Control of stationary Görtler vortices-induced high-speed boundary layer transition: Localized steady uniform blowing

Abstract

An investigation of effects of the localized steady uniform blowing (LSUB) on stationary Görtler vortices in a Mach 6.5 flow over a concave wall was carried out by solving two dimensional spatial eigenvalue problem (BiGlobal) and plane-marching parabolized stability equations (PSE3D) with help of direct numerical simulations (DNS). In the simulations, Görtler vortices are excited with spanwise wavelengths of 3 mm (1.5$\delta$, $\delta$ is the thickness of boundary layer at $x$ = 80 mm where the concave wall starts). No-slip and adiabatic conditions are prescribed at the wall. The flow visualization reveals prominent sinuous perturbations in the transition process. When the LSUB is applied to the wall, the boundary layer becomes thicker. With the increase in the amplitude of the LSUB within an appropriate range, Görtler streaks keep more regular and do not break down even at the end of the model when the amplitude of the LSUB is 0.01 of the free-stream velocity. Subsequent stability analyses based on BiGlobal and PSE3D confirm that sinuous secondary instability modes are the most unstable, responsible for the breakdown of Görtler vortices, and the growth rates of the dominant sinuous mode decrease significantly with increasing the amplitude of the LSUB. Further analysis indicates that the LSUB remarkably delays the growth of Görtler vortices, thus reducing the spanwise gradient of the streamwise velocity, which results in the decreases of energy production of the spanwise velocity shear. Therefore, the sinuous secondary instability is stabilized, leading to the delay of boundary layer transition. Our work suggests an appealing transition control strategy for high-speed flows dominated by Görtler vortices.