LASSEUX, Didier; VALDÉS-PARADA, Francisco; THOVERT, Jean-François; MOURZENKO, Valeri

doi:10.1017/jfm.2020.1081

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LASSEUX, Didier

Institut de Mécanique et d'Ingénierie [I2M]

VALDÉS-PARADA, Francisco
Universidad Autonoma Metropolitana - Iztapalapa
Departamento de Ingeniería de Procesos e Hidráulica

THOVERT, Jean-François
Combustion hétérogène et milieu poreux [Institut Pprime] [CH ]
Département Fluides, Thermique et Combustion [Institut Pprime] [Département FTC]
Institut Pprime [UPR 3346] [PPrime [Poitiers]]

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Journal of Fluid Mechanics. 2021-03-25, vol. 911, n° A48

Cambridge University Press (CUP)

Résumé en anglais

This work addresses the question of a pertinent macroscale model describing creeping, incompressible and single-phase flow of a Newtonian fluid in an exuding, rigid and homogeneous porous medium. The macroscopic model is derived by upscaling the pore-scale Stokes equations considering a normal mass flux at the solid–fluid interface. The upscaled mass equation shows that the average velocity is non-solenoidal. In addition, the macroscopic momentum equation involves a Darcy term with the classical permeability tensor accounting for macroscopic drag and a correction velocity vector which is a signature of the local fluid displacements induced by the exuding phenomenon. This correction is the sum of a term accounting for the local exuding effect and a compensation term associated with the assumption of spatial periodicity. Both the first term and the permeability tensor are obtained from the solution of the same unique and intrinsic closure problem, which corresponds to that involved in the classical Darcy’s law. The upscaled model is validated by comparisons with pore-scale numerical simulations in several illustrative examples. The different configurations evidence the richness of the problem, despite the apparent simplicity of its formulation. The results of this work motivate further investigation about the influence of internal flow sources in transport phenomena in porous media.< Réduire

Mots clés en anglais

general fluid mechanics

porous media

exuding porous media

momentum transport

upscaling

Darcy's law

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Exuding porous media: deviations from Darcy's law

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