Numerical calculation of the permeability in a dendritic mushy zone

An averaging procedure applied to the local Stokes equations in a columnar dendritic-like porous structure yields the heterogeneous form of Darcy's la w, with three Brinkman correction terms explicitly involving gradients of t he liquid volume fraction. Because of these extra terms, the associated clo sure problem leading to the determination of the permeability becomes very complex, and the full solution is still out of reach. However, in some case s, a simplified closure problem can be used to physically describe the spat ial evolution of the permeability components in the columnar dendritic mush y zone. From digitized images of dendritic structures observed experimental ly during solidification of a 26 wt pet solution of aqueous NH4Cl and succi nonitrile-4 wt pet acetone, components of the permeability tensor in a dire ction parallel and normal to the primary dendrite arm are numerically calcu lated. Comparisons to experimental correlations and physical models show th at the closure problem provides a more realistic physical description of th e structure, especially in the vicinity of the tip of the dendrites, Finall y, numerical calculations performed on a schematic dendritic structure poin t out that the permeability for flow parallel to the primary dendritic arms is hardly dependent on the secondary arm spacing (d(2)).