Diffusion flames flame sheets

Recall that we are assuming faem "C faff (°r fax, if turbulent flow). Anyone who has carefully observed a laminar diffusion flame - preferably one with little soot, e.g. burning a small amount of alcohol, say, in a whiskey glass of Sambucca - can perceive of a thin flame (sheet) of blue incandescence from CH radicals or some yellow from heated soot in the reaction zone. As in the premixed flame (laminar deflagration), this flame is of the order of 1 mm in thickness. A quenched candle flame produced by the insertion of a metal screen would also reveal this thin yellow (soot) luminous cup-shaped sheet of flame. Although wind or turbulence would distort and convolute this flame sheet, locally its structure would be preserved provided that faem fax. As a consequence of the fast chemical kinetics time, we can idealize the flame sheet as an infinitessimal sheet. The reaction then occurs at y = yf in our one dimensional model. 

As will be shown for the CD model, early mixing models used stochastic jump processes to describe turbulent scalar mixing. However, since the mixing model is supposed to mimic molecular diffusion, which is continuous in space and time, jumping in composition space is inherently unphysical. The flame-sheet example (Norris and Pope 1991 Norris and Pope 1995) provides the best illustration of what can go wrong with non-local mixing models. For this example, a one-step reaction is described in terms of a reaction-progress variable Y and the mixture fraction p, and the reaction rate is localized near the stoichiometric point. In Fig. 6.3, the reaction zone is the box below the flame-sheet lines in the upper left-hand corner. In physical space, the points with p = 0 are initially assumed to be separated from the points with p = 1 by a thin flame sheet centered at... 

Both imidogen (NH) and nitrous oxide (N20) may subsequently be oxidized to NO. Even though NNH, because of its low stability, never reaches significant concentrations, the NNH mechanism may contribute significantly to NO formation under certain conditions. It seems to be most important in diffusion flames, where NNH may form on the fuel-rich side of the flame sheet and then react with O inside the flame sheet [383]. 

For steady-state diffusion flames with thin reaction sheets, it is evident that outside the reaction zone there must be a balance between diffusion and convection, since no other terms occur in the equation for species conservation. Thus these flames consist of convective-diffusive zones separated by thin reaction zones. Since the stretching needed to describe the reaction zone by activation-energy asymptotics increases the magnitude of the diffusion terms with respect to the (less highly differentiated) convection terms, in the first approximation these reaction zones maintain a balance between diffusion and reaction and may be more descriptively termed reactive-diffusive zones. Thus the Burke-Schumann flame consists of two convective-diffusive zones separated by a reactive-diffusive zone. 

For burning in a reactive atmosphere, conditions may be encountered for which the analysis of the diffusion-flame regime is relevant. Under suitable conditions there are two thin reaction sheets, an inner one at which premixed decomposition of the monopropellant occurs and an outer one having a diffusion-flame character. Categorizations are available for potential limiting behaviors at large Damkohler numbers in reactive environments [206]. There are many flame-structure possibilities, not all of which have been analyzed thoroughly. 

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... 

FIGURE 10.4. Illustration of probability-density functions for the mixture fraction, fuel mass fraction, oxidizer mass fraction, and temperature for a jet-type diffusion flame in the flame-sheet approximation. 

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