Self-Consistent Open-Celled Metal Foam Model for Thermal Applications

Many engineering applications require thermal cycling of granular materials. Since these materials generally have poor effective thermal conductivity various techniques have been proposed to improve bed thermal transport. These include insertion of metal foam with the granular material residing in the interstitial space. The use of metal foam introduces a parasitic thermal capacitance, disrupts packing, and reduces the amount of active material. In order to optimize the combined high porosity metal foam-granular material matrix and study local thermal nonequilibrium, multiple energy equations are required. The interfacial conductance coefficients, specific interface area, and the effective thermal conductivities of the individual components, which are required for a multiple energy equation analysis, are functions of the foam geometry. An ideal three-dimensional geometric model of open-celled Duocell® foam is proposed. Computed tomography is used to acquire foam cell and ligament diameter distribution, ligament shape, and specific surface area for a range of foam parameters to address various shortcomings in the literature. These data are used to evaluate the geometric self-consistency of the proposed geometric model with respect to the intensive and extensive geometry parameters. Experimental thermal conductivity data for the same foam samples are acquired and are used to validate finite element analysis results of the proposed geometric model. A simple relation between density and thermal conductivity ratio is derived using the results. The foam samples tested exhibit a higher dependence on relative density and less dependence on interstitial fluid than data in the literature. The proposed metal foam geometric model is shown to be self-consistent with respect to both its geometric and thermal properties.