Significance of the Direct Excitation Mechanism for High-Frequency Response of Premixed Flames to Flow Oscillations

Premixed flames are sensitive to flow disturbances, which can arise from acoustic or vortical fluctuations. For transverse instabilities, it is known that a dominant mechanism for flame response is “injector coupling”, whereby pressure oscillations associated with transverse waves excite axial flow disturbances. These axial flow disturbances then excite heat release oscillations. The objective of this paper is to consider another mechanism — the direct sensitivity of the unsteady heat release to transverse acoustic waves, and to compare its significance relative to the induced axial disturbances, in a linear framework. The rate at which the flame adds energy to the disturbance field is quantified using the Rayleigh criterion and evaluated over a range of control parameters, such as flame length and swirl number. The results show that radial modes induce heat release fluctuations that always add energy to the acoustic field, whereas heat release fluctuations induced by mixed radial-azimuthal modes can add or remove energy. These amplification rates are then compared to the flame response from induced axial fluctuations. For combustor centered flames, these results show that the direct excitation mechanism has negligible amplification rates relative to the induced axial mechanism for radial modes. For transverse modes, the fact that the nozzle is located at a pressure node indicates that negligible induced axial velocity disturbances are excited; as such, the direct mechanism dominates. For flames that are not centered on pressure nodes, the direct mechanism for mixed-modes, dominates for certain nozzle locations and flame angles.