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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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References

Schmitt, P. , Poinsot, T. , Schuermans, B. , and Geigle, K. P. , 2007, “ Large-Eddy Simulation and Experimental Study of Heat Transfer, Nitric Oxide Emissions and Combustion Instability in a Swirled Turbulent High-Pressure Burner,” J. Fluid Mech., 570(2), pp. 17–46. [CrossRef]
Sengissen, A. X. , Van Kampen, J. F. , Huls, R. A. , Stoffels, G. G. M. , Kok, J. B. W. , and Poinsot, T. J. , 2007, “ LES and Experimental Studies of Cold and Reacting Flow in a Swirled Partially Premixed Burner With and Without Fuel Modulation,” Combust. Flame, 150(1–2), pp. 40–53. [CrossRef]
Krediet, H. J. , Portillo, J. , Krebs, W. , and Kok, J. , 2010, “ Prediction of Thermoacoustic Limit Cycles During Premixed Combustion Using the Modified Galerkin Approach,” AIAA Paper No. 2010-7150.
Krebs, W. , Krediet, H. , Portillo, E. , Hermeth, S. , Poinsot, T. , Schimek, S. , and Paschereit, O. , 2013, “ Comparison of Nonlinear to Linear Thermoacoustic Stability Analysis of a Gas Turbine Combustion System,” ASME J. Eng. Gas Turbines Power, 135(8), p. 081503. [CrossRef]
Palies, P. , Durox, D. , Schuller, T. , and Candel, S. , 2011, “ Nonlinear Combustion Instability Analysis Based on the Flame Describing Function Applied to Turbulent Premixed Swirling Flames,” Combust. Flame, 158(10), pp. 1980–1991. [CrossRef]
Noiray, N. , Durox, D. , Schuller, T. , and Candel, S. , 2008, “ A Unified Framework for Nonlinear Combustion Instability Analysis Based on the Flame Describing Function,” J. Fluid Mech., 615, pp. 139–167. [CrossRef]
Silva, C. F. , Nicoud, F. , Schuller, T. , Durox, D. , and Candel, S. , 2013, “ Combining a Helmholtz Solver With the Flame Describing Function to Assess Combustion Instability in a Premixed Swirled Combustor,” Combust. Flame, 160(9), pp. 1743–1754. [CrossRef]
Cuquel, A. , Silva, C. , Nicoud, F. , Durox, D. , and Schuller, T. , 2013, “ Prediction of the Nonlinear Dynamics of a Multiple Flame Combustor by Coupling the Describing Function Methodology With a Helmholtz Solver,” ASME Paper No. GT2013-95659.
Palies, P. , Durox, D. , Schuller, T. , and Candel, S. , 2011, “ Experimental Study on the Effect of Swirler Geometry and Swirl Number on Flame Describing Functions,” Combust. Sci. Technol., 183(7), pp. 704–717. [CrossRef]
Dowling, A. P. , and Stow, S. R. , 2003, “ Acoustic Analysis of Gas Turbine Combustors,” J. Propul. Power, 19(5), pp. 751–764. [CrossRef]
Laera, D. , Prieur, K. , Durox, D. , Schuller, T. , Camporeale, S. M. , and Candel, S. , 2017, “ Impact of Heat Release Distribution on the Spinning Modes of an Annular Combustor With Multiple Matrix Burners,” ASME J. Eng. Gas Turbines Power, 139(5), p. 051505. [CrossRef]
Kim, K. T. , Lee, J. G. , Quay, B. D. , and Santavicca, D. A. , 2010, “ Spatially Distributed Flame Transfer Functions for Predicting Combustion Dynamics in Lean Premixed Gas Turbine Combustors,” Combust. Flame, 157(9), pp. 1718–1730. [CrossRef]
Campa, G. , Camporeale, S. M. , Cosatto, E. , and Mori, G. , 2012, “ Thermoacoustic Analysis of Combustion Instability Through a Distributed Flame Response Function,” ASME Paper No. GT2012-68243.
Campa, G. , and Camporeale, S. M. , 2014, “ Prediction of the Thermoacoustic Combustion Instabilities in Practical Annular Combustors,” ASME J. Eng. Gas Turbines Power, 136(9), p. 91504. [CrossRef]
Hummel, T. , Temmler, C. , Schuermans, B. , and Sattelmayer, T. , 2015, “ Reduced-Order Modeling of Aeroacoustic Systems for Stability Analyses of Thermoacoustically Noncompact Gas Turbine Combustors,” ASME J. Eng. Gas Turbines Power, 138(5), p. 051502. [CrossRef]
Paschereit, C. O. , Schuermans, B. , Polifke, W. , and Mattson, O. , 2002, “ Measurement of Transfer Matrices and Source Terms of Premixed Flames,” ASME J. Eng. Gas Turbines Power, 124(2), pp. 239–247. [CrossRef]
Jang, S.-H. , 1998, “ On the Multiple Microphone Method for Measuring In-Duct Acoustic Properties in the Presence of Mean Flow,” J. Acoust. Soc. Am., 103(3), pp. 1520–1526. [CrossRef]
Åbom, M. , and Bodén, H. , 1988, “ Error Analysis of Two-Microphone Measurements in Ducts With Flow,” J. Acoust. Soc. Am., 83(6), pp. 2429–2438. [CrossRef]
Law, C. K. , 2006, Combustion Physics, Cambridge University Press, Cambridge, UK.
Rofi, L. , Campa, G. , Anisimov, V. , Daccá, F. , Bertolotto, E. , Gottardo, E. , and Bonzani, F. , 2015, “ Numerical Procedure for the Investigation of Combustion Dynamics in Industrial Gas Turbines: LES, RANS and Thermoacoustics,” ASME Paper No. GT2015-42168.
Laera, D. , Gentile, A. , Camporeale, S. M. , Bertolotto, E. , Rofi, L. , and Bonzani, F. , 2015, “ Numerical and Experimental Investigation of Thermo-Acoustic Combustion Instability in a Longitudinal Combustion Chamber: Influence of the Geometry of the Plenum,” ASME Paper No. GT2015-42322.
Polifke, W. , Paschereit, C. O. , and Döbbeling, K. , 2001, “ Constructive and Destructive Interference of Acoustic and Entropy Waves in a Premixed Combustor With a Choked Exit,” J. Acoust. Vib., 6(3), pp. 135–146.
Campa, G. , and Camporeale, S. M. , 2010, “ Influence of Flame and Burner Transfer Matrix on Thermoacoustic Combustion Instability Modes and Frequencies,” ASME Paper No. GT2010-23104.
Campa, G. , and Camporeale, S. , 2012, “ Eigenmode Analysis of the Thermoacoustic Combustion Instabilities Using a Hybrid Technique Based on the Finite Element Method and the Transfer Matrix Method,” Adv. Appl. Acoust., 1(1), pp. 1–14.
Alemela, P. R. , Fanaca, D. , Ettner, F. , Hirsch, C. , Sattelmayer, T. , and Schuermans, B. , 2008, “ Flame Transfer Matrices of a Premixed Flame and a Global Check With Modelling and Experiments,” ASME Paper No. GT2008-50111.
Laera, D. , Campa, G. , Camporeale, S. M. , Bertolotto, E. , Rizzo, S. , Bonzani, F. , Ferrante, A. , and Saponaro, A. , 2014, “ Modelling of Thermoacoustic Combustion Instabilities Phenomena: Application to an Experimental Test Rig,” Energy Procedia, 45, pp. 1392–1401. [CrossRef]
Laera, D. , Campa, G. , Camporeale, S. M. , Bertolotto, E. , Rizzo, S. , Bonzani, F. , and Ferrante, A. , 2014, “ Modelling of Thermoacoustic Combustion Instabilities Phenomena: Application to an Experimental Rig for Testing Full Scale Burners,” ASME Paper No. GT2014-25273.
Selle, L. , Lartigue, G. , Poinsot, T. , Koch, R. , Schildmacher, K. U. , Krebs, W. , Prade, B. , Kaufmann, P. , and Veynante, D. , 2004, “ Compressible Large Eddy Simulation of Turbulent Combustion in Complex Geometry on Unstructured Meshes,” Combust. Flame, 137(4), pp. 489–505. [CrossRef]
Hermeth, S. , Staffelbach, G. , Gicquel, L. Y. , Anisimov, V. , Cirigliano, C. , and Poinsot, T. , 2014, “ Bistable Swirled Flames and Influence on Flame Transfer Functions,” Combust. Flame, 161(1), pp. 184–196. [CrossRef]
Poinsot, T. , and Veynante, D. , 2005, Theoretical and Numerical Combustion, T. Poinsot and D. Veynante , eds., R. T. Edwards, Philadelphia, PA.
Dowling, A. , 1995, “ The Calculation of Thermoacoustic Oscillations,” J. Sound Vib., 180(4), pp. 557–581. [CrossRef]
Lieuwen, T. , and Yang, V. , eds., 2005, “ Combustion Instabilities in Gas Turbine Engines: Operational Experience, Fundamental Mechanisms and Modeling,” Progress in Astronautics and Aeronautics, American Institute of Aeronautics and Astronautics, Reston, VA.
Nicoud, F. , and Wieczorek, K. , 2009, “ About the Zero Mach Number Assumption in the Calculation of Thermoacoustic Instabilities,” Int. J. Spray Combust. Dyn., 1(1), pp. 67–111. [CrossRef]
Gikadi, J. , Sattelmayer, T. , and Peschiulli, A. , 2012, “ Effects of the Mean Flow Field on the Thermo-Acoustic Stability of Aero-Engine Combustion Chambers,” ASME Paper No. GT2012-69612.
Dowling, A. P. , 1997, “ Nonlinear Self-Excited Oscillations of a Ducted Flame,” J. Fluid Mech., 346, pp. 271–290. [CrossRef]
Li, J. , and Morgans, A. S. , 2015, “ Time Domain Simulations of Nonlinear Thermoacoustic Behaviour in a Simple Combustor Using a Wave-Based Approach,” J. Sound Vib., 346(1), pp. 345–360. [CrossRef]
Camporeale, S. M. , Fortunato, B. , and Campa, G. , 2010, “ A Finite Element Method for Three-Dimensional Analysis of Thermo-Acoustic Combustion Instability,” ASME J. Eng. Gas Turbines Power, 133(1), p. 11506. [CrossRef]
Laera, D. , 2015, “ Nonlinear Combustion Instabilities Analysis of Azimuthal Mode in Annular Chamber,” Energy Procedia, 82, pp. 921–928. [CrossRef]
Munjal, M. L. , 1987, Acoustics of Ducts and Mufflers With Application to Exhaust and Ventilation System Design, Wiley, New York.
Goh, C. S. , and Morgans, A. S. , 2013, “ The Influence of Entropy Waves on the Thermoacoustic Stability of a Model Combustor,” Combust. Sci. Technol., 185(2), pp. 249–268. [CrossRef]
Palies, P. , Durox, D. , Schuller, T. , and Candel, S. , 2010, “ The Combined Dynamics of Swirler and Turbulent Premixed Swirling Flames,” Combust. Flame, 157(9), pp. 1698–1717. [CrossRef]
Balusamy, S. , Li, L. K. , Han, Z. , and Hochgreb, S. , 2016, “ Extracting Flame Describing Functions in the Presence of Self-Excited Thermoacoustic Oscillations,” Proc. Combust. Inst., 36(3), pp. 3851–3861. [CrossRef]
Bourgouin, J.-F. F. , Durox, D. , Moeck, J. P. , Schuller, T. , and Candel, S. , 2014, “ Characterization and Modeling of a Spinning Thermoacoustic Instability in an Annular Combustor Equipped With Multiple Matrix Injectors,” ASME J. Eng. Gas Turbines Power, 137(2), p. 21503. [CrossRef]
Nicoud, F. , Benoit, L. , Sensiau, C. , and Poinsot, T. , 2007, “ Acoustic Modes in Combustors With Complex Impedances and Multidimensional Active Flames,” AIAA J., 45(2), pp. 426–441. [CrossRef]
Han, X. , Li, J. , and Morgans, A. S. , 2015, “ Prediction of Combustion Instability Limit Cycle Oscillations by Combining Flame Describing Function Simulations With a Thermoacoustic Network Model,” Combust. Flame, 162(10), pp. 3632–3647. [CrossRef]
Laera, D. , Campa, G. , and Camporeale, S. M. , 2017, “ A Finite Element Method for a Weakly Nonlinear Dynamic Analysis and Bifurcation Tracking of Thermo-Acoustic Instability in Longitudinal and Annular Combustors,” Appl. Energy, 187, pp. 216–227. [CrossRef]

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. 13

Contour plot of time delays on the flame front

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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. 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. 9

Mesh refinement, approximately 280,000 tetrahedral elements

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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. 7

Computational domain of the LRIA combustor

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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. 11

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

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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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