Generalized Equivalence Theory Used with Spatially Linear Sources in the Method of Characteristics for Neutron Transport

Abstract

A recent hybrid stochastic-deterministic calculation scheme using Monte Carlo–tallied group cross sections in a deterministic solver uses the best of both worlds for accurate and fast reactor agnostic transport simulations. However, neglecting the angular dependence of group cross sections induces large self-shielding errors in resonance groups, causing a large reactivity bias up to 300 pcm in light water reactors. To recover this error, we introduce a two-scale assembly transport calculation scheme: cross sections are tallied at the assembly level, while equivalence parameters are computed in a two-dimensional (2-D) pin cell system. We validate a novel equivalence method based on jump conditions on angular fluxes by comparing to the well-established superhomogenization method for 2-D and three-dimensional (3-D) linear source method of characteristics calculations. Test cases include 2-D and 3-D assemblies of two different enrichments with homogeneous and discretized cross-section discretizations. The linear source approximation enables using coarse source-region discretization for these hot zero-power problems. Both equivalence techniques perform similarly, recover the reactivity bias, and achieve near preservation of reaction rates, supporting this multiscale approach to equivalence.

Keywords:

• Generalized equivalence theory
• equivalence
• linear source
• angular dependence of group cross sections

Acknowledgments

The research work presented in this paper was supported by the U.S. Department of Energy Nuclear Energy University Program contract DE-NE0008578.