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On the stationary macroscopic inertial effects for one phase flow in ordered and disordered porous media

hal.structure.identifierInstitut de Mécanique et d'Ingénierie de Bordeaux [I2M]
dc.contributor.authorLASSEUX, Didier
IDREF: 131294474
hal.structure.identifierInstitut de Mécanique et d'Ingénierie de Bordeaux [I2M]
dc.contributor.authorABBASIAN ARANI, Ali Akbar
hal.structure.identifierInstitut de Mécanique et d'Ingénierie de Bordeaux [I2M]
dc.contributor.authorAHMADI-SENICHAULT, Azita
dc.date.accessioned2021-05-14T09:56:33Z
dc.date.available2021-05-14T09:56:33Z
dc.date.issued2011
dc.identifier.issn1070-6631
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/77798
dc.descriptionWe report on the controversial dependence of the inertial correction to Darcy’s law upon the filtration velocity (or Reynolds number) for one-phase Newtonian incompressible flow in model porous media. Our analysis is performed on the basis of an upscaled form of the Navier-Stokes equation requiring the solution of both the micro-scale flow and the associated closure problem. It is carried out with a special focus on the different regimes of inertia (weak and strong inertia) and the crossover between these regimes versus flow orientation and structural parameters, namely porosity and disorder. For ordered structures, it is shown that (i) the tensor involved in the expression of the correction is generally not symmetric, despite the isotropic feature of the permeability tensor. This is in accordance with the fact that the extra force due to inertia exerted on the structure is not pure drag in the general case; (ii) the Forchheimer type of correction (which strictly depends on the square of the filtration velocity) is an approximation that does not hold at all for particular orientations of the pressure gradient with respect to the axes of the structure; and (iii) the weak inertia regime always exists as predicted by theoretical developments. When structural disorder is introduced, this work shows that (i) the quadratic dependence of the correction upon the filtration velocity is very robust over a wide range of the Reynolds number in the strong inertia regime; (ii) the Reynolds number interval corresponding to weak inertia, that is always present, is strongly reduced in comparison to ordered structures. In conjunction with its relatively small magnitude, it explains why this weak inertia regime is most of the time overlooked during experiments on natural media. In all cases, the Forchheimer correction implies that the permeability is different from the intrinsic one.
dc.description.abstractEnWe report on the controversial dependence of the inertial correction to Darcy’s law upon the filtration velocity (or Reynolds number) for one-phase Newtonian incompressible flow in model porous media. Our analysis is performed on the basis of an upscaled form of the Navier-Stokes equation requiring the solution of both the micro-scale flow and the associated closure problem. It is carried out with a special focus on the different regimes of inertia (weak and strong inertia) and the crossover between these regimes versus flow orientation and structural parameters, namely porosity and disorder. For ordered structures, it is shown that (i) the tensor involved in the expression of the correction is generally not symmetric, despite the isotropic feature of the permeability tensor. This is in accordance with the fact that the extra force due to inertia exerted on the structure is not pure drag in the general case; (ii) the Forchheimer type of correction (which strictly depends on the square of the filtration velocity) is an approximation that does not hold at all for particular orientations of the pressure gradient with respect to the axes of the structure; and (iii) the weak inertia regime always exists as predicted by theoretical developments. When structural disorder is introduced, this work shows that (i) the quadratic dependence of the correction upon the filtration velocity is very robust over a wide range of the Reynolds number in the strong inertia regime; (ii) the Reynolds number interval corresponding to weak inertia, that is always present, is strongly reduced in comparison to ordered structures. In conjunction with its relatively small magnitude, it explains why this weak inertia regime is most of the time overlooked during experiments on natural media. In all cases, the Forchheimer correction implies that the permeability is different from the intrinsic one.
dc.language.isoen
dc.publisherAmerican Institute of Physics
dc.subject.enporous media
dc.subject.eninertial flow
dc.subject.enone phase and two phase
dc.subject.enordered and disordered media
dc.title.enOn the stationary macroscopic inertial effects for one phase flow in ordered and disordered porous media
dc.typeArticle de revue
dc.identifier.doi10.1063/1.3615514
dc.subject.halSciences de l'ingénieur [physics]/Mécanique [physics.med-ph]/Mécanique des fluides [physics.class-ph]
bordeaux.journalPhysics of Fluids
bordeaux.page19 p.
bordeaux.volume23
bordeaux.hal.laboratoriesInstitut de Mécanique et d’Ingénierie de Bordeaux (I2M) - UMR 5295*
bordeaux.issue7
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.institutionINRAE
bordeaux.institutionArts et Métiers
bordeaux.peerReviewedoui
hal.identifierhal-01174068
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01174068v1
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