Adjoint Neutron Flux Calculation Technique Based on Improved Variational Nodal Method
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摘要: 共轭中子通量密度对于核安全和压水堆（PWR）中的探测器计算有着重要的意义，为了消除现有节块方法在处理由于控制棒移动带来的非均匀节块（包括非均匀的截面和不连续因子）时所造成的较大误差，本文提出一种改进的变分节块法（VNM）。确定了不同于前向方程的共轭节块方法的连续条件，不同于传统VNM在全局建立泛函，本文方法为每一个节块建立泛函；构建了含非均匀不连续因子的乘子项，以显式处理表面不连续的共轭中子通量密度；除共轭体中子通量密度、截面和表面分中子流密度外，将表面不连续因子展开为分段正交多项式来构造响应矩阵。含有非均匀节块的BEAVRS基准题数值结果证明，同传统VNM相比，改进的VNM可以将非均匀问题的有效共轭增殖系数和燃料区共轭中子通量密度偏差降低2个量级，有利于实现前向与共轭中子通量密度的高精度内积计算。Abstract: The adjoint neutron flux is of great significance for nuclear safety and detector calculation in pressurized water reactor (PWR). However, existing nodal methods would cause a big error due to heterogeneous nodes, including heterogeneous cross sections and discontinuity factors, which will appear frequently with the control rod moving. In this paper, an improved variational nodal method (VNM) is proposed to reduce the error. It determines the continuous conditions for adjoint nodal methods that are different from forward equation. Unlike traditional VNM, which establishes a functional method globally, this paper establishes a functional method for each node. It constructs a multiplier term with a heterogeneous discontinuity factor to explicitly deal with the adjoint neutron flux with surface discontinuity. Apart from the expansions of adjoint neutron flux, cross section and surface partial neutron current densities, the surface discontinuity factor (DF) is also expanded into pieces-wise orthogonal polynomials to construct the nodal response matrixes. The numerical results of the BEAVRS benchmark problem with heterogeneous nodes existing demonstrate that compared with the traditional VNM, the improved VNM can reduce the error by two orders of magnitude for the adjoint neutron flux in fuel area and the adjoint effective multiplication factor, which can help realize high accuracy calculation for the inner product of forward and adjoint neutron flux.
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Key words:
- PWR /
- Heterogeneous node /
- VNM /
- Adjoint neutron flux
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图 1 B62H问题燃料区节块平均共轭中子通量密度偏差分布图
Figure 1. Error Distribution of Nodal Average Adjoint Neutron Flux in Fuel Area of B62H Case
图 2 B62问题燃料区节块平均共轭中子通量密度偏差分布图
Figure 2. Error Distribution of Nodal Average Adjoint Neutron Flux in Fuel Area of B62 Case
表 1 共轭有效增殖因子计算偏差
Table 1. Calculation Error of Adjoint Effective Multiplication Factor
验证算例 $k_{_{{\rm{eff}}}}^* $参考解 计算方法 $k_{_{{\rm{eff}}}}^*$偏差/pcm B62H 0.967789 HOM −30.5 HET 0.1 B62 0.967811 HOM −34.1 HET −0.1 
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表 2 节块平均共轭中子通量密度计算偏差
Table 2. Calculation Error of Nodal Average Adjoint Neutron Flux
验证算例 计算方法 能群 燃料区节块平均共轭中子
通量密度偏差/%最大值 均方根 B62H HOM 快群 7.229 0.595 热群 6.043 0.591 HET 快群 0.042 0.002 热群 0.028 0.001 B62 HOM 快群 7.979 0.658 热群 6.430 0.653 HET 快群 0.072 0.005 热群 0.050 0.004
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