Thermoacoustic instabilities occur in a wide range of combustors when one or several flames act as sources of acoustic energy that are not countervailed by acoustic damping inside and at the boundaries of the system. These instabilities are prejudicial since they can lead to increased mechanical fatigue or even catastrophic failure. A well-established formalism to predict the onset, growth and saturation of such instabilities is based on acoustic network models where the system is represented by a sequence of connected acoustic modules. Each module, represented by a 2x2 matrix called Scattering matrix or S-matrix, relates the ingoing and outgoing Riemann invariants across the module. For given acoustic boundary conditions, the thermoacoustic modes of the combustor are then determined by searching for the complex roots of a characteristic equation. The real and imaginary parts of these solutions correspond to the frequency and growth rate of the modes respectively. This approach has been successfully employed to predict the frequency and amplitude of limit cycle oscillations in a variety of combustors. However, the acoustic energy balance of the system during the onset, growth and saturation of these modes has not yet been systematically studied. The objective of this work is to propose a new physical interpretation of this pre-existing formalism using the acoustic absorption coefficient. In addition to the frequency and growth rate of the thermoacoustic modes, the absorption coefficient is employed to quantify the amount of acoustic amplification or damping across the combustor for each mode and each oscillation level.


Acoustic Energy Balance During the Onset, Growth and Saturation of Thermoacoustic Instabilities

Division / Sponsor:
International Gas Turbine Institute (IGTI)

Paper Proceedings: https://asmedigitalcollection.asme.org/GT/GT2020/volume/84058

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