Dynamics of coupled thermoacoustic modes: Noise and frequency spacing effects

Practical combustion systems consist of multiple thermoacoustic modes that are linearly stable or unstable at a wide range of frequencies. When coupled, the modal interactions are a strong function of the frequency spacing between them - having very significant implications on interpretation of linear stability or instability of modes from experimental data. Frequency spacing between the modes particularly influences the stability and existence of potential limit cycle solutions. In this paper, we extend earlier deterministic studies to include the effects of noise, studying how deterministic dynamics change with the addition of noise and the simultaneous impact of frequency spacing (i.e., closely, or widely spaced). Specifically, this paper characterizes three key effects of noise, which are (1) distribution of limit cycle amplitudes (diffusion), (2) shift in the average limit cycle amplitudes (noise induced drift), and (3) introduction of new bifurcations that are not present in the deterministic system. Key conclusions from this work are that in highly noisy practical environments, a deterministic/ low noise analysis will not be sufficient to explain even critical qualitative features of the system - such as existence of stable limit cycles or their amplitudes. Moreover, the nature of noise-induced effects on nonlinear modal interactions can be fundamentally different for degenerate, closely spaced, and widely spaced modes. (c) 2023 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Automated summary

Practical combustion systems consist of linearly stable or unstable thermoacoustic modes at a wide range of frequencies. The frequency spacing between the modes significantly affects their stability and existence of limit cycle solutions. This paper studies the effects of noise on deterministic dynamics and the impact of frequency spacing, highlighting that a low noise analysis is insufficient to explain critical features of the system in highly noisy environments. Furthermore, noise-induced effects on nonlinear modal interactions can vary fundamentally based on the degenerate, closely spaced, or widely spaced modes.