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

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.

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

“…This can be easily explained noticing that these vortical perturbations rapidly create sinuous streaks which bear many resemblances with the core structures mentioned by Davis and Park [68], whose transition is promoted by the presence of slip. This may appear in contrast with what found by Picella et al [64], where slip appeared to have no effect at all on the transition behavior of core perturbations such as the linear optimal disturbances. However, this behavior could stem from the linear character of these last perturbations, which have been computed in the total absence of nonlinear effects.…”

“…They showed that this particular type of transition can be delayed by wall slip; however, they did not explain how and why this effect is achieved, and they did not extend the analysis to other transition scenarios. The recent work of Picella et al [64] has analyzed the influence of slip at the wall on three different transition scenarios in channel flow, that we rapidly review here: (i) the K-type transition scenario, which is triggered setting as initial disturbances a sum of a twodimensional TS wave with streamwise and spanwise wavenumber (α, β) = (1.12, 0.0), and a sum of equal and opposite oblique three-dimensional fundamental Tollmien-Schlichting waves characterized by spatial wavenumbers (α, β) = (1.12, ±2.10) with amplitude 0.033 and 0.0011, respectively; (ii) an initial linear optimal perturbation computed in the chosen flow conditions and scaled with a sufficiently high amplitude for triggering nonlinear effects and consequently leading to transition; and (iii) an ad hoc volume forcing, constructed by a superposition of optimal forcing functions, able to trigger a large-amplitude response in the flow as a consequence of receptivity, which is referred to as F-type transition [89]. In all these cases, slippery walls with slip length L s = 0.00, 0.01, 0.02 have been considered, with the highest value resulting from a SHS having a roughness texture period of L + ≈ 15 in the turbulent regime [73].…”

“…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.…”

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

“…fluctuations occurring into the second (Q2) and fourth (Q4) quadrants of the u − v plane (Adrian 2007), representing respectively ejections, with negative streamwise disturbances lifted away from the wall by positive wall-normal fluctuations, and sweeps, characterised by positive streamwise velocity perturbations transported toward the wall by negative v. Figure 9 provides the wall-normal distribution of the Q2/Q4 events for the PPF, SNS and MVB cases. As previously shown in Picella et al (2019b), considering a slippery but rigid wall radically modifies the distribution of sweeps and ejections events with respect to the classical case of a no-slip wall. For K-type triggered transition over the benchmark no-slip flat surface (PPF), we first observe Q4 events close to the wall, identified by Malm et al (2011) as high-speed streaks (t ≈ 75, y = −0.8), which are due to the sweeping vortex tilting-stretching processes from which Λ vortices arise.…”

“…Setting a fixed laminar Reynolds number and reaching the turbulent flow regime keeping a constant flow rate, the friction Reynolds number will decrease due to the drag reduction effect of the superhydrophobic surfaces. In previous studies of transitional flows over SHS modelled with a homogeneous slip length (Picella et al 2019b…”