Analytical determination of the permeability for slow flow past periodic arrays of cylinders with different cross sections

This study proposes analytical methods for determining the permeability of porous media that are composed of periodic arrays of rods with different cross sections. The cylindrical rods used for modeling the porous media are in circular, square, and 45° rotated square cross sections, respectively. Analytical determination of the permeability has been carried out for porous media composed of different rod geometries, and results have been obtained for a wide porosity range. Furthermore, the analytical permeability determination method has been supported by auxiliary information obtained from computational solutions performed using a commercial CFD code. The permeability values obtained by the proposed analytical method have been compared with prior empirical and analytical studies. These comparisons indicated good agreement of the proposed model with the existing ones. Moreover, the analytical permeability determination methods proposed for square and 45° rotated square cross-sectioned rods can be evaluated as the contribution of this study since throughout the literature search no other analytical method has been encountered for these types of geometries.