Analysis of fabrication and crack-induced porosity migration in mixed oxide fuels for sodium fast reactors by the finite element method

Abstract

We present an engineering-scale model for the migration of porosity in a fuel pellet experiencing a temperature gradient. The system of coupled pore advection and heat diffusion equations governing the problem is solved by a fixed-point iteration technique. The coupling between porosity and temperature fields is considered via the dependency of pore advection velocity on the local temperature and temperature gradient, and via the dependency of fuel thermal conductivity and of the volumetric power source on the local porosity. We employ the finite element method to discretize the resulting equations. As pure advection solutions obtained by this method are well-known to present spurious spatial oscillations, we introduce stabilization techniques in the pore advection equation. The proposed model is first tested against a benchmark problem representative for the conditions of an uranium-plutonium oxide fuel pellet irradiated in a sodium fast reactor. The results are compared to the those obtained by a model implemented in the BISON fuel performance code. The analysis shows how the results of the newly developed model are in line with those obtained by the reference model, and underlines a superior stability of the solution. The model is then applied to analyze the contribution of as-fabricated and crack-induced porosities in determining the fuel restructuring and in particular the central hole formation. A comparison to experimental data shows the impact of considering crack-induced porosity to predict the extent of the central void.