Adaptive Collocation Method for Simultaneous Heat and Mass Diffusion With Phase Change

In post-accident heat removal applications, the use of a lead slab is being considered for protecting a porous bed of steel shot in an ex-vessel cavity from direct impingement of molten steel or fuel as released from the reactor vessel following a hypothetical core disassembly accident in an LMFBR. The porous bed is provided to increase the coolability of the fuel debris by the sodium coolant. The present study is carried out to determine melting rates of a lead slab of various thicknesses in contact with sodium coolant and to evaluate the extent of the penetration and the mixing rates of molten lead into liquid sodium by molecular diffusion alone. The study shows that these two calculations cannot be performed simultaneously without the use of adaptive coordinates which cause considerable stretching of the physical coordinates for mass diffusion. Because of the large difference in densities of these two liquid metals, the traditional constant density approximation for the calculation of mass diffusion cannot be used for studying their interdiffusion. The use of the orthogonal collocation method along with adaptive coordinates produces accurate results, which are ascertained by comparing with the existing analytical solutions for concentration distribution for the constant density approximation and for melting rates of infinite lead slab. The analysis further shows that the melting rate progressively increases as the thickness of lead slab decreases. The mixing of two liquid metals by molecular diffusion is extremely slow and the molten lead is likely to stay separated from the sodium coolant unless free convection exists in the sodium. Before any significant mixing takes place, the lead, upon melting, will sink to the bottom of the porous bed and not participate in removing heat from fuel debris lying on the top of the porous steel bed.