A review on Noise-Induced dynamics of thermoacoustic systems

Abstract

Practical combustion systems such as gas turbine combustors, rocket engines, industrial furnaces, and boilers are essentially thermoacoustic oscillators involving acoustic energy amplification through feedback interaction among fluctuations in the aerodynamic field, acoustic field, and the combustion process. Such systems are also noisy, in the sense that there inherently exists noise within the system. Noise may be associated with various sources–noise in fuel/air supply systems, fluctuations in the flow field, acoustic fluctuations, fluctuations in the heat release. Additionally, such noise may be correlated or uncorrelated, may have a specific spectral characteristic; but often noise will interact with/influence the feedback process. Since the importance of noise in determining the stability of the system discussed by Culick et al. (Combustion noise and combustion instabilities in propulsion systems, 1992) and group at Caltech, there have been several recent contributions to the theory of noise-induced phenomena in thermoacoustic systems–further advancements in the determination of system stability through noise-induced behaviour in the system prior to bifurcation as well as during the self-excited state, noise-induced effects in the presence of nonlinear interactions, noise-induced transitions (incl. dynamics in the bistable regime in the case of transition to self-excited oscillations via a subcritical Hopf bifurcation), as well as recent identification of interesting behaviour such as noise-induced coherence and stochastic bifurcations (stochastic P-bifurcations). The latter effects are based on new findings in the theory of dynamical systems and since reports on their influence in thermoacoustic systems are also being investigated in other aero/hydrodynamic systems such as in jets. The review will focus on the influence of developments in the theory of random noise (such as the FokkerPlank equations), the theory of oscillators and dynamical systems on noise induced behaviour in thermoacoustic systems; experiments, modelling, and predictions on noisy thermoacoustic systems; and the implications of these findings on practical systems.