NDLI: Stability and Limit Cycles of a Nonlinear Damper Acting on a Linearly Unstable Thermoacoustic Mode

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Stability and Limit Cycles of a Nonlinear Damper Acting on a Linearly Unstable Thermoacoustic Mode

Content Provider	The American Society of Mechanical Engineers (ASME) Digital Collection
Author	Bourquard, Claire Noiray, Nicolas
Copyright Year	2018
Abstract	The resonant coupling between flames and acoustics is a growing issue for gas turbine manufacturers. They can be reduced by adding acoustic dampers on the combustion chamber walls. Nonetheless, if the engine is operated out of the stable window, the damper may be exposed to high-amplitude acoustic levels, which may trigger unwanted nonlinear effects. This work aims at providing an overview of the dynamics associated with those limit cycles using a simple analytical model, where a perfectly tuned damper is coupled to the combustion chamber. The damper, crossed by a purge flow in order to prevent hot gas ingestion, is modeled as a non-linearly damped harmonic oscillator, with vortex shedding as the main dissipation mechanism. The combustion chamber featuring a linearly unstable thermoacoustic mode is modelled as a Van der Pol oscillator. The fixed points of the coupled system and their stability can be determined by analyzing the averaged amplitude equations. This allows the computation of a fixed point topology map as function of the growth rate of the unstable mode and the mean velocity through the damper neck. Simulink simulations are also performed and compared to the analytical predictions. Finally, experiments are performed on a simple rectangular cavity, where the thermoacoustic instability resulting from the interaction between heat release and acoustic pressure is mimicked by an electro-acoustic instability. A feedback loop is built, where the signal from a microphone is filtered, delayed, and amplified before being sent to a loudspeaker placed inside the rectangular cavity. The delay and gain of the feedback loop can be modified to change the growth rate of the instability. One Helmholtz damper can be added to the cavity and tuned to the unstable mode of interest. The growth rate reduction capabilities of the damper and the amplitude of the limit cycle in the unstable cases are in good agreement with the analytical and numerical predictions, underlining the potentially dangerous behavior of the limit cycles which should be taken into account for real engine cases.
Sponsorship	International Gas Turbine Institute
File Format	PDF
ISBN	9780791851067
DOI	10.1115/GT2018-76838
Volume Number	Volume 4B: Combustion, Fuels, and Emissions
Conference Proceedings	ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition
Language	English
Publisher Date	2018-06-11
Publisher Place	Oslo, Norway
Access Restriction	Subscribed
Subject Keyword	Dampers Limit cycles Acoustics Engines Sound pressure Cavities Flames Gas turbines Feedback Energy dissipation Engineering simulation Signals Vortex shedding Stability Topology Flow (dynamics) Harmonic oscillators Microphones Loudspeakers Heat Simulation Computation Dynamics (mechanics) Resonance Delays Combustion chambers
Content Type	Text
Resource Type	Article

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