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

Picella, Francesco; Robinet, Jean-Christophe; Cherubini, Stefania

doi:10.1017/jfm.2020.516

Cited by 24 publications

(7 citation statements)

References 89 publications

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“…Thus, the effect of the gas-liquid interface motion on the optimal growth and on the consequent transition scenarios, remains to be investigated. Using a moving-boundary technique for modeling the SHS surfaces, Picella et al [65] found that the strong ejection events induced by the interface motion can contrast the sweep-like effect of the boundary slip, leading to a transition scenario very similar to that observed in the no-slip case. This study suggests that the optimal solutions may remain robust also in the presence of interface motion.…”

Section: Discussionmentioning

confidence: 99%

“…Thus, the present work shows that wall slip has a strong potential in stabilizing optimal ejection-like events, although it can be not effective, or even detrimental, in the case of core perturbations. However, it has been recently shown [65] that, for sufficiently large (but wetting-stable) micro-roughnesses, the gas-liquid interface motion may partially hinder the transition delay effect of the wall slip. Thus, it would be crucial to investigate the robustness of these conclusions about the effect of SHS on optimal energy growth mechanisms with respect to the presence of gas-liquid interface motion.…”

Section: Discussionmentioning

confidence: 99%

“…Transition to turbulence has been found to be considerably delayed for sufficiently large (but still practically viable) slip lengths. This pioneer study has been followed, some years later, by two studies in which different transition scenarios have been analyzed in the presence of slippery boundaries [64] and feature-resolved SHS [65]. These studies reported very different behaviors of the transitional channel flow in the presence of SHS, depending on the particular type of perturbations used for triggering turbulence.…”

Section: Introductionmentioning

confidence: 99%

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Variational Nonlinear Optimization in Fluid Dynamics: The Case of a Channel Flow with Superhydrophobic Walls

2020

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Variational optimization has been recently applied to nonlinear systems with many degrees of freedom such as shear flows undergoing transition to turbulence. This technique has unveiled powerful energy growth mechanisms able to produce typical coherent structures currently observed in transition and turbulence. However, it is still not clear the extent to which these nonlinear optimal energy growth mechanisms are robust with respect to external disturbances or wall imperfections. Within this framework, this work aims at investigating how nano-roughnesses such as those of superhydrophobic surfaces affect optimal energy growth mechanisms relying on nonlinearity. Nonlinear optimizations have been carried out in a channel flow with no-slip and slippery boundaries, mimicking the presence of superhydrophobic surfaces. For increasing slip length, the energy threshold for obtaining hairpin-like nonlinear optimal perturbations slightly rises, scaling approximately with Re−2.36 no matter the slip length. The corresponding energy gain increases with Re with a slope that reduces with the slip length, being almost halved for the largest slip and Reynolds number considered. This suggests a strong effect of boundary slip on the energy growth of these perturbations. While energy is considerably decreased, the shape of the optimal perturbation barely changes, indicating the robustness of optimal perturbations with respect to wall slip.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Variational Nonlinear Optimization in Fluid Dynamics: The Case of a Channel Flow with Superhydrophobic Walls

2020

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“…The validity of linear stability results on laminar–turbulent transition itself, which is an intrinsically nonlinear phenomenon, has been recently assessed by Picella, Robinet & Cherubini (2019, 2020), who have confirmed that SH surfaces strongly influence transition induced by wall-close disturbances, such as TS waves, even at subcritical Reynolds number, but have a weak effect on the subcritical growth of coherent structures lying farther from the wall, such as streaks and streamwise vortices. Cherubini, Picella & Robinet (2021) reported a strong effect of boundary slip on the transient growth of nonlinear optimal perturbations: in particular, while the maximal energy growth is considerably decreased, the shape of the optimal perturbation barely changes, indicating the robustness of optimal perturbations with respect to wall slip.…”

Section: Introductionmentioning

confidence: 89%

Turbulent transition in a channel with superhydrophobic walls: anisotropic slip and shear misalignment effects

Jouin,

Cherubini,

Robinet

2024

J. Fluid Mech.

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Superhydrophobic surfaces dramatically reduce skin friction of overlying liquid flows. These surfaces are complex and numerical simulations usually rely on models to reduce this complexity. One of the simplest consists of finding an equivalent boundary condition through a homogenisation procedure, which in the case of channel flow over oriented riblets, leads to the presence of a small spanwise component in the homogenised base flow velocity. This work aims at investigating the influence of such a three-dimensionality of the base flow on stability and transition in a channel with walls covered by oriented riblets. Linear stability for this base flow is investigated: a new instability region, linked to cross-flow effects, is observed. Tollmien–Schlichting waves are also retrieved but the most unstable are three-dimensional. Transient growth is also affected as oblique streaks with non-zero streamwise wavenumber become the most amplified perturbations. When transition is induced by Tollmien–Schlichting waves, after an initial exponential growth regime, streaky structures with large spanwise wavenumber rapidly arise. Modal mechanisms appear to play a leading role in the development of these structures and a secondary stability analysis is performed to retrieve successfully some of their characteristics. The second scenario, initiated with cross-flow vortices, displays a strong influence of nonlinearities. The flow develops into large quasi-spanwise-invariant structures before breaking down to turbulence. Secondary stability on the saturated cross-flow vortices sheds light on this stage of transition. In both cases, cross-flow effects dominate the flow dynamics, suggesting the need to consider the anisotropicity of the wall condition when modelling superhydrophobic surfaces.

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“…They study the evolution of both modal and non-modal disturbances, and show that SHS may be used to delay transition in the former and have no effect on the latter. Extending these works, Picella, Robinet & Cherubini (2020) then impose correct mixed boundary conditions to study the effects of the interface dynamics on transition. They find that transition again occurs further downstream, however, the stabilisation effects are reduced relative to the slip conditions.…”

Section: Introductionmentioning

confidence: 99%

Linear instability of lid- and pressure-driven flows in channels textured with longitudinal superhydrophobic grooves

Tomlinson

Papageorgiou

2021

J. Fluid Mech.

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It is known that an increased flow rate can be achieved in channel flows when smooth walls are replaced by superhydrophobic surfaces. This reduces friction and increases the flux for a given driving force. Applications include thermal management in microelectronics, where a competition between convective and conductive resistance must be accounted for in order to evaluate any advantages of these surfaces. Of particular interest is the hydrodynamic stability of the underlying basic flows, something that has been largely overlooked in the literature, but is of key relevance to applications that typically base design on steady states or apparent-slip models that approximate them. We consider the global stability problem in the case where the longitudinal grooves are periodic in the spanwise direction. The flow is driven along the grooves by either the motion of a smooth upper lid or a constant pressure gradient. In the case of smooth walls, the former problem (plane Couette flow) is linearly stable at all Reynolds numbers whereas the latter (plane Poiseuille flow) becomes unstable above a relatively large Reynolds number. When grooves are present our work shows that additional instabilities arise in both cases, with critical Reynolds numbers small enough to be achievable in applications. Generally, for lid-driven flows one unstable mode is found that becomes neutral as the Reynolds number increases, indicating that the flows are inviscidly stable. For pressure-driven flows, two modes can coexist and exchange stability depending on the channel height and slip fraction. The first mode remains unstable as the Reynolds number increases and corresponds to an unstable mode of the two-dimensional Rayleigh equation, while the second mode becomes neutrally stable at infinite Reynolds numbers. Comparisons of critical Reynolds numbers with the experimental observations for pressure-driven flows of Daniello et al. (Phys. Fluids, vol. 21, issue 8, 2009, p. 085103) are encouraging.

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

Abstract: Abstract

Cited by 24 publications

References 89 publications

Variational Nonlinear Optimization in Fluid Dynamics: The Case of a Channel Flow with Superhydrophobic Walls

Variational Nonlinear Optimization in Fluid Dynamics: The Case of a Channel Flow with Superhydrophobic Walls

Turbulent transition in a channel with superhydrophobic walls: anisotropic slip and shear misalignment effects

Linear instability of lid- and pressure-driven flows in channels textured with longitudinal superhydrophobic grooves

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