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Asymptotic analysis of outwardly propagating spherical flames

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Abstract

Asymptotic analysis is conducted for outwardly propagating spherical flames with large activation energy. The spherical flame structure consists of the preheat zone, reaction zone, and equilibrium zone. Analytical solutions are separately obtained in these three zones and then asymptotically matched. In the asymptotic analysis, we derive a correlation describing the spherical flame temperature and propagation speed changing with the flame radius. This correlation is compared with previous results derived in the limit of infinite value of activation energy. Based on this correlation, the properties of spherical flame propagation are investigated and the effects of Lewis number on spherical flame propagation speed and extinction stretch rate are assessed. Moreover, the accuracy and performance of different models used in the spherical flame method are examined. It is found that in order to get accurate laminar flame speed and Markstein length, non-linear models should be used.

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References

  1. Taylor, S.C.: Burning velocity and the influence of flame stretch. [Ph.D. Thesis], University of Leeds (1991)

  2. Tseng, L.K., Ismail, M.A., Faeth, G.M.: Laminar burning velocities and Markstein numbers of hydrocarbon/air flames. Combust. Flame 95, 410–426 (1993)

    Article  Google Scholar 

  3. Bradley, D., Hicks, R.A., Lawes, M., et al.: The measurement of laminar burning velocities and Markstein numbers for isooctane-air and iso-octane-n-heptane-air mixtures at elevated temperatures and pressures in an explosion bomb. Combust Flame 115, 126–144 (1998)

    Article  Google Scholar 

  4. Tse, S.D., Zhu, D.L., Law, C.K.: Morphology and burning rates of expanding spherical flames in H2/O2/inert mixtures up to 60 atmospheres. Proc. Combust. Inst. 28, 1793–1800 (2000)

    Article  Google Scholar 

  5. Qin, X., Ju, Y.: Measurements of burning velocities of dimethyl ether and air premixed flames at elevated pressures. Proc. Combust. Inst. 30, 233–240 (2005)

    Article  Google Scholar 

  6. Huang, Z., Zhang, Y., Zeng, K., et al.: Measurements of laminar burning velocities for natural gas-hydrogen-air mixtures. Combust. Flame 146, 302–311 (2006)

    Article  Google Scholar 

  7. Chen, Z., Qin, X., Ju, Y.G., et al.: High temperature ignition and combustion enhancement by dimethyl ether addition to methane-air mixtures. Proc. Combust. Inst. 31, 1215–1222 (2007)

    Article  Google Scholar 

  8. Hu, E., Huang, Z., He, J., et al.: Experimental and numerical study on laminar burning characteristics of premixed methanehydrogen-air flames. Int. J. Hydrogen Energy 34, 4876–4888 (2009)

    Article  Google Scholar 

  9. Qiao, L., Gan, Y., Nishiie, T., et al.: Extinction of premixed methane/air flames in microgravity by diluents: Effects of radiation and Lewis number. Combust. Flame 157, 1446–1455 (2010)

    Article  Google Scholar 

  10. Tang, C.L., Huang, Z.H., Law, C.K.: Determination correlation and mechanistic interpretation of effects of hydrogen addition on laminar flame speeds of hydrocarbon-air mixtures. Proc. Combust. Inst. 33, 921–928 (2011)

    Article  Google Scholar 

  11. Chen, Z.: On the extraction of laminar flame speed and Markstein length from outwardly propagating spherical flames. Combust. Flame 158, 291–300 (2011)

    Article  Google Scholar 

  12. Chen, Z., Burke, M.P., Ju, Y.: Effects of Lewis number and ignition energy on the determination of laminar flame speed using propagating spherical flames. Proc. Combust. Inst. 32, 1253–1260 (2009)

    Article  Google Scholar 

  13. Bradley, D., Lawes, M., Liu, K., et al.: Laminar burning velocities of lean hydrogen-air mixtures at pressures up to 1.0 MPa. Combust. Flame 149, 162–172 (2007)

    Article  Google Scholar 

  14. Chen, Z., Burke, M.P., Ju, Y.: Effects of compression and stretch on the determination of laminar flame speed using propagating spherical flames. Combust. Theor. Model. 13, 343–364 (2009)

    Article  MATH  Google Scholar 

  15. He, L.T.: Critical conditions for spherical flame initiation in mixtures with high lewis numbers. Combust. Theor. Model. 4, 159–172 (2000)

    Article  MATH  Google Scholar 

  16. Chen, Z., Ju, Y.: Theoretical analysis of the evolution from ignition kernel to flame ball and planar flame. Combust. Theor. Model. 11, 427–453 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  17. Buckmaster, J.D., Lundford, G.S.S.: Theory of Laminar Flames. Cambridge University Press (1982)

  18. Williams, F.A.: Combustion Theory (2nd edn). Benjamin-Cummins, Menlo Park, California USA (1985)

    Google Scholar 

  19. Law, C.K.: Combustion Physics. Cambridge University Press (2006)

  20. Frankel, M.L., Sivashinsky, G.I.: On quenching of curved flames. Combust. Sci. Technol. 40, 257–268 (1984)

    Article  Google Scholar 

  21. Frankel, M.L., Sivashinsky, G.I.: On effects due to thermalexpansion and Lewis number in spherical flame propagation. Combust. Sci. Technol. 31, 131–138 (1983)

    Article  Google Scholar 

  22. Chen, Z., Gou, X., Ju, Y.: Studies on the outwardly and inwardly propagating spherical flames with radiative loss. Combust. Sci. Technol. 182, 124–142 (2010)

    Article  Google Scholar 

  23. Zhang, H., Chen, Z.: Spherical flame initiation and propagation with thermally sensitive intermediate kinetics. Combust. Flame 158, 1520–1531 (2011)

    Article  Google Scholar 

  24. Zeldovich, Y.B., Barenblatt, G.I., Librovich, V.B., et al.: The Mathematical Theory of Combustion and Explosions. New York: Consultants Bureau (1985)

    Book  Google Scholar 

  25. Champion, M., Deshaies, B., Joulin, G., et al.: Spherical flame initiation theory versus experiments for lean propane-air mixtures. Combust. Flame 65, 319–337 (1986)

    Article  Google Scholar 

  26. Bradley, D., Lawes, M., Mansour, M.S.: Explosion bomb measurements of ethanol-air laminar gaseous flame characteristics at pressures up to 1.4 MPa. Combust. Flame 156, 1462–1470 (2009)

    Article  Google Scholar 

  27. Ju, Y., Guo, H.S., Liu, F.S., et al.: Effects of the Lewis number and radiative heat loss on the bifurcation and extinction of CH4/O2/N2/He flames. J. Fluid Mech. 379, 165–190 (1999)

    Article  MATH  Google Scholar 

  28. Ju, Y., Masuya, G., Liu, F., et al.: Asymptotic analysis of radiation extinction of stretched premixed flames. Int. J. Heat Mass Tran. 43, 231–239 (2000)

    Article  MATH  Google Scholar 

  29. Chen, Z., Ju, Y.: Combined effects of curvature, radiation, and stretch on the extinction of premixed tubular flames. Int. J. Heat Mass Tran. 51, 6118–6125 (2008)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, Department of Aeronautics and Astronautics, College of Engineering, Peking University, 100871, Beijing, China

    Yun-Chao Wu & Zheng Chen

Authors
  1. Yun-Chao Wu
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  2. Zheng Chen
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Correspondence to Zheng Chen.

Additional information

The project was supported by the National Natural Science Foundation of China (50976003, 51136005) and Doctoral Fund of Ministry of Education of China (20100001120003).

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Wu, YC., Chen, Z. Asymptotic analysis of outwardly propagating spherical flames. Acta Mech Sin 28, 359–366 (2012). https://doi.org/10.1007/s10409-012-0008-8

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  • DOI: https://doi.org/10.1007/s10409-012-0008-8

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