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Research Papers: Gas Turbines: Controls, Diagnostics, and Instrumentation

A Theoretical Approach for Passive Control of Thermoacoustic Oscillations: Application to Ducted Flames

[+] Author and Article Information
Luca Magri

e-mail: lm547@cam.ac.uk

Matthew P. Juniper

e-mail: mpj1001@cam.ac.uk

Energy, Fluid Mechanics and
Turbomachinery Division,
Department of Engineering,
University of Cambridge,
Trumpington Street,
Cambridge CB2 1PZ, UK

1Corresponding author.

Contributed by the Controls, Diagnostics and Instrumentation Committee of ASME for publication in the Journal of Engineering for Gas Turbines and Power. Manuscript received June 27, 2013; final manuscript received July 8, 2013; published online August 21, 2013. Editor: David Wisler.

J. Eng. Gas Turbines Power 135(9), 091604 (Aug 21, 2013) (9 pages) Paper No: GTP-13-1197; doi: 10.1115/1.4024957 History: Received June 27, 2013; Revised July 08, 2013

In this paper, we develop a linear technique that predicts how the stability of a thermoacoustic system changes due to the action of a generic passive feedback device or a generic change in the base state. From this, one can calculate the passive device or base state change that most stabilizes the system. This theoretical framework, based on adjoint equations, is applied to two types of Rijke tube. The first contains an electrically heated hot wire, and the second contains a diffusion flame. Both heat sources are assumed to be compact, so that the acoustic and heat release models can be decoupled. We find that the most effective passive control device is an adiabatic mesh placed at the downstream end of the Rijke tube. We also investigate the effects of a second hot wire and a local variation of the cross-sectional area but find that both affect the frequency more than the growth rate. This application of adjoint sensitivity analysis opens up new possibilities for the passive control of thermoacoustic oscillations. For example, the influence of base state changes can be combined with other constraints, such as that the total heat release rate remains constant, in order to show how an unstable thermoacoustic system should be changed in order to make it stable.

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References

Lieuwen, T. C., and Yang, V., 2005, Combustion Instabilities in Gas Turbine Engines, (Progress in Astronautics and Aeronautics, Vol. 210), AIAA, Reston,VA.
Hill, D. C., 1992, “A Theoretical Approach for Analyzing the Restabilization of Wakes,” NASA Technical Memorandum No. 103858.
Giannetti, F., and Luchini, P., 2007, “Structural Sensitivity of the First Instability of the Cylinder Wake,” J. Fluid Mech., 581, pp. 167–197. [CrossRef]
Marquet, O., Sipp, D., and Jacquin, L., 2008, “Sensitivity Analysis and Passive Control of Cylinder Flow,” J. Fluid Mech., 615, pp. 221–252. [CrossRef]
Sipp, D., Marquet, O., Meliga, P., and Barbagallo, A., 2010, “Dynamics and Control of Global Instabilities in Open-Flows: A Linearized Approach,” ASME Appl. Mech. Rev., 63(3), p. 030801. [CrossRef]
Chandler, G. J., Juniper, M. P., Nichols, J. W., and Schmid, P. J., 2012, “Adjoint Algorithms for the Navier-Stokes Equations in the Low Mach Number Limit,” J. Comput. Phys., 231, pp. 1900–1916. [CrossRef]
Balasubramanian, K., and Sujith, R. I., 2008, “Thermoacoustic Instability in a Rijke Tube: Non-Normality and Nonlinearity,” Phys. Fluids, 20, p. 044103. [CrossRef]
Juniper, M. P., 2011, “Triggering in the Horizontal Rijke Tube: Non-Normality, Transient Growth and Bypass Transition,” J. Fluid Mech., 667, pp. 272–308. [CrossRef]
Magri, L., and Juniper, M. P., 2013, “Sensitivity Analysis of a Time-Delayed Thermo-Acoustic System Via an Adjoint-Based Approach,” J. Fluid Mech., 719, pp. 183–202. [CrossRef]
Burke, S. P., and Schumann, T. E. W., 1928, “Diffusion Flames,” Combust. Symp.20(10), pp. 998–1004.
Tyagi, M., Chakravarthy, S. R., and Sujith, R. I., 2007, “Unsteady Response of a Ducted Non-Premixed Flame and Acoustic Coupling,” Combust. Theory Modell., 11, pp. 205–226. [CrossRef]
Tyagi, M., Jamadar, N., and Chakravarthy, S. R., 2007, “Oscillatory Response of an Idealized Two-Dimensional Diffusion Flame: Analytical and Numerical Study,” Combust. Flame, 149, pp. 271–285. [CrossRef]
Balasubramanian, K., and Sujith, R. I., 2008, “Non-Normality and Nonlinearity in Combustion-Acoustic Interaction in Diffusion Flames,” J. Fluid Mech., 594, pp. 29–57. [CrossRef]
Magri, L., and Juniper, M. P., “Adjoint Sensitivity Analysis of Ducted Diffusion Flames for Control of Thermo-Acoustic Instabilities,” J. Fluid Mech. (submitted).
Magri, L., and JuniperM. P., 2013, “Using Direct and Adjoint Eigenfunctions to Find Optimal Control Strategies in Thermo-Acoustics,” Non-Normal and Nonlinear Effects in Aero- and Thermoacoustics (n3l) Conference, München, Germany, June 18–21.
Magri, L., Balasubramanian, K., Sujith, R. I., and Juniper, M. P., 2013, “Non-Normality in Combustion-Acoustic Interaction in Diffusion Flames: A Critical Revision,” J. Fluid Mech. (submitted).
Heckl, M., 1990, “Nonlinear Acoustic Effects in the Rijke Tube,” Acustica, 72, pp. 63–71.
Matveev, I., 2003, “Thermo-Acoustic Instabilities in the Rijke Tube: Experiments and Modeling,” Ph.D. thesis, CalTech, Pasadena, CA.
Stow, S. R., and Dowling, A. P., 2001, “Thermoacoustic Oscillations in an Annular Combustor,” ASME Turbo Expo, Paper No. 2001-GT-0037.
Poinsot, T., and Venyante, D., 2001, Theoretical and Numerical Combustion. Edwards, Ann Arbor, MI.
Chu, B. T., 1963, “Analysis of a Self-Sustained Thermally Driven Nonlinear Vibration,” Phys. Fluids, 6(11), p. 1638. [CrossRef]
Rayleigh, J. W. S., 1878, “The Explanation of Certain Acoustical Phenomena,” Nature, 18, pp. 319–321. [CrossRef]
Shapiro, A. H., 1953, The Dynamics and Thermodynamics of Compressible Fluid Flow, Ronald, New York.
Dowling, A. P., and Ffowcs Williams, J. E., 1983, Sound and Sources of Sound, Ellis Horwood, Chichester, UK.
Culick, F. E. C., 2006, “Unsteady Motions in Combustion Chambers for Propulsion Systems,” RTO AGARDograph Paper No. AG-AVT-030.
Illingworth, S. J., Waugh, I. C., and Juniper, M. P., 2013, “Finding Thermo-acoustic Limit Cycles for a Ducted Burke-Schumann Flame,” Proc. Combust. Inst., 34(1), pp. 911–920. [CrossRef]
Nicoud, F., and Wieczorek, K., 2009, “About the Zero Mach Number Assumption in the Calculation of Thermo-Acoustic Instabilities,” Int. J. Spray Combust. Dyn., 1(1), pp. 67–111. [CrossRef]

Figures

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Fig. 1

Schematic of the thermoacoustic system under investigation. (a) Electrically heated Rijke tube: the hot wire is placed at x = xh; (b) ducted diffusion flame: the flame is solved in the 2D domain (ξ,η) and forces the acoustics at x = xh.

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Fig. 2

Structural sensitivity tensor. Each component quantifies the effect of a feedback mechanism on the linear growth rate (solid line/left scale) and angular frequency (dashed line/right scale) of the oscillations. c1 = 0.01, c2 = 0.001, τ = 0.01, β = 0.39, xh = 0.25.

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Fig. 3

Top frames: structural sensitivity of the growth rate, Re(δσ/δβc), and of the angular frequency, Im(δσ/δβc), when a control hot wire is placed at position xc. Bottom frames: Rayleigh index for a control wire placed at xc. System parameters as in Fig. 2.

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Fig. 4

Stabilization with a control wire introduced at t = 1000 and placed at optimal position xc = 0.8 predicted by adjoint analysis. System parameters as in Fig. 2, βc = β/10.

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Fig. 5

An infinitesimal variation of the cross-sectional area A(x) of the Rijke tube is regarded as a localized feedback mechanism for passive control

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Fig. 6

Hot wire as heat source: sensitivity to base-state modifications. System parameters as in Fig. 2.

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Fig. 7

Diffusion flame as heat source: sensitivity to base-state modifications of Zsto and Pe

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Fig. 8

Flame shape, represented by the stoichiometric curve, as a function of Zsto (a) and Pe (b). In the top frame, Pe = 60; in the bottom frame, Zsto = 0.8.

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