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Research Papers: Gas Turbines: Combustion, Fuels, and Emissions

Describing Function Analysis of Limit Cycles in a Multiple Flame Combustor

[+] Author and Article Information
Frédéric Boudy1

Laboratoire EM2C, Ecole Centrale Paris, CNRS, Grande Voie des Vignes, 92295 Châtenay-Malabry, Francefrederic.boudy@em2c.ecp.fr

Daniel Durox, Thierry Schuller

Laboratoire EM2C, Ecole Centrale Paris, CNRS, Grande Voie des Vignes, 92295 Châtenay-Malabry, France

Grunde Jomaas2

Laboratoire EM2C, Ecole Centrale Paris, CNRS, Grande Voie des Vignes, 92295 Châtenay-Malabry, France

Sébastien Candel3

Laboratoire EM2C, Ecole Centrale Paris, CNRS, Grande Voie des Vignes, 92295 Châtenay-Malabry, France

1

Corresponding author.

2

Present address: Technical University of Denmark (DTU).

3

Also with Institut Universitaire de France.

J. Eng. Gas Turbines Power 133(6), 061502 (Feb 15, 2011) (8 pages) doi:10.1115/1.4002275 History: Received June 02, 2010; Revised June 06, 2010; Published February 15, 2011; Online February 15, 2011

A recently developed nonlinear flame describing function (FDF) is used to analyze combustion instabilities in a system where the feeding manifold has a variable size and where the flame is confined by quartz tubes of variable length. Self-sustained combustion oscillations are observed when the geometry is changed. The regimes of oscillation are characterized at the limit cycle and also during the onset of oscillations. The theoretical predictions of the oscillation frequencies and levels are obtained using the FDF. This generalizes the concept of flame transfer function by including dependence on the frequency and level of oscillation. Predictions are compared with experimental results for two different lengths of the confinement tube. These results are, in turn, used to predict most of the experimentally observed phenomena and in particular, the correct oscillation levels and frequencies at limit cycles.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Experimental setup used to characterize self-sustained instabilities

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Figure 2

Stable (L1=0.25 m) and unstable (L1=0.29 m) combustion regimes at 750 Hz for an equivalence ratio ϕ=1.03 and a confinement tube L2=0.1 m

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Figure 3

Forced flow setup used to determine the FDF. The forced flow fluctuations are created by a loudspeaker placed at the bottom of the burner. Velocity fluctuations are measured by LDV at the base of one flame 0.7 mm above the hole and heat release rate fluctuations are deduced from IOH∗′ measured by a photomultiplier.

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Figure 4

Frequency and pressure level evolutions with the L2=0.1 m confinement tube swept from 0.15 m to 0.54 m (o) and from 0.54 m to 0.15 m (x) of the feeding manifold. The acoustic eigenmodes without combustion are plotted with dashed lines.

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Figure 5

Frequency and pressure level evolutions with the L2=0.2 m confinement tube swept from 0.15 m to 0.54 m (o) and from 0.54 m to 0.15 m (x) of the feeding manifold. The acoustic eigenmodes without combustion are plotted with dashed lines.

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Figure 6

Burner and symbol conventions used for the analytical model

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Figure 7

Measurements of the gain G and phase φ of the FDF as function of frequency and input level. uRMS′ corresponds to the RMS value of the fluctuation amplitude and Ubulk corresponds to the mean flow velocity within one hole.

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Figure 8

Regions of positive values of growth rate (in s−1) calculated from the dispersion relation for the L2=0.1 m confinement as function of the length of the feeding manifold L1 and the relative fluctuation level uRMS′/Ubulk

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Figure 9

Experimental and predicted oscillation frequencies of self-sustained instabilities for the L2=0.1 m confinement tube for increasing (a) and decreasing (b) sweeps of the feeding manifold length L1

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Figure 10

Experimental and predicted oscillation frequencies of self-sustained instabilities for the L2=0.2 m confinement tube. Increasing and decreasing L1 has the same influence on the frequency evolution.

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Figure 11

Experimental and predicted amplitudes of the instabilities for the L2=0.1 m confinement tube for increasing (a) and decreasing (b) sweeps of the feeding manifold length L1

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Figure 12

Experimental and predicted amplitudes of the instabilities for the L2=0.2 m confinement tube. Increasing and decreasing L1 has the same influence on the amplitude evolution.

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