Flow through and over model porous media with or without inertial effects

Abstract

An experimental research program was designed to study laminar flows through and over models of porous media with or without inertial effects. The models used were made up of circular or square rods arranged to cover solid volume fraction ϕ ranging from 0.03 to 0.49, and filling fraction h / H ranging from 0.34 to 1 of the test channel. In this way, the ratios of the depth of the test section to the porous medium pore H / l ranged from 5.75 to 18.25. Three types of model porous media were tested: (1) two-dimensional ‘horizontal’ models, having rod axes aligned along the span of the channel in a staggered or non-staggered fashion; (2) three-dimensional ‘vertical’ models with rod axes aligned in the transverse direction; and (3) three-dimensional ‘mesh’ models with rod axes aligned along both transverse and spanwise directions. Using a pressure-driven viscous fluid, the bulk Reynolds number Rebulk was varied from 0.1 to 10.3. Velocity measurements were obtained using particle image velocimetry at various streamwise-transverse planes of the test section. Differential pressure measurements were also obtained using electronic transducers. These measurements were used to determine relevant governing equations for the flow through the porous media; to characterize the effects of ϕ rod shape and arrangement, h / H, H / l, porous media dimensionality, and Rebulk on the flow; and to predict the flow at the porous medium-free flow interface. The Izbash and quadratic Forchheimer equations were respectively found to describe well the flow through two- and three-dimensional porous media. Penetration of the free flow into the porous medium varied with ϕ and rod arrangement, but was nearly independent of the rod shape. At the interface between the porous medium and the free flow, h / H and H / l effects were found to be counteractive. Penetration was highest for the vertical models compared with the mesh and horizontal models. Inertial dependence of interfacial flow was weak when porous medium conditions were considered. The interfacial flow was found to follow a dose response formulation with a predictable slip coefficient.