基于先进节块法的六边形三维中子物理程序的开发与验证

六边形燃料组件在液态金属冷却快堆尤其是钠冷快堆中被广泛应用，针对这类堆型的设计与安全分析需要对堆芯中子通量与中子流进行三维全堆芯耦合计算。经过多年发展，目前已有多种解析节块法、积分节块法、节块展开法等先进节块法能在笛卡尔坐标系下较为精确求解多维中子扩散方程。本文通过径向半解析节块法耦合轴向高阶节块展开法的综合节块方法开发了反应堆三维中子物理计算软件SA HNHEX，并对VVER 440二维、三维基准题进行建模与仿真计算。计算结果与参考值符合较好，初步验证了使用该方法进行反应堆堆芯中子扩散计算的正确性。

Development and Validation of Three-dimensional Neutronics Code Based on Advanced Nodal Method for Hexagonal-z Geometry

Hexagonal fuel assemblies are widely used in liquid metal-cooled fast reactors (LMFR). The design and safety analysis of these reactors require three-dimensional full-core coupling calculations of neutron fluxes and currents in the core. After years of development, various advanced nodal methods, such as the analytical nodal method (ANM), nodal integral method (NIM), and nodal expansion method (NEM), are available to accurately solve the multi dimensional neutron diffusion equation in the Cartesian coordinate system. In the previous work, North China Electric Power University has developed a three dimensional space time dynamics program HNHEX based on the higher order nodal expansion method. The program uses hexagonal components as radial calculation nodes and divides the axial direction as needed, which can calculate the three dimensional neutron flux distribution. The program has been verified by benchmark problems and obtained good simulation results. However, it cannot be ignored that the method is based on the transverse integration method to couple the neutron diffusion equations inside the hexagonal nodal block through three radial directions and one axial direction of the one-dimensional neutron diffusion equations. This treatment creates singular terms when the second order derivative is found for the opposite mean flux. Compared with the analytical method, the singular terms created in the higher order nodal expansion method will lose some of the computational accuracies. Considering that the material inhomogeneity in the reactor is mainly from the radial direction, the inhomogeneity in the axial direction is not significant. In this work, the three dimensional neutron physics calculation software SA HNHEX was developed by coupling the two dimensional semi analytic nodal method in the radial direction with the one dimensional higher order nodal expansion method in the axial direction to solve the three dimensional neutron diffusion equation set for the entire core coupled with hexagonal components. The semi-analytic nodal block method was well established in the Cartesian coordinate system, and in order to apply it to the hexagonal component, the conformal mapping method was adopted. Firstly, the scale function was obtained by the conformal mapping method, and the coordinates of the points on the original hexagonal plane were mapped to the rectangular plane by the scale function. The solution of the two dimensional neutron diffusion equation was implemented by applying the semi analytic nodal block method on the mapped obtained plane. The higher order nodal block expansion method in HNHEX was retained in the radial direction to solve the axial 1D neutron diffusion equation method, and the three dimensional neutron diffusion equation was solved by coupling the axial 1D with the radial 2D through the leakage term. The method and the procedure are initially validated by using the 2D and 3D benchmark problems of the VVER 440 reactor. The calculation results are in good agreement with the reference values, comparable to similar programs in terms of computational accuracy, and significantly improved in terms of computational accuracy compared to the original program HNHEX, and more friendly in terms of the increase in computational time consumption.