Yuanzineng kexue jishu (Feb 2022)
Development and Validation of Three-dimensional Neutronics Code Based on Advanced Nodal Method for Hexagonal-z Geometry
Abstract
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 multidimensional neutron diffusion equation in the Cartesian coordinate system. In the previous work, North China Electric Power University has developed a threedimensional spacetime dynamics program HNHEX based on the higherorder nodal expansion method. The program uses hexagonal components as radial calculation nodes and divides the axial direction as needed, which can calculate the threedimensional 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 secondorder derivative is found for the opposite mean flux. Compared with the analytical method, the singular terms created in the higherorder 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 threedimensional neutron physics calculation software SAHNHEX was developed by coupling the twodimensional semianalytic nodal method in the radial direction with the onedimensional higherorder nodal expansion method in the axial direction to solve the threedimensional 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 twodimensional neutron diffusion equation was implemented by applying the semianalytic nodal block method on the mapped obtained plane. The higherorder nodal block expansion method in HNHEX was retained in the radial direction to solve the axial 1D neutron diffusion equation method, and the threedimensional 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 VVER440 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.
