Experimental and theoretical investigation of the nonmodal growth of steady streaks in a flat plate boundary layer

Abstract

International audienceAn experimental and theoretical investigation aimed at describing the nonmodal growth of steady and spanwise periodic streamwise streaks in a flat plate boundary layer is presented. Stable laminar streaks are experimentally generated by means of a spanwise periodic array of small cylindrical roughness elements fixed on the plate. The streamwise evolution of the streaks is measured and it is proved that, except in a small region near the roughness elements, they obey the boundary layer scalings. The maximum achievable amplitude is mainly determined by the relative height of the roughness elements. Results are compared with numerical simulations of optimal and suboptimal boundary layer streaks. The theory is able to elucidate some of the discrepancies recently noticed between experimentally realizable nonmodal growth and optimal perturbation theory. The key factor is found to be the wall normal location and the extension of the laminar standing streamwise vortices inducing the streaks. The differences among previous experimental works can be explained by different dominating streak generation mechanisms which can be linked to the geometry and to the ratio between the roughness height and the boundary layer scale. © 2004 American Institute of Physics

Advanced Fluid Research On Drag reduction In Turbulence Experiments –AFRODITE–

“…Comparison of the results by Fransson et al (2004) with similar experimental studies in the literature showed that the flow may be modulated differently depending on the roughness element configuration. They are all characterized by the formation of streamwise elongated velocity perturbations and differ in the relative position of the high and low speed streaks with respect to the roughness elements.…”

“…This is due to the presence of the wake, which persists downstream forming the low speed streak. Conversely, in the experiments reported in Fransson et al (2004), similarly to what was observed by Bakchinov et al (1995); Kendall (1990), after a complex region of growing and decaying modes a high speed region is induced behind the roughness element. An explanation for this behavior can be found by considering the perturbation induced by a roughness element in a wall-bounded shear flow (Hunt et al, 1978;Acarlar & Smith, 1987;Dèlery, 2001).…”

“…The legs of each vortex consist of two counter-rotating streamwise vortices, which in this case increase the defect velocity induced in the wake and generate relatively high levels of root means square (rms) velocity fluctuations (larger than 5% of U ∞ ). Nevertheless, the low level of the streamwise rms velocity fluctuations (less than 0.6% of U ∞ ) and the absence of any power spectra peak show that this phenomenon is not present in the experiment by Fransson et al (2004). It can be concluded that there is a competition between the perturbation induced by the vortex generated by the incoming vorticity upstream of the element and the wake downstream of it.…”

“…The maximum amplitude of the streaks was below 4% of U ∞ . This work was inspiring for Fransson et al (2004) who were searching for means to generate high amplitude streaks for TS-wave control. They were able to generate stable streaks up to 12% of U ∞ by using another roughness element configuration in where the streaks are generated by a completely different physical mechanism as explained below.…”

Algebraic/transcendental disturbance growth behind a row of roughness elements

“…It is also known that streaks can have a stabilizing effect on the small amplitude Tollmien-Schlichting waves that comprise the initial stage of transition in many applications with low levels of external forcing. Moreover it is now realized that the stable laminar streaks generated by surface roughness elements can be used to control transition in these applications (Fransson et al 2004(Fransson et al , 2006. It therefore seems important to understand the physical mechanisms related to the potential disturbance growth in the wake flow behind surface roughness elements.…”