摘要
随着堆芯中子学计算对精度要求的不断提高,基于栅元均匀化的pin-by-pin方法成为国内外研究热点。由于pin-by-pin计算巨大的空间网格量及栅元层面较强的非均匀性,目前常用的SP3/GSP3方法在平衡计算精度和计算效率方面还存在一定局限性,为此有必要寻找一种同时考虑计算精度与效率的堆芯计算方法。基于准扩散的堆芯pin-by-pin计算方法从中子输运理论出发,引入艾丁顿因子推导建立三维准扩散方程及边界条件,研究该方程泄漏项的特殊处理方法,同时基于节块展开法建立堆芯pin-by-pin数值计算方法并验证。数值结果表明,对于结构复杂、中子各向异性显著的堆芯,准扩散pin-by-pin计算精度要明显优于传统扩散计算,而两者计算效率相当。该方法是一种平衡了堆芯计算效率与精度的计算方法,为准扩散理论应用于堆芯pin-by-pin计算提供了基础。
Physical calculations of reactor cores are fundamental for reactor core design and nuclear safety analysis.The second generation of core calculation theory and methods based on advanced component homogenization theory and modern coarse grid block methods are commonly used in reactor core physics calculations.However,due to the fact that the two-step method of component homogenization does not accurately provide the grid rod power,the modified two-step method of cell homogenization based on the pin-by-pin homogenization theory of core calculations has gradually become a research hot spot in core calculations.Compared with the two-step method of component homogenization,the pin-by-pin calculation scheme only carries out the homogenization calculation for each cell in the component,which preserves the non-uniformity of different cells in the component,reduces the approximation and assumption in the core calculation,and can calculate the core number more accurately,which is conducive to the safety analysis of the core.However,the SP3/GSP3 methods currently in common use for pin-by-pin calculations still suffer from limitations in balancing computational accuracy and efficiency.In this regard,this paper aims to establish a core calculation method named quasi-diffusion theory which considers both computational efficiency and computational accuracy.First,the 3D quasi-diffusion equation was derived and established from neutron transport theory.Unlike the traditional diffusion equation,the formulation of the quasi-diffusion equation did not introduce a first-order approximation for the neutron angular flux,and the concept of the Eddington factor was introduced to deal with the leakage term of the neutron transport equation.The 3D quasi-diffusion equation was then formulated.In addition,a numerical solution model for the quasi-diffusion equation was developed by referring to traditional numerical solutions of the diffusion equation such as the transverse integral equation and using the nonlinear iterative cross section method.Second,since the Eddington factor was the key parameter in solving the quasi-diffusion equation,the solution of the quasi-diffusion equation depends on whether the Eddington factor was exact or not.In this paper,the Eddington factor was regarded as the homogenization parameter similar to other small group sections.The solution was obtained using Serpent,a modified version of the Monte Carlo program.Finally,several cases including the whole core model and the color-set assembly model were employed to validate the method,and the results were compared with the traditional diffusion and Monte Carlo reference solutions.By comparing the numerical output results under each model,the results show that for reactor cores with complex structures and strong heterogeneity,the accuracy of quasi-diffusion calculations is significantly better than that of traditional diffusion calculations,and the computationally efficient of the two methods is similar.In summary,the quasi-diffusion equation approximation,as a nonlinear method to approximate the neutron transport equation,is a computationally efficient and accurate method.It has great promise for new core calculations with strong neutron anisotropy and complex neutron energy spectrum.
作者
颜江涛
刘琨
庄坤
王森山
张开辉
张欣欣
YAN Jiangtao;LIU Kun;ZHUANG Kun;WANG Senshan;ZHANG Kaihui;ZHANG Xinxin(College of Materials Science and Technology,Nanjing University of Aeronautics and Astronautics,Nanjing 211106,China;Science and Technology on Reactor System Design Technology Laboratory,Nuclear Power Institute of China,Chengdu 610041,China)
出处
《原子能科学技术》
EI
CAS
CSCD
北大核心
2023年第6期1120-1130,共11页
Atomic Energy Science and Technology
基金
国家自然科学基金青年基金(12205150)
江苏省自然科学青年基金(BK20210304)
核反应堆系统设计技术重点实验室基金(NBC20008)
中国博士后基金(2020M681594,2019TQ0148)
江苏省博士后基金(2020Z231)。
