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Effects of porosity and inertia on the apparent permeability tensor in fibrous media

Luminari, Nicola and Airiau, Christophe and Bottaro, Alessandro Effects of porosity and inertia on the apparent permeability tensor in fibrous media. (2018) International Journal of Multiphase Flow, 106. 60-74. ISSN 0301-9322

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Official URL: http://doi.org/10.1016/j.ijmultiphaseflow.2018.04.013

Abstract

The flow in three-dimensional fibrous porous media is studied in the inertial regime by first simulating for the motion in unit, periodic cells, and then solving successive closure problems leading – after applying an intrinsic averaging procedure – to the components of the apparent permeability tensor. The parameters varied include the orientation of the driving pressure gradient, its magnitude (which permits to define a microscopic Reynolds number), and the porosity of the medium. All cases tested refer to situations for which the microscopic flow is steady. When the driving force is oriented in a direction whichlies on the plane perpendicular to the fibers’ axis, the results found agree with those available the literature. The fact that the medium is composed by bundles of parallel fibers favours a deviation of the mean flow towards the fibers’ axis when the driving pressure gradient has even a small component along it, and this is enhanced by a decreasing porosity; this phenomenon is well quantified by the knowledge of the components of the permeability. Contrary to our initial expectations, for the over one hundred cases which we have simulated, the apparent permeability tensor remains, to a very good approximation, diagonal, a fact mainly related to the transversely isotropic nature of the medium. To obtain a complete,albeit approximate, database of the diagonal components of the apparent permeability tensor we have developed a metamodel, based on kriging interpolation, and carefully calibrated it. The resulting response surfaces can be invaluable in determining the force caused by the presence of inclusions in macroscopic simulations of the flow through bundles of fibers whose orientations and dimensions can vary in space and/or time.

Item Type:Article
Additional Information:Thanks to Elsevier editor. The definitive version is available at : https://www.sciencedirect.com/science/article/pii/S0301932218300648
HAL Id:hal-01811015
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Other partners > Università degli Studi di Genova - UNIGE (ITALY)
Laboratory name:
Funders:
CALMIP center, Toulouse - IDEX Foundation, University of Toulouse
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Deposited On:08 Jun 2018 12:23

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