摘要
为了分析核反应堆堆芯内相关物理量分布,需要利用数值方法求解中子输运方程。其中,概率论方法计算效率尚无法满足大型工程计算的需求;而确定论方法大都采用多群近似技术,需要制作专门的多群数据库、进行复杂的共振计算。为了消除确定论方法中的多群近似,本研究提出了基于函数展开的连续能量确定论中子输运计算技术。针对核反应微观截面在非共振能区的特点,建立了多项式基函数展开技术,恰当地刻画了中子在能量维度上的耦合特性,给出了中子通量密度和核反应率等物理量随中子能量的分布。本文详细介绍了非共振能区函数展开技术的理论模型、程序开发与验证。数值结果表明,该技术思路可行。
In analyzing the power density distribution within the core of a nuclear reactor,it is necessary to employ numerical methods to solve the neutron transport equation and obtain the neutron flux density distribution.Deterministic method,either the two-step or the one-step scheme,employed multi-group approximation techniques,which inevitably required the production of a special multi-group database and intricate resonance calculations.Although the probabilistic method could be calculated based on the continuous energy library,the computational efficiency could not meet the needs of large-scale engineering calculations.According to the characteristics of the microscopic cross-section data of the reaction between neutrons and nuclide nuclei under different energy conditions,the all-energy range was divided into resonance energy range and non-resonance energy range.In order to eliminate the multi-group approximation in the deterministic method,a method for calculating neutron transport equation in the non-resonant energy region based on function expansion was proposed.Initially,the non-resonant energy region was subdivided into segments,and within each segment,orthogonal polynomials serve as base functions for expanding the neutron flux density,which realized the processing of single energy independent variable in the neutron flight and absorption process,as well as the handling of double energy independent variable in the neutron scattering process.On the one hand,thermal neutrons were affected by the target nuclear thermal motion,chemical bond binding and scattering wave interference effect,leading to the phenomenon of up-scattering.On the other hand,fast neutrons were affected by a variety of different scattering reactions,resulting in down-scattering.Ultimately forming the coupling calculations between different energy ranges.Based on this foundation,the coupling calculation method between different energy segments in the non-resonant energy range was investigated,and an effective iterative calculation and numerical solution method was established.The solution for the neutron flux density distribution was transformed into solving the corresponding expansion coefficient moments,and then provided the distribution of neutron flux density and nuclear reaction rates within each energy segment.Finally,the neutron transport calculation program of continuous energy determination theory in non-resonant energy range was developed,and the different non-resonant nuclides were preliminarily verified,including single nuclide and multi-nuclide media.The computed results were compared with the existing continuous energy probabilistic neutron transport calculation program NECP-MCX.The verification results show that the relative deviation between the calculated values and the reference values is within 3.5%,demonstrating the feasibility of the continuous energy deterministic neutron transport calculation method based on function expansion.
作者
刘浩泼
李云召
吴宏春
曹良志
LIU Haopo;LI Yunzhao;WU Hongchun;CAO Liangzhi(School of Nuclear Science and Technology,Xi’an Jiaotong University,Xi’an 710049,China)
出处
《原子能科学技术》
EI
CAS
CSCD
北大核心
2024年第6期1210-1217,共8页
Atomic Energy Science and Technology
基金
国家自然科学基金(11975181)。
关键词
中子输运方程
基函数展开
连续能量
确定论
非共振
neutron transport equation
base function expansion
continuous energy
determinism
non-resonant
