Research and Verification of High-Fidelity Physics Calculation Method for Hexagonal Reactor
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摘要: 俄罗斯商用压水堆VVER和大多数实验堆均采用了六角形紧凑型栅格布置，为了实现VVER和六角形实验堆的高保真数值模拟分析，本文基于数值反应堆物理计算程序（NECP-X）开展了六角形堆芯高保真计算方法研究和程序开发。首先，将全局-局部耦合共振自屏计算方法拓展至六角形堆芯，实现六角形堆芯燃料棒的全堆芯高精度共振计算；其次，基于2D/1D耦合输运计算方法研究了六角形堆芯的高保真计算方法；最后，为了提高全堆芯计算的计算效率，研究了基于区域分解松耦合的非结构网格的粗网有限差分（CMFD）加速方法，可以实现以矩形、六角形和其他多边形栅元为基础的pin-by-pin CMFD 加速。为了验证六角形堆芯高保真计算方法的精度和效率，计算了六角形C5G7基准问题，并分析了六角形输运计算方法的计算精度和CMFD方法的加速效果；将NECP-X程序应用于西安脉冲堆的2D全堆芯计算，与蒙特卡罗程序的结果对比表明NECP-X程序计算得到的特征值和功率分布均具有较高精度。因此，本文建立的六角形堆芯高保真计算方法可以应用于六角形堆芯的分析计算。
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关键词:
- 数值反应堆物理计算程序（NECP-X） /
- 六角形堆芯 /
- 特征线方法（MOC） /
- 粗网有限差分（CMFD）加速 /
- 2D/1D计算
Abstract: Russian commercial pressurized water reactor VVER and most experimental reactors adopt hexagonal compact lattice arrangement. To realize the high-fidelity numerical simulation analysis of the VVER and the hexagonal experimental reactor, in this paper, the high-fidelity calculation method and program development of hexagonal core are carried out based on NECP-X. First, the global-local coupled resonance self-shielding calculation method is extended to the hexagonal core to realize the high-precision resonance calculation of hexagonal core fuel rods; Second, based on 2D/1D coupled transport calculation method, the high-fidelity calculation method of hexagonal core is studied; Finally, in order to improve the calculation efficiency of the full-core calculation, the coarse-mesh finite-difference (CMFD) acceleration method based on the loosely coupled unstructured grid of domain decomposition is studied, which can realize pin-by-pin coarse-mesh finite-difference acceleration based on rectangular, hexagonal and other polygonal cells. In order to verify the accuracy and efficiency of the hexagonal core high-fidelity calculation method, the hexagonal C5G7 benchmark problem is calculated, and the calculation accuracy of the hexagonal transport calculation method and the acceleration effect of the CMFD method are analyzed; NECP-X is applied to the two-dimensional full core calculation of a pulsed reactor in Xi’an. The comparison with the results of Monte Carlo program shows that the eigenvalues and power distribution calculated by NECP-X have high accuracy. Therefore, the high-fidelity calculation method of hexagonal core established in this paper can be applied to the analysis and calculation of hexagonal core.-
Key words:
- NECP-X /
- Hexagonal core /
- Method of characteristics (MOC) /
- CMFD acceleration /
- 2D/1D calculation
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图 5 六角形模块化特征线示意图
$\Delta u$、$\Delta v$和$\Delta w$—特征线与对应面的交点之间的间距
Figure 5. Schematic Diagram of Hexagonal Modular Characteristic Line
图 6 特征线参数获取流程
$\Delta \widetilde A $—初始线宽；$\widetilde \alpha $—初始角度；$u$和$v$—在对应面上的特征线数目；P—六角形模块的边长
Figure 6. Process of Getting Characteristic Line Parameters
图 7 栅元面编号以及中子净流正方向
Figure 7. Numbers of Cell Surfaces and Positive Direction of Neutron Net Flow
图 9 非结构网格示意图
$l_{i}^k$—第$i$个网格里第$k$个面的网格质心距，$k=1,2,3 $；$\phi _{i}^k$—第$i$个网格第$k$个面上的平均注量率
Figure 9. Schematic Diagram of Unstructured Grid
图 13 插棒#B算例棒功率相对偏差分布图
Figure 13. Distribution Diagram of Relative Deviation of Rod Power for Example B of Inserting Rod
图 14 西安脉冲堆棒功率偏差分布图
Figure 14. Distribution Diagram of Rod Power Deviation of Pulsed Reactor in Xi'an
表 1 C5G7基准题计算条件
Table 1. Calculation Conditions of C5G7 Benchmark
计算条件 设置值 辐角（0~180°）数目 18 极角（0~90°）数目 3 特征线线宽/cm 0.03 特征值收敛限 10−5 裂变率收敛限 10−4 
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表 2 CMFD方法加速效果
Table 2. Acceleration Effect of CMFD
计算方法 外迭代次数 计算时间/min 纯MOC计算 281 104 CMFD方法加速的MOC计算 10 5
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表 3 NECP-X与MCNP特征值以及棒功率结果比较
Table 3. Eigenvalue and Rod Power Difference between NECP-X and MCNP
计算结果 未插棒 插棒#A 插棒#B MCNP特征值（统计误差/pcm） 1.12276（1） 1.11892（1） 1.10263（1） NECP-X特征值（偏差/pcm） 1.12223（−53） 1.11843（−49） 1.10212（−51） 第1层相对棒功率偏差 最大值/% 1.99 1.91 2.03 均方根/% 0.53 0.48 0.54 第2层相对棒功率偏差 最大值/% 1.85 1.79 1.80 均方根/% 0.50 0.44 0.52 第3层相对棒功率偏差 最大值/% 1.74 1.42 1.30 均方根/% 0.43 0.45 0.54 轴向积分相对棒功率偏差 最大值/% 1.77 1.63 1.74 均方根/% 0.46 0.41 0.49 偏差—NECP-X程序计算值与MCNP程序计算的参考解之间的差别
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