Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-29T22:45:41.158Z Has data issue: false hasContentIssue false
  • English
  • Français

Stability analysis of thermoacoustic interactions in vortex shedding combustors using Poincaré map

Published online by Cambridge University Press:  26 July 2016

Balasubramanian Singaravelu  and
Sathesh Mariappan
Balasubramanian Singaravelu
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India
Sathesh Mariappan*
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Vortex separation and breakdown are an important source of unsteady heat release rate fluctuations in thermoacoustic systems. The coupling between the acoustic field and the energy released by vortex breakdown can cause combustion instability. The objective of this work is to perform linear stability analyses and to quantify the stability of thermoacoustic interactions where vortex breakdown is the dominant cause of heat release rate fluctuations. The dynamics of the system is modelled as a kicked oscillator, where the energy released by vortex breakdown is represented as the kick. Assuming small fluctuations, periodic and low values of kick, a Poincaré map is derived analytically. The stability of the system is determined from the eigenvalues associated with the Poincaré map. The results allow us to identify the region where vortex shedding or the acoustic mode is dominant. Previous experimental investigations report the transition between the two modes for variation in the flow Mach number. Similar transitions are observed in the present study.

JFM classification

Acoustics: Aeroacoustics Reacting Flows: Laminar reacting flows Vortex Flows: Vortex shedding
Type
Papers
Information
Journal of Fluid Mechanics , Volume 801 , 25 August 2016 , pp. 597 - 622
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

Afanasiev, V. V., Chernikov, A. A., Sagdeev, R. Z. & Zaslavsky, G. M. 1990 The width of the stochastic web and particle diffusion along the web. Phys. Lett. A 144, 229–236.CrossRefGoogle Scholar
Balasubramanian, K. & Sujith, R. I. 2008a Thermoacoustic instability in a rijke tube: non-normality and nonlinearity. Phys. Fluids 20 (4), 044103.CrossRefGoogle Scholar
Balasubramanian, K. & Sujith, R. I. 2008b Non-normality and nonlinearity in combustion acoustic interaction in diffusion flames. J. Fluid Mech. 594, 29–57.CrossRefGoogle Scholar
Blomshield., F. S., Mathes, H. B., Crump, J. E., Beiter, C. A. & Beckstead, M. W. 1997 Stability testing of full-scale tactical motors. J. Propul. Power 13, 349–355.CrossRefGoogle Scholar
Candel, S. M. 1992 Combustion instabilities coupled by pressure waves and their active control. In Proceedings of the Twenty-Fourth Symposium (International) on Combustion, pp. 1277–1296. The Combustion Institute.Google Scholar
Chakravarthy, S. R., Shreenivasan, O. J., Boehm, B., Dreizler, A. & Janicka, J. 2007a Experimental characterization of onset of acoustic instability in a nonpremixed half-dump combustor. J. Acoust. Soc. Am. 122 (1), 120–127.CrossRefGoogle Scholar
Chakravarthy, S. R., Sivakumar, R. & Shreenivasan, O. J. 2007b Vortex-acoustic lock-on in bluff-body and backward-facing step combustors. Sadhana 32, 145–154.CrossRefGoogle Scholar
Chernikov, A. A., Sagdeev, R. Z. & Zaslavsky, G. M. 1988 Stochastic webs. Physica D 33, 65–76.CrossRefGoogle Scholar
Chirikov, B. V. 1979 A universal instability of many-dimensional oscillator systems. Phys. Rep. 52, 263–379.CrossRefGoogle Scholar
Collet, P., Eckmann, J. P. & Lanford, O. E. 1980 Universal properties of maps on an interval. Commun. Math. Phys. 76, 211–254.CrossRefGoogle Scholar
Culick, F. E. C. 1963 Stability of high-frequency pressure oscillations in rocket combustion chambers. AIAA. J. 1, 1097–1104.CrossRefGoogle Scholar
Culick, F. E. C.2006. Unsteady motions in combustion chambers for propulsion systems. Tech. Rep. AG-AVT-039. RTO AGARDorgraph.Google Scholar
Devaney, R. L. 1989 An Introduction to Chaotic Dynamical Systems. Addison-Wesley.Google Scholar
Dotson, A. P., Koshigoe, S. & Pace, K. K. 1997 Vortex shedding in a large solid rocket motor without inhibitors at the segment interfaces. J. Propul. Power 13, 197–206.CrossRefGoogle Scholar
Huang, Y. & Yang, V. 2009 Dynamics and stability of lean-premixed swirl-stabilized combustion. Prog. Energy Combust. Sci. 35 (4), 293–364.CrossRefGoogle Scholar
Lienhard, J. H. 1966 Synopsis of lift, drag and vortex frequency data for rigid circular cylinders. Washington State University College of Engineering Research Division Bulletin, vol. 300, p. 30.Google Scholar
Magri, L., Balasubramanian, K., Sujith, R. & Junpier, M. 2013 Non-normality in combustion acoustic interaction in diffusion flames: a critical revision. J. Fluid Mech. 733, 681–683.CrossRefGoogle Scholar
Mariappan, S., Sujith, R. I. & Schmid, P. J. 2015 Experimental investigation of non-normality of thermoacoustic interaction in an electrically heated Rijke tube. Intl J. Spray Combust. Dyn. 7 (4), 315–352.CrossRefGoogle Scholar
Matveev, K. & Culick, F. E. C. 2003 A model for combustion instability involving vortex shedding. Combust. Sci. Technol. 175, 1059–1083.CrossRefGoogle Scholar
McManus, K., Poinsot, T. & Candel, S. 1993 A review of active control methods for combustion instabilities. Prog. Energy Combust. Sci. 19, 1–29.CrossRefGoogle Scholar
Nair, V. & Sujith, R. I. 2015 A reduced-order model for the onset of combustion instability: physical mechanisms for intermittency and precursors. Proc. Combust. Inst. 3, 3193–3200.CrossRefGoogle Scholar
Orchini, A., Illingworth, S. & Junpier, M. 2015 Frequency domain and time domain analysis of thermoacoustic oscillations with wave-based acoustics. J. Fluid Mech. 775, 387–414.CrossRefGoogle Scholar
Rayleigh, Lord 1945 Theory of Sound. Dover.Google Scholar
Renard, P. H., Thévenin, D., Rolon, J. C. & Candel, S. 2000 Dynamics of flame/vortex interactions. Prog. Energy Combust. Sci. 26 (3), 225–282.CrossRefGoogle Scholar
Schadow, K. C. & Gutmark, E. 1992 Combustion instability related to vortex shedding in dump combustors and their passive control. Prog. Energy Combust. Sci. 18 (2), 117–132.CrossRefGoogle Scholar
Sivesegaram, S. & Whitelaw, J. H. 1987 Oscillations in axisymmetric dump combustors. Combust. Sci. Technol. 52 (4–6), 413–426.CrossRefGoogle Scholar
Smith, D. A. & Zukoski, E. E.1985. Combustion instability sustained by unsteady vortex combustion, AIAA 85-1248.Google Scholar
Sterling, J. D. & Zukoski, E. E. 1991 Nonlinear dynamics of laboratory combustor pressure oscillations. Combust. Sci. Technol. 77 (4–6), 225–238.CrossRefGoogle Scholar
Strogatz, S. H. 2000 Nonlinear Dynamics and Chaos. Westview Press.Google Scholar
Subramanian, P., Mariappan, S., Sujith, R. I. & Wahi, P. 2010 Bifurcation analysis of thermoacoustic instability in a horizontal rijke tube. Intl J. Spray Combust. Dyn. 2 (4), 325–355.CrossRefGoogle Scholar
Trefethen, L., Trefethen, A., Reddy, S. & Driscoll, T. 1993 Hydrodynamic stability without eigenvalues. Science 261, 578–584.CrossRefGoogle ScholarPubMed
Tulsyan, B., Balasubramanian, K. & Sujith, R. I. 2009 Revisiting a model for combustion instability involving vortex shedding. Combust. Sci. Technol. 181, 457–482.CrossRefGoogle Scholar
Waugh, I., Illingworth, S. & Junpier, M. 2013 Matrix-free continuation of limit cycles for bifurcation analysis of large thermoacoustic systems. J. Comput. Phys. 240, 225–247.CrossRefGoogle Scholar
Waugh, I., Illingworth, S. & Junpier, M. 2014 Matrix-free continuation of limit cycles and their bifurcations for a ducted premixed flame. J. Fluid Mech. 759, 1–27.CrossRefGoogle Scholar
Yu, K., Trouve, A. & Daily, J. W.1989 Low frequency pressure oscillations in a model ramjet combustor – the nature of frequency selection. AIAA Paper 89-0623.CrossRefGoogle Scholar
Yu, K., Trouve, A. & Daily, J. W. 1991 Low frequency pressure oscillations in a model ramjet combustor. J. Fluid Mech. 232, 47–72.CrossRefGoogle Scholar
Zinn, B. T. & Lieuwen, T. C. 2006 Combustion Instabilities: Basic Concepts – Combustion Instabilities in Gas Turbine Engines: Operational Experience, Fundamental Mechanisms, and Modeling. AIAA.Google Scholar