Dispersion in two-dimensional periodic porous media. Part I. Hydrodynamics

In this paper we investigate the hydrodynamics of two-dimensional spatially periodic porous media. The finite volume method is used to compute the flow field in these media with the Navier–Stokes equations. Two particular points are described: how to deal with the periodic boundary conditions on the surface of a unit cell; and how to avoid numerical dispersion. The fluid flow is computed for the Stokes regime and for moderate values of the particle Reynolds number Rep, up to Rep=200. Four types of media are studied. Three of them are “ordered,” with in-line or staggered square cylinders and zigzag medium. The fourth is “disordered,” with randomly distributed square cylinders. The effect of the direction of the average flow velocity is analysed in all these cases. In the Stokes regime, the results for the pressure drop agree with the usual evaluation in terms of permeability. For higher particle Reynolds numbers, the non-linear correction to Darcy’s law is discussed. The correction term for moderate Reynolds number is found to be cubic in the average flow velocity for isotropic media.