Global instability of the interaction between an oblique shock and a laminar boundary layer

Abstract

This study investigates the oblique shock-wave/boundary-layer interaction with a Mach number of 2.15 and a Reynolds number of 1 105. Both global stability analysis and direct numerical simulation are used to reveal the global instability characteristics and three-dimensional details of the incident shock flow. The results of global stability analysis indicate that stationary global instability occurs when the shock angle exceeds the critical angle 31:8 . At a shock angle equal to 33 , an additional unstable mode appears, which is oscillatory at large wavelength and gradually dominant when the wavelength decreases. As the wavelength is further reduced, the mode and its conjugation evolve into two stationary modes with different growth rates. A global instability criterion for incident shock flow is established based on the triple deck theory, which determines the instability only through free-stream conditions and shock angles. A direct numerical simulation is performed for the 32 shock angle case. It is found that secondary separation occurs during the nonlinear growth, which is absent in the two-dimensional base flow. Moreover, the separated flow undergoes a secondary perturbation growth, during which the dominant spanwise wavelength is doubled and the flow structures change significantly. The flow oscillates around a quasi-steady state in the end, indicating that a stationary unstable mode can develop unsteadiness without external disturbances.