The stabilizing effect of streaks on Tollmien-Schlichting and oblique waves: A parametric study

Abstract

The stabilizing effect of finite amplitude streaks on the linear growth of unstable perturbations ͓Tollmien-Schlichting ͑TS͒ and oblique waves͔ is numerically investigated by means of the nonlinear parabolized stability equations. We have found that for stabilization of a TS-wave, there exists an "optimal" spanwise spacing of the streaks. These streaks reach their maximum amplitudes close to the first neutral point of the TS-wave and induce the largest distortion of the mean flow in the unstable region of the TS-wave. For such a distribution, the required streak amplitude for complete stabilization of a given TS-wave is considerably lower than for ␤ = 0.45, which is the optimal for streak growth and used in previous studies. We have also observed a damping effect of streaks on the growth rate of oblique waves in Blasius boundary layer and for TS-waves in Falkner-Skan boundary layers.In boundary-layer flows, the transition from a laminar state to a turbulent one is usually caused by growth and breakdown of small amplitude perturbations. For a long time, the common understanding has been that any kind of flow perturbation inside the boundary layer has a promoting effect on transition. However, a number of recent studies 1-4 have indicated that certain types of perturbations inside the boundary layer can postpone the laminar-turbulent transition. A general feature of these perturbations seems to be a modification of mean velocity profile to a more stable one. In two-dimensional mean flows, these are streaky structures that create regions of alternating negative and positive streamwise velocity perturbations. Streaks are usually found inside the boundary layers subjected to high free-stream turbulence. A damping effect of moderate amplitude free-stream turbulence on Tollmien-Schlichting ͑TS͒ waves has been observed in some experiments. 5 Numerical investigations of Cossu and Brandt 2 showed a clear stabilizing effect of streaks on growth of TS waves in Blasius flow. They reported an increasing damping effect with increasing streak amplitude. These results were later verified by experimental works of Fransson et al., 3 who generated the streaks by means of small roughness elements. Recently, Fransson et al. 4 also showed that these streaks can truly delay the transition. Here, the transition was triggered by means of highamplitude two-dimensional disturbances generated through random suction and blowing at the wall. These new results have received great attention; e.g., Ref. 6. However, in all these studies, both experimental and numerical, a single spanwise spacing ͑␤ = 0.45͒ of streaks has been used, which corresponds to the most growing streaks. Therefore, we aim to investigate whether other distributions of streaks are more efficient for stabilizing TS-waves, so that a lower streak amplitude would be required for transition delay. This is important because the amplitude of the streaks should not exceed the threshold for secondary instability and instead promoting the transition to turbulence. The present work is...

Test section streaks originating from imperfections in a zither located upstream of a contraction

“…This is consistent with the behaviour of the optimal streak (Cossu & Brandt 2004;Bagheri & Hanifi 2007;Schlatter et al 2011), steady roughness or vortex generator streaks (Fransson et al 2005a(Fransson et al , 2006Shahinfar et al 2012), and Klebanoff streaks (Arnal & Juillen 1978;Boiko et al 1994;Watmuff 1998). However, it contrasts the results of Vaughan & Zaki (2011) for steady streaks generated from the free stream with a Squire mode that increased TS-wave growth rates at low streak amplitudes.…”

“…Computations (Cossu & Brandt 2002) and stability theory (Cossu & Brandt 2004;Bagheri & Hanifi 2007) have shown that the steady optimal streak (Andersson, Berggren & Henningson 1999;Luchini 2000) reduces TS-wave growth rates. Streaks forced by roughness elements (Fransson et al 2005a;Gürün 2006) or miniature vortex generators have also shown reduced TS-wave growth, and sometimes transition delay (Fransson et al 2006;Shahinfar et al 2012;Shahinfar, Sattarzadeh & Fransson 2014).…”

Streak generation in wind tunnels

“…This amplitude is well below published thresholds for streak secondary instability in a zero pressure gradient 3,19 and is likely to have a minimal affect on TS growth. 6,7 The strength and amplitude measures are not linearly related for the streaks considered. The ratio δ*/A varies with streamwise position and streak strength, Initial CFD attempts failed to reproduce the case4U streak using a free-stream wake composed only of U and W components that matched the experimental data.…”

“…Most recent computational studies use the Optimal streak 1, 2 at nonlinear amplitudes. [3][4][5][6][7][8] Experimental studies have used roughness elements, [9][10][11] micro-wings, [12][13][14] or more recently vortex generators 15,16 to create streaks. While these studies have produced streaks with some comparable characteristics to Klebanoff streaks, the disturbance mechanism does not model wind tunnel settling chamber screens which have been empirically linked to Klebanoff streaks.…”

Numerical Studies of Non-linear Intrinsic Streaks in the Flat Plate Boundary Layer

“…The stability of the boundary layer with finite amplitude streaky distortions has been deeply analyzed 4,5,2 , and experimentally tested 6,7 , detecting that the increase of the amplitude of the streaks can have an stabilizing effect in the Blasius boundary layer, delaying the onset of turbulence. The limit of this effect and streak stability characteristics are far from clear 1,15 , and they probably depend not only on the magnitude of its spanwise modulation but also on how the streaks are generated.…”