Abstract
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.
Highlights
Results forDarcy the pressure and viscous forces acting on the periodic unit cell (PUC) for different Reynolds numbers
Based on a numerical approach, both closure terms are calculated depending on, respectively, the viscous and pressure forces acting on a representative elementary volume of the studied open-cell foam
It was shown that in the creeping flow regime, the linear term in the Darcy law was due to both pressure forces and viscous forces
Summary
There is a continuous search for new fin designs and materials One of these designs is open cell-metal foam [1]. There are numerous types of open-cell metal foams, two of which are especially common. The second common type is based on a similar preform, but is made through an electrophoretic deposition process. To compare those two types of foam, the materials out of which they are made, and the inner volumes of the strut are different. As a result of the casting process, the strut is solid, while the strut is hollow after the electrophoretic process This has an impact on the thermal conductivity of the resulting foam material
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