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A Green's function approach to predict nonlinear thermoacoustic instabilities in combustors

Bigongiari, Alessandra; Heckl, Maria A.

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Authors

Alessandra Bigongiari



Abstract

The prediction of thermoacoustic instabilities is fundamental for combustion systems such as domestic burners and industrial gas turbine engines. High-amplitude pressure oscillations cause thermal and mechanical stress to the equipment, leading to premature wear or even critical damage. In this paper we present a new approach to produce nonlinear (i.e. amplitude-dependent) stability maps of a combustion system as a function of various parameters. Our approach is based on the tailored Green’s function of the combustion system, which we calculate analytically. To this end, we assume that the combustor is one-dimensional, and we describe its boundary conditions through reflection coefficients. The heat release is modelled by a generalised law. This includes a direct-feedback term in addition to the usual time-lag term; moreover, its parameters (time lag, coupling coefficients) depend on the oscillation amplitude. The model provides new insight into the physical mechanism of the feedback between heat release rate and acoustic perturbations. It predicts the key nonlinear features of the thermoacoustic feedback, such as limit cycles, bistability and hysteresis. It also explains the frequency shift in the acoustic modes.

Journal Article Type Article
Acceptance Date May 10, 2016
Publication Date Jun 15, 2016
Publicly Available Date Mar 28, 2024
Journal Journal of Fluid Mechanics
Print ISSN 0022-1120
Publisher Cambridge University Press
Peer Reviewed Peer Reviewed
Pages 970 - 996
DOI https://doi.org/10.1017/jfm.2016.332
Keywords acoustics; combustion; nonlinear instability
Publisher URL https://doi.org/10.1017/jfm.2016.332

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