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Weakly nonlinear analysis of thermoacoustic instabilities in annular combustors

Published online by Cambridge University Press:  16 September 2016

G. Ghirardo ,
M. P. Juniper  and
J. P. Moeck
G. Ghirardo*
Affiliation:
University of Cambridge, Engineering Department, Trumpington Street, Cambridge CB2 1PZ, UK
M. P. Juniper
Affiliation:
University of Cambridge, Engineering Department, Trumpington Street, Cambridge CB2 1PZ, UK
J. P. Moeck
Affiliation:
Institut für Strömungsmechanik und Technische Akustik, Technische Universität Berlin, Müller-Breslau-Strasse 8, 10623 Berlin, Germany
*
†Email address for correspondence: giulio.ghirardo@gmail.com
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Abstract

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.

JFM classification

Acoustics: Acoustics Nonlinear Dynamical Systems: Low-dimensional models Nonlinear Dynamical Systems: Nonlinear Dynamical Systems
Type
Papers
Information
Journal of Fluid Mechanics , Volume 805 , 25 October 2016 , pp. 52 - 87
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Copyright
© 2016 Cambridge University Press 

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