Cellular flames hydrodynamic instabilities

There are three basic distinct types of phenomena that may be responsible for intrinsic instabilities of premixed flames with one-step chemistry body-force effects, hydrodynamic effects and diffusive-thermal effects. Cellular flames—flames that spontaneously take on a nonplanar shape—often have structures affected most strongly by diffusive-thermal... 

Rq oo. Since the density ratio Rq typically has a value of about 5, with the estimate 10 < < 20, the corresponding value of Le certainly does not exceed 0.5, a value that may be compared with the limit 0.9 (which is obtained at = 20 for Rq = 1) to demonstrate the large influence of gas expansion. In fact, the influence probably is somewhat greater than would be implied by equation (102) because the decrease in diffusivity with decreasing temperature helps to make the reaction sheet less accessible to reactants, as has been shown in a further investigation of variable-property effects [223]. Thus it seems safe to conclude that Lei > Le for most real combustible mixtures and, therefore, that the observed instabilities, which lead to cellular-flame structures affected mainly by diffusive-thermal phenomena, are in fact first initiated by the hydrodynamic instability. 

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