364
Views
29
CrossRef citations to date
0
Altmetric
Original Articles

Nonlinear/chaotic behaviour in thermo-acoustic instability

&
Pages 541-557 | Received 07 May 2008, Accepted 06 Apr 2009, Published online: 02 Jul 2009

References

  • Lord Rayleigh . 1878 . The theory of sound. , Vol. II , 227 New York : Dover Publication . 1945
  • Chu , B. T. 1964 . On the energy transfer to small disturbances in fluid flow. Part I . Acta Mech. , 1 : 215 – 234 .
  • Culick , F. E. C. 1976 . Nonlinear behaviour of acoustic waves in combustion chambers–I . Acta Astr. , 3 : 715 – 734 .
  • Culick , F. E. C. 1976 . Nonlinear behaviour of acoustic waves in combustion chambers–II . Acta Astr. , 3 : 735 – 757 .
  • Yang , V. , Kim , S.-I. and Culick , F. E. C. 1987 . Third-order nonlinear acoustic waves and triggering of pressure oscillations in combustion chambers, Part I: Longitudinal modes AIAA Paper 87–1973
  • Yang , V. , Kim , S.-I. and Culick , F. E. C. 1988 . Third-order nonlinear acoustic waves and triggering of pressure oscillations in combustion chambers, Part I: Transverse modes AIAA Paper 88–0152
  • Yang , V. , Kim , S.-I. and Culick , F. E. C. 1990 . Triggering of longitudinal pressure oscillations in combustion chambers, I: Nonlinear gasdynamics . Combust. Sci. Technol. , 72 : 183 – 214 .
  • Sterling , J. D. 1993 . Nonlinear analysis and modelling of combustion instabilities in a laboratory combustor . Combust. Sci. Technol , 89 : 167 – 179 .
  • Levine , J. N. and Baum , J. D. 1981 . A numerical study of nonlinear instability phenomena in solid rocket motors AIAA-81–1524
  • Dubinkin , B. N. , Natanzon , M. S. and Cham'yan , A. E. 1978 . Two regimes of operation in a combustion chamber with a recirculation zone . Combust. Explosion and Shock Waves , 13 : 693 – 700 . (Translated from Fizika Goreniya I Vzryva, 14 (1978), pp. 3–11)
  • Huang , Y. , Wang , Z. and Zhou , J. 2002 . Nonlinear theory of combustion stability in liquid engine based on chemistry dynamics . Sc. of China (Series B) , 45 : 373 – 383 .
  • Ananthkrishnan , N. , Deo , S. and Culick , F. E. C. 2005 . Reduced-order modelling and dynamics of nonlinear acoustic waves in a combustion chamber . Combust. Sci. Technol. , 177 : 221 – 247 .
  • Huang , Y. and Yang , V. 2004 . Bifurcation of flame structure in a lean-premixed swirl-stabilized combustor: transition from stable to unstable flame . Combust. Flame , 136 : 383 – 389 .
  • Lieuwen , T. 2002 . Experimental investigation of limit cycle oscillations in an unstable gas turbine combustor . J. Prop. Power , 18 : 61 – 67 .
  • Seydel , R. 1994 . Practical bifurcation and stability analysis: From equilibrium to chaos, , 2nd edn. , New York : Springer-Verlag .
  • Jorgensen , D. V. and Rutherford , A. 1983 . On the dynamics of a stirred tank with consecutive reactions . Chem. Engng Sci. , 38 : 45 – 53 .
  • Smith , C. B. , Kuszta , B. , Lyberatos , G. and Bailey , J. E. 1983 . Period doubling and complex dynamics in an isothermal chemical reaction system . Chem. Engng Sci. , 38 : 425 – 430 .
  • Franceschini , V. and Tebaldi , C. 1979 . Sequences of infinite bifurcations and turbulence in a five-mode truncation of the Navier-Stokes equations . J. Stat. Phys. , 21 : 707 – 726 .
  • Roose , D. , Piessens , R. , Hlaváček , V. and van Rompay . 1984 . Direct evaluation of critical conditions for thermal explosion and catalytic reaction . Combust. Flame , 55 : 323 – 329 .
  • Sohn , C. H. , Kim , J. S. , Chung , S. H. and Maruta , K. 2000 . Nonlinear evolution of diffusion flame oscillations triggered by radiative heat loss . Combust. Flame , 123 : 95 – 106 .
  • He , L. and Clavin , P. 1993 . Premixed hydrogen-oxygen flames. Part II: Quasi-isobaric ignition near the flammability limits . Combust. Flame , 93 : 408 – 420 .
  • Mathews , J. H. 1992 . Numerical methods for mathematics, science, and engineering, , 2nd edn , London : Prentice Hall .
  • Lynch , S. 2005 . Analysis of a blood cell population model . Int. J. Bifur. Chaos , 15 : 2311 – 2316 .
  • Lieuwen , T. C. and Yang , V. 2005 . Combustion instability in gas turbine engines , AIAA, Inc .
  • Holodniok , M. and Kubíček , M. 1984 . New algorithms for the evaluation of complex bifurcation points in ordinary differential equations. A comparative numerical study . Appl. Math. Comput. , 15 : 261 – 274 .
  • Griewank , A. and Reddien , G. 1983 . The calculation of Hopf points by a direct method . IMA J. Numer. Anal. , 3 : 295 – 304 .
  • Kubíček , M. and Holodniock , M. 1984 . Evaluation of Hopf bifurcation points in parabolic equations describing heat and mass transfer in chemical reactors . Chem. Engng Sci. , 39 : 593 – 599 .
  • Roose , D. and Hlaváèek , V. 1983 . A new approach for the computation of Hopf bifurcation points . SIAM J. Appl. Math. , 43 : 1075 – 1085 .
  • Lei , S. and Turan , A. 2009 . Nonlinear/Chaotic Analysis Modelling and control of combustion instabilities due to vaporizing process, Chaos Solitons Fractals, doi:10.1016/j.chaos.2009.03.081
  • Culick , F. E. C. 1988 . Combustion instabilities in liquid-fueled propulsion systems Paper Number 1, AGARD Conference Proceedings No. 450
  • Culick , F. E. C. . Some recent results for nonlinear acoustics in combustion chambers . AIAA 13th Aeroacoustics Conference . AIAA Paper 90–3927
  • Natanzon , M. S. and Men'shikova , O. M. 1992 . Bifurcation of steady combustion regimes and their influence on the onset of high-frequency oscillations in combustion chambers . Combust. Explosion and Shock Waves , 28 : 326 – 333 .
  • Culick , F. E. C. 2006 . Unsteady motions in combustion chambers for propulsion systems RTO AGARDograph, AG-AVT-039
  • McIntosh , A. C. and Rylands , S. 1996 . A model of heat transfer in Rijke tube burners . Combust. Sci. Technol. , 113 : 273 – 289 .
  • Heckl , M. A. and Howe , M. S. 2007 . Stability analysis of the Rijke tube with a Green's function approach . J. Sound Vib. , 305 : 672 – 688 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.