Application Research on VITAS—a General-purpose Neutron Transport Code
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摘要: 为提高确定论全堆芯中子输运程序的适用性，开发了通用型中子输运程序VITAS。针对TAKEDA3基准题（矩形组件）、TAKEDA4基准题（六角形组件）、Dodds基准题（R-Z几何）和C5G7-TD5基准题（压水堆高保真计算）的验证结果表明，高阶的空间和角度基函数能够使结果稳定地向参考解渐进收敛，达到与多群蒙卡相当的计算精度水平。与参考解相比，TAKEDA3基准题有效增殖系数（keff）偏差低于60pcm（1pcm=10−5），控制棒价值偏差为−3pcm，中子通量密度分布均方根（RMS）偏差为1.03%；TAKEDA4基准题keff偏差低于20pcm，控制棒价值偏差为32pcm，中子通量密度分布RMS偏差为0.70%；Dodds基准题的功率最大偏差低于1%；C5G7-TD5基准题的功率偏差低于0.9%。本文研究表明VITAS有望成为一套精确求解中子输运问题的通用型计算工具。Abstract: In order to improve the applicability of deterministic whole-core neutron transport code, a general-purpose neutron transport code VITAS is developed. The verification results of TAKEDA3 benchmark problem (rectangular assembly), the TAKEDA4 benchmark problem (hexagonal assembly), the Dodds benchmark problem (R-Z geometry) and the C5G7-TD5 benchmark problem (PWR high fidelity calculation) show that higher-order spatial and angular basis functions can make the results converge asymptotically and steadily to the reference solution, reaching the calculation accuracy level equivalent to that of multi-group Monte Carlo method. Compared with the reference solution, the deviations are less than 60pcm (1pcm = 10−5) in effective multiplication coefficient (keff), −3pcm in control rod worth and 1.03% in neutron flux distribution root mean square (RMS) for TAKEDA3 benchmark problem; less than 20pcm in keff, 32pcm in control rod worth and 0.70% in neutron flux distribution RMS for TAKEDA4 benchmark problem; less than 1% (maximum) in power for Dodds benchmark problem; and less than 0.9% in power for C5G7-TD5 benchmark problem. The research in this paper shows that VITAS has the potential to become a general-purpose calculation tool for accurately solving the neutron transport problems.
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图 2 非结构化三棱柱节块的坐标映射示意图
ξ、η、τ、x、y、z—坐标轴；p1、p2、p3、p1′、p2′、p3′、k、n、p、k'、n'、p'—节块顶点
Figure 2. Coordinate Mapping Diagram of the Unstructured Triangular Prism Node
图 4 TAKEDA3基准题CR-In算例计算结果
Figure 4. Calculation Results of the CR-In Example for TAKEDA3 Benchmark Problem
图 5 TAKEDA4基准题CRi算例计算结果
Figure 5. Calculation Results of CRi Example for TAKEDA4 Benchmark Problem
图 6 Dodds基准题归一化功率的对比结果
Figure 6. Comparison of the Normalized Power for the Dodds Benchmark Problem
图 7 C5G7-TD5基准题燃料栅元的3种有限元网格划分
Figure 7. Three Finite-Element Meshing Schemes for Fuel Lattice Cell of the C5G7-TD5 Benchmark Problem
图 8 三维C5G7-TD5基准题对比结果
Figure 8. Comparative Results of Three-dimensional C5G7-TD5 Benchmark Problem
表 1 计算基准题介绍
Table 1. Introduction to Calculation Benchmark Problems
基准题名称 问题类型 计算所用节块类型 TAKEDA3 三维、矩形、稳态 Cartesian TAKEDA4 三维、六角形、稳态 Hexagonal-z Dodds 三维、R-Z、瞬态 Triangular-z C5G7-TD5 三维、燃料棒精细描述、瞬态 Cartesian-FE 
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表 2 TAKEDA3基准题的keff偏差对比
Table 2. Comparison of keff Deviations for TAKEDA3 Benchmark Problem
计算对象 角度阶数 keff偏差/pcm 4/0阶 5/1阶 6/2阶 7/2阶 7/3阶 8/4阶 CR-In P1 2081 281 246 247 244 243 P3 1952 122 91 92 88 88 P5 1931 98 66 66 63 63 P7 1925 90 58 58 / / CR-Out P1 1637 216 199 199 198 197 P3 1547 99 85 85 83 83 P5 1531 80 65 65 63 63 P7 1526 74 59 59 / / 控制棒价值 P1 −551 −82 −62 −63 −61 −61 P3 −507 −30 −12 −13 −10 −10 P5 −501 −24 −5 −5 −4 −4 P7 −500 −21 −3 −3 / / “/”—计算超出了内存的限制，计算未启动，其余同
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表 3 TAKEDA4基准题的keff偏差对比
Table 3. Comparison of keff Deviations for TAKEDA4 Benchmark Problem
计算对象 角度阶数 keff偏差/pcm 4/0阶 5/1阶 6/2阶 7/3阶 8/4阶 CRi P1 6783 821 518 544 560 P3 6336 353 52 59 67 P5 6278 289 −14 −17 / P7 6261 277 −29 / / CRh P1 6048 706 504 516 527 P3 5658 278 73 76 79 P5 5615 222 10 6 / P7 5603 210 −7 / / CRo P1 4841 460 376 377 381 P3 4549 163 70 70 69 P5 4519 120 17 12 / P7 4510 109 2 / / 控制棒价值 P1 −4268 −669 −353 −385 −402 P3 −3992 −318 −9 −18 −29 P5 −3950 −272 32 32 / P7 −3938 −266 39 / /
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表 4 二维C5G7问题的计算结果对比
Table 4. Comparison of Calculation Results for Two-dimensional C5G7 Problem
角度阶数 keff偏差/pcm 棒功率偏差/% 最大值 RMS 32FE/2阶 96FE/4阶 144FE/6阶 32FE/2阶 96FE/4阶 144FE/6阶 32FE/2阶 96FE/4阶 144FE/6阶 P3_3 477 526 551 2.03 1.79 1.83 0.87 0.76 0.79 P5_3 261 313 325 1.48 1.27 1.28 0.57 0.48 0.48 P7_3 199 239 252 1.31 1.08 1.09 0.48 0.37 0.37 P9_3 132 160 168 1.14 0.88 0.88 0.39 0.27 0.27 P11_3 102 123 132 1.07 0.80 0.80 0.36 0.24 0.23 P13_3 71 86 93 1.00 0.71 0.70 0.32 0.21 0.20 P15_3 56 69 75 0.97 0.67 0.65 0.31 0.19 0.19 P17_3 41 51 56 0.93 0.62 0.60 0.29 0.18 0.18 P19_3 33 42 46 0.92 0.60 0.60 0.29 0.18 0.18 P21_3 24 30 33 0.89 0.61 0.64 0.28 0.18 0.17 P23_3 18 23 26 0.88 0.62 0.66 0.27 0.17 0.17
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