Bridging pore scale and macroscopic scale foam structure enhanced channel flow cooling with three-dimensional mesoscale simulations

Metal foams with larger interface areas and higher effective conductivities are widely used to increase heat transfer in engineering applications. To reveal the quantitative relation between the pore scale and the macroscale convective thermal transport, foams immersed in a water cooling channel for two high temperature flat plates were simulated by the mesoscale non-dimensional lattice Boltzmann method. The generated structure parameters are global porosities from 0.70 to 0.95 and pore sizes from 6% to 16% of the square channel height. The flow simulation parameters are macroscopic Reynolds numbers from 50 to 1500 and pore scale Reynolds numbers from 3 to 240. Three-dimensional spirals inside foam pores and behind foam structures, which induce the third spatial direction convection, are observed to be positively related to pore sizes, Reynolds numbers, and the volume fractions of fluid and solid phases, respectively. The pore scale drag and heat transfer coefficient constants are inversely correlated from the pressure drop and heat flux of mesoscale simulation results with deviations of 13.2% and 12.5%, respectively. Together with the pore scale geometry factor and the global porosity, the correlations of pore scale and macroscopic scale drag and heat transfer are bridged by microscopic coefficient constants (0.0004, 4.59, 0.47) and (0.0001, 0.096, 0.50, 0.33), respectively. The cross scale correlations provide a practical tool for further engineering applications of enhancing convective cooling through porous structures.