Scaling in the shock–bubble interaction

Abstract

The passage of a shock wave through a spherical bubble results in the formation of a vortex ring. In the present study, simple dimensional analysis is used to show that the circulation is linearly dependent on the surrounding material speed of soundcsand the initial bubble radiusR. In addition, it is shown that the velocities characterizing the flow field are linearly dependent on the speed of sound, and are independent of the initial bubble radius. The dependence of the circulation on the shock wave Mach numberMis derived by Samtaney and Zabusky (1994) as (1 + 1/M+ 2/M2) (M− 1). Experiments were performed for slow/fast (air-helium) and fast/slow (air-SF6) interactions. Full numerical simulations were conducted resulting in good agreement. From the results, it is seen that in both cases, according to the proposed scaling, the vortex ring velocity is bubble radius independent. The numerical results for the slow/fast interaction show that the proposed Mach scaling is valid forM< 2. AboveM≅ 2, the topology of the bubble changes due to a competition between the upstream surface of the bubble and the undisturbed shock wave.

Experimental investigation of the shock wave interaction with a spherical gas inhomogeneity

“…We know that a spherical inhomogeneity submitted to a shock wave passage distorts differently according to the shock wave propagation direction across the density gradient as experimentally shown by Haas and Sturtevant, 4 Layes et al, 12 and Levy et al 13 After the shock wave passage, two directions are significant for the bubble deformation. The a͒ Electronic mail: Lazhar.Houas@polytech.univ-mrs.fr first one is parallel to the shock wave propagation direction while the second is perpendicular to it.…”

Experimental Investigation of Primary and Secondary Features in High-Mach-Number Shock-Bubble Interaction

“…024502-2 Figure 4 shows the presence of secondary and tertiary counterrotating vortex rings in the flow field, which are absent in the case of low Mach number experiments [4,5]. These features are generated by complex shock refraction and reflection phenomena arising at high Mach numbers which are visible in simulations reported by Levy et al [14]. A very small portion of helium appears to be stripped off from the top part of the PVR, which is entrained by the secondary vortex ring (SVR).…”

Richtmyer-Meshkov instability induced by shock-bubble interaction: Numerical and analytical studies with experimental validation

“…15 Zoldi 9 has also proposed a numerical study of her own experiments. The shock-bubble interaction was also studied by Zabusky and Zeng 16 and Levy et al 17 In these references, the numerical and experimental studies are strongly dependent. After validating numerical models to the experiments, the access to all physical variables with computational results is helpful to better describe this instability.…”