Journal of Fusion Energy

, Volume 14, Issue 4, pp 389–392 | Cite as

Stability of imploding spherical shock waves

  • H. B. Chen
  • L. Zhang
  • E. Panarella

Abstract

The stability of spherically imploding shock waves is systematically investigated in this letter. The basic state is Guderley and Landau's unsteady self-similar solution of the implosion of a spherical shock wave. The stability analysis is conducted by combining Chandrasekhar's approach to the stability of a viscous liquid drop with Zel'dovich's approach to the stability of spherical flames. The time-dependent amplitudes of the perturbations are obtained analytically by using perturbation method. The relative amplification and decay of the amplitudes of perturbations decides the stability/instability of the spherical imploding shock waves. It is found that the growth rate of perturbations is not in exponential form and near the collapse phase of the shocks, the spherically imploding shock waves are relatively stable.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ya. B. Zel'dovich and Yu. P. Raizer (1966).Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena (Academic Press), p. 794.Google Scholar
  2. 2.
    L. D. Landau and E. M. Lifshitz (1987).Fluid Mechanics, Second Edition, Course of Theoretical Physics, Vol. 6 (Pergamon Press).Google Scholar
  3. 3.
    H. B. Chen, J. Chen, B. Hilko, and E. Panarella (1994). Numerical comparison between ICF and ICF-spherical pinch.J. Fusion Energy,13, 45.Google Scholar
  4. 4.
    H. B. Chen, B. Hilko, and E. Panarella (1994). The Rayleigh-Taylor instability in the spherical pinch.J. Fusion Energy 13, 275.Google Scholar
  5. 5.
    I. B. Bernstein and D. L. Book. Rayleigh-Taylor instability of a self-similar spherical expansion.Astrophys. J.,225, 633.Google Scholar
  6. 6.
    G. B. Whitham (1974).Linear and Nonlinear Waves (Wiley, New York).Google Scholar
  7. 7.
    J. H. Gardner, D. L. Book, and I. B. Bernstein (1982). Stability of imploding shocks in the CCW approximation.J. Fluid Mechanics,114.Google Scholar
  8. 8.
    D. L. Book (1990). Linearized geometrical-dynamics treatment of the stability of converging shocks.Phys. Fluids A,2(4).Google Scholar
  9. 9.
    E. S. Oran, and C. R. DeVore (1994). The stability of imploding detonations: Results of numerical simulations.Phys. Fluids,6(1).Google Scholar
  10. 10.
    K. Takayama, H. Kleine, and H. Grönig (1987). An experimental investigation of the stability of converging cylindrical shock waves in air.Exp. Fluids,5, 315.Google Scholar
  11. 11.
    K. Terao and H. G. Wagner (1991). Experimental study on spherically imploding detonation waves.Shock Waves,1, 27.Google Scholar
  12. 12.
    S. Chandrasekhar (1961).Hydrodynamic and Hydromagnetic Stability (Oxford University Press).Google Scholar
  13. 13.
    Ya. B. Zel'dovich, G. I. Barenblatt, V. B. Librovich and G. M. Makhviladze (1985).The Mathematical Theory of Combustion and Explosions (Plenum Publishing Corporation).Google Scholar
  14. 14.
    E. Panarella, ed. (1994).Proceedings of 1st International Symposium on Evaluation of Current Trends in Fusion Research (Washington, D.C.).Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • H. B. Chen
    • 1
  • L. Zhang
    • 1
  • E. Panarella
    • 2
  1. 1.Advanced Laser and Fusion Technology, Inc.HullCanada
  2. 2.Department of Electrical and Computer EngineeringUniversity of TennesseeKnoxville

Personalised recommendations