Skip to main content
Log in

Effect of stochasticity of the spatial distribution of particles in a gas suspension on combustion front propagation

  • Published:
Combustion, Explosion, and Shock Waves Aims and scope

Abstract

A statistical model of combustion of a gas suspension of solid particles is proposed. The model takes into account the influence of the stochastic spatial distribution of particles on the combustion front velocity. The Bose-Einstein distribution in the presentation of occupation numbers is used as the basic mathematical apparatus of the model. The model offers an explanation for the effect observed in some experiments, which is associated with the shift of the combustion front velocity peak to the range of fuel-rich gas suspensions. The limits of applicability of the proposed statistical model to real gas suspensions are estimated.

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. A. P. Il’in and A. A. Gromov, Combustion of Aluminum and Boron in a Superfine state (Tomsk State University, Tomsk, 2002) [in Russian].

    Google Scholar 

  2. Yu. A. Gosteev and A. V. Fedorov, “Ignition of the Gas-Coal Dust Mixture. Pointwise approximation,” Fiz. Goreniya Vzryva 37(6), 36–45 (2001) [Combust., Expl., Shock Waves 37 (6), 646–654 (2001)].

    Google Scholar 

  3. H. Kobayashi, N. Ono, Y. Okuyama, and T. Niioka, “Flame Propagation Experiment of PMMA Particle Cloud in a Microgravity Environment,” Proc. Combust. Inst. 25, 1693–1699 (1994).

    Article  Google Scholar 

  4. E. P. Bocanegra, V. Sarou-Kanian, D. Davidenko, C. Chauveau, and I. Gökalp, “Studies on the Burning of Micro- and Nano-Aluminum Particle Clouds in Air,” Prog. Propuls. Phys. 1, 47–62 (2009).

    Article  Google Scholar 

  5. N. D. Ageev, S. V. Goroshin, A. N. Zolotko, N. I. Poletaev, and Yu. L. Shoshin, “Velocity of the Steady Flame in Gas Suspensions of Aluminum,” in Combustion of Heterogeneous and Gas Systems, Proc. IX All-Union Symp. on Combustion and Explosion, Chernogolovka, November 19–24, 1989.

  6. Ya. B. Zel’dovich, G. I. Barenblatt, V. B. Librovich, and G. M. Makhviladze, Mathematical Theory of Combustion and Explosion (Nauka, Moscow, 1980; Plenum, New York, 1985).

    Google Scholar 

  7. K. Seshadri, A. L. Berlad, and V. Tangirala, “The Structure of Premixed Particle-Cloud Flame,” Combust. Flame 89, 333–342 (1992).

    Article  Google Scholar 

  8. V. R. Kuznetsov and V. A. Sabel’nikov, Turbulence and Combustion (Nauka, Moscow, 1986) [in Russian].

    Google Scholar 

  9. P. S. Grinchuk and O. S. Rabinovich, “Percolation Phase Transition in Combustion of Heterogeneous Mixtures,” Fiz. Goreniya Vzryva 40(4), 41–53 (2004) [Combust., Expl., Shock Waves 40 (4), 408–418 (2004)].

    Google Scholar 

  10. P. S. Grinchuk and O. S. Rabinovich, “Effect of Random Internal Structure on Combustion of Binary Powder Mixtures,” Phys. Rev. E 71(2), Art. No. 026116 (2005).

    Google Scholar 

  11. P. S. Grinchuk, O. S. Rabinovich, A. S. Rogachev, and N. A. Kochetov, “Fast and Slow Modes of Combustion Front Propagation in Heterogeneous Systems,” Pis’ma Zh. Eksp. Teor. Fiz. 84(1), 13–17 (2006).

    Google Scholar 

  12. S. A. Rashkovskii, “Statistical Simulation of Aluminum Agglomeration during Combustion of Heterogeneous Condensed Systems,” Fiz. Goreniya Vzryva 41(2), 62–74 (2005) [Combust., Expl., Shock Waves 41 (2), 174–184 (2005)].

    Google Scholar 

  13. V. G. Shevchuk, E. N. Kondrat’ev, A. N. Zolotko, and S. V. Goroshin, “Effect of the Structure of a Gas Suspension on the Process of Flame Propagation,” Fiz. Goreniya Vzryva 15(6), 41–45 (1979) [Combust., Expl., Shock Waves 15 (6), 723–726 (1979)].

    Google Scholar 

  14. A. N. Zolotko, Ya. I. Vovchuk, V. G. Shevchuk, and N. I. Poletaev, “Ignition and Combustion of Dust-Gas Suspensions,” Fiz. Goreniya Vzryva 41(6), 3–14 (2005) [Combust., Expl., Shock Waves 41 (6), 611–621 (2005)].

    Google Scholar 

  15. D. A. Yagodnikov, A. V. Voronetskii, A. V. Sukhov, and D. G. Pavlov, “Propagation of the Laminar Flame in Mono- and Polydisperse Suspensions in Air,” Khim. Fiz. 9(12), 1611–1614 (1990).

    Google Scholar 

  16. D. A. Yagodnikov, “Statistical Model of Flame-Front Propagation in a Boron-Air Mixture,” Fiz. Goreniya Vzryva 32(6), 29–46 (1996) [Combust., Expl., Shock Waves 32 (6), 623–636 (1996)].

    Google Scholar 

  17. A. R. Kerstein and C. K. Law, “Percolation in Combusting Sprays I: Transition from Cluster Combustion to Percolate Combustion in Non-Premixed Sprays,” Proc. Combust. Inst. 19(1), 961–969 (1982).

    Article  Google Scholar 

  18. A. Umemura and S. Takamori, “Percolation Theory for Flame Propagation in Non- or Less-Volatile Fuel Spray: A Conceptual Analysis to Group Combustion Excitation Mechanism,” Combust. Flame 141(4), 336–349 (2005).

    Article  Google Scholar 

  19. R. Samson, D. Bedeaux, M. J. Saxton, and J. M. Deutch, “A Simple Model of Fuel Spray Burning I: Random Sprays,” Combust. Flame 31, 215–221 (1978).

    Article  Google Scholar 

  20. F. D. Tang, A. J. Higgins, and S. Goroshin, “Effect of Discreteness on Heterogeneous Flames: Propagation Limits in Regular and Random Particle Arrays,” Combust. Theory Model. 13(2), 2319–2341 (2009).

    Article  Google Scholar 

  21. D. Stauffer and A. Aharony, Introduction to Percolation Theory (Taylor&Francis, London, 1995).

    MATH  Google Scholar 

  22. J. C. Yang, A. Hamins, and M. K. Donnelly, “Combustion of a Polymer (PMMA) Sphere in Microgravity,” Report No. 6331 (National Inst. of Standards and Technology, May, 1999); http://fire.nist.gov/bfrlpubs/fire99/art044.html.

    Google Scholar 

  23. Tables of Physical Quantities: Handbook, Ed. by I. K. Kikoin (Atomizdat, Moscow, 1976) [in Russian].

    Google Scholar 

  24. I. A. Semenov and B. V. Matsevich, “Dynamic Features of Combustion of Polydisperse Aluminum Powders in a Gas,” Fiz. Goreniya Vzryva 41(4), 78–83 (2005) [Combust., Expl., Shock Waves 41 (4), 430–434 (2005)].

    Google Scholar 

  25. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 5: Statistical Physics (Nauka, Moscow, 1987; Pergamon Press, 1980).

    Google Scholar 

  26. P. S. Grinchuk, “Bose-Einstein Statistics for a Microcanonical Ensemble in the Presentation of Occupation Numbers,” Dokl. Nats. Akad. Nauk Belarusi 56(6), 37–43 (2012); http://csl.bas-net.by/xfile/doklad/2012/6/cg40r3.pdf.

    Google Scholar 

  27. G. E. Andrews, The Theory of Partitions (Encyclopedia of Mathematics and Its Application, No. 2 (Cambridge University Press, 1984).

    Google Scholar 

  28. Polymer Flammability, Office of Aviation Research, Washington, U.S. Tech. Report (May 2005); http://www.fire.tc.faa.gov/pdf/05-14.pdf.

  29. L. V. Boichuk, V. G. Shevchuk, and A. I. Shvets, “Flame Propagation in Two-Component Aluminum-Boron Gas Suspensions,” Fiz. Goreniya Vzryva 38(6), 51–54 (2002) [Combust., Expl., Shock Waves 38 (6), 651–654 (2002)].

    Google Scholar 

  30. S. Goroshin, I. Fomenko, and J. H. S. Lee, “Burning Velocities in Fuel-Rich Aluminum Dust Clouds,” Proc. Combust. Inst. 26(2), 1961–1967 (1996).

    Article  Google Scholar 

  31. G. A. Risha, Y. Huang, R. A. Yetter, and V. Yang, “Experimental Investigation of Aluminum Particle Dust Cloud Combustion,” in 43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 2005; AIAA Paper No. 2005-739.

  32. A. G. Merzhanov, Yu. M. Grigorjev, and Yu. A. Gal’chenko, “Aluminum Ignition,” Combust. Flame 29, 1–14 (1977).

    Article  Google Scholar 

  33. N. D. Ageev, S. V. Goroshin, A. N. Zolotko, N. I. Poletaev, and Yu. L. Shoshin, “Steady Flame Velocity in Gas Suspensions of Aluminum,” in Combustion of Heterogeneous and Gas Systems, Proc. IX All-Union Symp. on Combustion and Explosion, November 19–24, 1989 (Chernogolovka, 1989), pp. 83–85.

    Google Scholar 

  34. J. Sun, R. Dobashi, and T. Hirano, “Temperature Profile across the Combustion Zone Propagating through an Iron Particle Cloud,” J. Loss Prev. Process Indust. 14, 463–467 (2001).

    Article  Google Scholar 

  35. V. V. Golovko, N. I. Poletaev, and A. V. Florko, “Role of Radiation in the Heat Balance of a Laminar Diffusion Plume of Iron,” in Physics of Aerodisperse Systems, No. 41 (Astroprint, Odessa, 2004), pp. 66–75.

    Google Scholar 

  36. A. P. Grosvenor, B. A. Kobe, and N. S. McIntyre, “Activation Energies for the Oxidation of Iron by Oxygen Gas and Water Vapour,” Surface Sci. 574, 317–321 (2005).

    Article  ADS  Google Scholar 

  37. G. Peskir, “On the Diffusion Coefficient: the Einstein Relation and Beyond,” Stoch. Models 19(3), 383–405 (2003).

    Article  MATH  MathSciNet  Google Scholar 

  38. J. Suna, R. Dobashib, and T. Hiranoc, “Concentration Profile of Particles across a Flame Propagating through an Iron Particle Cloud,” Combust. Flame 134(4), 381–387 (2003).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to P. S. Grinchuk.

Additional information

Original Russian Text © P.S. Grinchuk.

Published in Fizika Goreniya i Vzryva, Vol. 50, No. 3, pp. 32–42, May–June, 2014.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Grinchuk, P.S. Effect of stochasticity of the spatial distribution of particles in a gas suspension on combustion front propagation. Combust Explos Shock Waves 50, 272–281 (2014). https://doi.org/10.1134/S0010508214030046

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0010508214030046

Keywords

Navigation