A multiple-scales systematic theory for the simultaneous homogenization of lattice cells and fuel assemblies

Abstract

A systematic theory for the simultaneous homogenization of lattice cells and fuel assemblies and a self-consistent debomogenization theory for the reconstruction of the heterogeneous transport flux are developed simultaneously by introducing three spatial scales into the neutron transport equation for a three-dimensional heterogeneous medium, and carrying out an analysis based on an asymptotic expansion. The development provides both a theoretical basis and practical homogenization and dehomogenizaion procedures for use in coarse-mesh nodal diffusion calculations, and it yields: a lattice-cell homogenized diffusion equation for a fuel assembly with consistent definitions of the homogenized diffusion tensor, homogenized cross sections, and flux discontinuity factors at the lattice cell interfaces; an assembly-homogenized global diffusion equation with consistent definitions of the homogenized diffusion tensor, homogenized cross sections, and flux discontinuity factors at the fuel assembly interfaces; and a self-consistent de-homogenization procedure for the reconstruction of the local heterogeneous transport theory fluxes. The theoretical development shows that the exact transport theory angular flux obtained to leading order from the whole-reactor nodal diffusion calculations, done using the homogenized nuclear data and discontinuity factors, is the product of three computed quantities: a “cell shape function” (the fundamental unit-cell transport theory eigenfunction); an “assembly shape function” (the fundamental cell-homogenized unit-assembly diffusion theory eigenfunction); and a “global shape function” (the fundamental solution to the assembly-homogenized overall reactor diffusion equation). Numerical examples that illustrate the application of the theoretical results are presented.