Determination of cell averaged diffusion constants based on transport/diffusion perturbation theory.

Abstract

A unified definition for cell-averaged diffusion constants has been established on the basis of transport and/or diffusion perturbation theories. The diffusion constants are derived by equating each component of reactivities obtained by transport theory for a heterogeneous cell to a corresponding component of reactivities by diffusion theory for a homogenized cell. The derived diffusion constants are applied to infinite uniform lattices and heterogeneous lattices composed of different cells. In infinite lattices the present diffusion constants are compared to the conventional flux-weighted cross sections and Benoist's anisotropic diffusion coefficients. In heterogeneous lattices they are compared with Rowlands-Eaton cross sections and the extended Benoist's diffusion coefficient. The present formula is applied to a heterogeneous slab lattice. It reveals that the present method gives a more accurate result for Κen compared to the case with the conventional diffusion coefficient defined by D = 1/3Σιγ or the extended Benoist's diffusion coefficient together with the conventional flux-weighted cross sections.