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Asymptotic solution to the viscous/inertial flow in wavy channels with permeable walls

Abstract : Flow in a wavy channel immersed in the porous medium can be described neither as the flow in porous media nor as the flow in a regular pipe. The flow through the walls and the irregular wavy geometry of the walls result in non-negligible inertial and visco-inertial effects. The quadratic and cubic corrections to Darcy’s law proposed since Forchheimer have always been the subject of debate. In this paper, the complete set of Navier-Stokes equations is solved in a channel with wavy walls immersed in a porous medium. The asymptotic solution is obtained using the perturbation method considering the channel’s aspect ratio as the perturbation parameter. The two-scale homogenization technique is used to capture the effect of the wavy corrugations on the overall flow in the channel. The averaged pressure drop along the channel is represented as quadratic and cubic corrections to the linear law for a cylindrical and parallel-plate wavy channel.
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Submitted on : Tuesday, June 22, 2021 - 10:24:24 AM
Last modification on : Friday, August 20, 2021 - 10:58:34 AM

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Mojdeh Rasoulzadeh, Mikhail Panfilov. Asymptotic solution to the viscous/inertial flow in wavy channels with permeable walls. Physics of Fluids, American Institute of Physics, 2018, 30 (10), pp.106604. ⟨10.1063/1.5041748⟩. ⟨hal-03265507⟩

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