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Generalized slip condition over rough surfaces

Zampogna, Giuseppe Antonio and Magnaudet, Jacques and Bottaro, Alessandro Generalized slip condition over rough surfaces. (2019) Journal of Fluid Mechanics, 858. 407-436. ISSN 0022-1120

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Official URL: https://doi.org/10.1017/jfm.2018.780

Abstract

A macroscopic boundary condition to be used when a fluid flows over a rough surface is derived. It provides the slip velocity uS on an equivalent (smooth) surface in the form uS =EL:E, where the dimensionless parameter E is a measure of the roughness amplitude, E denotes the strain-rate tensor associated with the outer flow in the vicinity of the surface and L is a third-order slip tensor arising from the microscopic geometry characterizing the rough surface. This boundary condition represents the tensorial generalization of the classical Navier slip condition. We derive this condition, in the limit of small microscopic Reynolds numbers, using a multi-scale technique that yields a closed system of equations, the solution of which allows the slip tensor to be univocally calculated, once the roughness geometry is specified. We validate this generalized slip condition by considering the flow about a rough sphere, the surface of which is covered with a hexagonal lattice of cylindrical protrusions. Comparisons with direct numerical simulations performed in both laminar and turbulent regimes allow us to assess the validity and limitations of this condition and of the mathematical model underlying the determination of the slip tensor L.

Item Type:Article
HAL Id:hal-01924709
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)
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Funders:
Fondation IDEX Université de Toulouse
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Deposited On:16 Nov 2018 09:43

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