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Non-normality and nonlinearity in combustion–acoustic interaction in diffusion flames

Published online by Cambridge University Press:  14 December 2007

KOUSHIK BALASUBRAMANIAN  and
R. I. SUJITH
KOUSHIK BALASUBRAMANIAN
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600036, India
R. I. SUJITH*
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600036, India
*
†Author to whom correspondence should be addressed: [email protected].
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Abstract

The role of non-normality and nonlinearity in flame–acoustic interaction in a ducted diffusion flame is investigated in this paper. The infinite rate chemistry model is employed to study unsteady diffusion flames in a Burke–Schumann type geometry. It has been observed that even in this simplified case, the combustion response to perturbations of velocity is non-normal and nonlinear. This flame model is then coupled with a linear model of the duct acoustic field to study the temporal evolution of acoustic perturbations. The one-dimensional acoustic field is simulated in the time domain using the Galerkin technique, treating the fluctuating heat release from the combustion zone as a compact acoustic source. It is shown that the coupled combustion–acoustic system is non-normal and nonlinear. Further, calculations showed the occurrence of triggering; i.e. the thermoacoustic oscillations decay for some initial conditions whereas they grow for some other initial conditions. It is shown that triggering occurs because of the combined effect of non-normality and nonlinearity. For such a non-normal system, resonance or ‘pseudoresonance’ may occur at frequencies far from its natural frequencies. Non-normal systems can be studied using pseudospectra, as eigenvalues alone are not sufficient to predict the behaviour of the system. Further, both necessary and sufficient conditions for the stability of a thermoacoustic system are presented in this paper.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 594 , 10 January 2008 , pp. 29 - 57
Copyright
Copyright © Cambridge University Press 2008

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