Skip to main content
SpringerLink
Log in

Mach reflection of a ZND detonation wave

  • Original Article
  • Published:
Shock Waves Aims and scope Submit manuscript

Abstract

The Mach reflection of a ZND detonation wave on a wedge is investigated numerically. A two-step chain-branching reaction model is used giving a thermally neutral induction zone followed by a chemical reaction zone for the detonation wave. The presence of a finite reaction zone thickness renders the Mach reflection process non-self-similar. The variation of the height of the Mach stem with distance of propagation does not correspond to a straight curve from the wedge apex as governed by self-similar three-shock theory. However, the present results indicate that in the near field around the wedge apex, and in the far field where the reaction zone thickness is small compared to the distance of travel of the Mach stem, the behavior appears to be self-similar. This corresponds to the so-called frozen and equilibrium limit pointed out by Hornung and Sanderman for strong discontinuity shock waves and by Shepherd et al. for cellular detonations. The critical wedge angle for the transition from regular to Mach reflection is found to correspond to the value determined by self-similar three-shock theory, but not by reactive three-shock theory for a discontinuous detonation front.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  1. Gvozdeva, L.G., Predvoditeleva, O.A.: Triple configurations of detonation waves in gases. Combust. Explo. Shock. 5, 451–461 (1969)

    Google Scholar 

  2. Ong, R.S.: On the interaction of a Chapman–Jouguet detonation wave with a wedge. PhD. Thesis, University of Michigan, Ann Arbor (1955)

  3. Guo, C., Zhang, D., Xie, W.: The Mach reflection of a detonation based on soot track measurements. Combust. Flame 127, 2051–2058 (2001)

    Article  Google Scholar 

  4. Li, H., Ben-Dor, G., Grönig, H.: Analytical study on the oblique reflection of detonation waves. AIAA J. 35(11), 1712–1720 (1997)

    Article  MATH  Google Scholar 

  5. Meltzer, J., Shepherd, J.E., Akbar, R., Sabet, A.: Mach reflection of detonation waves. In: Kuhl et al. (eds.) AIAA Progress in Astronautics and Aeronautics, pp. 78–94. AIAA, New York (1993)

  6. Yu, Q., Grönig, H.: Numerical simulation on the reflection of detonation waves. In: Proceedings of the 20th International Symposium on Shock Waves, pp. 1143–1148. Pasadena, USA (1995)

  7. Edwards, D.H., Walker, J.R., Nettleton, M.A.: On the propagation of detonation waves along wedges. Archivum Combustionis 4, 197–209 (1984)

    Google Scholar 

  8. Ohyagi, S., Obara, T., Nakata, F., Hoshi, S.: A numerical simulation of reflection processes of a detonation wave on a wedge. Shock Waves 10, 185–190 (2000)

    Article  MATH  Google Scholar 

  9. Gavrilenko, T.P., Nikolaev, Y.A., Tpchiyan, M.R.: Supercompressed detonation waves. Combust. Explos. Shock. 15(5), 659–692 (1980)

    Article  Google Scholar 

  10. Thomas, G.O., Williams, R.L.: Detonation interaction with wedges and bends. Shock Waves 11, 481–492 (2002)

    Article  Google Scholar 

  11. Ben-Dor, G.: Shock Wave Reflection Phenomena. Springer, New York (2007)

    MATH  Google Scholar 

  12. Hornung, H.: Regular and Mach reflection of shock waves. Annu. Rev. Fluid Mech. 18, 33–58 (1986)

    Article  Google Scholar 

  13. von Neumann, J.: Collected Works, vol. 6. Pergamon, New York (1963)

    Google Scholar 

  14. Vysk, N.D., Smirnov, N.N.: Mach reflection in a detonating gas with a stem in the form of a shock wave. Mosc. Univ. Mech. Bull. 41(4), 1–8 (1986)

    Google Scholar 

  15. Akbar, R.: Mach reflection of gaseous detonation. Ph.D. Thesis, Rensselaer Polytechnic Institute, Troy (1997)

  16. Ben-Dor, G., Dewey, J.M., Takayama, K.: The reflection of a plane shock over a double wedge. J. Fluid Mech. 176, 483–520 (1987)

    Article  Google Scholar 

  17. Ben-Dor, G., Dewey, J.M., McMillin, D.J., Takayama, K.: Experimental investigation of the asymptotically approached Mach reflection over the second surface in a double wedge reflection. Exp. Fluids 6, 429–434 (1988)

    Article  Google Scholar 

  18. Takayama, K., Ben-Dor, G.: Application of streak camera photography for the study of shock wave reflections over a double wedge. Exp. Fluids 6(1), 11–15 (1988)

    Article  Google Scholar 

  19. Lau-Chapdelaine, S.S.-M., Radulescu, M.I.: Non-uniqueness of solutions in asymptotically self-similar shock reflections. Shock Waves 23(6), 595–602 (2013)

    Article  Google Scholar 

  20. Sandeman, J., Leitch, A., Hornung, H.: The influence of relaxation on transition to Mach reflection in pseudosteady flow. Shock tubes and waves. In: Proceedings of the 12th International Symposium, pp. 298–307. Jerusalem (1979)

  21. Hornung, H.G., Oertel, H., Sandeman, R.J.: Transition to Mach reflexion of shock waves in steady and pseudosteady flow with and without relaxation. J. Fluid Mech. 90, 541–560 (1979)

    Article  Google Scholar 

  22. Shepherd, J.E., Schultz, E., Akbar, R.: Detonation diffraction. In: Proceedings of the 22th International Symposium on Shock Waves, pp. 18–23. Imperial College, London (1999)

  23. Mach, P., Radulescu, M.I.: Mach reflection bifurcations as a mechanism of cell multiplication in gaseous detonations. Proc. Combust. Inst. 33, 2279–2285 (2011)

    Article  Google Scholar 

  24. Radulescu, M.I., Papi, A., Quirk, J.J., Mach, P., Maxwell, B.M.: The origin of shock bifurcations in cellular detonations. In: 22nd International Colloquium on the Dynamics of Explosions and Reactive Systems. Minsk, Belarus (2009)

  25. Ziegler, J.L., Deiterding, R., Shepherd, J.E., Pullin, D.I.: An adaptive high-order hybrid scheme for compressive, viscous flows with detailed chemistry. J. Comput. Phys. 230(20), 7598–7630 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  26. Trotsyuk, A.V.: Numerical study of the reflection of detonation waves from a wedge. Combust. Explos. Shock. 35, 690–697 (1999)

    Article  Google Scholar 

  27. Ng, H.D., Radulescu, M.I., Higgins, A.J., Nikiforakis, N., Lee, J.H.S.: Numerical investigation of the instability for one-dimensional Chapman–Jouguet detonations with chain-branching kinetics. Combust. Theor. Model. 9(3), 385–401 (2005)

  28. Fickett, W., Davis, W.C.: Detonation. University of California Press, Berkeley (1979)

    Google Scholar 

  29. Jiang, G., Shu, C.-W.: Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126, 202–228 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  30. Xu, S., Aslam, T., Stewart, D.S.: High resolution numerical simulation of ideal and non-ideal compressible reacting flow with embedded internal boundaries. Combust. Theory Model. 1, 113–142 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  31. Strehlow, R.A.: Reactive gas Mach stems. Phys. Fluids 7, 908–910 (1964)

    Article  Google Scholar 

Download references

Acknowledgments

This work is supported by the National Science and Engineering Research Council of Canada (NSERC) under Grant A3347 and National Natural Science Foundation of China under Grant No.11390363.

Author information

Authors and Affiliations

  1. State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing, 100081, China

    J. Li & J. Ning

  2. Department of Mechanical Engineering, McGill University, Montreal, QC, H3A 2K6, Canada

    J. H. S. Lee

Authors
  1. J. Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Ning
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. H. S. Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. Li.

Additional information

Communicated by N. Smirnov.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, J., Ning, J. & Lee, J.H.S. Mach reflection of a ZND detonation wave. Shock Waves 25, 293–304 (2015). https://doi.org/10.1007/s00193-015-0562-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00193-015-0562-7

Keywords

Search

Navigation