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Theoretical description of shock-wave formation in a spatially inhomogeneous combustible medium for chain-branching combustion kinetics

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Combustion, Explosion, and Shock Waves Aims and scope

Abstract

For combustion reactions with chain-branching kinetics, the time scales of induction and heat release vary independently and can be significantly different as well as comparable, depending on the initial conditions. A theoretical study was performed to investigate the influence of the heat-release rate and kinetics on the mechanisms and conditions of shock-wave formation in a spatially inhomogeneous combustible medium — the first step of detonation initiation in systems with an induction time gradient. The study used the transport equation method developed by the authors previously.

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References

  1. Ya. B. Zel’dovich, V. B. Librovich, G. M. Makhviladze, and G. I. Sivashinsky “Development of detonation in a nonuniformly pre-heated gas,” Astronaut. Acta, 15, 313–321 (1970).

    Google Scholar 

  2. Ya. B. Zel’dovich, “Regime classification of an exothermic reaction with nonuniform initial conditions,” Combust. Flame, 39, 211–214 (1980).

    Article  Google Scholar 

  3. B. E. Gel’fand, A. N. Polenov, S. M. Frolov, and S. A. Tsyganov “Detonation in systems with nonuniform temperature and concentration distributions,” Khim. Fiz., 5, No. 9, 1277–1284 (1986).

    Google Scholar 

  4. B. E. Gel’fand, S. M. Frolov, and S. A. Tsyganov “Mechanism of explosions in gas pumping units for gas mains,” Combust., Expl., Shock Waves, 24, No. 3, 356–358 (1988).

    Article  Google Scholar 

  5. G. M. Makhviladze and D. I. Rogatykh, “Initial temperature and concentration inhomogeneities — the cause of explosive chemical reaction in a combustible gas,” Khim. Fiz., 8, No. 2, 272–285 (1989).

    Google Scholar 

  6. G. M. Makhviladze and D. I. Rogatykh, “Formation and attenuation of a quasi-steady-state detonation complex in a nonuniformly heated combustible gas,” Izv. Akad. Mauk SSSR, Mekh. Zhidk. Gaza, No. 2, 161–168 (1991).

  7. M. Short, “On the critical conditions for the detonation initiation in a nonuniformly perturbed reactive fluid,” SIAM J. Appl. Math., 57, No. 5, 1242–1280 (1997).

    Article  MATH  MathSciNet  Google Scholar 

  8. A. K. Kapila, D. W. Schwendeman, J. J. Schwendeman, and T. Hawa, “Mechanisms of detonation formation due to a temperature gradient,” Combust. Theory Model., 6, 553–594 (2002).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  9. G. J. Sharpe and M. Short, “Detonation ignition from a temperature gradient for a two-step chain-branching kinetics model,” J. Fluid Mech., 476, 267–292 (2003).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  10. X. J. Gu, D. R. Emerson, and D. Bradley, “Modes of reaction front propagation from hot spots,” Combust. Flame., 133, 63–74 (2003).

    Article  Google Scholar 

  11. A. M. Bartenev and B. E. Gelfand, “Spontaneous initiation of detonations,” Prog. Energ. Combust. Sci., 26, 29–55 (2000).

    Article  Google Scholar 

  12. I. A. Zaev and I. A. Kirillov, “Transport equation for gas-dynamic perturbations in a spatially inhomogeneous self-igniting medium,” Combust., Expl., Shock Waves, 44, No. 3, 310–316 (2008).

    Article  Google Scholar 

  13. I. A. Zaev and I. A. Kirillov, “Parametric study of shock-wave formation in a spatially inhomogeneous selfigniting medium for Arrhenius combustion kinetics,” Combust., Expl., Shock Waves, 45, No. 2, 174–181 (2009).

    Article  Google Scholar 

  14. V. P. Korobeinikov, V. A. Levin, V. V. Markov, and G. G. Chernyi, “Propagation of blast waves in a combustible gas,” Astronaut. Acta., 17, Nos. 5–6, 529–537 (1972).

    Google Scholar 

  15. V. P. Korobeinikov, Problems of the Theory of Point Explosion [in Russian] Nauka, Moscow (1985).

    Google Scholar 

  16. N. M. Marinov, C. K. Westbrook, and W. J. Pitz, “Detailed and global chemical kinetic model for hydrogen,” Eighth (Int.) Symp. on Transport Processes (1995), Vol. 1, pp. 118–129.

    Google Scholar 

  17. M. Deminsky, V. Chorkov, G. Belov, I. Cheshigin, A. Knizhnik, E. Shulakova, M. Shulakov, I. Iskandarova, V. Alexandrov, A. Petrusev, I. Kirillov, M. Strelkova, S. Umanski, and B. Potapkin, “Chemical workbench — integrated medium for materials science,” Comput. Materials Sci., 28, 169–178 (2003).

    Article  Google Scholar 

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Authors and Affiliations

  1. Kurchatov Institute, Moscow, 123182, Russia

    I. A. Zaev & I. A. Kirillov

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  1. I. A. Zaev
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  2. I. A. Kirillov
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Correspondence to I. A. Zaev.

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Translated from Fizika Goreniya i Vzryva, Vol. 45, No. 6, pp. 63–72, November–December, 2009.

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Zaev, I.A., Kirillov, I.A. Theoretical description of shock-wave formation in a spatially inhomogeneous combustible medium for chain-branching combustion kinetics. Combust Explos Shock Waves 45, 692–699 (2009). https://doi.org/10.1007/s10573-009-0086-5

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  • DOI: https://doi.org/10.1007/s10573-009-0086-5

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