Permeability of periodic porous media

The permeability of the two-dimensional periodic arrays of cylinders is obtained numerically as a function of the dimensionless wave number [Formula Presented], where k is the wave number based on the distance between particles in the streamwise direction and D is the diameter. To isolate the [Formula Presented] dependence, D and the porosity are held fixed. The latter is achieved by making the product of distance between particles in the cross-stream and streamwise directions constant. The numerical results show that the permeability increases with [Formula Presented], but the increase is not monotonic. In particular, the permeability decreases for [Formula Presented], and becomes locally minimum at [Formula Presented]. This value of [Formula Presented] is significant because it is the smallest wave number for which the streamwise area-fraction spectrum is zero. For [Formula Presented] and [Formula Presented], the permeability increases with [Formula Presented]. Our numerical simulations also show that for [Formula Presented] the pressure distribution in the cross-stream direction is relatively flat which again is a consequence of the fact that the area-fraction distribution in the flow direction is approximately constant.