Effect of Mach number on transonic flow past a circular cylinder

The effect of Mach number on transonic flow past a circular cylinder is investigated numerically for the free-stream Mach number M∞ from 0.85 to 0.98 and the Reynolds number 2×10^5 based on the diameter of the cylinder. The work provides an insight into several salient features, including unsteady and quasi-steady flow state, formation of local supersonic zone, and evolution of turbulent shear layer. Results show that there exist two flow states dependent of a critical Mach number Mcr around 0.9. One is an unsteady flow state characterized by moving shock waves interacting with the turbulent flow in the near region of the cylinder for M∞〈Mcr, and the other is a quasi-steady flow state with nearly stationary shock waves formed in the near wake for M∞〉Mcrs, suppressing vortex shedding from the cylin- der. Some flow behaviors in the unsteady and quasi-steady flow states are revealed. From time evolu- tion of flow structures, local supersonic zones are identified in the wake and generated by two typical processes, i.e. reverse flow behind the cylinder and shed vortices in the near wake. The convective Mach number Mc of turbulent shear layers shed from the cylinder is identified nearly as Mc〈I in the unsteady flow regime and Mc〉I in the quasi-steady flow regime, resulting in different evolutions of the shear layers.