Abstract

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Annular combustion chambers of gas turbines and aircraft engines are subject to unstable azimuthal thermoacoustic modes leading to high amplitude acoustic waves propagating in the azimuthal direction. For certain operating conditions, the propagating direction of the wave switches randomly. The strong turbulent noise prevailing in gas turbine combustors is a source of random excitation for the thermoacoustic modes and can be the cause of these switching events. A low-order model is proposed to describe qualitatively this property of the dynamics of thermoacoustic azimuthal modes. This model is based on the acoustic wave equation with a destabilizing thermoacoustic source term to account for the flame's response and a stochastic term to account for the turbulent combustion noise. Slow-flow averaging is applied to describe the modal dynamics on times scales that are slower than the acoustic pulsation. Under certain conditions, the model reduces formally to a Fokker-Planck equation describing a stochastic diffusion process in a potential landscape with two symmetric wells: One well corresponds to a mode propagating in the clockwise direction, the other well corresponds to a mode propagating in the anticlockwise direction. When the level of turbulent noise is sufficient, the stochastic force makes the mode jump from one well to the other at random times, reproducing the phenomenon of direction switching. Experiments were conducted on a laboratory scale annular combustor featuring 12 hydrogen-methan flames. System identification techniques were used to fit the model on the experimental data, allowing to extract the potential shape and the intensity of the stochastic excitation. The statistical predictions obtained from the Fokker-Planck equation on the mode's behaviour and the direction switching time are in good agreement with the experiments.

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This article deals with the symmetry breaking of azimuthal thermoacoustic modes in annular combustors. Using a nominally symmetric annular combustor, we present experimental evidence of a predicted spontaneous reflectional symmetry breaking, and also an unexpected explicit rotational symmetry breaking in the neighbourhood of the Hopf bifurcation which separates linearly stable azimuthal thermoacoustic modes from self-oscillating modes. We derive and solve a multidimensional Fokker–Planck equation to unravel a unified picture of the phase space topology. We demonstrate that symmetric probability density functions of the thermoacoustic state vector are elusive, because the effect of asymmetries, even imperceptible ones, is magnified close to the bifurcation. This conclusion implies that the thermoacoustic oscillations of azimuthal modes in real combustors will systematically exhibit a statistically dominant orientation of the mode in the vicinity of the Hopf bifurcation.

In this paper we investigate how supervised machine learning can be leveraged to improve online prediction of thermoacoustic combustion instabilities using dynamic pressure readings. We discuss the current state of the art tools for the online detection of combustion instabilities, namely the Hurst exponent and Auto-Regressive model, the precursors they detect and how they go about doing so. We show that the generality of these tools comes at the cost of predictive power, which can be recovered using supervised machine learning. To demonstrate this we apply two different supervised machine learning approaches (using Hidden Markov Models and Automatic Machine Learning) to the classification of the state of a combustor given the dynamic pressure readings. We then observe the changes in predictive power when different information is added or removed from the signal. We find that the HMM based approach reduces to the AR model when the signal is normalised. We also find that the performance of a model trained on a signal transformed using the Detrended Fluctuation Analysis (DFA) can be met by a model trained on the Hurst exponent and the DFA transformation at a single (short) scale.

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