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Negative erosion effect and the emergence of unstable combustion. 2. numerical simulation

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Combustion, Explosion, and Shock Waves Aims and scope

Abstract

This paper describes the numerical simulation of combustion with the manifestation of the Vilyunov–Dvoryashin effect that comes down to reduction of the burning rate in the case of blowing of gaseous combustion products past the propellant gasification surface. The cases of endothermic and exothermic reactions of gasification of the solid propellant are considered. The Vilyunov–Dvoryashin effect can terminate combustion even before the erosion coefficient reaches a minimum value of 0.61. Self-oscillating combustion may also occur. The simulation of propellant combustion similar in its properties to the propellant N shows qualitative agreement between the theoretical and experimental results. However, it also reveals the need for more accurate data with regard to performance conditions and experimental results. The existing models of solid-propellant combustion require significant updates as well.

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References

  1. V. N. Vilyunov and A. A. Dvoryashin, “An Experimental Investigation of the Erosive Burning Effect,” Fiz. Goreniya Vzryva 7 (1), 45–51 (1971) [Combust., Expl., Shock Waves 7 (1), 38–42 (1971)].

    Google Scholar 

  2. F. A. Williams, Combustion Theory (Addison-Wesley, 1965).

    Google Scholar 

  3. H. S. Mukunda, “A Comprehensive Theory of Erosive Burning in Solid Rocket Propellants,” Combust. Sci. Technol. 18 (3–4), 105–118 (1978).

    Article  Google Scholar 

  4. 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 

  5. V. K. Bulgakov and A. M. Lipanov, “Combustion of Condensed Material with Blowing,” Fiz. Goreniya Vzryva 19 (3), 32–41 (1983) [Combust., Expl., Shock Waves 19 (3), 279–287 (1983)].

    Google Scholar 

  6. V. K. Bulgakov and A. M. Lipanov, “Model of the Combustion of Solid Fuel with Blow-Off, Taking Account of the Interaction of Turbulence with the Chemical Reaction,” Fiz. Goreniya Vzryva 20 (5), 68–74 (1984) [Combust., Expl., Shock Waves 20 (5), 538–542 (1984)].

    Google Scholar 

  7. D. R. Greatrix, “Model for Prediction of Negative and Positive Erosive Burning,” Canad. Aeronaut. Space J. 53 (1), 13–21 (2007).

    Article  ADS  Google Scholar 

  8. K. Srinivasan, S. Narayanan, and O. P. Sharma, “Numerical Studies on Erosive Burning in Cylindrical Solid Propellant Grain,” Heat Mass Transfer 44, 579–585 (2008); DOI: 10.1007/s00231-007-0280-5.

    Article  ADS  Google Scholar 

  9. M. A. Willcox, M. Q. Brewster, K. C. Tang, D. S. Stewart, and I. Kuznetzov, “Solid RocketMotor Internal Ballistics Simulation Using Three-Dimensional Grain Burnback,” J. Propul. Power. 23 (3), 575–584 (2007).

    Article  Google Scholar 

  10. K. O. Sabdenov, “On the Threshold Nature of Erosive Burning,” Fiz. Goreniya Vzryva 44 (3), 61–71 (2008) [Combust., Expl., Shock Waves 44 (3), 300–309 (2008)].

    Google Scholar 

  11. K. O. Sabdenov and M. Erzada, “Mechanism of the Negative Erosion Effect,” Fiz. Goreniya Vzryva 49 (3), 22–33 (2013) [Combust., Expl., Shock Waves 49 (3), 273–282 (2013)].

    Google Scholar 

  12. K. O. Sabdenov, V. E. Zarko, and M. Erzada, “Nature and Calculation of Erosive Burning Rate of a Solid Propellant,” Inzh. Zh.: Nauka Innovatsii 4 (16) (2013); http://engjournal.ru/catalog/machin/rocket/710.html.

    Google Scholar 

  13. K. O. Sabdenov and M. Erzada, “Analytical Calculation of the Negative Erosive Burning Rate,” Fiz. Goreniya Vzryva 49 (6), 76–86 (2013) [Combust., Expl., Shock Waves 49 (6), 690–699 (2013)].

    Google Scholar 

  14. D. I. Abugov and V. M. Bobylev, Theory and Calculation of Solid Rocket Motor Fuel (Mashinostroenie, Moscow, 1987) [in Russian].

    Google Scholar 

  15. M. Barrere, A. Jaumotte, B. F. de Veubeke, and J. Vandenkerckhove, Rocket Propulsion (Elsevier, Amsterdam, 1960).

    Google Scholar 

  16. L. G. Loitsyanskii, Mechanics of Liquids and Gases (Nauka, Moscow, 1987; Pergamon Press, Oxford–New York, 1966).

    MATH  Google Scholar 

  17. K. O. Sabdenov, Unstable Combustion of Solid Propellants. Problems and Success of Simulation (Lambert Acad. Publ., Saarbrucken, Germany, 2012).

    Google Scholar 

  18. K. O. Sabdenov and M. Erzada, “Negative Erosion Effect and the Emergence of Unstable Combustion. 1. Analysis of the models,” Fiz. Goreniya Vzryva 52 (1), 76–83 (2016) [Combust., Expl., Shock Waves 52 (1), 67–73 (2016)].

    Google Scholar 

  19. A. G. Merzhanov and F. I. Dubovitskii, “Theory of Stable Powder Combustion,” Dokl. Akad. Nauk SSSR 129, 153–156 (1959).

    Google Scholar 

  20. B. V. Novozhilov, Unsteady Combustion of Solid Propellants (Nauka, Moscow, 1973) [in Russian].

    Google Scholar 

  21. M. R. Denison and E. Baum, “A Simplified Model of Instable Burning in Solid Propellant,” AIAA J. 31 (8), 1112–1132 (1961).

    MATH  Google Scholar 

  22. D. M. Boskovic and M. Krstic, “Stabilization of a Solid Propellant Rocket Instability by State Feedback,” Int. J. Robust and Nonlinear Control. 13, 483–495 (2003); DOI: 10.1002/rnc.732.

    Article  MathSciNet  MATH  Google Scholar 

  23. K. O. Sabdenov and M. Erzada, “Equation for Prandtls Mixing Length,” Frontiers in Aerospace Eng. 3 (2), 50–55 (2014).

    Article  Google Scholar 

  24. A. A. Samarskii and A. V. Gulin, Numerical Methods (Nauka, Moscow, 1989) [in Russian].

    Google Scholar 

  25. B. V. Novozhilov, “Effect of Gas Phase Inertia on the Combustion Stability of Volatile Condensed Systems,” Khim. Fiz. 7 (3), 388–396 (1988).

    MathSciNet  Google Scholar 

  26. S. S. Kutateladze and A. I. Leont’ev, Heat and Mass Transfer and Friction in a Turbulent Boundary Layer (Energoatomizdat, Moscow, 1985) [in Russian].

    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. 52, No. 2, pp. 76–87, March–April, 2016.

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Sabdenov, K.O., Erzada, M. Negative erosion effect and the emergence of unstable combustion. 2. numerical simulation. Combust Explos Shock Waves 52, 193–202 (2016). https://doi.org/10.1134/S001050821602009X

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  • DOI: https://doi.org/10.1134/S001050821602009X

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