The permeability of replicated microcellular structures in the Darcy regime

Abstract

This study provides an extension to previously published articles on measurements and computational fluid dynamic (CFD) modeling and simulations of airflow across “bottleneck‐type” structures in the Forchheimer regime to purely inertial‐neglected (Darcy regime) incompressible flowing fluid via tomography datasets. A linear‐dependent relationship between the CFD computed unit pressure drop developed across the samples and the superficial fluid inlet velocity was observed for all the samples for creeping fluid flow (0–7 × 10−03m·s−1). The permeability of the structures was observed to be dependent on the structural parameters of the porous medium and most importantly, its pore diameter openings. Linear graphical relations between permeability and pore‐structure related properties of these materials were observed and these could assist in minimizing the number of design iterations needed for the processing of self‐supporting porous metals.

Computational evaluation of effective transport properties of differential microcellular structures

“…Cellular metallic structures are classified as load‐bearing and multifunctional materials which are attributable to their attractive mechanical, vibrational, lightweight (low‐density), electrical, corrosion resistance and fluid transport with excellent mixing properties 1‐5 . Porous metallic structures are widely classified into open‐celled and close‐celled cellular materials with no moving parts (control pore network and distinctive pore volume) resulting in comparatively simple and less frequent maintenance.…”

“…While the close‐celled cellular structures are cited to offer high resistance to fluid flow due to their low pore volume, 5‐7 the open‐celled cellular structures are characterized by higher open porosity, random topologies with greater accessible surface area per unit volume or specific surface 8‐10 . Typical applications of porous metallic structures are in the fabrication of reactors, heat exchangers, aero‐engine fuel separators, vibrational and emission control in cars, lightweight solar collectors, fuel cells, and biomedical devices 3,4,6 . Porous metallic filters are also utilized in the design and fabrication of oil and gas industrial equipment, most especially, as a catalyst and product recovery in gas catalytic reactions (downstream sector) and in the screening of sands from heavy oil, that is, steam‐assisted gravity challenge in the upstream sector 11 .…”

“…These properties can be obtained by fitting measured unit pressure drop data (pressure drop per unit sample thickness) developed for flowing fluids across the interstices of a porous matrix into the well‐known Darcy (Equation )) and Darcy–Dupuit–Forchheimer (Equation (2)) models. Darcy flow regimes of fluid are characterized by viscous‐dominated fluids or for very slow fluid velocities, typically, for pore diameter Reynolds number ( R D ) below unity 4,14 . Experimental, numerical modeling, and simulation in Reference 3 indicates that nonlinearity effects dominate fluids at very high velocities, typically in the fully laminar (Forchheimer) and turbulent flow regimes thereby giving greater significance to the Form drag, over permeability, in describing accurately fluid transport across porous structures.…”

“…Several authors 3‐5,10,12,13,15‐18,22,24 in the field of transport in porous media maintain that the implementation of molecular‐dynamic equations and fundamental flow equations at the pore level is fundamental for a better understanding of the flow dynamics developed across porous media. Analogous research work has seen the utilization of X‐ray micro‐computed tomography (μCT) and virtual packing of structures to accurately represent the pore morphology of porous metallic structures.…”

“…Ranut et al 15 adopted the pore‐scale technique using tomography data sets to account for the permeability and Form drag of highly porous metals with reasonable fits to experimentally measured data. The contributory effects imposed by pore sizes and pore openings on the pressure drop developed across bottleneck‐type microcellular structures are described in References 4, 21, and 22. Della Torre et al 24 described the combined utilisation of image processing and computational fluid dynamics (CFD) modeling and simulation to account for the flow properties of highly porosity metal foams.…”