改进准静态本征函数法求解反应堆时空中子动力学方程

Improved Quasi-static Eigenfunction Method for Solving Spatial-time Neutron Kinetics Equation

本文提出一种改进准静态本征函数法并用于求解时空中子动力学方程。在改进准静态近似条件下,利用因子分解法将中子通量密度分解为幅函数和形状函数,进而采用本征函数法求解形状函数轴向和径向的近似解析解。在求解幅函数过程中,将幅函数化简为点堆模型下的形式进行求解,最终导出反应堆三维时空中子动力学方程的解析解。与其他解析法和数值解相比,改进准静态本征函数法的适用范围更广,计算速度更快。

An improved quasi-static method was proposed to solve the space-time neutron kinetics equation.Under the improved quasi-static approximation condition,the neutron flux density was decomposed into the range-function and shape-function by the factorization method.Then the approximate analytical solutions in the axial and radial directions were obtained using the eigenfunction method to solve the shape-function.In the solving process,the range-function was simplified as the form of point reactor model,and the analytical solution of three-dimensional space-time neutron kinetic equation for reactor was derived.Compared with other analytical method and numerical solution,the improved quasi-static eigenfunction method has wider application scope and faster computation speed.