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

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.

Automated summary

A nonlinear phenomenological model consisting of two coupled oscillators is proposed to describe the rich nonlinear behavior of a simple combustion system. The model accurately reproduces the different observed regimes, including supercritical Hopf bifurcation, limit cycle, quasi-periodic, and period-2 limit cycle oscillations. Parameter estimation shows a good quantitative match between the model response and experimental data, suggesting that the model effectively captures the nonlinear self-excited acoustic behavior of premixed flames.