Non-normality and nonlinearity in thermoacoustic instabilities

Thermoacoustic instability has traditionally been investigated by linearizing the equations of combustion-acoustic interaction and testing for unstable eigenvalues of the linearized problem. However, it was observed that often the results of linear stability analysis agree poorly with experiments. Nevertheless, linear effects play a central role in combustion instability. The consequence of non-normality in the occurrence of subcritical transition to instability is illustrated in the context of a horizontal Rijke tube. It is shown that the coupled thermoacoustic system is non-normal as well as nonlinear. Non-normality can cause algebraic growth of oscillations for a short time even though all the eigenvectors of the system could be decaying exponentially with time. This feature of non-normality combined with the effect of nonlinearity causes the occurrence of subcritical transition to instability from initial states that have small energy. Measures to quantify transient growth are also discussed. Examples discussed include thermoacoustic instabilities in ducted premixed and diffusion flames and solid rocket motor. Copyright © 2004-06 by Asian Fluid Mechanics Committee.