Andrei Lipatnikov

Turbulent flame speed and thickness: phenomenology, evaluation, and application in multi-dimensional simulations

Due to their fundamental importance for premixed combustion theory, turbulent flame speed and thickness were a subject of a large number of investigations for many decades. The paper reviews the research and extensively discusses the still unresolved issues in an attempt to define a foundation for evaluating different combustion models and defining a simple approach to multi-dimensional computations of premixed turbulent combustion. The approach consists of the use of an algebraic expression for the local turbulent flame speed in order to close the averaged balance equations describing the combustion process. Several models have been suggested utilizing this approach and the first laboratory and industrial applications of them have shown encouraging results. These successful applications motivate a thorough discussion and further development of the approach. Models utilizing the approach are reviewed and two issues are emphasized. First, certain models focus on the combustion regime characterized by a growing mean flame brush thickness, whereas other models are associated with fully developed flames of asymptotically stationary structure. Second, many different expressions for flame speed are invoked by different models. Thus, the behavior of the mean flame brush thickness and flame speed should be analyzed in order to provide a more solid phenomenological base for the approach and this is the main goal of the paper. Moreover, such an analysis also aims at selecting experimentally well-established trends and, thus, contributes to the development of a database necessary for testing various models of premixed turbulent combustion. Sources of errors in measurements of turbulent flame speeds are discussed and strong quantitative scatter of the published data is demonstrated. Nevertheless, turbulent flame speed, St, is shown to be a phenomenologically meaningful quantity, because various experimental investigations indicate the same qualitative trends in the behavior of St at moderate turbulence. The following trends: (1) an increase in St by rms turbulent velocity u′; (2) an increase in St and dSt/du′ by the laminar burning velocity; and (3) an increase in St by pressure despite the decrease in the laminar burning velocity, are well-established and can be used for testing various models of premixed turbulent combustion. Moreover, certain experimental results indicate a decrease in St by molecular transfer coefficients, other things being equal, and this trend may also be used for testing models. A number of various expressions for St, available in the literature, are tested against well-established trends, but only a few expressions are shown to be able to predict all the basic trends. An analysis of numerous experimental data obtained by various teams under different conditions indicates that a self-similar regime of premixed turbulent combustion, characterized by growing mean flame brush thickness, δt, and by the universal dimensionless spatial profile of the progress variable across the brush, occurs in most laboratory and industrial burners. The development of δt is mainly controlled by turbulent diffusion. Only certain models are able to describe this regime. From the group of models evaluated positively, the Flame Speed Closure (FSC) model is highlighted since: (1) it corresponds to the regime of growing mean flame brush thickness; and (2) it utilizes an experimentally well-supported expression for turbulent flame speed. Various numerical tests of the model, performed by numerous teams under substantially different conditions are summarized. Further development and validation of the model and it applications are reviewed. Finally, the paper shows that, after decades of long research, a simple, robust, conceptually straightforward, and extensively validated premixed combustion simulation tool is available for applications now.

Fundamentals of premixed turbulent combustion

General Knowledge on Reacting Gas Mixtures Basic Characteristics of Gas Mixtures Chemical Reactions in Flames Balance Equations Unperturbed Laminar Premixed Flame Flow in a Laminar Premixed Flame AEA Theory of Unperturbed Laminar Premixed Flame Laminar Flame Speed and Thickness Summary A Brief Introduction to Turbulence Characteristics of an Incompressible Turbulent Flow Theory of Homogeneous Isotropic Turbulence Reynolds-Averaged Navier-Stokes Approach to Numerical Simulations of Turbulent Flows Turbulent Diffusion Notes Phenomenology of Premixed Turbulent Combustion Mean Flame Brush Thickness Turbulent Flame Speed and Burning Velocity Mean Structure of a Premixed Turbulent Flame Summary Physical Mechanisms and Regimes of Premixed Turbulent Combustion Flame Wrinkling and Flamelet Regime Variations in Flamelet Structure Due to Turbulent Stretching Flame Instabilities Regimes of Premixed Turbulent Combustion Flame Propagation along Vortex Tubes Concluding Remarks Influence of Premixed Combustion on Turbulence Countergradient Scalar Transport in Turbulent Premixed Flames Turbulence in Premixed Flames Summary Modeling of Premixed Burning in Turbulent Flows Fractal Approach to Evaluating Turbulent Burning Velocity Zimont Model of Burning Velocity in Developing Turbulent Premixed Flames Modeling of Effects of Turbulence on Premixed Combustion in RANS Simulations Models of Molecular Transport Effects in Premixed Turbulent Flames Chemistry in RANS Simulations of Premixed Turbulent Combustion: Flamelet Library Large Eddy Simulation of Premixed Turbulent Combustion Introduction to Nonpremixed Combustion Laminar Diffusion Flames Turbulent Diffusion Flames Summary Partially Premixed Turbulent Flames Effects Addressed in RANS or LES Studies of Partially Premixed Turbulent Flames Effects Ignored in RANS or LES Studies of Partially Premixed Turbulent Flames Use of Presumed PDFs for Modeling Both Premixed and Diffusion Burning Modes Summary References Index

Finding the Markstein number using the measurements of expanding spherical laminar flames

Abstract Depedencies of the radii of expanding spherical flames on time elapsed after spark ignition have been measured using a high-speed Schlieren technique in a constant volume bomb. These dependencies are analyzed in order to find the Markstein numbers. Various methods of finding different Markstein numbers are considered. Phenomenological Markstein numbers with respect to the combustion products are obtained by means of the comparison between the measurements of the flame radii as a function of time and the results of the analytical integration of the linear relation between the flame speed and either flame stretch rate or flame curvature. The linear equation with respect to the flame stretch rate cannot approximate the experimental data corresponding to high flame curvature, while the linear equation with respect to the flame curvature approximates all the experimental data with a satisfactory accuracy. The correctness of this linear relation for highly curved flames and the effect of different data fitting schemes are briefly discussed.

A test of an engineering model of premixed turbulent combustion

The aim of this paper is to test a model of premixed turbulent combustion that joins a closed balance equation for progress variable and a submodel for the chemical timescale that characterizes the maximum possible increase in the local combustion rate under the influence of preferential diffusion into flamelets stretched by turbulent eddies. Since the effect of mixture properties is the main peculiarity of this model, measurements of turbulent combustion velocities, conducted for an extensive set of mixtures with substantially different properties, are chosen to test it. These measurements are simulated by combining the Bray-Moss thermochemistry, the model to be tested, the Bray parameterization of the stretch factor, and the k-∈ submodel of turbulence. Based on the concept of leading points, the dominating role played by critically curved flamelets in premixed turbulent combustion is emphasized. A method for computing a chemical timescale characterizing such flamelets is developed. This method is simple; it involves neither adjustable parameters nor empirical constants but the laminar burning velocity is considered to be an input parameter known from measurements. A comparison between the dependencies of combustion velocities on turbulent velocity, measured previously and computed here for a set of burning mixtures with substantially different properties, is presented. The model quantitatively predicts the dependence of combustion velocities not only on turbulent velocity but also on physicochemical properties of burning mixtures, including the strong effect of preferential diffusion. For moderate turbulence, the quantitative agreement between the measurements and computations has been obtained for various mixtures without any variations in the single remaining model constant unknown a priori.

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.

Lewis Number Effects in Premixed Turbulent Combustion and Highly Perturbed Laminar Flames

Abstract Various perturbed laminar flames are numerically simulated by reducing combustion chemistry to a single reaction. The following flame configurations are addressed: expanding spherical, cylindrical, and symmetrical planar flames; converging spherical flame; expanding cylindrical and symmetrical planar flames affected by external steady or time-dependent strain rate; steady strained cylindrical and symmetrical planar flames. The results (1) show that a simple linear relation between the local consumption velocity and flame stretch rate is valid only for weakly perturbed laminar flames; (2) highlight the importance of transient effects; and (3) show that, in the case of a small Lewis number, the highest local combustion rate is reached in the expanding spherical flame ignited by the hot pocket of the critical radius. This highest local combustion rate is successfully used to describe the extensive Karpovs experimental data base on turbulent burning velocities for mixtures characterized by substanti...

Turbulent burning velocity and speed of developing, curved, and strained flames

The problem of a physically meaningful definition of speed and burning velocity of a developing turbulentpremixed flame of a finite thickness is studied analytically and numerically in planar and spherical cases. Analytical studies are based on the well-documented self-similarity of the normalized profiles of the mean density across the turbulent flame brush. Numerical simulations have been performed with the flame speed closure model of turbulent combustion. The goals of the study are to develop methods for determining two reference surfaces: (1) a flame speed surface, that is, a surface the speed of which is controlled by the burning rate integrated across the brush but is not directly affected by the rate of flame thickness growth, and (2) a burning velocity surface, that is, a surface the area of which multiplied by the flame speed defined above characterizes the aforementioned burning rate. For planar flames, the former surface is defined and proven to be an isoscalar one. For spherical flames,expressions for determining both surfaces are derived, but these surfaces are different and they are not isoscalar ones. Simulations have shown that (1) these features are not well pronounced under typical conditions and (2) when investigating spherical flames, one may associate flame speed and burning velocity with the same isoscalar surface. A method for evaluating the unburned mixture velocity, which is needed to convert the observed speed of expanding spherical flames to the speed with respect to unburned mixture, is developed. The method is shown to be applicable to measurements of turbulent flame speeds in stagnation flows also. In all the cases studied, a reference value of the progress variable is found to be a roughly invariant (with respect to flame geometry and development) characteristic determining flame speed and burning velocity surfaces.

A direct numerical simulation study of vorticity transformation in weakly turbulent premixed flames

Database obtained earlier in 3D Direct Numerical Simulations (DNS) of statistically stationary, 1D, planar turbulent flames characterized by three different density ratios σ is processed in order to investigate vorticity transformation in premixed combustion under conditions of moderately weak turbulence (rms turbulent velocity and laminar flame speed are roughly equal to one another). In cases H and M characterized by σ = 7.53 and 5.0, respectively, anisotropic generation of vorticity within the flame brush is reported. In order to study physical mechanisms that control this phenomenon, various terms in vorticity and enstrophy balance equations are analyzed, with both mean terms and terms conditioned on a particular value c of the combustion progress variable being addressed. Results indicate an important role played by baroclinic torque and dilatation in transformation of average vorticity and enstrophy within both flamelets and flame brush. Besides these widely recognized physical mechanisms, two other effects are documented. First, viscous stresses redistribute enstrophy within flamelets, but play a minor role in the balance of the mean enstrophy Ω ¯ ¯ ¯ within turbulent flame brush. Second, negative correlation u ′ ⋅∇Ω ′ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ between fluctuations in velocity u and enstrophy gradient contributes substantially to an increase in the mean Ω ¯ ¯ ¯ within turbulent flame brush. This negative correlation is mainly controlled by the positive correlation between fluctuations in the enstrophy and dilatation and, therefore, dilatation fluctuations substantially reduce the damping effect of the mean dilatation on the vorticity and enstrophy fields. In case L characterized by σ = 2.5, these effects are weakly pronounced and Ω ¯ ¯ ¯ is reduced mainly due to viscosity. Under conditions of the present DNS, vortex stretching plays a minor role in the balance of vorticity and enstrophy within turbulent flame brush in all three cases.

Some issues of using Markstein number for modeling premixed turbulent combustion

Various Markstein numbers are considered and the relations between them are discussed using qualitative estimations and numerical simulations of expanding and converging spherical laminar flames. Measurements with expanding spherical flames permit finding the Markstein number characterizing flame speed with respect to products. To model turbulent combustion, the Markstein number characterizing the consumption velocity is required. It differs markedly from various Markstein numbers characterizing flame speeds. The effect of non-linear (with respect to the flame stretch rate) mechanisms on the consumption velocity is studied by analyzing the data of numerical simulations. The relations between the consumption velocity and flame curvature or stretch rate are non-linear and unambiguous for highly curved flames. For weakly curved flames, the non-linear effects are of importance too and prevent from correctly measuring a Markstein number as a physico-chemical parameter.

APPLICATION OF THE MARKSTEIN NUMBER CONCEPT TO CURVED TURBULENT FLAMES

Effects of large-scale stretching of premixed turbulent flames on flame speed are discussed and an extension of the classical Markstein number concept is proposed to parameterize flame speed modifications by the stretch rate. The concept is applied to fit various experimental data on the growth of the radius of expanding, statistically spherical, premixed, turbulent flames, obtained by different groups under different conditions. In all the cases studied, the suggested extension approximates the experimental data very well. It is shown also that this phenomenological approach may be utilized to determine the values of unperturbed turbulent flame speeds, , by processing the experimental data for spherical flames. The difference between the obtained values of unperturbed and the mean speeds of spherical flames, observed during expansion, may be as large as 200–300%. The strong influence of the perturbations discussed shows that such effects should be properly addressed when analyzing experimental data or invoking a presumed turbulent flame speed in simulations, for example, in large-eddy simulation based on the G-equation approach.