Computation of the Permeability Tensor of Non-Periodic Anisotropic Porous Media from 3D Images

The direct proportionality between the flow rate and pressure gradient of creeping flows was experimentally discovered by H. Darcy in 19th century theoretically justified a couple decades ago using upscaling methods such as volume averaging or homogenization. X-ray computed micro-tomography (CMT) pore-scale numerical simulations are increasingly used to estimate permeability porous media. However, most general case non-periodic anisotropic media still needs be completely numerically defined. Pore-scale can split into two families. first family is based on resolution solving Navier–Stokes equations under assumption flow. second one relies an indirect problem—such closure problem derived from theory. They known provide same results periodic isotropic when dealing with representative element volumes. To address media, we have identified four possible approaches for second. We compared analyzed them three-dimensional generated geometries increasing complexity, sphere cylinder arrangements. Only one, belonging family, has been proved remain rigorously correct case. This successfully applied high-resolution 3D CMT Carcarb, carbon fiber preform thermal protection systems space vehicles. study concludes detailed analysis behavior (streamlines vorticity). A quantitative technique vorticity criterion determine characteristic length material proposed. Once characterized known, critical Reynolds number estimated physical limit regime identified.