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Laminar–turbulent transition in channel flow with superhydrophobic surfaces modelled as a partial slip wall

Published online by Cambridge University Press:  24 October 2019

Francesco Picella Open the ORCID record for Francesco 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]
Francesco Picella
Affiliation:
DynFluid – Arts et Métiers Paris, 151 Bd de l’Hôpital, 75013 Paris, France
J.-Ch. Robinet*
Affiliation:
DynFluid – Arts et Métiers Paris, 151 Bd de l’Hôpital, 75013 Paris, France
S. Cherubini
Affiliation:
Dipartimento di Meccanica, Matematica e Management (DMMM), Politecnico di Bari, Via Re David 200, 70126 Bari, Italy
*
†Email address for correspondence: jean-christophe.robinet@ensam.eu
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Abstract

Superhydrophobic surfaces are capable of trapping gas pockets within the micro-roughnesses on their surfaces when submerged in a liquid, with the overall effect of lubricating the flow on top of them. These bio-inspired surfaces have proven to be capable of dramatically reducing skin friction of the overlying flow in both laminar and turbulent regimes. However, their effect in transitional conditions, in which the flow evolution strongly depends on the initial conditions, has still not been deeply investigated. In this work the influence of superhydrophobic surfaces on several scenarios of laminar–turbulent transition in channel flow is studied by means of direct numerical simulations. A single phase incompressible flow has been considered and the effect of the micro-structured superhydrophobic surfaces has been modelled imposing a slip condition with given slip length at both walls. The evolution from laminar, to transitional, to fully developed turbulent flow has been followed starting from several different initial conditions. When modal disturbances issued from linear stability analyses are used for perturbing the laminar flow, as in supercritical conditions or in the classical K-type transition scenario, superhydrophobic surfaces are able to delay or even avoid the onset of turbulence, leading to a considerable drag reduction. Whereas, when transition is triggered by non-modal mechanisms, as in the optimal or uncontrolled transition scenarios, which are currently observed in noisy environments, these surfaces are totally ineffective for controlling transition. Superhydrophobic surfaces can thus be considered effective for delaying transition only in low-noise environments, where transition is triggered mostly by modal mechanisms.

JFM classification

Instability: Transition to turbulence Flow Control: Drag reduction
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 881 , 25 December 2019 , pp. 462 - 497
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© 2019 Cambridge University Press 

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