Interactions Of Shock Wave-multiple Vortices-sound Field, With POD Analysis

The shock and vortex are two fundamental subjects of fluid dynamics, the interac-tion between the two covers wide fields. It has been studied both analytically and ex-perimentally for many decades, not only because of their wide application in technology but also because of their fundamental significance to the scientific research community. When a plane shock wave meets a vortex, disturbance is generated, which propagates along the shock wave and results in its deformation. Behind the curved shock wave, the flow field is compressed and rarefied locally and forms acoustic waves. It is very impor-tant to understand the evolution process of the flow structure during the interaction, which will help us apprehend the mechanisms of interaction between a shock wave and turbulent flow.The interaction between an oblique shock wave and multiple vortices is simulat-ed systematically through solving the two-dimensional, unsteady compressible Navier-Stokes equations using a fifth order weighted essentially non-oscillatory finite difference scheme. The following research work has been done:The current situation of research of shock-vortex(vortices) interaction are inves-tigated in detail, the basic understandings of the interaction process and mechanisms of sound generation are summarized and based on these understandings the problems needed further study are proposed.The numerical method of the fifth order weighted essentially non-oscillatory finite difference scheme is studied and the parallel program for this paper is obtained. In addition, the sound wave generated by the interaction is very weak comparing with the pressure jump across the shock, a good resolution of the detailed flow structures requires a high-order, non-oscillatory scheme with enough grid, so the code is validated.The interactions between the vortices of Mach number Mv= 0.25 and the two typical shock wave of Mach number Ms= 1.2, Ms=1.05 respectively are simulated. Based on the analysis of the shock structure and the evolution of sound generation, the shock structures and the mechanisms of sound generation are characterized and understood for complex interactions further. The method of Snapshots-POD is applied to the sound pressure field, velocity field and vorticity field of the interactions.The results show that the interactions between a shock wave and multiple vortices lead to shock deformation, forming shock focusing and three triple points. And the disturbance effects of the deformed shock to the vortices decrease. There are two sources of sound generation below:One is the interaction between the shock and vortices, the other is the vortex coupling, while the latter plays an important role. The vortex coupling results in the formation of pairs of vortex dipoles, so that the shock-vortices interaction is like the interaction between a shock wave and different mach number of vortices in fact, which helps understanding the interaction between the shock wave and turbulent flow.