燃料棒接触问题的新型自适应预处理方法

doi:10.19596/j.cnki.1001-246x.8868

摘要/Abstract

摘要：

通过分析接触前后雅可比矩阵的稀疏结构, 构造基于接触压力判断准则的新型自适应预处理方法。在接触压力为零时使用完全的雅可比矩阵作为Preconditioned Jacobian-free Newton-Krylov(PJFNK)方法的预处理矩阵, 在接触压力非零时使用雅可比矩阵的块对角作为预处理矩阵。数值试验表明: 本文的自适应预处理方法能够有效提升模拟效率, 求解总时间与Multiphysics Object-Oriented Simulation Environment(MOOSE)中现有方法相比减少了15.2%~33.1%。

关键词: MOOSE, PJFNK, 燃料棒, 力学接触, 自适应预处理

Abstract:

The contact problem between the fuel core block and the cladding is a key point in the simulation of nuclear reactor fuel rods, and the inclusion of a contact model increases the difficulty of solving the set of algebraic equations. By analyzing the sparse structure of the Jacobi matrix before and after contact, a novel adaptive preprocessing method based on the contact pressure judgment criterion is constructed. The full Jacobi matrix is used as the preprocessing matrix for the Preconditioned Jacobian-free Newton-Krylov (PJFNK) method when the contact pressure is zero, and the block diagonal of the Jacobi matrix is used as the preprocessing matrix when the contact pressure is non-zero. Numerical experiments show that the adaptive preprocessing method in this paper can effectively improve the simulation efficiency, and the total solution time is reduced by 15.2%~33.1% compared with the existing methods in Multiphysics Object-Oriented Simulation Environment(MOOSE).

Key words: MOOSE, PJFNK, fuel rod, mechanical contact, adaptive preconditioning

中图分类号:

O242.1

刘威震, 刘振海, 辛勇, 叶舒愉, 张世全. 燃料棒接触问题的新型自适应预处理方法[J]. 计算物理, 2024, 41(5): 596-606.

Weizhen LIU, Zhenhai LIU, Yong XIN, Shuyu YE, Shiquan ZHANG. Novel Adaptive Preconditioner for Contact Problem in Fuel Rod[J]. Chinese Journal of Computational Physics, 2024, 41(5): 596-606.

图/表 10

图1 燃料棒求解区域

Fig.1 Solution region of fuel rod

表1 燃料棒材料参数

Table 1 Material parameters of fuel rods

参数	热膨胀系数/K^-1	蠕变系数/(Pa^-n·s^-1)	应力指数	激活能/(J·mol^-1)	密度/(kg·m^-3)
燃料芯块	1.0×10^-5	4.531 3×10^-25	4	552 334	10 431.0
包壳	1.0×10^-6	9.032 0×10^-33	4	270 000	6 551.0

图2 雅可比矩阵的稀疏结构(a)接触前; (b)接触后

Fig.2 Sparse structure of Jacobian matrix (a) before contact; (b) after contact

表2 燃料棒规格参数

Table 2 Specifications of fuel rods

参数	数值	参数	数值
燃料芯块半径/mm	2.78	包壳内径/mm	2.801
包壳外径/mm	3.27	燃料芯块高度/cm	10
包壳高度/cm	11	单侧气腔高度/mm	3
冷却剂温度/K	576	换热系数/(W·(m²·K)^-1)	7 500

图3 燃料棒的网格剖分(比例缩放：高度压缩2倍，半径增加3倍。)

Fig.3 Grid profile of fuel rods (Scaling: height compression by 2 times, radius by 3 times.)

图4 不同时间步的间隙变化和接触压力

Fig.4 Gap variation and contact pressure at different time steps

图5 单独的预处理矩阵在每个时间步的用时

Fig.5 The time taken by the individual preprocessing matrix in each time step

图6 不同预处理矩阵的累计CPU用时

Fig.6 Cumulative CPU times for different preprocessing matrices

图7 热源和修正系数(a)热源随时间的变化; (b)热源沿轴向的修正系数; (c) 热源沿半径的修正系数; (d)热源沿x轴的修正系数

Fig.7 Heat source and correction factor (a) heat source over time; (b) correction factor for heat source along axial direction; (c) correction factor for heat source along radius; (d) correction factor for heat source along x-axis

图8 模拟时间为一天的不同预处理矩阵的求解结果(a)不同时间步的用时及接触压力; (b)累计CPU用时

Fig.8 Solution results for different preprocessing matrices with simulation time of one day (a) time spent and contact pressure for different time steps; (b) cumulative CPU time spent

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