Abstract
A new geometric modeling of isotropic highly-porous cellular media, e.g., open-cell metal, ceramic, and graphite foams, is developed. The modelling is valid strictly for macroscopically two-dimensional heat transfer due to the fluid flow in highly-porous media. Unlike the current geometrical modelling of such media, the current model employs simple geometry, and is derived from equivalency conditions that are imposed on the model’s geometry a priori, in order to ensure that the model produces the same pressure drop and heat transfer as the porous medium it represents. The model embodies the internal structure of the highly-porous media, e.g., metal foam, using equivalent parallel strands (EPS), which are rods arranged in a spatially periodic two-dimensional pattern. The dimensions of these strands and their arrangement are derived from equivalency conditions, ensuring that the porosity and the surface area density of the model and of the foam are indeed equal. In order to obtain the pressure drop and heat transfer results, the governing equations are solved on the geometrically-simple EPS model, instead of the complex structure of the foam. By virtue of the simple geometry of parallel strands, huge savings on computational time and cost are realized. The application of the modeling approach to metal foam is provided. It shows how an EPS model is obtained from an actual metal foam with known morphology. Predictions of the model are compared to experimental data on metal foam from the literature. The predicted local temperatures of the model are found to be in very good agreement with their experimental counterparts, with a maximum error of less than 11%. The pressure drop in the model follows the Forchheimer equation.
Highlights
The present model avoids the use of the volume-average theory, which seems to produce unacceptable results when applied to highly-porous media such as metal foam
It is clear that the equivalent parallel strands (EPS) model produces pressure drop data that strongly sufficiently far location from the heated base, the air temperature is cooler, and it is equal follow the Forchheimer equation for porous media, including metal foam [8]: to the inlet air temperature shown in blue
Heat transfer due to the fluid flow inof highly-porous for example, metal-foam heat phological and transport properties the foam, so media; that pressure drop and heat transfer sinks and metal foam packed between two parallel plates, with one or both plates heated
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. The resulting macroscopic momentum and energy equations require four closure terms: permeability, inertial coefficient, thermal dispersion conductivity, and interstitial heat transfer coefficient These capture and reconstruct the 3D structure of the foam from 2D images, and to solve the governing equations over this complex structure. Modeling efforts seem to be primarily focused on trying to match the geometrical shape of the internal structure of the foam [27,56,57,58], not on matching pertinent morphological properties (e.g., porosity and surface area) By doing so, they inadvertently compromise the critical matching of key transport properties, e.g., effective thermal conductivity and convection heat transfer coefficient. The current modeling effort is focused on matching pertinent heat transfer properties, e.g., effective thermal conductivity and convection heat transfer area, in order to better predict the combined conduction/convection heat transfer in metal foam. The present model avoids the use of the volume-average theory, which seems to produce unacceptable results when applied to highly-porous media such as metal foam
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