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

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.

Pore-Scale Numerical Investigation of Pressure Drop Behaviour Across Open-Cell Metal Foams

“…26, are expected to become negligible. This is in agreement with the findings of De Schampheleire et al (2016) who state that at high Reynolds numbers the contribution from the Darcy term is negligible, with the bulk of the pressure losses being due to the form drag of the filaments.…”

“…They showed that as the Reynolds number (based on the average filament diameter) increased through the laminar, transitional and turbulent regimes, the contribution from the viscous drag decreased dramatically until it became almost negligible. 1 The contribution of the Darcy (viscous) and Forchheimer (form) terms to the pressure gradient for a metal foam (De Schampheleire et al 2016) This study aims to address some points commonly overlooked in previous studies. Direct pore-scale simulations are performed on several commercial open-cell metal foams with different pore sizes.…”

“…De Schampheleire et al (2016) use direct numerical simulations (DNS) to investigate the relative contributions to the pressure drop from the viscous and form drag terms in a open metal foam. They showed that as the Reynolds number (based on the average filament diameter) increased through the laminar, transitional and turbulent regimes, the contribution from the viscous drag decreased dramatically until it became almost negligible.…”

Teach Second Law of Thermodynamics via Analysis of Flow through Packed Beds and Consolidated Porous Media

“…Laminar flow in consolidated porous media (see Figure 7) is usually described by Darcy's law given as follows [19]:…”

“…The pressure-gradient in the turbulent regime is much higher compared with that in the laminar regime at the same superficial velocity V s . In order to extend the Darcy law to turbulent regime, Forchheimer [19] modified the Darcy law by adding a quadratic term as follows:…”