Strong wall and transverse size effects on pressure drop of flow through open-cell metal foam

Abstract In applications where a fluid flows through the open pores of metal foam, the foam is treated as an infinite porous medium for which the Darcy law and the Forchheimer equation are applied, in order to describe the pressure drop and to obtain the permeability and form drag coefficient. However, in many practical applications the foam is confined, and depending on the transverse size of the foam (perpendicular to the flow direction), the confining walls and the size may have a strong effect on the velocity field and the resulting pressure drop and its behavior. Actually, for small confined foam size, the above flow relations may not be applicable, or they may require modifications in order to account for the added pressure drop due to the confining walls and size effects. Little or no attention has been paid to the transverse size of the foam perpendicular to the confining wall, which may explain some of the divergence in reported pressure drop in the literature. For confined cylindrical foam systems, this paper experimentally establishes a minimum diameter necessary for the foam to have diameter-independent pressure drop, i.e., negligible wall and size effects and constant permeability and form drag coefficient. This minimum diameter is obtained for two types of open-cell aluminum foam subjected to fully-developed airflow in the Forchheimer regime. Below this diameter, values of the two key flow properties show strong dependence on diameter. The Reynolds number ranged from approximately 15,000 to 115,000, and the foam diameters ranged from five to forty five cells for 10- and 20- pore per inch aluminum foam. The intertwined wall and size effect is isolated and studied.