Effect of entropy waves on transient energy growth of flow disturbances in triggering thermoacoustic instability

In a linearly stable but nonlinearly unstable thermoacoustic system, thermoacoustic instability may be triggered by small-amplitude acoustic perturbation undergoing transient growth. The present work study the effect of entropy waves on transient energy growth of acoustic disturbances in triggering thermoacoustic instability. For this, modal and non-normality analysis of these thermoacoustic systems is performed first. It is shown that the systems are non-normal due to the non-orthogonality of the entropy modes and the acoustic modes. The contribution to the non-orthogonality of the acoustic modes is identified to consist of (1) the non-trivial boundary conditions, (2) unsteady heat release and (3) the mean flow present. To quantify the amplification of the energy of the acoustic disturbances, transient growth is characterized and calculated. It is found that the initial acoustic energy can be amplified by a factor of the order of 10³, if the system is ended with choked outlet. It is 2-order greater than the G_ac^max (10⁰-10¹) observed in the open-ended thermoacoustic system. Such dramatic amplification is mainly due to the energy transfer occurred at the system outlet from entropy to acoustic modes. The detailed analysis reveals that the entropy waves in the choked system have much greater potential to trigger thermoacoustic instability than expected. Neglecting the entropy waves might lead to wrong prediction of the transient growth of acoustic disturbances in triggering thermoacoustic instability.