The Stability of Imploding Detonations

  • Elaine S. Oran
  • C. Richard DeVore
Conference paper


The relative stability of cylindrically imploding shock and detonation waves has been examined using a two-dimensional numerical model. A sequence of increasingly realistic chemistry models is used to explore the effect of model selection on the results. Comparisons with the predictions of the Chester-Chisnell-Whitham (CCW) theory for the acceleration of nonreactive shocks and detonations show quantitative agreement between theory and simulation for symmetrically imploding waves. The influence of structural supports in laboratory experiments on the symmetry of imploding waves is simulated by placing an obstacle in the path of the converging flow. Changes in the convergence time, reductions of the peak pressure at implosion, and deviations from symmetry during the implosion induced by the obstacle are greater for detonations than for the corresponding nonreactive shocks, in qualitative agreement with the linearized CCW theory for shocks and Chapman-Jouguet detonations. These conclusions continue to hold when more sophisticated Zel’dovich-von Neumann-Doering or finite-rate chemistry models are assumed. For these models, a substantial amount of new asymmetrical, dynamical structure is evident in the reaction zone behind the leading shock. The results concur with and extend previous theoretical work suggesting that imploding detonation waves are relatively more unstable than nonreactive shocks.

Key words

Detonations Implosions Stability 


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  1. Ahlborn B, Huni JP (1969) Stability and space-time measurements of concentric detonations. AIAA Journal 7: 1191CrossRefADSGoogle Scholar
  2. Burks TL, Oran ES (1981) A computational study of the chemical kinetics of hydrogen combustion. Naval Research Laboratory Memorandum Report No. 4446, Naval Research Laboratory, Washington DCGoogle Scholar
  3. DeVore CR (1989) Flux-corrected transport algorithms for two-dimensional compressible magnetohydrodynamics. Naval Research Laboratory Memorandum Report No. 6544, Naval Research Laboratory, Washington DCGoogle Scholar
  4. DeVore CR, Oran ES (1992) The stability of imploding detonations in the geometrical shock dynamics (CCW) model. Phys. Fluids A 4: 835Google Scholar
  5. Fujiwara T, Sugimura T, Mizoguchi K, Taki S (1973) Stability of converging cylindrical detonation. J. Jpn. Soc. Aero. Space Sci. 21: 8Google Scholar
  6. Jones DA, Sichel M, Oran ES (1993) Reignition of detonations by reflected shocks (in preparation)Google Scholar
  7. Knystautas R, Lee JH (1971) Experiments on the stability of converging cylindrical detonations. Combust. Flame 16: 61Google Scholar
  8. Lee JH, Lee BHK (1965), Cylindrical imploding shock waves. Phys. Fluids 8: 2148Google Scholar
  9. Lefebvre M, Oran ES, Kailasanath K (1993) The influence of the heat capacity and diluent on detonation structure. Combust. Flame (in press)Google Scholar
  10. Oran ES, Boris JP (1987) Numerical Simulation of Reactive Flow. Elsevier, New York, Chapt. 4Google Scholar
  11. Oran ES, Jones DA, Sichel M (1992) Numerical simulations of detonation transmission. Proc. Roy. Soc. Lond. A 436: 267Google Scholar
  12. Oran ES, Boris JP, Jones DA, Sichel M (1993) Ignition in a complex Mach structure. Progr. Aeron. Astron. 153: 241Google Scholar
  13. Oran ES, DeVore CR (1994) The stability of imploding detonations: results of numerical simulations. Phys. Fluids (in press)Google Scholar
  14. Takayama K, Kleine H, Grönig H (1987) An experimental investigation of the stability of converging cylindrical shock waves in air. Exp. in Fluids 5: 315Google Scholar
  15. Terao K, Wagner HG (1991) Experimental study on spherically imploding detonation waves. Shock Waves 1: 27CrossRefADSGoogle Scholar
  16. Whitham GB (1974) Linear and Nonlinear Waves. Wiley, New York, Chapt. 8MATHGoogle Scholar
  17. Zel’dovich YaB (1959) Converging cylindrical detonation wave. Soviet Phys. JETP 36: 550Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Elaine S. Oran
    • 1
  • C. Richard DeVore
    • 1
  1. 1.Laboratory for Computational Physics and Fluid DynamicsNaval Research LaboratoryUSA

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