.. _sec-module.keno.examples: KENO 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 :numref:`sec-module.keno.input_outline`) 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.inp" and "kenovi.inp" 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 **=KENOVA**, respectively **=KENOVI**. The ".inp" file contains all 33/27 problems one after the other. A similar input file "cekenova.inp", respectively "cekenovi.inp" 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_v7.1_endf** to indicate the mode of calculation is continuous energy and the continuous energy cross section directory file is "ce_v7.1_endf" indicating ENDF/B-VII.1-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, material-specific albedos have also been removed from the continuous-energy input because they are not supported with continuous-energy mode. The same 33/27 problems are also executed as individual cases with filenames "k5smp??.inp", respectively "k6smp??.inp", 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??.inp", respectively "cek6smp??.inp", 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 "v7.1-252" to "ce_v7.1". 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 ".inp" file. The CSAS-MG input file for these cases is in the next section. .. warning:: Some input might show differences in **NPG**, **NSK** and **GEN** parameters between multigroup and continuous energy input files. .. _8-1c-1: CSAS-MG data ~~~~~~~~~~~~ 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. Note that "kenovi.inp" also has its own CSAS-MG data which is identical to the below input with some minor updates in the comment lines. .. code-block:: scale =csas-mg xsproc to prepare 252 group working format xsec lib for kenova smp prbs v7.1-252 read composition ' 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 92234 1 92235 93.2 92236 0.2 92238 5.6 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 92236 0.5 molar[hno3]=0.009783 density=? temperature=300 vol_frac=1 end solution ' uranium metal for smp prbs 13,14 uranium 3 den=18.69 1 300 92234 1 92235 93.2 92236 0.2 92238 5.6 end ' uranium metal for smp prb 15 uranium 4 den=18.794 1 300 92234 1.09 92235 97.67 92236 0.21 92238 1.03 end ' uranyl fluoride solution for smp prb 16 solution mix=5 rho[uo2f2]=578.7 92235 93.2 92238 6.8 density=? temperature=300 vol_frac=1 end solution ' borated uranyl fluoride solution for smp prb 16 solution mix=6 rho[uo2f2]=578.7 92235 93.2 92238 6.8 density=? temperature=300 vol_frac=1 end solution boron 6 den=0.0266 1 300 end ' uranyl fluoride solution for smp prb 17 solution mix=7 rho[uo2f2]=133 92235 93 92238 7 density=? temperature=300 vol_frac=1 end solution ' uranyl fluoride solution for smp prb 20 solution mix=8 rho[uo2f2]=576.87 92235 93.2 92238 6.8 density=? temperature=300 vol_frac=1 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 density=? temperature=300 vol_frac=1 end solution ' paraffin for smp prbs 3,4,18 paraffin 10 1 300 end ' plexiglas for smp prbs 12,15,18,19 plexiglas 11 1 300 end ' water for smp prbs 15 h2o 12 1 300 end ' pyrex glass for smp prb 16 pyrex 13 1 300 end ' aluminum for smp prb 20,21 al 14 1 300 end ' low density water for smp prb 18 h2o 15 1e-09 300 end ' uranium metal for smp prbs 29 - 32 uranium 16 den=18.747 1 300 92234 0.9844 92235 93.21 92236 0.0359 92238 5.7697 end ' uranium metal for water moderated portion of smp prb 33 uranium 17 den=19 1 300 92234 0.002 92235 1.95 92236 0.006 92238 98.042 end ' internal (2nd) moderator water for smp prb 33 h2o 18 1 300 end ' external moderator water and reflector for smp prb 33 h2o 19 1 300 end ' uranium metal for bare portion of smp prb 33 uranium 20 den=19 1 300 92234 0.002 92235 1.95 92236 0.006 92238 98.042 end end composition read celldata 'latticecell data for samp prb 33 latticecell atriangpitch imodr=3.302 18 fuelr=9.144 17 hpitch=10.414 19 end latticecell atriangpitch imodr=3.302 0 fuelr=9.144 20 hpitch=10.414 0 end end celldata end .. _8-1c-2: KENO V.a sample problem data ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ A brief problem description and the associated input data are included for each multigroup mode KENO sample problems. 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/KENO-VI 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 :numref:`8-1c-1`. The unit number is defined by the parameter **LIB=** in the parameter data. .. _8-1c-2-1: Sample Problem 1 2C8 BARE ^^^^^^^^^^^^^^^^^^^^^^^^^^^ This is a simple 2 :math:`\times` 2 :math:`\times` 2 array of uranium metal cylinders as described in the article "Critical Three-Dimensional Arrays of U(93.2)-Metal Cylinders," :cite:`KENO-C-thomas_critical_1973` by J. T. Thomas. This critical experiment is designated in Table II of that article as cylinder index 11 and reflector index 1. :numref:`fig8-1c-1` shows the critical experiment. .. centered:: Input Data KENO V.a .. code-block:: scale =kenova sample problem 1 case 2c8 bare read parameters flx=yes fdn=yes far=yes gas=no lib=4 htm=no end parameters read mixt sct=2 mix=1 ncm=1 92234 4.82717e-04 92235 4.47971e-02 92236 9.57233e-05 92238 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 fill f1 end fill end array end data end KENO-VI .. code-block:: scale =kenovi kenovi sample problem 1 case 2c8 bare read parameters flx=yes fdn=yes far=yes gas=no lib=4 htm=no end parameters read mixt sct=2 mix=1 ncm=1 92234 4.82717e-04 92235 4.47971e-02 92236 9.57233e-05 92238 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 .. figure:: figs/KenoC/fig1.png :align: center :width: 400 :name: fig8-1c-1 Critical 2C8 bare assembly. .. _8-1c-2-2: 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. .. centered:: Input Data KENO V.a .. code-block:: scale =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 htm=no 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 ncm=1 92234 4.82717e-04 92235 4.47971e-02 92236 9.57233e-05 92238 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 .. code-block:: scale =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 htm=no end parameters read mixt sct=2 mix=1 ncm=1 92234 4.82717e-04 92235 4.47971e-02 92236 9.57233e-05 92238 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 .. _8-1c-2-3: Sample Problem 3 2C8 15.24-CM PARAFFIN REFL ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ A 2 :math:`\times` 2 :math:`\times` 2 array of uranium metal cylinders is reflected by 6 in. of paraffin on all faces (:numref:`fig8-1c-1`). This critical experiment\ :sup:`1` is designated as cylinder index 11 and reflector index 5 in Table II of Ref. 1. :numref:`fig8-1c-2` 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 :numref:`fig8-1c-2`, but was present when criticality was achieved. .. figure:: figs/KenoC/fig2.png :align: center :width: 500 :name: fig8-1c-2 Half of the paraffin reflected 2C8 assembly before the top reflector was added. .. centered:: Input Data KENO V.a .. code-block:: scale =kenova sample problem 3 2c8 15.24 cm paraffin refl read param lib=4 flx=yes fdn=yes pwt=yes htm=no end param read array nux=2 nuy=2 nuz=2 fill f1 end fill end array read mixt mix=1 ncm=1 92234 4.82717e-04 92235 4.47971e-02 92236 9.57233e-05 92238 2.65767e-03 mix=2 ncm=10 6000 3.84193e-02 9001001 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 .. code-block:: scale =kenovi keno-vi sample problem 3 2c8 15.24 cm paraffin refl read param lib=4 flx=yes fdn=yes pwt=yes htm=no gen=300 nsk=10 npg=2000 end param read mixt mix=1 ncm=1 92234 4.82717e-04 92235 4.47971e-02 92236 9.57233e-05 92238 2.65767e-03 mix=2 ncm=10 6000 3.84193e-02 9001001 7.99120e-02 sct=2 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 .. _8-1c-2-4: 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. .. centered:: Input Data KENO V.a .. code-block:: scale =kenova sample problem 4 2c8 15.24 cm paraffin refl automatic refl read param pwt=yes lib=4 flx=yes fdn=yes htm=no 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 ncm=1 92234 4.82717e-04 92235 4.47971e-02 92236 9.57233e-05 92238 2.65767e-03 mix=2 ncm=10 6000 3.84193e-02 9001001 7.99120e-02 end mixt read arra nux=2 nuy=2 nuz=2 fill f1 end fill end array read bias id=400 2 7 end bias end data end KENO-VI .. code-block:: scale =kenovi keno-vi sample problem 4 2c8 15.24 cm paraffin refl read param lib=4 flx=yes fdn=yes pwt=yes htm=no end param read mixt sct=2 mix=1 ncm=1 92234 4.82717e-04 92235 4.47971e-02 92236 9.57233e-05 92238 2.65767e-03 mix=2 ncm=10 6000 3.84193e-02 9001001 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 .. _8-1c-2-5: 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 :cite:`KENO-C-whitesides_use_1969`. .. centered:: Input Data KENO V.a .. code-block:: scale =kenova sample problem 5 2c8 12 inch paraffin albedo reflector read para flx=yes far=yes gas=no fdn=yes lib=4 htm=no end para read array nux=2 nuy=2 nuz=2 fill f1 end fill end array read mixt mix=1 ncm=1 92234 4.82717e-04 92235 4.47971e-02 92236 9.57233e-05 92238 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 .. code-block:: scale =kenovi kenovi sample problem 5 2c8 12 inch paraffin albedo reflector read para flx=yes far=yes gas=no fdn=yes lib=4 htm=no end para read mixt mix=1 ncm=1 92234 4.82717e-04 92235 4.47971e-02 92236 9.57233e-05 92238 2.65767e-03 sct=2 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 .. _8-1c-2-6: Sample Problem 6 ONE 2C8 UNIT (SINGLE UNIT) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ One of the 2C units\ :sup:`1` is described and run as a single-unit problem, and its k-effective is calculated. .. centered:: Input Data KENO V.a .. code-block:: scale =kenova sample problem 6 one 2c8 unit (single unit) read para lib=4 flx=yes fdn=yes far=yes gas=no htm=no end para read mixt sct=2 mix=1 ncm=1 92234 4.82717e-04 92235 4.47971e-02 92236 9.57233e-05 92238 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 .. code-block:: scale =kenovi kenovi sample problem 6 one 2c8 unit (single unit) read para lib=4 flx=yes fdn=yes far=yes gas=no htm=no end para read mixt sct=2 mix=1 ncm=1 92234 4.82717e-04 92235 4.47971e-02 92236 9.57233e-05 92238 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 .. _8-1c-2-7: Sample Problem 7 BARE 2C8 USING SPECULAR REFLECTION ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ One of the 2C units\ :sup:`1` is described and the 2 :math:`\times` 2 :math:`\times` 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. .. centered:: Input Data KENO V.a .. code-block:: scale =kenova sample problem 7 bare 2c8 using specular reflection read para lib=4 flx=yes fdn=yes far=yes gas=no htm=no end parameters read mixt sct=2 mix=1 ncm=1 92234 4.82717e-04 92235 4.47971e-02 92236 9.57233e-05 92238 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 .. code-block:: scale =kenovi keno-vi sample problem 7 bare 2c8 using specular reflection read para flx=yes fdn=yes far=yes gas=no lib=4 htm=no end parameters read mixt sct=2 mix=1 ncm=1 92234 4.82717e-04 92235 4.47971e-02 92236 9.57233e-05 92238 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 .. _8-1c-2-8: 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. .. centered:: Input Data KENO V.a .. code-block:: scale =kenova sample problem 8 infinitely long cylinder from 2c8 unit read param lib=4 htm=no end param read mixt sct=2 mix=1 ncm=1 92234 4.82717e-04 92235 4.47971e-02 92236 9.57233e-05 92238 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 .. code-block:: scale =kenovi keno-vi sample problem 8 infinitely long cylinder from 2c8 unit read parameters lib=4 htm=no end parameters read mixt sct=2 mix=1 ncm=1 92234 4.82717e-04 92235 4.47971e-02 92236 9.57233e-05 92238 2.65767e-03 end mixt 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 .. _8-1c-2-9: Sample Problem 9 INFINITE ARRAY OF 2C8 UNITS ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .. centered:: Input Data KENO V.a .. code-block:: scale =kenova sample problem 9 infinite array of 2c8 units read param lib=4 gen=103 htm=no end param read mixt sct=2 mix=1 ncm=1 92234 4.82717e-04 92235 4.47971e-02 92236 9.57233e-05 92238 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 .. code-block:: scale =kenovi keno-vi sample problem 9 infinite array of 2c8 units read parameters lib=4 htm=no end parameters read mixt sct=2 mix=1 ncm=1 92234 4.82717e-04 92235 4.47971e-02 92236 9.57233e-05 92238 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 .. _8-1c-2-10: 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. .. centered:: Input Data KENO V.a .. code-block:: scale =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 htm=no end parameters read mixt sct=2 mix=1 ncm=1 92234 4.82717e-04 92235 4.47971e-02 92236 9.57233e-05 92238 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 fill f1 end fill end array end data end KENO-VI .. code-block:: scale =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 htm=no end parameters read mixt sct=2 mix=1 ncm=1 92234 4.82717e-04 92235 4.47971e-02 92236 9.57233e-05 92238 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 .. _8-1c-2-11: 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). .. centered:: Input Data KENO V.a .. code-block:: scale =kenova sample problem 11 2c8 bare read restart data read param beg=51 rst=94 res=0 htm=no end param end data end KENO-VI .. code-block:: scale =kenovi sample problem 11 2c8 bare read restart data read param beg=51 rst=94 res=0 htm=no end param end data end .. _8-1c-2-12: Sample Problem 12 4 AQUEOUS 4 METAL ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ This problem is a critical experiment consisting of a composite array\ :sup:`1` 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 :numref:`fig8-1c-3`. .. figure:: figs/KenoC/fig3.png :align: center :width: 500 :name: fig8-1c-3 Critical assembly of 4 solution units and 4 metal units. .. centered:: Input Data KENO V.a .. code-block:: scale =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 htm=no end param read mixt sct=2 mix=1 ncm=1 92234 4.82717e-04 92235 4.47971e-02 92236 9.57233e-05 92238 2.65767e-03 mix=2 ncm=2 1001 5.77931e-02 7014 2.13092e-03 8016 3.74114e-02 92234 1.06784e-05 92235 9.84602e-04 92236 5.29386e-06 92238 6.19414e-05 mix=3 ncm=11 1001 5.67873e-02 6000 3.54921e-02 8016 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 .. code-block:: scale =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 htm=no end param read mixt sct=2 mix=1 ncm=1 92234 4.82717e-04 92235 4.47971e-02 92236 9.57233e-05 92238 2.65767e-03 mix=2 ncm=2 1001 5.77931e-02 7014 2.13092e-03 8016 3.74114e-02 92234 1.06784e-05 92235 9.84602e-04 92236 5.29386e-06 92238 6.19414e-05 mix=3 ncm=11 1001 5.67873e-02 6000 3.54921e-02 8016 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 .. _8-1c-2-13: Sample Problem 13 TWO CUBOIDS IN A CYLINDRICAL ANNULUS ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ This critical experiment :cite:`KENO-C-irving_monte_1964` consists of two assemblies of 93.2% :sup:`235`\ U-enriched uranium metal :math:`(\rho=18.69 \mathrm{^g} / \mathrm{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 :numref:`fig8-1c-4`. .. figure:: figs/KenoC/fig4.png :align: center :width: 500 :name: fig8-1c-4 Drawing of two cuboids in an annulus critical assembly. .. centered:: Input Data KENO V.a .. code-block:: scale =kenova sample problem 13 two cuboids in a cylindrical annulus read param lib=4 htm=no 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 ncm=3 92234 4.80916e-04 92235 4.46300e-02 92236 9.53661e-05 92238 2.64776e-03 end mixt read array gbl=1 nux=1 nuy=1 nuz=3 fill 1 2 3 end fill end array end data end KENO-VI .. code-block:: scale =kenovi sample problem 13 two cuboids in a cylindrical annulus read param lib=4 htm=no end param read mixt sct=2 mix=1 ncm=3 92234 4.80916e-04 92235 4.46300e-02 92236 9.53661e-05 92238 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 .. _8-1c-2-14: Sample Problem 14 U METAL CYLINDER IN AN ANNULUS ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ This critical experiment\ :sup:`3` consists of a 93.2 :sup:`235`\ U-enriched uranium metal cylinder within a cylindrical annulus of the same material as shown in :numref:`fig8-1c-5`. The uranium metal specification is identical to that used in sample problem 13. .. figure:: figs/KenoC/fig5.png :align: center :width: 500 :name: fig8-1c-5 Drawing of the cylinder in an annulus critical assembly. .. centered:: Input Data KENO V.a .. code-block:: scale =kenova sample problem 14 u metal cylinder in an annulus read param lib=4 htm=no end param read mixt sct=2 mix=1 ncm=3 92234 4.80916e-04 92235 4.46300e-02 92236 9.53661e-05 92238 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 .. code-block:: scale =kenovi sample problem 14 u metal cylinder in an annulus read param lib=4 htm=no end param read mixt sct=2 mix=1 ncm=3 92234 4.80916e-04 92235 4.46300e-02 92236 9.53661e-05 92238 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 .. _8-1c-2-15: Sample Problem 15 SMALL WATER REFLECTED SPHERE ON PLEXIGLAS COLLAR ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ This critical experiment :cite:`KENO-C-byers_critical_1977` 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 :numref:`fig8-1c-6`. 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. .. figure:: figs/KenoC/fig6.png :align: center :width: 400 :name: fig8-1c-6 Drawing of a critical assembly consisting of a uranium sphere on a Plexiglas collar with a cylindrical water reflector. .. centered:: Input Data KENO V.a .. code-block:: scale =kenova sample problem 15 small water reflected sphere on plexiglas collar read param lib=4 flx=yes fdn=yes htm=no end param read mixt sct=2 mix=1 ncm=4 92234 5.27115e-04 92235 4.70308e-02 92236 1.00692e-04 92238 4.89708e-04 mix=2 ncm=11 1001 5.67873e-02 6000 3.54921e-02 8016 1.41968e-02 mix=3 ncm=12 1001 6.67554e-02 mix=3 ncm=12 8016 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 .. code-block:: scale =kenovi sample problem 15 small water reflected sphere on plexiglas collar read param lib=4 flx=yes fdn=yes plt=yes htm=no end param read mixt sct=2 mix=1 ncm=4 92234 5.27115e-04 92235 4.70308e-02 92236 1.00692e-04 92238 4.89708e-04 mix=2 ncm=11 1001 5.67873e-02 6000 3.54921e-02 8016 1.41968e-02 mix=3 ncm=12 1001 6.67554e-02 mix=3 ncm=12 8016 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 .. _8-1c-2-16: 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 :math:`\times` 10\ :sup:`-27` atoms of boron per milliliter are present in the borated solution. .. centered:: Input Data KENO V.a .. code-block:: scale =kenova sample problem 16 uo2f2 infinite slab k-infinity read parameters lib=4 amx=yes xap=no htm=no end parameters read mixt sct=2 mix=1 ncm=5 9019 2.96287e-03 1001 6.08125e-02 8016 3.33691e-02 92235 1.38188e-03 92238 9.95505e-05 mix=2 ncm=13 11023 2.39503e-03 13027 4.97720e-04 14028 1.66260E-02 14029 8.41845E-04 14030 5.58826E-04 5010 9.14627e-04 5011 3.68149e-03 8016 4.49174e-02 mix=3 ncm=6 9019 2.96287e-03 1001 6.08125e-02 8016 3.33691e-02 92235 1.38188e-03 92238 9.95505e-05 5010 2.94862e-04 5011 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 .. code-block:: scale =kenovi sample problem 16 uo2f2 infinite slab k-infinity read parameters lib=4 amx=yes xap=no htm=no end parameters read mixt sct=2 mix=1 ncm=5 9019 2.96287e-03 1001 6.08125e-02 8016 3.33691e-02 92235 1.38188e-03 92238 9.95505e-05 mix=2 ncm=13 11023 2.39503e-03 13027 4.97720e-04 14028 1.66260E-02 14029 8.41845E-04 14030 5.58826E-04 5010 9.14627e-04 5011 3.68149e-03 8016 4.49174e-02 mix=3 ncm=6 9019 2.96287e-03 1001 6.08125e-02 8016 3.33691e-02 92235 1.38188e-03 92238 9.95505e-05 5010 2.94862e-04 5011 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 .. _8-1c-2-17: 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. .. centered:: Input Data KENO V.a .. code-block:: scale =kenova sample problem 17 93% uo2f2 solution sphere adjoint calculation read parameters lib=4 npg=10000 nbk=10500 adj=yes amx=yes xap=no htm=no end parameters read mixt sct=2 mix=1 ncm=7 1001 6.55892e-02 8016 3.34755e-02 9019 6.80925e-04 92235 3.16910e-04 92238 2.35522e-05 end mixt read geometry global unit 1 sphere 1 1 16.0 end geom end data end KENO-VI .. code-block:: scale =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 tba=0.5 htm=no end parameters read mixt sct=2 mix=1 ncm=7 1001 6.55892e-02 8016 3.34755e-02 9019 6.80925e-04 92235 3.16910e-04 92238 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 .. _8-1c-2-18: Sample Problem 18 1F27 DEMONSTRATION OF OPTIONS ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ A reflected cubic array of 27 cylinders of aqueous uranyl nitrate in Plexiglas bottles :cite:`KENO-C-thomas_critical_1964`. 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 :math:`\times` 3 :math:`\times` 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 :numref:`fig8-1c-7`. A photograph of one of the experiments utilized 27 of the Plexiglas bottles is shown in :numref:`fig8-1c-8`. Sample problem 18 has 15.24 cm of paraffin on all six faces rather than the 2.54-cm Plexiglas shown on five faces. .. figure:: figs/KenoC/fig7.png :align: center :width: 500 :name: fig8-1c-7 Perspective of critical 1F27 experiment. .. figure:: figs/KenoC/fig8.png :align: center :width: 500 :name: fig8-1c-8 View of a 27-unit array with 2.54-cm. thick Plexiglas reflector on five sides and a 15.24-cm. thick paraffin base. .. centered:: Input Data KENO V.a .. code-block:: scale =kenova sample problem 18 1f27 demonstration of options problem read para gen=103 npg=1000 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 htm=no end para read mixt sct=2 mix=1 ncm=2 1001 5.77931e-02 7014 2.13092e-03 8016 3.74114e-02 92234 1.06784e-05 92235 9.84602e-04 92236 5.29386e-06 92238 6.19414e-05 mix=2 ncm=11 1001 5.67873e-02 6000 3.54921e-02 8016 1.41968e-02 mix=3 ncm=10 6000 3.84193e-02 9001001 7.99120e-02 mix=4 ncm=15 8016 3.33757e-11 1001 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=1000 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 .. code-block:: scale =kenovi sample problem 18 1f27 critical experiment read para gen=103 npg=1000 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 htm=no end para read mixt sct=2 mix=1 ncm=2 1001 5.77931e-02 7014 2.13092e-03 8016 3.74114e-02 92234 1.06784e-05 92235 9.84602e-04 92236 5.29386e-06 92238 6.19414e-05 mix=2 ncm=11 1001 5.67873e-02 6000 3.54921e-02 8016 1.41968e-02 mix=3 ncm=10 6000 3.84193e-02 9001001 7.99120e-02 mix=4 ncm=15 8016 3.33757e-11 1001 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 .. _8-1c-2-19: 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 :numref:`fig8-1c-3`. .. centered:: Input Data KENO V.a .. code-block:: scale =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 htm=no end param read mixt mix=1 ncm=1 92234 4.82717e-04 92235 4.47971e-02 92236 9.57233e-05 92238 2.65767e-03 mix=2 ncm=2 1001 5.77931e-02 7014 2.13092e-03 8016 3.74114e-02 92234 1.06784e-05 92235 9.84602e-04 92236 5.29386e-06 92238 6.19414e-05 mix=3 ncm=11 1001 5.67873e-02 6000 3.54921e-02 8016 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 .. code-block:: scale =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 htm=no end param read mixt mix=1 ncm=1 92234 4.82717e-04 92235 4.47971e-02 92236 9.57233e-05 92238 2.65767e-03 mix=2 ncm=2 1001 5.77931e-02 7014 2.13092e-03 8016 3.74114e-02 92234 1.06784e-05 92235 9.84602e-04 92236 5.29386e-06 92238 6.19414e-05 mix=3 ncm=11 1001 5.67873e-02 6000 3.54921e-02 8016 1.41968e-02 sct=2 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 .. _8-1c-2-20: 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 :numref:`fig8-1c-9`. .. figure:: figs/KenoC/fig9.png :align: center :width: 500 :name: fig8-1c-9 Typical arrangement for critical experiments with interacting arrays of aluminum cylinders containing enriched :sup:`235`\ U solutions. .. centered:: Input Data KENO V.a .. code-block:: scale =kenova sample problem 20 triangular pitched array read param lib=4 htm=no end param read mixt sct=2 mix=1 ncm=8 92235 1.37751e-03 92238 9.92357e-05 8016 3.33717e-02 9019 2.95350e-03 1001 6.08364e-02 mix=2 ncm=14 13027 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 .. code-block:: scale =kenovi sample problem 20 triangular pitched array 7 pins in a circle read parameters lib=4 htm=no end parameters read mixt sct=2 mix=1 ncm=8 92235 1.37751e-03 92238 9.92357e-05 8016 3.33717e-02 9019 2.95350e-03 1001 6.08364e-02 mix=2 ncm=14 13027 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 .. _8-1c-2-21: 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/\ :sup:`235`\ U 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 :numref:`fig8-1c-10`. The steel tank was ignored. .. centered:: Input Data KENO V.a .. code-block:: scale =kenova sample problem 21 partially filled sphere read param lib=4 htm=no 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 ncm=9 1001 6.19770e-02 8016 3.34895e-02 9019 2.50098e-03 92234 2.54224e-07 92235 6.18924e-05 92238 1.18835e-03 mix=2 ncm=14 13027 6.03067e-02 end mixt end data end KENO-VI .. code-block:: scale =kenovi sample problem 21 partially filled sphere read param lib=4 htm=no end param read mixt sct=2 mix=1 ncm=9 1001 6.19770e-02 8016 3.34895e-02 9019 2.50098e-03 92234 2.54224e-07 92235 6.18924e-05 92238 1.18835e-03 mix=2 ncm=14 13027 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 .. figure:: figs/KenoC/fig10.png :align: center :width: 500 :name: fig8-1c-10 Schematic of bare partially filled sphere experiment inside a 9.5-ft-diameter, 9-ft-high steel tank. .. _8-1c-2-22: 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 :math:`\times` 2 :math:`\times` 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 :math:`\times` 2 :math:`\times` 2 array. .. centered:: Input Data KENO V.a .. code-block:: scale =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 htm=no end parameters read mixt sct=2 mix=1 ncm=1 92234 4.82717e-04 92235 4.47971e-02 92236 9.57233e-05 92238 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 .. code-block:: scale =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 htm=no end parameters read mixt sct=2 mix=1 ncm=1 92234 4.82717e-04 92235 4.47971e-02 92236 9.57233e-05 92238 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 .. _8-1c-2-23: 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 :math:`\times` 2 :math:`\times` 2 array using Z hemicylinders (in KENO V.a) or hemicylinders with different chord sizes and directions (in KENO-VI). .. centered:: Input Data KENO V.a .. code-block:: scale =kenova sample problem 23 case 2c8 bare as mixed zhemicylinders read parameters npg=1000 fdn=yes lib=4 htm=no end parameters read mixt sct=2 mix=1 ncm=1 92234 4.82717e-04 92235 4.47971e-02 92236 9.57233e-05 92238 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 .. code-block:: scale =kenovi sample problem 23 case 2c8 bare as mixed unrotated zcylinders read parameters npg=1000 fdn=yes lib=4 htm=no end parameters read mixt sct=2 mix=1 ncm=1 92234 4.82717e-04 92235 4.47971e-02 92236 9.57233e-05 92238 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 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 .. _8-1c-2-24: 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 :math:`\times` 2 :math:`\times` 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. .. centered:: Input Data KENO V.a .. code-block:: scale =kenova sample problem 24 case 2c8 bare as mixed xhemicylinders read parameters npg=1000 fdn=yes lib=4 htm=no end parameters read mixt sct=2 mix=1 ncm=1 92234 4.82717e-04 92235 4.47971e-02 92236 9.57233e-05 92238 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 .. code-block:: scale =kenovi sample problem 24 case 2c8 bare as mixed x-rotated cylinders read parameters rnd=4c6a61962572 npg=1000 fdn=yes lib=4 htm=no end parameters read mixt sct=2 mix=1 ncm=1 92234 4.82717e-04 92235 4.47971e-02 92236 9.57233e-05 92238 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 .. _8-1c-2-25: 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 :math:`\times` 2 :math:`\times` 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. .. centered:: Input Data KENO V.a .. code-block:: scale =kenova sample problem 25 case 2c8 bare as mixed yhemicylinders read parameters npg=1000 fdn=yes lib=4 htm=no end parameters read mixt sct=2 mix=1 ncm=1 92234 4.82717e-04 92235 4.47971e-02 92236 9.57233e-05 92238 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 .. code-block:: scale =kenovi sample problem 25 case 2c8 bare as mixed y-rotated cylinders read parameters npg=1000 fdn=yes lib=4 htm=no end parameters read mixt sct=2 mix=1 ncm=1 92234 4.82717e-04 92235 4.47971e-02 92236 9.57233e-05 92238 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 .. _8-1c-2-26: 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 :math:`\times` 2 :math:`\times` 2 array using zhemicylinders with origins. KENO V.a .. code-block:: scale =kenova sample problem 26 case 2c8 bare as mixed zhemicylinders with origins read parameters npg=1000 fdn=yes lib=4 run=yes htm=no end parameters read mixt sct=2 mix=1 ncm=1 92234 4.82717e-04 92235 4.47971e-02 92236 9.57233e-05 92238 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 .. _8-1c-2-27: 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 :math:`\times` 2 :math:`\times` 2 array using hemicylinders whose axes are in the x direction. Origins are specified for each hemicylinder. .. centered:: Input Data KENO V.a .. code-block:: scale =kenova sample problem 27 case 2c8 bare as mixed xhemicylinders with origins read parameters npg=1000 fdn=yes lib=4 run=yes htm=no end parameters read mixt sct=2 mix=1 ncm=1 92234 4.82717e-04 92235 4.47971e-02 92236 9.57233e-05 92238 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 .. _8-1c-2-28: 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 :math:`\times` 2 :math:`\times` 2 array using hemicylinders whose axes are in the y direction. Origins are specified for each hemicylinder. .. centered:: Input Data KENO V.a .. code-block:: scale =kenova sample problem 28 case 2c8 bare as mixed yhemicylinders with origins read parameters npg=1000 fdn=yes lib=4 run=yes htm=no end parameters read mixt sct=2 mix=1 ncm=1 92234 4.82717e-04 92235 4.47971e-02 92236 9.57233e-05 92238 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 .. _8-1c-2-29: Sample Problem 29 BARE CRITICAL SPHERE 3.4420-IN. RADIUS ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ This problem is a critical experiment :cite:`KENO-C-mihalczo_measurements_1993` consisting of a critical Oralloy sphere. The density of the Oralloy is 18.747 g/cc, and the isotopic enrichment (wt %) is 93.21% :sup:`235`\ U, 5.7697% :sup:`238`\ U, 0.9844% :sup:`234`\ U, and 0.0359% :sup:`236`\ U. The critical radius was 8.74268 cm. A photograph of the experiment is given in :numref:`fig8-1c-11`. The support structure was ignored in the input data. .. figure:: figs/KenoC/fig11.png :align: center :width: 500 :name: fig8-1c-11 Critical Oralloy sphere. .. centered:: Input Data KENO V.a .. code-block:: scale =kenova sample problem 29 bare critical sphere 3.4420" radius read parameters npg=1000 fdn=yes lib=4 htm=no end parameters read mixt sct=2 mix=16 ncm=16 92235 4.47709e-02 92238 2.73631e-03 92234 4.74858e-04 92236 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 .. code-block:: scale =kenovi sample problem 26 bare critical sphere 3.4420" radius read parameters npg=1000 fdn=yes lib=4 htm=no end parameters read mixt sct=2 mix=1 ncm=16 92235 4.47709e-02 92238 2.73631e-03 92234 4.74858e-04 92236 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 .. _8-1c-2-30: 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. .. centered:: Input Data KENO V.a .. code-block:: scale =kenova sample problem 30 bare critical sphere z hemisphere model 3.4420" radius read parameters npg=1000 fdn=yes lib=4 htm=no end parameters read mixt sct=2 mix=16 92235 4.47709e-02 92238 2.73631e-03 92234 4.74858e-04 92236 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=unit end plt2 end plot end data end .. _8-1c-2-31: 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. .. centered:: Input Data KENO V.a .. code-block:: scale =kenova sample problem 31 bare critical sphere x hemisphere model 3.4420" radius read parameters fdn=yes lib=4 htm=no end parameters read mixt sct=2 mix=16 ncm=16 92235 4.47709e-02 92238 2.73631e-03 92234 4.74858e-04 92236 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=unit end plt2 end plot end data end .. _8-1c-2-32: 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. .. centered:: Input Data KENO V.a .. code-block:: scale =kenova sample problem 32 bare critical sphere y hemisphere model 3.4420" radius read parameters fdn=yes lib=4 htm=no end parameters read mixt sct=2 mix=16 ncm=16 92235 4.47709e-02 92238 2.73631e-03 92234 4.74858e-04 92236 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=unit end plt2 end plot end data end .. _8-1c-2-33: Sample Problem 33 CRITICAL TRIANGULAR PITCHED ARRAY OF ANNULAR RODS ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ This sample problem represents a critical experiment :cite:`KENO-C-johnson_critical_1966` 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% :sup:`235`\ U, 98.02% :sup:`238`\ U, 0.006% :sup:`236`\ U, and 0.002% :sup:`234`\ U. 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. :numref:`fig8-1c-12` and :numref:`fig8-1c-13` provide a representation of the model. A photograph of a single annular billet is shown in :numref:`fig8-1c-14`. .. centered:: Input Data KENO V.a .. code-block:: scale =kenova sample problem 33 critical triangular pitched array of annular rods read parameters fdn=yes nub=yes lib=4 htm=no npg=2000 end parameters read mixt sct=2 mix=17 ncm=17 92235 9.49270e-04 92238 4.71245e-02 92234 9.77785e-07 92236 2.90844e-06 mix=18 ncm=18 8016 3.33757e-02 1001 6.67515e-02 mix=19 ncm=19 1001 6.67515e-02 8016 3.33757e-02 mix=20 ncm=20 92235 9.49270e-04 92238 4.71245e-02 92234 9.77785e-07 92236 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 .. code-block:: scale =kenovi sample problem 27 critical triangular pitched array of annular rods read parameters fdn=yes nub=yes lib=4 htm=no npg=4000 end parameters read mixt sct=2 mix=1 ncm=17 92235 9.49270e-04 92238 4.71245e-02 92234 9.77785e-07 92236 2.90844e-06 mix=2 ncm=18 8016 3.33757e-02 1001 6.67515e-02 mix=3 ncm=19 1001 6.67515e-02 8016 3.33757e-02 mix=4 ncm=20 92235 9.49270e-04 92238 4.71245e-02 92234 9.77785e-07 92236 2.90844e-06 mix=5 ncm=18 8016 3.33757e-02 1001 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 .. figure:: figs/KenoC/fig12.png :align: center :width: 500 :name: fig8-1c-12 Horizontal slice through a critical triangular pitched array of partially flooded 1.95% enriched uranium metal annular billets. .. figure:: figs/KenoC/fig13.png :align: center :width: 500 :name: fig8-1c-13 Vertical slice through the center of a critical triangular-pitched array of partially flooded 1.9% enriched uranium metal annular billets. .. figure:: figs/KenoC/fig14.png :align: center :width: 500 :name: fig8-1c-14 1.95% Enriched uranium metal annular billet used in critical experiments .. only:: html .. rubric:: References .. bibliography:: zSCALE.bib :cited: :keyprefix: KENO-C- :labelprefix: KENO-Appendix-C