Wrinkled flame front

The ignition delay is followed by a period of rapid growth. As the flame grows in diameter, the surface begins to get stretched and distorted by turbulence, and becomes what is generally referred to as a wrinkled flame front. 

Consider initially the hydrodynamic instability—that is, the one due to the flow—first described by Darrieus [52], Landau [53], and Markstein [54], If no wrinkle occurs in a laminar flame, the flame speed SL is equal to the upstream unbumed gas velocity U0. But if a minor wrinkle occurs in a laminar flame, the approach flow streamlines will either diverge or converge as shown in Fig. 4.45. Considering the two middle streamlines, one notes that, because of the curvature due to the wrinkle, the normal component of the velocity, with respect to the flame, is less than U(). Thus, the streamlines diverge as they enter the wrinkled flame front. Since there must be continuity of mass between... 

The effect of the finite thickness of the turbulent flame was introduced in theories [18, 19]. In [18], the set of governing gas dynamic equations is supplemented by the empirical dependency of flame thickness on the distance to the ignition source, obtained by means of statistical processing of the instantaneous position of a thin wrinkled flame front in model experiments. Semi-empirical the-... 

To analy2e premixed turbulent flames theoretically, two processes should be considered (/) the effects of combustion on the turbulence, and (2) the effects of turbulence on the average chemical reaction rates. In a turbulent flame, the peak time-averaged reaction rate can be orders of magnitude smaller than the corresponding rates in a laminar flame. The reason for this is the existence of turbulence-induced fluctuations in composition, temperature, density, and heat release rate within the flame, which are caused by large eddy stmctures and wrinkled laminar flame fronts. 

What are the mechanisms by which slow, laminar combustion can be transformed into an intense, blast-generating process This transformation is most strongly influenced by turbulence, and secondarily by combustion instabilities. A laminar-flame front propagating into a turbulent mixture is strongly affected by the turbulence. Low-intensity turbulence will only wrinkle the flame front and enlarge its surface area. With increasing turbulence intensity, the flame front loses its more-or-less smooth, laminar character and breaks up into a combustion zone. In an intensely turbulent mixture, combustion takes place in an extended zone in which... 

At places where the front is concave toward the unburnt gas, the heat flux is locally convergent. The local flame temperature increases and the local propagation velocity also increases, see the red arrows in Figure 5.1.5. The converse holds for portions of the front that are convex. The effect of thermal diffusion is to stabilize a wrinkled flame. 

Under low-frequency excitation, the flame front is wrinkled by velocity modulations (Fig. 5.2.5). The number of undulations is directly linked to frequency. This is true as far as the frequency remains low (in this experiment, between 30 and 400 Hz). The flame deformation is created by hydrodynamic perturbations initiated at the base of the flame and convected along the front. When the velocity modulation amplitude is low, the undulations are sinusoidal and weakly damped as they proceed to the top of the flame. When the modulation amplitude is augmented, a toroidal vortex is generated at the burner outlet and the flame front rolls over the vortex near the burner base. Consumption is fast enough to suppress further winding by the structure as it is convected away from the outlet. This yields a cusp formed toward burnt gases. This process requires some duration and it is obtained when the flame extends over a sufficient axial distance. If the acoustic modulation level remain low (typically v /v < 20%),... 

Premixed turbulent combustion regime diagram proposed by Chen and Bilger. Two intermediate regimes are delineated between distributed flame front and wrinkled laminar flamelets. (Reprinted from Chen, Y.C. and Bilger, R., Combust. Flame, 131, 400, 2002. With permission. Figure 9, p. 411, copyright Elsevier editions.)... 

In an experimental effort, measurements of turbulent flame speeds in gaseous reactants in a classic cylindrical Taylor-Couette burner were made by Ralph Aldredge at the University of California at Davis (Chapter 15). The study established sensitivity of the turbulent flame speed to turbulence intensity, and provided some influence of flame front wrinkling on flame propagation. 

In turbulent reacting cases the Dynamically Thickened Flame model [311 321 355 361] is used, where a thickening factor F is introduced to thicken the flame front and the efficiency function developed by Colin et al. [269] is used to account for subgrid scale wrinkling. 

Obstacle density is classified as low, medium, and hig as shown in Table 3.5, as a function of the blockage ratio and pitch. The blockage ratio is defined as the ratio of the area blocked by obstacles to the total cross-section area. The pitch is defined as the distance between successive obstacles or obstacle rows. There is normally an optimum value for the pitch when the pitch is too large, the wrinkles in the flame front wiU burn out and the flame front will slow down before the next obstacle is reached. When the pitch is too small, the gas pockets between successive obstacles are relatively unaffected by the flow (Baker et al., 1994). 

Recently the coupling between diffusion and hydrodynamics has been properly taken into account for describing the wrinkled flame structure in an anlytical work by Clavin Williams (1982). The as3miptotic expansion 3 is used together with a multiscale method based on the assumption e=d/A smaller than unity. The corresponding result was used by Pelce Clavin (1982) to study the stability limits of planar fronts propagating downward. The results can be summarized as follows ... 

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