Numerical determination of liquid flow permeabilities for equiaxed dendritic structures

Abstract Darcy's law has been applied to the 3D finite difference numerical determination of the influence of solid fraction and geometry on the permeability of equiaxed dendritic structures. The micro-model computes the permeability for flow through a domain equivalent to the volume ultimately occupied by a single solid solution dendritic grain in an Al3Cu3Si alloy. Evolution of the dendrite shape during solidification was simulated using a novel cellular automaton-finite difference technique. Numerically determined permeabilities compare well with reported experimental data for aluminium alloys. For solid fractions in excess of ∼20%, there is also reasonable correlation with the Kozeny–Carman (KC) expression for a KC constant of unity. A significant feature of the micro-model is that it is able to account for the isolation of interdendritic liquid pools in calculating the effective values of the solid–liquid interfacial area and of the fraction liquid.