Modelling of localised shrinkage pressure in a directionally solidifying domain

Abstract

A novel approach to modelling shrinkage during solidification has been proposed. It combines Phase-field (PF) simulation with fluid mechanics for a solidifying medium. A mass balance method, based on a viscous creeping flow in two phases (liquid, solid and interface) with an applied penalisation coefficient is proposed. The role of this coefficient is to continually separate the fluid from the solid domain in correspondence to any change due to a phase transformation process. The advantage of the method is that the medium is modelled with no explicit tracking of the interface which significantly improves computational cost and the ease of implementation. This is achieved via the application of a monolithic ‘single-field’ formulation to the system of equations. The method has the potential to locally calculate shrinkage pressure by taking into account multiple parameters, including thermal gradient, permeability, viscosity and morphology.