The Development and Implementation of an Asymptotically Derived Diffusion Coefficient for the 3-D Reactor Analysis Code MPACT

Thomas Saller, University of Michigan

Traditional nuclear reactor analysis involves a two-step process. First, detailed space- and energy-dependent cross-sections are spatially homogenized and collapsed to a few energy groups for a single fuel assembly by preserving the reaction rates. The homogenized cross-sections are then used in a few-group, coarse geometry, full-core diffusion calculation. However, the generation of surface-dependent diffusion coefficients is ambiguous during the homogenization process and can have a significant impact on the accuracy of the full-core diffusion solution. A mathematically rigorous method for homogenizing a diffusion coefficient was derived using asymptotic diffusion theory.

This new diffusion coefficient is anisotropic and requires the calculation of two lattice functions: the standard eigenvalue neutron transport equation and a fixed-source equation. MPACT (Michigan Parallel Characteristics based Transport tool), a method-of-characteristics neutron transport code developed at the University of Michigan, was modified to calculate homogenized cross-sections and the new anisotropic diffusion coefficient. Results with the new diffusion coefficient are compared to calculations with traditional diffusion coefficients. The extension of this asymptotic analysis to more advanced methods, in particular the SP3 (simplified P3) method for heterogeneous systems, is investigated.

Abstract Author(s): Thomas G. Saller, Travis J. Trahan, Brendan Kochunas, Benjamin Collins, Edward W. Larsen, Thomas Downar