Centrifugal instabilities in curved compressible wakes

Abstract

This investigation is concerned with the linear development of Görtler vortices in the high-Reynolds-number laminar compressible wake behind a flat plate which is aligned with the centerline of a curved mixing-layer system. The Görtler modes were previously found to exist within curved compressible mixing layers by Owen et al. ͓Phys. Fluids 8, 2506 ͑1997͔͒. This study extends that investigation and demonstrates the effect a wake has on the growth rate and location of such modes. The investigations were made by examining the growth rate and the location of the Görtler modes in the limit of large Görtler number and high wave number within the wake-dominated curved compressible mixing-layer systems based on three wake flow models. An analytic Gaussian wake profile is first used to model the behavior of the basic flow within the mixing layer at the trailing edge of the splitter plate. It is found that the wake has an amplification effect on the growth of the Görtler instability within the concavely curved or "unstably" curved compressible mixing layers. It is also found that within the convexly curved or "stably" curved compressible mixing layers wake modes can occur that behave differently to the "thermal modes," which were previously found within the plain curved compressible system by Owen et al. Another analytic composite model which has some practical applications is then used to predict the behavior of the modes within the systems. Solutions from a numerical wake flow model have been compared with the predictions based on the analytic wake flow models.

Gauging Centrifugal Instabilities in Compressible Free-Shear Layers via Nonlinear Boundary Region Equations

“…One way to increase the mixing is to insert a thin splitter plate into the mixing layer, which causes rapid variation of velocity in proximity to the solid boundary. Under these conditions, supersonic curved mixing layers can easily develop because of the curvature stemming from the drop in the pressure across the layer (Lin and Stephen [5]).…”

“…Sarkies and Otto [15] showed that centrifugal instabilities can develop in curved compressible shear layers and that there are several similarities with the incompressible counterpart, such as the effect of changing the curvature or the velocity difference across the shear layer. Lin and Stephen [5] investigated a curved compressible mixing layer focusing on the wake effect that was triggered by a splitter plate inserted into the stream. The linear Görtler mode was analyzed using the Gaussian model, the composite wake flow model, and the numerical model, and it was shown that the modes could exist within both the stable and the unstable curved compressible mixing layers (see also Lin [16]).…”