Modelling of the Mushy Zone Permeability for Solidification of Binary Alloys

An ensemble averaging technique is used to obtain both macroscopic equations of transport phenomena in a two-phase region and new models of permeability and thermal conductivity of the columnar mushy zone through the analysis of most likely configurations of the local microstructure. The obtained formulae are incorporated into a FEM computer code for the macroscopic analysis of binary mixture solidification with convection. The influence of various models of mushy zone permeability on temporal shapes of the two-phase region as well as on velocity and temperature fields is studied for a test case of solidification of a dilute solution of ammonium chloride and water in a square cavity. For this case, relatively small differences in liquid flow patterns and temporal shapes of the two-phase region are observed for significantly different models of mushy zone permeability.