Author(s)

M. Cloete & J. P. du Plessis

Abstract

In the present paper a model to predict the hydrodynamic permeability of viscous flow through an array of squares is generalized to include flow through arrays of rectangles of any aspect ratio. This involves different channel widths in the streamwise and the transverse flow directions. It is shown how, with the necessary care taken during description of the interstitial geometry, a volume averaged approach can be used to obtain results identical to a direct method. Insight into the physical situation is gained during the modelling of the two-dimensional interstitial flow processes and resulting pressure distributions and this may prove valuable when the volume averaging method is applied to more complex three-dimensional cases. The analytical results show close correspondence to numerical calculations except in the higher porosity range for which a more realistic model is needed. Keywords: porous media, volume averaging, hydrodynamic permeability, rectangles. 1 Introduction Apart from the spatial dimension of the microstructure, the analytical result involves two parameters, the first of which relates to the extent of staggeredness that a fluid particle experiences on its way downstream. The second parameter introduced is a measure of aspect ratio of the rectangles which will allow us to vary the length of the transverse channels. In this paper the influence of these two parameters on the hydrodynamic permeability will be discussed. 2 Direct analytical modelling Following Firdaouss and Du Plessis [1], the solid phase and the unit cell are represented by rectangles of the same aspect ratio. This was done to incorporate

Keywords

porous media, volume averaging, hydrodynamic permeability, rectangles.