Direct numerical simulation of supersonic turbulent flows around a tandem expansion-compression corner

Abstract

The M=2.9 supersonic turbulent flows over a tandem expansion-compression corner configuration with a sharp deflection angle of 25° at three Reynolds numbers Re = 20000, 40000 and 80000 were studied by using direct numerical simulation (DNS). The flow statistics were validated against available experimental measurements and other numerical predictions. The flow structures and turbulence statistics were detailed visualized and analysed for the Re = 40000 case, especially in the interaction region where flow separation and reattachment occurred. It was found that during the expansion process the boundary layer exhibited a characteristic two-layer structure also discovered in previous experimental studies, and the turbulence evolved differently within these two layers. In the outer layer the turbulence was consistently suppressed along the ramp to a large extent, while in the inner layer it was suppressed only in a small region around the expansion corner, and the near-wall quasi-streamwise vortices were well preserved. Flow patterns near the reattachment line have shown the existence of the Görtler-type vortices, which would largely amplify turbulence fluctuations in the near-wall region, thus promoting the regeneration of wall turbulence that in turn contributed to the redevelopment of a downstream turbulent boundary layer. The Reynolds number effects and the characteristics of coherent structures were also discussed. With the increase of the Reynolds number, the separation bubble size decreased, but the pattern and the characteristic size of wall streamlines near the reattachment line were preserved.

Recovery of a supersonic turbulent boundary layer after an expansion corner

“…Fig.8b) A higher value of the shape factor implies that the expanded supersonic flow has a lower resistance flow separation. This partially explains why large separation occurred on the expanded wall in previous experimental results [22] . …”

“…Those structures grow from the inner layer of the boundary layer and lift up to the outer layer. In the 4° 22 expansion case, as shown in Fig.16a), the flow suddenly accelerates across the expansion corner and the velocity profile becomes fuller in the outer layer, which smears all the small structures from Temperature iso-surfaces of / TT  =2.1 are shown in Fig.17. The evolution illustrated in Fig.17 agrees well with the streamwise velocity field shown in Fig.15, which indicates that the temperature field is transported by the velocity field.…”

“…Many DNS databases of wall-bounded supersonic flows are attainable, including fundamental supersonic boundary layer [15][16][17][18] , supersonic boundary layer interaction with shock waves [19,20] , and supersonic boundary layer over a 4 compression ramp [21] etc. Recently Fang et al [22] calculated a supersonic flow at Ma=2.9 over an expansion-compression corner and found that the re-laminarized expansion flow is far from recovered before the separation region in the compression corner. This paper presents DNS studies of supersonic flows at Mach 2.7 over expansion corners with deflection angles of 0° (i.e.…”

Direct Numerical Simulation of Supersonic Turbulent Boundary Layer with Spanwise Wall Oscillation

“…A good agreement between the present DNS and other data in the linear sub-layer and log-law layer is obtained. The difference in the wake layer is attributed to the Reynolds number effects [35].…”

“…A good agreement between the present DNS and other data in the linear sub-layer and log-law layer is obtained. The difference in the wake layer is attributed to the Reynolds number effects [35]. number boundary layer experimental data [31,36], incompressible DNS [37,38], compressible DNS at transonic speed [39], and DNS of supersonic boundary layer at Mach number of 2.5 [33,34] as indicated in Figure 3.…”