Effects of non-uniform temperature field, mean flow, and noise on nonlinear thermoacoustic instabilities

Abstract

In industrial combustion systems, noise from various sources can significantly impact the system’s dynamics. External noise introduces complexities, potentially leading to untimely transitions and alterations in stability behaviours. This study extends the adjoint Green’s function (AGF) framework to investigate the stability of a one-dimensional thermoacoustic system, which includes a mean flow field, a temperature jump, and stochastic forcings. The theoretical framework is applied to a one-dimensional Rijke tube and is validated against a wave-based network modelling approach. The results provide a prediction of the limit cycles, triggering phenomena, hystereses, and Hopf bifurcations observed in experiments. Suitable open-end boundary conditions for a flow duct system are discussed. The role of mean temperature difference in the stability behaviour of the system is studied. Additionally, the influence of additive noise is examined, demonstrating that both white and pink noise can accelerate the transition to limit cycles without altering growth rates. Pink noise is shown to be more effective in triggering instabilities, particularly in systems operating near stability margins. The effect of the non-negligible but small mean flow is discussed in systems with and without noise. The findings enhance understanding of the complex interplay between mean flow, noise, and temperature fields, providing insights for better prediction and control of thermoacoustic instabilities