Weighted Monte Carlo solution of neutron kinetics equations
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摘要: 为了实现基于蒙特卡罗方法的中子动力学计算，在传统的直接蒙特卡罗动力学方法的基础上，提出了一种加权蒙特卡罗动力学方法。该方法通过引入粒子权重的概念，隐式考虑中子俘获反应和裂变反应过程中中子数目的变化，避免了模拟粒子的数目随时间的变化，降低了统计偏差，消除了程序计算过程中粒子的存库操作，提高了计算精度。基于单能点堆模型，开发了中子动力学计算程序NECP-Dandi，进行了大量数值验证与分析，包括无缓发中子、单组缓发中子、六组缓发中子、正阶跃反应性引入、负阶跃反应性引入、正脉冲反应性、负脉冲反应性和正线性反应性引入等情况。数值结果表明，相比于直接蒙特卡罗动力学方法，加权蒙特卡罗动力学方法在计算结果的精度和计算效率上有较为明显的改进，程序结构更为简洁。Abstract: The solution of time dependent neutronics equations still remains a challenging problem. A weighted Monte Carlo kinetics method (wMCk) is proposed based on traditional analog Monte Carlo kinetics method (aMCk). The "implicit capture" is introduced to avoid the problem of low efficient tallies in aMCk; the definition of particle weighting leads to a more compact simulation flow due to the elimination of stack operation to particle bank. Using this method, a code named NECP-Dandi was developed in mono-energetic point-kinetics model for numerical verification and analysis. 11 test cases with different reactivity insertions were employed to verify the method. Numerical results demonstrate that wMCk is superior to aMCk in terms of accuracy, efficiency and code structure.
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表 1 11个测试算例
Table 1. Definition of 11 test cases
case No. of precursor group reactivity insertion duration of insertion/ms No. of initial particle/106 1 1 0 1 2500 2 6 0 1 2500 3 0 +0.006 5 1 1 4 0 -0.006 5 1 1 5 1 +0.006 5 1 2500 6 1 -0.006 5 1 2500 7 6 +0.006 5 1 2500 8 6 -0.006 5 1 2500 9 6 +0.006 5 0.1 2500 10 6 -0.006 5 0.1 2500 11 6 ≈0.03t 100 2500 
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表 2 单群宏观截面
Table 2. Macroscopic cross-section utilized in reactivity insertion
ρ Σt/cm-1 Σs/cm-1 Σf/cm-1 ν v/(cm·s-1) 0 0.165 258 0.156 187 0.003 657 47 2.48 3.046 655 10×106 +0.006 5 0.165 258 0.156 187 0.003 681 40 2.48 3.046 655 10×106 -0.006 5 0.165 258 0.156 187 0.003 633 84 2.48 3.046 655 10×106 0.65t 0.165 258 0.156 187 0.003 657 47+0.000 109 724t 2.48 3.046 655 10×106
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表 3 最后一个时间点的统计误差与相对误差
Table 3. Largest statistic and relative errors
No. wMCk aMCk δerrR/% δerrS δerrR/% δerrS ① -0.014 6.56×10-4 0.73 9.76×10-3 ② 5.38×10-6 2.67×10-7 1.91×10-5 5.51×10-7 ③ 3.83×10-3 6.75×10-5 1.06 1.24×10-2 ④ -3.48×10-3 6.67×10-5 0.559 1.35×10-2 ⑤ -0.12 6.62×10-4 0.76 9.44×10-3 ⑥ 1.40×10-6 2.93×10-7 2.79×10-5 5.97×10-7 ⑦ 0.098 9 6.62×10-4 1.02 1.01×10-2 Note: Numbers in the first column correspond to those marked in Figures 1-5.
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