Flame cellular

Figure A3.14.14. A cellular flame in butane oxidation on a burner. (Courtesy of A C McIntosh.)...

P. Pelce and D. Rochwerger. Vibratory instability of cellular flames propagating in tubes. Journal of Fluid Mechanics, 239 293-307,1992. 

Sivashinsky, G.L, Diffusional-thermal theory of cellular flames. Combust. Sci. Technol., 15,137,1977. 

Refs 1)J. Manton et al, JChemPhys 20, 153-7(1952) CA 46, 6385(1952)(Nonisotropic propagation of combustion waves in explosive gas mixts and development of cellular flames) 2)G.H. Mark stein, JChemPhys 20, 1051-52 (1952) CA 46, 11688(1952)(Nonisotropic propagation of combustion waves)... 

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. 

Fig. 6. Model of the cellular flame from the work of Zeldovich (1966).

Comparison of Flame Propagation m a Channel and Cellular Flames If one considers the disturbances of finite amplitude at the infinite thin flame surface from the point of view of Huygens principle, then with time there appear angular points, which diminish the flame front surface, i.e.,... 

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. 

The condition Le > 1 is the opposite from that (Lej < 1) identified in Section 9.5.2.3 as conducive to the formation of cellular flames. 

Figure 7.1 Four stages of propagation found in the TC burner Stage A — wrinkled flame, due to the Darrieus-Landau instability Stage B — flat flame, due to the primary pyroacoustic instability Stage C — pulsating cellular flame, due to the secondary pyroacoustic instability and Stage D — turbulent flame.

Such diffusion-driven instabilities have been observed earlier in combustion systems. As early as 1892, Smithells reported the observation of cellular flames in fuel-rich mixtures [40]. An example is shown in figure A3.14.14. These were explained theoretically by Sivashinsky in terms of a thermodifflisive mechanism [41]. The key feature here involves the role played by the Lewis number, Le, the ratio of the thermal to mass diffusivity. If Le <1, which may arise with fuel-rich flame, for which H-atoms are the relevant species, of relatively low thermal conductivity (due to the high hydrocarbon content), a planar flame is unstable to spatial perturbations along the front. This mechanism has also been shown to operate for simple one-off chemical wave fronts, such as the iodate-arsenite system [42] and for various pH-driven fronts [43], if... 

A. Bayliss, B. J. Matkowsky, Structure and Dynamics of Kink and Cellular Flames Stabilized on a Rotating Burner, Physica D 99 (1996), 276. 

A nonlinear theory of cellular flames," SIAM J. Appl. Math. 38, pp. 489-504. 

In this paper, we present two recent results of our work in this area. First, we consider the transition from periodic pulsating to quasi-periodic pulsating flames. Then, we consider the transition from a stationary cellular flame to a pulsating cellular flame. In each case, we characterize the transition as a secondary (or higher order) bifurcation. 

Both pulsating and cellular flames have been observed experimentally (cf. [3]). 

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