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A new perspective on the flame describing function of a matrix flame

Heckl

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Abstract

This paper considers a fundamental thermoacoustic test rig developed by Noiray (“Linear and nonlinear analysis of combustion instabilities, application to multipoint injection systems and control strategies”, PhD thesis, École Centrale Paris, 2007) and models it with an entirely analytical approach. The test rig is treated as a system of two coupled elements: an acoustic resonator and a flame with oscillating rate of heat release. We describe the acoustics of the combustion rig in terms of modes, and derive a governing equation for one such mode. This turns out to be the equation for a damped harmonic oscillator, forced by the heat release rate from the flame. In order to model the heat release rate, and in particular its nonlinear aspects, we develop a generalised nt-law with amplitude-dependent coefficients and multiple time-lag. The coefficients are determined from Noiray's measured flame describing function. Stability predictions are made by evaluating the sign of the damping coefficient in the governing equation. These predictions are in excellent qualitative agreement with the measured stability behaviour. Finally, the physical mechanisms of the amplitude-dependence are explored.

Acceptance Date Aug 4, 2014
Publication Date May 25, 2015
Publicly Available Date Mar 29, 2024
Journal International Journal of Spray and Combustion Dynamics
Print ISSN 1756-8277
Publisher SAGE Publications
Pages 91 - 112
DOI https://doi.org/10.1260/1756-8277.7.2.91
Publisher URL https://doi.org/10.1260%2F1756-8277.7.2.91

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