Evolution of subsonic and supersonic corner vortices in a supersonic cascade

Abstract

Numerical investigations on a supersonic cascade are conducted at the flow-through, high-backpressure, and low-speed modes to obtain a deeper understanding of the generation, development, and transformation of the subsonic and supersonic corner vortices. The geometry considered is the SAV21 supersonic cascade designed by the German Aerospace Centre operating under incoming Mach number of 2.4 and flow turning angle equal to 45 degrees. The corner vortex is generated by the impinging and glancing of shock waves on the boundary layer and drives the low-kinetic energy fluid moving spanwise. The cross-flow topology of the supersonic corner vortex follows Zhang's theory that considers flow with high Reynolds number and excludes the incorrect solutions generated by the expression of the velocity gradient along the vortex axis. The Hopf bifurcation position of the subsonic corner vortex can be accurately predicted by describing the velocity gradient along the vortex axis, while deviation occurs when using Zhang's theory. By observing the development process of corner vortices, the reason for the limitations in the range of application of Zhang's theory is analyzed. In general, the key factors for the evolution of the subsonic and supersonic corner vortices are the velocity gradient and pressure gradient along the vortex axis, respectively. The bifurcation processes of the corner vortex can be classified into four types. And the bifurcation principle can be summarized, the appearance of limit cycle does not immediately change the rotating direction of the vortex and the bifurcation process is gradual.