Ph.D. Proposal Presentation by Steven E. Keller
Wednesday, June 15, 2005

(Dr. Farzad Rahnema, Chair)

"Flux-limited Diffusion Coefficient Applied to Reactor Analysis"

Abstract

Nuclear reactor calculations are performed in a two-stage process. It starts with a fine energy-group, transport theory calculation performed on the fuel assembly level, homogenizing the fuel assembly into one homogeneous cell. The second stage consists of diffusion theory calculations on a whole core level, where the homogenized cells comprise the core, and diffusion theory parameters calculated by the transport code are used as input in the diffusion code.

In addition to multigroup cross sections, multigroup diffusion coefficients and/or transport cross sections are provided by the transport calculation. The diffusion coefficient is important in diffusion theory calculations because it accounts for the anisotropy in the scattering. Although an exact expression exists for the diffusion coefficient in one energy group, there is no exact expression for more than one group. This has encouraged the development of many multigroup approximations.

This work proposes to estimate a new definition of the diffusion coefficient based on flux-limited diffusion theory (FDT) that is expected to be more accurate than current methods. This theory is more accurate than other types of diffusion methods because it adheres to a physical principle derived from the definitions of the current and the scalar flux, which is that the magnitude of the current can never be greater than the scalar flux. Other types of diffusion theories can violate this physical principle in regions in which the flux has a strong spatial gradient. Flux-limited diffusion theory has been shown to be more accurate than the standard diffusion theory when applied to radiative transfer, but has not yet been applied to reactor calculations. It is expected that a diffusion coefficient based on FDT would also yield improved results in reactor calculations.