Nonlinear Behaviors of Pulsating Instabilities in Counterflow Diffusion Flames with Radiation Heat Loss

복사 열손실을 받는 대향류 확산화염의 맥동 불안정성의 비선형 거동

  • 이수룡 (서울과학기술대학교 기계자동차공학과) ;
  • 박성천 (여주대학교 자동차과)
  • Received : 2012.07.14
  • Accepted : 2012.09.14
  • Published : 2012.09.30

Abstract

Nonlinear dynamics of pulsating instability in radiating counterflow diffusion flames is numerically investigated by imposing Damk$\ddot{o}$hler number perturbation. Stable limit-cycle solutions occur in small ranges of Damk$\ddot{o}$hler numbers past bifurcation point of instability. Period doubling cascade and chaotic behaviors appear just before dynamic extinction occurs. Nonlinear dynamics is also studied when large disturbances are imposed to flames. For weak steady flames, the dynamic extinction range shrinks as the magnitudes of disturbances are increased. However, strong steady flames can overcome relatively large disturbances, thereby the dynamic extinction range extending. Stable limit-cycle behaviors reappears prior to dynamic extinction when the steady flames are strong enough.

Keywords

References

  1. J. S. Kim, "Linear analysis of diffusional-thermal instability in diffusion flames with Lewis numbers close to unity", Combust. Theory Model., Vol. 1, 1997, pp. 13-40. https://doi.org/10.1080/713665228
  2. Kim, J. S., and Lee, S. R., "Diffusional-Thermal Instability in Strained Diffusion Flames with Unequal Lewis Numbers", Combust. Theory Model., Vol. 3, 1999, pp. 123-146. https://doi.org/10.1088/1364-7830/3/1/007
  3. Kukuck, S. and Matalon, M., "The Onset of Oscillations in Diffusion Flames", Combustion Theory and Modelling, Vol. 5, 2001, pp. 217-240. https://doi.org/10.1088/1364-7830/5/2/306
  4. Sohn, C. H., Kim J. S., Chung, S. H. and Maruta, K., "Nonlinear Evolution of Diffusion Flame Oscillations Triggered by Radiative Heat Loss", Combust. Flame, Vol. 123, 2000, pp. 95-106. https://doi.org/10.1016/S0010-2180(00)00148-6
  5. Miklavcic, M., Moore, A. B., and Wichman I. S., "Oscillations and Island Evolution in Radiating Diffusion Flames", Combust. Theory Model., Vol. 9, 2005, pp.403-416. https://doi.org/10.1080/13647830500293099
  6. Miklavcic, M, "Period doubling cascade in diffusion flames", Combust. Theory Model., Vol. 11, 2007, pp. 103-12. https://doi.org/10.1080/13647830600812749
  7. Lee, S. R., "Instability Analysis of Counterflow Diffusion Flames with Radiation Heat Loss", Trans. of the KSME(B), Vol. 36, No. 8, to appear.
  8. Park, J. S., Hwang D. J., Park J., Kim J. S., Kim S, Keel S. I., Kim T. K., Noh D. S., "Edge Flame Instability in Low-Strain-Rate Counterflow Diffusion Flames", Combust. Flame, Vol. 146, 2006, pp. 612-619. https://doi.org/10.1016/j.combustflame.2006.06.009
  9. Ju, Y, Guo, H., Liu, F., Maruta, K., "Effects of the Lewis number and Radiative Heat Loss on the Bifurcation and Extinction of CH4/O2-N2-He Flames", J. Fluid Mech., Vol. 379, 1999, pp. 165-190. https://doi.org/10.1017/S0022112098003231
  10. Law, C. K., Combustion Physics, Cambridge University Press, New York, 2006.
  11. Nanduria, J. R., Sung, C. J., and T'ien, J. S., "Structure and Dynamic Response of Radiative Diffusion Flames", Combust. Theory Model., Vol. 9, 2005, pp.515-548. https://doi.org/10.1080/13647830500277373
  12. Wang, H. Y., Chen, W. H. and Law, C. K., "Extinction of Counterflow Diffusion Flames with Radiative Heat Loss and Nonunity Lewis Numbers", Combust. Flame, Vol. 148, 2007, pp. 100-116. https://doi.org/10.1016/j.combustflame.2006.10.005
  13. Ng, H. D., Higgins, A. J., Kiyanda, C. B., Radulescu, M. I., Lee, J. H. S., Bates, K. R., Nikiforakis, N., "Nonlinear dynamics and chaos analysis of one-dimensional pulsating detonations", Combust. Theory Model., Vol. 9, 2005, pp. 159-70 https://doi.org/10.1080/13647830500098357