Hostname: page-component-7479d7b7d-8zxtt Total loading time: 0 Render date: 2024-07-10T07:55:58.021Z Has data issue: false hasContentIssue false
  • English
  • Français

An experimental study of the high Mach number and high initial-amplitude effects on the evolution of the single-mode Richtmyer–Meshkov instability

Published online by Cambridge University Press:  03 March 2004

O. SADOT ,
A. RIKANATI ,
D. ORON ,
G. BEN-DOR  and
D. SHVARTS
O. SADOT
Affiliation:
Department of Physics, Nuclear Research Center–Negev, Beer-Sheva, Israel Department of Mechanical Engineering, Ben Gurion University of the Negev, Beer-Sheva, Israel
A. RIKANATI
Affiliation:
Department of Physics, Nuclear Research Center–Negev, Beer-Sheva, Israel Department of Physics, Ben Gurion University of the Negev, Beer-Sheva, Israel
D. ORON
Affiliation:
Department of Physics, Nuclear Research Center–Negev, Beer-Sheva, Israel Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot, Israel
G. BEN-DOR
Affiliation:
Department of Mechanical Engineering, Ben Gurion University of the Negev, Beer-Sheva, Israel
D. SHVARTS
Affiliation:
Department of Physics, Nuclear Research Center–Negev, Beer-Sheva, Israel Department of Mechanical Engineering, Ben Gurion University of the Negev, Beer-Sheva, Israel Department of Physics, Ben Gurion University of the Negev, Beer-Sheva, Israel
Get access Rights & Permissions [Opens in a new window]

Abstract

The present article describes an experimental study that is a part of an integrated theoretical (Rikanati et al.2003) and experiential investigation of the Richtmyer–Meshkov (RM) hydrodynamic instability that develops on a perturbed contact surface by a shock wave. The Mach number and the high initial-amplitude effects on the evolution of the single-mode shock-wave-induced instability were studied. To distinguish between the above-mentioned effects, two sets of shock-tube experiments were conducted: high initial amplitudes with a low-Mach incident shock and small amplitude initial conditions with a moderate-Mach incident shock. In the high-amplitude experiments a reduction of the initial velocity with respect to the linear prediction was measured. The results were compared to those predicted by a vorticity deposition model and to previous experiments with moderate and high Mach numbers done by others and good agreement was found. The result suggested that the high initial-amplitude effect is the dominant one rather than the high Mach number effect as suggested by others. In the small amplitude–moderate Mach numbers experiments, a reduction from the impulsive theory was noted at late stages. It is concluded that while high Mach number effect can dramatically change the behavior of the flow at all stages, the high initial-amplitude effect is of minor importance at the late stages. That result is supported by a two-dimensional numerical simulation.

Keywords

Richtmyer–Meshkov instabilityShock-tube experimentsTurbulent mixing
Type
Research Article
Information
Laser and Particle Beams , Volume 21 , Issue 3 , July 2003 , pp. 341 - 346
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

Aleshin, A.N., Lazareva, E.V., Chebotareva, E.I., Sergeev, S.V., & Zaytsev, S.G. (1997). Investigation of the Richtmyer–Meshkov instability induced by the incident and reflected shock wave. Proc. 6th Int. Workshop on Compressible Turbulent Mixing, pp. 1–6. France: IUSTI, Universite de Provence.
Aleshin, A.N., Lazareva, E.V., Zaitsev, S.G, Rozanov, V.B., Gamali, E.G., & Lebo, I.G. (1990). Linear, nonlinear and transient stages in development of Richtmyer–Meshkov instability. Sov. Phys. Dokl. 35, 159–161.Google Scholar
Alon, U., Hecht, J., Ofer, D., & Shvarts, D. (1995). Power laws and similarity of Rayleigh–Taylor and Richtmyer–Meshkov mixing fronts at all density ratios. Phys. Rev. Lett. 74, 534–537.Google Scholar
Dimonte, G., Frerking, C.E., Schneider, M., & Remington, B. (1996). Richtmyer–Meshkov instability with strong radiatively driven shocks. Phys. Plasmas 3, 614–630.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 10, 241–251.CrossRefGoogle Scholar
Hecht, J., Alon, U., & Shvarts, D. (1994). Potential flow models of Rayleigh–Taylor and Richtmyer–Meshkov bubble fronts. Phys. Fluids 6, 4019–4030.CrossRefGoogle Scholar
Holmes, R.L., Dimonte, G., Fryxell, B., Gittings, M.L., Grove, J.W., Schneider, M., Sharp, D.H., Velikovich, A.L., Weaver, R.P., & Zhang, Q. (1999). Richtmyer–Meshkov instability growth: Experiment, simulation and theory. J. Fluid Mech. 389, 55–79.CrossRefGoogle Scholar
Meshkov, E.E. (1969). Instability of the interface of two gases by a shock wave. Fluid Dyn. 4, 101–104.Google Scholar
Meyer, K.M., & Blewett, P.J. (1972). Numerical investigation of the stability of a shock-accelerated interface between two fluids. Phys. Fluids 15, 753–759.Google Scholar
Ofer, D., Hecht, J., Alon, U., Shvarts, D., McCrory, R.L., & Verdon, C.P. (1996) Phys. Plasmas 3, 3073.
Richtmyer, R.D. (1960). Taylor instability in shock acceleration of compressible fluids. Comm. Pure Appl. Math. 13, 297–319.CrossRefGoogle Scholar
Rikanati, A., Alon, U., & Shvarts, D. (1998). Vortex model for the nonlinear evolution of the multimode Richtmyer–Meshkov instability at low Atwood numbers. Phys. Rev. E. 58, 7410–7418.CrossRefGoogle Scholar
Rikanati, A., Oron, D., Sadot, O., & Shvarts, D. (2003). High-Mach number and high-initial amplitudes effects on the evolution of the single-mode Richtmyer–Meshkov instability. Phys. Rev. E. 67, 26307–26318.Google Scholar
Sadot, O., Erez, L., Alon, U., Oron, D., Levin, L.A., Erez, G., Ben-Dor, G., & Shvarts, D. (1998). Study of nonlinear evolution of single-mode and two-bubble interaction under Richtmyer–Meshkov instability. Phys. Rev. Lett. 80, 1654–1657.CrossRefGoogle Scholar
Zhang, Q., & Sohn, S.-I. (1997). Padé approximation to an interfacial fluid mixing problem. Appl. Maths Lett. 10, 121–127.CrossRefGoogle Scholar