Flow pattern diagram of compressible non-equilibrium gas flow around a circular cylinder

Abstract

An investigation into the non-equilibrium gas flow around a circular cylinder within the Knudsen number (Kn) range of 0.001–1 and the free-stream Mach number (Ma) range of 0.01–6 is presented using the unstructured grid unified gas kinetic scheme. The primary objective is to examine the impact of Kn and Ma on flow patterns. The flow pattern diagram illustrating seven flow patterns in the Ma-Kn space is provided, including the transition boundary between bow shock-wave with laminar flow (BS+L) and bow shock-wave with vortex flow (BS+V). The relationships between Re-Kn and Ma-Re both follow the power function: y=eβxα, where α and β are constants. The study also provides a more precise critical curve of vortex shedding in subsonic inflow, the boundary of tailing shock-wave, and the boundary of vortex shedding in a transonic inflow. The flow pattern diagram indicates that the variation of flow separation with Kn is non-monotonic across the entire Ma range but is monotonic at Ma>1. In the subsonic inflow, the critical Re of flow separation (Rec) increases with Ma, while Rec initially increases and then decreases with Kn. The critical Ma at the turning point is about 0.72. In supersonic inflow, the critical Re associated with the onset of flow separation either increases or decreases with the increase in Ma or Kn. The critical Re of vortex shedding is non-monotonic with Kn. The critical Re of the trailing shock-wave decreases with both Kn and Ma. In the transonic inflow, the critical Re and critical Ma of vortex shedding decrease with Kn. As rarefaction increases, the type of flow patterns decreases. The flow pattern diagram provides a visual representation of the impact of rarefaction and compressibility effects on flow pattern transitions and assists in determining the applicable range of the drag coefficient model.