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Determination of the transfer coefficient of natural turbulence occurring near the solid-propellant gasification zone. I. Two-phase model of the gasification zone

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Combustion, Explosion, and Shock Waves Aims and scope

Abstract

A model for solid propellant gasification is proposed which contains a two-phase medium in an intermediate stage. The formation of the gas phase proceeds in two ways: chemical reactions result in gaseous products, which, in turn, initiate the formation of bubbles in which vapor forms from the liquid phase of the propellant. Gaseous products play an important role only in the very early stage of bubble development; their critical pressure is used to determine the minimum size of gas-phase nuclei. The bubble volume grows primarily by evaporation of the liquid phase. A kinetic equation for the bubble concentration and the necessary boundary conditions are formulated. Arguments are given suggesting that a temperature maximum cannot occur in the gasification zone and that natural turbulence can be generated by collapsing bubbles. The sound produced by solid propellant combustion is explained by the collapse of a huge number of microscopic bubbles. If the processes in the two-phase zone are neglected, the formulated system of equations is transformed into the Belyaev–Zel’dovich model equations.

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References

  1. Theory of Combustion of Propellants and Explosives, Ed. by O. I. Leipunskii and Yu. V. Frolov (Nauka, Moscow, 1982) [in Russian].

  2. G. B. Manelis, G. M. Nazin, Yu. I. Rubtsov, and V. A. Strunin, Thermal Decomposition and Combustion of Explosives and Propellants (Nauka, Moscow, 1996) [in Russian].

    Google Scholar 

  3. L. K. Gusachenko and V. E. Zarko, “Analysis of Contemporary Models of Steady State Combustion of Composite Solid Fuels,” Fiz. Goreniya Vzryva 22 (6), 3–15 (1986) [Combust., Expl., Shock Waves 22 (6), 643–653 (1986)].

    Google Scholar 

  4. L. K. Gusachenko and V. E. Zarko, “Combustion Models for Energetic Materials with Completely Gaseous Reaction Products,” Fiz. Goreniya Vzryva 41 (1), 24–40 (2005) [Combust., Expl., Shock Waves 41 (1), 20–34 (2005)].

    Google Scholar 

  5. M. V. Bekstead, “Recent Progress in Modeling Solid Propellant Combustion,” Fiz. Goreniya Vzryva 42 (6), 4–24 (2006) [Combust., Expl., ShockWaves 42 (6), 623–641 (2006)].

    Google Scholar 

  6. L. K. Gusachenko, V. E. Zarko, and A. D. Rychkov, “Instability of a Combustion Model with Surface Evaporation and Overheat in the Condensed Phase,” Fiz. Goreniya Vzryva 33 (1), 43–50 (1997) [Combust., Expl., Shock Waves 33 (1), 34–40 (1997).

    Google Scholar 

  7. B. V. Novozhilov, Nonstationary Combustion of Solid Rocket Fuels (Nauka, Moscow, 1973 [in Russian].

    Google Scholar 

  8. K. O. Sabdenov, J. Dueck, and M. Erzada, “Limits of Steady Burning Propellants in the Phenomenological Theory Using Effective Initial Temperature,” J. Therm. Sci. Technol. 10 (1), (2015); DOI: 10.1299/jtst.2015jtst0006.

    Google Scholar 

  9. K. O. Sabdenov and J. Dueck, “Limits of Stable Combustion in an Engine of Ultra-Small Spacecrafts,” Frontiers in Aerospace Eng. 5 (1), 49–64 (2016).

    Article  Google Scholar 

  10. V. A. Strunin and G. B. Manelis, “Stability of the Steady-State Process of Explosive Combustion Limited by the Reaction in the Condensed Phase,” Fiz. Goreniya Vzryva 7 (4), 498–501 (1971) [Combust., Expl., Shock Waves 7 (4), 427–430 (1971)].

    Google Scholar 

  11. L. K. Gusachenko and V. E. Zarko, “Erosive Burning. Modeling Problems,” Fiz. Goreniya Vzryva 43 (3), 47–58 (2007) [Combust., Expl., Shock Waves 43 (3), 286–296 (2007)].

    Google Scholar 

  12. K. O. Sabdenov, Theory of Nonstationary Combustion of Solid Rocket Propellants (Izd. Tom. Politekh. Univ., Tomsk, 2006) [in Russian].

    Google Scholar 

  13. K. O. Sabdenov, Unstable Burning of Solid Rocket Propellants. Problems and Advances of Modeling (Lambert Academy Publ., Saarbrucken, Germany, 2012).

    Google Scholar 

  14. Y. M. Timnat, Advanced Chemical Rocket Propulsion, (Academic Press, 1987).

    Google Scholar 

  15. V. S. Ilyukhin, M. I. Levichuk, A. D. Margolin, and P. F. Pokhil, “Investigation of the Acoustic Instability of Propellant Combustion by High-Speed Filming,” in Vibration Combustion in Some Model Devices (Izd. Kazan. Gos. Univ., Kazan, 1970) [in Russian].

    Google Scholar 

  16. T.-S. Roh, I.-S. Tseng, and V. Yang, “Effect of Acoustic Oscillation on Flame Dynamics of Homogeneous Propellants in Rocket Motors,” J. Propul. Power 11 (4), 640–650 (1995).

    Article  Google Scholar 

  17. S. Apte and V. Yang, “Unsteady Flow Evolution and Combustion Dynamics of Homogeneous Solid Propellant in Rocket Motors,” Combust. Flame 131, 110–131 (2002).

    Article  Google Scholar 

  18. W. Cai, F. Ma, and V. Yang, “Two-Phase Vorticoacoustic Flow Interactions in Solid-Propellant Rocket Motors,” J. Propul. Power 19 (3), 385–396 (2003).

    Article  Google Scholar 

  19. V. E. Annikov and V. N. Kondrikov, “Effect of Charge Diameter on the Burning Rate of Explosives,” Fiz. Goreniya Vzryva 4 (3), 350–357 (1968) [Combust., Expl., Shock Waves 4 (3), 197–201 (1968)].

    Google Scholar 

  20. É. I. Maksimov, Yu. M. Maksimov, and V. F. Chukov, “Investigation of the Combustion of DINA,” Fiz. Goreniya Vzryva 7 (2), 197–204 (1971) [Combust., Expl., Shock Waves 7 (2), 165–170 (1971)].

    Google Scholar 

  21. V. V. Aleksandrov, A. V. Boldyreva, V. V. Boldyrev, and R. K. Tukhtaev, “Combustion of DINA at Atmospheric Pressure,” Fiz. Goreniya Vzryva 9 (1), 140–142 (1973) [Combust., Expl., Shock Waves 9 (1), 117–119 (1973)].

    Google Scholar 

  22. E. I. Maksimov and A. G. Merzhanov, “Theory of Combustion of Condensed Substances,” Fiz. Goreniya Vzryva 2 (1), 47–58 (1966) [Combust., Expl., Shock Waves 2 (1), 25–31 (1966)].

    Google Scholar 

  23. S. B. Margolis, F. A. Williams, and R. C. Armstrong, “Influences of Two-Phase Flow in the Deflagration of Homogeneous Solids,” Combust. Flame 67 (3), 249–258 (1987).

    Article  Google Scholar 

  24. S. C. Li, F. A. Williams, and S. B. Margolis, “Effect of Two-Phase Flow in a Model for Nitramine Deflagration,” Combust. Flame 80 (3), 329–349 (1990).

    Article  Google Scholar 

  25. L. K. Gusachenko and V. E. Zarko, “The Marangoni Effect in Combustion of Energetic Materials with a Liquid Surface Layer,” Fiz. Goreniya Vzryva 32 (2), 141–142 (1996) [Combust., Expl., Shock Waves 32 (2), 239240 (1996)].

    Google Scholar 

  26. K. O. Sabdenov, “Generation of Hydrodynamic Instability in the Gasification Region of Propellant,” Fiz. Goreniya Vzryva 52 (6), 70–82 (2016) [Combust., Expl., Shock Waves 52 (6), 683–693 (2016)].

    Google Scholar 

  27. Y.-C. Liau and V. Yangt, “Analysis of RDX Monopropellant Combustion with Two-Phase Subsurface Reactions,” J. Propul. Power 11 (4), 729–739 (1995).

    Article  Google Scholar 

  28. Th.K. Sherwood, R. L. Pigford, and Ch. R. Wilke, Mass Transfer (McGraw-Hill, New York, 1975).

    Google Scholar 

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

    Google Scholar 

  30. D. V. Sivukhin, Thermodynamics and Molecular Physics (Fizmatlit, Moscow, 2005) [in Russian].

    Google Scholar 

  31. Ya. I. Frenkel’, Kinetic Theory of Liquids (Nauka, Leningrad, 1975) [in Russian].

    MATH  Google Scholar 

  32. M. Volmer, Kinetik der Phasenbildung (T. Steinkopff, Dresden, 1939).

    Google Scholar 

  33. B. M. Ma, Nuclear Reactor Materials and Applications (Reinhold, New York, 1983).

    Google Scholar 

  34. Physical Materials Science, Vol. 4: Physical Basis of Strength. Radiation Physics of Solids. Computer Simulation (Izd. MIFI, Moscow, 2008) [in Russian].

    Google Scholar 

  35. N. B. Vargaftik, Handbook of Thermophysical Properties of Liquids and Gases (Nauka, Moscow, 1972) [in Russian].

    Google Scholar 

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

    Google Scholar 

  37. J. Knacke and I. N. Stransky, “Evaporation Mechanism,” Prog. Metal Phys. 6, 181–235 (1956).

    Article  ADS  Google Scholar 

  38. N. J. A. Sloane, “The Packing of Spheres,” Scientific American, January, 116–125 (1984).

    Google Scholar 

  39. A. A. Zenin, V. M. Puchkov, S. B. Finyakov, “Characteristics of HMX Combustion Waves at Various Pressures and Initial Temperatures,” Fiz. Goreniya Vzryva 34 (2), 59–66 (1998) [Combust., Expl., Shock Waves 34 (2), 170–176 (1998)].

    Google Scholar 

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Correspondence to K. O. Sabdenov.

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Original Russian Text © K.O. Sabdenov, M. Erzada.

Published in Fizika Goreniya i Vzryva, Vol. 53, No. 5, pp. 70–82, September–October, 2017.

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Sabdenov, K.O., Erzada, M. Determination of the transfer coefficient of natural turbulence occurring near the solid-propellant gasification zone. I. Two-phase model of the gasification zone. Combust Explos Shock Waves 53, 554–564 (2017). https://doi.org/10.1134/S0010508217050082

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  • DOI: https://doi.org/10.1134/S0010508217050082

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