SYSTEMATIC HOMOGENIZATION AND SELF-CONSISTENT FLUX AND PIN POWER RECONSTRUCTION FOR NODAL DIFFUSION METHODS. PART II: TRANSPORT EQUATION BASED THEORY

摘要

Starting from the transport equation, a systematic homogenization theory and a sell-consistent de-homogenization theory for fuel assemblies have been developed using a multiple-scales asymptotic expansion method. The resulting theory provides a framework for coarse-mesh nodal diffusion calculations of light water reactors. The theoretical development is carried out through second order in a small parameter — the ratio of the neutron mean free path to the reactor characteristic dimension. Introducing two spatial scales — a fast scale for the rapid variation of the flux over a fuel assembly and a slow scale for the slow variation of the flux over the whole core — into the neutron transport equation for a three-dimensional heterogeneous medium, the development systematically yields: an assembly-homogenized global diffusion equation with self-consistent expressions for the assembly-homogenized diffusion tensor elements and cross sections, and assembly-surface flux discontinuity factors. The analysis shows that the solution of the assembly-homogenized global diffusion equa?tion leads to a reactor eigenvalue that is second order in the small parameter, and a heterogeneous transport theory angular flux that is leading order, The resulting framework also provdies a natural and self-consistent procedure for the reconstruction of the local heterogeneous angular fluxes which makes it possible to calculate the pin powers.