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Flame-acoustic resonance initiated by vortical disturbances

Published online by Cambridge University Press:  26 August 2009

XUESONG WU  and
CHUNG K. LAW
XUESONG WU*
Affiliation:
Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2AZ, UK
CHUNG K. LAW
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, NJ 08544, USA
*
†Email address for correspondence: x.wu@ic.ac.uk
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Abstract

By adapting the general flame-acoustic interaction theory developed in Wu et al. (J. Fluid Mech., vol. 497, 2003, pp. 23–53), a systematic analysis is carried out for the interaction of a stable premixed flame in a duct with vortical disturbances superimposed on the oncoming mixture. A small-amplitude vortical perturbation, assumed to be a convecting gust with a frequency ω, induces a hydrodynamic field in the vicinity of the flame, causing an initially planar flame to wrinkle. The unsteady heat release resulting from the increased surface area of the wrinkling flame then generates a sound wave with frequency 2ω. When 2ω coincides with the natural frequency of an acoustic mode of the duct, a flame-acoustic resonance takes place, through which the flame-induced sound may attain an amplitude sufficiently large to modulate the flame through the unsteady Rayleigh–Taylor effect. A novel evolution system is derived to describe this two-way coupling for two cases: (a) a flame with a fixed mean position and (b) a moving flame. Numerical solutions show that for (a), the mutual flame-acoustic interaction initiates a violent subharmonic parametric instability, and the flame-acoustic system quickly evolves into a fully nonlinear regime, which probably corresponds to a state of self-sustained oscillation. This finding presents a peculiar instability scenario: a small-amplitude vortical perturbation may, by initiating acoustic-flame resonance, completely destabilize an otherwise stable planar flame. For a moving flame, the flame-acoustic resonance is of transient nature. The acoustic pressure gains substantially, but the parametric flame instability is induced only when the vortical disturbance exceeds a finite threshold.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 634 , 10 September 2009 , pp. 321 - 357
Copyright
Copyright © Cambridge University Press 2009

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