Nonequilibrium processes in meta-stable media

  • N. N. SmirnovEmail author
  • O. G. Penyazkov
  • K. L. Sevrouk
  • V. F. Nikitin
  • L. I. Stamov
  • V. V. Tyurenkova
Regular Article
Part of the following topical collections:
  1. Non-equilibrium processes in multicomponent and multiphase media


Meta-stable systems are those staying in the local equilibrium state: being slightly deviated from it they return to the equilibrium, but in case deviation surpasses a critical value those systems fall down to another equilibrium state. Chemically reacting gaseous mixture provides a typical example of a meta-stable system. The paper is aimed at numerical and experimental investigation of detonation initiation in hydrogen-air mixtures due to focusing of a shock wave reflected inside a wedge. Both numerical and experimental investigations were conducted. Comparison of numerical and experimental results made it possible to validate the developed 3D transient mathematical model of chemically reacting gas mixture flows incorporating hydrogen-air mixtures. Kinetic schemes and turbulence models were improved based on comparison of numerical and experimental results. Several different flow scenarios manifest in the reflection of shock waves all being dependent on the incident shock wave intensity: reflection of the shock wave with lagging behind the combustion zone, formation of a detonation wave in reflection and focusing, and intermediate transient regimes.

Graphical abstract


Topical issue: Non-equilibrium processes in multicomponent and multiphase media 


  1. 1.
    V.B. Betelin, N.N. Smirnov, V.F. Nikitin, Acta Astronaut. 109, 269 (2015)ADSCrossRefGoogle Scholar
  2. 2.
    N.M. Marinov, W.J. Pitz, C.K. Westbrook, M. Hori, N. Matsunaga, An Experimental and Kinetic Calculation of the Promotion Effect of Hydrocarbons on the NO-NO$_{2}$ Conversion in a Flow Reactor, in Proceedings of the Combustion Institute, Vol. 27 (1998) pp. 389-396 (UCRL-JC-129372) UCRL-WEB-204236Google Scholar
  3. 3.
    R.J. Kee, J.A. Miller, T.H. Jefferson, Chemkin: a general-purpose, problem-independent, transportable Fortran chemical kinetics code package, Sandia National Laboratories Report SAND80-8003 (1980)Google Scholar
  4. 4.
    S. Browne, J. Ziegler, J.E. Shepherd, Numerical Solution Methods for Shock and Detonation Jump Conditions, GALCIT Report FM2006.006, July 2004-Revised August 29, 2008Google Scholar
  5. 5.
    S. Gordon, B.J. McBride, Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications I. Analysis, NASA RP-1311, October 1994Google Scholar
  6. 6.
    Z.G. Pozdnyakov, B.D. Rossi, Handbook of Industrial Explosives and Means of Blasting (M. Nedra, 1977)Google Scholar
  7. 7.
    E.J. Orlova, Chemistry and Technology of High Explosives, Textbook for universities, 3rd edition (L. “Chemistry”, Leningrad branch, 1981)Google Scholar
  8. 8.
    U. Maas, J. Warnatz, Combus. Flame 74, 53 (1988)CrossRefGoogle Scholar
  9. 9.
    N.N. Smirnov, V.F. Nikitin, Int. J. Hydrog. Energy 39, 1122 (2014)CrossRefGoogle Scholar
  10. 10.
    N.N. Smirnov, V.B. Betelin, R.M. Shagaliev, V.F. Nikitin, I.M. Belyakov, Yu.N. Deryuguin, S.V. Aksenov, D.A. Korchazhkin, Int. J. Hydrog. Energy 39, 10748 (2014)CrossRefGoogle Scholar
  11. 11.
    N.N. Smirnov, V.B. Betelin, V.F. Nikitin, Yu.G. Phylippov, Jaye Koo, Acta Astronaut. 104, 134 (2014)ADSCrossRefGoogle Scholar
  12. 12.
    NVIDIA CUDA, Programming Guide, 2016,
  13. 13.
    J.T. Ferziger, M. Peric, Computational Methods for Fluid Dynamics, 3d edition (Springer, 2002)Google Scholar
  14. 14.
    B. van Leer, J. Comput. Phys. 32, 101 (1979)ADSCrossRefGoogle Scholar
  15. 15.
    M.-S. Liou, J. Comput. Phys. 129, 364 (1996)ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    K. Fletcher, Computational Methods in Fluid Dynamics, in 2 volumes (Wiley, New York, 1991) English translationGoogle Scholar
  17. 17.
    E.A. Novikov, L-stable (4,2)-method of fourth order to solve hard problems, Vestnik SamGU -- Natural Science Series B, Vol. 8(89) (2011) pp. 59--68Google Scholar
  18. 18.
    B. Koren, A robust upwind discretisation method for advection, diffusion and source terms, in Numerical Methods for Advection -- Diffusion Problems, edited by C.B. Vreugdenhil, B. Koren (Braunschweig, Vieweg, 1993) p. 117, ISBN: 3-528-07645-3Google Scholar
  19. 19.
    N.N. Smirnov, V.F. Nikitin, Sh. Alyari-Shourekhdeli, Combus. Explos. Shock Waves 44, 517 (2008)CrossRefGoogle Scholar
  20. 20.
    N.N. Smirnov, V.F. Nikitin, Yu.G. Phylippov, J. Eng. Phys. Thermophys. 83, 1287 (2010)CrossRefGoogle Scholar
  21. 21.
    N.N. Smirnov, V.F. Nikitin, S. Alyari Shurekhdeli, J. Propuls. Power 25, 593 (2009)CrossRefGoogle Scholar
  22. 22.
    V.F. Nikitin, V.R. Dushin, Y.G. Phylippov, J.C. Legros, Acta Astronaut. 64, 281 (2009)ADSCrossRefGoogle Scholar
  23. 23.
    Y. Wang, J. Wang, Y. Li, Y. Li, Int. J. Hydrog. Energy 39, 11792 (2014)CrossRefGoogle Scholar
  24. 24.
    A. Heidari, J.X. Wen, Int. J. Hydrog. Energy 39, 21317 (2014)CrossRefGoogle Scholar
  25. 25.
    Dan Wu, Yan Liu, Yusi Liu, Jianping Wang, Int. J. Hydrog. Energy 39, 15803 (2014)CrossRefGoogle Scholar
  26. 26.
    Yu.G. Phylippov, V.R. Dushin, V.F. Nikitin, V.A. Nerchenko, N.V. Korolkova, V.M. Guendugov, Acta Astronaut. 76, 115 (2012)ADSCrossRefGoogle Scholar
  27. 27.
    Min-cheol Gwak, Younghun Lee, Ki-hong Kim, Jack J. Yoh, Int. J. Hydrog. Energy 40, 3006 (2015)CrossRefGoogle Scholar
  28. 28.
    Yuhui Wang, Jianping Wang, Int. J. Hydrog. Energy 40, 7949 (2015)CrossRefGoogle Scholar
  29. 29.
    F.A. Bykovskii, S.A. Zhdan, E.F. Vedernikov, A.N. Samsonov, A.S. Zintsova, Combust. Explos. Shock Waves 52, 446 (2016)CrossRefGoogle Scholar
  30. 30.
    F.A. Bykovskii, S.A. Zhdan, E.F. Vedernikov, Combust. Explos. Shock Waves 52, 371 (2016)CrossRefGoogle Scholar
  31. 31.
    F. Falempin, Tuijin Jishu/J. Propuls. Technol. 31, 650 (2010)Google Scholar
  32. 32.
    F. Jouot, G. Dupré, A. Quilgars, I. Gökalp, E. Cliquet, Proc. Combust. Inst. 33, 2235 (2011)CrossRefGoogle Scholar
  33. 33.
    G. Roy, S. Frolov, K. Kailasanath, N. Smirnov (Editors), Gaseous and Heterogeneous Detonations: Science to Applications (ENAS Publ., Moscow, 1999) ISBN: 5-89055-016-0Google Scholar
  34. 34.
    Gene M. Amdahl, Computer 46, 38 (2013)CrossRefGoogle Scholar
  35. 35.
    N.N. Smirnov, Acta Astronaut. 126, 497 (2016)ADSCrossRefGoogle Scholar
  36. 36.
    G.A. Sod, J. Comput. Phys. 27, 1 (1978)ADSMathSciNetCrossRefGoogle Scholar
  37. 37.
    R. Liska, B. Wendroff, SIAM J. Sci. Comput. 25, 995 (2003)MathSciNetCrossRefGoogle Scholar
  38. 38.
    N.N. Smirnov, V.B. Betelin, V.F. Nikitin, L.I. Stamov, D.I. Altoukhov, Acta Astronaut. 117, 338 (2015)ADSCrossRefGoogle Scholar
  39. 39.
    N.N. Smirnov, V.F. Nikitin, L.I. Stamov, V.A. Nerchenko, V.V. Tyrenkova, Int. J. Comput. Methods 14, 1750038 (2017)MathSciNetCrossRefGoogle Scholar
  40. 40.
    N.N. Smirnov, O.G. Penyazkov, K.L. Sevrouk, V.F. Nikitin, L.I. Stamov, V.V. Tyurenkova, Acta Astronaut. 135, 114 (2017)ADSCrossRefGoogle Scholar
  41. 41.
    V.V. Martynenko, O.G. Penyaz’kov, K.A. Ragotner, S.I. Shabunya, J. Eng. Phys. Thermophys. 77, 785 (2004)CrossRefGoogle Scholar
  42. 42.
    O.G. Penyazkov, K.A. Ragotner, A.J. Dean, B. Varatharajan, Proc. Combust. Inst. 30, 1941 (2005)CrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • N. N. Smirnov
    • 1
    • 2
    • 4
    Email author
  • O. G. Penyazkov
    • 3
    • 4
  • K. L. Sevrouk
    • 3
  • V. F. Nikitin
    • 1
    • 4
  • L. I. Stamov
    • 1
    • 2
    • 4
  • V. V. Tyurenkova
    • 2
    • 4
  1. 1.Moscow Lomonosov State UniversityMoscowRussia
  2. 2.Scientific Research Institute for System Analysis of Russian Academy of SciencesMoscowRussia
  3. 3.Lykov’s Heat and Mass Transfer Institute of National Academy of Science of BelarusMinskBelarus
  4. 4.LLC “Center for Numerical Modeling”Moscow, ZelenogradRussia

Personalised recommendations