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.
Similar content being viewed by others
References
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)].
F. A. Williams, Combustion Theory (Addison-Wesley, 1965).
H. S. Mukunda, “A Comprehensive Theory of Erosive Burning in Solid Rocket Propellants,” Combust. Sci. Technol. 18 (3–4), 105–118 (1978).
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)].
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)].
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)].
D. R. Greatrix, “Model for Prediction of Negative and Positive Erosive Burning,” Canad. Aeronaut. Space J. 53 (1), 13–21 (2007).
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.
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).
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)].
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)].
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.
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)].
D. I. Abugov and V. M. Bobylev, Theory and Calculation of Solid Rocket Motor Fuel (Mashinostroenie, Moscow, 1987) [in Russian].
M. Barrere, A. Jaumotte, B. F. de Veubeke, and J. Vandenkerckhove, Rocket Propulsion (Elsevier, Amsterdam, 1960).
L. G. Loitsyanskii, Mechanics of Liquids and Gases (Nauka, Moscow, 1987; Pergamon Press, Oxford–New York, 1966).
K. O. Sabdenov, Unstable Combustion of Solid Propellants. Problems and Success of Simulation (Lambert Acad. Publ., Saarbrucken, Germany, 2012).
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)].
A. G. Merzhanov and F. I. Dubovitskii, “Theory of Stable Powder Combustion,” Dokl. Akad. Nauk SSSR 129, 153–156 (1959).
B. V. Novozhilov, Unsteady Combustion of Solid Propellants (Nauka, Moscow, 1973) [in Russian].
M. R. Denison and E. Baum, “A Simplified Model of Instable Burning in Solid Propellant,” AIAA J. 31 (8), 1112–1132 (1961).
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.
K. O. Sabdenov and M. Erzada, “Equation for Prandtls Mixing Length,” Frontiers in Aerospace Eng. 3 (2), 50–55 (2014).
A. A. Samarskii and A. V. Gulin, Numerical Methods (Nauka, Moscow, 1989) [in Russian].
B. V. Novozhilov, “Effect of Gas Phase Inertia on the Combustion Stability of Volatile Condensed Systems,” Khim. Fiz. 7 (3), 388–396 (1988).
S. S. Kutateladze and A. I. Leont’ev, Heat and Mass Transfer and Friction in a Turbulent Boundary Layer (Energoatomizdat, Moscow, 1985) [in Russian].
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © K.O. Sabdenov, M. Erzada.
Published in Fizika Goreniya i Vzryva, Vol. 52, No. 2, pp. 76–87, March–April, 2016.
Rights and permissions
About this article
Cite this article
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
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S001050821602009X