Non-Darcy Flow Through Fibrous Porous Media

Abstract

Experiments are performed to explore the flow characteristics of porous media having the form of a latticework of metallic fibers. Five such media are investigated, four among which share the characteristic that there are no free fiber ends within the medium. The operating conditions of the experiments extend over a wide range of velocities greater than those for Darcy flow, but permeabilities deduced from the data are applicable to the Darcy regime. It is shown that for all the investigated media, the axial pressure gradient is representable as the sum of two terms, one linear in the velocity (viscous contribution) and the second quadratic in the velocity (inertia contribution). The flow-pressure characteristics for the structurally similar porous media are representable by a single dimensionless expression wherein the square root of the permeability is used as the characteristic dimension. Significant departures from Darcy’s law first occur at Reynolds numbers on the order of one; similar values of the Reynolds number are known to mark the termination of the regime of viscous unseparated flow about spheres and cylinders. This accord lends further support to the use of the square root of the permeability as the characteristic dimension.