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Model ID: 4413

Forchheimer Flow

The coupling of free media flow with porous media flow is common in the fields of earth science and chemical engineering.

Perhaps the most common way to deal with coupled free and porous media flow is to incorporate flow described by Darcy’s law with the Navier-Stokes Equations that describes the free flow. However, this approach does not account for viscous effects arising from the free media flow, which may still be important in the region close to the free-porous structure interface.

The Brinkman equations account for momentum transport by macroscopic viscous effects as well as pressure gradients. Still, the Brinkman equations assume completely laminar flow. Looking at processes in relatively open structures, like gas flow through packed beds, there is also a turbulent contribution to the resistance to flow. In those cases, an addtional term must account for the turbulent flow's contribution to the resistance to flow in the porous domain.

The Forchheimer equation (also accredited to Ergun) simulated in this model is widely used to predict pressure drops in packed beds with turbulent flow.

Results from this model show that without the Forchheimer correction, the resistance to flow is underestimated in the porous domain. The added correction gives a solution with slower flow in the porous domain and subsequently faster in the free domain, due to incompressibility.

Surface plot showing the velocity field.

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