Pore-scaled analytical modelling of permeability and inertial coefficient for pressure drop prediction of open-cell metallic foams

Amongst various porous media, open-cell metallic foams exhibit distinctive properties: relatively low manufacturing cost, ultra-low density, moderate stiffness and strength, and high surface area-to-volume ratio. They have been, therefore, utilized in a variety of applications such as microelectronics cooling, fuel cells, and compact heat exchangers. For such applications, the knowledge of pressure drop of fluid flowing across the foam is often a key issue, enabling control of fluid flow, heat transfer enhancement, planning and designing chemical engineering processes, optimal flow analysis as well as practical designs. We present in this paper an analytical model capable of predicting the pressure drop of a Newtonian incompressible fluid flowing unidirectionally across isotropic and fullysaturated micro open-cell cellular foams within the Darcy and Forchheimer flow regimes. Analytical exploitations are conducted to determine the foam permeability and inertial coefficient. The analytical model is based on the basis of volume-averaging approach and the assumption of piece-wise plane Poiseuille flow with the modified cubic lattice with spherical node at the junction of struts. To better mimic the foam struts shape, a concave-triangular-shaped strut consisting of two nose-to-nose cones is considered and particular attentions have been paid to both analytically and numerically examine the node shape as well as struts shape effect. Built upon a generalized tortuosity model derived from the modified cubic unit cell, an analytical model of permeability on the basis of a cubic unit cell is developed, valid within a typical engineering range of porosity (ϵ = 0.86 ∼ 0.98) and pore size (0.254 mm ∼ 5.08 mm). With the effect of Reynolds number considered, the pore-scaled Reynolds number dependent drag coefficient expression is introduced and through this the inertial coefficient is analytically modeled on the basis of flow over bluff bodies, which is found to agree well with experimental data from various sources. The modeling procedure for pressure drop (permeability and inertial coefficient) is based on physical principles and geometrical considerations, and the model predictions agree satisfactorily with existing experimental data. Results show that by building the analytical model on the basis of a cubic unit cell to represent the topology of metallic foams, pressure drops as well as hydrodynamic conditions within both the Darcy and Forchheimer regimes in a Newtonian fluid can be analytically predicted.