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Homogenization-based design of microstructured membranes: wake flows past permeable shells

Published online by Cambridge University Press:  29 September 2021

Pier Giuseppe Ledda Open the ORCID record for Pier Giuseppe Ledda [Opens in a new window] ,
E. Boujo Open the ORCID record for E. Boujo [Opens in a new window] ,
S. Camarri Open the ORCID record for S. Camarri [Opens in a new window] ,
F. Gallaire Open the ORCID record for F. Gallaire [Opens in a new window]  and
G.A. Zampogna Open the ORCID record for G.A. Zampogna [Opens in a new window]
Pier Giuseppe Ledda*
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
E. Boujo
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
S. Camarri
Affiliation:
Dipartimento di Ingegneria Civile e Industriale, Università degli Studi di Pisa, 56122 Pisa, Italy
F. Gallaire
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
G.A. Zampogna
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
*
†Email address for correspondence: pier.ledda@epfl.ch
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Abstract

A formal framework to characterize and control/optimize the flow past permeable membranes by means of a homogenization approach is proposed and applied to the wake flow past a permeable cylindrical shell. From a macroscopic viewpoint, a Navier-like effective stress jump condition is employed to model the presence of the membrane, in which the normal and tangential velocities at the membrane are respectively proportional to the so-called filtrability and slip numbers multiplied by the stresses. Regarding the particular geometry considered here, a characterization of the steady flow for several combinations of constant filtrability and slip numbers shows that the flow morphology is dominantly influenced by the filtrability and exhibits a recirculation region that moves downstream of the body and eventually disappears as this number increases. A linear stability analysis further shows the suppression of vortex shedding as long as large values of the filtrability number are employed. In the control/optimization phase, specific objectives for the macroscopic flow are formulated by adjoint methods. A homogenization-based inverse procedure is proposed to obtain the optimal constrained microscopic geometry from macroscopic objectives, which accounts for fast variations of the filtrability and slip profiles along the membrane. As a test case for the proposed design methodology, a cylindrical membrane is designed to maximize the resulting drag coefficient.

JFM classification

Flow Control: Flow Control Biological Fluid Dynamics: Membranes Low-Reynolds-number flows: Porous media
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 927 , 25 November 2021 , A31
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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