[01] B. I. Basok, Department of Thermophysical Fundamentals of Energy-Saving Technologies, Institute of Engineering Thermal Physics of NAS of Ukraine, Kiev, Ukraine. [02] V. V. Gotsulenko, Department of Thermophysical Fundamentals of Energy-Saving Technologies, Institute of Engineering Thermal Physics of NAS of Ukraine, Kiev, Ukraine.

Self-oscillations and certain of their regularities determined by solution of a system of differential equations with variable delay argument equations that is used in considering combustion instability in combustion chambers of liquid-propellant rocket engines are modeled mathematically. Periodic solutions of the system of equations of nonstationary motion of a medium in a liquid-propellant rocket engine were obtained, with the aid of which the possibility of lowering the amplitude of the longitudinal self-oscillations of vibration combustion or their complete removal has been substantiated. Analytically determined critical time delay combustion, above which a stationary combustion becomes unstable and self-excited oscillations.

Vibration Combustion, Instability, Self - Oscillation, Limiting Cycle, the Time Delay of Combustion

[01] 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). [02] V. V. Gotsulenko, Special modes of the Rijke phenomenon, Inzh.-Fiz. Zh., 16, No. 9, 160–164 (2005). [03] V. V. Gotsulenko, Mathematical modeling of the decrease in the amplitudes of vibrations of vibrational combustion in large industrial units, Mat. Modelir., 17, No. 11, 16–24 (2005). [04] Ya. B. Zel’dovich, O. I. Leipunskii, and V. B. Librovich, Theory of Nonstationary Combustion of Gunpowder [in Russian], Nauka, Moscow (1975). [05] M. S. Natanzon, Instability of Combustion [in Russian], Mashinostroenie, Moscow (1986). [06] K. I. Artamonov, Thermoacoustic Stability [in Russian], Mashinostroenie, Moscow (1982). [07] L. Crocco and Sin-I Cheng, Theory of Combustion Instability in Liquid-Propellant Rocket Engines [Russian translation], IL, Moscow (1958). [08] V. V. Gotsulenko and V. N. Gotsulenko, Mathematical modeling of the self-oscillations of vibrational combustion in liquid-propellant rocket engines due to combustion heat release, Mat. Modelyuv. (Dneprodzerzhinsk Gos. Tekh. Univ.), No. 1, 2 (15), 16–24 (2006). [09] Gotsulenko V. V. and Gotsulenko V. N. On the Problem of Control of the Amplitude of Self-Oscillations of a Singing Flame // Journal of Engineering Physics and Thermophysics, Volume 87, Issue 2, 319–324 (2014). [10] B. I. Basok and V.V. Gotsulenko, Negative thermal resistance in one-dimensional steady inviscid flow of a perfect gas, Journal of the Moscow physical-technical Institute, Vol 6, No. 4(24), 153–157 (2014). [11] Basok B. I. and Gotsulenko V.V. Calculating the Parameters of Self - Oscillations in the Vertical Combustion Chamber of the Blast - Furnace Air Heater during Unstable Combustion // Thermal Engineering, Vol. 62, No. 1, 58–63 (2015).