Numerical simulation of fluid flow through random packs of polydisperse cylinders

The macroscopic properties of two-dimensional random periodic packs of polydisperse cylinders are investigated by means of numerical methods. We solve the unsteady, two-dimensional Navier-Stokes equations on a staggered Cartesian grid and use the immersed boundary method to treat internal flow boundaries. The effects of porosity, polydispersity, and Reynolds numbers on the macroscopic permeability are studied. For small Reynolds numbers, we show that the permeability can be correlated to the underlying microstructure by means of a suitably defined statistical descriptor, the mean shortest Delaunay edge. With proper scaling, the results for polydisperse cylinders collapse onto the data for monodisperse cylinders, which can then be fitted with a universal curve. We also carry out a statistical analysis of the permeability computed for 500 samples and show that rare events, where the permeability lies outside the mean plus/minus three times the standard deviation, are possible. Finally, for larger Reynolds numbers, we show that a modified Forchheimer equation can characterize the flow.