Spatially-dependent nuclear reactor kinetic calculations with the explicit fission product model

Abstract

In order to simulate complicated physical phenomena induced by fission product nuclides directly, we have developed the explicit fission product nuclides (EFP) model and have applied to one-point nuclear reactor kinetics problems in the past. In the present study, we extend the EFP model to spatially-dependent kinetics problems. Explicit representations of neutron diffusion kinetic equations with the EFP model are provided, and a new numerical method, a partial matrix exponential (PME) method, is proposed to solve differential equations for FP nuclides number densities analytically. Verification tests of the PME method against the θ method with fine time discretization are carried out, and the PME method is well verified. Numerical tests reveal that accuracy of the PME method is better than the θ method in coarse time mesh discretization, but accuracy of these two methods is comparable in typical time mesh discretization in actual kinetic calculations.Also to demonstrate effectiveness and usefulness of the EFP model, we carry out several two-dimensional kinetics calculations with the EFP model considering leakage of gaseous FP nuclides from nuclear fuel. It is shown that gaseous FP leakage affects reactor power transient and this effect is dependent on magnitude of the leakage. Time transient of number densities of some FP nuclides is presented, and this shows different trend specific to each of FP nuclides.