ON THE PERMEABILITY OF UNIDIRECTIONAL FIBROUS MEDIA - A PARALLEL COMPUTATIONAL APPROACH

The problems of viscous and inertial flows through unidirectional fibrous porous media are addressed using an entirely parallel computational approach. The pertinent partial differential equations, derived from homogenization theory, are solved by a parallel finite element method in conjunction with Monte Carlo techniques to predict the statistical permeability coefficient. A nip-element method, which mitigates the frequent geometry-induced numerical difficulties, while providing both accurate approximations for the permeability coefficient, and rigorous error estimates, is also presented. The seepage permeability coefficient is determined for a wide range of fiber concentration. It is shown to deviate markedly at low porosities from the behavior predicted by earlier cell models, while exhibiting generally good agreement at high, and moderate porosities with the cell models, and with the limited available experimental and analytical results. Limited but illustrative inertial flow results at moderate Reynolds numbers are also presented for both regular and random arrays. For regular arrays, the flow is found to be unsteady for Reynolds numbers greater than approximately 150 at which traveling waves characterized by distinct periods and amplitudes are observed. Some modest discrepancy is found in comparison with available data which is attributed to the unsteady effects and other numerical issues. For random arrays, several configuration permeability values are calculated and compared satisfactorily against the Ergun correlation. (C) 1995 American Institute of Physics.