A numerical investigation of thermal stress induced cracking pattern in the solidifying nuclear fuel droplet during MFCI

Abstract

During Molten Fuel Coolant Interaction (MFCI) occurring in a Sodium-cooled Fast Reactor (SFR) following a severe accident, the corium jet breaks up into coarse droplets due to hydrodynamic instabilities and fine flaked debris are generated due to the thermal stress cracking occurring on the solidifying droplet. In particular mixed oxide core debris quenched by liquid sodium are more prone to thermal stress cracking because of the excellent heat transport properties of liquid sodium, which leads to a large temperature gradient across the crust of the ceramic fuel. In this paper, thermal stress initiated cracking of solid crust of the nuclear fuel droplet is studied using Fracture Bifurcation Theory (FBT) and Minimum Potential Energy Principle (MPEP). FBT is able to predict the minimum crack length needed for crack propagation or catastrophic failure depending on the computed KI values. On the other hand, MPEP can predict the periodic and hierarchical cracking pattern that can develop on the core debris. This helps in the prediction of number of cracks and the crack length that can develop on the solid crust. Parametric studies have been carried out by varying MOX droplet sizes, crust thickness and cooling conditions and calculating KI by semi-analytical means and comparing it with KIC. The analysis revealed that solidifying droplets with radius equal to or more than 2 mm are susceptible to thermal stress initiated crack growth and catastrophic breakage even if a few tens of micron size initial crack develops on its surface. Then a particular case of 2 mm radius core debris is considered and its cracking pattern is studied by applying MPEP. This optimal crack configuration is obtained by minimizing potential energy for a given range of crack length and spacing. The analysis has been carried out with ANSYS APDL code which calculates the strain energy for a given initial crack length and spacing. The 2D computational model is validated with a similar study carried out for Alumina disc quenched in water and the results are in good agreement. The minimum fine fragment size predicted by the analysis for mixed oxide debris is a flake like debris with equivalent radius of 41 µm when approximated to be a sphere. The particle size correlates well with the fine debris sizes reported in literature of MFCI experiments.