In many continuous combustion processes, such as those found in aeroengines or gas turbines, the flame is stabilized by a swirling flow formed by aerodynamic swirlers. The dynamics of such swirling flames is of technical and fundamental interest. This article reviews progress in this field and begins with a discussion of the swirl number, a parameter that plays a central role in the definition of the flow structure and its response to incoming disturbances. Interaction between the swirler response and incoming acoustic perturbations generates a vorticity wave convected by the flow, which is accompanied by azimuthal velocity fluctuations. Axial and azimuthal velocities in turn define the flame response in terms of heat release rate fluctuations. The nonlinear response of swirling flames to incoming disturbances is conveniently represented with a flame describing function (FDF), in other words, with a family of transfer functions depending on frequency and incident axial velocity amplitudes. The FDF, however, does not reflect all possible nonlinear interactions in swirling flows. This aspect is illustrated with experimental data and some theoretical arguments in the last part of this article, which concerns the interaction of incident acoustic disturbances with the precessing vortex core, giving rise to nonlinear fluctuations at the frequency difference.

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Can-annular combustors consist of a set of independent cans, connected on the upstream side to the combustor plenum and on the downstream side to the turbine inlet, where a transition duct links the round geometry of each can with the annular segment of the turbine inlet. Each transition duct is open on the sides toward the adjacent transition ducts, so that neighboring cans are acoustically connected through a so-called cross-talk open area. This theoretical, numerical, and experimental work discusses the effect that this communication has on the thermoacoustic frequencies of the combustor. We show how this communication gives rise to axial and azimuthal modes, and that these correspond to particularly synchronized states of axial thermoacoustic oscillations in each individual can. We show that these combustors typically show clusters of thermoacoustic modes with very close frequencies and that a slight loss of rotational symmetry, e.g., a different acoustic response of certain cans, can lead to mode localization. We corroborate the predictions of azimuthal modes, clusters of eigenmodes, and mode localization with experimental evidence.

Rotationally symmetric annular combustors are of practical importance because they generically resemble combustion chambers in gas turbines, in which thermoacoustically driven oscillations are a major concern. We focus on azimuthal thermoacoustic oscillations and model the fluctuating heat release rate as being dependent only on the local pressure in the combustion chamber. We study the dynamics of the annular combustor with a finite number of compact flames equispaced around the annulus, and characterize the flames' response with a describing function. We discuss the existence, amplitude and the stability of standing and spinning waves, as a function of: (i) the number of the burners; (ii) the acoustic damping in the chamber; (iii) the flame response. We present the implications for industrial applications and the future direction of investigations. We then present as an example the first theoretical study of thermoacoustic triggering in annular combustors, which shows that rotationally symmetric annular chambers that are thermoacoustically unstable do not experience only stable spinning solutions, but can also experience stable standing solutions. We finally test the theory on one experiment with good agreement.