Modeling of permeability with the aid of 3D interdendritic flow simulation for equiaxed dendritic structures

In this study, the permeability for interdendritic liquid flow through equiaxial mushy zone has been modeled and experimentally measured. In the present work, by applying a virtual dendrite in a micro-domain and solving Navier-Stokes equation, flow pattern around the dendrite has been obtained and then by applying Darcy's law to this 3D domain the permeability has been determined. In this micro-model the influence of solid fraction and geometry of dendrites have been assessed. Numerically determined values of permeabilities have been analyzed by the use of SPSS statistical software. Then an experimental method is used to measure the permeability for flow through equiaxial mushy zone of Pb-Sn alloys in high solid fractions. Results show that increasing the solid fraction and perturbation has been led to decreasing the permeability but unlike the solid fraction, perturbation has less effect on the permeability. The results are in good agreement with the available experimental data and analytical solutions. The empirical relationship presented in this article could be used to estimate permeability in the mushy Pb-Sn alloys.