Goertler vortices in supersonic and hypersonic boundary layers

Abstract

The problem of Goertler vortices in compressible boundary layers over concave walls is considered. At O(1) wavelengths, the instability is governed by parabolic partial differential equations that are solved numerically to determine the effect of various initial conditions on the development of Goertler vortex instability in compressible boundary layers. The results show that both the velocity and temperature fluctuations may lead to a Goertler vortex. The vortex growth rates determined from the present method are found to differ somewhat from those given by a normal mode solution. At both the supersonic and hypersonic Mach numbers, cooling has a small destabilizing effect. In addition, the most unstable disturbances shift toward lower wavelengths because of thinning of the boundary layer. Our results also show that compressibility has a stabilizing effect on the Goertler instability, while the effect of an adverse pressure gradient is found to be destabilizing. The behavior of the Goertler vortex structure with Mach number is also examined. At hypersonic Mach numbers, vortices are located near the edge of the boundary layer for adiabatic wall conditions. However, the entire boundary layer is affected when the wall is cooled.

Numerical simulation of Görtler vortices in hypersonic compression ramps

“…Numerical effects were used to initiate a disturbance by [5,24], while [46] introduced a forced disturbance. Other numerical studies use boundary layer assumptions with constant curvature walls [14,21,40]. Domrö se et al [5] obtained good qualitative agreement with experiments in a shock impingement-boundary layer interaction by setting the domain width to four times the vortex diameter obtained in experiments.…”

Goertler instability of a hypersonic boundary layer

“…Ginoux (1971) observed the presence of Goertler vortices in the reattaching flow downstream of a descendent step at a Mach number of 5.3. More recently E1 Hady and Verma (1983), Spall and Malik (1989), Jallade (1990), Aymer de la Chevalerie et al (1991) published numerical results about the compressible Goertler problem, including the pressure gradient as well as wall temperature influence. All these papers are concerned with the instability of supersonic and/or hypersonic flows over concave walls, having a constant streamwise curvature radius.…”

Investigation of the spectrum of short-wave Görtler vortices in a gas

“…Obviously, for moderate free-stream Mach numbers, the structure of the vortices should not be significantly different from their structure in a liquid. Thus, Spall and Malik [13] and Wadey [14] studied long-wave vortices in a gas for which it is necessary to take into account the "growth" of the boundary layer. It has been found that unstable vortices shift toward the outer edge of the boundary layer as the Mach number increases [14].…”