Analytic Benchmark for Fuel-Reflector PHWR Configurations

Abstract

Verification of neutronic-analysis codes involves comparing their results to some benchmark, whose correctness is accepted. Analytical results are particularly useful as benchmarks because they are exact. This work presents analytic solutions of the two-group neutron-diffusion equation for three two-region reactor configurations comprised of fuel and reflector, which are symmetric about the origin: an infinite slab, an infinite cylinder and a sphere. The solutions are based on examples appearing in advanced reactor-physics texts, which have been extended to account for all the terms appearing in the two-group diffusion equation (e.g. up-scattering) and to include a method for determining k_eff for a given set of material properties and reactor dimensions. Results are generated for macroscopic cross-sections representative of PHWR configurations, namely 37-element zero-burnup natural-uranium fuel bundles with D₂O coolant and moderator bounded by a D₂O reflector. These results offer a benchmark for existing and future two-group diffusion codes used for PHWR configurations.