Fig. 1. Preliminary calculation results of ICSBEP benchmarks: HEU, IEU and U-233
Fig. 2. Preliminary calculation results of ICSBEP benchmarks: MIX, Pu and SPEC
Fig. 3. Proportion of major intermediate-weight nuclides in the benchmark
Fig. 4. Geometrical model of the HMF021-002 benchmark
Fig. 5. Normalization neutron flux
Fig. 6. U-235 microscopic total cross section
Fig. 7. Fe-56 Microscopic scattering cross section
Fig. 8. Fe-56 microscopic capture cross section
Fig. 9. Microscopic total cross section of intermediate-weight nuclides
Fig. 10. Normalization neutron flux
Fig. 11. U-235 microscopic total cross section
Fig. 12. Fe-56 microscopic scattering section
Fig. 13. Calculation results of ICSBEP benchmarks: HEU, IEU, and U-233
Fig. 14. Calculation results of ICSBEP benchmarks: MIX, Pu, and SPEC
Fig. 15. Statistical deviations for the calculation results of ICSBEP benchmarks
燃料类型 Fuel type | 数量 Number | 几何 Geometry | 能谱 Spectrum |
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HEU | 53 | 圆球Sphere | 快谱Fast | IEU | 10 | 圆球Sphere | 快谱Fast | U-233 | 10 | 圆球Sphere | 快谱Fast | MIX | 29 | 圆球Sphere | 快谱Fast | Pu | 35 | 圆球Sphere | 快谱Fast | SPEC | 10 | 圆球Sphere | 快谱Fast |
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Table 1. Selection of ICSBEP experimental device
基准题Benchmark | TULIP keff | MCNP keff | Δkeff / 10-2 |
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HMF-003-012 | 0.993 80 | 1.008 44 | -1.464 | HMF-021-001 | 0.986 28 | 0.997 43 | -1.115 | HMF-021-002 | 0.986 48 | 0.997 58 | -1.110 | IMF-005-001 | 0.993 05 | 1.001 89 | -0.884 | IMF-005-002 | 0.992 94 | 1.001 76 | -0.882 | PMF-025-001 | 0.993 66 | 0.998 82 | -0.516 | PMF-025-002 | 0.993 69 | 0.998 85 | -0.516 | PMF-026-001 | 0.984 29 | 0.998 60 | -1.431 | PMF-026-002 | 0.984 34 | 0.998 59 | -1.425 | PMF-028-001 | 0.982 99 | 0.998 65 | -1.566 | PMF-028-002 | 0.982 91 | 0.998 54 | -1.563 | PMF-032-001 | 0.988 21 | 0.998 63 | -1.042 | PMF-032-002 | 0.988 28 | 0.99869 | -1.041 |
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Table 2. Benchmarks with large keff deviations
燃料区Fuel region | 反射层1 Reflector 1 | 反射层2 Reflector 2 |
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核素Nuclide | 核子密度Density | 核素Nuclide | 核子密度Density | 核素Nuclide | 核子密度Density |
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U-234 | 5.208 70×10-4 | Fe-54 | 4.641 90×10-3 | Fe-54 | 4.620 20×10-3 | U-235 | 4.202 30×10-2 | Fe-56 | 7.286 80×10-2 | Fe-56 | 7.252 70×10-2 | U-238 | 4.361 30×10-3 | Fe-57 | 1.682 90×10-3 | Fe-57 | 1.675 00×10-3 | W-182 | 1.454 40×10-5 | Fe-58 | 2.239 60×10-4 | Fe-58 | 2.229 10×10-4 | W-183 | 7.861 10×10-6 | C-12 | 1.126 90×10-3 | C-12 | 1.121 70×10-3 | W-184 | 1.690 00×10-5 | Si-28 | 1.481 60×10-4 | Si-28 | 1.474 60×10-4 | W-186 | 1.574 40×10-5 | Si-29 | 7.526 50×10-6 | Si-29 | 7.491 30×10-6 | Fe-54 | 1.136 00×10-5 | Si-30 | 4.967 30×10-6 | Si-30 | 4.944 10×10-6 | Fe-56 | 1.783 20×10-4 | Cr-50 | 1.131 10×10-5 | Cr-50 | 1.125 80×10-5 | Fe-57 | 4.118 30×10-6 | Cr-52 | 2.181 20×10-4 | Cr-52 | 2.171 00×10-4 | Fe-58 | 5.481 00×10-7 | Cr-53 | 2.473 30×10-5 | Cr-53 | 2.461 70×10-5 | C-12 | 1.091 90×10-3 | Cr-54 | 6.156 60×10-6 | Cr-54 | 6.127 70×10-6 | | | Mn-55 | 3.285 10×10-4 | Mn-55 | 3.269 70×10-4 | | | Ni-58 | 1.570 10×10-4 | Ni-58 | 1.562 70×10-4 | | | Ni-60 | 6.047 80×10-5 | Ni-60 | 6.019 50×10-5 | | | Ni-61 | 2.629 00×10-6 | Ni-61 | 2.616 60×10-6 | | | Ni-62 | 8.382 20×10-6 | Ni-62 | 8.343 00×10-6 | | | Ni-64 | 2.134 70×10-6 | Ni-64 | 2.124 70×10-6 | | | Cu-63 | 1.473 00×10-4 | Cu-63 | 1.466 10×10-4 | | | Cu-65 | 6.571 40×10-5 | Cu-65 | 6.540 50×10-5 |
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Table 3. Material data for the HMF021-002 Benchmark
核素名称 Nuclide | 核子密度 Density | 比例 Proportion / % |
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U-235 | 3.517 62×10-3 | 5.02 | Fe-56 | 6.652 08×10-2 | 94.98 |
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Table 4. Material data for the homogeneous two-nuclide problem
核素Nuclide | 能量上限Maximum energy / eV |
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可分辨共振Resolved resonance | 不可分辨共振区Unresolved resonance |
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Na-23 | 5.00×105 | — | Ti-48 | 3.00×105 | — | V-51 | 1.00×105 | — | Cr-52 | 9.80×105 | — | Mn-55 | 1.00×105 | — | Fe-56 | 8.50×105 | — | Co-59 | 1.00×105 | — | Ni-58 | 8.12×105 | — | Cu-63 | 9.95×104 | — | Zn-64 | 1.00×105 | — | Zr-90 | 6.00×104 | — | U-235 | 2.25×103 | 2.50×104 | U-238 | 2.00×104 | 1.49×105 | Pu-239 | 2.50×103 | 3.00×104 | Pu-241 | 3.00×102 | 4.02×104 |
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Table 5. Energy division of common nuclides in fast reactors
基准题Benchmark | TULIP keff | MCNP keff | Δkeff / 10-5 |
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HMF-003-012 | 1.005 15 | 1.008 44 | -329 | HMF-021-001 | 0.994 37 | 0.997 43 | -306 | HMF-021-002 | 0.994 55 | 0.997 58 | -303 | IMF-005-001 | 0.998 68 | 1.001 89 | -321 | IMF-005-002 | 0.998 59 | 1.001 76 | -317 | PMF-025-001 | 0.997 27 | 0.998 82 | -155 | PMF-025-002 | 0.997 30 | 0.998 85 | -155 | PMF-026-001 | 0.996 23 | 0.998 60 | -237 | PMF-026-002 | 0.996 28 | 0.998 59 | -231 | PMF-028-001 | 0.995 84 | 0.998 65 | -281 | PMF-028-002 | 0.995 78 | 0.998 54 | -276 | PMF-032-001 | 0.996 25 | 0.998 63 | -238 | PMF-032-002 | 0.996 32 | 0.998 69 | -237 |
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Table 6. Calculation results of benchmarks with high intermediate-weight nuclide loading