Low order modelling of thermoacoustic instabilities and intermittency: Flame response delay and nonlinearity

This paper investigates the simplifying assumptions used for deriving low order models of thermoacoustic instabilities and thermoacoustic intermittency in turbulent combustor. These models consists in self-sustained oscillators subject to parametric and additive stochastic forcing. The main aspects of the thermoacoustic dynamics investigated in the present work are the phase between acoustic pressure and heat release rate oscillations, and the nonlinearity ruling the saturation of the flame response. We propose a model of coupled acoustic oscillators subject to delayed nonlinear source term from the flame, with parametric and additive stochastic forcing. This model qualitatively reproduces the experimentally observed thermoacoustic dynamics, including the intermittency in the vicinity of supercritical Hopf bifurcations, as well as the full spectral signature of the acoustic pressure. It is also shown that a simpler model, consisting of a single Van der Pol oscillator, is capable of capturing the essential aspects of the thermoacoustic coupling at the fundamental oscillation frequency and can serve as a basis for an effective estimation of the system’s linear growth rate via output-only identification methods.