Thermoacoustic interplay between intrinsic thermoacoustic and acoustic modes: non-normality and high sensitivities

Abstract

This study analyses the interplay between classical acoustic modes and intrinsic thermoacoustic (ITA) modes in a simple thermoacoustic system. The analysis is performed using a frequency-domain low-order network model as well as a time-domain spatially discretised model. Anti-correlated modal sensitivities are found to arise due to a pairwise interplay between acoustic and ITA modes. The magnitude of the sensitivities increases as the interplay between the modes grows stronger. The results show a global behaviour of the modes linked to the presence of exceptional points in the spectrum. The time-domain analysis results in a delay-differential equation and allows the investigation of non-normal behaviour and its consequences. Pseudospectral analysis reveals that energy amplification is crucially linked to an interplay between acoustic and ITA modes. While higher non-orthogonality between two modes is correlated with peaks in modal sensitivity, transient energy growth does not necessarily involve the most sensitive modes. In particular, growth estimates based on the Kreiss constant demonstrate that transient amplification relies critically on the proximity of the non-normal modes to the imaginary axis. The time scale for transient amplification is identified as the flame time delay, which is further corroborated by determining the optimal initial conditions responsible for the bulk of the non-modal energy growth. The flame is identified as an active and dominant contributor to energy gain. The frequency of the optimal perturbation matches the acoustic time scale, once more confirming an interplay between acoustic and ITA structures. Flame-based amplification factors of two to five are found, which are significant when feeding into the acoustic dynamics and eventually triggering nonlinear limit-cycle behaviour.