Evaluation of Permeability for Columnar Dendritic Structures by Three Dimensional Numerical Flow Analysis

To evaluate the permeability for columnar dendritic structures, three dimensional (3D) flow simulations of interdendritic liquid were carried out. The 3D columnar dendrites were made by means of the computer aided design (CAD), which were based on two-dimensional dendrite morphologies calculated by a phase-field method. The artificial 3D columnar dendrites were regularly-arranged, and six kinds of 3D columnar dendritic structures were obtained, which have different volume fractions of liquid between 0.56 and 0.95. For these columnar dendritic structures, the flows parallel and normal to the primary dendrite arms were calculated by the FLUENT, and the permeability for six 3D columnar dendritic structures and both flow directions were determined by using the Darcy law. The values of our simulated permeability were compared with those of the experimental permeability [K.Murakami, A.Shiraishi and T.Okamoto: Acta metall., 31 (1983), p.1417, 32 (1984), p.1423, C.Y.Liu, K.Murakami and T.Okamoto: Mater. Sci. Tech., 5 (1989), p.1148]. For both flow directions, our simulated permeability was in good agreement with their experimental permeability. Therefore, we confirmed that our 3D flow simulations are valid to obtain the permeability for columnar dendritic structures. Also, from these results, we discussed the marginal volume fraction of solid for interdendritic flow, and we suggest that it is effective to define the marginal permeability of interdendritic flow to estimate exactly the marginal volume fraction of solid for interdendritic flow considered the morphology of interdendritic structures.