Modelling of a thin mushy layer evolution during binary solid-liquid interactions

Abstract

Further development of the Brody-Flemings approximation in application to a thin mushy zone at the interface between binary liquid and solid phases, typical in the context of corium evolution in the reactor pressure vessel during severe accidents at nuclear power plants, is presented. The main assumption of the Brody-Flemings approximation concerning local equilibrium between the solid and liquid phases in the two-phase zone is confirmed for the considered case of a thin mushy layer and supplemented with the heat and diffusion flux matches at its interfaces. The approach allows a relatively simple description of the mass and heat transfer through the mushy zone along with the zone formation, growth and/or shrinkage (depending on varying external conditions) in the course of solid-liquid material interactions. In order to prove consistency of the developed approach, two important limiting cases, when the solidification rate is controlled either by the diffusion of heat or by solute diffusion, are studied analytically in a steady-state approximation. It is shown that in both limiting cases, explicit expressions for the mushy zone thickness are directly associated with the criterion of the plane front instability. In particular, this implies that the emergence or vanishing of the mushy zone in the course of liquid-solid interactions is described in a self-consistent manner in the developed approach.