Effects of strain on laminar flames

Given any velocity field v for a fluid, the motion in the vicinity of a point on the reaction sheet can be resolved into a uniform translation with velocity v, a rigid-body rotation with angular velocity x v and a pure straining motion [97]. The first two of these motions have no effect on the 

A general definition of flame stretch for planar flames is the time derivative of the logarithm of an area of the flame sheet [15], [93], the boundary of the area being considered to move with the local transverse component of the fluid velocity at the sheet. This definition is applied to an infinitesimal element of surface area at each point on the flame sheet to provide the distribution of stretch over the sheet. Thus at any given point on 

The influence of stretch on flame structure can be seen qualitatively without going through a formal analysis of the equations of Section 9.5.1, For illustrative purposes, it is sufficient first to put= l,andLe = 1 in equation (9-95) for i — 1, thereby obtaining (with V / = 0 and dependent only on and t) 

The nature of the solution to equation (52) depends on the sign of k. Positive stretch corresponds to /c 0 and negative stretch, flame-sheet compression, corresponds to k 0. For positive stretch, according to the sign of in equation (52), material flows toward the flame from 

Steady-State solution of some kind. Most studies of the influences of flame stretch are restricted to positive stretch (k 0) and work with steady-state conservation equations [for example, equation (52) with dYJdx — 0]. 

Many further analyses of structures of stretched laminar flames have now been published [101]-[113]. With one exception [113], they essentially apply activation-energy asymptotics for one-step kinetics multistep kinetics can have a significant influence on the responses of flames to strain [113], through enhanced diffusive losses of reaction intermediaries from the reaction zone. Most of the analyses employ a constant-density approximation, but a few [106], [110]-[112] have taken density variations into account. As a consequence of these studies, we now have a good understanding of many aspects of the influences of strain. 

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Chapter 10 on turbulent-flame theory also is long, as it must be because so many different viewpoints and approaches to the subject now are available. Included in this chapter are discussions of analyses of effects of strain on laminar flame sheets, topics of interest in themselves as well as in connection with turbulent combustion. Evolution equations for laminar flames in non-uniform flows also are given. The results outlined for turbulent burning velocities emphasize those aspects that have the strongest basic theoretical justifications. Since turbulent-flame theory is a subject of continuing development, improvements of results presented herein might be anticipated to be available in the not-too-distant future. 

Darabiha, N., Candel, S., and Marble, R, The effect of strain rate on a premixed laminar flame. Combust. Flame, 64, 203, 1986. 

Laminar flames in turbulent flows are subjected to strain and develop curvature as consequences of the velocity fluctuations. These influences modify the internal structure of the flame and thereby affect its response to the turbulence. The resulting changes are expected to be of negligible consequence at sufficiently large values of Jb in Figure 10.5, but as turbulence scales approach laminar-flame thicknesses, they become important. Therefore, at least in part of the reaction-sheet regime, consideration of these effects is warranted. The effects of curvature were discussed in Section 9.5.2.3. Here we shall focus our attention mainly on influences of strain. 

Egolfopoulos, F.N., Zhang, H., and Zhang, Z., Wall effects on the propagation and extinction of steady, strained, laminar premixed flames. Combust. Flame, 109,237,1997. 

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