Thermophysical properties of high porosity metal foams

Direct numerical simulations (DNS) have been performed of turbulent flow in a plane channel with a solid top wall and a permeable bottom wall The permeable wall is a packed bed, which is characterized by the mean particle diameter and the porosity The main objective is to study the influence of wall permeability on the structure and dynamics of turbulence The flow inside the permeable wall is described by means of volume-averaged Navier–Stokes equations Results from four simulations are shown, for which only the wall porosity (, the wall is classified as a highly permeable wall near which viscous effects are of minor importance It is observed that streaks and the associated quasi-streamwise vortices are absent near a highly permeable wall This is attributed to turbulent transport across the wall interface and the reduction in mean shear due to a weakening of, respectively, the wall-blocking and the wall-induced viscous effect The absence of streaks is consistent with a decrease in the peak value of the streamwise root mean square (rms) velocity normalized by the friction velocity at the permeable wall Despite the increase in the peak values of the spanwise and wall-normal rms velocities, the peak value of the turbulent kinetic energy is therefore smaller Turbulence near a highly permeable wall is dominated by relatively large vortical structures, which originate from a Kelvin–Helmholtz type of instability These structures are responsible for an exchange of momentum between the channel and the permeable wall This process contributes strongly to the Reynolds-shear stress and thus to a large increase in the skin friction

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The influence of wall permeability on turbulent channel flow

A general two-equation macroscopic turbulence model for incompressible flow in porous media

The impact of porous media heterogeneity on non-Darcy flow behaviour from pore-scale simulation

Previous reports of experiments performed with water (Fand et al., and Kececioglu and Jiang) indicated that beyond the Forchheimer regime the rate of change of the hydrostatic pressure gradient along a porous medium suddenly decreases. This abnormal behavior has been termed transition to turbulence in a porous medium. We investigate the relationship between the hydrostatic pressure gradient of a fluid (air) through a porous medium and the average seepage fluid velocity. Our experimental results, reported here, indicate an increase in the hydrostatic pressure rate beyond a certain transition speed, not a decrease. Physical arguments based on a consideration of internal versus extemal incompressible viscous flow are used to justify this distinct behavior, a consequence of the competition between a form dominated transition and a viscous dominated transition. We establish a criterion for the viscous dominated transition from consideration of the results of three porous media with distinct hydraulic characteristics. A theoretical analysis based on the semivariance model validation principle indicates that the pressure gradient versus fluid speed relation indeed departs from the quadratic Forchheimer-extended Darcy flow model, and can be correlated by a cubic function of fluid speed for the velocity range of our experiments.

Two Types of Nonlinear Pressure-Drop Versus Flow-Rate Relation Observed for Saturated Porous Media

The existing literature on the flow of fluids through porous packed beds gives very limited quantitative information of the criteria employed in marking the applicability of the different flow regimes. It is the objective of this paper to provide experimental evidence for determining the demarcation criteria during the flow of water through a bed of randomly packed spherical beads. Two different sizes of glass beads, 3 mm and 6 mm, were employed as the porous matrix through which water flowed at rates varying from 5.07 [times] 10[sup [minus]6] m[sup 3]/s to 4,920 [times] 10[sup [minus]6] m[sup 3]/s. The dimensionless pressure drop data showed less variation when the characteristic length of the porous medium was taken to be proportional to the square root of the permeability over the porosity and not the bead diameter. Curves of properly nondimensionalized pressure drop plotted against the actual flow Reynolds number based on the porous medium permeability provided the following information. It was found that Darcy's law has very limited applicability and is valid for a small range of Reynolds numbers. This leads to a pre-Darcy flow that is valid for a much broader range of Reynolds numbers than expected. Alternatively, the range of validitymore » of the post-Darcy laminar Forchheimer flow is also found to be of much more limited applicability than previous studies have indicated. Transition to turbulence takes place earlier than expected and turbulent flow prevails from then on. The dimensionless pressure drop in both the Forchheimer and turbulent flow regimes can be modeled by an appropriately nondimensionalized Ergun's equation i.e., a first-order inertia term correction is sufficient in both flow regimes.« less

Yuxiang Jiang

Papers

Flow Through Porous Media of Packed Spheres Saturated With Water