Estimating method for azimuthal thermoacoustic mode in annular combustors

Combustion instabilities can excite various thermoacoustic modes. Once the mode is identified, it becomes possible to estimate the overall pressure field or its maximum magnitude. However, determining the specific mode of being excited remains a challenging problem. Methods that estimate the thermoacoustic modes solely based on experimental measurements are essential. This paper focuses on azimuthal modes in annular combustors and proposes a method for estimating the mode order by minimizing residuals using the least squares approach with fewer sensors. The effectiveness and accuracy of this method are verified through simulations under various disturbances. When the estimated mode order aligns with the actual dominant mode order, the residual is minimized. Even under disturbances such as random noise and non-dominant modes, the dominant mode order can still be accurately estimated, with the residual indicating the dominance of the primary mode over the disturbance terms.