Nonlinear interactions between the fundamental and its harmonics of self-excited azimuthal thermoacoustic instabilities

Abstract

Thermoacoustic instabilities in combustors are inherently nonlinear processes, manifested by multiple peaks in the spectrum. Analyzing these signals is crucial to understand the mechanism of nonlinear limit cycle oscillations. The goal of this study is to investigate the acoustic modal dynamic relation between the fundamental of azimuthal instabilities and its first harmonic. The paper first demonstrates that the nonlinear interaction of the fundamental azimuthal mode produces not only higher order azimuthal modes but also an axial mode in the harmonic. This is confirmed by the experimental data showing a correlation between the axial mode in the harmonic and two counter-rotating modes in the fundamental. Furthermore, the study shows that neglecting this axial mode may result in inaccurate estimation of the maximum pressure in the chamber, potentially leading to safety concern. The combustor is operated under various conditions to examine the correlation between the fundamental and its harmonic in terms of dominant spinning direction, orientation of the acoustic structure, and the maximum pressure magnitude. It is found that the azimuthal components of the fundamental and its harmonic rotate in the same direction under a wide range of operating conditions. Additionally, the maximum pressure magnitudes are positively correlated with each other despite the difference in the order of magnitude between them. Specifically, the harmonic's magnitude shows quadratic dependence on the fundamental's, even when the mode transitions from a standing wave to a spinning wave. However, the anti-node locations of the fundamental and its harmonic exhibit no correlation, and their difference in location varies with operating conditions.