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Thermoacoustic instability has been an important challenge in the development of high-performance combustion systems, as it can have catastrophic consequences. The process of a sudden change in the dynamical behavior of a thermoacoustic system from a low- to high-amplitude thermoacoustic instability actually entails as a tipping point phenomenon. It has been found that when rate-dependent parameters are considered, a tipping-delay phenomenon may arise, which helps in the control of undesirable states that give rise to thermoacoustic instabilities. This work aims at understanding rate-dependent tipping dynamics of the thermoacoustic system with both time-varying parameters and a non-Gaussian Lévy noise. The latter better describes the severe operating environment of such systems than simpler types of noise. Through numerical simulations, the tipping dynamical behavior is analyzed by considering the rate-dependent parameters coupled with the main parameters of the Lévy noise, including the stability and skewness indices and the noise intensity. In addition, we investigate the effectiveness of early warning indicators in rate-dependent systems under Lévy noise excitation and uncover a relationship between warning measures and the rate of change in the parameters. These results inform and enlighten the development and design of power combustion devices and also provide researchers and engineers with effective ideas to control thermoacoustic instability and the associated tipping dynamics.
Thermoacoustic systems are closely related to propulsion combustion devices such as solid and liquid rocket motors, aero engines, and gas turbines. A thermoacoustic instability arises when there is a positive feedback between the non-constant exothermic rate in the combustion chamber and the acoustic field. Thermoacoustic instabilities lead to self-excited large amplitude pressure oscillations in the combustion chamber. These typically undesirable pressure oscillations can lead to catastrophic consequences such as structural damage due to excessive heat transfer and vibration, ballistic anomalies in the engine, damage to electronic equipment in aircrafts and satellites, and even to rocket launch missions due to engine disintegration. Therefore, the occurrence of thermoacoustic instability has been a major problem faced during the development of high-performance combustion systems. So far, studies of the thermoacoustic instability are limited to the excitation of Gaussian noise, which has limitations in describing large jumps. However, the effect of extreme severe operating environments on thermoacoustic instability cannot be ignored. Therefore, it is crucial to introduce a more appropriate noise portrayal in the study: non-Gaussian Lévy noise. Considering that the control parameters in real industrial thermoacoustic systems are time-varying, this work provides referenceable control strategies and early warning signals for thermoacoustic instability avoidance based on the rate-dependent mathematical model of thermoacoustic systems.
