Table of Contents
Journal of Thermodynamics
Volume 2015 (2015), Article ID 949384, 9 pages
http://dx.doi.org/10.1155/2015/949384
Research Article

Thermoacoustic Instability in a Rijke Tube with a Distributed Heat Source

1School of Mechanical, Aerospace and Civil Engineering, The University of Manchester, P.O. Box 88, Manchester M60 1QD, UK
2Thermal Management Research Group, Efficient Energy Transfer Department (ηET), Bell Labs, Alcatel-Lucent, Dublin 15, Ireland

Received 7 July 2015; Revised 8 October 2015; Accepted 12 October 2015

Academic Editor: Philip De Goey

Copyright © 2015 Xiaochuan Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. T. Poinsot, S. Candel, E. Esposito, W. Lang, and F. Bourienne, “Suppression of combustion instabilities by active control,” Journal of Propulsion and Power, vol. 5, no. 1, pp. 14–20, 1989. View at Google Scholar
  2. A. P. Dowling, “The calculation of thermoacoustic oscillations,” Journal of Sound and Vibration, vol. 180, no. 4, pp. 557–581, 1995. View at Publisher · View at Google Scholar · View at Scopus
  3. K. T. Kim, J. G. Lee, B. D. Quay, and D. A. Santavicca, “Spatially distributed flame transfer functions for predicting combustion dynamics in lean premixed gas turbine combustors,” Combustion and Flame, vol. 157, no. 9, pp. 1718–1730, 2010. View at Publisher · View at Google Scholar · View at Scopus
  4. S. Lei and A. Turan, “Nonlinear/chaotic modeling and control of combustion instabilities,” International Journal of Bifurcation and Chaos, vol. 20, no. 4, pp. 1245–1254, 2010. View at Publisher · View at Google Scholar · View at Scopus
  5. H. Gotoda, Y. Shinoda, M. Kobayashi, Y. Okuno, and S. Tachibana, “Detection and control of combustion instability based on the concept of dynamical system theory,” Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, vol. 89, no. 2, Article ID 022910, 2014. View at Publisher · View at Google Scholar · View at Scopus
  6. M. Hoeijmakers, V. Kornilov, I. L. Arteaga, P. de Goey, and H. Nijmeijer, “Flames in context of thermo-acoustic stability bounds,” Proceedings of the Combustion Institute, vol. 35, no. 1, pp. 1073–1078, 2015. View at Publisher · View at Google Scholar · View at Scopus
  7. A. P. Dowling and A. S. Morgans, “Feedback control of combustion oscillations,” Annual Review of Fluid Mechanics, vol. 37, pp. 151–182, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  8. M. A. Heckl and M. S. Howe, “Stability analysis of the Rijke tube with a Green's function approach,” Journal of Sound and Vibration, vol. 305, no. 4-5, pp. 672–688, 2007. View at Publisher · View at Google Scholar · View at Scopus
  9. D. Zhao, “Transient growth of flow disturbances in triggering a Rijke tube combustion instability,” Combustion and Flame, vol. 159, no. 6, pp. 2126–2137, 2012. View at Publisher · View at Google Scholar · View at Scopus
  10. A. C. Noble, G. B. King, N. M. Laurendeau, J. R. Gord, and S. Roy, “Nonlinear thermoacoustic instability dynamics in a Rijke tube,” Combustion Science and Technology, vol. 184, no. 3, pp. 293–322, 2012. View at Publisher · View at Google Scholar · View at Scopus
  11. K. T. Feldman Jr., “Review of the literature on Rijke thermoacoustic phenomena,” Journal of Sound and Vibration, vol. 7, no. 1, pp. 83–89, 1968. View at Publisher · View at Google Scholar · View at Scopus
  12. G. Bisio and G. Rubatto, “Sondhauss and Rijke oscillations—thermodynamic analysis, possible applications and analogies,” Energy, vol. 24, no. 2, pp. 117–131, 1999. View at Publisher · View at Google Scholar · View at Scopus
  13. R. L. Raun, M. W. Beckstead, J. C. Finlinson, and K. P. Brooks, “Review of Rijke tubes, Rijke burners and related devices,” Progress in Energy and Combustion Science, vol. 19, no. 4, pp. 313–364, 1993. View at Publisher · View at Google Scholar · View at Scopus
  14. F. E. C. Culick, “Nonlinear behavior of acoustic waves in combustion chambers—I,” Acta Astronautica, vol. 3, no. 9-10, pp. 715–734, 1976. View at Publisher · View at Google Scholar · View at Scopus
  15. F. E. C. Culick, “Nonlinear behavior of acoustic waves in combustion chambers—II,” Acta Astronautica, vol. 3, no. 9-10, pp. 735–757, 1976. View at Publisher · View at Google Scholar · View at Scopus
  16. M. A. Heckl, “Non-linear acoustic effects in the Rijke tube,” Acta Acustica United with Acustica, vol. 72, no. 1, pp. 63–71, 1990. View at Google Scholar
  17. C.-C. Hantschk and D. Vortmeyer, “Numerical simulation of self-excited thermoacoustic instabilities in a Rijke tube,” Journal of Sound and Vibration, vol. 227, no. 3, pp. 511–522, 1999. View at Publisher · View at Google Scholar · View at Scopus
  18. K. Matveev, Thermoacoustic Instabilities in the Rijke Tube, Experiments and Modeling, California Institute of Technology, 2003.
  19. K. I. Matveev and F. E. C. Culick, “A study of the transition to instability in a Rijke tube with axial temperature gradient,” Journal of Sound and Vibration, vol. 264, no. 3, pp. 689–706, 2003. View at Publisher · View at Google Scholar · View at Scopus
  20. N. Ananthkrishnan, S. Deo, and F. E. C. Culick, “Reduced-order modeling and dynamics of nonlinear acoustic waves in a combustion chamber,” Combustion Science and Technology, vol. 177, no. 2, pp. 221–248, 2005. View at Publisher · View at Google Scholar · View at Scopus
  21. K. Balasubramanian and R. I. Sujith, “Thermoacoustic instability in a Rijke tube: non-normality and nonlinearity,” Physics of Fluids, vol. 20, no. 4, Article ID 044103, 2008. View at Publisher · View at Google Scholar · View at Scopus
  22. P. Subramanian, S. Mariappan, R. I. Sujith, and P. Wahi, “Bifurcation analysis of thermoacoustic instability in a horizontal Rijke tube,” International Journal of Spray and Combustion Dynamics, vol. 2, no. 4, pp. 325–355, 2010. View at Publisher · View at Google Scholar
  23. M. P. Juniper, “Triggering in the horizontal Rijke tube: non-normality, transient growth and bypass transition,” Journal of Fluid Mechanics, vol. 667, pp. 272–308, 2011. View at Publisher · View at Google Scholar · View at Scopus
  24. D. Veynante and T. Poinsot, Theoretical and Numerical Combustion, Edwards, Philadelphia, Pa, USA, 2005.
  25. J. Jarosinski and B. Veyssiere, Combustion Phenomena, Selected Mechanisms of Flame Formation, Propagation and Extinction, CRC Press, 2009.
  26. C. E. Baukal Jr., The John Zink Hamworthy Combustion Handbook, Volume 1-Fundamentals, CRC Press, 2012.
  27. M. A. Heckl, “Green's function model for a Rijke tube with a distributed heat source,” The Journal of the Acoustical Society of America, vol. 123, no. 5, p. 3404, 2008. View at Publisher · View at Google Scholar
  28. K. Engelborghs, T. Luzyanina, and D. Roose, “Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL,” ACM Transactions on Mathematical Software, vol. 28, no. 1, pp. 1–21, 2002. View at Publisher · View at Google Scholar · View at Scopus
  29. K. Engelborghs, T. Luzyanina, and G. Samaey, DDE-BIFTOOL, a Matlab package for bifurcation analysis of delay differential equations [Ph.D. thesis], Department of Computer Science, Katholieke Universiteit Leuven, Leuven, Belgium, 2000.
  30. L. Rayleigh, “The explanation of certain acoustical phenomena,” Nature, vol. 18, no. 455, pp. 319–321, 1878. View at Publisher · View at Google Scholar · View at Scopus
  31. M. S. Howe, Acoustics of Fluid-Structure Interactions, Cambridge University Press, 1998.
  32. S. Nagaraja, K. Kedia, and R. I. Sujith, “Characterizing energy growth during combustion instabilities: singularvalues or eigenvalues?” Proceedings of the Combustion Institute, vol. 32, no. 2, pp. 2933–2940, 2009. View at Publisher · View at Google Scholar · View at Scopus
  33. I. Waugh, Methods for Analysis of Nonlinear Thermoacoustic Systems, Emmanuel College, Department of Engineering, University of Cambridge, 2013.
  34. M. J. Lighthill, “The response of laminar skin friction and heat transfer to fluctuations in the stream velocity,” Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences, vol. 224, no. 1156, pp. 1–23, 1954. View at Google Scholar
  35. S. G. Mikhlin, Variational Methods in Mathematical Physics, Pergamon Press, New York, NY, USA, 1964, distributed by Macmillan.
  36. W. E. Schiesser, The Numerical Method of Lines: Integration of Partial Differential Equations, Academic Press, 1991.
  37. E. Doedel, H. B. Keller, and J. P. Kernevez, “Numerical analysis and control of bifurcation problems (I), bifurcation in finite dimensions,” International Journal of Bifurcation and Chaos, vol. 1, no. 3, pp. 493–520, 1991. View at Publisher · View at Google Scholar
  38. R. Seydel, Practical Bifurcation and Stability Analysis, Springer, 2010.
  39. W.-S. Song, S. Lee, D.-S. Shin, and Y. Na, “Thermo-acoustic instability in the horizontal Rijke tube,” Journal of Mechanical Science and Technology, vol. 20, no. 6, pp. 905–913, 2006. View at Publisher · View at Google Scholar · View at Scopus
  40. S. M. Sarpotdar, N. Ananthkrishnan, and S. D. Sharma, “The Rijke tube—a thermo-acoustic device,” Resonance, vol. 8, no. 1, pp. 59–71, 2003. View at Publisher · View at Google Scholar