Convex flame, propagation

The steady states of such systems result from nonlinear hydrodynamic interactions with the gas flow field. For the convex flame, the flame surface area F can be determined from the relation fSl = b zv, where Sl is the laminar burning velocity, the cross-section area of the channel, and w is the propagation velocity at the leading point. 

The fact that the quenching limits of upward propagating rich limit flames are much wider in comparison with those moving downward can be explained in terms of preferential diffusion. When the molecular diffusivity of the deficient reactant is higher than the thermal diffusivity of the mixture and when the flame is stretched (upward propagating convex flames... 

In connection with the investigation of the problem of flame propagation in a reacting mixture, a paper by Ya.B.7 posed the question of how to describe flame waves in intermediate regimes for which the function f(v) at small v, though small, is still non-zero and is not convex, i.e., the condition / (v) < f (0) is not satisfied. 

In the scheme considered, as shown above, the convex flame front affects the hydrodynamics of the gas flow, and forms some velocity distribution ahead of it. This is associated with the pressure difference at the flame front. In other words, it is always necessary to solve a conjugate problem on the front propagation and the gas motion. Restricting the analysis by the first term in the series describing the flow field before the flame and taking into account the corresponding shape of the flame front, as was shown,... 

At places where the front is concave toward the unburnt gas, the heat flux is locally convergent. The local flame temperature increases and the local propagation velocity also increases, see the red arrows in Figure 5.1.5. The converse holds for portions of the front that are convex. The effect of thermal diffusion is to stabilize a wrinkled flame. 

In connection with Kokochashvili s observations there arises an important fundamental question about the stability of normal propagation of a continuous plane flame front. We must analyze the influence of convexity and concavity of the flame front on the propagation velocity. In mixtures in which the diffusion coefficient is equal to or less than the thermal diffusivity, a convexity (in the direction of propagation) decreases and a concavity increases the flame velocity. The increase in the velocity is explained by the fact that the mixture, enveloped by the concave flame from all sides, heats up more rapidly.12... 

Ya.B. s more recent papers have been devoted to the study of nonlinear problems. In 1966 Ya.B. turned his attention to the stabilizing effect of accelerated motion through a hot mixture of a boundary of intersection of two flame fronts, convex in the direction of propagation, and proposed an approximate model of a steady cellular flame. G. I. Sivashinsky, on the basis of this work, proposed a nonlinear model equation of thermodiffusional instability which describes the development of perturbations of a bent flame in time and, together with J. M. Michelson, studied its solution near the stability boundary Le = Lecrit. It was shown numerically that the flat flame is transformed into a three-dimensional cellular one with a non-steady, chaotically pulsating structure. The formation of a two-dimensional cellular structure was also the subject of a numerical investigation by A. P. Aldushin, S. G. Kasparyan and K. G. Shkadinskii, who obtained steady flames in a wider parameter interval. 

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