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

A systematic theory for the simultaneous homogenization of lattice cells and fuel assemblies and a self-consistent dehomogenization 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 dehomogenization 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.