Convective Scaling of Intrinsic Thermo-Acoustic Eigenfrequencies of a Premixed Swirl Combustor

Spectral distributions of the sound pressure level (SPL) observed in a premixed, swirl stabilized combustion test rig are scrutinized. Spectral peaks in the SPL for stable as well as unstable cases are interpreted with the help of a novel criterion for the resonance frequencies of the intrinsic thermo-acoustic (ITA) feedback loop. This criterion takes into the account the flow inertia of the burner and indicates that in the limit of very large flow inertia, ITA resonance should appear at frequencies where the phase of the flame transfer function (FTF) approaches $−π/2$⁠. Conversely, in the limiting case of vanishing flow inertia, the new criterion agrees with previous results, which state that ITA modes may arise when the phase of the FTF is close to $−π$⁠. Relying on the novel criterion, peaks in the SPL spectra are identified to correspond to either ITA or acoustic modes. Various combustor configurations are investigated over a range of operating conditions. It is found that in this particular combustor, ITA modes are prevalent and dominate the unstable cases. Remarkably, the ITA frequencies change significantly with the bulk flow velocity and the position of the swirler but are almost insensitive to changes in the length of the combustion chamber (CC). These observations imply that the resonance frequencies of the ITA feedback loop are governed by convective time scales. A scaling rule for ITA frequencies that relies on a model for the overall convective flame time lag shows good consistency for all operating conditions considered in this study.