Flame thickness

Summerfield then argues that at low pressures, the combustion process should behave as a premixed flame. If the reaction is second-order, the flame thickness is given by the equation... 

Summerfield then suggests that the flame thickness for the intermediate pressure case should be some weighted average between these two extremes, such as... 

Because the flame thickness in this equation is the same parameter discussed and analyzed by Summerfield (S7), Penner (P3), and Nachbar (Nl), this equation suggests that the pressure effect on burning rate should approximate... 

The equation is written here in a nondimensional form, where kS is the wave number nondimensionalized by the flame thickness, 3 = and the growth rate... 

Example of dispersion relations calculated from Equation 5.1.5 for six lean propane-air flames. The wave number, k, is nondimensionalized by the flame thickness, S, and the growth rate, cr, is nondimensionalized by the transit time through the flame, r, = S/S. ... 

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. 

The question here is twofold first, how to prescribe a precise experimental procedure for defining the "turbulent flame speed" and second, is this quantity independent of the way used to initiate the flame This is the case for a laminar flame, and the flame propagation velocity Sl as well as the characteristic laminar flame thickness is 3 intrinsic quantity. 

An individual isothermal surface can be traced with the help of laser tomography, also known as laser sheet imaging, where a laser sheet and oil droplets are combined to visualize the instantaneous flame surface in a plane. This technique is ideal when wrinkling of an isoline is of interest besides, typically it shows the area occupied by the combustion products if the instantaneous flame thickness is small, such as a black area in... 

The results reproduced from Ref. [28] and presented in Figure 7.1.9 show that the internal structure of the "flamelets" within the studied flames displays strong departures from both unstretched laminar flamelet and stretched counterflow flamelets. Figure 7.1.9 supports the picture of the perturbed flamelet model recently introduced in Ref. [29]. In this model, depending on the local value of the ratio of laminar flame thickness and... 

The reaction rate, m ", and flame thickness, <5r, are related to the ideal burning speed by... 

Equation (9.103) can give an estimate for the flame thickness that is similar to that of the premixed flame by using Equation (9.100) and an estimate of 3 for the temperature ratio ... 

For ignition by flame contact (to a wall or ceiling), the flame heat flux will increase with Dp, the flame thickness of the igniter, estimated by... 

Since ( /cp) does not vary with pressure and >h(j increases with pressure as specified by Eq. (4.23), then Eq. (4.24) verifies that the flame thickness must decrease with pressure. It follows from Eq. (4.24) as well that... 

If the same criteria are applied to the analysis of the H2-air results in Figs. 4.1H12, some initially surprising conclusions are reached. At best, it can be concluded that the flame thickness is approximately 0.5 mm. At most, if any preheat zone exists, it is only 0.1 mm. In essence, then, because of the formation of large H atom concentrations, there is extensive upstream H atom diffusion that causes the sharp rise in H02. This H02 reacts with the H2 fuel to form H atoms and H202, which immediately dissociates into OH radicals. Furthermore, even at these low temperatures, the OH reacts with the H2 to form water and an abundance of H atoms. This reaction is about 50kJ exothermic. What appears as a rise in the 02 is indeed only a rise in mole fraction and not in mass. 

Thus, the criterion to be satisfied if a laminar flame is to exist in a turbulent flow is that the laminar flame thickness <5L be less than the Kolmogorov microscale 4 of the turbulence. 

The effect of the finite thickness of the turbulent flame was introduced in theories [18, 19]. In [18], the set of governing gas dynamic equations is supplemented by the empirical dependency of flame thickness on the distance to the ignition source, obtained by means of statistical processing of the instantaneous position of a thin wrinkled flame front in model experiments. Semi-empirical the-... 

The above analysis, which is exceedingly brief and simplified is designed to demonstrate how, even in a pre-mixed flame, the question arises as to what is the appropriate reaction volume (i.e. the flame thickness). In heterogeneous reactions, this is a question that will recur again and ain and the designer of reactors must not attempt to avoid it. It is interesting to note that, in the next but one example to be treated, the overall reaction rate (a flame speed cm s in the above) becomes a mass transfer coefficient (also cms" ) when considering the absorption of gas into a liquid with which it reacts quickly. Furthermore, exactly the same sort of analysis as the above leads to the dependence of the mass transfer coefficient fej on the reaction rate coefficient and the diffusivity, D, in the liquid phase, of ki o. (rD), cf. z a RKY above. 

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