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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(Document in English)
PDF (Author's version) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader 2MB |
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 |
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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) |
Laboratory name: | |
Funders: | Fondation IDEX Université de Toulouse |
Statistics: | download |
Deposited On: | 16 Nov 2018 09:43 |
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