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

Abstract

AbstractPerturbations 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.