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TECHNICAL PAPERS: Gas Turbines: Combustion and Fuels

Transfer Function Calculations for Aeroengine Combustion Oscillations

[+] Author and Article Information
M. Zhu

Department of Thermal Engineering, Tsinghua University, Beijing 100084, Chinae-mail: zhumin@tsinghua.edu.cn

A. P. Dowling, K. N. C. Bray

Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK

J. Eng. Gas Turbines Power 127(1), 18-26 (Feb 09, 2005) (9 pages) doi:10.1115/1.1806451 History: Received December 01, 2000; Revised March 01, 2001; Online February 09, 2005
Copyright © 2005 by ASME
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References

Zhu,  M., Dowling,  A. P., and Bray,  K. N. C., 2001, “Self-Excited Oscillations in Combustors With Spray Atomizers,” Trans. ASME: J. Eng. Gas Turbines Power, 123, pp. 779–786.
Cumpsty,  N. A., and Marble,  F. E., 1977, “The Interaction of Entropy Fluctuations With Turbine Blade Rows: A Mechanism of Turbojet Engine Noise,” Proc. R. Soc. London, Ser. A, 357, pp. 323–344.
Marble,  F. E., and Candel,  S. M., 1977, “Acoustics Disturbances From Gas Non-Uniformities Convected Through a Nozzle,” J. Sound Vib., 55, pp. 225–243.
Lawn, C. J., 2000, “Thermo-Acoustic Frequency Selection by Swirled Premixed Flames,” in Proceedings of the Combustion Institute, 28 , pp. 823–830, Edinburgh, Scotland.
Lieuwen, T., and Neumeier, Y., 2002, “Nonlinear Pressure-Heat Release Transfer Function Measurements in a Premixed Combustor,” in Proceedings of the Combustion Institute, 29 , pp. 99–105, Sapporo, Japan.
Bohn,  D., Deutsch,  G., and Krüger,  U., 1998, “Numerical Prediction of the Dynamic Behavior of Turbulent Diffusion Flames,” Trans. ASME: J. Eng. Gas Turbines Power, 120, pp. 713–720.
Hobson, D., Fackrell, J., and Hewitt, G., 1999, “Combustion Instabilies in Industrial Gas Turbines: Measurements on Operating Plant and Thermoacoustic Modelling,” ASME Paper No. 99-GT-110, Indianapolis, Indiana, June 1999, ASME International Gas Turbine and Aeroengine Congress and Exhibition.
Krüger, U., Hüren, J., Hoffmann, S., Krebs, W., and Bohn, D., 1999, “Prediction of Thermoacoustic Instabilities With Focus on the Dynamic Flame Behavior for the 3A-Series Gas Turbine of Siemens KWU,” ASME Paper No. 99-GT-111, Indianapolis, Indiana, June 1999. ASME International Gas Turbine and Aeroengine Congress and Exhibition.
Polifke,  W., Poncet,  A., Paschereit,  C. O., and Döbbeling,  K., 2001, “Reconstruction of Acoustic Transfer Matrices by Instationary Computational Fluid Dynamics,” J. Sound Vib., 245, pp. 483–510.
Kaufmann,  A., Nicoud,  F., and Poinsot,  T., 2002, “Flow Forcing Techniques for Numerical Simulation of Combustion Instabilities,” Combust. Flame, 131, pp. 371–385.
Huang,  Y., Sung,  H. G., Hsieh,  S. Y., and Yang,  V., 2003, “Large-Eddy Simulation of Combustion Dynamics of Lean-Premixed Swirl-Stabilized Combustor,” J. Propul. Power, 19, pp. 782–794.
Zhu,  M., Dowling,  A. P., and Bray,  K. N. C., 2002, “Forced Oscillations in Combustors With Spray Atomizers,” Trans. ASME: J. Eng. Gas Turbines Power, 124, pp. 20–30.
Nelson, P. A., and Elliott, S. J., 1992, Active Control of Sound, Academic Press, London.
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Zhu, M., Dowling, A. P., and Bray, K. N. C., 2001, “Integration of CFD and Low-Order Models for Combustion Oscillations in Aero-Engines,” ISABE-2001-1088, Bangalore, India, 2–7 September, 2001. XV International Symposium on Air-Breathing Engines.

Figures

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Schematic diagram of the geometry
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Contour plot of the mean temperature distribution chamber at idle conditions. The black line indicates the mean position of the stoichiometric curve and arrows denote the direction and magnitude of the mean velocity.
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Sinusoidal changes of the total pressure in the atomiser air inlet lead to oscillations in the mixture fraction, scalar dissipation, and heat release rate at points A and B
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The transfer function between the heat release rate per unit length and the sinusoidal changes of air flow rate through the atomizer at the forcing frequency of 50 Hz
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(a) The air mass flow rate at the inlet boundary as the impulse function was applied. (b) The downstream response of the heat release rate at the location x=0.088 m, where the solid lines indicate the result from the CFD calculation and dashed line indicates that from the IIR filter in time domain.
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The transfer function between the heat release rate per unit length and the sinusoidal changes of air flow rate through the atomizer at frequency 50 Hz, where the dashed lines indicate the result from the harmonic forcing calculation and solid lines indicate that from the IIR filter
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The variations of the total pressure, air mass flow rate, and the Sauter mean diameter in the atomizer inlet due to the forcing of the random binary signal
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The variations of the total pressure, air mass flow rate, and the Sauter mean diameter in the atomizer inlet due to the forcing by the sum of the random sinusoids
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The transfer function between the heat release rate per unit length and the sinusoidal changes of air flow rate through the atomizer at frequency 50 Hz, where the dashed lines indicate the result from the harmonic forcing calculation and solid lines indicate that from the random binary signal forcing calculation
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The transfer function between the heat release rate per unit length and the sinusoidal changes of air flow rate through the atomizer at frequency 50 Hz, where the dashed lines indicate the result from the harmonic forcing calculation and solid lines indicate that from the sum of the random sinusoids forcing calculation
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Magnitude and phase of the transfer function between heat release rate per unit length and air flow rate through the atomizer, for a location x0=0.014 m in the primary zone, calculated by forcing by the sum of random sinusoids
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Magnitudes (a) and phases (b) of the frequency response of local heat release rate, mixture fraction, and scalar dissipation calculated by forcing by the sum of sinusoids at point A in Fig. 1
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Magnitudes (a) and phases (b) of the frequency response of local heat release rate, mixture fraction, and scalar dissipation calculated by forcing by the sum of sinusoids at point B in Fig. 1
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Magnitude and phase of the transfer function between heat release rate per unit length and air flow rate through the atomiser, for a location x0=0.226 m in the dilution zone, calculated by forcing by the sum of random sinusoids
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The lag-time τ against axial coordinate

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