Multi-layer models to neutron reflection and transmission for whole-core transport calculations

The aim of this article is to provide mathematical models to neutron reflection by and transmission through multi-layered boundary regions for whole nuclear reactor core transport calculations. A multi-layered boundary region is to be understood here as a region consisting of two or more contiguous and disjoint uniform layers of nonactive (nonfissionable) material surrounding the active (fissionable) region of a nuclear reactor core, e.g. the baffle-reflector region of a pressurized water reactor core. We firstly consider a two-layered boundary region and we develop for such a region mathematical models to the diffuse reflection and transmission of neutrons in the discrete ordinates formulation of neutron transport theory for one-speed slab-geometry nuclear reactor core problems with anisotropic scattering. We then perform numerical experiments in order to show that our models to neutron reflection and transmission can be used to replace efficiently and accurately two nonactive boundary layers in whole-core transport calculations. We conclude by showing how the theory can be extended to include an arbitrary number of boundary layers and by reporting ongoing research.