Criticality calculations by neutron diffusion theory: a comparative analysis of current density approximations

Abstract

This work presents a comparative analysis of different approaches to approximate current densities in criticality calculations using the neutron diffusion theory. As the nuclear reactors are composed of several materials, defining heterogeneous regions, where the nuclear parameters vary significantly, it is necessary to express the currents in such a way as to preserve continuity at the interfaces of the regions. Based on a nodal integration applied to the stationary neutron diffusion equation, we present four proposals to approximate the current densities at the interfaces. Once the model is built, the calculation of the parameter that defines criticality depends on the determination of the dominant eigenvalue. Here we present and discuss three methods of calculating this eigenvalue. The comparison of the numerical results is carried out on the basis of three test problems, in heterogeneous environments, available in the literature. The results obtained indicate that the most effective approximations for the current densities at the interfaces, for calculating the eigenvalue and the fluxes, are those that correlate the diffusion coefficients of the two common nodes to the interface (proposals 3 and 4). In addition, the secant method proved to be more efficient in determining the criticality parameter.