Hostname: page-component-745bb68f8f-cphqk Total loading time: 0 Render date: 2025-01-09T21:52:53.708Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonlinear self-excited thermoacoustic oscillations: intermittency and flame blowout

Published online by Cambridge University Press:  17 October 2012

Lipika Kabiraj  and
R. I. Sujith
Lipika Kabiraj*
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai, 600 036, India
R. I. Sujith
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai, 600 036, India
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Nonlinear self-excited thermoacoustic oscillations appear in systems involving confined combustion in the form of coupled acoustic pressure oscillations and unsteady heat release rate. In this paper, we investigate the nonlinear transition undergone by thermoacoustic oscillations to flame blowout via intermittency, in response to variation in the location of the combustion source with respect to the acoustic field of the confinement. A ducted laminar premixed conical flame, stabilized on a circular jet exit with a fully developed exit velocity profile, was investigated. Transition to limit cycle oscillations from a non-oscillatory state was observed to occur via a subcritical Hopf bifurcation. Limit cycle oscillations underwent a further bifurcation to quasi-periodic oscillations characterized by the repeated formation of elongated necks in the flame that pinch off as pockets of unburned fuel–air mixture. The quasi-periodic state loses stability, resulting in an intermittent state identified as type II through recurrence analysis of phase space trajectories reconstructed from the acoustic pressure time trace. In this state, the flame undergoes repeated lift-off and reattachment. Instantaneous flame images suggest that the intermittent flame behaviour is influenced by jet flow dynamics.

JFM classification

Acoustics: Acoustics Instability: Instability Nonlinear Dynamical Systems: Nonlinear Dynamical Systems
Type
Papers
Information
Journal of Fluid Mechanics , Volume 713 , 25 December 2012 , pp. 376 - 397
Copyright
©2012 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

Abarbanel, H. D. I. 1996 Analysis of Observed Chaotic Data. Springer.CrossRefGoogle Scholar
Batiste, O., Knobloch, E., Mercader, I. & Net, M. 2001 Simulations of oscillatory binary fluid convection in large aspect ratio containers. Phys. Rev. E 65, 016303.Google Scholar
Becker, H. A. & Massaro, T. A. 1968 Vortex evolution in a round jet. J. Fluid Mech. 31, 435–448.CrossRefGoogle Scholar
Bérge, P., Dubois, M., Manneville, P. & Pomeau, Y. 1980 Intermittency in Rayleigh–Bénard convection. J. Physique Lett. 41, 341–345.Google Scholar
Bondar, M. L. 2007 Acoustically perturbed Bunsen flames: modelling, analytical investigations and numerical simulations. PhD thesis, Technische Universiteit Eindhoven, The Netherlands.Google Scholar
Bourehla, A. & Baillot, F. 1998 Appearance and stability of a laminar conical premixed flame subjected to an acoustic perturbation. Combust. Flame 114 (3–4), 303–318.Google Scholar
Candel, S. 2002 Combustion dynamics and control: progress and challenges. Proc. Combust. Inst. 29 (1), 1–28.CrossRefGoogle Scholar
Dowling, A. P. 1997 Nonlinear self-excited oscillations of a ducted flame. J. Fluid Mech. 346, 271–290.Google Scholar
Dowling, A. P. 1999 A kinematic model of a ducted flame. J. Fluid Mech. 394, 51–72.CrossRefGoogle Scholar
Eckmann, J. P., Kamphorts, S. O. & Ruelle, R. 1987 Recurrence plots of dynamical systems. Europhys. Lett. 4, 973–977.CrossRefGoogle Scholar
Fraser, A. M. & Swinney, H. L. 1986 Independent coordinates for strange attractors from mutual information. Phys. Rev. A 33, 1134–1140.Google Scholar
Gollub, J. P & Benson, S. V. 1980 Many routes to turbulent convection. J. Fluid Mech. 100, 449–470.Google Scholar
Han, S. K. & Postnov, D. E. 2003 Chaotic bursting as chaotic itinerancy in coupled neural oscillators. Chaos 13, 1105–1109.CrossRefGoogle ScholarPubMed
Jahnke, C. C. & Culick, F. E. C. 1994 An application of dynamical systems theory to nonlinear combustion instabilities. J. Propul. Power 10, 508–517.CrossRefGoogle Scholar
Jegadeesan, V. & Sujith, R. I. 2012 Experimental investigation of noise induced triggering in thermoacoustic systems. Proc. Combust. Inst. 34.Google Scholar
Juniper, M. P. 2010 Triggering in the horizontal Rijke tube: non-normality, transient growth and bypass transition. J. Fluid Mech. 667, 272–308.Google Scholar
Kabiraj, L. & Sujith, R. I. 2011 Investigation of subcritical instability in ducted premixed flames. In ASME Turbo Expo, paper GT 2011-46155. ASME.Google Scholar
Kabiraj, L., Sujith, R. I. & Wahi, P. 2012a Bifurcations of self-excited ducted premixed flames. J. Engng Gas Turbines and Power 134 (3), 031502.CrossRefGoogle Scholar
Kabiraj, L., Sujith, R. I. & Wahi, P. 2012b Investigating dynamics of combustion driven oscillations leading to lean blowout. Fluid Dyn. Res. 44, 031408.Google Scholar
Kantz, H. & Schreiber, T. 2003 Nonlinear Time Series Analysis. Cambridge University Press.Google Scholar
Karimi, N., Brear, M. J., Jin, S. H. & Monty, J. P. 2009 Linear and nonlinear forced response of conical, ducted, laminar, premixed flames. Combust. Flame 156, 2201–2212.Google Scholar
Kennel, M. B., Brown, R. & Abarbanel, H. D. I. 1992 Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys. Rev. A 45, 3403–3411.CrossRefGoogle ScholarPubMed
Klimaszewska, K. & Żebrowski, J. J. 2009 Detection of the type of intermittency using characteristic patterns in recurrence plots. Phys. Rev. E 80, 026214.CrossRefGoogle ScholarPubMed
Knoop, P., Culick, F. E. C. & Zukoski, E. E. 1997 Extension of the stability of motions in a combustion chamber by nonlinear active control based on hysteresis. Combust. Sci. Technol. 123 (1–6), 363–376.Google Scholar
Lei, S. & Turan, A. 2009 Nonlinear/chaotic behaviour in thermo-acoustic instability. Combust. Theory Model. 13 (3), 541–557.CrossRefGoogle Scholar
Liepmann, D. & Gharib, M. 1992 The role of streamwise vorticity in the near-field entrainment of round jets. J. Fluid Mech. 245, 643–668.Google Scholar
Lieuwen, T. C. 2002 Experimental investigation of limit cycle oscillations in an unstable gas turbine combustor. J. Propul. Power 18, 61–67.CrossRefGoogle Scholar
Lisa, H. & Thomas, E. 1993 Understanding bursting oscillations as periodic slow passages through bifurcation and limit points. J. Math. Biol. 31, 351–365.Google Scholar
Mariappan, S., Schmid, P. J. & Sujith, R. I. 2010 Role of transient growth in subcritical transition to thermoacoustic instability in a horizontal Rijke tube. In 16th AIAA/CEAS Aeroacoustics Conference, AIAA paper 2010-3857. AIAA.Google Scholar
Marwan, N. 2003 Encounters with neighbours: current developments of concepts based on recurrence plots and their applications. PhD thesis, University of Potsdam.Google Scholar
Marwan, N., Carmenromano, M., Thiel, M. & Kurths, J. 2007 Recurrence plots for the analysis of complex systems. Phys. Rep. 438, 237–329.CrossRefGoogle Scholar
Matveev, I. 2003 Thermo-acoustic instabilities in the Rijke tube: experiments and modeling. PhD thesis, Caltech, Pasadena, CA.Google Scholar
Nayfeh, A. H. & Balachandran, B. 2004 Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods. Wiley–VCH.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, 139–167.CrossRefGoogle Scholar
Okamoto, H., Tanaka, N. & Naito, M. 1998 Intermittencies and related phenomena in the oxidation of formaldehyde at a constant current. J. Phys. Chem. A 102 (38), 7353–7361.CrossRefGoogle Scholar
Packard, N. H., Crutchfield, J. P., Farmer, J. D. & Shaw, R. S. 1980 Geometry from a time series. Phys. Rev. Lett. 45, 712–716.Google Scholar
Paschereit, C. O., Oster, D., Long, T. A., Fiedler, H. E. & Wygnanski, I. 1992 Vortex evolution in a round jet. Exp. Fluids 12, 189–199.Google Scholar
Pomeau, Y. & Manneville, P. 1980 Intermittent transition to turbulence in dissipative dynamical systems. Commun. Math. Phys. 74, 189–197.Google Scholar
Rayleigh, J. S. W. 1878 The explanation of certain acoustic phenomena. Nature 18 (455), 319–321.CrossRefGoogle Scholar
Sterling, J. D. 1993 Nonlinear analysis and modeling of combustion instabilities in a laboratory combustor. Combust. Sci. Technol. 89 (1), 167–179.CrossRefGoogle Scholar
Straube, R., Flockerzi, D. & Hauser, M. J. B. 2006 Sub-Hopf/fold-cycle bursting and its relation to (quasi-) periodic oscillations. J. Phys.: Conf. Ser. 55, 214–231.Google Scholar
Strogatz, S. H. 1994 Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering. Westview.Google Scholar
Subramanian, P., Mariappan, S., Wahi, P. & Sujith, R. I. 2010 Bifurcation analysis of thermoacoustic instability in a horizontal Rijke tube. Intl J. Spray Combust. Dyn. 2 (4), 325–356.Google Scholar
Swinney, H. L. 1983 Observations of order and chaos in nonlinear systems. Physica D 7, 3–15.CrossRefGoogle Scholar
Takens, F. 1981 Detecting strange attractors in turbulence. In Dynamical Systems and Turbulence, Warwick 1980 (ed. David, R. & Young, L.-S.). Lecture Notes in Mathematics , vol. 898, pp. 366–381. Springer.Google Scholar
Waugh, I. C. W. & Juniper, M. 2011 Triggering in a thermoacoustic system with stochastic noise. Intl J. Spray Combust. Dyn. 3 (3), 225–242.CrossRefGoogle Scholar
Wettlaufer, J. S. 2011 The universe in a cup of coffee. Phys. Today 64 (5), 66–67.Google Scholar
Zbilut, J. P. & Webber, C. L. Jr. 1992 Embeddings and delays as derived from quantification of recurrence plots. Phys. Lett. A 171, 199–203.Google Scholar
Zinn, B. T. & Lieuwen T. C. (ed.) 2005 Combustion instabilities: basic concepts. In Combustion Instabilities in Gas Turbine Engines: Operational Experience, Fundamental Mechanisms, and Modeling, Progress in Astronautics and Aeronautics, pp. 3–26. AIAA.Google Scholar
Zou, Y. 2007 Exploring recurrences in quasi-periodic systems. PhD thesis, University of Potsdam.Google Scholar