Experimental Investigation of Interactions Between Two Closely Spaced Azimuthal Modes in a Multi-Nozzle Can Combustor

Abstract

Abstract Thermoacoustic instabilities in annular or circular combustors are often coupled with azimuthal modes. These modes can be characterized by a spin ratio, which quantifies the dominant mode between two counter-rotating waves, and a phase difference between them, which is directly related to the orientation of the anti-nodal line. This study investigates the instability amplitudes, spin ratio, and phase difference of two closely spaced (3% frequency difference), yet distinct azimuthal modes; one is the first azimuthal (1A) mode, and the other is a combination of first azimuthal and first longitudinal (1A1L) mode. Each mode itself consists of two peaks that are spaced even more closely in frequency (0.8% difference). Furthermore, distinct harmonics at 2X and 3X of these frequencies, presumably associated with nonlinearities, are also evident in the spectra. Each mode is band-pass filtered in spectrum to analyze them separately. For the 1A mode, the spin ratio and phase difference exhibit a variety of behaviors — including quasi-periodic standing waves, spinning waves, and intermittency — depending on operating conditions such as thermal power and azimuthal fuel staging. Similar trends are observed for the 1A1L mode. Moreover, there is clear coupling between the 1A and 1A1L modes, as their spin ratios are almost synchronized during the quasi-periodic standing wave. This synchronization is observed in phase differences as well, but not in the instability amplitude. For spinning dominant wave conditions, the spin ratio and phase difference of the two modes fluctuate in a seemingly random fashion, but the instability amplitudes are correlated, with modulation of the 1A mode leading that of the 1A1L mode. These results clearly indicate that complex coupling occurs across closely spaced and harmonically space frequencies under instability conditions, coupling that must be understood in order to capture limit cycle dynamics.