| The ghost cell immersed boundary method coupled with a finite difference based Navier-Stokes solver has been developed. The flow solver is used to analyze the two-dimensional, unsteady and viscous flow at low Reynolds numbers through packings of ordered or disordered arrays of mono-, bi- and polydisperse cylinders and ellipses. A variety of verification problems are presented. The macroscopic permeabilities of the packs are computed from the well-known Darcy's law in the low Reynolds number regime, and have been investigated through various geometric parameters, such as porosity, polydispersity, numeric distributions of unique diameters and aspect ratios. It is shown that the permeability can be correlated to the statistical descriptor of the underlying microstructure, the mean shortest Delaunay edge. The permeability, which is a function of the geometric parameters, collapses onto the monodisperse data with proper scalings, and the monodisperse data can be then fitted with a universal prediction curve. The effect of the Reynolds numbers in the inertial flow regime has also been studied. The inertial effect at moderate Reynolds numbers can be correlated through a modified friction factors with a parameter, which is also a function of porosity. |
