Hostname: page-component-77c89778f8-vpsfw Total loading time: 0 Render date: 2024-07-21T03:28:42.406Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Ding, Z., & Gracewski, S.M. (1996). The behaviour of a gas cavity impacted by a weak or strong shock wave. J. Fluid Mech. 309, 183–209.Google Scholar
Erez, L., Sadot, O., Levin, L.A., Shvarts, D., & Ben-Dor, G. (2000). Study of the membrane effect on turbulent mixing measurements in shock tubes. Shock Waves J. 10, 241.Google Scholar
Gracewski, S.M., Dahake, G., Ding, Z., Burns, S.J., & Everbach, E.C. (1993). Internal stress wave measurements in solid subjected to lithotripter pulses. J. Acoust. Soc. Am. 94, 652–661.Google Scholar
Klein, R.I., Mckfee, C.F., & Colella, P. (1994). On the hydrodynamic interaction of shock waves with interstellar clouds. I. Non-radiative shock in small clouds. Astrophys. J. 420, 213–236.Google Scholar
Ray, J., Samtaney, R., & Zabusky, N.J. (2000). Shock interactions with heavy gaseous elliptic cylinders: Two leeward-side shock competition modes and a heuristic model for interfacial circulation deposition at early times. Phys. Fluids 12, 707–716.Google Scholar
Saffman, P.G. (1970). The velocity of viscous vortex rings. Stud. Appl. Math. 49, 371–380.Google Scholar
Samtaney, R., & Zabusky, N.J. (1994). Circulation deposition on shock-accelerated planar and curved density-stratified interfaces: Models and scaling laws. J. Fluid Mech. 269, 45–78.Google Scholar
Zabusky, N.J., & Zeng, S.M. (1998). Shock cavity implosion morphologies and vortical projectile generation in axis-symmetric shock-spherical fast/slow bubble interactions. J. Fluid Mech. 362, 327–346.Google Scholar