3D Lattice Boltzmann flow simulations through dendritic mushy zones

Literature data on permeability of dendritic microstructures show a wide scatter. For a given solid fraction the permeability may vary easily by two orders of magnitude. This might be caused by some unavoidable technical problems in doing the corresponding experiments. However, even numerical results may vary greatly depending on the source of the input microstructure and/or the dimension of flow simulation (2D vs. 3D) and/or the applied boundary conditions. In the present work we have used the Lattice Boltzmann technique to perform flow simulations through 2D and 3D dendritic microstructures coming from (i) simplified geometrical approximations, (ii) phase field simulations of binary alloys and (iii) computer tomographs on AlCu alloys. The discussion of the results shows that for low solid fraction, simple geometries can be used as substitute for dendritic structures. However, once the secondary arms are more prominent, large deviations and scattering occur. These deviations are caused by the strong variation of the dendrites geometry along the growth direction, making simplified structures insufficient to derive a reasonable value for the permeability.