Diffusion Flame Propagation

Under the present conditions of negligible diffusion, flame propagation in the solid is associated with an excess enthalpy per unit area given by PsCps(T — Tq) dx just ahead of the reaction sheet. This excess provides a local reservoir of heated reactant in which a flame may propagate at an increased velocity. If = KI(Ps ps) denotes the thermal diffusivity of the solid, then for the steady-state solution, the thickness of the heated layer of reactant is on the order of where is the steady-state flame... 

A theory of diffusion flame propagation under isothermal conditions has been proposed [145]. It has been found that in a simple case the reaction kinetics corresponds to second-order autocatalysis accompanied by first order-consumption of active species. Recently, the burning rate and the flammability limits of a cool carbon suHide flame have been computed [14] making use of the mechanism and rate constants given in a review [233, 234]. The ideas stated in this review apparently provide an explanation for the experimental facts observed the shift of... 

Diffusion Flame Propagation in the Presence of Large Vortices... 

The mechanism of flame propagation into a stagnant fuel-air mixture is determined largely by conduction and molecular diffusion of heat and species. Figure 3.1 shows the change in temperature across a laminar flame, whose thickness is on the order of one millimeter. 

Heat is produced by chemical reaction in a reaction zone. The heat is transported, mainly by conduction and molecular diffusion, ahead of the reaction zone into a preheating zone in which the mixture is heated, that is, preconditioned for reaction. Since molecular diffusion is a relatively slow process, laminar flame propagation is slow. Table 3.1 gives an overview of laminar burning velocities of some of the most common hydrocarbons and hydrogen. 

Liquid Pool Flames. Liquid fuel or flammable spills often lead to fires involving a flame at the surface of the liquid. This type of diffusion flame moves across the surface of the liquid driven by evaporation of the fuel through heat transfer ahead of the flame. If the liquid pool or spill is formed at ambient conditions sufficient to vaporize enough fuel to form a flammable air/fuel mixture, then a flame can propagate through the mixture above the spill as a premixed flame. 

Real-life premixed flame fronts are rarely planar. Of course, if the flow is turbulent, gas motion will continuously deform and modify the geometry of the flame front, see Chapter 7. However, even when a flame propagates in a quiescent mixture, the front rapidly becomes structured. In this chapter, we will discuss hydrodynamic flame instability, thermo-diffusive instability, and thermo-acoushc instability. 

Hirschfelder et al. [7] reasoned that no dissociation occurs in the cyanogen-oxygen flame. In this reaction the products are solely CO and N2, no intermediate species form, and the C=0 and N=N bonds are difficult to break. It is apparent that the concentration of radicals is not important for flame propagation in this system, so one must conclude that thermal effects predominate. Hirschfelder et al. [7] essentially concluded that one should follow the thermal theory concept while including the diffusion of all particles, both into and out of the flame zone. 

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. 

A flame is quenched in a tube when the two mechanisms that permit flame propagation—diffusion of species and of heat—are affected. Tube walls extract heat the smaller the tube, the greater is the surface area to volume ratio within the tube and hence the greater is the volumetric heat loss. Similarly, the smaller the tube, the greater the number of collisions of the active radical species that are destroyed. Since the condition and the material composition of the tube wall affect the rate of destruction of the active species [5], a specific analytical determination of the quenching distance is not feasible. 

COSILAB Combustion Simulation Software is a set of commercial software tools for simulating a variety of laminar flames including unstrained, premixed freely propagating flames, unstrained, premixed burner-stabilized flames, strained premixed flames, strained diffusion flames, strained partially premixed flames cylindrical and spherical symmetrical flames. The code can simulate transient spherically expanding and converging flames, droplets and streams of droplets in flames, sprays, tubular flames, combustion and/or evaporation of single spherical drops of liquid fuel, reactions in plug flow and perfectly stirred reactors, and problems of reactive boundary layers, such as open or enclosed jet flames, or flames in a wall boundary layer. The codes were developed from RUN-1DL, described below, and are now maintained and distributed by SoftPredict. Refer to the website http //www.softpredict.com/cms/ softpredict-home.html for more information. 

FlameMaster v3.3 A C+ + Computer Program for OD Combustion and ID Laminar Flame Calculations. FlameMaster was developed by H. Pitsch. The code includes homogeneous reactor or plug flow reactors, steady counter-flow diffusion flames with potential flow or plug flow boundary conditions, freely propagating premixed flames, and the steady and unsteady flamelet equations. More information can be obtained from http //www.stanford.edu/group/pitsch/Downloads.htm. 

Calcs rate of flame propagation for a specific relation between diffusion and heat conductance) 2) Ya.B. Zel dovich, Natl-AdvisoryComm Aeronaut, Tech Mem No 1282,... 

The so-called diffusion theories of flame propagation, as exemplified by the work of Tanford and Pease 38), emphasize the transport of mass, in that concentration of an active radical is assumed to be the rate-controlling property. Its use seems to be fairly limited in that only a few specific reactions have been successfully studied with this theory. What is more interesting, however, is that this theory forms the counterpart to the thermal theory. These two extreme views bracket the actual case, and their study allows a consideration of each of two of the basic flame mechanisms, unencumbered by the other. Actual deflagration depends on both the transport of heat and the transport of mass, and a successful theory should contain both phenomena. 

The calculation gave a combustion rate which differed by 15% from the experimental one. Thus, for the first time, the combustion rate was calculated from independent data, and for the first time in this example the practical possibility was demonstrated of reducing the laws of flame propagation to the laws of phenomena which lie at the basis of the process, i.e., to the laws of chemical kinetics and of heat conductivity and diffusion. 

When /k < 1, conditions in the flame pellet, which receives fuel from the surrounding medium by diffusion, are even less favorable than for normal flame propagation with respect to the gas. Therefore the flame moves normally with respect to the gas in both directions, upward and downward, and identical mechanisms yield practically identical limits z is close to unity. 

In lean hydrogen mixtures the flame temperature in diffusive combustion is higher than in normal propagation and so, in a wide region of concentrations (from 4 to 9% H2 in a mixture of hydrogen with air), normal propagation is impossible, only diffusive combustion is possible. Our point of view is in accord with the observed properties of flame propagation in this concentration interval. 

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