Nonlinear analysis of self-sustained oscillations in an annular combustor model with electroacoustic feedback

Self-excited pressure oscillations can occur in combustion systems due to the thermoacoustic coupling between the unsteady acoustics and flame heat release fluctuations. Usually, the knowledge of a Flame Transfer Function is used to predict the onset of thermoacoustic instabilities. However, it is also possible to take advantage of it to model a flame response and study experimentally thermoacoustic phenomena without flames. This is exploited in the present study, in which a novel annular setup for the study of thermoacoustics in annular combustors is presented. The thermoacoustic feedback is replaced by electroacoustic feedback. The pressure fluctuations, measured by a microphone, are delayed and filtered and then sent to a loudspeaker, which produces acoustic perturbations, closing the loop. Each flame model parameter can be varied in a flexible way, which allows to choose combinations of parameters that generate modal behaviours of interest in the experiments. For example, this setup can trigger on demand various configurations which exhibit multiple unstable modes, leading to diverse modal competition scenarios. This allows to assess the multi-input Describing Function method, which is used to predict the frequency and amplitude of each mode contributing to thermoacoustic oscillations, when multiple modes are linearly unstable. The experimental validation of predictions from this method, which can be somewhat cumbersome and expensive in the presence of flames, is facilitated by this setup, in which all parameters and boundary conditions are well known and the noise remains negligible. Prediction uncertainties connected to approximations intrinsic of this method when operating in the vicinity of bifurcation points are also discussed.