Skip to main content
Log in

Cellular detonation diffraction in gas–particle mixtures

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

Abstract

Diffraction of cellular heterogeneous detonation out of a channel into open half-space in a mixture of aluminum particles and oxygen is investigated numerically. The flow is found to be very similar to gas detonation diffraction. The detonation weakening behind the step results in combustion front deceleration and decoupling from the leading shock wave. Subsequent re-initiation takes place in a transverse wave. New transverse waves are generated along the expanding front. The computations that were performed show that the critical number of cells is several times less than that for gases. This is confirmed by theoretical estimates based upon the Mitrofanov–Soloukhin approach.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Vasil’ev A.A., Mitrofanov V.V., Topchian M.E.: Detonation waves in gases. Combust. Explos. Shock Waves 23, 605–623 (1987)

    Article  Google Scholar 

  2. Nettleton M.A.: Recent work on gaseous detonations. Shock Waves 12, 3–12 (2002). doi:10.1007/s001930200134

    Article  MATH  Google Scholar 

  3. Bazhenova T.V., Golub V.V.: Use of gas detonation in a controlled frequency mode (review). Combust. Explos. Shock Waves 39, 365–381 (2003)

    Article  Google Scholar 

  4. Mitrofanov V.V., Soloukhin R.I.: The diffraction of multi-front detonation waves. Sov. Phys. Doklady 9, 1055–1058 (1965)

    Google Scholar 

  5. Vasil’ev A.A.: Critical conditions for initiation of multifront cylindrical detonation. Combust. Explos. Shock Waves 34, 220–225 (1998)

    Article  Google Scholar 

  6. Jones D.A., Oran E.S., Sichel M.: Reignition of detonation by reflected shocks. Shock Waves 5, 47–57 (1995)

    Article  Google Scholar 

  7. Jones D.A., Kemister G., Oran E.S., Sichel M.: The influence of cellular structure on detonation transmission. Shock Waves 6, 119–129 (1996)

    Article  Google Scholar 

  8. Pantow E.G., Fischer M., Kratzel Th.: Decoupling and recoupling of detonation waves associated with sudden expansion. Shock Waves 6, 131–137 (1996)

    Article  Google Scholar 

  9. Jones D.A., Kemister G., Tonello N.A., Oran E.S., Sichel M.: Numerical simulation of detonation reignition in H2 − O2 mixtures in area expansions. Shock Waves 10, 33–41 (2000)

    Article  MATH  Google Scholar 

  10. Liu Y.K., Lee J.H., Knystautas R.: Effect of geometry on the transition of detonation through an orifice. Combust. Flame 56, 215–225 (1984). doi:10.1016/0010-2180(84)90038-5

    Article  Google Scholar 

  11. Sochet I., Lamy T., Brossard J., Vaglio C., Cayzac R.: Critical tube diameter for detonation transmission and critical initiation energy of spherical detonation. Shock Waves 9, 113–123 (1999)

    Article  Google Scholar 

  12. Pintgen F., Shepherd J.E.: Detonation diffraction in gases. Combust. Flame 156, 665–677 (2009). doi:10.1016/j.combustflame.2008.09.008

    Article  Google Scholar 

  13. Arienty M., Shepherd J.E.: A numerical study of detonation diffraction. J. Fluid Mech. 529, 117–146 (2005). doi:10.1017/S0022112005003319

    Article  MathSciNet  Google Scholar 

  14. Roy G.D., Frolov S.V., Borisov A.A., Netzler D.W.: Pulse detonation propulsion: challenges, current status, and future perspective. Prog. Energy Combust. Sci. 30, 545–672 (2004). doi:10.1016/j.pecs.2004.05.001

    Article  Google Scholar 

  15. Weng Ch., Gore J.P.: A numerical study of two- and three-dimensional detonation dynamics of pulse detonation engine by the CE/SE method. Acta Mech. Sin. 21, 32–39 (2005). doi:10.1007/s10409-004-0004-8

    Article  Google Scholar 

  16. Canteins G., Franzetti F., Zoclonska E., Khasainov B., Zitoin R., Desbordes D.: Experimental and numerical investigations on PDE performance augmentation by means an ejector. Shock Waves 15, 103–112 (2005). doi:10.1007/s00193-006-0006-5

    Article  Google Scholar 

  17. Levin V., Markov V., Zhuravskaya T., Osinkin S.: Initiation and propagation of detonation in channels of complex shape. In: Roy, G.D., Frolov, S.M. (eds) Pulse and Continuous Detonation Propulsion., pp. 97–106. Torus Press, Moscow (2006)

    Google Scholar 

  18. Levin, V., Markov, V., Zhuravskaya, T., Osinkin, S.: Propagation of cellular detonation in the plane channel with obstacles. In: Hannemann, K., Seiler, F. (eds.) Shock Waves, vol. 1. 26th International Symposium on Shock Waves, vol. 1, Part IV, pp. 347–351. Springer, Berlin Heidelberg (2009). doi:10.1007/978-3-540-85168-4_55

  19. Sorin R., Ratiba Z., Khasainov B., Desbordes D.: Detonation diffraction through different geometries. Shock Waves 19, 11–23 (2009). doi:10.1007/s00193-008-0179-1

    Article  Google Scholar 

  20. Kutushev A.G., Shorohova L.V.: Numerical investigation of burning and detonation of monofuel mixtures suspensions in sharply extended tubes. In: Roy, G.D., Frolov, S.M., Santoro, R.J., Tsyganov, S.A. (eds) Advances in Confined Detonations, pp. 161–166. Torus Press Ltd., Moscow (2002)

    Google Scholar 

  21. Kutushev A.G., Shorokhova L.V.: Numerical investigation of the processes of combustion and detonation of air-fuel mixtures of unitary fuel in abruptly expanding pipes. Chem. Phys. 22(8), 94–99 (2003)

    Google Scholar 

  22. Fedorov A.V., Kratova Yu.V., Khmel T.A.: Shock and detonation wave diffraction at a sudden expansion in gas–particle Mixtures. Shock Waves 18, 281–290 (2008). doi:10.1007/s00193-008-0162-x

    Article  MATH  Google Scholar 

  23. Kratova Yu.V., Fedorov A.V., Khmel T.A.: Diffraction of a plane detonation wave on a back-facing step in a gas suspension. Combust. Explos. Shock Waves 45(5), 591–602 (2009)

    Article  Google Scholar 

  24. Fedorov, A.V., Khmel, T.A., Kratova, Yu.V.: Cellular detonation formation and propagation in polydisperse mixtures. In: Proceedings of 7th international symposium on hazards, prevention, and mitigation of industrial explosions, vol. II, p. 238 (2008)

  25. Fedorov A.V.: Structure of heterogeneous detonation of aluminum particles dispersed in oxygen. Combust. Explos. Shock Waves. 28(3), 277–286 (1992). doi:10.1007/BF00749644

    Article  Google Scholar 

  26. Fedorov A.V., Khmel T.A., Fomin V.M.: Non-equilibrium model of steady detonations in aluminum particles-oxygen suspensions. Shock Waves 9, 313–318 (1999). doi:10.1007/s001930050191

    Article  MATH  Google Scholar 

  27. Strauss W.A.: Investigation of the detonation of aluminum powder-oxygen mixtures. AIAA J. 6(12), 1753–1761 (1968). doi:10.2514/3.4855

    Article  Google Scholar 

  28. Fedorov A.V., Khmel T.A.: Numerical simulation of formation of cellular heterogeneous detonation of aluminum particles in oxygen. Combust. Expl. Shock Waves 41(4), 435–448 (2005). doi:10.1007/s10573-005-0054-7

    Article  Google Scholar 

  29. Ingignoli, W., Veyssiere, B., Khasainov, B.A.: Study of detonation initiation in unconfined aluminum dust clouds. In: Roy, G. et al. (eds.) Gaseous and Heterogeneous Detonations, pp. 337–350. ENAS-Publishers, Moscow (1999)

  30. Zhang F., Gronig H., Van de Ven A.: DDT and detonation waves in dust-air mixtures. Shock Waves 11, 53–71 (2001)

    Article  Google Scholar 

  31. Benkiewicz K., Hayashi A.K.: Two-dimensional numerical simulations of multi-headed detonations in oxygen-aluminum mixtures using an adaptive mesh refinement. Shock Waves 13, 385–402 (2003)

    Article  Google Scholar 

  32. Barthel H.O.: Predicted spacings in hydrogen–oxygen–argon detonations. Phys. Fluids 17(8), 1547–1553 (1974)

    Article  Google Scholar 

  33. Khmel T.A.: Numerical simulation of two-dimensional detonation flows in reactive particle gas suspensions. Matematicheskoe modelirovanie (in Russian) 16(6), 73–77 (2004)

    MATH  Google Scholar 

  34. Fedorov A.V., Khmel T.A.: Numerical technologies for investigations of heterogeneous detonations of gas particle suspensions. Matematicheskoe modelirovanie (in Russian) 18(8), 49–63 (2006)

    Google Scholar 

  35. Fedorov A.V., Khmel T.A.: Cellular detonations in bi-dispersed gas–particle mixtures. Shock Waves 18(4), 277–280 (2008)

    Article  MATH  Google Scholar 

  36. Fedorov A.V., Kharlamova Yu.V.: Ignition of an aluminum particle. Combust. Explos. Shock Waves 39(5), 544–547 (2003). doi:10.1023/A:1026109801863

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to T. A. Khmel.

Additional information

Communicated by L. Bauwens.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fedorov, A.V., Khmel, T.A. & Kratova, Y.V. Cellular detonation diffraction in gas–particle mixtures. Shock Waves 20, 509–519 (2010). https://doi.org/10.1007/s00193-010-0290-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00193-010-0290-y

Keywords

Navigation