Combustion, Explosion and Shock Waves

, Volume 34, Issue 3, pp 273–279 | Cite as

Solitary traveling waves in a heterogeneous medium with a chemical reaction

  • V. N. Snytnikov
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Abstract

A correct method for constructing autowave solutions is proposed for single-temperature models of unsteady processes in a dissipative medium with Arrhenius type chemical reactions. It is based on extending the temperature range to 0 K and using the Kolmogorov-Petrovskii-Piskunov approach. Solutions that are not inconsistent with the Nernst theorem are selected from the obtained finite spectrum of autowave solutions. For a quasihomogeneous model of gas filtration in a dissipative heterogeneous medium with a single irreversible chemical reaction, such an autowave solution is unique. A nondimensional parameter is found whose critical value for the selected Zel’dovich number defines the existence condition for this self-similar solution. A criterion is obtained for the initial temperature range in which the chemical transformations in the reaction are negligibly small for autowave processes.

Keywords

Singular Point Solitary Wave Heterogeneous Medium Unsteady Combustion Autowave Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References

  1. 1.
    V. A. Vasil’ev, Yu. M. Romanovskii, and V. G. Yakhno,Autowave Processes [in Russian], Nauka, Moscow (1987).MATHGoogle Scholar
  2. 2.
    N. V. Kel’tsev,Fundamentals of Adsorption Technology [in Russian], Khimiya, Moscow (1984).Google Scholar
  3. 3.
    A. P. Aldushin, and A. G. Merzhanov, “Theory of filtration combustion: general concepts and the state of investigations,” in:Thermal-Wave Propagation in Heterogeneous Media [in Russian], Nauka, Novosibirsk (1988), pp. 9–52.Google Scholar
  4. 4.
    A. P. Aldushin, and I. P. Borovinskaya, “Self-propagating high-temperature synthesis of refractory inorganic compounds,”Dokl. Akad. Nauk SSSR,204, No. 2, 366–369 (1972).Google Scholar
  5. 5.
    A. G. Merzhanov, and ’E. N. Rumanov, “Nonlinear effects in macroscopic kinetics”Usp. Fiz. Nauk,151, No. 4, 553–594 (1987).Google Scholar
  6. 6.
    Yu. Sh. Matros,Catalytic Processes under Unsteady Conditions [in Russian], Nauka, Novosibirsk (1987).Google Scholar
  7. 7.
    G. I. Barenblatt,Similarity, Self-Similarity, and Intermediate Asymptotics. Theory and Application to Geophysical Hydrodynamics [in Russian], Gidrometeoizdat, Leningrad (1982).Google Scholar
  8. 8.
    V. P. Maslov, V. G. Danilov, and K. A. Volosov,Mathematical Modeling of Heat-Transfer Processes [in Russian], Nauka, Moscow (1980).Google Scholar
  9. 9.
    Ya. B. Zel’dovich, G. I. Barenblatt, V. B. Librovich, and G. M. Makhviladze,Mathematical Theory of Combustion and Explosion [in Russian], Nauka, Moscow (1980).Google Scholar
  10. 10.
    D. A. Frank-Kamenetskii,Diffusion and Heat Transfer in Chemical Kinetics [in Russian], Nauka, Moscow (1987).Google Scholar
  11. 11.
    O. V. Kiselev, Yu. Sh. Matros, and N. A. Chumakova, “The phenomenon of thermal-front propagation in a catalyst layer,” in:Thermal-Wave Propagation in Heterogeneous Media [in Russian], Nauka, Novosibirsk (1988), pp. 145–202.Google Scholar
  12. 12.
    V. N. Snytnikov, N. A. Chumakova, and N. V. Vernikovskaya, “Autosoliton structure in heterogeneous media,” in:Unsteady Combustion, NATO ASI on “Unsteady Combustion” (Praia da Granja, Portugal, Sept. 6–17, 1993), Part II (1993), pp. 7–9.Google Scholar
  13. 13.
    N. V. Vernikovskaya, V. N. Snytnikov, and N. A. Chumakova, “Methods for correcting flows in separation schemes for the calculation of autosolitons in a dissipative heterogeneous medium with chemical reactions,”Vychisl. Tekhnol.,2, No. 4, 169–176, (1993).Google Scholar
  14. 14.
    O. V. Kiselev, and Yu. Sh. Matros, “Propagation of fast thermal waves through a catalyst layer,”Dokl. Akad. Nauk SSSR,308, No. 3, 667 (1989).Google Scholar
  15. 15.
    Ya. B. Zel’dovich, and D. A. Frank-Kamenetskii, “Theory of thermal-flame propagation,”Zh. Fiz. Khim.,12, No. 1, 100–105 (1938).Google Scholar
  16. 16.
    A. N. Kolmogorov, I. G. Petrovskii, and N. S. Piskunov, “Investigation of the equation of diffusion combined with an increase in the amount of material, and its application to a biological problems,”Byul. Mosk. Univ., Sek. A,1, No. 6, 1–26 (1937).Google Scholar
  17. 17.
    A. P. Aldushin, Ya. B. Zel’dovich, and S. I. Khudyaev, “Numerical investigation of flame propagation through a mixture reacting at the initial temperature,”Fiz. Goreniya Vzryva,15, No. 6, 20–27, (1979).Google Scholar
  18. 18.
    Ya. B. Zel’dovich,Selected Papers. Chemical Physics and Hydrodynamics [in Russian], Nauka, Moscow (1984), pp. 5, 231, and 279.Google Scholar
  19. 19.
    A. I. Vol’pert, “Propagation of waves described by nonlinear parabolic equations,” in: I. G. Petrovskii,Selected Papers. Differential Equations. Probability Theory, [in Russian], Nauka, Moscow (1987), pp. 333–358.Google Scholar
  20. 20.
    V. I. Gol’danskii, L. I. Trakhtenberg, and V. N. Flerov,Tunneling Phenomena in Chemical Physics [in Russian], Nauka, Moscow (1986).Google Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 1999

Authors and Affiliations

  • V. N. Snytnikov
    • 1
  1. 1.Siberian Division, Russian Academy of SciencesBoreskov Catalysis InstituteNovosibirsk

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