Thermal conduction in open-cell metal foams: Anisotropy and Representative Volume Element

It is well known that the manufacturing process of open-cell foams slightly elongates their struts in one direction, thus making them anisotropic; in turn, anisotropy affects foam characteristics. Furthermore, actual foams can be characterized with reference to a Representative Volume Element (RVE), defined as the cubic sub-volume having the same characteristics as those of the whole foam. An appropriately chosen RVE is very helpful to pass simulation data from a micro-to a macro-scale. The important role played by RVE in characterizing foams performance suggests further research in its determination, in order to reduce computational power and to allow to apply the volume-averaging technique to open-cell foams. In this paper, anisotropy and RVE for the effective thermal conductivity of open-cell metal foams are numerically analyzed. After scanning with Computed Tomography (CT) and postprocessing four open-cell aluminum foams with different porosities and the same Pores Per Inch (PPI) value, their morphologies are investigated in order to evaluate the effects of porosity on cells anisotropy. Foam cell elongation is quantified by an anisotropy ratio. Simulations are performed on CT data with a finite-element method to compute the effective thermal conductivities along three orthogonal directions, and results are compared with data published in the literature. A new correlation between effective thermal conductivity, porosity and direction is presented. The dependence of effective thermal conductivity on cells elongation is also pointed out. RVE sizes for different porosities, directions and inaccuracy thresholds are then investigated. Finally, an existing analytical model is suitably adapted to reliably predict the RVE size with a new correlations which accounts for the directionally-averaged effective thermal conductivity.