Delaying Transition to Turbulence by a Passive Mechanism

We compute the optimal transient growth of perturbations sustained by a turbulent channel flow following the same approach recently used by del Álamo and Jiménez ͓J. Fluid Mech. 559, 205 ͑2006͔͒. Contrary to this previous analysis, we use generalized Orr-Sommerfeld and Squire operators consistent with previous investigations of mean flows with variable viscosity. The optimal perturbations are streamwise vortices evolving into streamwise streaks. In accordance with del Álamo and Jiménez, it is found that for very elongated structures and for sufficiently large Reynolds numbers, the optimal energy growth presents a primary peak in the spanwise wavelength, scaling in outer units, and a secondary peak scaling in inner units and corresponding to z + Ϸ 100. Contrary to the previous results, however, it is found that the maximum energy growth associated with the primary peak increases with the Reynolds number. This growth, in a first approximation, scales linearly with an effective Reynolds number based on the centerline velocity, the channel half width and the maximum eddy viscosity associated. The optimal streaks associated with the primary peak have an optimal spacing of z =4h and scale in outer units in the outer region and in wall units in the near wall region, where they still have up to 50% of their maximum amplitude near y + = 10.

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“…26 Forcing large amplitude streaks could be interesting to manipulate the flow, as already shown in the case of laminar boundary layers. 27,28 …”

Section: Summary and Discussionmentioning

confidence: 99%

A note on optimal transient growth in turbulent channel flows

et al. 2009

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“…The damping abilities of streaks has been demonstrated for cases with dominant two-dimensional waves, see the references mentioned above [2,3,5]. Consequently, for the case which leads to TS-wave dominated transition (2D small-scale noise), transition delay can be observed, see Fig.…”

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confidence: 92%

Interaction of noise disturbances and streamwise streaks

Schlatter

Deusebio

Brandt

et al. 2009

Seventh IUTAM Symposium on Laminar-Turbulent Transition

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Disturbance evolution in a boundary layer with streamwise streaks and random two-and three-dimensional noise of various amplitudes is studied via numerical simulations. The aim of the present work is to determine the impact of the interaction on the arising flow structures and, eventually, on the location and details of the breakdown to turbulence. It is shown that largescale 2D noise can be controlled via streaks, whereas the more general 3D noise configuration is prone to premature transition due to increased instability of the introduced streaks. It is interesting to note that the latter transition scenario closely resembles the flow structures found in bypass transition.A recent theoretical and numerical study by Cossu and Brandt [2] has shown that a substantial stabilisation of a boundary layer subject to essentially two-dimensional disturbances (i.e. Tollmien-Schlichting (TS) waves) can be achieved by a spanwise modulation of the mean flow, i.e. via superimposed streamwise streaks on the laminar Blasius flow. In particular, it has been shown both experimentally via finite-amplitude roughness [3] and later via large-eddy simulation (LES, [5]) that transition to turbulence can effectively by moved to a more downstream position via this essentially passive control mechanism. However, the disturbances considered in the mentioned studies have all had their maximum energy in two-dimensional (spanwise invariant) modes. It is therefore interesting to examine the interaction of streamwise streaks with disturbences of a more general nature, i.e. 2D and 3D random noise at various frequencies and (spanwise) wavenumbers.The present study uses a spectral numerical method [1] together with LES based on high-order filtering (ADM-RT model [6]), in a similar setup as presented in Ref. [5]. In particular, the computational domain starts at Re x = 32000 extending up to Re x = 590000. The streaks are introduced at the inlet as optimal disturbances computed from PSE (parabolised stability equations), subsequently evolving nonlinearly inside the domain. Conversely, the noise is forced within the computational domain at Re x = 60000 by a volume force close to the wall. Two frequency spectra of the noise are shown in Fig.

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“…Over the past two decades, most investigations on topics of laminar-turbulent transition in a boundary layer have focused on two kinds of problem: the receptivity mechanism (Wu 2001a,b;Saric, Reed & Kerschen 2002;Ruban, Bernots & Pryce 2013) and stabilisation/destabilisation of TS waves (Cossu & Brandt 2002Fransson et al 2005Fransson et al , 2006Garzon & Roberts 2013). Meanwhile, we need to point out that TS waves are important basically in two-dimensional (2D) subsonic boundary-layers on flat or convex surfaces, while in many other cases other instabilities dominate and are being extensively investigated.…”

Section: Motivation Behind the Study Of Steps In Boundary Layersmentioning

confidence: 99%

Influence of localised smooth steps on the instability of a boundary layer

Lombard

Sherwin

2017

J. Fluid Mech.

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We consider a smooth, spanwise-uniform forward-facing step defined by a Gauss error function of height 4 %-30 % and four times the width of the local boundary layer thickness δ 99 . The boundary layer flow over a smooth forward-facing stepped plate is studied with particular emphasis on stabilisation and destabilisation of the twodimensional Tollmien-Schlichting (TS) waves and subsequently on three-dimensional disturbances at transition. The interaction between TS waves at a range of frequencies and a base flow over a single or two forward-facing smooth steps is conducted by linear analysis. The results indicate that for a TS wave with a frequency F ∈ [140, 160] (F = ων/U 2 ∞ × 10 6 , where ω and U ∞ denote the perturbation angle frequency and free-stream velocity magnitude, respectively, and ν denotes kinematic viscosity), the amplitude of the TS wave is attenuated in the unstable regime of the neutral stability curve corresponding to a flat plate boundary layer. Furthermore, it is observed that two smooth forward-facing steps lead to a more acute reduction of the amplitude of the TS wave. When the height of a step is increased to more than 20 % of the local boundary layer thickness for a fixed width parameter, the TS wave is amplified, and thereby a destabilisation effect is introduced. Therefore, the stabilisation or destabilisation effect of a smooth step is typically dependent on its shape parameters. To validate the results of the linear stability analysis, where a TS wave is damped by the forward-facing smooth steps direct numerical simulation (DNS) is performed. The results of the DNS correlate favourably with the linear analysis and show that for the investigated frequency of the TS wave, the K-type transition process is altered whereas the onset of the H-type transition is delayed. The results of the DNS suggest that for the perturbation with the non-dimensional frequency parameter F = 150 and in the absence of other external perturbations, two forward-facing smooth steps of height 5 % and 12 % of the boundary layer thickness delayed the H-type transition scenario and completely suppressed for the K-type transition. By considering Gaussian white noise with both fixed and random phase shifts, it is demonstrated by DNS that transition is postponed in time and space by two forward-facing smooth steps.

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Delaying Transition to Turbulence by a Passive Mechanism

Cited by 231 publications

References 34 publications

A note on optimal transient growth in turbulent channel flows

A note on optimal transient growth in turbulent channel flows

Interaction of noise disturbances and streamwise streaks

Influence of localised smooth steps on the instability of a boundary layer

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