Passive Control of Limit Cycle Oscillations in a Thermoacoustic System Using Asymmetry

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. DOI: 10.1115/1.2745399

[1]  Gregory Hagen,et al.  A linear model for control of thermoacoustic instabilities on annular domain , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[2]  Balth. van der Pol,et al.  VII. Forced oscillations in a circuit with non-linear resistance. (Reception with reactive triode) , 1927 .

[3]  F. Culick.  A Note on Rayleigh's Criterion , 1987 .

[4]  W. I. Newman,et al.  The method of variation of constants and multiple time scales in orbital mechanics. , 2003, Chaos.

[5]  A. Dowling,et al.  Thermoacoustic Oscillations in an Annular Combustor , 2001 .

[6]  A. Banaszuk,et al.  Uncertainty propagation in a reduced order thermo-acoustic model , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[7]  P. Bressloff,et al.  Traveling Waves in a Chain of Pulse-Coupled Oscillators , 1998 .

[8]  E. Gutmark,et al.  The Effectiveness of Passive Combustion Control Methods , 2004 .

[9]  A. Dowling.  Nonlinear self-excited oscillations of a ducted flame , 1997, Journal of Fluid Mechanics.

[10]  Werner Krebs,et al.  Thermoacoustic analysis of annular combustor , 1999 .

[11]  Ann P. Dowling,et al.  Modelling of Circumferential Modal Coupling Due to Helmholtz Resonators , 2003 .

[12]  S. Candel,et al.  A review of active control of combustion instabilities , 1993 .

[13]  M. Krstic,et al.  Multivariable adaptive control of instabilities arising in jet engines , 2003, Proceedings of the 2003 American Control Conference, 2003..

[14]  Tim Lieuwen,et al.  Nonlinear kinematic response of premixed flames to harmonic velocity disturbances , 2005 .

[15]  Bruno Schuermans,et al.  Thermoacoustic Modeling and Control of Multi Burner Combustion Systems , 2003 .

[16]  S. Strogatz,et al.  Phase diagram for the Winfree model of coupled nonlinear oscillators. , 2000, Physical review letters.

[17]  Ann P. Dowling,et al.  Low-Order Modelling of Thermoacoustic Limit Cycles , 2004 .

[18]  A. Dowling,et al.  Experimental investigation of the nonlinear response of turbulent premixed flames to imposed inlet velocity oscillations , 2005 .

[19]  A. Annaswamy,et al.  Response of a laminar premixed flame to flow oscillations: A kinematic model and thermoacoustic instability results , 1996 .

[20]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[21]  Sébastien Candel,et al.  Combustion instabilities coupled by pressure waves and their active control , 1992 .

[22]  Jeffrey M. Cohen,et al.  Active Control of Combustion Instabilities in Gas Turbine Engines for Low Emissions. Part I: Physics-Based and Experimentally Identified Models of Combustion Instability , 2000 .

[23]  Y. Neumeier,et al.  Nonlinear pressure-heat release transfer function measurements in a premixed combustor , 2002 .

[24]  Mauricio Barahona,et al.  Synchronization in small-world systems. , 2002, Physical review letters.

[25]  Lawrence E. Kinsler,et al.  Fundamentals of acoustics , 1950 .

[26]  A. A. Peracchio,et al.  Nonlinear heat-release/acoustic model for thermoacoustic instability in lean premixed combustors , 1999 .

[27]  B. Van Der Pol,et al.  Forced Oscillations in a Circuit with Nonlinear Resistance , 1924 .