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Mixed acoustic–entropy combustion instabilities in gas turbines

Published online by Cambridge University Press:  16 May 2014

Emmanuel Motheau Open the ORCID record for Emmanuel Motheau [Opens in a new window] ,
Franck Nicoud  and
Thierry Poinsot
Emmanuel Motheau*
Affiliation:
CERFACS, 42 avenue Gaspard Coriolis, 31057 Toulouse, France
Franck Nicoud
Affiliation:
CNRS – I3M, University Montpellier II, 34095 Montpellier, France
Thierry Poinsot
Affiliation:
CNRS – Institut de Mécanique des Fluides, 1 Allée du Professeur Camille Soula, 31000 Toulouse, France
*
†Email address for correspondence: [email protected]
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Abstract

A combustion instability in a combustor terminated by a nozzle is analysed and modelled based on a low-order Helmholtz solver. A large eddy simulation (LES) of the corresponding turbulent, compressible and reacting flow is first performed and analysed based on dynamic mode decomposition (DMD). The mode with the highest amplitude shares the same frequency of oscillation as the experiment (approximately 320 Hz) and shows the presence of large entropy spots generated within the combustion chamber and convected down to the exit nozzle. The lowest purely acoustic mode being in the range 700–750 Hz, it is postulated that the instability observed around 320 Hz stems from a mixed entropy–acoustic mode, where the acoustic generation associated with entropy spots being convected throughout the choked nozzle plays a key role. The DMD analysis allows one to extract from the LES results a low-order model that confirms that the mechanism of the low-frequency combustion instability indeed involves both acoustic and convected entropy waves. The delayed entropy coupled boundary condition (DECBC) (Motheau, Selle & Nicoud, J. Sound Vib., vol. 333, 2014, pp. 246–262) is implemented into a numerical Helmholtz solver where the baseline flow is assumed at rest. When fed with appropriate transfer functions to model the entropy generation and convection from the flame to the exit, the Helmholtz/DECBC solver predicts the presence of an unstable mode around 320 Hz, in agreement with both LES and experiments.

JFM classification

Acoustics: Acoustics Reacting Flows: Combustion Reacting Flows: Reacting Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 749 , 25 June 2014 , pp. 542 - 576
Copyright
© 2014 Cambridge University Press 

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References

Abouseif, G. E., Keklak, J. A. & Toong, T. Y. 1984 Ramjet rumble: the low-frequency instability mechanism in coaxial dump combustors. Combust. Sci. Technol. 36 (1–2), 83–108.Google Scholar
Bake, F., Richter, C., Muhlbauer, B., Kings, N., Rohle, I., Thiele, F. & Noll, B. 2009 The entropy wave generator (EWG): a reference case on entropy noise. J. Sound Vib. 326 (3–5), 574–598.Google Scholar
Bell, W., Daniel, B. & Zinn, B. 1973 Experimental and theoretical determination of the admittances of a family of nozzles subjected to axial instabilities. J. Sound Vib. 30 (2), 179–190.CrossRefGoogle Scholar
Bloy, A. W. 1979 The pressure waves produced by the convection of temperature disturbances in high subsonic nozzle flows. J. Fluid Mech. 94, 465–475.Google Scholar
Bodony, D. J. 2009 Scattering of an entropy disturbance into sound by a symmetric thin body. Phys. Fluids 21 (9), 096101.Google Scholar
Bohn, M. S. 1977 Response of a subsonic nozzle to acoustic and entropy disturbances. J. Sound Vib. 52 (2), 283–297.Google Scholar
Candel, S., Durox, D., Ducruix, S., Birbaud, A. L., Noiray, N. & Schuller, T. 2009 Flame dynamics and combustion noise: progress and challenges. Intl J. Aeroacoust. 8, 1–56.Google Scholar
CERFACS 2009 AVBP Handbook. See http://www.cerfacs.fr/4-26334-The-AVBP-code.php.Google Scholar
Chedevergne, F., Casalis, G. & Majdalani, J. 2012 Direct numerical simulation and biglobal stability investigations of the gaseous motion in solid rocket motors. J. Fluid Mech. 706, 190–218.Google Scholar
Chen, K. K., Tu, J. H. & Rowley, C. W. 2012 Variants of dynamic mode decomposition: boundary condition, Koopman, and Fourier analyses. J. Nonlinear Sci. 22 (6), 887–915.Google Scholar
Colin, O., Ducros, F., Veynante, D. & Poinsot, T. 2000 A thickened flame model for large eddy simulations of turbulent premixed combustion. Phys. Fluids 12 (7), 1843–1863.Google Scholar
Colin, O. & Rudgyard, M. 2000 Development of high-order Taylor–Galerkin schemes for unsteady calculations. J. Comput. Phys. 162 (2), 338–371.Google Scholar
Crocco, L. 1952 Aspects of combustion instability in liquid propellant rocket motors. Part II. J. Am. Rocket Soc. 22, 7–16.CrossRefGoogle Scholar
Culick, F. E. C. & Kuentzmann, P.2006 Unsteady motions in combustion chambers for propulsion systems. RTO AGARDograph AG-AVT-039. NATO Research and Technology Organization.Google Scholar
Cumpsty, N. A. & Marble, F. E. 1977 The interaction of entropy fluctuations with turbine blade rows; a mechanism of turbojet engine noise. Proc. R. Soc. Lond. A 357, 323–344.Google Scholar
Doak, P. E. 1998 Fluctuating total enthalpy as the basic generalized acoustic field. Theor. Comput. Fluid Dyn. 10 (1), 115–133.Google Scholar
Dowling, A. P. & Stow, S. R. 2003 Acoustic analysis of gas turbine combustors. J. Propul. Power 19 (5), 751–764.CrossRefGoogle Scholar
Duran, I. & Moreau, S. 2013 Solution of the quasi-one-dimensional linearized Euler equations using flow invariants and the Magnus expansion. J. Fluid Mech. 723, 190–231.Google Scholar
Duran, I., Moreau, S. & Poinsot, T. 2013 Analytical and numerical study of combustion noise through a subsonic nozzle. AIAA J. 51 (1), 42–52.Google Scholar
Eckstein, J., Freitag, E., Hirsch, C. & Sattelmayer, T. 2006 Experimental study on the role of entropy waves in low-frequency oscillations in a RQL combustor. Trans. ASME: J. Engng Gas Turbines Power 128 (2), 264–270.Google Scholar
Ffowcs-Williams, J. E. & Howe, M. S. 1975 The generation of sound by density inhomogeneities in low Mach number nozzle flows. J. Fluid Mech. 70 (3), 605–622.CrossRefGoogle Scholar
Franzelli, B., Riber, E., Sanjosé, M. & Poinsot, T. 2010 A two-step chemical scheme for large-eddy simulation of kerosene–air flames. Combust. Flame 157 (7), 1364–1373.Google Scholar
Gicquel, L. Y. M., Staffelbach, G. & Poinsot, T. 2012 Large eddy simulations of gaseous flames in gas turbine combustion chambers. Prog. Energy Combust. Sci. 38 (6), 782–817.Google Scholar
Goh, C. S. & Morgans, A. S. 2011 Phase prediction of the response of choked nozzles to entropy and acoustic disturbances. J. Sound Vib. 330 (21), 5184–5198.Google Scholar
Goh, C. S. & Morgans, A. S. 2013 The influence of entropy waves on the thermoacoustic stability of a model combustor. Combust. Sci. Technol. 185 (2), 249–268.Google Scholar
Hield, P., Brear, M. & Jin, S. H. 2009 Thermoacoustic limit cycles in a premixed laboratory combustor with open and choked exits. Combust. Flame 156 (9), 1683–1697.CrossRefGoogle Scholar
Hochgreb, S., Dennis, D. J. C., Ayranci, I., Bainbridge, W. & Cant, S.2013 Forced and self-excited instabilities from lean premixed, liquid-fuelled aeroengine injectors at high pressures and temperatures. In Proceedings of ASME Turbo Expo 2013, Paper GT2013-9531.Google Scholar
Howe, M. S. 2010 Indirect combustion noise. J. Fluid Mech. 659, 267–288.Google Scholar
Karimi, N., Brear, M. J., Jin, S.-H. & Monty, J. P. 2009 Linear and nonlinear forced response of a conical, ducted, laminar premixed flame. Combust. Flame 156 (11), 2201–2212.Google Scholar
Karlsson, M. & Åbom, M. 2010 Aeroacoustics of T-junctions – an experimental investigation. J. Sound Vib. 329 (10), 1793–1808.Google Scholar
Keller, J. J. 1995 Thermoacoustic oscillations in combustion chambers of gas turbines. AIAA J. 33 (12), 2280–2287.Google Scholar
Keller, J. J., Egli, W. & Hellat, J. 1985 Thermally induced low-frequency oscillations. Z. Angew. Math. Phys. 36, 250–274.Google Scholar
Kim, K. T., Lee, J. G., Quay, B. D. & Santavicca, D. A. 2010 Response of partially premixed flames to acoustic velocity and equivalence ratio perturbations. Combust. Flame 157 (9), 1731–1744.Google Scholar
Kornilov, V., Rook, R., ten Thije Boonkkamp, J. & de Goey, L. 2009 Experimental and numerical investigation of the acoustic response of multi-slit Bunsen burners. Combust. Flame 156 (10), 1957–1970.Google Scholar
Lawn, C. J., Evesque, S. & Polifke, W. 2004 A model for the thermoacoustic response of a premixed swirl burner. Part I: Acoustic aspects. Combust. Sci. Technol. 176 (8), 1331–1358.Google Scholar
Leyko, M., Moreau, S., Nicoud, F. & Poinsot, T. 2011 Numerical and analytical modelling of entropy noise in a supersonic nozzle with a shock. J. Sound Vib. 330 (16), 3944–3958; 1.Google Scholar
Lieuwen, T. & Yang, V. 2005 Combustion Instabilities in Gas Turbine Engines: Operational Experience, Fundamental Mechanisms, and Modeling. (Progress in Astronautics and Aeronautics) , vol. 210. AIAA.Google Scholar
Macquisten, M. A. & Dowling, A. P. 1994 Low-frequency combustion oscillations in a model afterburner. Combust. Flame 94 (4), 253–264.Google Scholar
Marble, F. E. & Candel, S. 1977 Acoustic disturbances from gas nonuniformities convected through a nozzle. J. Sound Vib. 55, 225–243.CrossRefGoogle Scholar
Martin, C., Benoit, L., Sommerer, Y., Nicoud, F. & Poinsot, T. 2006 LES and acoustic analysis of combustion instability in a staged turbulent swirled combustor. AIAA J. 44 (4), 741–750.CrossRefGoogle Scholar
McManus, K., Poinsot, T. & Candel, S. 1993 A review of active control of combustion instabilities. Prog. Energy Combust. Sci. 19, 1–29.Google Scholar
Mendez, S. & Nicoud, F. 2008a Adiabatic homogeneous model for flow around a multiperforated plate. AIAA J. 46 (10), 2623–2633.Google Scholar
Mendez, S. & Nicoud, F. 2008b Large-eddy simulation of a bi-periodic turbulent flow with effusion. J. Fluid Mech. 598, 27–65.Google Scholar
Miles, J. H. 2010 Separating direct and indirect turbofan engine combustion noise using the correlation function. J. Propul. Power 26 (5), 1144–1152.Google Scholar
Moase, W. H., Brear, M. J. & Manzie, C. 2007 The forced response of choked nozzles and supersonic diffusers. J. Fluid Mech. 585, 281–304.Google Scholar
Morfey, C. L. 1973 Amplification of aerodynamic noise by convected flow inhomogeneities. J. Sound Vib. 31, 391–397.Google Scholar
Morgans, A. S., Goh, C. S. & Dahan, J. A. 2013 The dissipation and shear dispersion of entropy waves in combustor thermoacoustics. J. Fluid Mech. 733, R2.Google Scholar
Motheau, E., Méry, Y., Nicoud, F. & Poinsot, T. 2013 Analysis and modeling of entropy modes in a realistic aeronautical gas turbine. Trans. ASME: J. Engng Gas Turbines Power 135 (9), 092602.Google Scholar
Motheau, E., Nicoud, F. & Poinsot, T. 2012 Using boundary conditions to account for mean flow effects in a zero Mach number acoustic solver. Trans. ASME: J. Engng Gas Turbines Power 134 (11), 111502.Google Scholar
Motheau, E., Selle, L. & Nicoud, F. 2014 Accounting for convective effects in zero-Mach-number thermoacoustic models. J. Sound Vib. 333 (1), 246–262.Google Scholar
Nicoud, F., Baya Toda, H., Cabrit, O., Bose, S. & Lee, J. 2011 Using singular values to build a subgrid-scale model for large eddy simulations. Phys. Fluids 23 (8), 085106.Google Scholar
Nicoud, F., Benoit, L., Sensiau, C. & Poinsot, T. 2007 Acoustic modes in combustors with complex impedances and multidimensional active flames. AIAA J. 45, 426–441.Google Scholar
Nicoud, F. & Wieczorek, K. 2009 About the zero Mach number assumption in the calculation of thermoacoustic instabilities. Intl J. Spray Combust. Dyn. 1, 67–112.Google Scholar
Peters, M., Hirschberg, A., Reijnen, A. J. & Wijnands, A. P. J. 1993 Damping and reflection coefficient measurements for an open pipe at low Mach and low Helmholtz numbers. J. Fluid Mech. 256, 499–534.Google Scholar
Pierce, A. D. 1981 Acoustics: An Introduction to its Physical Principles and Applications. McGraw-Hill.Google Scholar
Pitsch, H. 2006 Large eddy simulation of turbulent combustion. Annu. Rev. Fluid Mech. 38, 453–482.Google Scholar
Poinsot, T. & Lele, S. 1992 Boundary conditions for direct simulations of compressible viscous flows. J. Comput. Phys. 101 (1), 104–129.Google Scholar
Poinsot, T. & Veynante, D. 2011 Theoretical and Numerical Combustion. 3rd edn Available at: www.cerfacs.fr/eLearning.Google Scholar
Polifke, W., Paschereit, C. & Doebbeling, K. 2001 Constructive and destructive interference of acoustic and entropy waves in a premixed combustor with a choked exit. Intl J. Acoust. Vib. 6, 135–146.Google Scholar
Rayleigh, Lord 1878 The explanation of certain acoustic phenomena. Nature 18, 319–321.Google Scholar
Rowley, C. W., Mezic, I., Bagheri, S., Schlatter, P. & Henningson, D. S. 2009 Spectral analysis of nonlinear flows. J. Fluid Mech. 641, 115–127.Google Scholar
Sattelmayer, T. 2003 Influence of the combustor aerodynamics on combustion instabilities from equivalence ratio fluctuations. Trans. ASME: J. Engng Gas Turbines Power 125, 11–19.Google Scholar
Schmid, P. J. 2010 Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656, 5–28.Google Scholar
Schmid, P. J., Li, L., Juniper, M. P. & Pust, O. 2011 Applications of the dynamic mode decomposition. Theor. Comput. Fluid Dyn. 25 (1–4), 249–259.Google Scholar
Schmitt, P., Poinsot, T., Schuermans, B. & 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, 17–46.Google Scholar
Selimefendigil, F. & Polifke, W. 2011 A nonlinear frequency domain model for limit cycles in thermoacoustic systems with modal coupling. Intl J. Spray Combust. Dyn. 3 (4), 303–330.Google Scholar
Silva, C. F., Nicoud, F., Schuller, T., Durox, D. & 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), 1743–1754.Google Scholar
Sisco, J. C., Yu, Y. C., Sankaran, V. & Anderson, W. E. 2011 Examination of mode shapes in an unstable model combustor. J. Sound Vib. 330 (1), 61–74.Google Scholar
Smagorinsky, J. 1963 General circulation experiments with the primitive equations: 1. The basic experiment. Mon. Weather Rev. 91, 99–164.Google Scholar
Tsien, H. S. 1952 The transfer functions of rocket nozzles. J. Am. Rocket Soc. 22 (3), 139–143.Google Scholar
Vuillot, F. 1995 Vortex-shedding phenomena in solid rocket motors. J. Propul. Power 11 (4), 626–639.Google Scholar
Wolf, P., Staffelbach, G., Gicquel, L. Y. M., Müller, J. D. & Poinsot, T. 2012 Acoustic and large eddy simulation studies of azimuthal modes in annular combustion chambers. Combust. Flame 159 (11), 3398–3413.Google Scholar
Yao, Z., Gao, Y., Zhu, M., Dowling, A. P. & Bray, K. N. C. 2012 Combustion rumble prediction with integrated computational-fluid-dynamics/low-order-model methods. J. Propul. Power 28 (5), 1015–1025.Google Scholar
You, D., Huang, Y. & Yang, V. 2005 A generalized model of acoustic reponse of turbulent premixed flame and its application to gas-turbine combustion instability analysis. Combust. Sci. Technol. 177 (5–6), 1109–1150.CrossRefGoogle Scholar
Yu, K. H., Trouvé, A. & Daily, J. W. 1991 Low-frequency pressure oscillations in a model ramjet combustor. J. Fluid Mech. 232, 47–72.Google Scholar
Yu, Y. C., Sisco, J. C., Sankaran, V. & Anderson, W. E. 2010 Effects of mean flow, entropy waves, and boundary conditions on longitudinal combustion instability. Combust. Sci. Technol. 182 (7), 739–776.Google Scholar
Zhu, M., Dowling, A. P. & Bray, K. N. C. 2001 Self-excited oscillations in combustors with spray atomizers. Trans. ASME: J. Engng Gas Turbines Power 123 (4), 779–786.Google Scholar
Zinn, B. T. 1972 Longitudinal mode acoustic losses in short nozzles. J. Sound Vib. 22 (1), 93–105.Google Scholar
Zinn, B. T., Bell, W. A., Daniel, B. R. & Smith, A. J. 1973 Experimental determination of three-dimensional liquid rocket nozzle admittances. AIAA J. 11, 267–272.Google Scholar