Numerical study of high speed separated flows

Abstract

Instability, flow separation and transition are essential aspects of high speed flows with shock-wave/boundary-layer interaction. Supersonic flows with jet injection, compression ramp and cavity, either individually or in combination, are numerically studied by solving directly the compressible Navier-Stokes equations to better understand the transition of high speed laminar boundary layer to turbulence and the influence of flow separation. A sonic jet injected into a Mach 6.69 crossflow is studied through both two-dimensional(2D) and three-dimensional (3D) simulations. Effects of the momentum flux ratio (Jp) are evaluated. A 3D global instability is observed with a critical value of Jp below but close to 0.1. The most unstable mode is found to have a spanwise wavelength of 8 times the incoming boundary layer displacement thickness. Streamwise vortices are observed at the saturated stage. Ramp flow is studied at Mach number 4.8 and Reynolds numbers of 6,843 and 3,422. The flow is stable in two dimensions. Simulations in 3D show that the flow is globally unstable at higher Reynolds number, while being stable at the lower Reynolds number, suggesting that a critical Reynolds number for instability exists between these two Reynolds numbers. The most unstable mode for the ramp flow has a spanwise wavelength of 12 times the incoming boundary layer displacement thickness. For the ramp flow with higher Reynolds number, breakdown to turbulence is observed, however this occurs downstream of the region where the global mode is active, suggesting that the global mode does not lead to transition directly but provides a disturbance seed which gives rise to transient growth, leading to streaks which subsequently breakdown to turbulence. Effects of an upstream cavity and a downstream sonic jet injection on the Mach 4.8 ramp flow are studied. It is found that the jet could greatly increase flow separation while the cavity has little effect. Similar configuration is studied for a supersonic ramp flow at Mach 5.3 with a Mach 3.6 jet injection for a practical application to rocket stage separation. Effects of cavity and jet on laminar boundary layer separation are firstly evaluated through a 2D parametric study. Ramp flow with turbulent boundary layer is simulated at greater detail in 3D. Then a slot jet is switched on to evaluate the laminar and turbulent inflow effect on the flow separation. A shorter separation bubble is observed, though the rates at which the separation point moves upstream are comparable for laminar and turbulent inflow.

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ORCID for N.D. Sandham: orcid.org/0000-0002-5107-0944

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