核反应堆全堆芯非均匀中子学分析的高精度高效率计算方法研究

The pursuit of nuclear reactor with better safety and economy forces the increasing accuracy improvement of neutronics calculations, making the legacy algorithm based on pin-cell and assembly homogenizations severely insufficient to our current demands and attracting more and more investigation interests to whole core heterogeneous neutron transport calculation methods. However, there are still approximations or problems within the current so called advanced methods, such as homogenization approximation, 2D+1D approximiation, control rod cusping effect and convergence property. This proposal is dedicated to the development of a whole core heterogeneous neutron transport calculation method with both high accuracy and high efficiency. To entirely eliminate the homogenization approximations and to accurately account the control rod cusping effect, heterogeneous variational nodal method will be established by handling the heterogeneous distribution of macroscopic parameters within each pin-cell using finite elements as sub-elements within the frame of variational principle. To efficiently solve the whole core heterogeneous problem with tremendous unknowns and extremely slow convergence, quasi-reflective boundary condition will be applied to the interface of two adjacent pin-cell meshes to decrease the inside coupling degree of the entire problem. It is believed that this foundamental cutting-edge investigation will not only play a significant scientific role in developing neutron transport theory, but also provide a better tool for nuclear design and safety analysis.

为了提高核反应堆的安全性和经济性，人们对堆芯中子学计算的精度要求不断提高，传统的基于栅元均匀化和组件均匀化的计算方法已经无法满足当前的需求，使得全堆芯非均匀中子输运计算方法已经成为国内外的最新研究热点。但是，现有的方法，要么仍有均匀化近似、二维加一维的近似、控制棒的尖齿效应等，要么有源项的收敛性问题。本研究拟针对全堆芯非均匀中子输运计算的难题开展高精度高效率的计算方法研究，拟根据变分原理采用有限元技术来处理节块内宏观截面参数的非均匀分布，建立非均匀变分节块法，从而消除栅元和组件的均匀化近似，并精确地处理控制棒尖齿效应；拟通过在栅元边界上引入准反射边界条件降低问题的耦合度，从而攻克全堆芯非均匀输运计算的未知数个数多、迭代收敛速度慢等难题，显著提高计算效率。本项目的研究不仅对中子输运理论的发展和完善有着重要的科学意义，而且在核反应堆的设计和安全分析中也有着广泛的应用前景，属于前沿性的基础研究。

随着对核反应堆安全性和经济性的要求不断提高，对堆芯中子学计算精度的要求也不断提高，高效的全堆芯非均匀中子输运计算的研究也越来越迫切。本项目按照申请书的研究内容和目标，针对全堆芯非均匀中子输运计算进行了高精度高效率的非均匀变分节块法研究。具体包括：（1）建立了非均匀变分节块法的理论模型，通过理论与数值分析相结合的方式，对比分析了基函数展开、等参有限元展开和2D/1D展开的三种空间离散方式、基于Pn展开和基于积分方法的两种角度离散方式；（2）研究了一系列提高非均匀变分节块法计算效率的加速技术，包括平源加速技术、准反射边界加速技术、矩阵分块加速技术、基于对称群理论的响应矩阵分块对角化技术等，从响应矩阵构造、迭代求解等多个方面大幅度节省了全堆芯非均匀大规模问题的计算量；（3）分析并有效解决了一系列堆芯物理计算难题，包括截面连续变化问题、控制棒尖齿效应问题、Pin-by-pin全堆计算问题以及燃料和慢化剂分离的压水堆三维全堆非均匀问题。目前，已培养博士研究生1名、另有6名博士研究生仍在读、其中有2名博士研究生赴美国联合培养；已发表学术论文30篇，其中SCI收录7篇，EI收录12篇，参加国内外学术会议18人次；形成发明专利1项。