Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-12-01T04:58:47.128Z Has data issue: false hasContentIssue false
  • English
  • Français

Weakly nonlinear analysis of thermoacoustic instabilities in annular combustors

Published online by Cambridge University Press:  16 September 2016

G. Ghirardo ,
M. P. Juniper  and
J. P. Moeck
G. Ghirardo*
Affiliation:
University of Cambridge, Engineering Department, Trumpington Street, Cambridge CB2 1PZ, UK
M. P. Juniper
Affiliation:
University of Cambridge, Engineering Department, Trumpington Street, Cambridge CB2 1PZ, UK
J. P. Moeck
Affiliation:
Institut für Strömungsmechanik und Technische Akustik, Technische Universität Berlin, Müller-Breslau-Strasse 8, 10623 Berlin, Germany
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Rotationally symmetric annular combustors are of practical importance because they generically resemble combustion chambers in gas turbines, in which thermoacoustically driven oscillations are a major concern. We focus on azimuthal thermoacoustic oscillations and model the fluctuating heat release rate as being dependent only on the local pressure in the combustion chamber. We study the dynamics of the annular combustor with a finite number of compact flames equispaced around the annulus, and characterize the flames’ response with a describing function. We discuss the existence, amplitude and the stability of standing and spinning waves, as a function of: (i) the number of the burners; (ii) the acoustic damping in the chamber; (iii) the flame response. We present the implications for industrial applications and the future direction of investigations. We then present as an example the first theoretical study of thermoacoustic triggering in annular combustors, which shows that rotationally symmetric annular chambers that are thermoacoustically unstable do not experience only stable spinning solutions, but can also experience stable standing solutions. We finally test the theory on one experiment with good agreement.

JFM classification

Acoustics: Acoustics Nonlinear Dynamical Systems: Low-dimensional models Nonlinear Dynamical Systems: Nonlinear Dynamical Systems
Type
Papers
Information
Journal of Fluid Mechanics , Volume 805 , 25 October 2016 , pp. 52 - 87
Check for updates
Copyright
© 2016 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Acharya, V. & Lieuwen, T. 2014 Response of non-axisymmetric premixed, swirl flames to helical disturbances. In Proceedings of ASME Turbo Expo 2014. Paper no. GT2014-27059.Google Scholar
Acharya, V., Shreekrishna, S., D.-H. & Lieuwen, T. 2012 Swirl effects on harmonically excited, premixed flame kinematics. Combust. Flame 159 (3), 1139–1150.Google Scholar
Assier, R. C. & Wu, X. 2014 Linear and weakly nonlinear instability of a premixed curved flame under the influence of its spontaneous acoustic field. J. Fluid Mech. 758, 180–220.Google Scholar
Bauerheim, M., Cazalens, M. & Poinsot, T. 2015 A theoretical study of mean azimuthal flow and asymmetry effects on thermo-acoustic modes in annular combustors. Proc. Combust. Inst. 35, 3219–3227.Google Scholar
Bauerheim, M., Salas, P., Nicoud, F. & Poinsot, T. 2014 Symmetry breaking of azimuthal thermo-acoustic modes in annular cavities: a theoretical study. J. Fluid Mech. 760, 431–465.Google Scholar
Blimbaum, J., Zanchetta, M., Akin, T., Acharya, V., O’Connor, J., Noble, D. R. & Lieuwen, T. 2012 Transverse to longitudinal acoustic coupling processes in annular combustion chambers. Intl J. Spray Combust. Dyn. 4 (4), 275–298.CrossRefGoogle Scholar
Bothien, M. R., Noiray, N. & Schuermans, B. 2015 Analysis of azimuthal thermo-acoustic modes in annular gas turbine combustion chambers. Trans. ASME J. Engng Gas Turbines Power 137, 061505.Google Scholar
Boudy, F., Durox, D., Schuller, T., Jomaas, G. & Candel, S. 2011 Describing function analysis of limit cycles in a multiple flame combustor. J. Engng Gas Turbines Power 133 (6), 061502.Google Scholar
Bourgouin, J.-F.2014, Dynamique de flamme dans les foyers annulaires comportant des injecteurs multiples. PhD thesis, Ecole Centrale Paris.Google Scholar
Bourgouin, J.-F., Durox, D., Moeck, J. P., Schuller, T. & Candel, S. 2013 Self-sustained instabilities in an annular combustor coupled by azimuthal and longitudinal acoustic modes. In Proceedings of ASME Turbo Expo 2013, paper no. GT2013-95010.Google Scholar
Bourgouin, J.-F., Durox, D., Moeck, J. P., Schuller, T. & Candel, S. 2015 Characterization and modeling of a spinning thermoacoustic instability in an annular combustor equipped with multiple matrix injectors. J. Engng Gas Turbines Power 137, 021503.Google Scholar
Brillouin, L. 1953 Wave Propagation in Periodic Structures: Electric Filters and Crystal Lattices, 2nd edn. Chapter VIII, pp. 139–140. Dover publications.Google Scholar
Campa, G. & Camporeale, S. M. 2014 Prediction of the thermoacoustic combustion instabilities in practical annular combustors. J. Engng Gas Turbines Power 136, 091504.Google Scholar
Campa, G., Cinquepalmi, M. & Camporeale, S. M. 2013 Influence of nonlinear flame models on sustained thermoacoustic oscillations in gas turbine combustion chambers. In Proceedings of ASME Turbo Expo 2013. Paper no. GT2013-94495, pp. 1–13.Google Scholar
Ćosić, B., Moeck, J. P. & Paschereit, C. O. 2014 Nonlinear instability analysis for partially premixed swirl flames. Combust. Sci. Technol. 186 (6), 713–736.CrossRefGoogle Scholar
Ćosić, B., Reichel, T. G. & Paschereit, C. O. 2012 Acoustic response of a Helmholtz resonator exposed to hot–gas penetration and high amplitude oscillations. J. Engng Gas Turbines Power 134 (10), 101503.Google Scholar
Dowling, A. P. 1997 Nonlinear self-excited oscillations of a ducted flame. J. Fluid Mech. 346, 271–290.Google Scholar
Durox, D., Bourgouin, J.-F., Moeck, J. P., Philip, M., Schuller, T. & Candel, S. 2013 Nonlinear interactions in combustion instabilities coupled by azimuthal acoustic modes. In International Summer School and Workshop on Non-Normal and Nonlinear Effects in Aero- and Thermoacoustics, June 18–21, 2013, Munich.Google Scholar
Evesque, S. & Polifke, W. 2002 Low-order acoustic modelling for annular combustors: validation and inclusion of modal coupling. In Proceedings of ASME Turbo Expo 2002.Google Scholar
Gelb, A. & Vander Velde, W. E. 1968 Multiple Input Describing Functions and Nonlinear System Design. McGraw-Hill.Google Scholar
Ghirardo, G., Ćosić, B., Juniper, M. P. & Moeck, J. P. 2015 State-space realization of a describing function. Nonlinear Dyn 82 (1), 9–28.CrossRefGoogle Scholar
Ghirardo, G. & Juniper, M. P. 2013 Azimuthal instabilities in annular combustors: standing and spinning modes. Proc. R. Soc. Lond. A 469, 20130232.Google Scholar
Hirschberg, A. & Rienstra, S. W.2015 An introduction to acoustics. Rep. IWDE 92-06. Eindhoven University.Google Scholar
Lepers, J., Krebs, W., Prade, B., Flohr, P., Pollarolo, G. & Ferrante, A. 2005 Investigation of thermoacoustic stability limits of an annular gas turbine combustor test-Rig with and without Helmholtz-resonators. In Proceedings of ASME Turbo Expo 2005, pp. 177–189.Google Scholar
Mensah, G. A. & Moeck, J. P. 2015 Efficient computation of thermoacoustic modes in annular combustion chambers based on Bloch-wave theory. In Proceedings of ASME Turbo Expo 2015, paper no. GT2015-43476, pp. 1–11.Google Scholar
Moeck, J. P., Bothien, M. R., Schimek, S., Lacarelle, A. & Paschereit, C. O. 2008 Subcritical thermoacoustic instabilities in a premixed combustor. In 14th AIAA/CEAS Aeroacoustics Conference, paper no. AIAA-2008-2946.Google Scholar
Moeck, J. P., Paul, M. & Paschereit, C. O. 2010 Thermoacoustic instabilities in an annular Rijke tube. In Proceedings of ASME Turbo Expo 2010, paper no. GT2010-23577.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 (2), 426–441.Google Scholar
Noiray, N., Bothien, M. R. & Schuermans, B. 2011 Investigation of azimuthal staging concepts in annular gas turbines. Combust. Theor. Model. 15 (5), 585–606.Google Scholar
Noiray, N., Durox, D., Schuller, T. & Candel, S. 2008 A unified framework for nonlinear combustion instability analysis based on the flame describing function. J. Fluid Mech. 615 (2008), 139–167.Google Scholar
Noiray, N. & Schuermans, B. 2013 On the dynamic nature of azimuthal thermoacoustic modes in annular gas turbine combustion chambers. Proc. R. Soc. Lond. A 469, 20120535.Google Scholar
Palies, P., Durox, D., Schuller, T. & Candel, S. 2011 Nonlinear combustion instability analysis based on the flame describing function applied to turbulent premixed swirling flames. Combust. Flame 158 (10), 1980–1991.Google Scholar
Salas, P.2013, Aspects numériques et physiques des instabilités thermoacoustiques dans les chambres de combustion annulaires. PhD thesis, University of Bordeaux I.Google Scholar
Sanders, J. A. & Verhulst, F. 2007 Applied Mathematical Sciences, 2nd edn. vol. 59. Springer.Google Scholar
Saurabh, A., Steinert, R., Moeck, J. P. & Paschereit, C. O. 2014 Swirl flame response to traveling acoustic waves. In Proceedings of ASME Turbo Expo 2014, Paper no. GT2014-26829.Google Scholar
Schuermans, B., Bellucci, V. & Paschereit, C. O. 2003 Thermoacoustic modeling and control of multi burner combustion systems. In Proceedings of ASME Turbo Expo 2003.Google Scholar
Schuermans, B., Paschereit, C. O. & Monkewitz, P. 2006 Non-linear combustion instabilities in annular gas-turbine combustors. In 44th AIAA Aerospace Sciences Meeting and Exhibit. Paper no. AIAA-2006-0549, American Institute of Aeronautics and Astronautics.Google Scholar
Schuller, T., Durox, D. & Candel, S. 2003 A unified model for the prediction of laminar flame transfer functions. Combust. Flame 134 (1–2), 21–34.Google Scholar
Schuller, T., Tran, N., Noiray, N., Durox, D., Ducruix, S. & Candel, S. 2009 The role of nonlinear acoustic boundary conditions in combustion/acoustic coupled instabilities. In Proceedings of ASME Turbo Expo 2009, paper no. GT2009-59390.Google Scholar
Seume, J. R., Vortmeyer, N., Krause, W., Hermann, J., Hantschk, C. C., Gleis, S., Vortmeyer, D. & Orthmann, A. 1998 Application of active combustion instability control to a heavy duty gas turbine. Trans. ASME J. Engng Gas Turbines Power 120, 721–726.Google Scholar
Stow, S. R. & Dowling, A. P. 2001 Thermoacoustic oscillations in an annular combustor. In Proceedings of ASME Turbo Expo 2001. Paper no. GT2014-26829. New Orleans, Louisiana, USA.Google Scholar
Wahi, P. & Chatterjee, A. 2004 Averaging oscillations with small fractional damping and delayed terms. Nonlinear Dyn. 38, 3–22.Google Scholar
Wolf, P., Staffelbach, G., Balakrishnan, R., Roux, A. & Poinsot, T. 2010 Azimuthal instabilities in annular combustion chambers. In Center for Turbulence Research, Proceedings of the Summer Program, pp. 259–269.Google Scholar
Supplementary material: File

Ghirardo supplementary material

Ghirardo supplementary material

Download Ghirardo supplementary material(File)
File 228.2 KB