Numerical Results for the Effective Flow and Thermal Properties of Idealized Graphite Foam

Abstract

To simulate the heat transfer performance of devices incorporating high-conductivity porous materials, it is necessary to determine the relevant effective properties to close the volume-averaged momentum and energy equations. In this work, we determine these effective properties by conducting direct simulations in an idealized spherical void phase geometry and use the results to establish closure relations to be employed in a volume-averaged framework. To close the volume-averaged momentum equation, we determine the permeability as defined by Darcy’s law as well as a non-Darcy term, which characterizes the departure from Darcy’s law at higher Reynolds numbers. Results indicate that the non-Darcy term is nonlinearly related to Reynolds number, not only confirming previous evidence regarding such behavior in the weak inertia flow regime, but demonstrating that this is generally true at higher Reynolds numbers as well. The volume-averaged energy equation in the fluid phase is closed by the thermal dispersion conductivity tensor, the convecting velocity, and the interfacial Nusselt number. Overall, it has been found that many existing correlations for the effective thermal properties of graphite foams are oversimplified. In particular, it has been found that the dispersion conductivity is not well characterized using the Péclet number alone, rather the Reynolds and Prandtl numbers must be considered as separate influences. Additionally, the convecting velocity modification, which is not typically considered, was found to be significant, while the interfacial Nusselt number was found to exhibit a nonzero asymptote at low Péclet numbers. Finally, simulations using the closed volume-averaged equations reveal significant differences in heat transfer when employing the present dispersion model in comparison to a simpler dispersion model commonly used for metallic foams, particularly at high Péclet numbers and for thicker foam blocks.