A hexagonal percolation model for zone-dependent pore interlinkage fraction and its application to the prediction of fission gas release

A percolation model is proposed to determine the interlinkage fraction of intergranular pores in the restructured and cracked fuel. A fuel rod is simulated as a large hexagon which consists of many small hexagonal grains. The fuel rod is divided into four zones of which boundaries are determined depending on their morphological and thermal properties. Grain size grown during irradiation is calculated using the F ASTGRASS code and is used to calculate the number of hexagonal rings in zones. It is assumed that there is a circumferential crack at each zone boundary and radial cracks dividing zones radially. The algorithm for calculation of the pore interlinkage fraction (PIF) includes several steps; checking the site-occupancy, labeling the occupied sites, checking the siteʹs connectivity te. the nearest occupied sites, and counting the number of sites in the cluster connected to the free space. The Monte Carlo method is used for checking site-occupancy and the HoshenKopelman method is applied to labeling. The site occupation probability is assumed to be the ratio of the current swelling to the maximum fractional swelling of pores in the grain edge, which is approximately 8.7%. The proposed model provides zone-dependent PIFs as a function of the site occupation probability. Comparisons of the calculated results with experimental data including the AECL-2230,CBX fuel rod of fractional gas release are done by replacing the PIF function in the F ASTGRASS code with the calculated zone-dependent PIFs. Restructuring with cracks is found to affect fission gas release significantly. The calculated fission gas release as a function of linear heat rate shows better fitting to the experimental data than the simple model in the FASTGRASS code. The fission gas release is also sensitive to the maximum fractional volume swelling. The main advantage of this model is to treat the interlinkage phenomena in the grain boundaries more realistically than the single PIF correlation and to take into account of grain growth and cracks parametrically.