Effects of interface diffusion and shock strength on shock-accelerated SF6 cylinder

Abstract

The effects of interface diffusion and incident shock strength on the evolution of a shock-accelerated SF6 cylinder are numerically instigated. These two effects are manifested by measuring two essential issues that determine the material mixing of a shock–cylinder interaction (SCI), namely, the variations of the cylinder area and the material line length. Three interface types (with one sharp interface and two diffuse interfaces) and five incident shock strengths (Mach number ranges from 1.21 to 2.00) are examined. The numerical results provided in the present study show that both these effects play important roles in deforming the SF6 cylinders and the corresponding cylinder area and material line stretching. The cylinder area variation histories of the present results prove that the one-dimensional theoretical prediction of Giordano and Burtschell [“Richtmyer–Meshkov instability induced by shock–bubble interaction: Numerical and analytical studies with experimental validation,” Phys. Fluids 18, 036102 (2006)] applies not only to those sharp interface cylinders but also to these diffuse interface cylinders. The material line stretching histories prove that the exponential law of Yang et al. [“Applications of shock-induced mixing to supersonic combustion,” AIAA J. 31, 854 (1993)] applies well for diffuse interfaces but not for sharp interfaces. It is found that the exponential growth of the material line for the diffuse cylinders is dominated by the mass transport, and that the secondary instabilities only play their role in the primary vortex region. Finally, a predictive law of the development of material line length on the basis of circulation prediction theory is built. It is interesting that the use of the original circulation prediction model can be extended in such a way.