Calculation of the permeability and apparent permeability of three-dimensional porous media |
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Authors: | Rodrigo P A Rocha Manuel E Cruz |
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Institution: | (1) Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, ON, Canada, M5S 3G8; |
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Abstract: | In this study, creeping and inertial incompressible fluid flows through three-dimensional porous media are considered, and
an analytical–numerical approach is employed to calculate the associated permeability and apparent permeability. The multiscale
homogenization method for periodic structures is applied to the Stokes and Navier–Stokes equations (aided by a control-volume
type argument in the latter case), to derive the appropriate cell problems and effective properties. Numerical solutions are
then obtained through Galerkin finite-element formulations. The implementations are validated, and results are presented for
flows through cubic lattices of cylinders, and through the dendritic zone found at the solid–liquid interface during solidification
of metals. For the interdendritic flow problem, a geometric configuration for the periodic cell is built by the approximate
matching of experimental and numerical results for the creeping-flow problem; inertial effects are then quantified upon solution
of the inertial-flow problem. Finally, the functional behavior of the apparent permeability results is analyzed in the light
of existing macroscopic seepage laws. The findings contribute to the (numerical) verification of the validity of such laws. |
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