One Dimensional Model for the Solid and Mushy Crust Surrounding a Terminal Debris Corium Pool

In CANDU or similar pressurized heavy water reactors (PHWRs), in-vessel retention of core materials and removal of decay heat from the calandria vessel (CV) exterior is an important strategy in maintaining CV integrity and mitigating severe accidents. Heat loss from the terminal debris bed to the CV results in the formation of a crust surrounding a molten corium pool. Knowledge of the crust properties such as its thickness, and the heat transfer through the crust adjacent to the CV and above the pool, support modelling with integrated severe accident codes. In this work, a quasi-1D heat transfer model for the crust is developed, accounting for convection or pool boiling from the CV to the vault-water, contact resistance at the crust-CV interface, decay heat generation in the crust, and heat loss above the terminal debris through convection and radiation. For the crust adjacent to the CV, closed-form dimensionless solutions are derived for the thicknesses of the solid and mushy regions, as well as temperature distribution in both the crust and the external vessel wall. Radiative heat loss above the terminal debris makes the development of fully closed-form solutions for the crust above the corium pool non-trivial. Hence, semi-analytical solutions involving piecewise approximations are provided for the top domain, and compared against iteratively-computed numerical solutions. Additionally, finite element simulations are carried out to verify the analytical technique, with representative cases encapsulating all crust configurations: solid- or mushy-only crust, full crust, and no crust.