Turbulent wrinkled flames

G. Searby and P. Clavin. Weakly turbulent wrinkled flames in premixed gases. Combustion Science and Technology, 46 167-193, 1986. 

P. Clavin, G. Joulin, Flamelet library for turbulent wrinkled flames. Lecture notes in engineering turbulent reactive flows, vol. 40, 1989, pp. 213-239... 

Thomas, A., The development of wrinkled turbulent premixed flames, Combustion and Flame, 65,291-312,1986. 

Localized extinction of the flame surface can readily occur in the turbulent combustion devices, where wrinkled flames interact with turbulent eddies and gas... 

In the so-called "wrinkled flame regime," the "turbulent flame speed" was expected to be controlled by a characteristic value of the turbulent fluctuations of velocity u rather than by chemistry and molecular diffusivities. Shchelkin [2] was the first to propose the law St/Sl= (1 + A u /Si) ), where A is a universal constant and Sl the laminar flame velocity of propagation. For the other limiting regime, called "distributed combustion," Summerfield [4] inferred that if the turbulent diffusivity simply replaces the molecular one, then the turbulent flame speed is proportional to the laminar flame speed but multiplied by the square root of the turbulence Reynolds number Re. ... 

In this study, the flame can be classified as a wrinkled flame throughout most of the flow field. The main findings of [25] are related to both (1) the question of how the turbulent velocity field is affected by the chemical reaction and induced expansion phenomena and (2) the measurements of mean flame surface density and the... 

This recent attempt differs from the previous classification where the wrinkled flamelet regime has been considered up to rj = (5l- Chen and Bilger have proposed to tentatively classify the different turbulent premixed flame structures they observed among four different regimes ... 

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. 

The flames themselves can alter the turbulence. In simple open Bunsen flames whose tube Reynolds number indicates that the flow is in the turbulent regime, some results have shown that the temperature effects on the viscosity are such that the resulting flame structure is completely laminar. Similarly, for a completely laminar flow in which a simple wire is oscillated near the flame surface, a wrinkled flame can be obtained (Fig. 4.41). Certainly, this example is relevant to <5L < /k that is, a wrinkled flame. Nevertheless, most open flames... 

In his attempts to analyze the early experimental data, Damkohler [55] considered that large-scale, low-intensity turbulence simply distorts the laminar flame while the transport properties remain the same thus, the laminar flame structure would not be affected. Essentially, his concept covered the range of the wrinkled and severely wrinkled flame cases defined earlier. Whereas a planar laminar flame would appear as a simple Bunsen cone, that cone is distorted by turbulence as shown in Fig. 4.43. It is apparent then, that the area of the laminar flame will increase due to a turbulent field. Thus, Damkohler [55] proposed for large-scale, small-intensity turbulence that... 

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-... 

The more recent view, adopted by Summerfield and his coworkers, is that the turbulent flame brush is a thickened or extended reaction zone (70). The evidence for this idea, like that for the wrinkled flame, must still be considered inconclusive. 

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]. 

The formulation of Section 9.5.1 has served to remove the chemistry from the field equations, replacing it by suitable jump conditions across the reaction sheet. The expansion for small S/l, subsequently serves to separate the problem further into near-field and far-field problems. The domains of the near-field problems extend over a characteristic distance of order S on each side of the reaction sheet. The domains of the far-field problems extend upstream and downstream from those of the near-field problems over characteristic distances of orders from to /. Thus the near-field problems pertain to the entire wrinkled flame, and the far-field problems pertain to the regions of hydrodynamic adjustment on each side of the flame in essentially constant-density turbulent flow. Either matched asymptotic expansions or multiple-scale techniques are employed to connect the near-field and far-field problems. The near-field analysis has been completed for a one-reactant system with allowance made for a constant Lewis number differing from unity (by an amount of order l/P) for ideal gases with constant specific heats and constant thermal conductivities and coefficients of viscosity [122], [124], [125] the results have been extended to ideal gases with constant specific heats and constant Lewis and Prandtl numbers but thermal conductivities that vary with temperature [126]. The far-field analysis has been... 

FIGURE 10.8. Schematic illustration of the relationship between the turbulent flame speed and the wrinkled flame area for a premixed turbulent flame consisting of a wrinkled laminar flame. 

If the wrinkled flame does not tend to fold back on itself—that is, if the flame sheet nowhere becomes parallel to the vector e—then the location of the reaction sheet everywhere may be described by putting G(x, t) = X — F(y, z, t), where F is defined at the beginning of Section 9.5.1, and x is a coordinate in the propagation direction e of the turbulent flame. With this... 

This formula indicates that modifications of the wrinkled-flame structure by the turbulence tend to decrease Vj if Le > 1 and to increase it for cellularly stable flames with Le < 1. It seems likely [125] that through changes in factors like and 12 of equations (57) and (58) with Rq, F(Rq, ft Le J will decrease in magnitude with increasing Rq and typically produce only small effects on for flames of practical interest. No experimental tests of equation (73) have been made. 

P. Clavin and F. A. Williams, Effects of Lewis Number on Propagation of Wrinkled Flames in Turbulent Flow, in Combustion in Reactive Systems, vol. 76 of Progress in Astronautics and Aeronautics, J. R. Bowen, N. Manson, A. K. Oppenheim, and R. I. Soloukhin, eds.. New York American Institute of Aeronautics and Astronautics, 1981, 403-411. 

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