Flame sheets turbulent diffusion

The relevance of premixed edge flames to turbulent premixed flames can also be understood in parallel to the nonpremixed cases. In the laminar flamelet regime, turbulent premixed flames can be viewed as an ensemble of premixed flamelets, in which the premixed edge flames can have quenching holes by local high strain-rate or preferential diffusion, corresponding to the broken sheet regime [58]. 

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... 

The theoretical results that have been discussed here allow k to be of order unity, a condition that sometimes has been referred to as one of strong strain, although the term moderate strain seems better, with strong strain reserved for large values of k. Small values of k are identified as conditions of weak strain under these conditions the reaction sheet remains far to the reactant side of the stagnation point, and by integrating across the convective-diffusive zone, a formulation in terms of the location of the reaction sheet can be derived [102], like that discussed at the end of Section 9.5.1. By combining the approximations of weak strain and weak curvature, convenient approaches to analyses of wrinkled flames in turbulent flows can be obtained [38]. 

Although flows in combustors usually are turbulent, analyses of flame stabilization are often based on equations of laminar flow. This may not be as bad as it seems because in the regions of the flow where stabilization occurs, distributed reactions may be dominant, since reaction sheets may not have had time to develop an approximation to the turbulent flow might then be obtained from the laminar solutions by replacing laminar diffusivities by turbulent difTu-sivities in the results. Improved approximations may b "sought by moment methods (Section 10.1.2). Turbulent-flow theories are not discussed here, but some comments on results for turbulent flows are made. A review of theories for stabilization in turbulent flows is available [2]. 

One of the main benefits of a premixed head in comparison with a diffusive head is the low noise emission at the stack. A premixed burner is generally quieter than a diffusive burner because of the lower combustion turbulence, on the condition there is no instability in the combustion, an instability that is possible with diffusive flames too. Figure 25.7 shows the comparison between the noise at the stack of the configurations previously examined. Like gas emissions, noise measurements are influenced by the combustion chamber type. Regarding sound emissions at the stack, the mat head still exhibits lower emissions in comparison with the metal sheet head as seen in Figure 25.8. 

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