Effects of the parameters of inner air cylinder on evolution of annular SF6 cylinder accelerated by a planar shock wave

Abstract

Based on the compressible Navier–Stokes equations combined with the fifth-order weighted essentially non-oscillatory scheme, this paper discusses the interaction of a planar shock wave with an annular SF6 cylinder. The influence of the position and radius of inner cylinder on the evolution of the annular cylinder is examined in detail. Numerical schlieren results clearly show the evolution of the inner and outer interfaces induced by the Richtmyer–Meshkov instability and reveal the evolution of complex shock wave structures as the incident planar shock interacts with the annular cylinder. Shock transformation from the free precursor refraction pattern to the free precursor von Neumann refraction pattern occurs when the inner cylinder position shifts forward, while the shock transformation from the twin von Neumann refraction pattern to the free precursor refraction pattern and the shock transformation from free precursor refraction pattern to the free precursor von Neumann refraction pattern occur when the radius of the inner cylinder gradually becomes larger. The generation and transportation of vorticity on the interfaces are also analyzed, revealing that changes to the inner cylinder play a significant role. The distribution and evolution of vorticity on the interfaces influence the formation of the primary vortex structure at later stages. Quantitative analysis of the circulation and enstrophy indicates that the smaller the inner radius, the larger the value of circulation and enstrophy at the later stage.