An analytical solution for simulation of the fission gas behaviors with time-dependent piece-wise boundary resolution

An analytical solution of gas concentration for the equivalent spherical grain is obtained first in Laplace space, then the inverse-Laplace transformed solution is further developed. The corresponding analytical expressions for the grain boundary gaseous swelling and the fission gas release in UO2 nuclear fuels are developed in the absence of grain growth. The following phenomena and assumptions are taken into account in our model, including the gas atom diffusion, saturation and the time-varying piece-wise inter-granular resolution. The explicit expression for saturation time of the grain boundary gas atoms is also obtained. Our approximated analytical solutions for the fission gas behaviors are validated through comparison with those solved by finite difference method. Good agreement has been achieved for the cases with different input parameters. Based on the developed analytical solutions, the effects of the grain sizes and the external pressure on the fission gas behaviors are investigated. This study lays a foundation for the multi-scale simulation of the thermo-mechanical behaviors in nuclear fuel elements.