TEST 7 -- ZPR-6/7 SPH. HOMOGENEOUS MODEL 0 1 0 1 1 1 0 3 0 0 80 1 50 0 0 2 2 20 1 0 CORE BLANKET CORE 300. 1. 1 10000/ HOMOGENEOUS SELFSHIELDING BLANKT 300. 1. 1 10000/ HOMOGENEOUS SELFSHIELDING 1 1 PU239 8.8672E-4/ 1 1 PU240 1.1944E-4/ 1 1 PU241 1.33E-5/ 1 1 U235 1.26E-5/ 1 1 U238 5.78036E-3/ 1 1 MONAT 2.357E-4/ 1 1 NA23 9.2904E-3/ 1 1 016u .01398/ 1 1 FE56 1.297E-2/ 1 1 CR52 2.709E-3/ 1 1 NI58 1.240E-3/ 1 1 MN55 2.12E-4/ 2 2 U235 8.56E-5/ 2 2 U238 3.96179E-2/ 2 2 MONAT 3.8E-6/ 2 2 016 2.4E-5/ 2 2 FE56 4.637E-3/ 2 2 CR52 1.295E-3/ 2 2 NI58 5.635E-4/ 2 2 MN55 9.98E-5/ CHI STOPThe ENDF/B-VI libraries (which are used for all the test problems for TRANSX 2.0) contain the isotopes for iron, nickel, and chromium instead of the elemental evaluations given in previous versions. The dominant isotope of each element has been used here to keep the problem input compact.
The cross sections are appropriate for diffusion theory or P0 transport theory. Note that the table length is less than the maximum 80+3+1. The scattering matrix is truncated in a way that preserves the scattering cross section (i.e., down the diagonal). In this problem, there are two regions and two mixes. The mixes are macroscopic, and the fission $\chi$ will be different in each region because the compositions are different. Self-shielding uses the constant-escape option with a temperature of 300 K. The region sizes are not needed for this problem, and they have been set to 1.0 for simplicity. The mean chord length for each region has been made very large (i.e., no escape from the region) in order to obtain the mixture part of the self-shielding only. The background cross sections obtained are displayed on the printed output.
This homogeneous model is not completely adequate because the core and blanket regions are really made up of stacks of long slabs of the various materials arranged as repeating cells in a stainless-steel matrix. This figure shows a simplified core cell. Region A is the SS304 structure (0.222 cm), B is a U$_3$O$_8$ slab (0.635 cm), C is Na in an SS304 can (1.270 cm), D is an Fe$_2$O$_3$ slab (0.3175 cm), and E is a Pu/U/Mo fuel slab in a can (0.635 cm). All can thicknesses are 0.0381 cm). This heterogeneity has two effects; first, the background cross section for a material in a slab is changed because of the change in density and the addition of a slab escape probability; and second, the flux will be slightly different in each slab due to the sources and absorptions. The first effect is called heterogeneous self-shielding, and the second leads to the advantage and disadvantage factors for cell homogenization.
For the cell of this figure, the self-shielding of Pu-239 in E should be fairly well represented by the mixture effect in region E plus the escape cross section for a 0.5588-cm slab with a Dancoff correction corresponding to outside regions 4.965-cm thick ($\overline{\ell}_{\rm m}$ = 9.930 cm) with the homogenized composition of A+B+C+D+clad on each side of the fuel slab. For the U-238 in E, the outside regions extend only to B and would, therefore, be 1.626-cm thick with the C+D+clad composition on each side. The U-238 in E sees different outside regions to the left (A+B+C+D+clad) and to the right (B+C+D+clad). The SS304 structures should be well represented by a 0.444-cm slab with outside regions with the A+B+C+D+E composition. Note that the mean chord would be only one-half of the infinite slab value, as $\overline{\ell}_{\rm m}$ = 5.08 cm. These kinds of arguments can be completed for the other materials and regions in the cell.
This approach leads to separate two-region cell problems for each class of material (i.e., all the plutonium isotopes in E from one two-region calculation, all the U isotopes in B from another), and TRANSX is capable of setting up the problem in this way. However, the result is very complex, and many dummy compositions are required. A simpler representation is the multiregion slab cell shown in this figure. The dashed lines represent reflection planes. Region 1 is the SS304 end slab (0.2223cm), 2 is the U$_3$O$_8$ slab (0.6350 cm), 3 is the sodium (1.270 cm), 4 is the Fe$_2$O$_3$ slab (0.3175), 5 is the cladding (0.0381 cm), and 6 is the fuel (0.2794 cm).} This cell neglects the egg-crate SS304 structure and will overestimate the $\sigma_0$ values for region 1. It also neglects the effect of the structure on any paths to regions 2 through 3; thus, there will be too much sodium and not enough iron. The resulting model is given in the following sample problem.
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