Interaction of an oblique shock wave with a pair of parallel vortices: Shock dynamics and mechanism of sound generation

The interaction between an oblique shock wave and a pair of parallel vortices is simulated systematically through solving the two-dimensional, unsteady compressible Navier-Stokes equations using a fifth order weighted essentially nonoscillatory finite difference scheme. The main purpose of this study is to characterize the flow structure and the mechanism of sound generation in the interaction between an oblique shock wave and a pair of vortices. We study two typical shock waves of Mach number Ms=1.2 and Ms=1.05, which correspond to two typical shock structures of Mach reflection and regular reflection, respectively, in the problem of shock-vortex interaction. The effects of the strength of the vortices and the geometry parameters are investigated. In addition, we have also considered both cases of passing and colliding vortex pairs. The interaction is classified into four types for the passing case and seven types for the colliding case according to different patterns of the shock structure. Our simulation shows that the sound field is the result of three mechanisms. The first mechanism is related directly to the interaction of the shock wave and the pair of vortices. The second mechanism is related to the coupling process of the vortex pair. The third mechanism is related to the interaction of the reflected shock waves and sound waves. The first mechanism is dominating if the vortex pair is weak. The combination of the first and the second mechanisms is dominating if the vortex pair is of moderate strength. If the vortex pair is strong, the acoustic field is also significantly affected by the interaction of the reflected shock waves and sound waves. © 2006 American Institute of Physics. DOI: 10.1063/1.2391806