Skip to main content
SpringerLink
Log in

Modeling of Plane Detonation Waves in a Gas Suspension of Aluminum Nanoparticles

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

Abstract

A physicomathematical model of detonation of a gas suspension of aluminum nanoparticles with allowance for the transition from the continuum to free-molecular flow regime and heat transfer between the particles is proposed. A formula for logarithmic interpolation for the thermal relaxation time in the transitional regime is derived. A semi-empirical model of Arrheniustype reduced kinetics of combustion is developed, which ensures good agreement with available experimental data. Steady (Chapman–Jouguet and overdriven) structures and also attenuating detonation waves in suspensions of nanoparticles are analyzed. Typical features of detonation in nanoparticle suspensions are found: the normal detonation regimes correspond to the solution in the Chapman–Jouguet plane with a sonic final state in terms of the equilibrium velocity of sound; combustion occurs in an almost equilibrium mixture in terms of velocities and temperatures; a strong dependence of the combustion region length on the amplitude of the leading shock wave is observed.

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

Similar content being viewed by others

References

  1. A. E. Medvedev, A. V. Fedorov, and V. M. Fomin, “Description of Ignition and Combustion of Gas Mixtures with Solid Particles by Methods of the Mechanics of Continuous Media,” Fiz. Goreniya Vzryva 20 (2), 3–9 (1984) [Combust., Expl., Shock Waves 20 (2), 127–132 (1984)].

    Google Scholar 

  2. E. A. Afanas’eva and V. A. Levin, “Aluminum-Particle Ignition and Combustion behind Shock and Detonation Waves,” Fiz. Goreniya Vzryva 23 (1), 8–14 (1987) [Combust., Expl., Shock Waves 23 (1), 1–5 (1987)].

    Google Scholar 

  3. B. Veyssiere and B. Khasainov, “A Model for Steady, Plane, Double-Front Detonations (DFD) in Gaseous Explosive Mixtures with Aluminum Particles in Suspension,” Combust. Flame 85, 241–253 (1991).

    Article  Google Scholar 

  4. F. Zhang, K. Gerrard, and R. C. Ripley, “Reaction Mechanism of Aluminum-Particle–Air Detonation,” J. Propul. Power 25, 845–858 (2009).

    Article  Google Scholar 

  5. P. I. Nigmatulin, Dynamics of Multiphase Media (Nauka, Moscow, 1987; Hemisphere, New York, 1991).

    Google Scholar 

  6. N. N. Yanenko, P. I. Soloukhin, A. N. Papyrin, and V. M. Fomin, Supersonic Two-Phase Flows under Conditions of Velocity Nonequilibrium of Particles (Nauka, Novosibirsk, 1980) [in Russian].

    Google Scholar 

  7. A. V. Fedorov, “Structure of the Heterogeneous Detonation of Aluminum Particles Dispersed in Oxygen,” Fiz. Goreniya Vzryva 28 (3), 72–83 (1992) [Combust., Expl., Shock Waves 28 (3), 277–286 (1992)].

    Google Scholar 

  8. A. V. Fedorov, V. M. Fomin, and T. A. Khmel’, “Non-Equilibrium Model of Steady Detonations in Aluminum Particle-Oxygen Suspensions,” Shock Waves 9 (5), 313–318 (1999).

    Article  ADS  MATH  Google Scholar 

  9. W. A. Strauss, “Investigation of the Detonation of Aluminum Powder–Oxygen Mixtures,” AIAA J. 6 (12), 1753–1761 (1968).

    Article  ADS  Google Scholar 

  10. A. V. Fedorov and T. A. Khmel’, “Numerical Simulation of Formation of Cellular Heterogeneous Detonation of Aluminum Particles in Oxygen,” Fiz. Goreniya Vzryva 41 (4), 84–98 (2005) [Combust., Expl., Shock Waves 41 (4), 435–448 (2005)].

    Google Scholar 

  11. A. V. Fedorov and T. A. Khmel’, “Formation and Degeneration of Cellular Detonation in Bidisperse Gas Suspensions of Aluminum Particles,” Fiz. Goreniya Vzryva 44 (3), 109–120 (2008) [Combust., Expl., Shock Waves 44 (3), 343–353 (2008)].

    Google Scholar 

  12. Yu. V. Kratova, A. V. Fedorov, and T. A. Khmel’, “Specific Features of Cellular Detonation in Polydisperse Suspensions of Aluminum Particles in a Gas,” Fiz. Goreniya Vzryva 47 (5), 85–94 (2011) [Combust., Expl., Shock Waves 47 (5), 572–580 (2011)].

    Google Scholar 

  13. A. V. Fedorov, V. M. Fomin, and T. A. Khmel’, Wave Processes in Gas Suspensions of Metal Particles (Parallel, Novosibirsk, 2015) [in Russian].

    Google Scholar 

  14. D. S. Sundaram, V. Yang, and V. E. Zarko, “Combustion of Nano Aluminum Particles (Review),” Fiz. Goreniya Vzryva 51 (2), 37–63 (2015) [Combust., Expl., Shock Waves 51 (2), 173–196 (2015)].

    Google Scholar 

  15. A. V. Fedorov and A. V. Shulgin, “Mathematical Modeling of Melting of Nano-Sized Metal Particles,” Fiz. Goreniya Vzryva 47 (2), 23–29 (2011) [Combust., Expl., Shock Waves 47 (2), 129–146 (2011)].

    Google Scholar 

  16. A. V. Fedorov and A. V. Shulgin, “Complex Modeling of Melting of an Aluminum Nanoparticle,” Fiz. Goreniya Vzryva 49 (4), 68–75 (2013) [Combust., Expl., Shock Waves 49 (4), 442–449 (2013)].

    Google Scholar 

  17. A. V. Fedorov and A. V. Shulgin, “Molecular Dynamics of Modeling of Melting of Aluminum Nanoparticles by the Embedded Atom Method,” Fiz. Goreniya Vzryva 51 (3), 55–59 (2015) [Combust., Expl., Shock Waves 51 (3), 333–337 (2015)].

    Google Scholar 

  18. A. V. Fedorov and A. V. Shulgin, “Molecular Dynamics and Phenomenological Simulations of an Aluminum Nanoparticle,” Fiz. Goreniya Vzryva 52 (3), 45–50 (2016) [Combust., Expl., Shock Waves 52 (3), 294–299 (2016)].

    Google Scholar 

  19. A. V. Fedorov, A. V. Shulgin, and S. A. Lavruk, “Description of Melting of Aluminum Nanoparticles,” Fiz. Goreniya Vzryva 52 (4), 94–100 (2016) [Combust., Expl., Shock Waves 52 (4), 457–462 (2016)].

    Google Scholar 

  20. A. V. Fedorov and A. V. Shulgin, “Point Model of Combustion of Aluminum Nanoparticles in the Reflected Shock Wave,” Fiz. Goreniya Vzryva 47 (3), 47–51 (2011) [Combust., Expl., Shock Waves 47 (3), 289–293 (2011)].

    Google Scholar 

  21. A. V. Fedorov and T. A. Khmel’, “Numerical Simulation of Detonation Initiation with a Shock Wave Entering a Cloud of Aluminum Particles,” Fiz. Goreniya Vzryva 38 (1), 114–122 (2002) [Combust., Expl., Shock Waves 38 (1), 101–108 (2002)].

    Google Scholar 

  22. C. Wang, S. K. Friedlander, and L. Madler, “Nanoparticle Aerosol Science and Technology: An Overview,” China Particuology 3 (5), 243–254 (2005).

    Article  Google Scholar 

  23. L. Madler and S. K. Friedlander, “Transport of Nanoparticles in Gases: Overview and Recent Advances,” Aerosol Air Qual. Res. 7 (3), 304–342 (2007).

    Article  Google Scholar 

  24. A. V. Filippov and D. E. Rosner, “Energy Transfer between an Aerosol Particle and Gas at High Temperature Ratios in the Knudsen Transition Regime,” Int. J. Heat Mass Transf. 43 (1), 127–138 (2000).

    Article  MATH  Google Scholar 

  25. S.-A. Kuhlmann, J. Reimann, and S. Will, “On Heat Conduction between Laser-Heated Nanoparticles and a Surrounding Gas,” Aerosol Sci. 37, 1696–1716 (2006).

    Article  ADS  Google Scholar 

  26. Y. Huang, G. A. Risha, V. Yang, and R. A. Yetter, “Combustion of Bimodal Nano/Micron-Sized Aluminum Particle Dust in Air,” Proc. Combust. Inst. 31, 2001–2009 (2007).

    Article  Google Scholar 

  27. Y. Huang, G. A. Risha, V. Yang, and R. A. Yetter, “Effect of Particle Size on Combustion of Aluminum Particle Dust in Air,” Combust. Flame 156, 5–13 (2009).

    Article  Google Scholar 

  28. T. Bazyn, H. Krier, and N. Glumac, “Combustion of Nanoaluminum at Elevated Pressure and Temperature behind Reflected Shock Waves,” Combust. Flame 145, 703–713 (2006).

    Article  Google Scholar 

  29. P. Lynch, H. Krier, and N. Glumac, “A Correlation for Burn Time of Aluminum Particles in the Transition Regime,” Proc. Combust. Inst. 32, 1887–1893 (2009).

    Article  Google Scholar 

  30. A. V. Fedorov and T. A. Khmel’, “Characteristics and Criteria of Ignition of Suspensions of Aluminum Particles in Detonation Processes,” Fiz. Goreniya Vzryva 48 (2), 76–88 (2012) [Combust., Expl., Shock Waves 48 (2), 191–202 (2012)].

    Google Scholar 

  31. V. I. Levitas, M. L. Pantoya, G. Chauhan, and I. Rivero, “Effect of the Alumina Shell on the Melting Temperature Depression for Aluminum Nanoparticles,” J. Phys. Chem. C 113 (32), 14088–14096 (2009).

    Article  Google Scholar 

  32. A. V. Fedorov, T. A. Khmel, and S. A. Lavruk, “Exit of a Heterogeneous Detonation Wave into a Channel with Linear Expansion. II. Critical Propagation Condition,” Fiz. Goreniya Vzryva 54 (1), 81–90 (2018) [Combust., Expl., Shock Waves 54 (1),72–81 (2018)].

    Google Scholar 

  33. A. V. Fedorov, T. A. Khmel, and Yu. A. Gosteev, “Theoretical Investigation of Ignition and Detonation of Coal–Particle Gas Mixtures,” Shock Waves 13, 453–463 (2004).

    Article  ADS  MATH  Google Scholar 

  34. F. Zhang, S. B. Murray, and R. B. Gerrard, “Aluminum Particle–Air Detonation at Elevated Pressures,” Shock Waves 15, 313–324 (2006).

    Article  ADS  Google Scholar 

  35. A. Briand, B. Veyssiere, and B. A. Khasainov, “Investigation of Detonation Initiation in Aluminium Suspensions,” Shock Waves 18, 307–315 (2008).

    Article  ADS  MATH  Google Scholar 

  36. V. M. Vasil’ev et al., “Calculation of Fuel–Air Mixture Detonation Parameters,” Fiz. Goreniya Vzryva 16 (3), 127–134 (1980) [Combust., Expl., Shock Waves 16 (3), 354–360 (1980)].

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia

    T. A. Khmel & A. V. Fedorov

Authors
  1. T. A. Khmel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. V. Fedorov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. A. Khmel.

Additional information

Original Russian Text © T.A. Khmel, A.V. Fedorov.

Published in Fizika Goreniya i Vzryva, Vol. 54, No. 2, pp. 71–81, March–April, 2018.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khmel, T.A., Fedorov, A.V. Modeling of Plane Detonation Waves in a Gas Suspension of Aluminum Nanoparticles. Combust Explos Shock Waves 54, 189–199 (2018). https://doi.org/10.1134/S0010508218020089

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0010508218020089

Keywords

Search

Navigation