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

A Weakly Nonlinear Approach Based on a Distributed Flame Describing Function to Study the Combustion Dynamics of a Full-Scale Lean-Premixed Swirled Burner

[+] Author and Article Information
Davide Laera

DMMM,
Sez. Macchine ed Energetica,
Politecnico di Bari,
Via Re David 200,
Bari 70125, Italy
e-mail: davide.laera@poliba.it

Sergio M. Camporeale

DMMM,
Sez. Macchine ed Energetica,
Politecnico di Bari,
Via Re David 200,
Bari 70125, Italy

1Corresponding author.

Contributed by the Combustion and Fuels Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received July 20, 2016; final manuscript received January 23, 2017; published online April 11, 2017. Assoc. Editor: Joseph Zelina.

J. Eng. Gas Turbines Power 139(9), 091501 (Apr 11, 2017) (11 pages) Paper No: GTP-16-1354; doi: 10.1115/1.4036010 History: Received July 20, 2016; Revised January 23, 2017

Modern combustion chambers of gas turbines for power generation and aero-engines suffer of thermo-acoustic combustion instabilities generated by the coupling of heat release rate fluctuations with pressure oscillations. The present article reports a numerical analysis of limit cycles arising in a longitudinal combustor. This corresponds to experiments carried out on the longitudinal rig for instability analysis (LRIA) test facility equipped with a full-scale lean-premixed burner. Heat release rate fluctuations are modeled considering a distributed flame describing function (DFDF), since the flame under analysis is not compact with respect to the wavelengths of the unstable modes recorded experimentally. For each point of the flame, a saturation model is assumed for the gain and the phase of the DFDF with increasing amplitude of velocity fluctuations. A weakly nonlinear stability analysis is performed by combining the DFDF with a Helmholtz solver to determine the limit cycle condition. The numerical approach is used to study two configurations of the rig characterized by different lengths of the combustion chamber. In each configuration, a good match has been found between numerical predictions and experiments in terms of frequency and wave shape of the unstable mode. Time-resolved pressure fluctuations in the system plenum and chamber are reconstructed and compared with measurements. A suitable estimate of the limit cycle oscillation is found.

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Figures

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Fig. 1

(a) Sketch of the LRIA combustor with the components details and (b) with the indication of the pressure fluctuation measurement positions (distances are reported in terms of the diameter D). (c) Full-scale swirled burner details [29].

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Fig. 2

Pressure signals recorded by pressure transducers in the plenum (a) and in the combustion chamber (b) at limit cycle in the rig configuration with lcc/lcc,max = 0.53. Signals are filtered on a narrow bandwidth around the self-excited eigenmode peak.

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Fig. 3

Spectrum of the pressure records in the combustion chamber in the rig configuration with lcc/lcc,max = 0.53 shown in Fig. 2(b)

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Fig. 4

Pressure signals recorded by the first two pressure transducers placed in the combustion chamber for the configuration with the lcc/lcc,max = 0.53. During the unstable conditions, the length of the plenum (dashed line) is reduced 20% of its maximum extension showing a damping of pressure fluctuations. When the length of the plenum is changed back at its maximum value, the amplitude returns to its level.

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Fig. 5

Spectrum of the pressure signals shown in Fig. 4 for the (a) long plenum and (b) short plenum configuration

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Fig. 6

Spectrum analysis of the pressure records of the combustion chamber in the configuration with lcc/lcc,max = 0.84

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Fig. 7

Computational domain of the LRIA combustor

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Fig. 8

Detail of the upstream and downstream sections of the transfer matrix of the burner

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Fig. 9

Mesh refinement, approximately 280,000 tetrahedral elements

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Fig. 10

Contour plots of the baseline flow quantities: (a) normalized temperature (T/Tair), (b) normalized density (ρ/ρair), and (c) normalized reaction rate (rr/rrmax)

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Fig. 11

Pattern of the G function for μ0 = n = 1 and μ2 = −2

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Fig. 12

(a) Influence of the extension of the flame domain (hfs) on the frequency and growth rate α of the first three modes of the combustion chamber for the configuration with lcc/lcc,max = 0.53 assuming a time delay τ/T = 0.43. (b) Influence of the time delay on the mode fn = 1 assuming a flame model extension hfs,1/λ = 1%.

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Fig. 13

Contour plot of time delays on the flame front

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Fig. 14

Linear stability analysis performed on the first five modes of the system plotted on a stability plane in terms of normalized frequency and growth rate α. Only the mode at normalized frequency fn = 1 is predicted unstable.

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Fig. 15

Numerical (continuous line with triangular marks) and experimental (dashed line with rectangular marks) wave shape comparison in the plenum (a) and in the combustion chamber (b) for the resonant mode at fn = 1. The pressure transducers' measurements used for the experimental reconstructions are reported with the plain circular marks.

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Fig. 16

Growth rate (a) and frequency (b) for different velocity fluctuation levels |û/u¯| for the configuration with lcc/lcc,max = 0.5. The limit cycle condition is indicated with the square symbol.

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Fig. 17

Five pressure signals recorded by pressure transducers in the combustion chamber (dashed lines) compared with numerical reconstructions (continuous line) for the unstable mode at normalized frequency fn ≃ 1

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Fig. 18

Three pressure signals recorded by pressure transducers in the plenum (dashed lines) compared with numerical reconstructions (continuous line) for the unstable mode at frequency fn = 1

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Fig. 19

Growth rate trajectories in a α-|û/u¯| plane for the long plenum configuration (dashed line) and the short plenum configuration (continuous line). The two limit cycle conditions are indicated, respectively, with a square and a circle.

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Fig. 20

Numerical reconstruction of the PTC1 and PTC2 pressure transducers' signals in the combustion chamber. When the length of the plenum is reduced to its minimum value, an amplitude drop of approximately 50% is observed. These results are in line with the experimental observation shown in Fig. 4.

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Fig. 21

Numerical (continuous line with triangular marks) and experimental (dashed line with rectangular marks) wave shape comparison in the plenum (a) and in the combustion chamber (b) for the resonant mode at fn = 0.62. The pressure transducers' measurements used for the experimental reconstructions are reported with the plain circular marks.

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Fig. 22

Growth rate (a) and frequency (b) for different amplitudes of velocity fluctuations |û/u¯| for the configuration with lcc/lcc,max = 0.84. The limit cycle condition is indicated with the square symbol.

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Fig. 23

Two pressure signals recorded by pressure transducers (dashed lines) compared with numerical reconstructions (continuous line) in the (a) plenum and (b) combustion chamber for the unstable mode at frequency fn = 0.62

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