Three dimensional calculations of the effective Kapitza resistance of UO₂ grain boundaries containing intergranular bubbles

A parametric study has been performed that quantifies the effective change in grain boundary Kapitza resistance due to the presence of intergranular bubbles. The steady-state heat conduction equation was solved in three-dimensional space using INL's MOOSE finite element software, with which spacial mesh adaptivity was used to resolve interfacial widths down to several nanometers while investigating bubble sizes up to a micrometer. Three critical parameters were systematically varied: the intergranular bubble radius, the fractional grain boundary bubble coverage, and the Kapitza resistance of the intact grain boundary. Using the simulation results, a mathematical model dependent on each of these parameters was developed to describe the effective Kapitza resistance. Furthermore, we illustrate how this model can be implemented in a fuel performance code to predict the temperature profile of a cylindrical fuel pellet.