MATHEMATICAL METHODS FOR VORTEX IDENTIFICATION WITH APPLICATION ON SHOCK WAVE VORTEX RING INTERACTION

Abstract

Vortices are seen everywhere in nature, from smoke rings to tornadoes. Vortical structures play an essential role in the turbulence dynamics such as turbulence generation, kinetic energy production and dissipation, enhancement of transport of mass, heat and momentum and so on. In this dissertation, we present several vortex identification methods and compare them by the visualization of the examples studied by direct numerical simulation for flows with different speeds. The comparisons show the Omega method is much close to give vortex a mathematical definition and better visualization for vortical structures. We apply our method on the Micro Vortex Generator (MVG) data to reveal the significant role of the transport of vortices in the shock wave boundary layer interaction. A wedge-shaped MVG is placed on a flat plate over which a turbulent boundary layer at Mach number 2.5 is developed. We investigate the interaction between an oblique shock and high-speed vortex rings in the MVG controlled ramp flow by using a high order implicit large eddy simulation with the fifth order bandwidth optimized WENO scheme. By tracking several typical vortex rings before, when and after they pass through the shock front, the quantitative changes of flow properties are studied in detail. The vortex ring propagation is found to be responsible for the shock motion, and thus cause the pulsation of the separation bubble. The shock ring interaction will provide an insight for the study of flow control.