Novel Adaptive Preconditioner for Contact Problem in Fuel Rod

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

Abstract

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

CLC Number:

O242.1

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.

Figures/Tables 10

Fig.1 Solution region of fuel rod

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

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

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

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

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

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

Fig.6 Cumulative CPU times for different preprocessing matrices

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

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

References 27

1	ZINKLE S J , TERRANI K A , GEHIN J C , et al. Accident tolerant fuels for LWRs: A perspective[J]. Journal of Nuclear Materials, 2014, 448 (1/3): 374- 379.
2	International Atomic Energy Agency. Fuel modelling in accident conditions(FUMAC): IAEA-TECDOC-1889[R]. Vienna: IAEA, 2019: 1-2.
3	GEELHOOD K, LUSCHER W G, RAYNAUD P A, et al. FRAPCON-4.0: A computer code for the calculation of steady-state, thermal-mechanical behavior of oxide fuel rods for high burnup: PNNL-19418[R]. Richland: Pacific Northwest National Laboratory, 2015: 1-50.
4	GAMIER C, MAILHE P, SONTHEIMER F, et al. Validation of advanced fuel performance COPERNIC3 code on AREVA global database up to 100 GWd/tM: INIS-FR-09-1168[C]. Paris: WRFPM/Top Fuel, 2009: 1-10.
5	SIEFKEN L J, CORYELL E W, HARVEGO E A, et al. SCDAP/RELAP5/Mod 3.3 code manual: MATPRO-A library of materials properties for Light-Water-Reactor accident analysis: NUREG/CR-6150[R]. Idaho Falls: Idaho National Engineering and Environmental Laboratory, 2001.
6	王柱, 张纯禹, 李奥林, 等. 压水堆燃料棒三维热-力学性能的精细模拟[J]. 原子能科学技术, 2017, 51 (6): 1038- 1044.
7	VAN UFFELEN P , HALES J , LI W , et al. A review of fuel performance modelling[J]. Journal of Nuclear Materials, 2019, 516, 373- 412. DOI
8	王严培, 刘振海, 齐飞鹏, 等. 三维燃料棒精细化模拟软件FUPAC3D与FUPAC的对比验证研究[J]. 核动力工程, 2022, 43 (4): 46- 52.
9	ZHANG Cheng , WU Yingwei , LIU Shichao , et al. Multidimensional multiphysics modeling of TRISO particle fuel with SiC/ZrC coating using modified fission gas release model[J]. Annals of Nuclear Energy, 2020, 145, 107599. DOI
10	GASTON D , NEWMAN C , HANSEN G , et al. MOOSE: A parallel computational framework for coupled systems of nonlinear equations[J]. Nuclear Engineering and Design, 2009, 239 (10): 1768- 1778. DOI
11	WILLIAMSON R L , GAMBLE K A , PEREZ D M , et al. Validating the BISON fuel performance code to integral LWR experiments[J]. Nuclear Engineering and Design, 2016, 301, 232- 244. DOI
12	HE Yanan , CHEN Ping , WU Yingwei , et al. Preliminary evaluation of U3Si2-FeCrAl fuel performance in light water reactors through a multi-physics coupled way[J]. Nuclear Engineering and Design, 2018, 328, 27- 35. DOI
13	KNOLL D A , KEYES D E . Jacobian-free Newton–Krylov methods: A survey of approaches and applications[J]. Journal of Computational Physics, 2004, 193 (2): 357- 397. DOI
14	冯涛, 蔚喜军, 安恒斌, 等. 预处理JFNK方法求解非平衡辐射扩散方程组(英文)[J]. 计算物理, 2013, 30 (4): 483- 490.
15	BALAY S, BRUNE P, BUSCHELMAN K, et al. PETSc users manual: Revision 3.7[R]. Argonne: Argonne National Laboratory, 2016: 91-92.
16	POPP A , GITTERLE M , GEE M W , et al. A dual mortar approach for 3D finite deformation contact with consistent linearization[J]. International Journal for Numerical Methods in Engineering, 2010, 83 (11): 1428- 1465. DOI
17	TOPTAN A , KROPACZEK D J , AVRAMOVA M N . Gap conductance modeling Ⅰ: Theoretical considerations for single- and multi-component gases in curvilinear coordinates[J]. Nuclear Engineering and Design, 2019, 353, 110283. DOI
18	BELYTSCHKO T , LIU W K , MORAN B , et al. Nonlinear finite elements for continua and structures[M]. 2nd New York: John Wiley & Sons Inc, 2014: 597- 642.
19	POPP A , WALL W A . Dual mortar methods for computational contact mechanics-overview and recent developments[J]. GAMM Mitteilungen, 2014, 37 (1): 66- 84. DOI
20	于平安, 朱瑞安, 喻真烷, 等. 核反应堆热工分析[M]. 3版上海: 上海交通大学出版社, 2002: 44- 66.
21	LUSCHER W G, GEELHOOD K J. Material property correlations: Comparisons between FRAPCON-3.4, FRAPTRAN 1.4, and MATPRO: PNNL-19417[R]. Richland: Pacific Northwest National Lab, 2010: 4-5.
22	International Atomic Energy Agency. Thermophysical properties database of materials for light water reactors and heavy water reactors: IAEA-TECDOC-1496[R]. Vienna: IAEA, 2006: 328-333.
23	DUUNE F , PETRINIC N . Introduction to computational plasticity[M]. New York: Oxford University Press, 2005: 143- 168.
24	RASHID M M . Incremental kinematics for finite element applications[J]. International Journal for Numerical Methods in Engineering, 1993, 36 (23): 3937- 3956. DOI
25	BIRD R B , STEWART W E , LIGHTFOOT E N . Transport phenomena[M]. New York: John Wiley & Sons, 1960: 487- 507.
26	HALES J D, NOVASCONE S R, PASTORE G, et al. BISON theory manual the equations behind nuclear fuel analysis: INL/EXT-13-29930[R]. Idaho Falls: Idaho National Laboratory, 2016: 50-51.
27	HENSON V E , YANG U M . BoomerAMG: A parallel algebraic multigrid solver and preconditioner[J]. Applied Numerical Mathematics, 2002, 41 (1): 155- 177. DOI