An implicit enthalpy formulation for oxidation of nuclear reactor fuel cladding by steam

The oxidation of the zircaloy cladding of fuel rods in nuclear reactors, important during a severe accident, is governed by the diffusion of oxygen in solid zirconium. The latter exists in many phases which depend on the content of oxygen and have different diffusion coefficients. Discontinuous changes in oxygen concentrations occur at the phase boundaries, which also move in the course of diffusion, obeying an equation similar to the Stefan condition in heat transfer problems with phase change. We have devised and implemented a scheme for 1-D problems using the finite-difference approach, which involves setting the diffusion coefficient to zero in 'forbidden' concentration ranges. The method is shown to be mathematically equivalent to the enthalpy formulation for the Stefan problem. With a boundary condition at the vapour/solid interface which takes into account steam diffusion and dissociation, the code is applied to analyse the phenomena of steam starvation and the dissolution of the oxide layer, which are relevant to severe accidents.