Abstract
This paper analyzes the dynamics of unstable azimuthal thermoacoustic modes in a lean premixed combustor. Azimuthal modes can be decomposed into two counter rotating waves where they can either compete and potentially suppress one of them (spinning) or coexist (standing), depending on the operating conditions. This paper describes experimental results of the dynamical behaviors of these two waves. The experimental data were taken at different mass flow rates as well as different azimuthal fuel staging in a multi-nozzle can combustor. It is shown that at a low flow rate with uniform fuel distribution, the two waves have similar amplitudes, giving rise to a standing wave. However, the two amplitudes are slowly oscillating out of phase to each other, and the phase difference between the two waves also shows oscillatory behavior. For an intermediate flow rate, the dynamics show intermittency between standing and spinning waves, indicating that the system is bistable. In addition, the phase difference dramatically shifts when the mode switches between standing and spinning waves. For a high flow rate, the system stabilizes at a spinning wave most of the time. These experimental observations demonstrate that not only the amplitudes of two waves but also the phase difference plays an important role in the dynamics of azimuthal mode. For non-uniform azimuthal fuel staging, the modal dynamics exhibit only an oscillatory standing wave behavior regardless of the mass flow rate. Compared to the uniform fuel staging, however, the pressure magnitude is considerably reduced, which provides a potential strategy to mitigate and/or suppress the instabilities.
Two-to-one resonant multi-modal dynamics of horizontal/inclined cables. Part I: Theoretical formulation and model validation
