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 perturbatlon 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 k _eff compared to the case with the conventional diffusion coefficient defined by D= 1/3Σ_tr or the extended Benoist's diffusion coefficient together with the conventional flux-weighted cross sections.

KEYWORDS:

• accuracy
• Benoist's anisotropic diffusion coefficient
• cell homogenization
• diffusion constants
• flux-weighted cross section
• heterogeneous lattices
• infinite uniform lattices
• numerical calculation
• reactivity
• transport/diffusion perturbation theory