The complex interaction of turbulent flow, combustion and acoustic field in gas turbine engines often results in thermoacoustic instability that produces ruinously high-amplitude pressure oscillations. These self-sustained periodic oscillations often leads to a sudden failure of engine components and associated electronics, increased thermal and vibrational loads. Traditionally, thermoacoustic instability was believed to be an abrupt transition to periodic oscillations as control parameters are varied. Recent studies revealed that in turbulent systems, the onset of thermoacoustic instability is presaged by a state of intermittency. Quantifying this intermittency provides precursors to thermoacoustic instability so that appropriate stability margins may be devised.The aim of this study is to estimate the amplitude of the limit-cycle oscillations (LCO) observed during thermoacoustic instability. Previous works utilize the flame describing function (FDF) to estimate the amplitude and frequency of LCO. However, forcing the system at high amplitudes to obtain FDF may be difficult and undesirable for industrial engines. We propose a methodology to estimate the amplitude using only the pressure measurements during the stable operation.We quantify the fractal characteristics of a state variable such as acoustic pressure at different operating conditions using a measure known as Hurst exponent (H), which is related to the memory in the signal. While the amplitude of pressure fluctuations increases abruptly near the onset of the thermoacoustic instability, H decreases smoothly and relatively much earlier than the rise in amplitude. We have shown in a recent study that the amplitude of dominant mode of oscillations follows an inverse power law with the Hurst exponent. Further, this power law exponent is found to be constant for various configurations of thermoacoustic system. In the current study, we use this concept to predict the amplitude of the LCO during thermoacoustic instability. As all the data collapse to a single power law irrespective of the frequency of oscillations or the underlying physics of the problem, we estimate the amplitude of LCO by extrapolating the power law relation towards H tending to zero.We also present a methodology to separately estimate the amplitudes of different modes of oscillations using spectral measures which quantify the sharpening of peaks in the power spectrum. The spectral measures are calculated as the product of different moments of the normalized power spectrum raised to integer powers, and they follow inverse power law relations with the corresponding peak power. Once we have the time series of acoustic pressure oscillations during the stable operation, we generate the power spectrum and identify all the possible modes that are expected to grow. The scaling relation enables us to predict the peak power at thermoacoustic instability, given the value of spectral measures and the peak power at the safe operating condition. Knowing beforehand the amplitudes of oscillations that are expected during thermoacoustic instability helps in devising strategies to mitigate thermoacoustic instability and also helps in testing the hardware more economically.

Predicting the Amplitude of Thermoacoustic Instability Using Universal Scaling Behaviour

Paper Proceedings: https://asmedigitalcollection.asme.org/GT/GT2021/volume/84898

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