Simulation of a sodium fast core: Effect of B1 leakage models on group constant generation

Abstract

Due to their complexity, neutronic calculations are usually performed in two steps. Once the neutron transport equation has been solved over the elementary domains that compose the core (cells or assemblies with translation or reflexion boundary conditions), a set of parameters – namely macroscopic cross sections and potentially diffusion coefficients – are generated in order to model the whole core as a simplified problem which is often treated in diffusion theory.The first calculation being over a periodic lattice of cells or assemblies, leakage between different domains of the core and out of the lattice needs to be explicitly taken into account by an additional term that must be added in the neutron transport equation. For historical reasons, the leakage term is in most cases modeled by a homogeneous and isotropic probability within a “homogeneous leakage model” that is compatible with the classical collision probability method often used to solve the neutron transport equation. Driven by technological innovation in the field of computer science, “heterogeneous leakage models” have been developed and implemented in several neutron transport calculation codes.The present work discusses the effect of the leakage model used for the generation of diffusion parameters on sodium fast reactor diffusion calculations. Homogenized and condensed cross sections as well as diffusion coefficients are calculated for hexagonal sodium fast reactor assemblies using the lattice code DRAGON-3. Three different calculations are performed for each assembly: without taking neutron leakage into account, using the classical homogeneous B1 procedure or with the heterogeneous B1 TIBERE model. Furthermore, a homogeneous core and a simple heterogeneous core are calculated within diffusion theory using the DONJON-5 code and the results are compared with a Monte Carlo calculation.It is shown that, even if a fissile assembly can be calculated without leakage, the heterogeneous TIBERE model is best suited for “cluster calculations” (a fertile or reflector assembly surrounded by fuel assemblies). Moreover, the homogeneous B1 model should be avoided in such calculations since it is not able to handle streaming effects between the different assemblies.