Predicting the Amplitude of Thermoacoustic Instability Using Universal Scaling Behavior

Abstract

The complex interaction between the turbulent flow, combustion and the acoustic field in gas turbine engines often results in thermoacoustic instability that produces ruinously high-amplitude pressure oscillations. These self-sustained periodic oscillations may result in a sudden failure of engine components and associated electronics, and increased thermal and vibrational loads. Estimating the amplitude of the limit cycle oscillations (LCO) that are expected during thermoacoustic instability helps in devising strategies to mitigate and to limit the possible damages due to thermoacoustic instability. We propose two methodologies to estimate the amplitude using only the pressure measurements acquired during stable operation. First, we use the universal scaling relation of the amplitude of the dominant mode of oscillations with the Hurst exponent to predict the amplitude of the LCO. We also present a methodology to estimate the amplitudes of different modes of oscillations separately using ''spectral measures' which quantify the sharpening of peaks in the amplitude spectrum. The scaling relation enables us to predict the peak amplitude at thermoacoustic instability, given the data during the safe operating condition. The accuracy of prediction is tested for both methods, using the data acquired from a laboratory-scale turbulent combustor. The estimates are in good agreement with the actual amplitudes.

Universality of oscillatory instabilities in fluid mechanical systems

“…Recently, it was reported that the amplitude A of the dominant mode of oscillations increases and follows a universal scaling law A ∝ H −2.0±0.2 [15]. A spectral measure µ, which quantifies the sharpening of peaks in the power spectrum as the system dynamics approaches OI, has also been introduced and another universal scaling law A ∝ µ −0.66±0.10 [37,38] has been discovered. In both cases, the scaling exponents are invariant across aero-acoustic, thermoacoustic and aeroelastic systems.…”