Azimuthal instabilities in annular combustors: standing and spinning modes

Abstract

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.

An analytical model for azimuthal thermoacoustic modes in an annular chamber fed by an annular plenum

“…The bifurcation [29] from weakly to strongly coupled situations is triggered by increasing the flame interaction index controlling the flame response to the acoustic flow. Results show that ATACAMAC allows to predict azimuthal turning and standing modes in a PBC configuration and performs as well as a 3D Helmholtz solver for all three regimes while simple annular rigs [5,23] or BC models [22,27] are not able to capture the bifurcation from weakly to strongly coupled regimes.…”

“…Noiray et al [5] and Ghirardo and Juniper [23] have proposed analytical analysis of complex non-linear mechanisms but only on simple configurations where the combustor is modeled with an annular rig alone. Parmentier et al [22] have derived an analytical method called ATACAMAC (for Analytical Tool to Analyze and Control Azimuthal Modes in Annular Combustors) for a more realistic configuration called BC (N Burners + Chamber) (Fig.1 left).…”

“…For example, standing and turning modes [1,24] are both observed [1,5,17,25] but predicting which mode type will appear in practice and whether they can be studied and controlled with the same method remains difficult [23]. Similarly, most large scale annular chambers exhibit multiple acoustic modes in the frequency range of interest (typically 10 to 30 acoustic modes can be identified in a large scale industrial chamber between 0 and 300 Hz) and classifying them into categories is the first step to control them.…”

“…Recently, the development of smaller annular chambers in laboratories has opened the path to investigate flow fields [10,11], ignition [12], flame response to acoustics [13] as well as azimuthal instabilities in these configurations [4,14,15]. At the same time, theoretical and numerical approaches have progressed in three directions: (1) full 3D LES of annular chambers have been developed [16,17], (2) 3D acoustic tools have been adapted to annular chambers [18,19,20,21] and (3) analytical approaches have been proposed to avoid the costs of 3D formulations and allow to investigate the stability and control of modes at low cost [5,22,23]. This last class of approach is especially interesting to elucidate mechanisms (such as transverse forcing effect [23], symmetry breaking [5] and mode nature [24]) because they can provide explicit solutions for the frequency and the growth rate of all modes.…”

“…At the same time, theoretical and numerical approaches have progressed in three directions: (1) full 3D LES of annular chambers have been developed [16,17], (2) 3D acoustic tools have been adapted to annular chambers [18,19,20,21] and (3) analytical approaches have been proposed to avoid the costs of 3D formulations and allow to investigate the stability and control of modes at low cost [5,22,23]. This last class of approach is especially interesting to elucidate mechanisms (such as transverse forcing effect [23], symmetry breaking [5] and mode nature [24]) because they can provide explicit solutions for the frequency and the growth rate of all modes. The difficulty in these methods is to be able to construct a model which can be handled by simple analytical approaches while retaining most of the important physical phenomena and geometrical specificities of annular chambers.…”