Transition in boundary layers subject to free-stream turbulence

Abstract

The effect of high levels of free-stream turbulence on the transition in a Blasius boundary layer is studied by means of direct numerical simulations, where a synthetic turbulent inflow is obtained as superposition of modes of the continuous spectrum of the Orr-Sommerfeld and Squire operators. In the present bypass scenario the flow in the boundary layer develops streamwise elongated regions of high and low streamwise velocity and it is suggested that the breakdown into turbulent spots is related to local instabilities of the strong shear layers associated with these streaks. Flow structures typical of the spot precursors are presented and these show important similarities with the flow structures observed in previous studies on the secondary instability and breakdown of steady symmetric streaks.Numerical experiments are performed by varying the energy spectrum of the incoming perturbation. It is shown that the transition location moves to lower Reynolds numbers by increasing the integral length scale of the free-stream turbulence. The receptivity to free-stream turbulence is also analysed and it is found that two distinct physical mechanisms are active depending on the energy content of the external disturbance. If low-frequency modes diffuse into the boundary layer, presumably at the leading edge, the streaks are induced by streamwise vorticity through the linear lift-up effect. If, conversely, the free-stream perturbations are mainly located above the boundary layer a nonlinear process is needed to create streamwise vortices inside the shear layer. The relevance of the two mechanisms is discussed.

Stability of zero-pressure-gradient boundary layer distorted by unsteady Klebanoff streaks

“…The most unstable streamwise wavenumber was around α = 0.3, which agrees closely with the instability predicted by Andersson et al (2001). The corresponding wavelength is of the same order as the streak instabilities observed in the DNS of Brandt et al (2004), where λ x ∼ 5δ * .…”

“…The instability very closely resembles the flow patterns reported by Zaki & Durbin (2005), where their streak was perturbed by a highfrequency free-stream mode. It also bears a clear similarity to the flow patterns which preceded boundary-layer breakdown in previous simulations of bypass transition due to free-stream turbulence, in the absence of a leading edge (Jacobs & Durbin 2001;Brandt et al 2004). The mechanism was described by Jacobs & Durbin (2001) as an irregularity which resembles a Kelvin-Helmholtz instability.…”

“…The sinuous and varicose instabilities were also identified, albeit empirically, in experiments (Mans et al 2005;Mans, de Lange & van Steenhoven 2007) and simulations (Brandt, Sclatter & Henningson 2004) of bypass transition. However, a discrepancy remains between the critical streak amplitude based on stability theory and experimental observations.…”

“…The plane bisects the region where breakdown is initiated, and shows that the instability is near the wall, at the intersection of the low-and high-speed streaks. The importance of this region was suggested by Brandt et al (2004) based on their DNS. It was also noted by Zaki et al (2010) in simulations of transition in compressor passages, where the overall pressure gradient is adverse and the interaction of streak and instability waves leads to breakdown to turbulence.…”

“…(ii) The second explanation, which is the focus of the current work, is motivated by empirical evidence of the importance of streak unsteadiness. For example, based on their simulations, Brandt et al (2004) asserted that varicose breakdown is initiated where the streamwise velocity perturbation changes direction between passing streaks. Also, Mans et al (2007) studied the sinuous instability mechanism experimentally, and identified its origin near the upstream terminus of the low-speed streak.…”