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Symmetry breaking of azimuthal thermo-acoustic modes in annular cavities: a theoretical study

Bauerheim, Michaël and Salas, Pablo and Nicoud, Franck and Poinsot, Thierry Symmetry breaking of azimuthal thermo-acoustic modes in annular cavities: a theoretical study. (2014) Journal of Fluid Mechanics, vol. 760. pp. 431-465. ISSN 0022-1120

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Official URL: http://dx.doi.org/10.1017/jfm.2014.578

Abstract

Many physical problems containing rotating symmetry exhibit azimuthal waves, from electromagnetic waves in nanophotonic crystals to seismic waves in giant stars. When this symmetry is broken, clockwise (CW) and counter-clockwise (CCW) waves are split into two distinct modes which can become unstable. This paper focuses on a theoretical study of symmetry breaking in annular cavities containing a number N of flames prone to azimuthal thermo-acoustic instabilities. A general dispersion relation for non-perfectly-axisymmetric cavities is obtained and analytically solved to provide an explicit expression for the frequencies and growth rates of all azimuthal modes of the configuration. This analytical study unveils two parameters affecting the stability of the mode: (i) a coupling strength corresponding to the cumulative effects of the N flames and (ii) a splitting strength due to the symmetry breaking when the flames are different. This theory has been validated using a 3D Helmholtz solver and good agreement is found. When only two types of flames are introduced into the annular cavity, the splitting strength is found to depend on two parameters: the difference between the two burner types and the pattern used to distribute the flames along the azimuthal direction. To first order, this theory suggests that the most stable configuration is obtained for a perfectly axisymmetric configuration. Therefore, breaking the symmetry by mixing different flames cannot improve the stability of an annular combustor independently of the flame distribution pattern.

Item Type:Article
HAL Id:hal-01117498
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National des Etudes Spatiales - CNES (FRANCE)
French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)
French research institutions > Institut National de la Recherche en Informatique et en Automatique - INRIA (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Other partners > Université de Montpellier 2 (FRANCE)
Other partners > Société nationale d'étude et de constructions de moteurs d'avion - SNECMA (FRANCE)
Laboratory name:
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Deposited By: Thierry POINSOT
Deposited On:17 Feb 2015 10:50

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