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Non-normality in combustion–acoustic interaction in diffusion flames: a critical revision

  • Luca Magri (a1), K. Balasubramanian (a2), R. I. Sujith (a3) and M. P. Juniper (a1)


Perturbations in a non-normal system can grow transiently even if the system is linearly stable. If this transient growth is sufficiently large, it can trigger self-sustained oscillations from small initial disturbances. This has important practical consequences for combustion–acoustic oscillations, which are a persistent problem in rocket and aircraft engines. Balasubramanian & Sujith (J. Fluid Mech., vol. 594, 2008, pp. 29–57) modelled an infinite-rate chemistry diffusion flame in an acoustic duct and found that the transient growth in this system can amplify the initial energy by a factor, ${G}_{max} $ , of the order of $1{0}^{5} $ to $1{0}^{7} $ . However, recent investigations by L. Magri and M. P. Juniper have brought to light certain errors in that paper. When the errors are corrected, ${G}_{max} $ is found to be of the order of 1 to 10, revealing that non-normality is not as influential as it was thought to be.


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Balasubramanian, K. & Sujith, R. I. 2008 Non-normality and nonlinearity in combustion–acoustic interaction in diffusion flames. J. Fluid Mech. 594, 2957.
Chu, B. T. 1965 On the energy transfer to small disturbances in fluid flow (Part I). Acta Mechanica 1 (3), 215234.
Juniper, M. P. 2011 Triggering in the horizontal Rijke tube: non-normality, transient growth and bypass transition. J. Fluid Mech. 667, 272308.
Illingworth, S. J., Waugh, I. C. & Juniper, M. P. 2013 Finding thermoacoustic limit cycles for a ducted Burke–Schumann flame. Proc. Combust. Inst. 34 (1), 911920.
Trefethen, L. N. & Embree, M. 2005 Spectra and Pseudospectra. Princeton University Press.
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