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Analysis of degenerate mechanisms triggering finite-amplitude thermo-acoustic oscillations in annular combustors

Published online by Cambridge University Press:  24 October 2019

Sandeep R. Murthy Open the ORCID record for Sandeep R. Murthy [Opens in a new window] ,
Taraneh Sayadi ,
Vincent Le Chenadec Open the ORCID record for Vincent Le Chenadec [Opens in a new window] ,
Peter J. Schmid Open the ORCID record for Peter J. Schmid [Opens in a new window]  and
Daniel J. Bodony Open the ORCID record for Daniel J. Bodony [Opens in a new window]
Sandeep R. Murthy*
Affiliation:
Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, Urbana, USA
Taraneh Sayadi
Affiliation:
Jean le Rond d’Alembert Institute, Sorbonne University, 75252 Paris CEDEX 05, France
Vincent Le Chenadec
Affiliation:
Multi-Scale Modeling and Simulation Laboratory, University of Paris-Est, 77454 Marne-la-Vallée CEDEX 2, France
Peter J. Schmid
Affiliation:
Department of Mathematics, Imperial College London, London SW7 2AZ, UK
Daniel J. Bodony
Affiliation:
Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, Urbana, USA
*
†Email address for correspondence: srmurth2@illinois.edu
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Abstract

A simplified model is introduced to study finite-amplitude thermo-acoustic oscillations in $N$-periodic annular combustion devices. Such oscillations yield undesirable effects and can be triggered by a positive feedback between heat-release and pressure fluctuations. The proposed model, comprising the governing equations linearized in the acoustic limit, and with each burner modelled as a one-dimensional system with acoustic damping and a compact heat source, is used to study the instability caused by cross-sector coupling. The coupling between the sectors is included by solving the one-dimensional acoustic jump conditions at the locations where the burners are coupled to the annular chambers of the combustion device. The analysis takes advantage of the block-circulant structure of the underlying stability equations to develop an efficient methodology to describe the onset of azimuthally synchronized motion. A modal analysis reveals the dominance of global instabilities (encompassing the large-scale dynamics of the entire system), while a non-modal analysis reveals a strong response to harmonic excitation at forcing frequencies far from the eigenfrequencies, when the overall system is linearly stable. In all presented cases, large-scale, azimuthally synchronized (coupled) motion is observed. The relevance of the non-modal response is further emphasized by demonstrating the subcritical nature of the system’s Hopf point via an asymptotic expansion of a nonlinear model representing the compact heat source within each burner.

JFM classification

Instability: Nonlinear instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 881 , 25 December 2019 , pp. 384 - 419
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Copyright
© 2019 Cambridge University Press 

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