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For velocity sensitive premixed flames, intrinsic thermoacoustic (ITA) feedback results from flow-flame-acoustic interactions as follows: perturbations of velocity upstream of the flame result in modulations of the heat release rate, which in turn generate acoustic waves that travel in the downstream as well as the upstream direction. The latter perturb again the upstream velocity, and thus close the ITA feedback loop. This feedback mechanism exhibits resonance frequencies that are not related to acoustic eigenfrequencies of a combustor and generates — in additional to acoustic modes — so-called ITA modes. In this work spectral distributions of the sound pressure level (SPL) observed in a perfectly premixed, swirl stabilized combustion test rig are analyzed. Various burner configurations and operating points are investigated. Spectral peaks in the SPL data for stable as well as for unstable cases are interpreted with the help of a newly developed simple criterion for the prediction of burner intrinsic ITA modes. This criterion extends the known −π measure for the flame transfer function (FTF) by including the burner acoustic. This way, the peaks in the SPL spectra are identified to correspond to either ITA or acoustic modes. It is found that ITA modes are prevalent in this particular combustor. Their frequencies change significantly with the power rating (bulk flow velocity) and the axial position of the swirler, but are insensitive to changes in the length of the combustion chamber. It is argued that the resonance frequencies of the ITA feedback loop are governed by convective time scales. For that reason, they arise at rather low frequencies, which scale with the bulk flow velocity.

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Acoustic waves passing through a swirler generate inertial waves in rotating flow. In the present study, the response of a premixed flame to an inertial wave is scrutinized, with emphasis on the fundamental fluid-dynamic and flame-kinematic interaction mechanism. The analysis relies on linearized reactive flow equations, with a two-part solution strategy implemented in a finite element framework: Firstly, the steady state, low-Mach number, Navier-Stokes equations with Arrhenius type one-step reaction mechanism are solved by Newton's method. The flame impulse response is then computed by transient solution of the analytically linearized reactive flow equations in the time domain, with mean flow quantities provided by the steady-state solution. The corresponding flame transfer function is retrieved by fitting a finite impulse response model. This approach is validated against experiments for a perfectly premixed, lean, methane-air Bunsen flame, and then applied to a laminar swirling flame. This academic case serves to investigate in a generic manner the impact of an inertial wave on the flame response. The structure of the inertial wave is characterized by modal decomposition. It is shown that axial and radial velocity fluctuations related to the eigenmodes of the inertial wave dominate the flame front modulations. The dispersive nature of the eigenmodes plays an important role in the flame response.

Thermo-acoustic combustion instabilities arise from feedback between flow perturbations and the unsteady heat release rate of a flame in a combustion chamber. In the case of a premixed, swirl stabilized flame, an unsteady heat release rate results from acoustic velocity perturbations at the burner inlet on the one hand, and from azimuthal velocity perturbations, which are generated by acoustic waves propagating across the swirler, on the other. The respective time lags associated with these flow–flame interaction mechanisms determine the overall flame response to acoustic perturbations and therefore thermo-acoustic stability. The propagation of azimuthal velocity perturbations in a cylindrical duct is commonly assumed to be convective, which implies that the corresponding time lag is governed by the speed of convection. We scrutinize this assumption in the framework of small perturbation analysis and modal decomposition of the Euler equations by considering an initial value problem. The analysis reveals that azimuthal velocity perturbations in swirling flows should be regarded as dispersive inertial waves. As a result of the restoring Coriolis force, wave propagation speeds lie above and below the mean flow bulk velocity. The differences between wave propagation speed and convection speed increase with increasing swirl. A linear, time invariant step response solution for the dynamics of inertial waves is developed, which can be approximated by a concise analytical expression. This study enhances the understanding of the flame dynamics of swirl burners in particular, and contributes physical insight into the inertial wave dynamics in general.