The turbulent flame speed

Although a laminar flame speed. S L is a physicochemical and chemical kinetic property of the unbumed gas mixture that can be assigned, a turbulent flame speed. S T is, in reality, a mass consumption rate per unit area divided by the unbumed gas mixture density. Thus,. S r must depend on the properties of the turbulent field in which it exists and the method by which the flame is stabilized. Of course, difficulty arises with this definition of. S T because the time-averaged turbulent flame is bushy (thick) and there is a large difference between the area on the unbumed gas side of the flame and that on the burned gas side. Nevertheless, many experimental data points are reported as. S T. 

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 

Many groups of experimental data have been evaluated by semiempirical correlations of the type 

The first expression here is very similar to the Damkohler result for A and B equal to 1. Since the turbulent exchange coefficient (eddy diffusivity) correlates well with IqU for tube flow and, indeed, /0 is essentially constant for the tube flow characteristically used for turbulent premixed flame studies, it follows that 

For large values of (U ISL), that is, high-intensity turbulence, the preceding expression reduces to that developed by Damkohler ST U.  

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In high speed dusted, premixed flows, where flames are stabili2ed in the recirculation 2ones, the turbulent flame speed grows without apparent limit, in approximate proportion to the speed of the unbumed gas flow. In the recirculation 2ones the intensity of the turbulence does not affect the turbulent flame speed (1). 

In the reaction 2one, an increase in the intensity of the turbulence is related to the turbulent flame speed. It has been proposed that flame-generated turbulence results from shear forces within the burning gas (1,28). The existence of flame-generated turbulence is not, however, universally accepted, and in unconfined flames direct measurements of velocity indicate that there is no flame-generated turbulence (1,2). 

The solid lines in Figure 4.5 represent extrapolations of experimental data to full-scale vessel bursts on the basis of dimensional arguments. Attendant overpressures were computed by the similarity solution for the gas dynamics generated by steady flames according to Kuhl et al. (1973). Overpressure effects in the environment were determined assuming acoustic decay. The dimensional arguments used to scale up the turbulent flame speed, based on an expression by Damkohler (1940), are, however, questionable. 

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. ... 

The question here is twofold first, how to prescribe a precise experimental procedure for defining the "turbulent flame speed" and second, is this quantity independent of the way used to initiate the flame This is the case for a laminar flame, and the flame propagation velocity Sl as well as the characteristic laminar flame thickness is 3 intrinsic quantity. 

In this simplified situation, can we really consider that the mean flame structure and thickness are steady, after certain delay and distance from initiation, and then the "turbulent flame speed" is a well-defined intrinsic quantity Indeed, with the present state of knowledge, there is no certainty in any answer to this question. Of course, it is hardly possible to build an experiment with nondecaying turbulence without external stirring. In deca)dng turbulence, the independence of the turbulent flame speed on the choice of reference values of progress variable has been verified in neither experiment nor theory. 

If the turbulent flame is ever proven to have asymptotically a constant flame brush thickness and constant speed in constant, i.e., nondecaying, turbulence, then the aforementioned turbulent flame speed and the flame brush thickness (5 give a well-defined sufficient characterization of the flame in its asymptotic behavior. However, it is not proven up to now that the studied experimental devices have been large enough to ensure that this asymptotic state can be reached. Besides, the correct definitions for the turbulent flame speed or flame brush thickness, as given above, are far from... 

It is worth noticing that the "turbulent burning rates" reported in Figure 7.1.2 have been defined similarly but not exactly as the "turbulent flame speed" mentioned in Section 7.1.2. The mixture has been ignited at the center of the bomb and the dependence of the pressure on time has been recorded. This has enabled to determine the derivative of the burned mixture volume. This derivative is ascribed to a spherical surface whose volume is simply equal to the volume of fully burned products, thus leading to an estimate of the turbulent combustion rate. 

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. 

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. 

In the range of 13% H2 25%, the flame speed showed a continuous steady increase with the H2 concentration. This regime is probably dominated by the pressure losses and gasdynamic "choking" at the orifice. A higher rate of energy release (i.e., flame power) accounts for the steady continuous increase of the turbulent flame speed with fuel (i.e., H2) concentration. Preliminary experiments in the 30 cm diameter tube obtained recently showed similar qualitative results. 

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