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Research Papers

Flame Describing Functions of a Confined Premixed Swirled Combustor With Upstream and Downstream Forcing

[+] Author and Article Information
R. Gaudron, M. Gatti, C. Mirat

Laboratoire EM2C,
CNRS, CentraleSupélec,
Université Paris-Saclay,
3, rue Joliot Curie,
Gif-sur-Yvette cedex 91192, France

T. Schuller

Laboratoire EM2C,
CNRS, CentraleSupélec,
Université Paris-Saclay,
3, rue Joliot Curie,
Gif-sur-Yvette cedex 91192, France;
Institut de Mécanique des Fluides
de Toulouse (IMFT),
Université de Toulouse,
CNRS, INPT, UPS,
2 allée du Professeur Camille Soula,
Toulouse 31400, France
e-mail: renaud.gaudron@centralesupelec.fr

Manuscript received June 22, 2018; final manuscript received June 29, 2018; published online January 9, 2019. Editor: Jerzy T. Sawicki.

J. Eng. Gas Turbines Power 141(5), 051016 (Jan 09, 2019) (9 pages) Paper No: GTP-18-1306; doi: 10.1115/1.4041000 History: Received June 22, 2018; Revised June 29, 2018

The frequency response of a confined premixed swirled flame is explored experimentally through the use of describing functions that depend on both the forcing frequency and the forcing level. In these experiments, the flame is forced by a loudspeaker connected to the bottom of the burner in the fresh gas region or by a set of loudspeakers connected to the combustion chamber exhaust tube in the burnt gas region. The experimental setup is equipped with a hot-wire (HW) probe and a microphone, both of which located in front of each other below the swirler. The forcing level is varied between |v0|/v¯0=0.10 and 0.72 RMS, where v¯0 and v0 are, respectively, the mean and the fluctuating velocity at the HW probe. An additional microphone is placed on a water-cooled waveguide connected to the combustion chamber backplate. A photomultiplier equipped with an OH* filter is used to measure the heat release rate fluctuations. The describing functions between the photomultiplier signal and the different pressure and velocity reference signals are then analyzed in the case of upstream and downstream forcing. The describing function measured for a given reference signal is shown to vary depending on the type of forcing. The impedance of the injector at the HW location is also determined for both upstream and downstream forcing. For all describing functions investigated, it is found that their phase lags do not depend on the forcing level, whereas their gains strongly depend on |v0|/v¯0 for certain frequency ranges. It is furthermore shown that the flame describing function (FDF) measured with respect to the HW signal can be retrieved from the specific impedance at the HW location and the describing function determined with respect to the signal of the microphone located in front of the HW. This relationship is not valid when the signal from the microphone located at the combustion chamber backplate is considered. It is then shown that a one-dimensional (1D) acoustic model allows to reproduce the describing function computed with respect to the microphone signal inside the injector from the microphone signal located at the combustion chamber backplate in the case of downstream forcing. This relation does not hold for upstream forcing because of the acoustic dissipation across the swirler which is much larger compared to downstream forcing for a given forcing level set at the HW location. This study sheds light on the differences between upstream and downstream acoustic forcing when measuring describing functions. It is also shown that the upstream and downstream forcing techniques are equivalent only if the reference signal used to determine the FDF is the acoustic velocity in the fresh gases just before the flame.

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References

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Figures

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Fig. 1

Experimental setup used to determine various describing functions

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Fig. 2

Mean OH* chemiluminescence distribution for steady flow injection conditions. ϕ = 0.82, Ub = 5.4 m/s.

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Fig. 3

Zoomed view on the injector and acoustic model representing the injector dynamics. All dimensions are in mm.

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Fig. 4

Describing functions obtained with downstream forcing for six different forcing levels |v′0|/v¯0 measured at the HW location. FHW: (Q˙′/Q˙¯)/(v′0/v¯0); FMHW: (Q˙′/Q˙¯)/(p0′/p¯0); FMC: (Q˙′/Q˙¯)/(p8′/p¯8); and FMHW→HW=zv¯0FMHW/p¯0.

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Fig. 5

Describing function determined with microphone MHW and its reconstruction from microphone MC and Eq. (9). Results are shown for six forcing levels |v′0|/v¯0 and for downstream forcing.

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Fig. 6

Describing functions obtained with upstream forcing for six different forcing levels |v′0|/v¯0 measured at the HW location. FHW: (Q˙′/Q˙¯)/(v′0/v¯0); FMHW: (Q˙′/Q˙¯)/(p0′/p¯0); FMC: (Q˙′/Q˙¯)/(p8′/p¯8); and FMHW→HW=zv¯0FMHW/p¯0.

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Fig. 7

Describing function determined with microphone MHW and its reconstruction from microphone MC and Eq. (9). Results are shown for six forcing levels |v′0|/v¯0 and for upstream forcing.

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Fig. 8

Describing function determined with microphone MHW and its reconstruction from microphone MC and the new model accounting for acoustic dissipation at the swirler holes according to Eq. (13). Results are shown for six forcing levels |v′0|/v¯0 and for upstream forcing.

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Fig. 9

Reconstructed FDFs with respect to the acoustic velocity at the injector outlet (section (7) in Fig. 3) for six different forcing levels |v′0|/v¯0 measured by the HW probe. Left: upstream forcing; right: downstream forcing.

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