In this paper we investigate oscillations of a dynamical system containing passive dynamics driven by a positive feedback and how spatial characteristics (i.e., symmetry) affect the amplitude and stability of its nominal limit cycling response. The physical motivation of this problem is thermoacoustic dynamics in a gas turbine combustor. The spatial domain is periodic (passive annular acoustics) which are driven by heat released from a combustion process, and with sufficient driving through this nonlinear feedback a limit cycle is produced which is exhibited by a traveling acoustic wave around this annulus. We show that this response can be controlled passively by spatial perturbation in the symmetry of acoustic parameters. We find the critical parameter values that affect this oscillation, study the bifurcation properties, and subsequently use harmonic balance and temporal averaging to characterize periodic solutions and their stability. In all of these cases, we carry a parameter associated with the spatial symmetry of the acoustics and investigate how this symmetry affects the system response. The contribution of this paper is a unique analysis of a particular physical phenomena, as well as illustrating the equivalence of different nonlinear analysis tools for this analysis.
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January 2008
Research Papers
Passive Control of Limit Cycle Oscillations in a Thermoacoustic System Using Asymmetry
Bryan Eisenhower,
Bryan Eisenhower
Student
Department of Mechanical and Environmental Engineering,
University of California
, Santa Barbara, CA
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Gregory Hagen,
Gregory Hagen
Senior Researcher
United Technologies Research Center
, 411 Silver Lane, East Hartford, CT 06108
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Andrzej Banaszuk,
Andrzej Banaszuk
United Technologies Research Center
, 411 Silver Lane, East Hartford, CT 06108
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Igor Mezić
Igor Mezić
Professor
Department of Mechanical and Environmental Engineering,
University of California
, Santa Barbara, CA
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Bryan Eisenhower
Student
Department of Mechanical and Environmental Engineering,
University of California
, Santa Barbara, CA
Gregory Hagen
Senior Researcher
United Technologies Research Center
, 411 Silver Lane, East Hartford, CT 06108
Andrzej Banaszuk
United Technologies Research Center
, 411 Silver Lane, East Hartford, CT 06108
Igor Mezić
Professor
Department of Mechanical and Environmental Engineering,
University of California
, Santa Barbara, CAJ. Appl. Mech. Jan 2008, 75(1): 011021 (9 pages)
Published Online: February 6, 2008
Article history
Received:
November 6, 2006
Revised:
February 15, 2007
Published:
February 6, 2008
Citation
Eisenhower, B., Hagen, G., Banaszuk, A., and Mezić, I. (February 6, 2008). "Passive Control of Limit Cycle Oscillations in a Thermoacoustic System Using Asymmetry." ASME. J. Appl. Mech. January 2008; 75(1): 011021. https://doi.org/10.1115/1.2745399
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