Experimental Determination of Permeability and Inertia Coefficients of Mechanically Compressed Aluminum Porous Matrices

Abstract

A heat exchanger, using mechanically compressed microporous matrices, is being developed for cooling high power electronics. The thermal efficiency of this new device depends on the hydraulic characteristics (porosity φ, permeability K, and Forchheimer coefficient cF) of the matrix inserted in it. These quantities have to be obtained experimentally as predictive models do not exist. Twenty-eight compressed matrices are initially chosen for experimental testing. Based on structural requirements, nine matrices are selected for full hydraulic characterization. The determination of permeability and inertia coefficient of each matrix is performed following a proposed direct methodology based on the curve fitting of the experimental results. This methodology is found to yield more consistent and accurate results than existing methods. The uncertainty of the experimental results is evaluated with a new and general procedure that can be applied to any curve fitting technique. Results indicate that the tested matrices have a unique characteristic, that of a relatively wide porosity range, from 0.3 to 0.7, within a relatively narrow permeability range, from 1.0 × 10−10 m2 to 12 × 10−10 m2. The inertia coefficient varies from 0.3 to 0.9. These hydraulic characteristics lead to a microporous heat exchanger performing within requirements.

Experimental Demonstration of Entrance/Exit Effects on the Permeability Measurements of Porous Materials

“…[11] These values are smaller than those estimated in theoretical uncertainty analyses where uncertainties range between 3.1-13.9 % and 7.9-15.2 % for K and C respectively. [12] Results and Discussion…”

Permeability of open-pore microcellular materials

“…Characteristic foam parameters K and C of Eq. (1) have thus been measured by various authors for nickel foams [22,23] or for ERGÕs cast aluminium foams, at times compressed beforehand by plastic deformation along one direction to improve their heat-transfer characteristics (this, of course, renders the foams anisotropic) [3,5,6,9,16,[24][25][26][27].…”

“…Heat can then be exchanged between the fluid and the solid foam, or alternatively the foam can be used to change the fluid, acting as a filter, mixer, electrode or catalyser. Open-cell metal foams can thus provide performance advantages in forced convection heat-exchangers for electronics or aerospace applications [1][2][3][4][5][6][7][8][9], in the flow-field of bipolar/end plates of stacked polymer electrolyte fuel cells [10], in aerospace fluid storage tanks, and as battery electrodes [11,12].…”

Identification of Drag Parameters of Flow in High Permeability Materials by U-Tube Method

“…In the case of linear model (for low or moderate flow velocity), the drag is uniquely represented by permeability of porous material and viscosity of fluid, while in the nonlinear model (for high flow velocity), an additional drag parameter (non-Darcy, Forchheimer or inertia coefficient) must be known (Hassanizadeh and Gray 1987;Zeng and Grigg 2006). An estimation of the two drag parameters is most frequently performed by steady flow methods using (i) extrapolation of experimental results to zero velocity limit (for determining permeability) and infinite velocity limit (for determining inertia coefficient) or (ii) finding the parameters at once by best fit of model prediction to experimental data throughout, e.g., the least-square method (Antohe et al 1997). When porous materials have high permeability, as for example foams or trabecular bones, the identification of the drag parameters can be related to relatively significant uncertainty in permeability measurements (Antohe et al 1997;Bhattacharya et al 2002;Sharma and Siginer 2010) which results from limited precision of controlling pressure gradient and/or flow velocities as well as from boundary effects, i.e., mainly friction loss in conduits.…”

“…An estimation of the two drag parameters is most frequently performed by steady flow methods using (i) extrapolation of experimental results to zero velocity limit (for determining permeability) and infinite velocity limit (for determining inertia coefficient) or (ii) finding the parameters at once by best fit of model prediction to experimental data throughout, e.g., the least-square method (Antohe et al 1997). When porous materials have high permeability, as for example foams or trabecular bones, the identification of the drag parameters can be related to relatively significant uncertainty in permeability measurements (Antohe et al 1997;Bhattacharya et al 2002;Sharma and Siginer 2010) which results from limited precision of controlling pressure gradient and/or flow velocities as well as from boundary effects, i.e., mainly friction loss in conduits. The measurements become yet more problematic if only small samples of homogeneous materials are available (e.g., trabecular bone samples).…”