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

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 continual problem in rocket and aircraft engines. Balasubramanian and Sujith (Journal of Fluid Mechanics, 2008, 594, 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 order $10^5$ to $10^7$. However, recent investigations by L. Magri & M. P. Juniper have brought to light certain errors in that paper. When the errors are corrected, $G_{max}$ is found to be of order 1 to 10, revealing that non-normality is not as influential as it was thought to be.