NUCLEAR TECHNIQUES, Volume. 48, Issue 1, 010603(2025)
Development of neutron diffusion and transport algorithms based on finite volume method
Figures & Tables(27)
Fig. 1. Implementation flowchart of neutron diffusion and transportation in OpenFOAM
Fig. 2. Comparison of 2D-IAEA assembly normalized powers for benchmark problems
Fig. 3. Comparison of 3D-IAEA assembly normalized powers for benchmark problems
Fig. 4. The three-dimensional power distribution of the 3D-IAEA benchmark problem
Fig. 5. Comparison of assembly normalized powers for 3D-LMW under steady state
Fig. 7. The three-dimensional power distribution of the 3D-LMW benchmark problem
Fig. 10. The three-dimensional power distribution of the 3D-TAKED benchmark problem
Fig. 14. Neutron fluxes distribution of group 1 (a) and group 7 (b)
Table 1. Summary of results for the benchmark problems under steady state
View tableView in ArticleTable 1. Summary of results for the benchmark problems under steady state
基准问题
Benchmark problem
参考值
Reference value
模拟值
This work
误差 / 10-5 Error
二维IAEA（2D IAEA） 1.029 585 1.029 54 -4.4 三维IAEA（3D IAEA） 1.029 03 1.028 91 -11.7 三维LMW（3D LMW） 0.999 66 0.999 626 -3.4
Table 2. Summary of calculation conditions for the benchmark problems under steady state
View tableView in ArticleTable 2. Summary of calculation conditions for the benchmark problems under steady state
基准问题
Benchmark problem
网格剖分数量
Number of
grid divisions
网格剖分形式
Grid generation form
计算条件
Calculation conditions
计算时间
Computing time
/ s
二维IAEA（2D IAEA） 24 100 结构化网格 Structured grid 20核并行 20-core parallelism 1 三维IAEA（3D IAEA） 1 144 750 结构化网格 Structured grid 20核并行 20-core parallelism 45 三维LMW（3D LMW） 7 897 500 结构化网格 Structured grid 20核并行 20-core parallelism 436
Table 3. Simulation results of 2D-IAEA for benchmark problems
View tableView in ArticleTable 3. Simulation results of 2D-IAEA for benchmark problems
程序Program 二维广义横向积分方法和SANM半解析方法的综合[
13 ]Synthesis of 2D generalised transverse integral methods and SANM semi-analytic methods
1.029 490 RBF无网格法[ 14 ] RBF meshless method1.029 312 TriVNM[ 15 ]1.029 560 7 OpenFOAM 1.029 540
Table 4. Simulation results of 3D-IAEA for benchmark problems
View tableView in ArticleTable 4. Simulation results of 3D-IAEA for benchmark problems
程序Program COMSOL Multiphysics[ 16 ]1.029 090 cosCORE[ 17 ]1.029 170 ParaFidi[ 18 ]1.029 040 OpenFOAM 1.028 914
Table 5. Simulation results of 3D-LMW for benchmark problems
View tableView in ArticleTable 5. Simulation results of 3D-LMW for benchmark problems
程序Program NDEFoam[ 19 ]1.000 120 ParaFidi[ 18 ]0.999 600 二维广义横向积分方法和SANM
半解析方法的综合[
13 ]Synthesis of 2D generalised transverse integral methods and SANM semi-analytic methods
0.999 719 OpenFOAM 0.999 626
Table 6. Summary of calculation conditions for the benchmark problems under steady state
View tableView in ArticleTable 6. Summary of calculation conditions for the benchmark problems under steady state
基准问题
Benchmark
problem
网格剖分数量
Number of grid
divisions
网格剖分形式
Grid generation form
计算条件
Calculation conditions
计算时间
Computing time
/ s
C5G7 123 644 结构化网格Structured grid 20核并行运算20-core parallelism 4 835 IAEA 70 848 结构化网格Structured grid 20核并行运算20-core parallelism 38 TAKEDA 862 665 结构化网格Structured grid 20核并行运算20-core parallelism 9 644
Table 7. Comparison of local neutron flux and k-eigenvalue factors
View tableView in ArticleTable 7. Comparison of local neutron flux and k-eigenvalue factors
区域Zone SURCU DNTR 本文工作This work 区域平均
中子注量率
Area-average
neutron flux
/ cm-2·s-1
1 0.016 860 0.016 860 0.016 856 2 0.000 125 0.000 125 0.000 124 3 0.000 041 0.000 035 0.000 038 4 0.000 295 0.000 295 0.000 295 5 0.000 791 0.000 791 0.000 814 — 1.008 3 1.008 5 1.008 5
Table 8. Simulation results of IAEA for benchmark problems
View tableView in ArticleTable 8. Simulation results of IAEA for benchmark problems
求解程序Program SURCU[ 22 ]1.008 3 FELICIT[ 22 ]1.006 9 TEPFEM[ 22 ]1.007 9 OpenFOAM 1.008 5
Table 9. Comparison of k-eigenvalue factors under TAKEDA
View tableView in ArticleTable 9. Comparison of k-eigenvalue factors under TAKEDA
-全提All withdrawn -插入一半Half inserted 控制棒价值Control rod worth Monte Carlo 0.973 2 0.959 4 1.47×10-2 DNTR 0.973 6 0.959 7 1.54×10-2 PN 0.979 4 0.964 7 1.56×10-2 CTDOS[ 26 ]0.977 667 5 0.961 868 9 1.481×10-2 TORT[ 26 ]0.976 750 0.962 007 1.474×10-2 本文工作
This work
0.973 5 0.959 5 1.49×10-2
Table 10. Comparison of average neutron flux under control rod all out
View tableView in ArticleTable 10. Comparison of average neutron flux under control rod all out
中子注量率
Neutron flux density / cm-2·s-1
Monte Carlo DNTR PN 本文工作
This work
燃料区
Fuel region
4.281 4×10-5 -0.03a -1.04a 0.02a 2.408 1×10-4 0.03 -0.64 0.01 1.641 1×10-4 -0.01 1.63 0.00 6.224 7×10-6 -0.25 0.98 -0.23 轴向增殖区
Axial breeder zone
5.185 0×10-6 0.06 5.10 0.12 4.691 2×10-5 -0.26 14.5 -0.32 4.697 8×10-5 -0.31 22.5 -0.77 3.773 6×10-6 -1.12 32.7 -1.98 径向增殖区
Radial breeder zone
3.325 2×10-6 0.31 7.05 0.05 3.089 3×10-5 -0.21 6.84 -0.48 3.283 4×10-5 -0.37 22.6 -0.87 2.047 3×10-6 -0.50 30.8 -1.16 钠填充区
Sodium filling zone
2.534 4×10-5 0.89 -0.84 1.27 1.665 8×10-4 0.01 0.82 0.03 1.264 8×10-4 0.10 4.26 0.15 6.984 0×10-6 -0.38 13.4 -0.14
Table 11. Comparison of average neutron flux under control rod half inserted
View tableView in ArticleTable 11. Comparison of average neutron flux under control rod half inserted
中子注量率
Neutron flux / cm-2·s-1
Monte Carlo DNTR PN 本文工作
This work
燃料区
Fuel region
4.348 2×10-5 -0.10a -1.74a -0.05a 2.417 1×10-4 0.05 -1.19 0.05 1.620 0×10-4 0.06 -3.70 0.05 6.043 8×10-6 -0.24 0.82 -0.26 轴向增殖区
Axial breeder zone
5.220 9×10-6 0.45 5.39 0.61 4.677 2×10-5 -0.21 11.6 -0.16 4.619 0×10-5 -0.31 27.7 -0.62 3.628 7×10-6 -0.20 34.3 -0.89 径向增殖区
Radial breeder zone
3.317 6×10-6 0.08 6.25 -0.16 3.043 8×10-5 -0.13 13.9 -0.39 3.212 6×10-5 -0.43 21.8 -0.95 2.001 6×10-6 -0.91 29.7 -1.61 钠填充区
Sodium filling zone
2.590 2×10-5 0.24 -1.95 0.74 1.677 9×10-4 -0.39 0.00 -0.27 1.255 1×10-4 -0.73 3.27 -0.64 7.064 8×10-6 -5.12 9.27 -4.90 控制棒
Control rod
1.655 6×10-5 0.71 — 0.21 9.105 0×10-5 0.47 — 0.16 5.181 5×10-5 0.31 — 0.05 1.107 3×10-6 1.03 — -0.82
Table 12. Comparison of 2D-C5G7 benchmark eigenvalue solutions
View tableView in ArticleTable 12. Comparison of 2D-C5G7 benchmark eigenvalue solutions
程序
Program
OpenFOAM MCNP RMC APOLL02 HELIOS SN2D[ 30 ]APOLLO2[ 31 ]DORT-GRS[ 31 ]TWODANT[ 30 ]1.186 49 1.186 55 1.186 43 1.186 18 1.193 299 1.187 023 1.186 180 1.184 818 1.186 677
Table 13. Comparison of 3D-C5G7 benchmark eigenvalue solutions
View tableView in ArticleTable 13. Comparison of 3D-C5G7 benchmark eigenvalue solutions
程序
Program
OpenFOAM MCNP PANDA VARIANT-ISE 1.143 82 1.143 08 1.142 04 1.145 01
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Wei LI, Xiaojing LIU, Xiang CHAI, Pengcheng ZHAO. Development of neutron diffusion and transport algorithms based on finite volume method[J]. NUCLEAR TECHNIQUES, 2025, 48(1): 010603
Paper Information
Category: NUCLEAR ENERGY SCIENCE AND ENGINEERING
Received: Feb. 28, 2024
Accepted: --
Published Online: Feb. 26, 2025
The Author Email: ZHAO Pengcheng (赵鹏程)
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