Parameter estimation of two coupled oscillator model for pure intrinsic thermo-acoustic instability

• Published in: Nonlinear dynamics Vol. 111; no. 14; pp. 12835 - 12853
• Main Authors: Wildemans, Roeland, Kornilov, Viktor, Lopez Arteaga, Ines
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01-07-2023; Springer Nature B.V
• Subjects: Acoustic instability; Acoustics; Automotive Engineering; Classical Mechanics; Control; Coupled nonlinear oscillators; Dynamic models; Dynamical Systems; Engineering; Flame dynamics; Frequency modulation; Hopf bifurcation; Intrinsic thermo-acoustics instability; Limit cycle oscillations; Mechanical Engineering; Original Paper; Oscillators; Parameter estimation; Premixed flames; Quasi-Periodic Oscillations; Vibration; Flame dynamics; Intrinsic thermo-acoustics instability; Parameter estimation; Coupled nonlinear oscillators
• ISSN: 0924-090X; 1573-269X; 1573-269X
• DOI: 10.1007/s11071-023-08541-4

A nonlinear phenomenological model of two coupled oscillators is proposed, which is able to describe the rich nonlinear behaviour stemming from an unstable pure intrinsic thermo-acoustic (ITA) mode of a simple combustion system. In an experimental bifurcation analysis of a pure ITA mode, it was observed that for increasing mean upstream velocity the flames loose stability through a supercritical Hopf bifurcation and subsequently exhibit limit cycle, quasi-periodic and period-2 limit cycle oscillations. The quasi-periodic oscillations were characterised by low frequent amplitude and frequency modulation. It is shown that a phenomenological model consisting of two coupled oscillators is able to reproduce qualitatively all the different experimentally observed regimes. This model consists of a nonlinear Van der Pol oscillator and a linear damped oscillator, which are nonlinearly coupled to each other. Furthermore, a parameter estimation of the model parameters is conducted, which reveals a good quantitative match between the model response and the experimental data. Hence, the presented phenomenological dynamical model accurately describes the nonlinear self-excited acoustic behaviour of premixed flames and provides a promising model structure for nonlinear time-domain flame models.