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Nonlinear thermoacoustic mode synchronization in annular combustors

Moeck, Jonas P. and Durox, Daniel and Schuller, Thierry and Candel, Sébastien Nonlinear thermoacoustic mode synchronization in annular combustors. (2018) Proceedings of the Combustion Institute, 37 (4). 5343-5350. ISSN 1540-7489

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Official URL: https://doi.org/10.1016/j.proci.2018.05.107

Abstract

Nonlinear coupling between azimuthal and axisymmetric modes in annular combustors is studied analyti- cally. Based on the thermoacoustic wave equation, a model featuring three nonlinearly coupled oscillators is derived. Two oscillators represent the dynamics of an azimuthal mode, and the third accounts for the axisym- metric mode. A slow-time system for the evolution of the mode amplitudes and phases is obtained through the application of the method of averaging. The averaged system is shown to accurately reproduce the solu- tions of the full oscillator model. Analysis of this five-dimensional dynamical system shows that a standing azimuthal mode may synchronize with an axisymmetric mode, provided that their individual resonance fre- quencies and growth rates are similar. This phase-coupled two-mode oscillation corresponds to the so-called slanted mode, observed in recent experiments involving an annular model combustion chamber. Quantitative conditions for the occurrence of mode synchronization are derived in terms of the growth rate ratio and a frequency detuning parameter. The analysis results are found to be consistent with experimental observations of the slanted mode.

Item Type:Article
HAL Id:hal-02135736
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Other partners > Norwegian University of Science and Technology - NTNU (NORWAY)
Other partners > Technische Universität Berlin - TU Berlin (GERMANY)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
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Deposited On:21 Mar 2019 14:08

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