Mean Flame Brush Research Articles

Simultaneous 2-D Imaging Measurements of Reaction Progress Variable and OH Radical Concentration in Turbulent Premixed Flames: Experimental Methods and Flame Brush Structure

Experimental methods are detailed for comprehensive further investigation of the turbulent premixed flames of natural-gas/air mixtures stabilized on a Bunsen-type burner already studied by joint imaging of OH and velocity (Franker et.al, 1999). Simultaneous two-dimensional measurements of reaction progress variable and OH mole fraction are made from planar imaging of Rayleigh scattering and laser-induced fluorescence of OH. Image in-plane and out-of-plane spatial resolution of the order of 100 μm has been achieved. Care is taken to ensure that the instantaneous flame-front structure can be adequately resolved, and the measured scalar structure in laminar flames agrees well with flame calculations with a C-3 mechanism. Mean velocity and turbulence intensity profiles are presented for the non-reacting flows together with measurements of longitudinal and transverse correlation functions, their associated length scales, and the dissipation rate of the turbulence kinetic energy. In this paper, we report the mean structure of the turbulent flame brush in terms of Reynolds- and Favre-averaged profiles of the reaction progress variable and its standard deviation, and selected probability density functions. The results are compared with those derived from the OH images using the thin flamelet assumption. The mean and standard deviation of OH mole fraction are also presented. Preliminary conclusions are drawn about the relationship of the mean flame brush structure to the turbulence and the admixture of co-flowing air. The validity of the thin-flamelet assumption appears to be questionable for the lean flames investigated. Results for the structure of the instantaneous flame fronts are reported in a companion paper (Chen and Bilger, 2001).

Developing Premixed Turbulent Flames: Part II. Pressure-Driven Transport and Turbulent Diffusion

The effects of premixed turbulent flame development on the transition from gradient to counter-gradient transport are modeled phenomenologically. By analyzing the balance equation for the second order velocity-progress variable correlation, the terms controlling the transition are singled out. These terms are evaluated for a self-similar regime of premixed turbulent flame development discussed, in detail, in the first part of the paper (Lipatnikov and Chomiak, 2000c). The regime is characterized by the fact that the progress variable profiles, measured by various teams under a wide range of conditions along the normal to the mean flame brush, collapse to a universal curve when presenting the profiles in the dimensionless form by using the mean flame brush thickness which depends on the flame development time. Based on these observation, analytical estimates of the mean pressure gradient in free, one-dimensional, statistically planar and spherical, turbulent flames are obtained. The results indicate a strong time-dependence of the pressure gradient and, hence, of the transition studied. The transition curves are computed for different flames and are drawn in the plane of the Dam-kohler number and flame development time. The predictions agree reasonably well with the available experimental and DNS data. An analysis of the behavior of various terms in the progress variable balance equation, performed for self-similar premixed turbulent flames, has shown that the normalized spatial profile of the progress variable across the flame brush is mainly controlled by the mean rate of product creation. Thus, detailed modeling of the transport term pu'Jc" appears to be of minor importance for many applications, especially as the development of the mean flame brush thickness is mainly controlled by classical turbulent diffusion.

Transient and Geometrical Effects in Expanding Turbulent Flames

To study turbulent combustion, experiments with expanding, statistically spherical flames ignited by a spark are widely used. The goal of the work is to show that certain trends in the behavior of turbulent flame speed 5, observed in such experiments, are substantially affected by the curvature of the mean flame brush and by the ignition conditions. For this purpose, simulations of expanding, spherical, premised flames were performed using the k - ϵ turbulence model and the Turbulent Flame Speed Closure of the balance equation for a progress variable. Three major trends have been observed in the simulations. First, the analysis of various physical mechanisms controlling the increase of St, has shown that the time-dependence of the mean heat release rate, invoked by the model, is of substantial importance for small kernels only. For moderately large flames, the development of St, is mainly controlled by the relaxation of the reduction effect of the mean flame curvature on the flame speed. The second manifestation of the mean curvature mechanism is the opposite effects of the turbulent length scale L on the speed of asymptotically stationary, planar flames and of moderately large, statistically spherical flames. In the spherical case, a stronger reduction of the flame speed of small kernels is observed in turbulence with a larger scale. As the kernel grows, the reduction effect relaxes and the dependence of St, on L reverses. Third, when the ignition energy is close to the critical value igniting the turbulent mixture, a regime of kernel expansion characterized by substantially reduced flame speed and burning velocity can occur even in relatively large, statistically spherical turbulent flames. The physical cause of this memory effect consists in the formation of a highly dispersed kernel followed by slow after-burning, When the spark energy is kept constant, the increase in turbulent velocity u′ increases the critical ignition energy and the transformation to the aforementioned regime occurs. This mechanism can contribute to the decrease of St, with u′, observed in many experiments. Finally, the suppression of counter-gradient diffusion in spherical flames is discussed at the end of the paper.

Dependence of heat release on the progress variable in premixed turbulent combustion

An analysis of various experimental data obtained for different turbulent flames under a wide range of conditions shows that spatial profiles of the progress variable across the flame brush, presented in the dimensionless form by using the flame brush thickness, are described by a universal curve or, in other words, are self-similar. This observation offers the opportunity to suggest the following simple test for any model of premixed turbulent combustion: It should be able to predict such universal profiles for the simplest, one-dimensional planar flames propagating in frozen turbulence, as a minimum. Various models of premixed turbulent combustion, utilizing the balance equation for the mean progress variable, are tested in this simple case. For these purposes, balance equations for the mean progress variable, resulting from different models, are written in the same dimensionless general form by using model-dependent time and length scales and a gradient-diffusion closure of the transport term. The results of numerical computations show that a proper definition of the mean flame brush thickness δt is of importance when performing such tests. When the evaluation of δt in the numerical simulations corresponds to the measurements, the dependencies like Q ∼ c ¯ ( 1 − c ¯ ) or Q ∼ p ¯ c ˜ ( 1 − c ˜ ) , invoked by many submodels of the mean heat release rate Q in the Favre-averaged balance equation, cannot lead to the aforementioned universal profile, whereas the dependence of Q ∼ c ˜ ( 1 − c ˜ ) , not commonly used in the simulations, can do so. The gradient-type, Q ∼ | ∇ c ˜ | , and the flame surface density closures can also lead to the universal profiles discussed. The ability of certain numerical models invoking the gradient closure of the transport term to predict the measured dimensionless spatial profiles of the progress variable reasonably well shows that modeling this transport term is of secondary importance for many applications.

Two-dimensional numerical modeling of a turbulent premixed flame stabilized in a stagnation flow

A numerical study of a turbulent premixed flame stabilized by a stagnation flow is presented. Such a geometry has been chosen because it features most of the phenomena that are encountered in systems of practical interest such as the interaction between the flame and a solid wall and the presence of important streamlines curvature. This study is based on a full second-order modeling, namely a Bray-Moss-Libby combustion model associated with a low-Reynolds number Reynolds-stress turbulence model. With respect to the mean flow properties, it is shown that, along the symmetry axis and in a large part of the mean flame brush, the turbulent diffusion term plays a minor role in the balance of the mean progress variable equation except in a thin zone. Such a finding is of importance because it confirms the results of recent studies of the literature that are based on an asymptotic analysis of the flow structure on the symmetry axis. Thus, the present results give a clear proof of what was so far an hypothesis. Concerning the balance of the turbulent fluxes of mass, the dominant role played by the correlation with the mean pressure gradient is clearly put into evidence. Although the agreement with experimental results is fair enough to recommend the use of such a modeling for systems of practical interest, some improvements have to be brought in the modeling of the correlations between the pressure fluctuations and the gradients of both the velocity and the progress variable fluctuations. Indeed, such quantities are expected to play a leading role for such a flow geometry especially in situations where the mean flame brush is close to the solid wall.

A time-accurate scheme for the calculations of unsteady reactive flows at low Mach number

The artificial compressibility method is extended to the case of unsteady turbulent reacting flows at low Mach number. The resulting scheme is applied to the calculation of a propagating one-dimensional (1D) planar turbulent flame with a realistic heat release parameter. An eddy break-up-like approach, with a conventional gradient expression for the turbulent fluxes, is retained to model this reacting turbulent flow. A quenched form of the mean reaction rate is used to ensure the existence of a steady regime of propagation, for which the present results are compared with those obtained by a steady analysis of the mean flame brush structure, with excellent agreement. A sensitivity analysis of the convergence rate to the values of the artificial compressibility factor and the pseudo-time is carried out

A time‐accurate scheme for the calculations of unsteady reactive flows at low Mach number

The artificial compressibility method is extended to the case of unsteady turbulent reacting flows at low Mach number. The resulting scheme is applied to the calculation of a propagating one-dimensional (1D) planar turbulent flame with a realistic heat release parameter. An eddy break-up-like approach, with a conventional gradient expression for the turbulent fluxes, is retained to model this reacting turbulent flow. A quenched form of the mean reaction rate is used to ensure the existence of a steady regime of propagation, for which the present results are compared with those obtained by a steady analysis of the mean flame brush structure, with excellent agreement. A sensitivity analysis of the convergence rate to the values of the artificial compressibility factor and the pseudo-time is carried out. It is shown that a reduced artificial compressibility factor of 5–10, combined with a pseudo-Courant number of ≈1000, represents a good compromise to optimize the convergence rate. Copyright © 1999 John Wiley & Sons, Ltd.

Introduction of Dilution in the BML Model: Application to a Stagnating Turbulent Flame

An extension of the BML model to the case of Combustion ol lean mixtures with variable equivalence ratio is presented in this paper. The Dilution of both burnt products are fresh reactants by the surrounding air is taken into account by introducing the mixture fraction f in addition to the progress variable c. Statistical analysis of the reactive flow is achieved by using a joint pdf of c and following calculation of mean quantities. Extinction of individual flamelets due to local dilution of fresh recants is also considered. The Influence of dilution, i.e. variable production rate is described. application of this modified model to the case of a stagnating turbulent flame stabilized close to a solid wall shows that the mean flame brush is predicated to be detached from the burner, in agreement with avaliable experimental observartions Qualitative and quantitative modifications of the mean structure of the flame due to dilution are also investigated.