The Mach 2.9 supersonic turbulent flow over an expansion-compression corner with a sharp deflection angle of 25° at three Reynolds numbers Re_δ=20000, Re_δ=40000 and Re_δ=80000 were studied by using a recently developed direct numerical simulation (DNS) code with the low-dissipation monotonicity-preserving (MP-LD) scheme. The turbulence statistics were validated against available experimental measurements and other numerical data for both equilibrium boundary layer and interaction corner regions, as seen in Fig. 1.
Detailed turbulent flow structures and statistics were then described and analyzed for the Re_δ=40000 case, especially in the interaction region where flow separation and reattachment occur. It was found that in the expansion ramp region, turbulent boundary layer exhibited a unique two-layer structure with different flow motions evolved within these two layers. Along two streamlines S1 and S2 in Fig. 2, turbulence kinetic energy (TKE) develops in different manner. In the outer layer, flow turbulence level has been consistently suppressed along the step, while in the inner layer it has been suppressed only in a small region around the expansion corner and the near-wall quasi-streamwise vortices are well-preserved in this region. Flow visualization of turbulence coherent structures in the ramp region is shown in Fig. 3, in which the evolution of the two-layer turbulence structures along the ramp can be clearly identified. The turbulence coherent structures from the undisturbed outer part of boundary layer are gradually damped with the disappearance of their coherence structures during the expansion process. In the inner layer, however, the quasi-streamwise structures are preserved all the way along the ramp. Therefore, downstream the separation line, large-scale quasi-streamwise vortices can be seen very clearly.
The existence of large-scale Görtler vortices observed in experiments can be proved by the visualization of turbulence coherent structures in Fig. 4, where some tube-like structures with a characteristic spanwise size of δ_ref can be identified. The Görtler vortices are responsible for the rapid increase of skin friction and high level of wall heat flux near the reattachment line. According to the analysis, the connection between the origin of the Görtler vortices and the well preserved large-scale streamwise vortices can be established, although the relation between the two factors will still be the subject for further investigation.