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.
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