Effects of background noises on nonlinear dynamics of a modelled thermoacoustic combustor

In this work, the effects of background noises on nonlinear dynamics of a modelled standing-wave thermoacoustic system with subcritical Hopf bifurcation behaviors are studied. These noises include (1) pressure-coupled (acoustic), (2) velocity-coupled (flow), and (3) external combustion noise. It is found that these three types of background noises play important, but different roles in changing the hysteresis width and stability boundary. In addition, the stochastic transition from stability to instability is investigated, as the noise intensity is varied. Two different stochastic P-bifurcations are identified. One is related to a craterlike probability density distribution. The other is associated with a probability density distribution characterized with two peaks and one trough. With each type of noise affecting the system's stochastic behaviors being evaluated, the effect of two different types of noises is then studied. It is shown that the combined noises (types 1 and 2) cannot only destabilize global stable thermoacoustic system, but also stabilize linearly unstable system. This depends strongly on the superimposition form of the two types of noises. In addition, when the thermoacoustic system is disturbed by the combined noise (types 3 and 1 or types 3 and 2), the transition process is dominated by the combustion noise.