Flame stretch

The flame stretch rate distribution was calculated based on experimental PIV data, using the semitheoretical... 

Ishizuka, S., Miyasaka, K., and Law, C.K., Effects of heat loss, preferential diffusion, and flame stretch on flame-front instability and extinction of propane/air mixtures. Combust. Flame, 45,293,1982. 

Various factors affecting the nonpremixed edge speed, such as flame stretch, preferential diffusion, and heat loss, have also been investigated, including cellular and oscillatory instabilities of edge flames [1,39 3]. 

The Lewis number, Le, is that of the deficient species (fuel or oxidant) in the mixture. In their analysis, Clavin and Williams used the simplifying approximation that the shear viscosity, the Lewis number, and the Prandtl numbers are all temperature-independent. They also showed that, at least for weak flame stretch and curvature, the change in local flame speed due to stretch and curvature is described by the same Markstein number ... 

The concept of turbulent flame stretch was introduced by Karlovitz long ago in [15]. The turbulent Karlovitz number (Ka) can be defined as the ratio of a turbulent strain rate (s) to a characteristic reaction rate (to), which has been commonly used as a key nondimensional parameter to describe the flame propagation rates and flame quenching by turbulence. For turbulence s >/ />, where the dissipation rate e and u, L and v... 

A number of theoretical (5), (19-23). experimental (24-28) and computational (2), (23), (29-32). studies of premixed flames in a stagnation point flow have appeared recently in the literature. In many of these papers it was found that the Lewis number of the deficient reactant played an important role in the behavior of the flames near extinction. In particular, in the absence of downstream heat loss, it was shown that extinction of strained premixed laminar flames can be accomplished via one of the following two mechanisms. If the Lewis number (the ratio of the thermal diffusivity to the mass diffusivity) of the deficient reactant is greater than a critical value, Lee > 1 then extinction can be achieved by flame stretch alone. In such flames (e.g., rich methane-air and lean propane-air flames) extinction occurs at a finite distance from the plane of symmetry. However, if the Lewis number of the deficient reactant is less than this value (e.g., lean hydrogen-air and lean methane-air flames), then extinction occurs from a combination of flame stretch and incomplete chemical reaction. Based upon these results we anticipate that the Lewis number of hydrogen will play an important role in the extinction process. 

In addition, the effects of gas phase retardants can change both A and E. If E is increased, our critical temperature criterion for extinction must accordingly be increased to maintain effectively a critical constancy for E/T. These chemical effects are complex and specific, and we will not be able to adequately quantify them. It is sufficient to remember that both velocity (flame stretch) and chemistry (retardant kinetics) can affect extinction. We will only examine the temperature extinction criterion. 

For a better understanding of this type of flame occurrence and for more explicit conditions that define each of these turbulent flame types, it is necessary to introduce the flame stretch concept. This will be done shortly, at which time the regions will be more clearly defined with respect to chemical and flow rates with a graph that relates the nondimensional turbulent intensity, Reynolds numbers, Damkohler number, and characteristic lengths /. 

Computational studies of partially premixed flames have also been reported [11-16], Authors have tried to explain the variation of NO emission indices with the level of partial premixing using one or more of the following residence time, flame stretch, radiation heat loss, and chemical mechanism-based arguments. However, a complete explanation of the NO emission has not been offered in the literature. 

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... 

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]. 

FIGURE 10.7. Schematic illustrations of influence of flame stretch and of flame curvature, through Lewis-number effects, on rates of heat release per unit area for adiabatic, one-reactant flames with one-step chemistry of large overall activation energy. 

A similar flat flame technique—one that does not require a heat loss correction—is the so-called opposed jet system. This approach to measuring flame speeds was introduced to determine the effect of flame stretch on the measured laminar flame velocity. The concept of stretch was introduced in attempts to understand the effects of turbulence on the mass burning rate of premixed systems. (This subject is considered in more detail in Section 4.E.) The technique uses two... 

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