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Scaling in the shock–bubble interaction

Published online by Cambridge University Press:  03 March 2004

K. LEVY ,
O. SADOT ,
A. RIKANATI ,
D. KARTOON ,
Y. SREBRO ,
A. YOSEF-HAI ,
G. BEN-DOR  and
D. SHVARTS
K. LEVY
Affiliation:
Department of Physics, Ben-Gurion University, Beer-Sheva, Israel Department of Physics, Nuclear Research Center–Negev, Beer-Sheva, Israel
O. SADOT
Affiliation:
Department of Physics, Nuclear Research Center–Negev, Beer-Sheva, Israel Department of Mechanical Engineering, Ben-Gurion University, Beer-Sheva, Israel
A. RIKANATI
Affiliation:
Department of Physics, Ben-Gurion University, Beer-Sheva, Israel Department of Physics, Nuclear Research Center–Negev, Beer-Sheva, Israel
D. KARTOON
Affiliation:
Department of Physics, Ben-Gurion University, Beer-Sheva, Israel Department of Physics, Nuclear Research Center–Negev, Beer-Sheva, Israel
Y. SREBRO
Affiliation:
Department of Physics, Ben-Gurion University, Beer-Sheva, Israel Department of Physics, Nuclear Research Center–Negev, Beer-Sheva, Israel
A. YOSEF-HAI
Affiliation:
Department of Physics, Nuclear Research Center–Negev, Beer-Sheva, Israel Department of Mechanical Engineering, Ben-Gurion University, Beer-Sheva, Israel
G. BEN-DOR
Affiliation:
Department of Mechanical Engineering, Ben-Gurion University, Beer-Sheva, Israel
D. SHVARTS
Affiliation:
Department of Physics, Ben-Gurion University, Beer-Sheva, Israel Department of Physics, Nuclear Research Center–Negev, Beer-Sheva, Israel
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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 sound cs and the initial bubble radius R. 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 number M is 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 for M < 2. Above M ≅ 2, the topology of the bubble changes due to a competition between the upstream surface of the bubble and the undisturbed shock wave.

Keywords

BubblesCirculationShock wavesVortex ringVorticity deposition model
Type
Research Article
Information
Laser and Particle Beams , Volume 21 , Issue 3 , July 2003 , pp. 335 - 339
Copyright
© 2003 Cambridge University Press

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References

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