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,
S
t, is shown to be a phenomenologically meaningful quantity, because various experimental investigations indicate the same qualitative trends in the behavior of
S
t at moderate turbulence. The following trends: (1) an increase in
S
t by rms turbulent velocity
u′; (2) an increase in
S
t and d
S
t/d
u′ by the laminar burning velocity; and (3) an increase in
S
t 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
S
t by molecular transfer coefficients, other things being equal, and this trend may also be used for testing models. A number of various expressions for
S
t, 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,
δ
t, and by the universal dimensionless spatial profile of the progress variable across the brush, occurs in most laboratory and industrial burners. The development of
δ
t 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.
To explore the direction of inter-scale transfer of scalar variance between subgrid scale (SGS) and resolved scalar fields, direct numerical simulation data obtained earlier from two ...complex-chemistry lean hydrogen–air flames are analysed by applying Helmholtz–Hodge decomposition (HHD) to the simulated velocity fields. Computed results show backscatter of scalar (combustion progress variable $c$) variance, i.e. its transfer from SGS to resolved scales, even in a highly turbulent flame characterized by a unity-order Damköhler number and a ratio of Kolmogorov length scale to thermal laminar flame thickness as low as 0.05. Analysis of scalar fluxes associated with the solenoidal and potential velocity fields yielded by HHD shows that the documented backscatter stems primarily from the potential velocity perturbations generated due to dilatation in instantaneous local flames, with the backscatter being substantially promoted by a close alignment of the spatial gradient of mean scalar progress variable and the potential-velocity contribution to the local SGS scalar flux. The alignment is associated with the fact that combustion-induced thermal expansion increases local velocity in the direction of $\boldsymbol {\nabla } c$. These results call for development of SGS models capable of predicting backscatter of scalar variance in turbulent flames in large eddy simulations.
The second-order structure functions (SFs) of the velocity field, which characterize the velocity difference at two points, are widely used in research into non-reacting turbulent flows. In the ...present paper, the approach is extended in order to study the influence of combustion-induced thermal expansion on turbulent flow within a premixed flame brush. For this purpose, SFs conditioned to various combinations of mixture states at two different points (reactant–reactant, reactant–product, product–product, etc.) are introduced in the paper and a relevant exact transport equation is derived in the appendix. Subsequently, in order to demonstrate the capabilities of the newly developed approach for advancing the understanding of turbulent reacting flows, the conditioned SFs are extracted from three-dimensional (3-D) direct numerical simulation data obtained from two statistically 1-D planar, fully developed, weakly turbulent, premixed, single-step-chemistry flames characterized by significantly different (7.53 and 2.50) density ratios, with all other things being approximately equal. Obtained results show that the conditioned SFs differ significantly from standard mean SFs and convey a large amount of important information on various local phenomena that stem from the influence of combustion-induced thermal expansion on turbulent flow. In particular, the conditioned SFs not only (i) indicate a number of already known local phenomena discussed in the paper, but also (ii) reveal a less recognized phenomenon such as substantial influence of combustion-induced thermal expansion on turbulence in constant-density unburned reactants and even (iii) allow us to detect a new phenomenon such as the appearance of strong local velocity perturbations (shear layers) within flamelets. Moreover, SFs conditioned to heat-release zones indicate a highly anisotropic influence of combustion-induced thermal expansion on the evolution of small-scale two-point velocity differences within flamelets, with the effects being opposite (an increase or a decrease) for different components of the local velocity vector.
By analyzing the statistically stationary stage of propagation of a Huygens front in homogeneous, isotropic, constant-density turbulence, a length scale l0 is introduced to characterize the smallest ...wrinkles on the front surface in the case of a low constant speed u0 of the front when compared to the Kolmogorov velocity uK. The length scale is derived following a hypothesis of dynamical similarity that highlights a balance between (i) creation of a front area due to advection and (ii) destruction of the front area due to propagation. Consequently, the front speed is compared with the magnitude of the fluid velocity difference in two points separated by a distance smaller than the Kolmogorov length scale. Appropriateness of the smallest wrinkle scale is demonstrated by applying a fractal approach to evaluating the mean area of the instantaneous front surface. Since the scales of the smallest and larger wrinkles belong to different subranges (dissipation and inertial, respectively) of the Kolmogorov turbulence spectrum, the front is hypothesized to be a bifractal characterized by two different fractal dimensions in the two subranges. Both fractal dimensions are evaluated adapting the aforementioned hypothesis of dynamical similarity. Such a bifractal model yields a linear relation between the mean fluid consumption velocity, which is equal to the front speed u0 multiplied with a ratio of the mean area of the instantaneous front surface to the transverse projected area, and the rms turbulent velocity u′ even if a ratio of u0/u′ tends to zero.
Direct Numerical Simulation (DNS) data obtained by Dave and Chaudhuri (2020) from a lean, complex-chemistry, hydrogen-air flame associated with the thin-reaction-zone regime of premixed turbulent ...burning are analyzed (by adapting five alternative definitions of combustion progress variable c) in order to examine three different models that (i) are based on the flamelet paradigm and (ii) aim at evaluating mean concentrations of various species in applied CFD research into turbulent combustion. Mean mole fractions of all considered species and mean density are predicted if the laminar-flame profiles of species mole fractions and density, respectively, are directly averaged using a Probability Density Function (PDF) P(c). The best predictions are obtained by extracting P(c) from the DNS data and defining c based on hydrogen mass fraction. These predictions suggest that mean mole fractions of various species in a premixed turbulent flame can be evaluated at a post-processing stage of a CFD study by adopting P(c), obtained at the major stage of the simulations, to average a flamelet library. When applied in such a way, the flamelet paradigm is useful even for lean hydrogen-air flames and even at Karlovitz number as large as 13. If the same PDF is applied to average reaction rates from the same flamelet library, the mean rates of production/consumption of species n are poorly predicted, e.g. for radicals H, O, OH, HO2, and H2O2 if c is defined using hydrogen mass fraction. A hypothesis that conditioned rates 〈Wn|c〉 can be predicted using conditioned mole fractions 〈Xn|c〉, temperature 〈T|c〉, and density 〈ρ|c〉 is not supported either, e.g. for radicals O and OH. These differences between predictive capabilities of the first approach (directly averaging concentration profiles) and two other approaches (averaging reaction rates) are attributed to weakly (highly) non-linear dependencies of the concentrations (rates, respectively) on c.
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