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Coriolis effects during fluid flow through rotating granular porous media

Sawicki E., Geindreau C., Auriault J.

Studia Geotechnica et Mechanica

2005

Vol. 27, nr 1-2

143-154

Recently, the filtration law of an incompressible viscous Newtonian fluid flowing through a rigid non-inertial porous medium (e.g. a soil sample placed in a centrifuge basket) which takes into account the Criolis effects was developed by using an upscaling technique [2], [3], [7]. The structure of the law obtained is similar to that of the Darcy's law but the permeability tensor depends on the angular velocity w of the porous matrix, i.e. on the Ekman number Ek. It satisfies the Hall-Onsager's relation and is a non-symmetric tensor. The present study aims at quantifying more precisely the Coriolis effects in a porous medium. For this purpose we performed some 3D numerical simulations for the flow through rotating periodic array of spheres. Our numerical results clearly show the influence of the Coriolis effects on the permeability at large Ekman number e Ť Ek-1 Ť 1 and Ekman number O(l). These results are analyzed according to the geometrical properties of the packings of spheres: soild volume fraction, arrangement and size. Under particular conditions, we finally show that in the first approximation the flow through rotating granular media can be described by a modified Darcy's law including a "macroscopic Coriolis force" which brakes and deviates the flow.

Homogenization of compressible fluid flow in porous media with interfacial flow barrier

Royer P., Auriault J.

Archives of Mechanics

1999

Vol. 51, nr 3-4

469-486

This work is concerned with modelling compressible fluid flow in a composite porous medium with interfacial flow barrier. The macroscopic behaviour and the effective permeability are obtained by homogenization, i.e. by upscaling the description at the heterogeneity scale. Five distinct macroscopic models are derived that relate to five relative orders of magnitude of the interfacial conductance with respect to the permeabilities of the constituents.