Linear wave dynamics and intrinsic axisymmetric thermoacoustic instability in swirling flame combustors

Abstract This paper investigates the intrinsic thermoacoustic (ITA) feedback and its possible interaction with the cavity acoustic resonance in swirling flame combustors under the configuration of axisymmetric perturbations. The dynamics of acoustic-vortical-entropic perturbations due to the unsteady heat release rate by a swirling flame are given in the presence of azimuthal and axial base flow velocities. The critical gain of ITA oscillations is given meanwhile parametric analysis show that the phase shift between acoustic and vortical waves plays an important role on the ITA critical gain. Applied to the configuration of a plenum-swirler-chamber combustor with the presence of swirling flames, the present work predicts correctly the thermoacoustic oscillations. Meanwhile, the criterion of ITA modes is given in matrix form. Analysis on the interaction between the ITA feedback and the cavity acoustic resonant feedback shows that the thermoacoustic modes of the whole system are composed of both ITA-oriented modes and the cavity-oriented resonant modes. Increasing the transit time difference between the acoustic and vortical waves reduces frequencies of ITA and ITA-oriented modes and worsens their stabilities. The cavity-oriented thermoacoustic mode, on the other hand, forms a spiral orbit and approaches to an attractor, which is independent of the transit time difference.