Amplitude statistics prediction in thermoacoustics

Abstract

We discuss the statistics of acoustic pressure of thermoacoustic oscillations, either axial or azimuthal in nature. We derive a model where the describing functions of the fluctuating heat release rate of the flame and of the acoustic losses appear directly in the equations. The background combustion noise is assumed to be additive, and we show how one can recover, from the measurement of the acoustic pressure at the flame location, the projected describing function of the flame minus the acoustic losses. Using the same equations, one can predict the statistics of the amplitude of acoustic pressure for a certain system. The theory is then tested on an azimuthal thermoacoustic instability in an industrial annular combustor by measuring the state of the system, predicting the acoustic pressure amplitude statistics after a design change and comparing the prediction with the measured statistics after the design change has been implemented.