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On the influence of the modelling of superhydrophobic surfaces on laminar–turbulent transition

Published online by Cambridge University Press:  25 August 2020

F. Picella Open the ORCID record for F. Picella [Opens in a new window] ,
J.-Ch. Robinet Open the ORCID record for J.-Ch. Robinet [Opens in a new window]  and
S. Cherubini Open the ORCID record for S. Cherubini [Opens in a new window]
F. Picella
Affiliation:
DynFluid – Arts et Métiers Paris, 151 Bd de l'Hôpital, 75013Paris, France
J.-Ch. Robinet
Affiliation:
DynFluid – Arts et Métiers Paris, 151 Bd de l'Hôpital, 75013Paris, France
S. Cherubini*
Affiliation:
Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, Via Re David 200, 70126Bari, Italy
*
†Email address for correspondence: [email protected]
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Abstract

Superhydrophobic surfaces dramatically reduce the skin friction of overlying liquid flows, providing a lubricating layer of gas bubbles trapped within their surface nano-sculptures. Under wetting-stable conditions, different models can be used to numerically simulate their effect on the overlying flow, ranging from spatially homogeneous slip conditions at the wall, to spatially heterogeneous slip–no-slip conditions taking into account or not the displacement of the gas–water interfaces. These models provide similar results in both laminar and turbulent regimes, but their effect on transitional flows has not been investigated yet. In this work we study, by means of numerical simulations and global stability analyses, the influence of the modelling of superhydrophobic surfaces on laminar–turbulent transition in a channel flow. For the K-type scenario, a strong transition delay is found using spatially homogeneous or heterogeneous slippery boundaries with flat, rigid liquid–gas interfaces. Whereas, when the interface dynamics is taken into account, the time to transition is reduced, approaching that of a no-slip channel flow. It is found that the interface deformation promotes ejection events creating hairpin heads that are prone to breakdown, reducing the transition delay effect with respect to flat slippery surfaces. Thus, in the case of modal transition, the interface dynamics must be taken into account for accurately estimating transition delay. Contrariwise, non-modal transition triggered by a broadband forcing is unaffected by the presence of these surfaces, no matter the surface modelling. Thus, superhydrophobic surfaces may or not influence transition to turbulence depending on the interface dynamics and on the considered transition process.

JFM classification

Flow Control: Drag reduction Instability: Transition to turbulence Turbulent Flows: Turbulent transition
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 901 , 25 October 2020 , A15
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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