Systematic homogenization and self-consistent flux and pin power reconstruction for nodal diffusion methods

Starting from the transport equation, a systematic homogenization theory and a self-consistent dohomogenization theory for fuel assemblies have been developed using a multiple-scales asymptotic expansion method. The resulting theory provides a framework for coarsemesh 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 equation leads to a reactor eigenvalue that is second order in the small parameter, and 'Thin reaarch WM rupporkd by the U.S. Department of Energy under Grant No. DEFb07!'Present d d r a : GE Nudear Enern. P.O. Box 780. M/C F21, Wilmington, NC 28402. 90ER12931. SAL.o Engineerins Phyria F'rogruny. ' A h Department of Applied Mathematics.