Lewis number effect

J. Buckmaster and M. Matalon, Anomalous Lewis number effects in tribrachial flames, Proc. Combust. Inst. 22 1527-1535, 1988. 

Nevertheless, despite all these remarkable achievements, some open questions still remain. Among them is the influence of the molecular transport properties, in particular Lewis number effects, on the structure of turbulent premixed flames. Additional work is also needed to quantify the flame-generated turbulence phenomena and its relationship with the Darrieus-Landau instability. Another question is what are exactly the conditions for turbulent scalar transport to occur in a coimter-gradient mode Finally, is it realistic to expect that a turbulent premixed flame reaches an asymptotic steady-state of propagation, and if so, is it possible, in the future, to devise an experiment demonstrating it ... 

If one of the scalars is enthalpy, the Schmidt number is replaced by the Prandtl number. The ratio of the Schmidt number to the Prandtl number is the Lewis number - a measure of the relative diffusivity of chemical species and enthalpy. Non-unity Lewis number effects can be important in combustion. 

R. G. Abdel-Gayed, D. Bradley, M. N. Hamid, and M. Lawes. Lewis number effects on turbulent burning velocity. Proc. Combust. Inst, 20 505-512, 1984. 

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. 

Three types of diffusion are known in the flame heat diffusion (thermal diffu-sivity) a), limiting reagent diffusion (D,) and excessive reagent diffusion Dj). Having three diffusion factors and comparing D, with a and Di with Dj for non-stoichiometric and near stoichiometric mixtures, it is possible to obtain two criteria for a selective diffusion. These two criteria specify the non-unity Lewis number effect (Le = a/D,) and the differential diffusion effect (D,/Dy). 

Unlike the flat flame model [57-59], the approach offered in [60] allows investigation of the ignition process and further development of the spherical flame source. At small source radii the flame velocity reproduces the Lewis number effect. Figure 2.8 illustrates the spherical source development and allows comparison of radii predicted and measured using the Schlieren photography in an H2 + air ((f) = 0.26) mixture. 

The flow structures of lean limit methane and propane flames are compared in Figures 3.1.2 and 3.1.3. The structure depends on the Lewis number for the deficient reactant. A stretched lean limit methane flame (Lepreferential diffusion, giving it a higher burning intensity. Hence, the flame extinction limit is extended. On the other hand, for a stretched lean limit propane flame (Le>l), the same effect reduces the burning intensity, which can... 

It can also be noted that the slope of the S , .,f-Ka plot reflects the combined effect of stretch rate and non-equidiffusion on the flame speed. Figure 4.1.6 clearly shows that the flame response with stretch rate variation differs for lean and rich mixtures. In particular, as Ka increases, the S for stoichiometric and rich mixtures increases, but decreases for the mixture of equivalence ratio = 0.7. This is because the effective Lewis numbers of lean w-heptane/ air and lean /so-octane/air flames are... 

Finally, we come to the effects of the Lewis number. Figure 4.2.14 shows the intensified images of vortex ring combustion of lean and rich propane/air mixtures. Since the flame is curved and stretched at the head region, the mass and heat is transferred through a stream tube. 

Frankel, M. L. and Sivashinsky, G. L, On effects due to thermal expansion and Lewis number in spherical flame propagation. Combustion Science and Technology, 31,131-138, 1983. 

Sato, ]., Effects of Lewis number on extinction behavior of premixed flames in a stagnation flow, Proc. Combust. Inst., 19, 1541,1982. 

One significant result from the studies of stretched premixed flames is that the flame temperature and the consequent burning intensity are critically affected by the combined effects of nonequidiffusion and aerodynamic stretch of the mixture (e.g.. Refs. [1-7]). These influences can be collectively quantified by a lumped parameter S (Le i-l)x, where Le is the mixture Lewis number and K the stretch rate experienced by the flame. Specifically, the flame temperature is increased if S > 0, and decreased otherwise. Since Le can be greater or smaller than unity, while K can be positive or negative, the flame response can reverse its trend when either Le or v crosses its respective critical value. For instance, in the case of the positively stretched, counterflow flame, with k>0, the burning intensity is increased over the corresponding unstretched, planar, one-dimensional flame for Le < 1 mixtures, but is decreased for Le > 1 mixtures. 

First, for nonequidiffusive, positively stretched counterflow flames, results showed that the flame response exhibited opposite behavior when the mixture s effective Lewis number was greater or less... 

Law [23] points out that since imoco is generally much less than 1, the denominator of the second term in Eq. (6.135) becomes [im0J(Le) a ], which indicates that the effect of (Le)foo is to change the oxygen concentration by a factor (LeA as experienced by the flame. Obviously, then, for (Le)lco > 1, the oxidizer concentration is effectively reduced and the flame temperature is also reduced from the adiabatic value obtained for Le = 1, the value given by Eq. (6.126). The effective Lewis number for the mass burning rate [Eq. (6.134)] is... 

Lewis number, 27 62, 64, 66 Liapunov exponent, 39 115 Lifetime effects, 34 213 Ligand... 

The deposition of an inert porous diflfusion barrier on top of the catalyst layer can significantly hinder the rate of mass transfer of reactants to the catalyst surface, at the same time affecting only negligibly the rate of heat transfer to the gas phase. The effect is equivalent to that observed with fuels, like higher hydrocarbons, whose mass diffusi vity in air is considerably lower than thermal diffusivity of the fuel-air mixture (Lewis number >1). Such unbalancing of heat and mass transfer rates results in a significant decrease in the catalyst wall temperature. 

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