Abstract
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.
Highlights
Thermoacoustic instabilities are a major issue in the development of new aeroengines combustion chambers aligned with the current ecological challenges because they induce vibrations that can severely damage the combustor and the turbine
Based on acoustic measurements in the combustors of practical gas turbines [2, 3], in academic annular chambers [4,5,6] and on high fidelity numerical simulations [7], these self-sustained azimuthal thermoacoustic modes have been classified as spinning modes that propagate at the speed of sound in the clockwise or the anticlockwise direction, standing modes whose nodal line stays at a constant azimuthal position or drifts slowly compared to the speed of sound, or mixed modes that result from the sum of a standing mode and a spinning mode
This paper aims at filling this gap with new experimental data and a loworder model, which is derived from first principles and describes the stochastic dynamics of these transitions in the same way as thermally activated barrier crossing in reaction rate theory [14]
Summary
Thermoacoustic instabilities are a major issue in the development of new aeroengines combustion chambers aligned with the current ecological challenges because they induce vibrations that can severely damage the combustor and the turbine. The seriousness of this problem lies in the fact that despite decades of intense research, these instabilities are still very difficult to predict, which calls for further advances in their modelling and understanding [1]. The present study falls within this context and deals with the modelling of an intriguing phenomenon occuring in annular aeroengine combustors: the intermittent transitions between clockwise and counterclockwise spinning thermoacoustic modes.
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