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Non-normality and its consequences in active control of thermoacoustic instabilities

Published online by Cambridge University Press:  22 February 2011

RAHUL KULKARNI ,
KOUSHIK BALASUBRAMANIAN  and
R. I. SUJITH
RAHUL KULKARNI
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600036, Tamil Nadu, India
KOUSHIK BALASUBRAMANIAN
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600036, Tamil Nadu, India
R. I. SUJITH*
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600036, Tamil Nadu, India
*
†Email address for correspondence: sujith@iitm.ac.in
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Abstract

Non-normality can cause transient growth of perturbations in thermoacoustic systems with stable eigenvalues. This can cause low-amplitude perturbations to grow to amplitudes high enough to make nonlinear effects significant, and the system can become nonlinearly unstable, even though it is stable under classical linear stability. In this paper, we have demonstrated that this feature can lead to the failure of the traditional controllers that were designed on the basis of classical linear stability analysis. We have also shown in a simple model that it is possible to prevent ‘nonlinear driving’ by controlling transient growth, using linear controllers. The analysis is performed in the context of a horizontal Rijke tube.

JFM classification

Acoustics: Aeroacoustics Instability: Instability Instability: Nonlinear instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 670 , 10 March 2011 , pp. 130 - 149
Copyright
Copyright © Cambridge University Press 2011

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