Role of appropriate permeability model on numerical prediction of macrosegregation

A continuum formulation based mathematical model was developed to predict macrosegregation during solidification of alloys and to investigate the role of permeability on macrosegregation. The model is based on the conservation of mass, momentum, energy, and solute. Darcy’s law was invoked to model the flow through the mushy region. The anisotropic nature of permeability was considered in the formulation of the model. Using the experimental data from the literature regarding macrosegregation in lead-tin alloys, commonly employed permeability models were assessed, and their inadequacies were demonstrated. The permeability model proposed by West, which is valid up to a very high liquid fraction of the mush and has some limitations, was generalized by incorporating a microstructural parameter into the model. Use of this generalized permeability model showed better agreement with the experimental data on the macrosegregation reported in the literature.