Dual scales of permeability in regularly structured packed beds of spheres

Dual scales of permeability are encountered in many situations, and one such instance is in water treatment where packed beds of permeable spheres are essential. For design purposes, it is necessary to know the relationship between the rate of fluid flow and the corresponding pressure drop in the packed beds. By the use of numerical simulation, a comprehensive investigation of the pressure drop in different geometric bed configurations and different degrees of sphere permeability was performed. Three ordered packings were considered (simple cubic, body-centered cubic, and face-centered cubic) and were studied over a range of Reynolds numbers between 0.01 and 150. A convenient dimensionless parameter ζ, for sphere permeability, was varied from 0.0001 to 0.01, where larger values of ζ represent higher permeability. In addition, results for nonpermeable spheres were obtained for comparison. Multiple pressure drop correlations for the different operating parameters are presented along with displays of flow visualization to enhance the understanding of the fluid mechanics occurring in the beds. The present numerical results are compared with well-established existing experimental-based correlations for nonpermeable spheres, and excellent agreement was found for the applicable cases.