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 kD, where k is the wave number based on the distance between particles in the streamwise direction and D is the diameter. To isolate the kD 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 kD, but the increase is not monotonic. In particular, the permeability decreases for similar to 5<kD<similar to 7.7, and becomes locally minimum at kD approximate to 7.7. This value of kD is significant because it is the smallest wave number for which the streamwise area-fraction spectrum is zero. For kD <5 and 7.7<kD<11, the permeability increases with kD. Our numerical simulations also show that for kD approximate to 7.7 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. [S1063-651X(99)04801-1].