Solidification with Buoyancy Induced Convection: Evaluation of Different Mushy Zone Formulations

Abstract

A comparative assessment is performed between purely porous formulation of the mushy zone controlled by permeability and the hybrid formulations controlled by both permeability and viscosity of the mushy zone during solidification of a binary alloy. The Darcy’s Carman-Kozeny equation is used to model the permeability of the mushy zone in porous formulation for all the models. The first hybrid model employs switching functions to simultaneously control the permeability and viscosity of the mushy zone up to a critical solid fraction and thereafter it switches to a purely permeability controlled porous formulation. The second hybrid model assumes mushy zone to be non-newtonian slurry with the liquid viscosity following a power law up to the critical solid fraction and a permeability controlled porous medium thereafter. A two dimensional computational domain of aqueous ammonium chloride (NH4Cl-H2O) solution employing continuum mixture approach is considered for the analysis. Model with purely porous mushy zone formulation showed higher solutal gradients in the mushy zone resulting in higher solutal buoyancy driven convection in mushy zone along with higher bulk macrosegregation effects in comparison to the hybrid models. Both the hybrid models showed potential of capturing the settled free floating particles and broken dendrites with the non-newtonian slurry hybrid model showing potential of capturing the liquidus irregularities.