SYSTEMATIC HOMOGENIZATION AND SELF-CONSISTENT FLUX AND PIN POWER RECONSTRUCTION FOR NODAL DIFFUSION METHODS .1. DIFFUSION EQUATION-BASED THEORY

A diffusion equation-based systematic homogenization theory and a self -consistent dehomogenization theory for fuel assemblies have been deve loped for use with coarse-mesh nodal diffusion calculations of light w afer reactors. The theoretical development is based on a multiple-scal es asymptotic expansion carried out through second order in a small pa rameter, the ratio of the average diffusion length to the reactor char acteristic dimension. By starting from the neutron diffusion equation for a three-dimensional heterogeneous medium and introducing two spati al scales, the development systematically yields an assembly-homogeniz ed global diffusion equation with self-consistent expressions for the assembly-homogenized diffusion tensor elements and cross sections and assembly-surface-flux discontinuity factors. The reactor eigenvalue 1/ k(eff) is shown to be obtained to the second order in the small parame ter, and the heterogeneous diffusion theory flux is shown to be obtain ed to leading order in that parameter. The latter of these two results provides a natural procedure for the reconstruction of the local flux es and the determination of pin powers, even though homogenized assemb lies are used in the global nodal diffusion calculation.