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.

This theoretical study investigates spinning and standing modes in azimuthally symmetric annular combustion chambers. Both modes are observed in experiments and simulations, and an existing model predicts that spinning modes are the only stable state of the system. We extend this model to take into account the effect that the acoustic azimuthal velocity, u, has on the flames, and propose a phenomenological model based on experiments performed on transversely forced flames. This model contains a parameter, δ, that quantifies the influence that the transversal excitation has on the fluctuating heat release. For small values of δ, spinning modes are the only stable state of the system. In an intermediate range of δ, both spinning and standing modes are stable states. For large values of δ, standing modes are the only stable state. This study shows that a flame's response to azimuthal velocity fluctuations plays an important role in determining the type of thermoacoustic oscillations found in annular combustors.

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.

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This paper concerns the influence of the phase of the heat release response on thermoacoustic systems. We focus on one pair of degenerate azimuthal acoustic modes, with frequency ω 0. The same results apply for an axial acoustic mode. We show how the value φ 0 and the slope −τ of the flame phase at the frequency ω 0 affects the boundary of stability, the frequency and amplitude of oscillation, and the phase φ qp between heat release rate and acoustic pressure. This effect depends on φ 0 and on the nondimensional number τ ω 0 , which can be quickly calculated. We find for example that systems with large values of τ ω 0 are more prone to oscillate, i.e. they are more likely to have larger growth rates, and that at very large values of τ ω 0 the value φ 0 of the flame phase at ω 0 does not play a role in determining the system's stability. Moreover for a fixed flame gain, a flame whose phase changes rapidly with frequency is more likely to excite an acoustic mode. We propose ranges for typical values of nondimensional acoustic damping rates, frequency shifts and growth rates based on a literature review. We study the system in the nonlinear regime by applying the method of averaging and of multiple scales. We show how to account in the time domain for a varying frequency of oscillation as a function of amplitude, and validate these results with extensive numerical simulations for the parameters in the proposed ranges. We show that the frequency of oscillation ω B and the flame phase φ qp at the limit cycle match the respective values on the boundary of stability. We find good agreement between the model and thermoacoustic experiments, both in terms of the ratio ω B /ω 0 and of the phase φ qp , and provide an interpretation of the transition between different thermoacoustic states of an experiment. We discuss the effect of neglecting the component of heat release rate not in phase with the pressure p as assumed in previous studies. We show that this component should not be neglected when making a prediction of the system's stability and amplitudes, but we present some evidence that it may be neglected when identifying a system that is unstable and is already oscillating

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