Flame sheets

Landau instabilities are the hydrodynamic instabilities of flame sheets that are associated neither with acoustics nor with buoyancy but instead involve only the density decrease produced by combustion in incompressible flow. The mechanism of Landau instability is purely hydrodynamic. In principle, Landau instabilities should always be present in premixed flames, but in practice they are seldom observed (26,27). 

Experiments in closed vessels by Abdel-Gayed and Bradley [19], left Ka.Le = 0.003 continuous laminar flame sheet, right Ka.Le = 0.238 breakup of the continuous flame sheet. (Reprinted from Lewis, B. and Von Elbe, G., Combustion, Flames and Explosions of Gases, Academic Press, New York, 1961. With permission. Figure 204, p. 401, copyright New York Academic Press (Elsevier editions).)... 

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. 

Since at the flame sheet Yq2 = Yf = 0, this is the definition of a stoichiometric system so that... 

Figure 6.3. Sketch of the flame sheet, reaction zone, and allowable region for a one-step localized reaction.

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... 

Si and Y = 1 in composition space.63 Since the reaction rate is assumed to be very large, all points that fall in the reaction zone will be immediately moved to the flame sheet defined by... 

A typical time-averaged picture of the flame sheet is shown in Fig. 17.2. Under most of the operating conditions, the flame is observed to have a nominally constant diameter along the entire length of the cylinder. The following description of the internal mechanics supporting such operation is based upon observations of the flame behavior and various measurements of the exhaust flow, but to date, no local velocity measurements have been made within the chamber. 

The front jet produces a countercurrent shear environment which entrains reactants and pumps them radially inward toward the flame as depicted in the sketch of Fig. 17.3a. Since the reactants are premixed, the flame sheet must reside at a position where the flame speed (determined by the reactant equivalence ratio and the local turbulence intensity) matches the radial inward velocity of reactants. Since the radial velocity must be zero at the cylinder axis and wall, a maximum must exist (as indicated in Fig. 17.36). As long as the flow rates are maintained at high enough rates, this maximum is greater than the local flame speed and the flame remains confined. If the flame speed exceeds the maximum radial velocity anywhere along the axis of the cylinder, the flame changes modes and flashes out to the cylinder wall. 

To simplify the discussion, let us reconsider the velocity profiles shown in Fig. 17.3 for the basic cyclone configuration where little or no rear drive flow is present. As reactants are entrained out of the front jet, conservation of mass and momentum requires that the axial velocity of the outer jet decrease with increasing distance from the front drive. But, as the reactants are converted to products when they cross the flame sheet, mass is added at fixed area to the product flow. This causes the axial velocity of the products to accelerate toward the exhaust nozzle as in classic constant-area heat addition. Thus, one expects... 

Figure 17.7 (a) Cylindrical flame sheet area as a function of gray scale threshold (6) corresponding flame image and (c) image contours at threshold values of 0.34, 0.54, and 0.69... 

Figure 27.2 shows measurements and predictions of CO2 and CO mole fractions. The sharp peaks in the mole fraction profiles of these species cause gradient-broadening errors near the flame sheet. The measurements also show the effects of broadening of the profiles caused by finite spatial resolution of the probe. However, overall the comparison between measurements and predictions is as good as any reported in the literature or better. 

The combustion wave of HMX is divided into three zones crystallized solid phase (zone 1), solid and/or liquid condensed phase (zone 11), and gas phase (zone 111). A schematic representation of the heat transfer process in the combustion wave is shown in Fig. 5.5. In zone 1, the temperature increases from the initial value Tq to the decomposition temperature T without reaction. In zone 11, the temperature increases from T to the burning surface temperature Tj (interface of the condensed phase and the gas phase). In zone 111, the temperature increases rapidly from to the luminous flame temperature (that of the flame sheet shown in Fig. 5.4). Since the condensed-phase reaction zone is very thin (-0.1 mm), is approximately equal to T . 

After the rapid oxidation that typically occurs in a flame sheet, the temperature is high and the concentration of the O and H radicals may be significant. In the postflame region these radicals react in three-body recombination reactions, mainly... 

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]. 

The use of laminar flamelet combustion models within FDS have been studied by Yang et al. [42] and Kang and Wen [43], Unfortunately, the performance or advantage over the simple flame-sheet model in large-scale fire simulation was not demonstrated in these studies. In full-scale calculations, the mixture fraction and temperature fields close to the flame sheet have overshoots, caused by the second-order transport scheme. It is still unclear how the laminar flamelet models that require both second and first moments of the local mixture fraction field could work in this situation. 

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