Application of Lévêque Analogy to Open Cellular Porous Materials

Abstract

Open-porous materials are used for thermal management applications, catalyst support, heat exchangers, and others owing to their enhanced heat transfer. Designing porous material for a specific heat transfer application requires quantifying effective thermal conductivity, pressure drop, and heat transfer as computed data or experimental correlations. This work extends the Lévêque analogy proposed for calculating heat transfer performance from pressure drop data for tube bundles and cross-rod matrices to porous materials. The current work shows the applicability of this analogy for periodic open-cellular porous materials. Seven unit cell geometries representing periodic cellular structures with 75% - 95% porosity are considered. Periodic flow and heat transfer simulation is performed in ANSYS Fluent for Reynolds numbers between 1 and 100 to provide pressure drop and heat transfer results. Permeability and inertial coefficient are estimated, and permeability is correlated successfully with the porosity and fiber diameter of the unit cell geometries. This correlation is validated using experimental data available in the literature, which allows for predicting pressure drops directly from the geometry. Lévêque’s analogy in the original form is explored using the pressure drop coefficient and Nusselt number, which provides a 44% frictional contribution to the total pressure drop. The correlation for the current geometries is further improved using a modified version of the Lévêque analogy, where the exponent is estimated using best fit instead of fixing at 1/3. The modified correlation is validated using experimental data from the literature, and a guideline to predict pressure drop and heat transfer from geometry is provided for periodic open-cellular porous materials.