The laminar flame speed

The flame velocity—also called the burning velocity, normal combustion velocity, or laminar flame speed—is more precisely defined as the velocity at which unbumed gases move through the combustion wave in the direction normal to the wave surface. 

The initial theoretical analyses for the determination of the laminar flame speed fell into three categories thermal theories, diffusion theories, and comprehensive theories. The historical development followed approximately the same order. 

there were improvements in the thermal theories. Probably the most significant of these is the theory proposed by Zeldovich and Frank-Kamenetskii. Because their derivation was presented in detail by Semenov [4], it is commonly called the Semenov theory. These authors included the diffusion of molecules as well as heat, but did not include the diffusion of free radicals or atoms. As a result, their approach emphasized a thermal mechanism and was widely used in correlations of experimental flame velocities. As in the 

FIGURE 4.4 Mallard—Le Chatelier description of the temperature in a laminar flame wave. 

Mallard-Le Chatelier theory, Semenov assumed an ignition temperature, but by approximations eliminated it from the final equation to make the final result more useful. This approach is similar to what is now termed activation energy asymptotics. 

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Turbulent flame speed, unlike laminar flame speed, is dependent on the flow field and on both the mean and turbulence characteristics of the flow, which can in turn depend on the experimental configuration. Nonstationary spherical turbulent flames, generated through a grid, have flame speeds of the order of or less than the laminar flame speed. This turbulent flame speed tends to increase proportionally to the intensity of the turbulence. 

Reference stretch-affected flame speeds as a function of Karlovitz number for various (a) n-heptane/air and (b) iso-octane/air flames, showing how the reference stretch-affected flame speed is extrapolated to zero stretch to obtain the laminar flame speed. The unburned mixture temperature T is 360 K. Solid lines represent linear extrapolation, while dotted lines denote nonlinear extrapolation... 

Sl is the laminar flame speed g the centrifugal acceleration k the thermal diffusivity of the mixture... 

No physical interpretation of the criterion was provided, but it can be regarded as the ratio of the square of the velocity of a gravity-driven "free fall bubble," of diameter equal to the flame thickness, to the square of the laminar flame speed. This leads to the conclusion that quenching occurs when a flame element quenched at the wall moves ahead of the flame, as observed and as described by Jarosinski et al. [4] (see Fig. 5 in the paper referred to) for downward propagating flames in tubes. 

In the so-called "wrinkled flame regime," the "turbulent flame speed" was expected to be controlled by a characteristic value of the turbulent fluctuations of velocity u rather than by chemistry and molecular diffusivities. Shchelkin [2] was the first to propose the law St/Sl= (1 + A u /Si) ), where A is a universal constant and Sl the laminar flame velocity of propagation. For the other limiting regime, called "distributed combustion," Summerfield [4] inferred that if the turbulent diffusivity simply replaces the molecular one, then the turbulent flame speed is proportional to the laminar flame speed but multiplied by the square root of the turbulence Reynolds number Re. ... 

Botha, J.P. and Spalding, D.B., The laminar flame speed of propane-air mixtures with heat extraction from the flame, Proc. Royal Soc. London, Ser. A., 1954, 225, 71-96. 

This initial condition is rather idealized. In reality, one would expect to see partially premixed zones with f = fst and 7 = 0 which will move towards 7 = 1 along the stoichiometric line. The movement along lines of constant f corresponds to premixed combustion, and occurs at a rate that is controlled by the interaction between molecular diffusion and chemical reactions (i.e., the laminar flame speed). 

The simple physical approaches proposed by Mallard and Le Chatelier [3] and Mikhelson [14] offer significant insight into the laminar flame speed and factors affecting it. Modem computational approaches now permit not only the calculation of the flame speed, but also a determination of the temperature profile and composition changes throughout the wave. These computational approaches are only as good as the thermochemical and kinetic rate values that form their database. Since these approaches include simultaneous chemical rate processes and species diffusion, they are referred to as comprehensive theories, which is the topic of Section C3. 

As implied in the previous section, the Russian investigators Zeldovich, Frank-Kamenetskii, and Semenov derived an expression for the laminar flame speed by an important extension of the very simplified Mallard-Le Chatelier approach. Their basic equation included diffusion of species as well as heat. Since their initial insight was that flame propagation was fundamentally a thermal mechanism, they were not concerned with the diffusion of radicals and its effect on the reaction rate. They were concerned with the energy transported by the diffusion of species. 

To determine the laminar flame speed and flame structure, it is now possible to solve by computational techniques the steady-state comprehensive mass, species, and energy conservation equations with a complete reaction mechanism for the fuel-oxidizer system which specifies the heat release. The numerical... 

The Mallard-Le Chatelier development for the laminar flame speed permits one to determine the general trends with pressure and temperature. When an overall rate expression is used to approximate real hydrocarbon oxidation kinetics experimental results, the activation energy of the overall process is found to be quite high—of the order of 160kJ/mol. Thus, the exponential in the flame speed equation is quite sensitive to variations in the flame temperature. This sensitivity is the dominant temperature effect on flame speed. There is also, of course, an effect of temperature on the diffusivity generally, the dif-fusivity is considered to vary with the temperature to the 1.75 power. 

In the introduction to this chapter a combustion wave was considered to be propagating in a tube. When the cold premixed gases flow in a direction opposite to the wave propagation and travel at a velocity equal to the propagation velocity (i.e., the laminar flame speed), the wave (flame) becomes stationary with respect to the containing tube. Such a flame would possess only neutral stability, and its actual position would drift [1], If the velocity of the unbumed mixture is increased, the flame will leave the tube and, in most cases, fix itself... 

The stratified gaseous layer established over the liquid fuel surface varies from a fuel-rich mixture to within the lean flammability limits of the vaporized fuel and air mixture. At some point above the liquid surface, if the fuel temperature is high enough, a condition corresponds to a stoichiometric equivalence ratio. For most volatile fuels this stoichiometric condition develops. Experimental evidence indicates that the propagation rate of the curved flame front that develops is many times faster than the laminar flame speed discussed earlier. There are many less volatile fuels, however, that only progress at very low rates. 

The inverse of the tunnel experiments discussed is the propagation of a flame across a layer of a liquid fuel that has a low flash point temperature. The stratified conditions discussed previously described the layered fuel vapor-air mixture ratios. Under these conditions the propagation rates were found to be 4-5 times the laminar flame speed. This somewhat increased rate compared to the other analytical results is apparently due to diffusion of air to the flame front behind the parabolic leading edge of the propagating flame [41],... 

The derivation is, of course, consistent with the characteristic velocity in the flame speed problem. This velocity is obviously the laminar flame speed itself, so that... 

Now it is important to stress that, whereas the laminar flame speed is a unique thermochemical property of a fuel-oxidizer mixture ratio, a turbulent flame speed is a function not only of the fuel-oxidizer mixture ratio, but also of the flow characteristics and experimental configuration. Thus, one encounters great difficulty in correlating the experimental data of various investigators. In a sense, there is no flame speed in a turbulent stream. Essentially, as a flow field is made turbulent for a given experimental configuration, the mass consumption rate (and hence the rate of energy release) of the fuel-oxidizer mixture increases. Therefore, some researchers have found it convenient to define a turbulent flame speed, S T as the mean mass flux per unit area (in a... 

In which of the two cases would the laminar flame speed be greater ... 

You want to measure the laminar flame speed at 273 K of a homogeneous gas mixture by the Bunsen burner tube method. If the mixture to be measured is 9% natural gas in air, what size would you make the tube diameter Natural gas is mostly methane. The laminar flame speed of the mixture can be taken as 34cm/s at 298 K. Other required data can be found in standard reference books. 

A consequence of the equivalence of the two problems is that any of the procedures discussed in Section 5.3 for determining the laminar flame-speed eigenvalue A of equation (5-45) can be applied without modification for finding A as a function of t., a, and P [defined in equation (5-44)] in the present problem. In using these procedures, one should recognize that co(t) is given by equation (5-43) only for t > ct = 0 for t < t-. Results... 

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