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.

本文研究了用于推导湍流燃烧室热声不稳定性和热声间歇性低阶模型的简化假设。这些模型包括受参数和加性随机强迫作用的自持振荡器。在本工作中研究的热声动力学的主要方面是声压与放热速率振荡之间的相位，以及支配火焰响应饱和的非线性。我们提出了一个耦合声振荡器的模型，该模型受到来自火焰的非线性源项的延迟，具有参数和加性随机强迫。该模型定性地再现了实验观察到的热声动力学，包括在超临界Hopf分叉附近的间歇性，以及声压的全部频谱特征。还表明，由单个Van der Pol振荡器组成的更简单的模型能够捕获基本振荡频率下的热声耦合的基本方面，并且可以作为有效估计系统线性增长率的基础通过仅输出识别方法。