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Green’s function analysis of nonlinear thermoacoustic effects under the influence of noise in a combustion chamber

Arabi, Sadaf; Heckl, Maria

Authors

Sadaf Arabi



Abstract

This paper presents an analytical study to predict the effect of noise in a thermoacoustic system. The starting point of our analysis is the acoustic analogy equation with two source terms: one represents the fluctuating heat release rate, and the other one represents the noise. The heat release rate is nonlinear and modelled by a generalised-law with amplitude-dependent time-lag and coupling coefficients. A Green’s function approach is used to convert the acoustic analogy equation (a PDE) into an integral equation. An essential element in this approach is the tailored Green’s function of the combustion chamber. We calculate this analytically for a 1-D combustion chamber with general end conditions and a non-uniform mean temperature. The integral equation is then used for predictions in the time-domain and frequency-domain. We focus on the following three phenomena: transient oscillations, noise-induced triggering, and hysteresis. Our predictions are in line with experimental observations reported in earlier studies: (1) Noise speeds up the time it takes a transient oscillation with growing amplitude to reach its limit cycle. (2) Noise can launch a linearly stable system into an unstable state. (3) Noise reduces the width of a hysteresis zone. Both white noise and pink noise are considered; pink noise is found to be more effective.

Citation

Arabi, S., & Heckl, M. (2025). Green’s function analysis of nonlinear thermoacoustic effects under the influence of noise in a combustion chamber. Journal of Sound and Vibration, 594, Article 118621. https://doi.org/10.1016/j.jsv.2024.118621

Journal Article Type Article
Acceptance Date Jul 7, 2024
Online Publication Date Jul 26, 2024
Publication Date 2025-01
Deposit Date Sep 13, 2024
Journal Journal of Sound and Vibration
Print ISSN 0022-460X
Electronic ISSN 1095-8568
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 594
Article Number 118621
DOI https://doi.org/10.1016/j.jsv.2024.118621
Keywords Green’s function; Thermoacoustic instability; Limit cycle; Noise-induced triggering; Transition time; Hysteresis
Public URL https://keele-repository.worktribe.com/output/920615
Publisher URL https://www.sciencedirect.com/science/article/pii/S0022460X24003833?via%3Dihub
Additional Information This article is maintained by: Elsevier; Article Title: Green’s function analysis of nonlinear thermoacoustic effects under the influence of noise in a combustion chamber; Journal Title: Journal of Sound and Vibration; CrossRef DOI link to publisher maintained version: https://doi.org/10.1016/j.jsv.2024.118621; Content Type: article; Copyright: © 2024 The Authors. Published by Elsevier Ltd.