随着核热耦合技术的发展,为了考虑多物理场之间的强耦合效应,实现高精度和大规模并行计算,有必要对多物理场守恒方程联立求解,统一处理建模、离散和迭代计算过程.本文基于开源计算流体力学(Computational Fluid Dynamics,CFD)平台OpenFOAM,使用有限体积法(Finite Volume Method,FVM)和高斯定理,对中子扩散和中子输运的控制方程进行离散,实现了对多群中子扩散方程和中子输运方程离散和迭代求解.中子输运方程的离散中使用离散纵标法对空间角度进行离散.为了验证开发程序的有效性,验证计算中采用包括国际原子能机构(International Atomic Energy Agency,IAEA)、TAKEDA和C5G7等在内的多个基准算例对开发的中子扩散和输运程序进行验证.通过对包括非均匀化堆芯基准问题在内的不同基准题中稳态和瞬态结果进行对比验证.验证结果表明:基于有限体积法可以同时实现对均匀化和非均匀化中子物理问题的精确求解,并且具有几何适应性强的特点.为未来实现统一编程框架下的物理与热工多物理场守恒方程的联立求解奠定了基础.
Development of neutron diffusion and transport algorithms based on finite volume method
[Background]With the development of nuclear-thermal coupling technology,it is essential to consider the strong coupling effects between multiple physics fields and achieve high precision and large-scale parallel computing.Simultaneous solutions to the conservation equations of multiple physics fields need to be pursued,providing a unified approach to modeling,discretization,and iterative computation processes.[Purpose]This study aims to achieve discrete and iterative solutions for multigroup neutron diffusion equations and neutron transport equations,considering the strong coupling between neutronics and thermal-hydraulics.[Methods]Firstly,based on the open-source computational fluid dynamics(CFD)platform OpenFOAM,the finite volume method(FVM)was employed to discretize the control equations for neutron diffusion and neutron transport using the Gauss theorem.Then,the discrete ordinates method was applied to the discretization of the neutron transport equation for spatial angular discretization,and FVM was used to discretize both neutron diffusion and neutron transport equations spatial variables whilst the multigroup method was employed for discretizing energy variables,and implicit Euler method was utilized for discretizing time variables.Finally,neutron diffusion was verified using three benchmark cases,i.e.,two-dimensional International Atomic Energy Agency(IAEA),three-dimensional IAEA,and three-dimensional LMW,to validate the effectiveness of the developed program,and neutron transport was verified using various benchmark cases including IAEA,TAKEDA,and C5G7.[Results]The verification results for the two-dimensional IAEA benchmark show excellent agreement,with a maximum error of 1.1%in normalized power.The three-dimensional IAEA benchmark results align closely with reference values,showing a maximum error of 3.4%.For the three-dimensional LMW benchmark,the total power at 20 s is slightly underestimated,with a maximum error below 2%.The IAEA criticality benchmark results show region-averaged flux and effective multiplication factor deviations of 6.9%and 22×10-⁵,respectively.The TAKEDA benchmark confirms the program's accuracy in three-dimensional problems,with effective multiplication factor,neutron flux,and control rod worth matching reference values.The C5G7 benchmark validates the FVM-based transport algorithm's strong geometric adaptability and ability to solve both uniform and non-uniform neutron physics problems accurately.[Conclusions]FVM-based neutron diffusion and transport algorithms developed in this study lay the foundation for the future simultaneous solution of conservation equations for physical and thermal multi-physics fields under a unified programming framework.The integrated verification of neutron diffusion and transport programs underscores the reliability and flexibility of the FVM in accurately solving complex neutron transport and diffusion scenarios,providing a pathway for enhancing precision and computational efficiency in nuclear engineering simulations under a unified programming framework.
Finite volume methodNeutron diffusion equationNeutron transport equationOpenFOAM
NETL
NSTL
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