Thermal Shrinkage–Based Model for Predicting the Voids During Solidification of Lead

Radioactive materials are transported in hollow steel casks filled with lead. The lead in these casks can melt in an accidental fire during transportation leading to an increase in its volume. This plastically deforms the steel shell housing the lead. When the cask subsequently cools after the fire is extinguished, voids will form in the solidified lead. This work deals with the simulation of solidification with void formation in these transportation casks. In these simulations, one has to deal with solid-liquid and void-material interfaces. Solid-liquid movement during solidification is treated using a modified enthalpy method. The void that is formed in the solidified lead is assumed to be a vacuum. Consistent with this assumption, the boundary conditions of zero pressure and zero stress are imposed on the interface. The growth of the void is handled using the volume of fluid method. The methodology is first benchmarked by comparing the simulations with some experimental results available in the literature. Simulations are then performed for solidification in the transportation cask to study the effect of orientation on the void formation. A methodology is then developed to quantify the overall shielding effectiveness of the cask in terms of the total amount of radiation leaked.