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Nonlinear self-excited thermoacoustic oscillations of a ducted premixed flame: bifurcations and routes to chaos

Published online by Cambridge University Press:  25 November 2014

Karthik Kashinath ,
Iain C. Waugh  and
Matthew P. Juniper
Karthik Kashinath*
Affiliation:
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
Iain C. Waugh
Affiliation:
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
Matthew P. Juniper
Affiliation:
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
*
†Present address: Climate Science Department, Earth Sciences Division, Lawrence Berkeley National Lab, 1 Cyclotron Road, MS74R316C, Berkeley, CA 94720, USA. Email address for correspondence: [email protected]
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Abstract

Thermoacoustic systems can oscillate self-excitedly, and often non-periodically, owing to coupling between unsteady heat release and acoustic waves. We study a slot-stabilized two-dimensional premixed flame in a duct via numerical simulations of a $G$-equation flame coupled with duct acoustics. We examine the bifurcations and routes to chaos for three control parameters: (i) the flame position in the duct, (ii) the length of the duct and (iii) the mean flow velocity. We observe period-1, period-2, quasi-periodic and chaotic oscillations. For certain parameter ranges, more than one stable state exists, so mode switching is possible. At intermediate times, the system is attracted to and repelled from unstable states, which are also identified. Two routes to chaos are established for this system: the period-doubling route and the Ruelle–Takens–Newhouse route. These are corroborated by analyses of the power spectra of the acoustic velocity. Instantaneous flame images reveal that the wrinkles on the flame surface and pinch-off of flame pockets are regular for periodic oscillations, while they are irregular and have multiple time and length scales for quasi-periodic and aperiodic oscillations. This study complements recent experiments by providing a reduced-order model of a system with approximately 5000 degrees of freedom that captures much of the elaborate nonlinear behaviour of ducted premixed flames observed in the laboratory.

JFM classification

Instability: Instability Nonlinear Dynamical Systems: Nonlinear Dynamical Systems Reacting Flows: Reacting Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 761 , 25 December 2014 , pp. 399 - 430
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© 2014 Cambridge University Press 

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