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Materials 2016, 9(6), 409; doi:10.3390/ma9060409

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

1
Department of Flow, Heat and Combustion Mechanics, Ghent University, Sint-Pietersnieuwstraat 41, Ghent 9000, Belgium
2
NV Bekaert SA, Bekaertstraat 1, Zwevegem 8500, Belgium
*
Author to whom correspondence should be addressed.
Academic Editor: Thomas Fiedler
Received: 8 April 2016 / Revised: 13 May 2016 / Accepted: 20 May 2016 / Published: 25 May 2016
(This article belongs to the Special Issue Metal Foams: Synthesis, Characterization and Applications)
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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. View Full-Text
Keywords: volume averaging theory; permeability; inertial coefficient; Darcy; Forchheimer; metal foam; pressure drop volume averaging theory; permeability; inertial coefficient; Darcy; Forchheimer; metal foam; pressure drop
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

De Schampheleire, S.; De Kerpel, K.; Ameel, B.; De Jaeger, P.; Bagci, O.; De Paepe, M. A Discussion on the Interpretation of the Darcy Equation in Case of Open-Cell Metal Foam Based on Numerical Simulations. Materials 2016, 9, 409.

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