Transient energy growth of acoustic disturbances in triggering self-sustained thermoacoustic oscillations

Thermoacoustic instability occurs in many modern combustion systems. It most often arises due to the coupling between unsteady heat release and acoustic waves. Transient energy growth of acoustic disturbances could trigger thermoacoustic instability in a non-normal combustion system. In this work, transient energy growth analysis of a modelled choked combustor with a gutter confined is conducted. The non-normal interaction between acoustic disturbances and the anchored V-shaped flame is studied first. The thermoacoustic system is shown to be non-normal and characterized by non-orthogonal eigenmodes. Transient energy growth analysis is then performed to gain insights on its finite-time stability behaviour, which cannot be predicted by classical linear theory. To characterize the non-normality, two different energy measures are defined and estimated. One involves with acoustic travelling waves. The other is concerned with not only the travelling waves but the monopole-like flame. Comparison is then made between the two measures. It is found that the maximum transient energy growth of combustion-excited oscillations is about 10²-10⁴ times greater than that of acoustic disturbances. Furthermore, the 'critical' time taken to reach the maximum transient growth rate is about half of period of the fundamental mode, which is about 90% shorter than that when only acoustic disturbances are considered. In addition, the most 'dangerous' location at which the flame is more susceptible to thermoacoustic instability is estimated. Finally, experiments are conducted on an open-ended thermoacoustic system. It is found that transient growth of flow disturbances can trigger nonlinear limit cycle oscillations.