71
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Stability of inclined planar flames as a local approximation of weakly curved flames

, &
Pages 587-615 | Received 01 Jun 2004, Accepted 15 Apr 2005, Published online: 20 Feb 2007

References

  • Zel'dovich , Y. B. and Frank-Kamenetski , D. A. 1938 . A theory of thermal propagation of flame . Acta Physicochimica , 9 : 341 – 350 . URSS[CSA]
  • Zel'dovich , Y. B. , Barenblatt , G. I. , Librovich , V. B. and Makhviladze , G. M. 1985 . The Mathematical Theory of Combustion and Explosions , New York : Consultants Bureau .
  • Darrieus , G. 1938 . “ Propagation d'un front de flamme ” . In Essai de théorie des vitesses anormales de déflagration par développement spontané de la turbulence Unpublished works presented at La Technique Moderne 1938, and at Le Congrès de Mécanique Appliquée 1945
  • Landau , L. 1944 . On the theory of slow combustion . Acta Physicochimica URSS , 19 : 77 – 85 . [CSA]
  • Clanet , C. and Searby , G. 1998 . First experimental study of the Darrieus-Landau instability . Physics Review Letters , 80 ( 17 ) : 3867 – 3870 . [CROSSREF] [CSA]
  • Markstein , G. H. 1951 . Experimental and theoretical studies of flame front stability . Journal of Aerosol Science , 18 : 199 [CSA]
  • Markstein , G. H. 1964 . Nonsteady Flame Propagation , Pergamon .
  • Sivashinsky , G. I. 1977 . Diffusional-thermal theory of cellular flames . Combustion Science and Technology , 15 : 137 – 146 . [CSA]
  • Joulin , G. and Clavin , P. 1979 . Linear stability analysis of nonadiabatic flames: Diffusional-thermal model . Combustion and Flame , 35 : 139 – 153 . [CROSSREF] [CSA]
  • Pelce , P. and Clavin , P. 1982 . Influence of hydrodynamics and diffusion upon the stability limits of laminar premixed flames . Journal of Fluid Mechanics , 124 : 219 – 237 . [CSA]
  • Williams , F. A. 1985 . Combustion Theory , Reading, MA : Addison–Wesley .
  • Bychkov , V. V. and Liberman , M. A. 2000 . Dynamics and stability of premixed flames . Physics Reports , 325 : 115 – 237 . [CROSSREF] [CSA]
  • Matalon , M. and Matkowsky , B. J. 1982 . Flames as gasdynamic discontinuity . Journal of Fluid Mechanics , 124 : 239 – 259 . [CSA]
  • Matalon , M. and Matkowsky , B. J. 1984 . On the stability of plane and curved flames . SIAM Journal of Applied Mathematics , 44 ( 2 ) : 327 – 343 . [CROSSREF] [CSA]
  • Frankel , M. L. and Sivashinsky , G. I. 1982 . The effect of viscosity on hydrodynamic stability of a plane flame front . Combustion Science and Technology , 29 : 207 – 224 . [CSA]
  • Hayes , W. D. 1959 . The vorticity jump across a gasdynamic discontinuity . Journal of Fluid Mechanics , 2 : 595 – 600 . [CSA]
  • Pindera , M.-Z. and Talbot , L. 1988 . Some fluid dynamic considerations in the modeling of flames . Combustion and Flame , 73 : 111 – 125 . [CROSSREF] [CSA]
  • Garcia-Ybarra , P. and Borghi , R. 1986 . Stability study of an oblique flame front model . Progress in Astronautics and Aeronautics , 105 : 296 – 319 . [CSA]
  • Drazin , P. G. and Reid , W. H. 1981 . Hydrodynamic Stability , New York, NY : Cambridge University Press .
  • Clavin , P. and Williams , F. A. 1982 . Effects of molecular diffusion and of thermal expansion on the structure and dynamics of premixed flames in turbulent flows of large scale and low intensity . Journal of Fluid Mechanics , 116 : 251 – 282 . [CSA]
  • Olver , F. W.J. 1974 . Introduction to Asymptotics and Special Functions , New York, NY : Academic Press .
  • Nayfeh , A. H. 1973 . Perturbation Methods , New York, NY : Wiley & Sons, Inc .
  • Van Dyke , M. D. 1964 . Perturbation Methods in Fluid Mechanics , New York, NY : Academic Press .
  • Sharpe , G. J. 2003 . Linear stability of planar premixed flames: reactive Navier–Stokes equations with finite activation energy and arbitrary Lewis number . Combustion Theory and Modelling , 7 : 45 – 65 . [CROSSREF] [CSA]
  • Clavin , P. and Garcia , P. 1983 . The influence of the temperature dependence of diffusivities on the dynamics of flame fronts . Journal of Mechanical Theoretical Applications , 2 : 245 [CSA]
  • Petersen , R. E. and Emmons , H. W. 1961 . Stability of laminar flames . The Physics of Fluids , 4 : 456 – 464 . [CROSSREF] [CSA]

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.