Yuanzineng kexue jishu (Jan 2023)
Development and Verification of Hexagonal Quasi-diffusion Code Based on Variational Nodal Method
Abstract
New type reactors usually adopt advanced fuel types and more anisotropic fuel arrangements, the neutron spectrum is very different from that of pressurized water reactor, and the neutron anisotropy is stronger. If using the neutron transport theory, although better results can be obtained, the computational efficiency is low. If the traditional diffusion theory is used, the calculation efficiency can be improved, however, the complex neutron energy spectrum and strong neutron anisotropy in the core decrease the calculation accuracy. In this study, the core calculation and analysis method based on quasi-diffusion equation was employed. One of the basic assumptions established by traditional diffusion theory is that the angular flux of neutrons is a first-order function of angle, but the quasi-diffusion equation does not adopt this assumption, and an Eddington factor is used to express product of the angular flux of neutrons and angle vectors. The Eddington factor can describe the anisotropic characteristics that cannot be reflected by traditional diffusion theory, and the form of quasi-diffusion equation is similar to the traditional diffusion equation. Most of the current researches applied the quasi-diffusion equation to accelerate the calculation neutron transport. Due to the computational complexity of the Eddington factor, the studies on the quasi-diffusion equation independently employed to the reactor calculation, especially for the reactor with hexagonal assembly are insufficient. Aiming at the characteristics of nonlinear calculation of the Eddington factor, this study regarded the Eddington factor as a special few-group constant based on “two-step” method, and adopted Monte Carlo code SERPENT of better neutron energy spectrum adaptability to calculate. For three-dimensional multi-group quasi-diffusion equation, based on Galerkin variation principle and Lagrange multiplier method, this study established a functional including the nodal balance relationship and boundary condition in the entire region, and used the Ritz discrete method to expand this functional by orthogonal basis function. Then the response relation between nodal neutron flux density and neutron current was built to solve the quasi-diffusion equation, and a code named VNMQD for reactor core with hexagonal assembly was developed. The VNMQD code was verified by using 3D VVER1000 benchmark, RBWR single assembly problem and 3D BN600 simplified model. The results show that the VNMQD code is developed correctly. For the core with strong anisotropy problem, VNMQD has a great improvement in the calculation accuracy for the effective core multiplication factor and neutron flux density compared with traditional diffusion calculation, and the calculation efficiency of both is similar. VNMQD achieves a balance between calculation accuracy and calculation efficiency.
