三维三棱柱多群中子扩散方程的解析基函数展开方法  

Analytic Basis Function Expansion Nodal Method for Multi-Group Neutron Diffusion Calculation in Three-Dimensional Triangular Prism Geometry

作　　者：王昆鹏[1] 吴宏春[1] 曹良志[1] 王常辉[1] 

机构地区：[1]西安交通大学核科学与技术学院,西安710049

出　　处：《核动力工程》2010年第S2期58-62,共5页Nuclear Power Engineering

基　　金：ITER专项国内配套项目(2010GB111007);国家自然科学基金(10976021;10875094)

摘　　要：提出了一种在三维三棱柱几何内不计算横向积分而直接求解中子扩散方程的节块方法。节块内的各群中子注量率分布用一组完全满足中子扩散方程的解析基函数近似展开,节块之间采用面偏流零次矩和一次矩进行耦合。用坐标变换对模型进行了简化,同时给出了三角形几何下的节块扫描方案,采用响应矩阵技术进行迭代求解。本文开发了三维三角形组件中子扩散计算程序ABFEM-3T。通过基准问题的校验计算,表明该方法能准确地给出有效增值系数及节块功率分布,可求解复杂的非结构几何区域的中子扩散问题。An analytic basis function expansion nodal method for directly solving the two-group neutron diffusion equation in the triangular geometry without transverse integration was proposed.The distributions of homogeneous neutron flux within a node were expanded into a set of analytic basis functions satisfying the diffusion equation at any point in a triangular node for each group.To improve the nodal coupling relations and computational accuracy,nodes were coupled with each other with both the zero-and first-order partial neutron current moments across all the three interface of the triangle at the same time.To simplify the derivation,coordinate conversion was used to transform the arbitrary triangle to regular triangle.With a new sweeping scheme developed for triangular geometry,the response matrix technique was used to solve the nodal diffusion equations iteratively.Based on the proposed model,the code ABFEM-3T was developed.Both rectangular and hexagonal assembly benchmark problems were calculated to validate the accuracy of the program.The numerical results for the series of benchmark problems show that both the core multiplication factor and nodal power distribution are predicted accurately.So this method can be used in complex unstructured neutron diffusion problems.

关 键 词：三角形几何 节块方法 解析基函数 坐标变换 

分 类 号：TL329[核科学技术—核技术及应用]