922
    boundary  20
  global
  unit  6
    cuboid 10  43.5 0.0 43.5 0.0 40.96 0.0
    array 1 +10 place 1 1 1 15.16 15.16 14.255
    boundary  10
END GEOM
READ ARRAY
  gbl=1 ara=1 nux=2 nuy=2 nuz=2  loop
  1 3r2 1 2 1 1 2 1
  2 9r1
  3 3r1 2 2 1 3r1
  4 6r1 2 2 1
  5 3r1 2 2 1 2 2 1  end loop
END ARRAY
END DATA
END

Sample Problem 13 TWO CUBOIDS IN A CYLINDRICAL ANNULUS

This critical experiment [IM64] consists of two assemblies of 93.2% 235U-enriched uranium metal (ρ = 18.69 g/cc) stacked vertically. The bottom assembly contains a uranium metal cuboid offset to the left within a uranium metal cylindrical annulus. The top assembly contains a uranium metal cuboid offset to the right within a uranium metal cylindrical annulus. The cuboid extends above the annulus. A drawing of the two sections and the total assembly is given in Fig. 263.

_images/fig412.png

Fig. 263 Drawing of two cuboids in an annulus critical assembly.

Input Data

KENO V.a

=KENOVA
sample problem 13  two cuboids in a cylindrical annulus
READ PARAM
   lib=4
END PARAM
READ GEOM
  unit 1
    cuboid  1 1 6.35 -6.35 6.35 -6.35 7.62 0.0
    cylinder  0 1 13.97 7.62 0.0 orig -6.0934 0.0
    cylinder  1 1 19.05 7.62 0.0 orig -6.0934 0.0
    cuboid  0 1 12.9566 -25.1434 19.05 -19.05 7.62 0.0
  unit 2
    cuboid  1 1 6.35 -6.35 6.35 -6.35 8.56 0.0
    cylinder  0 1 13.97 8.56 0.0 origin 6.0934 0.0
    cylinder  1 1 19.05 8.56 0.0 origin 6.0934 0.0
    cuboid  0 1 25.1434 -12.9566 19.05 -19.05 8.56 0.0
  unit 3
    cuboid  1 1 6.35 -6.35 6.35 -6.35 2.616 0.0
    cuboid  0 1 25.1434 -12.9566 19.05 -19.05 2.616 0.0
END GEOM
READ MIXT
  sct=2
  mix=1
    3092234 4.80916e-04  3092235 4.46300e-02  3092236 9.53661e-05 3092238 2.64776e-03
END MIXT
READ ARRAY
  gbl=1 nux=1 nuy=1 nuz=3  fill 1 2 3 t
END ARRAY
END DATA
END

KENO-VI

=KENOVI
sample problem 13  two cuboids in a cylindrical annulus
READ PARAM
  lib=4
END PARAM
READ MIXT
  sct=2
  mix=1  3092234 4.80916e-04  3092235 4.46300e-02  3092236 9.53661e-05
         3092238 2.64776e-03
END MIXT
READ GEOM
  unit 1
    cuboid    10 6.35 -6.35 6.35 -6.35 7.62 0.0
    cylinder  20 13.97 7.62 0.0 orig x=-6.0934
    cylinder  30 19.05 7.62 0.0 orig x=-6.0934
    cuboid    40 12.9566 -25.1434 19.05 -19.05 7.62 0.0
    media  1 1 10     vol=1229.0298
    media  0 1 20 -10 vol=3442.914497898
    media  1 1 30 -20 vol=4015.555429598
    media  0 1 40 -30 vol=2373.768472504
    boundary  40
  unit 2
    cuboid   10 6.35 -6.35 6.35 -6.35 8.56 0.0
    cylinder 20  13.97 8.56 0.0 origin x=6.0934
    cylinder 30  19.05 8.56 0.0 origin x=6.0934
    cuboid   40 25.1434 -12.9566 19.05 -19.05 8.56 0.0
    media  1 1 10     vol=1380.6424
    media  0 1 20 -10 vol=3867.630984515
    media  1 1 30 -20 vol=4510.912661071
    media  0 1 40 -30 vol=2666.595554414
    boundary  40
  unit 3
    cuboid 10  6.35 -6.35 6.35 -6.35 2.616 0.0
    cuboid 20 25.1434 -12.9566 19.05 -19.05 2.616 0.0
    media  1 1 10     vol=421.93464
    media  0 1 20 -10 vol=3375.47712
    boundary  20
  global unit 4
    cuboid  10 12.9566 -25.1434 2p19.05 18.796 0.
    array 1 10 place 1 1 1 3r0.
    boundary  10
END GEOM
READ ARRAY
  ara=1 nux=1 nuy=1 nuz=3  fill 1 2 3 end fill
END ARRAY
END DATA
END

Sample Problem 14 U METAL CYLINDER IN AN ANNULUS

This critical experiment3 consists of a 93.2 235U-enriched uranium metal cylinder within a cylindrical annulus of the same material as shown in Fig. 264. The uranium metal specification is identical to that used in sample problem 13.

_images/fig512.png

Fig. 264 Drawing of the cylinder in an annulus critical assembly.

Input Data

KENO V.a

=KENOVA
sample problem 14  u metal cylinder in an annulus
READ PARAM
  lib=4
END PARAM
READ MIXT
  sct=2
  mix=1
    3092234 4.80916e-04  3092235 4.46300e-02  3092236 9.53661e-05 3092238 2.64776e-03
END MIXT
READ GEOM
  global unit 1
    cylinder  1 1 8.89 10.109 0.0 orig 5.0799 0.0
    cylinder  0 1 13.97 10.109 0.0
    cylinder  1 1 19.05 10.109 0.0
END GEOM
END DATA
END

KENO-VI

=KENOVI
sample problem 14  u metal cylinder in an annulus
READ PARAM
  lib=4
END PARAM
READ MIXT
  SCT=2
  mix=1  3092234 4.80916e-04  3092235 4.46300e-02  3092236 9.53661e-05
         3092238 2.64776e-03
END MIXT
READ GEOM
  global unit 1
    cylinder 10  8.89 10.109 0.0 orig x=5.08
    cylinder 20  13.97 10.109 0.0
    cylinder 30  19.05 10.109 0.0
    media  1 1 10          vol=2509.929894
    media  0 1 20 -10      vol=3688.060252
    media  1 1 30 -20 -10  vol=5327.198142
    boundary  30
END GEOM
END DATA
END

Sample Problem 15 SMALL WATER REFLECTED SPHERE ON PLEXIGLAS COLLAR

This critical experiment [BKH+77] is a small highly enriched uranium sphere supported by a Plexiglas doughnut in a tank of water. The sphere extends down through the hole of the doughnut. However, the KENO geometry package cannot rigorously describe a doughnut (torus) with either KENO V.a or KENO-VI. Therefore, the KENO mockup of this problem describes the doughnut as an annular cylindrical plate and the sphere is supported by it. Both are contained in a cylindrical tank of water. A drawing of the experiment is given in Fig. 265. This drawing shows the sphere above the cylindrical collar for the sake of clarity. The sphere is actually supported by the collar and extends into the opening in its center. The actual experiment utilized a torus or doughnut instead of a cylindrical collar.

_images/fig68.png

Fig. 265 Drawing of a critical assembly consisting of a uranium sphere on a Plexiglas collar with a cylindrical water reflector.

Input Data

KENO V.a

=KENOVA
sample problem 15  small water reflected sphere on plexiglas collar
READ PARAM
  lib=4  flx=yes fdn=yes
END PARAM
READ MIXT
  sct=2
  mix=1
     4092234 5.27115e-04  4092235 4.70308e-02  4092236 1.00692e-04 4092238 4.89708e-04
  mix=2
    11001001 5.67873e-02  11006000 3.54921e-02  11008016 1.41968e-02
  mix=3
    12001001 6.67554e-02
  mix=3
    12008016 3.33757e-02
END MIXT
READ GEOM
  unit 1
    hemisphe-z 1 1 6.5537 chord -5.09066
    cylinder  3 1 4.1275 -5.09066 -7.63065
    cylinder  2 1 12.7   -5.09066 -7.63065
    cuboid  3 1 4p12.7 -5.09066 -7.63065
  unit 2
    hemisphe+z 1 1 6.5537 chord 5.09066
    cuboid  3 1 4p12.7 6.5537 -5.09066
  global unit 3
    array     1 -12.7 -12.7 -7.092175
    cylinder  3 1 17.97 2p7.0922
    replicate 3 2 3*3.0 5
END GEOM
READ BIAS
  id=500 2 6
END BIAS
READ ARRAY
  nux=1 nuy=1 nuz=2  fill 1 2 end fill
END ARRAY
READ PLOT
  scr=yes lpi=10
  ttl='x-z slice through the center of the sphere'
  xul=-20.0 zul=10.0 yul=0.0  xlr=20.0 ylr=0.0 zlr=-10.0
  uax=1.0 wdn=-1.0 nax=400
END PLOT
END DATA
END

KENO-VI

=KENOVI
sample problem 15  small water reflected sphere on plexiglas collar
READ PARAM
  lib=4 flx=yes fdn=yes plt=yes
END PARAM
READ MIXT
  sct=2
  mix=1  4092234 5.27115e-04   4092235 4.70308e-02   4092236 1.00692e-04
         4092238 4.89708e-04
  mix=2 11001001 5.67873e-02  11006000 3.54921e-02  11008016 1.41968e-02
  mix=3 12001001 6.67515e-02
  mix=3 12008016 3.33757e-02
END MIXT
READ GEOM
  global unit 1
    sphere   10  6.5537
    cylinder 20  4.1275 -5.09066 -7.63065
    cylinder 30  12.7   -5.09066 -7.63065
    cylinder 40  21.5537 21.5537 -21.5537
    media  1 1 10  vol=1179.093598091
    media  3 1 20 -10  vol=95.1516
    media  2 1 30 -20 -10  vol=1151.089182028
    media  3 1 40 -30 -20 -10  vol=60488.221616778
    boundary  40
END GEOM
READ PLOT
  scr=yes  lpi=10
  ttl='x-z slice through the center of the sphere'
  xul=-20.0 zul=10.0 yul=0.0  xlr=20.0 ylr=0.0 zlr=-10.0
  uax=1.0 wdn=-1.0 nax=400
END PLOT
END DATA
END

Sample Problem 16 UO2F2 INFINITE SLAB K-INFINITY

This problem solves for the k-infinity of an infinite number of slabs of uranyl fluoride solution contained in Pyrex glass and separated by borated uranyl fluoride solution. The uranyl fluoride slab is 4.958 cm thick, 93.2% enriched, and has a density of 578.7 g U/l. The Pyrex glass is 1.27 cm thick and is present on both faces of the uranyl fluoride solution. A total of 27.46 cm of borated solution separates the Pyrex glass of adjacent slabs of solution. 1.482 × 10–27 atoms of boron per milliliter are present in the borated solution.

Input Data

KENO V.a

=KENOVA
sample problem 16 uo2f2 infinite slab k-infinity
READ PARAMETERS
  lib=4  amx=yes xap=no
END PARAMETERS
READ MIXT
  sct=2
  mix=1
    5009019 2.96287e-03  5001001 6.08125e-02  5008016 3.33691e-02  5092235 1.38188e-03  5092238 9.95505e-05
  mix=2
   13011023 2.39503e-03 13013027 4.97720e-04 13014028 1.66260E-02 13014029 8.41845E-04 13014030 5.58826E-04 13005010 9.14627e-04 13005011 3.68149e-03 13008016 4.49174e-02  mix=3
    6009019 2.96287e-03  6001001 6.08125e-02  6008016 3.33691e-02  6092235 1.38188e-03  6092238 9.95505e-05  6005010 2.94862e-04  6005011 1.18686e-03
END MIXT
READ GEOMETRY
  global unit 1
    cuboid 1 1 2.479 -2.479 100 -100 100 -100
    cuboid 2 1 3.749 -3.749 100 -100 100 -100
    cuboid 3 1 17.479 -17.479 100 -100 100 -100
END GEOM
READ BOUNDS
  all=mirror
END BOUNDS
END DATA
END

KENO-VI

=KENOVI
sample problem 16 uo2f2 infinite slab k-infinity
READ PARAMETERS
  lib=4 amx=yes xap=no
END PARAMETERS
READ MIXT
  sct=2
  mix=1  5009019 2.96287e-03  5001001 6.08125e-02  5008016 3.33691e-02
         5092235 1.38188e-03  5092238 9.95505e-05
  mix=2 13011023 2.39503e-03 13013027 4.97720e-04 13014028 1.66260E-02
        13014029  8.41845E-04 13014030 5.58826E-04
        13005010 9.14627e-04 13005011 3.68149e-03 13008016 4.49174e-02
  mix=3  6009019 2.96287e-03  6001001 6.08125e-02  6008016 3.33691e-02
         6092235 1.38188e-03  6092238 9.95505e-05
         6005010 2.94862e-04  6005011 1.18686e-03
END MIXT
READ GEOMETRY
  global unit 1
    cuboid 10  2.479 -2.479 100.0 -100.0 100.0 -100.0
    cuboid 20  3.749 -3.749 100.0 -100.0 100.0 -100.0
    cuboid 30  17.479 -17.479 100.0 -100.0 100.0 -100.0
    media 1 1 10
    media 2 1 20 -10
    media 3 1 30 -20 -10
    boundary  30
END GEOM
READ BOUNDS
  all=mirror
END BOUNDS
READ VOLUME
  type=trace  iface=xface
END VOLUME
END DATA
END

Sample Problem 17 93% UO2F2 SOLUTION SPHERE ADJOINT CALCULATION

A single 93% enriched uranyl fluoride sphere is run as an adjoint calculation. The result for the forward and adjoint k-effectives should be the same within statistical error when the problem is run both ways.

Input Data

KENO V.a

=KENOVA
sample problem 17 93% uo2f2 solution sphere  adjoint calculation
READ PARAMETERS
  lib=4  npg=10000 nbk=10500 adj=yes amx=yes xap=no
END PARAMETERS
READ MIXT
  sct=2
  mix=1
    7001001 6.55892e-02 7008016 3.34755e-02 7009019 6.80925e-04 7092235 3.16910e-04 7092238 2.35522e-05
END MIXT
READ GEOMETRY
  global unit 1
    sphere 1 1 16.0
END GEOM
END DATA
END

KENO-VI

=KENOVI
sample problem 17 93% uo2f2 solution sphere  adjoint calculation
READ PARAMETERS
  lib=4 amx=yes pwt=yes xap=no adj=yes npg=10000 nbk=10500
END PARAMETERS
READ MIXT
  sct=2
  mix=1  7001001 6.55892e-02  7008016 3.34755e-02  7009019 6.80925e-04
         7092235 3.16910e-04  7092238 2.35522e-05
END MIXT
READ GEOMETRY
  global unit 1
    sphere 10 16.0
    media 1 1 10  vol=17157.284678
    boundary  10
END GEOM
END DATA
END

Sample Problem 18 1F27 DEMONSTRATION OF OPTIONS

A reflected cubic array of 27 cylinders of aqueous uranyl nitrate in Plexiglas bottles [Tho64]. The walls of the bottles were 0.64-cm thick, and each bottle was filled with 5 liters of 92.6% enriched solution at a concentration of 415 g/L, a specific gravity of 1.555 and 0.39 mg excess nitrate/g soln (From experimental facility documents. Not reported in ORNL/TM-719.) The 3 × 3 × 3 array was surrounded by a 6-in. paraffin reflector. Most of the print options available in KENO are exercised in this problem. A perspective of this critical experiment is shown in Fig. 266. A photograph of one of the experiments utilized 27 of the Plexiglas bottles is shown in Fig. 267. Sample problem 18 has 15.24 cm of paraffin on all six faces rather than the 2.54-cm Plexiglas shown on five faces.

_images/fig76.png

Fig. 266 Perspective of critical 1F27 experiment.

_images/fig84.png

Fig. 267 View of a 27-unit array with 2.54-cm. thick Plexiglas reflector on five sides and a 15.24-cm. thick paraffin base.

Input Data

KENO V.a

=KENOVA
sample problem 18   1f27 demonstration of options problem
READ PARA   gen=103 npg=500 fdn=yes nub=yes lib=4
  mku=yes fmu=yes mkh=yes fmh=yes mka=yes fma=yes rnd=f12c09ed2195
  pwt=yes far=yes flx=yes amx=yes pax=yes pgm=yes
END PARA
READ MIXT
  sct=2
  mix=1
     2001001 5.77931e-02   2007014 2.13092e-03   2008016 3.74114e-02
     2092234 1.06784e-05   2092235 9.84602e-04   2092236 5.29386e-06
     2092238 6.19414e-05
  mix=2
    11001001 5.67873e-02  11006000 3.54921e-02  11008016 1.41968e-02
  mix=3
    10006000 3.84193e-02  10001901 7.99120e-02
  mix=4
    15008016 3.33757e-11  15001001 6.67515e-11
 END MIXT
READ BOUNDS
  -zb= h2o
END BOUNDS
READ GEOM
  unit 1
    cylinder 1 1 9.52 8.7804 -8.7804
    cylinder 0 1 9.52 8.9896 -8.7804
    cylinder 2 1 10.16 9.6296 -9.4204
    cuboid 4 1 18.45 -18.45 18.45 -18.45 17.8946 -17.6854
  unit 2
    array 1 3*0.0
  unit 3
    array 2 3*0.0
  unit 4
    array 3 3*0.0
  unit 5
    array 4 3*0.0
  global
  unit 6
    cuboid 4 1 55.3501 -55.3501 55.3501 -55.3501 53.3701 -53.3701
     hole 2 -55.35   -18.45   -17.79
     hole 3 -55.35   -18.45   -53.3701
     hole 4  18.4501 -18.45   -53.3701
     hole 5 -55.3501 -55.3501 -53.3701
    replicate 3 2 6*3 5
    replicate 3 7 6*0.24 1
END GEOM
READ BIAS
  id=400 2 7
END BIAS
READ ARRAY
  ara=1 nux=2 nuy=2 nuz=2 fill f1 end fill
  ara=2 nux=2 nuy=2 nuz=1 fill f1 end fill
  ara=3 nux=1 nuy=2 nuz=3 fill f1 end fill
  ara=4 nux=3 nuy=1 nuz=3 fill f1 end fill
END ARRAY
READ START
  nst=6 tfx=0.0 tfy=0.0 tfz=0.0
  lnu=500 ps6=yes
END START
READ PLOT
  scr=yes  plt=yes lpi=10
  ttl=?  1f27 xy plot at z=0.0 ?
  xul=-71.0 yul= 71.0 zul=0.0
  xlr= 71.0 ylr=-71.0 zlr=0.0
  uax=1     vdn=-1    nax=400
  run=yes
  end plt1
  ttl=?unit map 1f27 xy plot at z=0.0?
  pic=unit
END PLOT
END DATA
END

KENO-VI

=KENOVI
sample problem 18   1f27  critical experiment
READ PARA
  gen=103 npg=500 fdn=yes nub=yes lib=4 plt=yes
  mku=yes cku=yes fmu=yes fmh=yes mka=yes cka=yes fma=yes pwt=yes
  far=yes flx=yes amx=yes pax=yes pgm=yes rnd=f12c09ed2195
END PARA
READ MIXT
  sct=2
  mix=1  2001001 5.77931e-02   2007014 2.13092e-03   2008016 3.74114e-02
         2092234 1.06784e-05   2092235 9.84602e-04   2092236 5.29386e-06
         2092238 6.19414e-05
  mix=2 11001001 5.67873e-02  11006000 3.54921e-02  11008016 1.41968e-02
  mix=3 10006000 3.84193e-02  10001901 7.99120e-02
  mix=4 15008016 3.33757e-11  15001001 6.67515e-11
END MIXT
READ BOUNDS
  -zb=h2o
END BOUNDS
READ GEOM
  unit 1
    cylinder 10  9.52 8.7804 -8.7804
    cylinder 20  9.52 8.9896 -8.7804
    cylinder 30  10.16 9.6296 -9.4204
    cuboid   40  18.45 -18.45 18.45 -18.45 17.8946 -17.6854
    media 1 1 10
    media 0 1 -10 20
    media 2 1 -10 -20 30
    media 0 1 40 -20 -30
    boundary  40
  unit 2
    cuboid 10  18.45 -55.35  55.35 -18.45  53.37 -17.79
    cuboid 20  18.45 -55.35  55.35 -18.45 -17.79 -53.37
    cuboid 30  55.35  18.45  55.35 -18.45  53.37 -53.37
    cuboid 40  55.35 -55.35 -18.45 -55.35  53.37 -53.37
    cuboid 50  55.35 -55.35  55.35 -55.35  53.37 -53.37
    array  1 10 place 1 1 1 -36.90 0.0 -0.1046
    array  2 20 -10 place 1 1 1 -36.90 0.0 -35.6846
    array  3 30 -20 -10 place 1 1 1 36.90 0.0 -35.6846
    array  4 40 -30 -20 -10 place 1 1 1 -36.90 -36.90 -35.6846
    media 0 1 50 -40 -30 -20 -10
    boundary  50
  global unit 3
    cuboid 10  55.35 -55.35 55.35 -55.35 53.37 -53.37
    cuboid 20  58.35 -58.35 58.35 -58.35 56.37 -56.37
    cuboid 30  61.35 -61.35 61.35 -61.35 59.37 -59.37
    cuboid 40  64.35 -64.35 64.35 -64.35 62.37 -62.37
    cuboid 50  67.35 -67.35 67.35 -67.35 65.37 -65.37
    cuboid 60  70.59 -70.59 70.59 -70.59 68.61 -68.61
    array 5 10 place 1 1 1 3*0.0
    media 3 2 -10 20
    media 3 3 -20 30
    media 3 4 -30 40
    media 3 5 -40 50
    media 3 6 60 -50
    boundary  60
 END GEOM
READ BIAS
  id=400 2 6
END BIAS
READ VOLUME
  type=random
END VOLUME
READ ARRAY
  ara=1 nux=2 nuy=2 nuz=2 fill f1 end fill
  ara=2 nux=2 nuy=2 nuz=1 fill f1 end fill
  ara=3 nux=1 nuy=2 nuz=3 fill f1 end fill
  ara=4 nux=3 nuy=1 nuz=3 fill f1 end fill
  gbl=5 ara=5 nux=1 nuy=1 nuz=1 fill f2 end fill
END ARRAY
READ PLOT
  scr=yes lpi=10
  ttl='  1f27 xy plot at z=0.0 '
  xul=-71.0 yul=71.0 zul=0.0 xlr=71.0 ylr=-71.0 zlr=0.0
  uax=1 vdn=-1 nax=400 end plt0
  ttl='unit map 1f27 xy plot at z=0.0'
  pic=unit
END PLOT
END DATA
END

Sample Problem 19 4 AQUEOUS 4 METAL ARRAY OF ARRAYS (SAMP PROB 12)

This critical experiment was described previously as SAMPLE PROBLEM 12. The input data given below utilize the array of arrays option. See Fig. 262.

Input Data

KENO V.a

=KENOVA
sample problem 19 4 aqueous 4 metal array of arrays (samp prob 12)
READ PARAM
  lib=4  flx=yes fdn=yes nub=yes smu=yes mkp=yes
  mku=yes fmp=yes fmu=yes
END PARAM
READ MIXT
  mix=1
    1092234 4.82717e-04  1092235 4.47971e-02  1092236 9.57233e-05  1092238 2.65767e-03
  mix=2
    2001001 5.77931e-02   2007014 2.13092e-03   2008016 3.74114e-02
    2092234 1.06784e-05   2092235 9.84602e-04   2092236 5.29386e-06
    2092238 6.19414e-05
  mix=3
   11001001 5.67873e-02  11006000 3.54921e-02  11008016 1.41968e-02
  sct=2
END MIXT
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
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

KENO-VI

=KENOVI
sample problem 19 4 aqueous 4 metal array of arrays (samp prob 12)
READ PARAM
  lib=4 flx=yes fdn=yes nub=yes smu=yes mkp=yes mku=yes fmp=yes fmu=yes
END PARAM
READ MIXT
  sct=2
  mix=1  1092234 4.82717e-04 1092235 4.47971e-02 1092236 9.57233e-05
         1092238 2.65767e-03
  mix=2  2001001 5.77931e-02   2007014 2.13092e-03   2008016 3.74114e-02
         2092234 1.06784e-05   2092235 9.84602e-04   2092236 5.29386e-06
         2092238 6.19414e-05
  mix=3 11001001 5.67873e-02  11006000 3.54921e-02  11008016 1.41968e-02
END MIXT
READ GEOMETRY
  unit 1
    com='uranyl nitrate solution in a plexiglas container'
    cylinder 10   9.525 2p8.89
    cylinder 20   10.16 2p9.525
    cuboid   30  4p10.875 2p10.24
    media 2 1 10      vol=20270.83270
    media 3 1 -10 20  vol=4440.27764
    media 0 1 30 -20  vol=14042.16966
    boundary  30
  unit 2
    com='uranium metal cylinder'
    cylinder 10  5.748 2p5.3825
    cuboid   20 4p6.59 2p6.225
    media 1 1 10      vol=4469.48431
    media 0 1 20 -10  vol=4181.39321
    boundary  20
  unit 3
    com='1x2x2 array of solution units'
    cuboid 10  21.75 0.0 43.5 0.0 40.96 0.0
    array 1 +10 place 1 1 1 10.875 10.875 10.240
    boundary  10
  unit 4
    com='1x2x2 array of metal units padded to match solution array'
    cuboid 10  13.18 0.0 26.36 0.0 24.9 0.0
    cuboid 20  13.18 0.0 34.93 -8.57 32.93 -8.03
    array 2 +10 place 1 1 1 6.59 6.59 6.225
    media 0 1 20 -10  vol=14830.750188
    boundary  20
  global unit 5
    com='global unit of arrays 1 and 2'
    cuboid 10 34.93 0.0 43.5 0.0 40.96 0.0
    array 3 +10 place 1 1 1 0 8.57 8.03
    boundary  10
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 20 TRIANGULAR PITCHED ARRAY

This problem is a critical experiment14 consisting of seven cylinders in a triangular-pitched unreflected array. The central cylinder has six cylinders arranged around it. The surface-to-surface separation between the units is 0.15 in. Each unit consists of a 60-mil-thick aluminum can with an 8-in. inside diameter, filled with a solution of 93.2% enriched uranyl fluoride with a H/235U atomic ratio of 44.3 and a density of 576.87 g U/L. The apparatus for conducting this experiment is shown in Fig. 268.

_images/fig95.png

Fig. 268 Typical arrangement for critical experiments with interacting arrays of aluminum cylinders containing enriched 235U solutions.

Input Data

KENO V.a

=KENOVA
sample problem 20 triangular pitched array
READ PARAM
  lib=4
END PARAM
READ MIXT
  sct=2
  mix=1
    8092235 1.37751e-03 8092238 9.92357e-05 8008016 3.33717e-02 8009019 2.95350e-03  8001001 6.08364e-02
  mix=2
   14013027 6.03067e-02
END MIXT
READ GEOM
  unit 1
    cylinder   1 1 10.16 18.288 0
    cylinder   2 1 10.312 18.288 -.152
  unit 2
    cuboid     0 1 4p50 50 -.152
    hole       1 3r0
    hole       1 21.006 2r0
    hole       1 -21.006 2r0
    hole       1 10.503 18.192 0
    hole       1 -10.503 18.192 0
    hole       1 10.503 -18.192 0
    hole       1 -10.503 -18.192 0
END GEOM
READ ARRAY
  gbl=1 nux=1 nuy=1 nuz=1 fill 2 end fill
END ARRAY
READ PLOT
  ttl='hex array' pic=mix lpi=10 scr=yes
  xul=0   yul=100 zul=10
  xlr=100 ylr=0   zlr=10
  uax=1   vdn=-1  nax=400
END PLOT
END DATA
END

KENO-VI

=KENOVI
sample problem 20  triangular pitched array 7 pins in a circle
READ PARAMETERS
  lib=4
END PARAMETERS
READ MIXT
  sct=2
  mix=1  8092235 1.37751e-03  8092238 9.92357e-05  8008016 3.33717e-02
         8009019 2.95350e-03  8001001 6.08364e-02
  mix=2 14013027 6.03067e-02
END MIXT
READ GEOMETRY
  unit 1
    com='single cell fuel can in hexprism'
    cylinder 10  10.16  18.288  0.0
    cylinder 20  10.312 18.288 -0.152
    hexprism 30  10.503 18.288 -0.152
    media  1 1 10      vol=41514.66537
    media  2 1 20 -10  vol=1606.91193
    media 0 1 30 -20   vol=6204.469507
    boundary  30
  unit 2
    com='empty cell'
    hexprism 10  10.503 18.288 -0.152
    media  0 1 10  vol=8155.956715
    boundary  10
  global unit 3
    cylinder 10  31.500 18.288 -0.152
    com='7 cylinders in a circle with cylindrical boundary'
    array  1 10 place 3 3 1 3*0.0
    boundary  10
END GEOMETRY
READ ARRAY
  ara=1 typ=triangular nux=5 nuy=5 nuz=1
  fill 7*2 2*1 2*2 3*1 2*2 2*1 7*2 end fill
END ARRAY
END DATA
END

Sample Problem 21 PARTIALLY FILLED SPHERE

This critical experiment consisted of a partially filled, unreflected spherical container. This aluminum container had an inside diameter of 27.244 in. and a wall thickness of 1/16 in. It is referred to in the report as the 27.3-in.-diameter vessel. The sphere was 98% filled with uranyl fluoride at an enrichment of 4.89% with an H/235U atomic ratio of 1099. The height of the solution in the sphere was 64.6 cm above the bottom of the sphere. A schematic diagram of the apparatus used in the experiment is given in Fig. 269. The steel tank was ignored.

Input Data

KENO V.a

=KENOVA
sample problem 21  partially filled sphere
READ PARAM
  lib=4
END PARAM
READ GEOM
  global unit 1
    hemisphe-z  1 1 34.6   chord 30.
    sphere      0 1 34.6
    sphere      2 1 34.759
END GEOM
READ MIXT
  sct=2
  mix=1
    9001001 6.19770e-02  9008016 3.34895e-02  9009019 2.50098e-03
    9092234 2.54224e-07  9092235 6.18924e-05  9092238 1.18835e-03
  mix=2
   14013027 6.03067e-02
END MIXT
END DATA
END

KENO-VI

=KENOVI
sample problem 21  partially filled sphere
READ PARAM
  lib=4
END PARAM
READ MIXT
  sct=2
  mix=1  9001001 6.19770e-02  9008016 3.34895e-02  9009019 2.50098e-03
         9092234 2.54224e-07  9092235 6.18924e-05  9092238 1.18835e-03
  mix=2 14013027 6.03067e-02
END MIXT
READ GEOM
  global unit 1
    sphere 10 34.6  chord -z=30.0
    sphere 20 34.6
    sphere 30 34.759
    media 1 1 10  vol=171309.
    media 0 1 20 -10  vol=2198.14
    media 2 1 30 -20 -10  vol=2403.00
    boundary  30
END GEOM
END DATA
END
_images/fig1012.png

Fig. 269 Schematic of bare partially filled sphere experiment inside a 9.5-ft-diameter, 9-ft-high steel tank.

Sample Problem 22 CASE 2C8 BARE WITH 3 NESTED HOLES, EACH IS EQUAL VOLUME

The physical representation of this sample problem is the critical experiment described in sample problem 1. It is a simple 2 × 2 × 2 array of 93.2% wt enriched uranium metal cylinders. This sample problem defines a uranium cylinder in a void spacing cuboid using nested holes. Eight of these units are stacked together in a 2 × 2 × 2 array.

Input Data

KENO V.a

=KENOVA
sample problem 22   case 2c8 bare with 3 nested, equal volume holes
READ PARAMETERS
  flx=yes fdn=yes far=yes gas=no lib=4
END PARAMETERS
READ MIXT
  sct=2
  mix=1
    1092234 4.82717e-04 1092235 4.47971e-02 1092236 9.57233e-05 1092238 2.65767e-03
END MIXT
READ GEOMETRY

  unit 1
    cylinder 1 1 3.621 2p3.3907

  unit 2
    cylinder 1 1 4.5622 2p4.2721
    hole 1 3*0.0

  unit 3
    cylinder 1 1 5.2224 2p4.8903
    hole 2 3*0.0

  unit 4
    cylinder 1 1 5.748 5.3825 -5.3825
    hole 3 3*0.0
    cuboid  0 1 6.87 -6.87 6.87 -6.87 6.505 -6.505

END GEOMETRY
READ ARRAY
  nux=2 nuy=2 nuz=2 fill f4 end fill
END ARRAY
END DATA
END

KENO-VI

=KENOVI
sample problem 22  case 2c8 bare with 3 nested, equal volume holes
READ PARAMETERS
  flx=yes fdn=yes far=yes gas=no lib=4 mkh=yes ckh=yes fmh=yes
END PARAMETERS
READ MIXT
  sct=2
  mix=1 1092234 4.82717e-04 1092235 4.47971e-02 1092236 9.57233e-05
        1092238 2.65767e-03
END MIXT
READ GEOMETRY
  unit 1
    cylinder 10 3.621 2p3.3907
    media 1 1 10  vol=279.335597542
    boundary  10
  unit 2
    cylinder 20 4.5622 2p4.2721
    hole 1
    media 1 1 20  vol=279.353142545
    boundary 20
  unit 3
    cylinder 20 5.2224 2p4.8903
    hole 2
    media 1 1 20  vol=279.333676489
    boundary  20
  unit 4
    cylinder 20  5.748 2p5.3825
    cuboid   30 6.87 -6.87 6.87 -6.87 6.505 -6.505
    hole 3
    media 1 1 20  vol=279.34866089
    media 0 1 30 -20  vol=1338.755598534
    boundary  30
  global unit 5
    cuboid 10 20.61 -6.87 20.61 -6.87 19.515 -6.505
    array 1 10 place 1 1 1 3*0.0
    boundary  10
END GEOMETRY
READ ARRAY
  ara=1 nux=2 nuy=2 nuz=2 fill f4 end fill
END ARRAY
END DATA
END

Sample Problem 23 CASE 2C8 BARE AS STACKED CYLINDERS

The physical representation of this sample problem is the critical experiment described in sample problem 1. This sample problem describes each of the eight units in the critical 2 × 2 × 2 array using Z hemicylinders (in KENO V.a) or hemicylinders with different chord sizes and directions (in KENO‑VI).

Input Data

KENO V.a

=KENOVA
sample problem 23  case 2c8 bare as mixed zhemicylinders
READ PARAMETERS
  fdn=yes lib=4
END PARAMETERS
READ MIXT
  sct=2
  mix=1
    1092234 4.82717e-04 1092235 4.47971e-02 1092236 9.57233e-05 1092238 2.65767e-03
END MIXT
READ GEOMETRY
  unit 1
    com='-x half of unit 3'
    zhemicyl-x 1 1 5.748 5.3825 -5.3825
    cuboid  0 1 0.0  -6.87 6.87 -6.87 6.505 -6.505
  unit 2
    com='+x half of unit 3'
    zhemicyl+x 1 1 5.748 5.3825 -5.3825
    cuboid  0 1 6.87  0.0  6.87 -6.87 6.505 -6.505
  unit 3
    com='cylinder composed of equal halves (zhemicylinders with x radii)'
    array 1 3*0.0
  unit 4
    com='-x portion (more than half) of unit 6'
    zhemicyl-x 1 1 5.748 5.3825 -5.3825 chord 3.0
    cuboid  0 1 3.0  -6.87 6.87 -6.87 6.505 -6.505
  unit 5
    com='+x portion (less than half) of unit 6'
    zhemicyl+x 1 1 5.748 5.3825 -5.3825 chord -3.0
    cuboid  0 1 6.87  3.0  6.87 -6.87 6.505 -6.505
  unit 6
    com='cylinder composed of unequal halves (zhemicylinders with x radii)'
    array 2 3*0.0
  unit 7
    com='cylinder of a single zhemicylinder in the -x direction'
    zhemicyl-x 1 1 5.748 5.3825 -5.3825 chord 5.748
    cuboid  0 1 6.87 -6.87 6.87 -6.87 6.505 -6.505
  unit 8
    com='cylinder of a single zhemicylinder in the +x direction'
    zhemicyl+x 1 1 5.748 5.3825 -5.3825 chord 5.748
    cuboid  0 1 6.87 -6.87 6.87 -6.87 6.505 -6.505
  unit 9
    com='-y half of unit 11'
    zhemicyl-y 1 1 5.748 5.3825 -5.3825
    cuboid  0 1 6.87 -6.87 0.0  -6.87 6.505 -6.505
  unit 10
    com='+y half of unit 11'
    zhemicyl+y 1 1 5.748 5.3825 -5.3825
    cuboid  0 1 6.87 -6.87 6.87  0.0  6.505 -6.505
  unit 11
    com='cylinder composed of equal halves (zhemicylinders with z radii)'
    array 3 3*0.0
  unit 12
    com='-y portion (more than half) of unit 14'
    zhemicyl-y 1 1 5.748 5.3825 -5.3825 chord 3.0
    cuboid  0 1 6.87 -6.87 3.0  -6.87 6.505 -6.505
  unit 13
    com='+y portion (less than half) of unit 14'
    zhemicyl+y 1 1 5.748 5.3825 -5.3825 chord -3.0
    cuboid  0 1 6.87 -6.87 6.87  3.0  6.505 -6.505
  unit 14
    com='cylinder composed of unequal halves (zhemicylinders with z radii)'
    array 4 3*0.0
  unit 15
    com='cylinder of a single zhemicylinder in the -y direction'
    zhemicyl-y 1 1 5.748 5.3825 -5.3825 chord 5.748
    cuboid  0 1 6.87 -6.87 6.87 -6.87 6.505 -6.505
  unit 16
    com='cylinder of a single zhemicylinder in the +y'
    zhemicyl+y 1 1 5.748 5.3825 -5.3825 chord 5.748
    cuboid  0 1 6.87 -6.87 6.87 -6.87 6.505 -6.505
END GEOMETRY
READ ARRAY
  com='array 1 defines unit 3 (zhemicylinders with x radii)'
  ara=1 nux=2 nuy=1 nuz=1 fill 1 2 end fill
  com='array 2 defines unit 6 (zhemicylinders with x radii)'
  ara=2 nux=2 nuy=1 nuz=1 fill 4 5 end fill
  com='array 3 defines unit 11 (zhemicylinders with y radii)'
  ara=3 nux=1 nuy=2 nuz=1 fill 9 10 end fill
  com='array 4 defines unit 14 (zhemicylinders with y radii)'
  ara=4 nux=1 nuy=2 nuz=1 fill 12 13 end fill
  com='array 5 defines the total 2c8 problem'
  gbl=5 ara=5 nux=2 nuy=2 nuz=2 fill 3 7 6 8 11 15 14 16 end fill
END ARRAY
END DATA
END

KENO-VI

=KENOVI
sample problem 23  case 2c8 bare as mixed unrotated zcylinders
READ PARAMETERS
  fdn=yes lib=4
END PARAMETERS
READ MIXT
  sct=2
  mix=1 1092234 4.82717e-04 1092235 4.47971e-02 1092236 9.57233e-05
        1092238 2.65767e-03
END MIXT
READ GEOMETRY
  unit 1
    com='-x half of unit 3'
    cylinder 10 5.748 5.3825 -5.3825 chord -x=0.0
    cuboid   20 0.0 -6.87 6.87 -6.87 6.505 -6.505
    media 1 1 10     vol=2234.742156
    media 0 1 20 -10 vol=2677.511196
    boundary  20
  unit 2
    com='+x half of unit 3'
    cylinder 10 5.748 5.3825 -5.3825 chord +x=0.0
    cuboid   20 6.87 0.0 6.87 -6.87 6.505 -6.505
    media 1 1 10     vol=2234.742156
    media 0 1 20 -10 vol=2677.511196
    boundary  20
  unit 3
    com='cylinder composed of equal halves (zhemicylinders with x radii)'
    cuboid 10 6.87 -6.87 6.87 -6.87 6.505 -6.505
    array 1 10 place 1 1 1 0.0 0.0 0.0
    boundary  10
  unit 4
    com='-x portion (more than half) of unit 6'
    cylinder 10 5.748 5.3825 -5.3825 chord -x=3.0
    cuboid   20 3.0 -6.87 6.87 -6.87 6.505 -6.505
    media 1 1 10     vol=2234.742156
    media 0 1 20 -10 vol=2677.511196
    boundary  20
  unit 5
    com='+x portion (less than half) of unit 6'
    cylinder 10 5.748 5.3825 -5.3825 chord +x=3.0
    cuboid   20 6.87 3.0 6.87 -6.87 6.505 -6.505
    media 1 1 10     vol=2234.742156
    media 0 1 20 -10 vol=2677.511196
    boundary  20
  unit 6
    com='cylinder composed of unequal halves (zhemicylinders with x radii)'
    cuboid 10 6.87 -6.87 6.87 -6.87 6.505 -6.505
    array 2 10 place 1 1 1 3*0.0
    boundary  10
  unit 7
    com='cylinder of a single zhemicylinder in the -x direction'
    cylinder 10 5.748 5.3825 -5.3825 chord -x=5.748
    cuboid   20 6.87 -6.87 6.87 -6.87 6.505 -6.505
    media 1 1 10     vol=2234.742156
    media 0 1 20 -10 vol=2677.511196
    boundary  20
  unit 8
    com='cylinder of a single zhemicylinder in the +x direction'
    cylinder 10 5.748 5.3825 -5.3825 chord +x=-5.748
    cuboid   20 6.87 -6.87 6.87 -6.87 6.505 -6.505
    media 1 1 10     vol=2234.742156
    media 0 1 20 -10 vol=2677.511196
    boundary  20
  unit 9
    com='-y half of unit 11'
    cylinder 10 5.748 5.3825 -5.3825 chord -y=0.0
    cuboid   20 6.87 -6.87 0.0 -6.87 6.505 -6.505
    media 1 1 10     vol=2234.742156
    media 0 1 20 -10 vol=2677.511196
    boundary  20
  unit 10
    com='+y half of unit 11'
    cylinder 10 5.748 5.3825 -5.3825 chord +y=0.0
    cuboid   20 6.87 -6.87 6.87 0.0 6.505 -6.505
    media 1 1 10     vol=2234.742156
    media 0 1 20 -10 vol=2677.511196
    boundary  20
  unit 11
    com='cylinder composed of equal halves (zhemicylinders with y radii)'
    cuboid 10 6.87 -6.87 6.87 -6.87 6.505 -6.505
    array 3 10 place 1 1 1 0.0 0.0 0.0
    boundary  10
  unit 12
    com='-y portion (more than half) of unit 14'
    cylinder 10 5.748 5.3825 -5.3825 chord -y=3.0
    cuboid   20 6.87 -6.87 3.0 -6.87 6.505 -6.505
    media 1 1 10     vol=2234.742156
    media 0 1 20 -10 vol=2677.511196
    boundary  20
  unit 13
    com='+y portion (less than half) of unit 14'
    cylinder 10 5.748 5.3825 -5.3825 chord +y=3.0
    cuboid   20 6.87 -6.87 6.87 3.0 6.505 -6.505
    media 1 1 10     vol=2234.742156
    media 0 1 20 -10 vol=2677.511196
    boundary  20
  unit 14
    com='cylinder composed of unequal halves (zhemicylinders with y radii)'
    cuboid 10 6.87 -6.87 6.87 -6.87 6.505 -6.505
    array 4 10 place 1 1 1 3*0.0
    boundary  10
  unit 15
    com='cylinder of a single zhemicylinder in the -y direction'
    cylinder 10 5.748 5.3825 -5.3825 chord -y=5.748
    cuboid   20 6.87 -6.87 6.87 -6.87 6.505 -6.505
    media 1 1 10     vol=2234.742156
    media 0 1 20 -10 vol=2677.511196
    boundary  20
  unit 16
    com='cylinder of a single zhemicylinder in the +y direction'
    cylinder 10 5.748 5.3825 -5.3825 chord +y=-5.748
    cuboid   20 6.87 -6.87 6.87 -6.87 6.505 -6.505
    media 1 1 10     vol=2234.742156
    media 0 1 20 -10 vol=2677.511196
    boundary  20
  global unit 17
    cuboid 10 13.74 -13.74 13.74 -13.74 13.010 -13.010
    array 5 10 place 1 1 1 -6.87 -6.87 -6.505
    boundary  10
END GEOMETRY
READ ARRAY
  com='array 1 defines unit 3 (zhemicylinders with x radii)'
  ara=1 nux=2 nuy=1 nuz=1 fill 1 2 end fill
  com='array 2 defines unit 6 (zhemicylinders with x radii)'
  ara=2 nux=2 nuy=1 nuz=1 fill 4 5 end fill
  com='array 3 defines unit 11 (zhemicylinders with y radii)'
  ara=3 nux=1 nuy=2 nuz=1 fill 9 10 end fill
  com='array 4 defines unit 14 (zhemicylinders with y radii)'
  ara=4 nuz=1 nuy=2 nuz=1 fill 12 13 end fill
  com='array 5 defines the total 2c8 problem'
  gbl=5 ara=5 nux=2 nuy=2 nuz=2 fill 3 7 6 8 11 15 14 16 end fill
END ARRAY
END DATA
END

Sample Problem 24 CASE 2C8 BARE AS STACKED ROTATED CYLINDERS

The physical representation of this sample problem is the critical experiment described in sample problem 1. This sample problem describes each of the eight units in the critical 2 × 2 × 2 array using hemicylinders whose axes are in the x direction. In KENO V.a this is realized using xhemicylinders, while in KENO-VI the hemycylinders with different chord sizes are rotated in the X-direction.

Input Data

KENO V.a

=KENOVA
sample problem 24  case 2c8 bare as mixed xhemicylinders
READ PARAMETERS
  fdn=yes lib=4
END PARAMETERS
READ MIXT
  sct=2
  mix=1
    1092234 4.82717e-04 1092235 4.47971e-02 1092236 9.57233e-05 1092238 2.65767e-03
END MIXT
READ GEOMETRY
  unit 1
    com='-y half of unit 3'
    xhemicyl-y 1 1 5.748 5.3825 -5.3825
    cuboid  0 1 6.505 -6.505 0.0 -6.87 6.87 -6.87
  unit 2
    com='+y half of unit 3'
    xhemicyl+y 1 1 5.748 5.3825 -5.3825
    cuboid  0 1 6.505 -6.505 6.87 0.0  6.87 -6.87
  unit 3
    com='cylinder composed of equal halves (xhemicylinders with y radii)'
    array 1 3*0.0
  unit 4
    com='-y portion (more than half) of unit 6'
    xhemicyl-y 1 1 5.748 5.3825 -5.3825 chord 3.0
    cuboid  0 1 6.505 -6.505 3.0 -6.87 6.87 -6.87
  unit 5
    com='+y portion (less than half) of unit 6'
    xhemicyl+y 1 1 5.748 5.3825 -5.3825 chord -3.0
    cuboid  0 1 6.505 -6.505 6.87 3.0  6.87 -6.87
  unit 6
    com='cylinder composed of unequal halves (xhemicylinders with y radii)'
    array 2 3*0.0
  unit 7
    com='cylinder of a single xhemicylinder in the -y direction'
    xhemicyl-y 1 1 5.748 5.3825 -5.3825 chord 5.748
    cuboid  0 1 6.505 -6.505 6.87 -6.87 6.87 -6.87
  unit 8
    com='cylinder of a single xhemicylinder in the +y direction'
    xhemicyl+y 1 1 5.748 5.3825 -5.3825 chord 5.748
    cuboid  0 1 6.505 -6.505 6.87 -6.87 6.87 -6.87
  unit 9
    com='-z half of unit 11'
    xhemicyl-z 1 1 5.748 5.3825 -5.3825
    cuboid  0 1 6.505 -6.505 6.87 -6.87 0.0 -6.87
  unit 10
    com='+z half of unit 11'
    xhemicyl+z 1 1 5.748 5.3825 -5.3825
    cuboid  0 1 6.505 -6.505 6.87 -6.87 6.87 0.0
  unit 11
    com='cylinder composed of equal halves (xhemicylinders with z radii)'
    array 3 3*0.0
  unit 12
    com='-z portion (more than half) of unit 14'
    xhemicyl-z 1 1 5.748 5.3825 -5.3825 chord 3.0
    cuboid  0 1 6.505 -6.505 6.87 -6.87 3.0 -6.87
  unit 13
    com='+z portion (less than half) of unit 14'
    xhemicyl+z 1 1 5.748 5.3825 -5.3825 chord -3.0
    cuboid  0 1 6.505 -6.505 6.87 -6.87 6.87 3.0
  unit 14
    com='cylinder composed of unequal halves (xhemicylinders with z radii)'
    array 4 3*0.0
  unit 15
    com='cylinder of a single xhemicylinder in the -z direction'
    xhemicyl-z 1 1 5.748 5.3825 -5.3825 chord 5.748
    cuboid  0 1 6.505 -6.505 6.87 -6.87 6.87 -6.87
  unit 16
    com='cylinder of a single xhemicylinder in the +z direction'
    xhemicyl+z 1 1 5.748 5.3825 -5.3825 chord 5.748
    cuboid  0 1 6.505 -6.505 6.87 -6.87 6.87 -6.87
END GEOMETRY
READ ARRAY
  com='array 1 defines unit 3 (xhemicylinders with y radii)'
  ara=1 nux=1 nuy=2 nuz=1 fill 1 2 end fill
  com='array 2 defines unit 6 (xhemicylinders with y radii)'
  ara=2 nux=1 nuy=2 nuz=1 fill 4 5 end fill
  com='array 3 defines unit 11 (xhemicylinders with z radii)'
  ara=3 nux=1 nuy=1 nuz=2 fill 9 10 end fill
  com='array 4 defines unit 14 (xhemicylinders with z radii)'
  ara=4 nux=1 nuy=1 nuz=2 fill 12 13 end fill
  com='array 5 defines the total 2c8 problem'
  gbl=5 ara=5 nux=2 nuy=2 nuz=2 fill 3 7 6 8 11 15 14 16 end fill
END ARRAY
END DATA
END

KENO-VI

=KENOVI
sample problem 24  case 2c8 bare as mixed x-rotated cylinders
READ PARAMETERS
  rnd=4c6a61962572 fdn=yes lib=4
END PARAMETERS
READ MIXT
  sct=2
  mix=1 1092234 4.82717e-04 1092235 4.47971e-02 1092236 9.57233e-05
        1092238 2.65767e-03
END MIXT
READ GEOMETRY
  unit 1
    com='-y half of unit 3'
    cylinder 10 5.748 5.3825 -5.3825 chord -x=0.0 rotate a1=90 a2=90
    cuboid   20 6.505 -6.505 0.0 -6.87 6.87 -6.87
    media 1 1 10     vol=2234.742156
    media 0 1 20 -10 vol=2677.511196
    boundary  20
  unit 2
    com='+y half of unit 3'
    cylinder 10 5.748 5.3825 -5.3825 chord +x=0.0 rotate a1=90 a2=90
    cuboid   20 6.505 -6.505 6.87 0.0 6.87 -6.87
    media 1 1 10     vol=2234.742156
    media 0 1 20 -10 vol=2677.511196
    boundary  20
  unit 3
    com='cylinder composed of equal halves (xhemicylinders with y radii)'
    cuboid 10 6.505 -6.505 6.87 -6.87 6.87 -6.87
    array 1 10 place 1 1 1 0.0 0.0 0.0
    boundary  10
  unit 4
    com='-y portion (more than half) of unit 6'
    cylinder 10 5.748 5.3825 -5.3825 chord -x=3.0 rotate a1=90 a2=90
    cuboid   20 6.505 -6.505 3.0 -6.87 6.87 -6.87
    media 1 1 10     vol=2234.742156
    media 0 1 20 -10 vol=2677.511196
    boundary  20
  unit 5
    com='+y portion (less than half) of unit 6'
    cylinder 10 5.748 5.3825 -5.3825 chord +x=3.0 rotate a1=90 a2=90
    cuboid   20 6.505 -6.505 6.87 3.0 6.87 -6.87
    media 1 1 10     vol=2234.742156
    media 0 1 20 -10 vol=2677.511196
    boundary  20
  unit 6
    com='cylinder composed of unequal halves (xhemicylinders with y radii)'
    cuboid 10 6.505 -6.505 6.87 -6.87 6.87 -6.87
    array 2 10 place 1 1 1 3*0.0
    boundary  10
  unit 7
    com='cylinder of a single xhemicylinder in the -y direction'
    cylinder 10 5.748 5.3825 -5.3825 chord -x=5.748 rotate a1=90 a2=90
    cuboid   20 6.505 -6.505 6.87 -6.87 6.87 -6.87
    media 1 1 10     vol=2234.742156
    media 0 1 20 -10 vol=2677.511196
    boundary  20
  unit 8
    com='cylinder of a single xhemicylinder in the +y direction'
    cylinder 10 5.748 5.3825 -5.3825 chord +x=-5.748 rotate a1=90 a2=90
    cuboid   20 6.505 -6.505 6.87 -6.87 6.87 -6.87
    media 1 1 10     vol=2234.742156
    media 0 1 20 -10 vol=2677.511196
    boundary  20
  unit 9
    com='-z half of unit 11'
    cylinder 10 5.748 5.3825 -5.3825 chord -y=0.0 rotate a1=90 a2=90
    cuboid   20 6.505 -6.505 6.87 -6.87 0.0 -6.87
    media 1 1 10     vol=2234.742156
    media 0 1 20 -10 vol=2677.511196
    boundary  20
  unit 10
    com='+z half of unit 11'
    cylinder 10 5.748 5.3825 -5.3825 chord +y=0.0 rotate a1=90 a2=90
    cuboid   20 6.505 -6.505 6.87 -6.87 6.87 0.0
    media 1 1 10     vol=2234.742156
    media 0 1 20 -10 vol=2677.511196
    boundary  20
  unit 11
    com='cylinder composed of equal halves (xhemicylinders with z radii)'
    cuboid 10 6.505 -6.505 6.87 -6.87 6.87 -6.87
    array 3 10 place 1 1 1 0.0 0.0 0.0
    boundary  10
  unit 12
    com='-z portion (more than half) of unit 14'
    cylinder 10 5.748 5.3825 -5.3825 chord -y=3.0 rotate a1=90 a2=90
    cuboid   20 6.505 -6.505 6.87 -6.87 3.0 -6.87
    media 1 1 10     vol=2234.742156
    media 0 1 20 -10 vol=2677.511196
    boundary  20
  unit 13
    com='+z portion (less than half) of unit 14'
    cylinder 10 5.748 5.3825 -5.3825 chord +y=3.0 rotate a1=90 a2=90
    cuboid   20 6.505 -6.505 6.87 -6.87 6.87 3.0
    media 1 1 10     vol=2234.742156
    media 0 1 20 -10 vol=2677.511196
    boundary  20
  unit 14
    com='cylinder composed of unequal halves (xhemicylinders with z radii)'
    cuboid 10 6.505 -6.505 6.87 -6.87 6.87 -6.87
    array 4 10 place 1 1 1 3*0.0
    boundary  10
  unit 15
    com='cylinder of a single xhemicylinder in the -z direction'
    cylinder 10 5.748 5.3825 -5.3825 chord -y=5.748 rotate a1=90 a2=90
    cuboid   20 6.505 -6.505 6.87 -6.87 6.87 -6.87
    media 1 1 10     vol=2234.742156
    media 0 1 20 -10 vol=2677.511196
    boundary  20
  unit 16
    com='cylinder of a single xhemicylinder in the +z direction'
    cylinder 10 5.748 5.3825 -5.3825 chord +y=-5.748 rotate a1=90 a2=90
    cuboid   20 6.505 -6.505 6.87 -6.87 6.87 -6.87
    media 1 1 10     vol=2234.742156
    media 0 1 20 -10 vol=2677.511196
    boundary  20
  global unit 17
    cuboid 10 13.01 -13.01 13.74 -13.74 13.74 -13.74
    array 5 10 place 1 1 1 -6.505 -6.87 -6.87
    boundary  10
END GEOMETRY
READ ARRAY
  com='array 1 defines unit 3 (xhemicylinders with y radii)'
  ara=1 nux=1 nuy=2 nuz=1 fill 1 2 end fill
  com='array 2 defines unit 6 (xhemicylinders with y radii)'
  ara=2 nux=1 nuy=2 nuz=1 fill 4 5 end fill
  com='array 3 defines unit 11 (xhemicylinders with z radii)'
  ara=3 nux=1 nuy=1 nuz=2 fill 9 10 end fill
  com='array 4 defines unit 14 (xhemicylinders with z radii)'
  ara=4 nux=1 nuy=1 nuz=2 fill 12 13 end fill
  com='array 5 defines the total 2c8 problem'
  ara=5 nux=2 nuy=2 nuz=2 fill 3 7 6 8 11 15 14 16 end fill
END ARRAY
END DATA
END

Sample Problem 25 CASE 2C8 BARE AS MIXED YHEMICYLINDERS

The physical representation of this sample problem is the critical experiment described in sample problem 1. This sample problem describes each of the eight units in the critical 2 × 2 × 2 array using hemicylinders whose axes are in the y direction. This is realized in KENO V.a by using yhemicylinders, while in KENO-VI it is realized using hemicylinders with different chord sizes and directions whose long axes are rotated in the Y-direction.

Input Data

KENO V.a

=KENOVA
sample problem 25  case 2c8 bare as mixed yhemicylinders
READ PARAMETERS
   fdn=yes lib=4
END PARAMETERS
READ MIXT
  sct=2
  mix=1
    1092234 4.82717e-04 1092235 4.47971e-02 1092236 9.57233e-05 1092238 2.65767e-03
END MIXT
READ GEOMETRY
  unit 1
    com='-x half of unit 3'
    yhemicyl-x 1 1 5.748 5.3825 -5.3825
    cuboid  0 1 0.0  -6.87 6.505 -6.505 6.87 -6.87
  unit 2
    com='+x half of unit 3'
    yhemicyl+x 1 1 5.748 5.3825 -5.3825
    cuboid  0 1 6.87  0.0  6.505 -6.505 6.87 -6.87
  unit 3
    com='cylinder composed of equal halves (yhemicylinders with x radii)'
    array 1 3*0.0
  unit 4
    com='-x portion (more than half) of unit 6'
    yhemicyl-x 1 1 5.748 5.3825 -5.3825 chord 3.0
    cuboid  0 1 3.0  -6.87 6.505 -6.505 6.87 -6.87
  unit 5
    com='+x portion (less than half) of unit 6'
    yhemicyl+x 1 1 5.748 5.3825 -5.3825 chord -3.0
    cuboid  0 1 6.87  3.0  6.505 -6.505 6.87 -6.87
  unit 6
    com='cylinder composed of unequal halves (yhemicylinders with x radii)'
    array 2 3*0.0
  unit 7
    com='cylinder of a single yhemicylinder in the -x direction'
    yhemicyl-x 1 1 5.748 5.3825 -5.3825 chord 5.748
    cuboid  0 1 6.87 -6.87 6.505 -6.505 6.87 -6.87
  unit 8
    com='cylinder of a single yhemicylinder in the +x direction'
    yhemicyl+x 1 1 5.748 5.3825 -5.3825 chord 5.748
    cuboid  0 1 6.87 -6.87 6.505 -6.505 6.87 -6.87
  unit 9
    com='-z half of unit 11'
    yhemicyl-z 1 1 5.748 5.3825 -5.3825
    cuboid  0 1 6.87 -6.87 6.505 -6.505 0.0 -6.87
  unit 10
    com='+z half of unit 11'
    yhemicyl+z 1 1 5.748 5.3825 -5.3825
    cuboid  0 1 6.87 -6.87 6.505 -6.505 6.87 0.0
  unit 11
    com='cylinder composed of equal halves (yhemicylinders with z radii)'
    array 3 3*0.0
  unit 12
    com='-z portion (more than half) of unit 14'
    yhemicyl-z 1 1 5.748 5.3825 -5.3825 chord 3.0
    cuboid  0 1 6.87 -6.87 6.505 -6.505 3.0 -6.87
  unit 13
    com='+z portion (less than half) of unit 14'
    yhemicyl+z 1 1 5.748 5.3825 -5.3825 chord -3.0
    cuboid  0 1 6.87 -6.87 6.505 -6.505 6.87 3.0
  unit 14
    com='cylinder composed of unequal halves (yhemicylinders with z radii)'
    array 4 3*0.0
  unit 15
    com='cylinder of a single  yhemicylinder in the -z direction'
    yhemicyl-z 1 1 5.748 5.3825 -5.3825 chord 5.748
    cuboid  0 1 6.87 -6.87 6.505 -6.505 6.87 -6.87
  unit 16
    com='cylinder of a single yhemicylinder in the +z direction'
    yhemicyl+z 1 1 5.748 5.3825 -5.3825 chord 5.748
    cuboid  0 1 6.87 -6.87 6.505 -6.505 6.87 -6.87
END GEOMETRY
READ ARRAY
  com='array 1 defines unit 3 (yhemicylinders with x radii)'
  ara=1 nux=2 nuy=1 nuz=1 fill 1 2 end fill
  com='array 2 defines unit 6 (yhemicylinders with x radii)'
  ara=2 nux=2 nuy=1 nuz=1 fill 4 5 end fill
  com='array 3 defines unit 11 (yhemicylinders with z radii)'
  ara=3 nux=1 nuy=1 nuz=2 fill 9 10 end fill
  com='array 4 defines unit 14 (zhemicylinders with z radii)'
  ara=4 nux=1 nuy=1 nuz=2 fill 12 13 end fill
  com='array 5 defines the total 2c8 problem'
  gbl=5 ara=5 nux=2 nuy=2 nuz=2 fill 3 7 6 8 11 15 14 16 end fill
END ARRAY
END DATA
END

KENO-VI

=KENOVI
sample problem 25  case 2c8 bare as mixed y-rotated cylinders
READ PARAMETERS
  fdn=yes lib=4
END PARAMETERS
READ MIXT
  sct=2
  mix=1 1092234 4.82717e-04 1092235 4.47971e-02 1092236 9.57233e-05
        1092238 2.65767e-03
END MIXT
READ GEOMETRY
  unit 1
    com='-x half of unit 3'
    cylinder 10 5.748 5.3825 -5.3825 chord -y=0.0 rotate a1=180 a2=90 a3=90
    cuboid   20 0.0 -6.87 6.505 -6.505 6.87 -6.87
    media 1 1 10     vol=2234.742156
    media 0 1 20 -10 vol=2677.511196
    boundary  20
  unit 2
    com='+x half of unit 3'
    cylinder 10 5.748 5.3825 -5.3825 chord +y=0.0 rotate a1=180 a2=90 a3=90
    cuboid   20 6.87 0.0 6.505 -6.505 6.87 -6.87
    media 1 1 10     vol=2234.742156
    media 0 1 20 -10 vol=2677.511196
    boundary  20
  unit 3
    com='cylinder composed of equal halves (yhemicylinders with x radii)'
    cuboid 10 6.87 -6.87 6.505 -6.505 6.87 -6.87
    array 1 10 place 1 1 1 0.0 0.0 0.0
    boundary  10
  unit 4
    com='-x portion (more than half) of unit 6'
    cylinder 10 5.748 5.3825 -5.3825 chord -y=3.0 rotate a1=180 a2=90 a3=90
    cuboid   20 3.0 -6.87 6.505 -6.505 6.87 -6.87
    media 1 1 10     vol=2234.742156
    media 0 1 20 -10 vol=2677.511196
    boundary  20
  unit 5
    com='+x portion (less than half) of unit 6'
    cylinder 10 5.748 5.3825 -5.3825 chord +y=3.0 rotate a1=180 a2=90 a3=90
    cuboid   20 6.87 3.0 6.505 -6.505 6.87 -6.87
    media 1 1 10     vol=2234.742156
    media 0 1 20 -10 vol=2677.511196
    boundary  20
  unit 6
    com='cylinder composed of unequal halves (yhemicylinders with x radii)'
    cuboid 10 6.87 -6.87 6.505 -6.505 6.87 -6.87
    array 2 10 place 1 1 1 3*0.0
    boundary  10
  unit 7
    com='cylinder of a single yhemicylinder in the -x direction'
    cylinder 10 5.748 5.3825 -5.3825 chord -y=5.748 rotate a1=180 a2=90 a3=90
    cuboid   20 6.87 -6.87 6.505 -6.505 6.87 -6.87
    media 1 1 10     vol=2234.742156
    media 0 1 20 -10 vol=2677.511196
    boundary  20
  unit 8
    com='cylinder of a single yhemicylinder in the +x direction'
    cylinder 10 5.748 5.3825 -5.3825 chord +y=-5.748 rotate a1=180 a2=90 a3=90
    cuboid   20 6.87 -6.87 6.505 -6.505 6.87 -6.87
    media 1 1 10     vol=2234.742156
    media 0 1 20 -10 vol=2677.511196
    boundary  20
  unit 9
    com='-z half of unit 11'
    cylinder 10 5.748 5.3825 -5.3825 chord -x=0.0 rotate a1=180 a2=90 a3=90
    cuboid   20 6.87 -6.87 6.505 -6.505 0.0 -6.87
    media 1 1 10     vol=2234.742156
    media 0 1 20 -10 vol=2677.511196
    boundary  20
  unit 10
    com='+z half of unit 11'
    cylinder 10 5.748 5.3825 -5.3825 chord +x=0.0 rotate a1=180 a2=90 a3=90
    cuboid   20 6.87 -6.87 6.505 -6.505 6.87 0.0
    media 1 1 10     vol=2234.742156
    media 0 1 20 -10 vol=2677.511196
    boundary  20
  unit 11
    com='cylinder composed of equal halves (yhemicylinders with z radii)'
    cuboid 10 6.87 -6.87 6.505 -6.505 6.87 -6.87
    array 3 10 place 1 1 1 0.0 0.0 0.0
    boundary  10
  unit 12
    com='-z portion (more than half) of unit 14'
    cylinder 10 5.748 5.3825 -5.3825 chord -x=3.0 rotate a1=180 a2=90 a3=90
    cuboid   20 6.87 -6.87 6.505 -6.505 3.0 -6.87
    media 1 1 10     vol=2234.742156
    media 0 1 20 -10 vol=2677.511196
    boundary  20
  unit 13
    com='+z portion (less than half) of unit 14'
    cylinder 10 5.748 5.3825 -5.3825 chord +x=3.0 rotate a1=180 a2=90 a3=90
    cuboid   20 6.87 -6.87 6.505 -6.505 6.87 3.0
    media 1 1 10     vol=2234.742156
    media 0 1 20 -10 vol=2677.511196
    boundary  20
  unit 14
    com='cylinder composed of unequal halves (yhemicylinders with z radii)'
    cuboid 10 6.87 -6.87 6.505 -6.505 6.87 -6.87
    array 4 10 place 1 1 1 3*0.0
    boundary  10
  unit 15
    com='cylinder of a single yhemicylinder in the -z direction'
    cylinder 10 5.748 5.3825 -5.3825 chord -x=5.748 rotate a1=180 a2=90 a3=90
    cuboid   20 6.87 -6.87 6.505 -6.505 6.87 -6.87
    media 1 1 10     vol=2234.742156
    media 0 1 20 -10 vol=2677.511196
    boundary  20
  unit 16
    com='cylinder of a single yhemicylinder in the +z direction'
    cylinder 10 5.748 5.3825 -5.3825 chord +x=-5.748 rotate a1=180 a2=90 a3=90
    cuboid   20 6.87 -6.87 6.505 -6.505 6.87 -6.87
    media 1 1 10     vol=2234.742156
    media 0 1 20 -10 vol=2677.511196
    boundary  20
  global unit 17
    cuboid 10 13.74 -13.74 13.01 -13.01 13.74 -13.74
    array 5 10 place 1 1 1 -6.87 -6.505 -6.87
    boundary  10
END GEOMETRY
READ ARRAY
  com='array 1 defines unit 3 (yhemicylinders with z radii)'
  ara=1 nux=2 nuy=1 nuz=1 fill 1 2 end fill
  com='array 2 defines unit 6 (yhemicylinders with z radii)'
  ara=2 nux=2 nuy=1 nuz=1 fill 4 5 end fill
  com='array 3 defines unit 11 (yhemicylinders with x radii)'
  ara=3 nux=1 nuy=1 nuz=2 fill 9 10 end fill
  com='array 4 defines unit 14 (yhemicylinders with x radii)'
  ara=4 nux=1 nuy=1 nuz=2 fill 12 13 end fill
  com='array 5 defines the total 2c8 problem'
  gbl=5 ara=5 nux=2 nuy=2 nuz=2 fill 3 7 6 8 11 15 14 16 end fill
END ARRAY
READ VOLUME
  type=random
END VOLUME
END DATA
END

Sample Problem 26 (KENO V.a ONLY) CASE 2C8 BARE AS MIXED ZHEMICYLINDERS WITH ORIGINS

The physical representation of this sample problem is the critical experiment described in sample problem 1. This sample problem describes each of the eight units in the critical 2 × 2 × 2 array using zhemicylinders with origins.

KENO V.a

=KENOVA
sample problem 26  case 2c8 bare as mixed zhemicylinders with origins
READ PARAMETERS
  fdn=yes lib=4  run=yes
END PARAMETERS
READ MIXT
  sct=2
  mix=1
    1092234 4.82717e-04 1092235 4.47971e-02 1092236 9.57233e-05 1092238 2.65767e-03
END MIXT
READ GEOMETRY
  unit 1
    com='-x half of first cylinder'
    zhemicyl-x 1 1 5.748 5.3825 -5.3825 origin 6.87 0.0
    cuboid  0 1 6.87 0.0 6.87 -6.87 6.505 -6.505
  unit 2
    com='+x half of first cylinder'
    zhemicyl+x 1 1 5.748 5.3825 -5.3825 origin 6.87 0.0
    cuboid  0 1 13.74 6.87 6.87 -6.87 6.505 -6.505
  unit 3
    com='1st cylinder composed of equal portions (z hemicylinders with x radii)'
    array 1 3*0.0
  unit 4
    com='-x portion (more than half) of second cylinder'
    zhemicyl-x 1 1 5.748 5.3825 -5.3825 chord 3.0 origin 6.87 0.0
    cuboid  0 1 9.87 0.0 6.87 -6.87 6.505 -6.505
  unit 5
    com='+x portion (less than half) of second cylinder'
    zhemicyl+x 1 1 5.748 5.3825 -5.3825 chord -3.0 origin 6.87 0.0
    cuboid  0 1 13.74 9.87 6.87 -6.87 6.505 -6.505
  unit 6
    com='2nd cylinder composed of unequal portions (z hemicylinders with x radii)'
    array 2 3*0.0
  unit 7
    com='3rd cylinder: described as a zhemicylinder in the -x direction'
    zhemicyl-x 1 1 5.748 5.3825 -5.3825 chord 5.748 origin 6.87 0.0
    cuboid  0 1 13.74 0.0 6.87 -6.87 6.505 -6.505
  unit 8
    com='4th cylinder: described as a zhemicylinder in the +x direction'
    zhemicyl+x 1 1 5.748 5.3825 -5.3825 chord 5.748 origin 6.87 0.0
    cuboid  0 1 13.74 0.0 6.87 -6.87 6.505 -6.505
  unit 9
    com='-y half of fifth cylinder'
    zhemicyl-y 1 1 5.748 5.3825 -5.3825 origin 0.0 6.87
    cuboid  0 1 6.87 -6.87 6.87 0.0 6.505 -6.505
  unit 10
    com='+y half of fifth cylinder'
    zhemicyl+y 1 1 5.748 5.3825 -5.3825 origin 0.0 6.87
    cuboid  0 1 6.87 -6.87 13.74 6.87  6.505 -6.505
  unit 11
    com='5th cylinder composed of equal portions (zhemicylinders with y radii)'
    array 3 3*0.0
  unit 12
    com='-y portion (more than half) of sixth cylinder'
    zhemicyl-y 1 1 5.748 5.3825 -5.3825 chord 3.0 origin 0.0 6.87
    cuboid  0 1 6.87 -6.87 9.87  0.0 6.505 -6.505
  unit 13
    com='+y portion (less than half) of sixth cylinder'
    zhemicyl+y 1 1 5.748 5.3825 -5.3825 chord -3.0 origin 0.0 6.87
    cuboid  0 1 6.87 -6.87 13.74  9.87  6.505 -6.505
  unit 14
    com='6th cylinder composed of unequal portions (zhemicylinders with y radii)'
    array 4 3*0.0
  unit 15
    com='7th cylinder: described as a zhemicylinder in the -y direction'
    zhemicyl-y 1 1 5.748 5.3825 -5.3825 chord 5.748 origin 0.0 6.87
    cuboid  0 1 6.87 -6.87 13.74 0.0 6.505 -6.505
  unit 16
    com='8th cylinder: described as a zhemicylinder in the +y direction'
    zhemicyl+y 1 1 5.748 5.3825 -5.3825 chord 5.748 origin 0.0 6.87
    cuboid  0 1 6.87 -6.87 13.74 0.0 6.505 -6.505
  global unit 17
    com='complete 2c8 bare configuration'
    array 5 3*0.0
END GEOMETRY
READ ARRAY
  com='array 1: 1st cylinder (unit 3) equal x portions of zhemicylinders'
  ara=1 nux=2 nuy=1 nuz=1 fill 1 2 end fill
  com='array 2: 2nd cylinder (unit 6) unequal x portions of zhemicylinders'
  ara=2 nux=2 nuy=1 nuz=1 fill 4 5 end fill
  com='array 3: 5th cylinder (unit 11) equal y portions of zhemicylinders'
  ara=3 nux=1 nuy=2 nuz=1 fill 9 10 end fill
  com='array 4: 6th cylinder (unit 14) unequal y portions of zhemicylinders'
  ara=4 nux=1 nuy=2 nuz=1 fill 12 13 end fill
  com='array 5 defines the total 2c8 problem'
  ara=5 nux=2 nuy=2 nuz=2 fill 3 7 6 8 11 15 14 16 end fill
END ARRAY
END DATA
END

Sample Problem 27 (KENO V.a oONLY) CASE 2C8 BARE AS MIXED XHEMICYLINDERS WITH ORIGINS

The physical representation of this sample problem is the critical experiment described in sample problem 1. This sample problem describes each of the eight units in the critical 2 × 2 × 2 array using hemicylinders whose axes are in the x direction. Origins are specified for each hemicylinder.

Input Data

KENO V.a

=KENOVA
sample problem 27  case 2c8 bare as mixed xhemicylinders with origins
READ PARAMETERS
  fdn=yes lib=4  run=yes
END PARAMETERS
READ MIXT
  sct=2
  mix=1
    1092234 4.82717e-04 1092235 4.47971e-02 1092236 9.57233e-05 1092238 2.65767e-03
END MIXT
READ GEOMETRY
  unit 1
    com='-y half of first cylinder'
    xhemicyl-y 1 1 5.748 5.3825 -5.3825 origin 6.87 0.0
    cuboid  0 1 6.505 -6.505 6.87 0.0 6.87 -6.87
  unit 2
    com='+y half of first cylinder'
    xhemicyl+y 1 1 5.748 5.3825 -5.3825 origin 6.87 0.0
    cuboid  0 1 6.505 -6.505 13.74 6.87 6.87 -6.87
  unit 3
    com='1st cylinder composed of equal portions (xhemicylinders with y radii)'
    array 1 3*0.0
  unit 4
    com='-y portion (more than half) of second cylinder'
    xhemicyl-y 1 1 5.748 5.3825 -5.3825 chord 3.0 origin 6.87 0.0
    cuboid  0 1 6.505 -6.505 9.87 0.0 6.87 -6.87
  unit 5
    com='+y portion (less than half) of second cylinder'
    xhemicyl+y 1 1 5.748 5.3825 -5.3825 chord -3.0 origin 6.87 0.0
    cuboid  0 1 6.505 -6.505 13.74 9.87  6.87 -6.87
  unit 6
    com='2nd cylinder composed of unequal portions (xhemicylinders with y radii)'
    array 2 3*0.0
  unit 7
    com='3rd cylinder: described as a xhemicylinder in the -y direction'
    xhemicyl-y 1 1 5.748 5.3825 -5.3825 chord 5.748 origin 6.87 0.0
    cuboid  0 1 6.505 -6.505 13.74 0.0 6.87 -6.87
  unit 8
    com='4th cylinder: described as a xhemicylinder in the +y direction'
    xhemicyl+y 1 1 5.748 5.3825 -5.3825 chord 5.748 origin 6.87 0.0
    cuboid  0 1 6.505 -6.505 13.74 0.0 6.87 -6.87
  unit 9
    com='-z half of fifth cylinder'
    xhemicyl-z 1 1 5.748 5.3825 -5.3825 origin 0.0 6.87
    cuboid  0 1 6.505 -6.505 6.87 -6.87 6.87 0.0
  unit 10
    com='+z half of fifth cylinder'
    xhemicyl+z 1 1 5.748 5.3825 -5.3825 origin 0.0 6.87
    cuboid  0 1 6.505 -6.505 6.87 -6.87 13.74 6.87
  unit 11
    com='5th cylinder composed of equal portions (xhemicylinders with z radii)'
    array 3 3*0.0
  unit 12
    com='-z portion (more than half) of sixth cylinder'
    xhemicyl-z 1 1 5.748 5.3825 -5.3825 chord 3.0 origin 0.0 6.87
    cuboid  0 1 6.505 -6.505 6.87 -6.87 9.87 0.0
  unit 13
    com='+z portion (less than half) of sixth cylinder'
    xhemicyl+z 1 1 5.748 5.3825 -5.3825 chord -3.0 origin 0.0 6.87
    cuboid  0 1 6.505 -6.505 6.87 -6.87 13.74 9.87
  unit 14
    com='6th cylinder composed of unequal portions (xhemicylinders with z radii)'
    array 4 3*0.0
  unit 15
    com='7th cylinder: described as a xhemicylinder in the -z direction'
    xhemicyl-z 1 1 5.748 5.3825 -5.3825 chord 5.748 origin 0.0 6.87
    cuboid  0 1 6.505 -6.505 6.87 -6.87 13.74 0.0
  unit 16
    com='8th cylinder: de3scribed as a xhemicylinder in the +z direction'
    xhemicyl+z 1 1 5.748 5.3825 -5.3825 chord 5.748 origin 0.0 6.87
    cuboid  0 1 6.505 -6.505 6.87 -6.87 13.74 0.0
  global unit 17
    com='complete 2c8 bare configuration'
    array 5 3*0.0
END GEOMETRY
READ ARRAY
  com='array 1: 1st cylinder (unit 3) equal y portions of xhemicylinders'
  ara=1 nux=1 nuy=2 nuz=1 fill 1 2 end fill
  com='array 2: 2nd cylinder (unit 6) unequal y portions of xhemicylinders'
  ara=2 nux=1 nuy=2 nuz=1 fill 4 5 end fill
  com='array 3: 5th cylinder (unit 11) equal z portions of xhemicylinders'
  ara=3 nux=1 nuy=1 nuz=2 fill 9 10 end fill
  com='array 4: 6th cylinder (unit 14) unequal z portions of xhemicylinders'
  ara=4 nux=1 nuy=1 nuz=2 fill 12 13 end fill
  com='array 5 defines the total 2c8 problem'
  gbl=5 ara=5 nux=2 nuy=2 nuz=2 fill 3 7 6 8 11 15 14 16 end fill
END ARRAY
END DATA
END

Sample Problem 28 (KENO V.a oONLY) CASE 2C8 BARE AS MIXED YHEMICYLINDERS WITH ORIGINS

The physical representation of this sample problem is the critical experiment described in sample problem 1. This sample problem describes each of the eight units in the critical 2 × 2 × 2 array using hemicylinders whose axes are in the y direction. Origins are specified for each hemicylinder.

Input Data

KENO V.a

=KENOVA
sample problem 28  case 2c8 bare as mixed yhemicylinders with origins
READ PARAMETERS
  fdn=yes lib=4  run=yes
END PARAMETERS
READ MIXT
  sct=2
  mix=1
    1092234 4.82717e-04 1092235 4.47971e-02 1092236 9.57233e-05 1092238 2.65767e-03
END MIXT
READ GEOMETRY
  unit 1
    com='-x half of first cylinder'
    yhemicyl-x 1 1 5.748 5.3825 -5.3825 origin 6.87 0.0
    cuboid  0 1 6.87 0.0 6.505 -6.505 6.87 -6.87
  unit 2
    com='+x half of unit 3'
    yhemicyl+x 1 1 5.748 5.3825 -5.3825 origin 6.87 0.0
    cuboid  0 1 13.74 6.87  6.505 -6.505 6.87 -6.87
  unit 3
    com='1st cylinder composed of equal portions (yhemicylinders with x radii)'
    array 1 3*0.0
  unit 4
    com='-x portion (more than half) of second cylinder'
    yhemicyl-x 1 1 5.748 5.3825 -5.3825 chord 3.0 origin 6.87 0.0
    cuboid  0 1 9.87 0.0 6.505 -6.505 6.87 -6.87
  unit 5
    com='+x portion (less than half) of second cylinder'
    yhemicyl+x 1 1 5.748 5.3825 -5.3825 chord -3.0 origin 6.87 0.0
    cuboid  0 1 13.74 9.87 6.505 -6.505 6.87 -6.87
  unit 6
    com='2nd cylinder composed of unequal portions (yhemicylinders with x radii)'
    array 2 3*0.0
  unit 7
    com='3rd cylinder: described as a single yhemicylinder in the -x direction'
    yhemicyl-x 1 1 5.748 5.3825 -5.3825 chord 5.748 origin 6.87 0.0
    cuboid  0 1 13.74 0.0 6.505 -6.505 6.87 -6.87
  unit 8
    com='4th cylinder: described as a single yhemicylinder in the +x direction'
    yhemicyl+x 1 1 5.748 5.3825 -5.3825 chord 5.748 origin 6.87 0.0
    cuboid  0 1 13.74 0.0 6.505 -6.505 6.87 -6.87
  unit 9
    com='-z half of fifth cylinder'
    yhemicyl-z 1 1 5.748 5.3825 -5.3825 origin 0.0 6.87
    cuboid  0 1 6.87 -6.87 6.505 -6.505 6.87 0.0
  unit 10
    com='+z half of sixth cylinder'
    yhemicyl+z 1 1 5.748 5.3825 -5.3825 origin 0.0 6.87
    cuboid  0 1 6.87 -6.87 6.505 -6.505 13.74 6.87
  unit 11
    com='5th cylinder composed of equal portions (yhemicylinders with z radii)'
    array 3 3*0.0
  unit 12
    com='-z portion (more than half) of sixth cylinder'
    yhemicyl-z 1 1 5.748 5.3825 -5.3825 chord 3.0 origin 0.0 6.87
    cuboid  0 1 6.87 -6.87 6.505 -6.505 9.87 0.0
  unit 13
    com='+z portion (less than half) of sixth cylinder'
    yhemicyl+z 1 1 5.748 5.3825 -5.3825 chord -3.0 origin 0.0 6.87
    cuboid  0 1 6.87 -6.87 6.505 -6.505 13.74 9.87
  unit 14
    com='6th cylinder composed of unequal portions (yhemicylinders with z radii)'
    array 4 3*0.0
  unit 15
    com='7th cylinder: described as a yhemicylinder in the -z direction'
    yhemicyl-z 1 1 5.748 5.3825 -5.3825 chord 5.748 origin 0.0 6.87
    cuboid  0 1 6.87 -6.87 6.505 -6.505 13.74 0.0
  unit 16
    com='8th cylinder: described as a yhemicylinder in the +z direction'
    yhemicyl+z 1 1 5.748 5.3825 -5.3825 chord 5.748 origin 0.0 6.87
    cuboid  0 1 6.87 -6.87 6.505 -6.505 13.74 0.0
  global unit 17
    com='complete 2c8 bare configuration'
    array 5 3*0.0
END GEOMETRY
READ ARRAY
  com='array 1: 1st cylinder (unit 3) equal x portions of yhemicylinders'
  ara=1 nux=2 nuy=1 nuz=1 fill 1 2 end fill
  com='array 2: 2nd cylinder (unit 6) unequal x portions of yhemicylinders'
  ara=2 nux=2 nuy=1 nuz=1 fill 4 5 end fill
  com='array 3: 5th cyllinder (unit 11) equal z portions of yhemicylinders'
  ara=3 nux=1 nuy=1 nuz=2 fill 9 10 end fill
  com='array 4: 6th cylinder (unit 14) unequal z portions of yhemicylinders'
  ara=4 nux=1 nuy=1 nuz=2 fill 12 13 end fill
  com='array 5 defines the total 2c8 problem'
  gbl=5 ara=5 nux=2 nuy=2 nuz=2 fill 3 7 6 8 11 15 14 16 end fill
END ARRAY
END DATA
END

Sample Problem 29 BARE CRITICAL SPHERE 3.4420-IN. RADIUS

This problem is a critical experiment [MLTH93] consisting of a critical Oralloy sphere. The density of the Oralloy is 18.747 g/cc, and the isotopic enrichment (wt %) is 93.21% 235U, 5.7697% 238U, 0.9844% 234U, and 0.0359% 236U. The critical radius was 8.74268 cm. A photograph of the experiment is given in Fig. 270. The support structure was ignored in the input data.

_images/fig1112.png

Fig. 270 Critical Oralloy sphere.

Input Data

KENO V.a

=KENOVA
sample problem 29  bare critical sphere   3.4420" radius
READ PARAMETERS
    fdn=yes lib=4
END PARAMETERS
READ MIXT
  sct=2
  mix=16
   16092235 4.47709e-02 16092238 2.73631e-03 16092234 4.74858e-04 16092236 1.71704e-05
END MIXT
READ GEOMETRY
  global unit 1
    sphere   16 1 8.74268
END GEOMETRY
READ PLOT
  scr=yes lpi=10
  ttl='x-y slice at z=0.0'
  xul=-9 yul= 9 zul=0.0
  xlr= 9 ylr=-9 zlr=0.0
  uax=1  vdn=-1 nax=400 nch=' *'
END PLOT
END DATA
END

KENO-VI

=KENOVI
sample problem 26  bare critical sphere   3.4420" radius
READ PARAMETERS
  fdn=yes lib=4
END PARAMETERS
READ MIXT
  sct=2
  mix=1   16092235   4.47709e-02
          16092238   2.73631e-03
          16092234   4.74858e-04
          16092236   1.71704e-05
END MIXT
READ GEOMETRY
  global unit 1
    sphere   10  8.74268
    media  1 1 10  vol=2799.1254126
    boundary 10
END GEOMETRY
END DATA
END

Sample Problem 30 (KENO V.a ONLY) BARE CRITICAL SPHERE Z HEMISPHERE MODEL 3.4420-IN. RADIUS

The physical representation of this sample problem is the critical experiment described in sample problem 29. This sample problem describes the sphere as two Z hemispheres, each with a chord and origin specified. One of the hemispheres is placed using the hole geometry option.

Input Data

KENO V.a

=KENOVA
sample problem 30   bare critical sphere    z hemisphere model 3.4420" radius
READ PARAMETERS
    fdn=yes lib=4
END PARAMETERS
READ MIXT
  sct=2
  mix=16
   16092235 4.47709e-02 16092238 2.73631e-03 16092234 4.74858e-04 16092236 1.71704e-05
END MIXT
READ GEOMETRY
   unit 1
     hemisphe+z   16 1 8.74268  chord +3.0 origin 8.9 8.9 8.9
   global unit 2
     hemisphe-z   16 1 8.74268  chord -3.0 origin 8.9 8.9 8.9
     cuboid       0 1 17.8 0.0 17.8 0.0 17.8 0.0
     hole 1 3*0.0
END GEOMETRY
READ PLOT
  scr=yes lpi=10
  ttl='y-z slice at x=8.9   mixture map'
  xul=8.9 yul=-0.5 zul=18.5
  xlr=8.9 ylr=18.5 zlr=-0.5
  vax=1   wdn=-1   nax=400   end plt1
  ttl='y-z slice at x=8.9   unit map'
  pic=box                    end plt2
END PLOT
END DATA
END

Sample Problem 31 (KENO V.a ONLY) BARE CRITICAL SPHERE X HEMISPHERE MODEL 3.4420-IN. RADIUS

The physical representation of this sample problem is the critical experiment described in sample problem 29. This sample problem describes the sphere as two X hemispheres, each with a chord and origin specified. One of the hemispheres is placed using the hole geometry option.

Input Data

KENO V.a

=KENOVA
sample problem 31   bare critical sphere    x hemisphere model 3.4420" radius
READ PARAMETERS
    fdn=yes lib=4
END PARAMETERS
READ MIXT
  sct=2
  mix=16
   16092235 4.47709e-02 16092238 2.73631e-03 16092234 4.74858e-04 16092236 1.71704e-05
END MIXT
READ GEOMETRY
   unit 1
     hemisphe-x   16 1 8.74268  chord +3.0
   global unit 2
     hemisphe+x   16 1 8.74268  chord -3.0 origin 8.9 8.9 8.9
     cuboid       0 1 17.8 0.0 17.8 0.0 17.8 0.0
     hole 1 3*8.9
END GEOMETRY
READ PLOT
  scr=yes lpi=10
  ttl='x-y slice at z=8.9     mixture map'
  xul=-0.5 yul=18.5 zul=8.9
  xlr=18.5 ylr=-0.5 zlr=8.9
  uax=1   vdn=-1    nax=400  end plt1
  ttl='y-z slice at x=8.9   unit map'
  pic=box                    end plt2
END PLOT
END DATA
END

Sample Problem 32 (KENO V.a ONLY) BARE CRITICAL SPHERE Y HEMISPHERE MODEL 3.4420-IN. RADIUS

The physical representation of this sample problem is the critical experiment described in sample problem 29. This sample problem describes the sphere as two Y hemispheres, each with a chord and origin specified. One of the hemispheres is placed using the hole geometry option.

Input Data

KENO V.a

=KENOVA
sample problem 32   bare critical sphere    y hemisphere model 3.4420" radius
READ PARAMETERS
    fdn=yes lib=4
END PARAMETERS
READ MIXT
  sct=2
  mix=16
   16092235 4.47709e-02 16092238 2.73631e-03 16092234 4.74858e-04 16092236 1.71704e-05
END MIXT
READ GEOMETRY
  unit 1
    hemisphe-y   16 1 8.74268  chord +3.0 origin 8.9 9.9 10.9
  global unit 2
    hemisphe+y   16 1 8.74268  chord -3.0 origin 8.9 8.9 8.9
    cuboid       0 1 17.8 0.0 17.8 0.0 17.8 0.0
    hole 1 0.0 -1.0 -2.0
END GEOMETRY
READ PLOT
  scr=yes lpi=10
  ttl='x-y slice at z=8.9     mixture map'
  xul=-0.5 yul=18.5 zul=8.9
  xlr=18.5 ylr=-0.5 zlr=8.9
  uax=1    vdn=-1   nax=400  end plt1
  ttl='y-z slice at x=8.9   unit map'
  pic=box                    end plt2
END PLOT
END DATA
END

Sample Problem 33 CRITICAL TRIANGULAR PITCHED ARRAY OF ANNULAR RODS

This sample problem represents a critical experiment [Joh66] that consists of a partially flooded array of 19 low enriched uranium metal cylindrical annuli billets arranged in a triangular pitched array. The density of the uranium metal was 19.0 g/cc, and the isotopic enrichment in weight percent was 1.95% 235U, 98.02% 238U, 0.006% 236U, and 0.002% 234U. The cylindrical annuli had an inside diameter of 6.604 cm, an outside diameter of 18.288 cm, and were placed with a pitch of 20.828 cm. Each billet was 101.6 cm long. The array was positioned in a very large tank. This configuration was critical when the tank was filled to a height of 47.7 cm on a scale whose zero point was 0.6 cm below the bottom of the billets. The bottom of the billets was 21.6 cm above the bottom of the tank. The tank and all support structures have been ignored in this model. The model utilizes only 15.24 cm of water reflector on all sides of the array. Fig. 271 and Fig. 272 provide a representation of the model. A photograph of a single annular billet is shown in Fig. 273.

Input Data

KENO V.a

=KENOVA
sample problem 33   critical triangular pitched array of annular rods
READ PARAMETERS  fdn=yes nub=yes lib=4
END PARAMETERS
READ MIXT
  sct=2
  mix=17
    17092235   9.49270e-04 17092238   4.71245e-02 17092234   9.77785e-07 17092236   2.90844e-06
  mix=18
    18008016   3.33757e-02 18001001   6.67515e-02
  mix=19
    19001001   6.67515e-02 19008016   3.33757e-02
  mix=20
    20092235   9.49270e-04 20092238   4.71245e-02 20092234   9.77785e-07 20092236   2.90844e-06
END MIXT
READ GEOM
  unit 1
    zhemicyl-x 18 1 3.302 47.7 0.6
    zhemicyl-x 17 1 9.144 47.7 0.6
  unit 2
    zhemicyl-y 18 1 3.302 47.7 0.6
    zhemicyl-y 17 1 9.144 47.7 0.6
  unit 3
    zhemicyl+x 18 1 3.302 47.7 0.6
    zhemicyl+x 17 1 9.144 47.7 0.6
  unit 4
    zhemicyl+y 18 1 3.302 47.7 0.6  origin 0.0 -18.03758
    zhemicyl+y 17 1 9.144 47.7 0.6  origin 0.0 -18.03758
    cuboid     19 1 2p10.414 2p18.03758 47.7 0.6
    hole      1       10.414    0.0      0.0
    hole      2        0.0     18.03758  0.0
    hole      3      -10.414    0.0      0.0
  unit 5
    cuboid     19 1 2p10.414 10.414 0.0 47.7 0.6
  unit 6
    zhemicyl-y 18 1 3.302 47.7 0.6
    zhemicyl-y 17 1 9.144 47.7 0.6
    cuboid     19 1 2p10.414 0.0 -10.414 47.7 0.6
  unit 7
    zhemicyl-y 18 1 3.302 47.7 0.6 origin 0.0 18.03758
    zhemicyl-y 17 1 9.144 47.7 0.6 origin 0.0 18.03758
    cuboid     19 1 2p10.414 2p18.03758 47.7 0.6
    hole     3      -10.414 0.0 0.0
  unit 8
    zhemicyl+y 18 1 3.302 47.7 0.6 origin 0.0 -18.03758
    zhemicyl+y 17 1 9.144 47.7 0.6 origin 0.0 -18.03758
    cuboid     19 1 2p10.414 2p18.03758 47.7 0.6
    hole     3      -10.414 0.0 0.0
  unit 9
    zhemicyl+y 18 1 3.302 47.7 0.6
    zhemicyl+y 17 1 9.144 47.7 0.6
    cuboid     19 1 2p10.414 10.414 0.0 47.7 0.6
  unit 10
    zhemicyl+y 18 1 3.302 47.7 0.6  origin 0.0 -18.03758
    zhemicyl+y 17 1 9.144 47.7 0.6  origin 0.0 -18.03758
    cuboid     19 1 2p10.414 2p18.03758 47.7 0.6
    hole     1       10.414 0.0 0.0
  unit 11
    zhemicyl-y 18 1 3.302 47.7 0.6  origin 0.0 18.03758
    zhemicyl-y 17 1 9.144 47.7 0.6  origin 0.0 18.03758
    cuboid     19 1 2p10.414 2p18.03758 47.7 0.6
    hole     1       10.414 0.0 0.0
  unit 21
    zhemicyl-x  0 1 3.302 102.2 47.7
    zhemicyl-x 20 1 9.144 102.2 47.7
  unit 22
    zhemicyl-y  0 1 3.302 102.2 47.7
    zhemicyl-y 20 1 9.144 102.2 47.7
  unit 23
    zhemicyl+x  0 1 3.302 102.2 47.7
    zhemicyl+x 20 1 9.144 102.2 47.7
  unit 24
    zhemicyl+y  0 1 3.302 102.2 47.7  origin 0.0 -18.03758
    zhemicyl+y 20 1 9.144 102.2 47.7  origin 0.0 -18.03758
    cuboid      0 1 2p10.414 2p18.03758 102.2 47.7
    hole      21      10.414    0.0      0.0
    hole      22       0.0     18.03758  0.0
    hole      23     -10.414    0.0      0.0
  unit 25
    cuboid      0 1 2p10.414 10.414 0.0 102.2 47.7
  unit 26
    zhemicyl-y  0 1 3.302 102.2 47.7
    zhemicyl-y 20 1 9.144 102.2 47.7
    cuboid      0 1 2p10.414 0.0 -10.414 102.2 47.7
  unit 27
    zhemicyl-y  0 1 3.302 102.2 47.7  origin 0.0 18.03758
    zhemicyl-y 20 1 9.144 102.2 47.7  origin 0.0 18.03758
    cuboid      0 1 2p10.414 2p18.03758 102.2 47.7
    hole     23      -10.414 0.0 0.0
  unit 28
    zhemicyl+y  0 1 3.302 102.2 47.7  origin 0.0 -18.03758
    zhemicyl+y 20 1 9.144 102.2 47.7  origin 0.0 -18.03758
    cuboid      0 1 2p10.414 2p18.03758 102.2 47.7
    hole     23      -10.414 0.0 0.0
  unit 29
    zhemicyl+y  0 1 3.302 102.2 47.7
    zhemicyl+y 20 1 9.144 102.2 47.7
    cuboid      0 1 2p10.414 10.414 0.0 102.2 47.7
  unit 30
    zhemicyl+y  0 1 3.302 102.2 47.7  origin 0.0 -18.03758
    zhemicyl+y 20 1 9.144 102.2 47.7  origin 0.0 -18.03758
    cuboid      0 1 2p10.414 2p18.03758 102.2 47.7
    hole     21       10.414 0.0 0.0
  unit 31
    zhemicyl-y  0 1 3.302 102.2 47.7  origin 0.0 18.03758
    zhemicyl-y 20 1 9.144 102.2 47.7  origin 0.0 18.03758
    cuboid      0 1 2p10.414 2p18.03758 102.2 47.7
    hole     21       10.414 0.0 0.0
  unit 32
    com='flooded portion of array with 15.24 cm of water in x and y'
    array 1 2*0.0 0.6
    replicate 19 1 4r15.24 0.0 0.6 1
    replicate 19 2 5r0.0 3.0 7
  unit 33
    com='unflooded upper portion of array'
    array 2 3*0.0
    replicate 0 1 4r15.24 2*0.0 1
  global
  unit 34
    array 3 -67.31 -61.72916 -21.0
END GEOM
READ BIAS
  id=500 2 8
END BIAS
READ ARRAY
   ara=1 nux=5 nuy=4 nuz=1  fill  5 3r 6  5   11 3r 4  7    10 3r 4  8      5 3r 9  5  end fill
   ara=2 nux=5 nuy=4 nuz=1  fill 25 3r26 25   31 3r24 27    30 3r24 28     25 3r29 25  end fill
   ara=3 nux=1 nuy=1 nuz=2  fill 32 33 end fill
END ARRAY
READ START
  nst=1   xsm=-52 xsp=52   ysm=-47 ysp=47   zsm=0.6 zsp=47.7
END START
READ PLOT
  scr=yes lpi=10
  clr=17 255 0 0
      18 128 255 255
      19 0 0 255
      20 255 0 128
  end color
  ttl='x-y plot of pins at z=45.0'
    xul=-52.0 yul= 47.0 zul=45.0
    xlr= 52.0 ylr=-47.0 zlr=45.0
    uax=  1.0 vdn=-1.0  nax=400
  end plt1
  ttl='x-z plot of pins at y=0.0'
    xul=-52.0 yul=0.0 zul=102.7
    xlr= 52.0 ylr=0.0 zlr=-3.0
    uax=  1.0 wdn=-1.0 nax=400
  end plt2
  ttl='x-z plot at y=0.0'
    xul=-68.0 yul=0.0 zul=102.7
    xlr= 70.0 ylr=0.0 zlr=-25.0
    uax=  1.0 wdn=-1.0 nax=400
  end plt3
END PLOT
END DATA
END

KENO-VI

=KENOVI
sample problem 27   critical triangular pitched array of annular rods
READ PARAMETERS
  fdn=yes nub=yes lib=4
END PARAMETERS
READ MIXT
  sct=2
  mix=1   17092235   9.49270e-04
          17092238   4.71245e-02
          17092234   9.77785e-07
          17092236   2.90844e-06
  mix=2   18008016   3.33757e-02
          18001001   6.67515e-02
  mix=3   19001001   6.67515e-02
          19008016   3.33757e-02
  mix=4   20092235   9.49270e-04
          20092238   4.71245e-02
          20092234   9.77785e-07
          20092236   2.90844e-06
  mix=5   18008016   3.33757e-02
          18001001   6.67515e-02
END MIXT
READ GEOM
  unit 1
    cylinder 10  3.302 102.2 0.6
    cylinder 20  9.144 102.2 0.6
    plane    30  zpl=1.0 con=-47.7
    hexprism 40 10.414 102.2 0.0
    media  2 1 10 -30
    media  1 1 20 -10 -30
    media  3 1 40 -20 -30
    media  0 1 10  30
    media  4 1 20 -10  30
    media  0 1 40 -20  30
    boundary 40
  unit 2
    plane    10  zpl=1.0 con=-47.7
    hexprism 20 10.414 102.2 0.0
    media  3 1 -10  20
    media  0 1  10  20
    boundary 20
  global unit 3
    cylinder 10  52.42 102.2 0.0
    plane    20  zpl=1.0 con=-47.7
    cylinder 30  82.9  102.2 -21.0
    array  1 10 place 4 4 1 3*0.0
    media  0 1 30  20 -10
    media  5 1 30 -20 -10
    boundary 30
END GEOM
READ ARRAY
  ara=1 nux=7 nuy=7 nuz=1 typ=tri fill
  2 2 2 2 2 2 2
   2 2 2 1 1 1 2
    2 2 1 1 1 1 2
     2 1 1 1 1 1 2
      2 1 1 1 1 2 2
       2 1 1 1 2 2 2
        2 2 2 2 2 2 2   end fill
END ARRAY
READ VOLUME
  type=random
END VOLUME
READ PLOT
  scr=yes lpi=10
  clr=1 255 0 0
      2 128 255 255
      3 0 0 255
      4 255 0 128
      5 200 200 200
  end color
  ttl='x-z plot of pins at y=0.0'
    xul=-68.0 yul= 0.0 zul=102.7
    xlr= 70.0 ylr= 0.0 zlr=-25.0
    uax=  1.0 wdn=-1.0
    nax=800
  end plt0
  ttl='x-y plot of pins and water at z=45.0'
    xul=-68.0 yul= 68.0 zul=45.0
    xlr= 68.0 ylr=-68.0 zlr=45.0
    uax=  1.0 vdn= -1.0
    nax=800
  end plt1
END PLOT
END DATA
END
_images/fig1212.png

Fig. 271 Horizontal slice through a critical triangular pitched array of partially flooded 1.95% enriched uranium metal annular billets.

_images/fig1312.png

Fig. 272 Vertical slice through the center of a critical triangular-pitched array of partially flooded 1.9% enriched uranium metal annular billets.

_images/fig1412.png

Fig. 273 1.95% Enriched uranium metal annular billet used in critical experiments

BKH+77

Clco C. Byers, Jerry J. Koelling, Gordon E. Hansen, David R. Smith, and Howard R. Dyer. Critical measurements of a water-reflected enriched uranium sphere. Transactions of the American Nuclear Society, 1977.

IM64

D. C. Irving and John T. Mihalczo. Monte Carlo Calculations for Enriched Uranium Metal Assemblies. Transactions of the American Nuclear Society (US), 1964. Publisher: Oak Ridge National Lab., Tenn.

Joh66

E. B. Johnson. Critical Parameters of Uranium (1.95) Metal Cylindrical Annuli. Trans. Amer. Nucl. Soc., 1966. Publisher: Oak Ridge National Lab., Tenn.

MLTH93

J. T. Mihalczo, J. J. Lynn, J. R. Taylor, and G. E. Hansen. Measurements with an unreflected uranium (93.2%) metal sphere. Technical Report, Oak Ridge National Lab., TN (United States), 1993.

Tho64

J. T. Thomas. CRITICAL THREE-DIMENSIONAL ARRAYS OF NEUTRON-INTERACTING UNITS. PART II. U (93.2) METAL. Technical Report, Oak Ridge National Lab., Tenn., 1964.

Tho73

Joseph T. Thomas. Critical three-dimensional arrays of U (93.2)-metal cylinders. Nuclear Science and Engineering, 52(3):350–359, 1973. Publisher: Taylor & Francis.

WT69

G. E. Whitesides and J. T. Thomas. USE OF DIFFERENTIAL CURRENT ALBEDOS IN MONTE CARLO CRITICALITY CALCULATIONS. Technical Report, Union Carbide Corp., Oak Ridge, Tenn., 1969.