Turbulent flame speeds

Turbulent flame speed, unlike laminar flame speed, is dependent on the flow field and on both the mean and turbulence characteristics of the flow, which can in turn depend on the experimental configuration. Nonstationary spherical turbulent flames, generated through a grid, have flame speeds of the order of or less than the laminar flame speed. This turbulent flame speed tends to increase proportionally to the intensity of the turbulence. 

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 knowledge of turbulent premixed flames has improved from this very simple level by following the progress made in experimental and numerical techniques as well as theoretical methods. Much employed in early research, the laboratory Bunsen burners are characterized by relatively low turbulence levels with flow properties that are not constant everywhere in the flame. To alleviate these restrictions, Karpov et al. [5] pioneered as early as in 1959 the studies of turbulent premixed flames initiated by a spark in a more intense turbulence, produced in a fan-stirred quasi-spherical vessel. Other experiments carried out among others by Talantov and his coworkers allowed to determine the so-called turbulent flame speed in a channel of square cross-section with significant levels of turbulence [6]. 

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. 

Now it is important to stress that, whereas the laminar flame speed is a unique thermochemical property of a fuel-oxidizer mixture ratio, a turbulent flame speed is a function not only of the fuel-oxidizer mixture ratio, but also of the flow characteristics and experimental configuration. Thus, one encounters great difficulty in correlating the experimental data of various investigators. In a sense, there is no flame speed in a turbulent stream. Essentially, as a flow field is made turbulent for a given experimental configuration, the mass consumption rate (and hence the rate of energy release) of the fuel-oxidizer mixture increases. Therefore, some researchers have found it convenient to define a turbulent flame speed, S T as the mean mass flux per unit area (in a... 

In open flames, the variation of ST with composition is generally much the same as for SL, and, S T has a well-defined maximum close to stoichiometric. Thus, many report turbulent flame speed data as the ratio of ST/SL. 

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. 

The values of laminar flame speeds for hydrocarbon fuels in air are rarely greater than 45cm/s. Hydrogen is unique in its flame velocity, which approaches 240cm/s. If one could attribute a turbulent flame speed to hydrocarbon mixtures, it would be at most a few hundred centimeters per second. However, in many practical devices, such as ramjet and turbojet combustors in which high volumetric heat release rates are necessary, the flow velocities of the fuel-air mixture are of the order of 50m/s. Furthermore, for such velocities, the boundary layers are too thin in comparison to the quenching distance for stabilization to occur by the same means as that obtained in Bunsen burners. Thus, some other means for stabilization is necessary. In practice, stabilization... 

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 contrast, most models of turbulent flame speeds assume homogeneous isotropic turbulence with no mean flow or strain. This leads to substantial differences between model predictions and experimental observations [4]. 

In Fig. 15.4, the measured turbulent flame speeds, normalized with mixture-specific laminar flame velocities obtained recently by Vagelopoulos et al. [14], are compared with experimental and theoretical results obtained in earlier studies. Also shown in the figure are the measurements made by Abdel-Gayed et al. [3] for methane-air mixtures with = 0.9 and = 1 a correlation of measured turbulent flame speeds with intensity obtained by Cheng and Shepherd [1] for rod-stabilized v-flames, tube-stabilized conical flames, and stagnation-flow stabilized flames, Ut/Ul = l + i.2 u /U ) a correlation of measured turbulent flame... 

Figure 15.4 A comparison of turbulent flame speeds measured in the TC apparatus with theoretical predictions and measurements by earlier investigators using other types of burners 1 — TC results, 2 — Abdel-Gayed et al. [3], 3 — Chang and Shepherd [1], 4 — Bedat and Cheng [2], 5 — Anand and Pope [15], and 6 — Yakhot [16]... 

Ronney, P. D., and V. Yakhot. 1992. Flame broadening effects on premixed turbulent flame speed. Combustion Science Technology 86 31-43. 

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