Brinkman-extended Darcy flow in metal foam: analysis and experiment

Abstract

Paper presented at the 9th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Malta, 16-18 July, 2012.

Fluid flow in porous media is found in numerous processes and applications of vital engineering interest, e.g., storage of nuclear waste, heat exchangers, ground water pollution and chemical reactors. Often, the porous medium is confined by solid boundaries for containment. These impermeable boundaries give rise to shear stress and boundary layers. The Brinkman-extended Darcy equation governs the momentum transport due to Newtonian fluid flow in such porous-media flow situations. Metal foam, especially aluminum-based, has gained a lot of academic and industrial interest over the past few years. The significance of metal foam is due to its low density (or, high porosity: 75 % to 95 %.), high thermal conductivity, interconnectivity of its solid ligaments and large surface area density. Metal foam applications include heat exchange system and chemical reactors. In these systems, the foam is usually cylindrical in shape and is contained in a cylindrical tube. The fluid flow in such systems is needed for further engineering and performance analysis of such systems. The flow field may be described by the Brinkman-extended Darcy equation. This equation is solved analytically in a cylindrical system, employing an existing fully-developed boundary-layer concept particular to porous media flows. As expected, the volume-averaged velocity is found to increase as the distance from the boundary increases reaching a maximum at the center. The friction factor is defined based on the mean velocity and is found to be inversely proportional to the Reynolds number, the Darcy number and the mean velocity. In order to check the validity of the Brinkman-extended Darcy flow model for the high-porosity metal foam, experiments were conducted on commercially-produced 20-ppi (pores per inch), i.e., 8 pores per centimeter using an-open loop wind tunnel. In the Darcy flow regime, reasonably good agreement is found between the analytical and the experimental friction factors. The implication of the results of this paper is that they can be applied in further engineering analysis that require knowledge of the velocity field and pressure drop, i.e., convection heat transfer and chemical reactors.