A Discussion on the Interpretation of the Darcy Equation in Case of Open-Cell Metal Foam Based on Numerical Simulations.

It is long known that for high-velocity fluid flow in porous media, the relation between the pressure drop and the superficial velocity is not linear. Indeed, the classical Darcy law for shear stress dominated flow needs to be extended with a quadratic term, resulting in the empirical Darcy-Forchheimer model. Another approach is to simulate the foam numerically through the volume averaging technique. This leads to a natural separation of the total drag force into the contribution of the shear forces and the contribution of the pressure forces. Both representations of the total drag lead to the same result. The physical correspondence between both approaches is investigated in this work. The contribution of the viscous and pressure forces on the total drag is investigated using direct numerical simulations. Special attention is paid to the dependency on the velocity of these forces. The separation of the drag into its constituent terms on experimental grounds and for the volume average approach is unified. It is shown that the common approach to identify the linear term with the viscous forces and the quadratic term with the pressure forces is not correct.

How to Study Thermal Applications of Open-Cell Metal Foam: Experiments and Computational Fluid Dynamics.

This paper reviews the available methods to study thermal applications with open-cell metal foam. Both experimental and numerical work are discussed. For experimental research, the focus of this review is on the repeatability of the results. This is a major concern, as most studies only report the dependence of thermal properties on porosity and a number of pores per linear inch (PPI-value). A different approach, which is studied in this paper, is to characterize the foam using micro tomography scans with small voxel sizes. The results of these scans are compared to correlations from the open literature. Large differences are observed. For the numerical work, the focus is on studies using computational fluid dynamics. A novel way of determining the closure terms is proposed in this work. This is done through a numerical foam model based on micro tomography scan data. With this foam model, the closure terms are determined numerically.

Influence of Orientation and Radiative Heat Transfer on Aluminum Foams in Buoyancy-Induced Convection.

Two differently-produced open-cell aluminum foams were compared to a commercially available finned heat sink. Further, an aluminum plate and block were tested as a reference. All heat sinks have the same base plate dimensions of four by six inches. The first foam was made by investment casting of a polyurethane preform and has a porosity of 0.946 and a pore density of 10 pores per linear inch. The second foam is manufactured by casting over a solvable core and has a porosity of 0.85 and a pore density of 2.5 pores per linear inch. The effects of orientation and radiative heat transfer are experimentally investigated. The heat sinks are tested in a vertical and horizontal orientation. The effect of radiative heat transfer is investigated by comparing a painted/anodized heat sink with an untreated one. The heat flux through the heat sink for a certain temperature difference between the environment and the heat sink's base plate is used as the performance indicator. For temperature differences larger than 30 °C, the finned heat sink outperforms the in-house-made aluminum foam heat sink on average by 17%. Furthermore, the in-house-made aluminum foam dissipates on average 12% less heat than the other aluminum foam for a temperature difference larger than 40 °C. By painting/anodizing the heat sinks, the heat transfer rate increased on average by 10% to 50%. Finally, the thermal performance of the horizontal in-house-made aluminum foam heat sink is up to 18% larger than the one of the vertical aluminum foam heat sink.