Structure of the flame sheet

Criteria for the validity of the flame-sheet approximation may be developed by analyzing the structure of the sheet (see Section 3.4). For calculation of flame shapes in the Burke-Schumann problem, the approximation usually is well justified, although uncertainties arise for strongly sooting flames. 

Laminar flames in turbulent flows are subjected to strain and develop curvature as consequences of the velocity fluctuations. These influences modify the internal structure of the flame and thereby affect its response to the turbulence. The resulting changes are expected to be of negligible consequence at sufficiently large values of Jb in Figure 10.5, but as turbulence scales approach laminar-flame thicknesses, they become important. Therefore, at least in part of the reaction-sheet regime, consideration of these effects is warranted. The effects of curvature were discussed in Section 9.5.2.3. Here we shall focus our attention mainly on influences of strain. 

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. 

In the reaction-sheet regime, the structure of the turbulent flame is determined by the dynamics of wrinkled laminar flames. Thus the thickness of the turbulent flame (if it is large compared with that of the laminar flame) is controlled by the distance to which fluctuations in the laminar-flame position may extend. Statistical aspects of distributions of temperature and of species concentrations in the turbulent flame can be expressed entirely in terms of statistics of the laminar-flame position (through /), orientation (through V //1V / ), and structure (through k). The simplest example is... 

When disruptions of flame sheets become sufficiently extensive, there is appreciable nonreactive mixing of reactants and products at molecular scales. The extent of disruption increases as IJS decreases certainly if l/S becomes small compared with unity, then the turbulent flame no longer can be composed of wrinkled laminar flames. The true structures of turbulent flames in the limit of small values of l/S are unknown. 

Typical flame structures of HMX pellets are shown in Fig. 5-4 as a function of pressure. A thin luminous flame sheet stands some distance from the burning surface and a reddish flame is produced above this luminous flame sheet. The flame sheet approaches the burning surface as pressure increases 16. When the pressure is < 0.18 MPa, the luminous flame sheet is blown away from the burning surface, as shown in Fig. 5-4 (a). As pressure increases, the luminous flame sheet rapidly approaches the burning surface. However, it becomes very unstable above the burning surface and forms a wave-shaped flame sheet in the pressure range between 0.18 MPa and 0.3 MPa, as shown in Fig. 5-4(b). At further increased pressure, above 0.3 MPa, the luminous flame sheet becomes stable and one-dimensional just above the burning surface, as shown in Fig. 5-4(c). 

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