On Non-Linear Instabilities of Cellular Premixed Flames

References

• Bechoefer J. and Libchaber A., ( 1987 ). Testing shape selection in directional solidification , Phys. Rev. B 35 ( 3 ), 1393 – 1396 .
   Web of Science ®Google Scholar
• Busse F. H. , ( 1978 ), Rep. Prog. Phys ., 41 , 1929 .
   Google Scholar
• Caroli B. , Caroti C.Roulet B., ( 1984 ). On the stability of hexagonal interfacial patterns in directional solidification of binary matures , 68 , 677 – 690 .
   Google Scholar
• Darrieus G. , ( 1938 ). Propaagation d“un front de flamme essai de théorie des vitesses anormales de déflagration par développement spontané de la turbulence, communication presented at La Technique Moderne .
   Google Scholar
• Denet B. and Haldenwang P. , ( 1992 ). Numerical study of the hydrodynamic instability of premixed flames, submitted to Combust. Sci. Tech
   Google Scholar
• Frankel M. I. and Sivashinsky G. I. , ( 1983 ). The effect of viscosity on hydrodynamic stability of a plane flame front , Combust. Sci. Tech ., 31 , 131 .
   Web of Science ®Google Scholar
• Fröhlich J. and Peyret R. , ( 1991 ), to appear. Joulin G. and Cambray P., (1992). On a tentative approximate evolution equation for markedly wrinkled premixed flames , Comb. Sci. Tech . 81 , 243 – 256
   Google Scholar
• Landau L. , ( 1944 ). On the theory of slow combustion , Acta Physicochim . URSS, 19 , 77 .
   Google Scholar
• Lorenz E. N. , ( 1963 ). Deterministic non periodic flow , J Atmos. Sci ., 20 , 130 – 141 .
   Web of Science ®Google Scholar
• Markstein G. H. , ( 1951 ). Experimental and theoretical studies of flame front stability , J. Aeronaut. Sci . 18 , 199 – 209 .
   Web of Science ®Google Scholar
• Pelcé P. and Clavin P. , ( 1982 ). Influence of hydrodynamics and diffusion upon the stability limit of laminar premixed flames , J. Fluid Mech . 124 , 219 .
   Web of Science ®Google Scholar
• Quinard J. , Searby G.Boyer L., ( 1984 ) Stability limits and critical size of structures in premixed flames In “ Cellular structures in instabilities ”, Lecture Notes in Physics, Weisfreid J. E. and Zaleski S. Ed ., Springer Verlag , vol. 210 , 331 – 341 .
   Google Scholar
• Matalon M. and Matkowsky B. J., ( 1982 ). Flames as gasdynamic discontinuities , J Fluid Mech . 124 , 239 .
   Web of Science ®Google Scholar
• Michelson D. M. and Sivashinsky G. I., ( 1982 ). Thermal expansion induced cellular flames , Comb, and Flame 48 , 211 – 217 .
   Web of Science ®Google Scholar
• Rakib Z. and Sivashinsky G. I., ( 1987 ). Instabilities in upward propagating flames , Comb. Sci. Tech . 54 , 69.
   Google Scholar
• Shtilman L. and Sivashinsky G. I., ( 1990 ). |at Canadian J. Physics 68 , 76 .
   Google Scholar
• Sivashinsky G. I. , ( 1977a ). Diffusional thermal theory of cellular flames , Comb. Sci. Tech . 15 , 137 .
   Web of Science ®Google Scholar
• Sivashinsky G. I. , ( 1977b ). Non-linear analysis of hydrodynamic stability in laminar flames; Part I Derivation of basic equations , Acta Astronautica 4 , 1177 .
   Web of Science ®Google Scholar
• Sivashinsky G. I. , ( 1990 ). Phil. Trans. R. Soc. London A332 , 172 .
   Google Scholar
• Sivashinsky G. I. and Clavin P. , ( 1987 ). On the non-linear theory of hydrodynamic instabilities in flames , J.Phys. France 48 , 193 , 198 .
   Google Scholar
• Thual O. , Frisch U. and Henon M. , ( 1985 ). |atApplication of pole decomposition to an equation governing the dynamics of wrinkled flame fronts. J. Phys. France 46 , 1485 – 1494 .
   Google Scholar
• Wesfreid J. E. and Zaleski S., eds., ( 1984 ). |atCellular structures in instabilities Lecture notes in physics . Springer Verlag vol. 210 .
   Google Scholar