Numerical investigation of the interaction between a converging shock wave and an offset cylindrical bubble containing different gases

Abstract

A numerical study investigating the interaction process between a converging shock wave and a gas bubble placed at an offset location is presented. As a first step, for proofing the reliability of the used numerical scheme, a simulation of relevant available experimental findings of Hosseini and Takayama [“Richtmyer–Meshkov instability induced by cylindrical shock wave loading of cylindrical gaseous inhomogeneities,” AIAA Paper No. 2000-2464, 2000] and Hosseini and Takayama [“Study of a converging shock wave interaction with a gaseous interfaces in an eccentric arrangement,” in Japanese Symposium on Shock Waves, 2000] is conducted; the tested gases were helium (He) and sulfur hexafluoride (SF6). The converging shock wave had a Mach number of 1.18 prior to its impact on the 50 mm diameter gas bubble. Achieving good agreement with the experimental findings ensures the reliability of the applied numerical scheme. After the converging shock wave impacted the gas bubble, different shock waves are created. These shock waves propagate differently than those observed in the case of planar shock wave impacting a cylindrical gas bubble or that of a converging shock wave where the gas bubble is located at the center. Furthermore, once the converging shock wave converged, a diverging shock wave expands and again impacts the remaining gas bubble, thus creating more complex shock wave patterns. The gas contained inside the bubble has an effect on the location of the converging shock wave focus point. In the case of the heavy gas SF6, the focus point is near the center of the converging shock wave, but in the case of light gas He, it is offset from the converging shock wave focus point and outside of the initial location of the He bubble. The new results from the current numerical simulation include more detailed results for both bubbles, which were not reported in Hosseini and Takayama [“Richtmyer–Meshkov instability induced by cylindrical shock wave loading of cylindrical gaseous inhomogeneities,” AIAA Paper No. 2000-2464, 2000] and Hosseini and Takayama [“Study of a converging shock wave interaction with a gaseous interfaces in an eccentric arrangement,” in Japanese Symposium on Shock Waves, 2000]. In addition, a shock wave focusing of the transmitted shock wave inside the SF6 bubble is observed. This later creates a secondary diverging shock wave. Higher pressure is achieved in the SF6 case.