A filtered tabulated chemistry model for LES of premixed combustion

A new modeling strategy called F-TACLES (Filtered Tabulated Chemistry for Large Eddy Simulation) is developed to introduce tabulated chemistry methods in Large Eddy Simulation (LES) of turbulent premixed combustion. The objective is to recover the correct laminar flame propagation speed of the filtered flame front when subgrid scale turbulence vanishes as LES should tend toward Direct Numerical Simulation (DNS). The filtered flame structure is mapped using 1-D filtered laminar premixed flames. Closure of the filtered progress variable and the energy balance equations are carefully addressed in a fully compressible formulation. The methodology is first applied to 1-D filtered laminar flames, showing the ability of the model to recover the laminar flame speed and the correct chemical structure when the flame wrinkling is completely resolved. The model is then extended to turbulent combustion regimes by including subgrid scale wrinkling effects in the flame front propagation. Finally, preliminary tests of LES in a 3-D turbulent premixed flame are performed.     

Transported PDF modeling of high-Reynolds-number premixed turbulent flames

The transported PDF approach, closed at the joint composition-enthalpy level, is applied to model premixed turbulent flames at a wide range of Reynolds numbers. The initial aim of the study is to establish the impact of closure approximations for the scalar dissipation rate upon the relationship between turbulence fluctuations and predicted turbulent burning velocities. The cases considered feature stoichiometric methane-air flames with the chemical source term extracted from a detailed chemistry simulation of the corresponding unstrained laminar flame. The transported PDF approach is subsequently combined with a systematically reduced C/H/O mechanism featuring 142 reactions and 14 solved and 15 steady-state species and applied to piloted premixed stoichiometric methane-air flames investigated experimentally by Chen et al. [Combust. Flame 107 (1996) 223-226]. The cases considered here feature Re=24,200 (flame F3) and 52,500 (flame F1) and Damköhler numbers approaching unity. The effects of variations in the time-scale ratio (2?C??8) and heat losses to the burner were investigated, along with the impact of an extended algebraic relationship for the scalar dissipation rate that accounts for small-scale properties. Comparisons with experimental data show that the modified Curl's model and the extended scalar dissipation-rate closure produce turbulent burning velocities in close agreement with measurements. The study further indicates that a closure at the joint scalar level combined with comprehensive chemistry has the potential to reproduce the detailed chemical structure of premixed turbulent flames. The importance of boundary conditions and comprehensive scalar statistics, including the scalar dissipation rate, is also emphasized by the study.     

Strained flamelets for turbulent premixed flames, I: Formulation and planar flame results

A strained flamelet model is proposed for turbulent premixed flames using scalar dissipation rate as a parameter. The scalar dissipation rate of reaction progress variable is a suitable quantity to describe the flamelet structure since it is governed by convection-diffusion-reaction balance and it is defined at every location in the flamelets, which are represented by laminar flames in reactant-to-product opposed flow configuration. The mean reaction rate is obtained by using the flamelets reaction rate and the joint pdf of the progress variable and its dissipation rate. The marginal pdf of the progress variable is presumed to be β-pdf and the pdf of the conditional dissipation rate is taken to be log-normal. The conditional mean dissipation rate is obtained from modelled mean dissipation rate. This reaction rate closure is assessed using RANS calculations of statistically planar flames in the corrugated flamelets and thin reaction zones regimes. The flame speeds calculated using this closure are close to the experimental data of Abdel-Gayed et al. (1987) [27] for flames in both the regimes. Comparisons with other reaction rate closures showed the benefits of the strained flamelets approach.     

Strained flamelets for turbulent premixed flames II: Laboratory flame results

The predictive ability of strained flamelets model for turbulent premixed flames is assessed using Reynolds Averaged Navier Stokes (RANS) calculations of laboratory flames covering a wide range of conditions. Reactant-to-product (RtP) opposed flow laminar flames parametrised using the scalar dissipation rate of reaction progress variable are used as strained flamelets. Two turbulent flames: a rod stabilised V-flame studied by Robin et al. [Combust. Flame 153 (2008) 288-315] and a set of pilot stabilised Bunsen flames studied by Chen et al. [Combust. Flame 107 (1996) 223-244] are calculated using a single set of model parameters. The V-flame corresponds to the corrugated flamelets regime. The strained flamelet model and an unstrained flamelet model yield similar predictions which are in good agreement with experimental measurements for this flame. On the other hand, for the Bunsen flames which are in the thin reaction zones regime, the unstrained flamelet model predicts a smaller flame brush compared to experiment. The predictions of the strained flamelets model allowing for fluid-dynamics stretch induced attenuation of the chemical reaction are in good agreement with the experimental data. This model predictions of major and minor species are also in good agreement with experimental data. The results demonstrate that the strained flamelets model using the scalar dissipation rate can be used across the combustion regimes.     

An a priori model for the effective species Lewis numbers in premixed turbulent flames

An a priori model for the effective species Lewis numbers in premixed turbulent flames is presented. This a priori   analysis is performed using data from a series of direct numerical simulations (DNS) of lean (?=0.4$?=0.4$) premixed turbulent hydrogen flames, with Karlovitz number ranging from 10 to 1562 (Aspden et al., 2011). The conditional mean profiles of various species mass fraction versus temperature are evaluated from the DNS and compared to unstretched laminar premixed flame profiles. The turbulent flame structure is found to be different from the laminar flame structure. However, the turbulent flame can still be mapped onto a laminar flame with an appropriate change in the Lewis numbers of the different species. A transition from “laminar” Lewis numbers to unity Lewis numbers as the Karlovitz number increases is clearly captured. A model for those effective Lewis numbers with respect to the turbulent Reynolds number is developed. This model is derived from a Reynolds-averaged Navier–Stokes (RANS) formulation of the reactive scalar and temperature balance equations. The dependency of the effective Lewis numbers on the Karlovitz number instead of the Reynolds number is discussed in this paper. Unfortunately, given that the ratio of the integral length to the laminar flame thickness is fixed throughout this series of DNS, a change in the Karlovitz number is equivalent to a change in the Reynolds number. Incorporating these effective Lewis numbers in simulations of turbulent flames would have several impacts. First, the associated laminar flame speed and laminar flame thickness vary by a factor of two through the range of obtained effective Lewis numbers. Second, the turbulent premixed combustion regime diagram changes because a unique pair of laminar flame speed and laminar flame thickness cannot be used, and a dependency on the effective Lewis numbers has to be introduced. Finally, a turbulent flame speed model that takes into account these effective Lewis numbers is proposed.     

Numerical analysis of reaction–diffusion effects on species mixing rates in turbulent premixed methane–air combustion

The scalar mixing time scale, a key quantity in many turbulent combustion models, is investigated for reactive scalars in premixed combustion. Direct numerical simulations (DNS) of three-dimensional, turbulent Bunsen flames with reduced methane–air chemistry have been analyzed in the thin reaction zones regime. Previous conclusions from single step chemistry DNS studies are confirmed regarding the role of dilatation and turbulence–chemistry interactions on the progress variable dissipation rate. Compared to the progress variable, the mixing rates of intermediate species is found to be several times greater. The variation of species mixing rates are explained with reference to the structure of one-dimensional premixed laminar flames. According to this analysis, mixing rates are governed by the strong gradients which are imposed by flamelet structures at high Damköhler numbers. This suggests a modeling approach to estimate the mixing rate of individual species which can be applied, for example, in transported probability density function simulations. Flame–turbulence interactions which modify the flamelet based representation are analyzed.     

Effect of dilatation on scalar dissipation in turbulent premixed flames

The scalar dissipation rate signifies the local mixing rate and thus plays a vital role in the modeling of reaction rate in turbulent flames. The local mixing rate is influenced by the turbulence, the chemical, and the molecular diffusion processes which are strongly coupled in turbulent premixed flames. Thus, a model for the mean scalar dissipation rate, and hence the mean reaction rate, should include the contributions of these processes. Earlier models for the scalar dissipation rate include only a turbulence time scale. In this study, we derive exact transport equations for the instantaneous and the mean scalar dissipation rates. Using these equations, a simple algebraic model for the mean scalar dissipation rate is obtained. This model includes a chemical as well as a turbulence time scale and its prediction compares well with direct numerical simulation results. Reynolds-averaged Navier-Stokes calculations of a test flame using the model obtained here show that the contribution of dilatation to local turbulent mixing rate is important to predict the propagation phenomenon.     

Experimental investigation of three-dimensional flame-front structure in premixed turbulent combustion—I: hydrocarbon/air bunsen flames

OH concentrations and three-dimensional gradients of the reaction progress variable have been measured in turbulent liquefied petroleum gas/air and compressed natural gas/air premixed flames stabilized on a Bunsen-type burner with a combined two-sheet Rayleigh scattering and planar LIF-OH imaging technique. The progress variable is observed to undergo a transition from lamella-like to non-flamelet front structure with increasing turbulence. This is consistent with the recently proposed change of the combustion regimes from complex-strain to turbulent flame front regime on a recently proposed premixed combustion diagram. The anisotropy of local flame-front orientation in three-dimensional space is explained by the forward propagation ability of the planar turbulent flame brush. Weighting functions have thus been derived for the isotropic pdf distributions of the in-plane and out-of-plane orientation angles to agree better with the experimental data. A linear scaling is found between the overall flame surface area and the turbulence intensity normalized by the laminar burning velocity. However, flames with excess backward-facing flame fronts do not comply with this linear relationship, showing enhanced flame surface folding. The thin-flame assumption breaks down when non-flamelet broadening effects become important, although the pdf’s of the progress variable are still bimodal-like. Non-unity Lewis-number combined curvature effects are evident for LPG/air flames of weak turbulence, in that the conditional mean scalar dissipation increases steadily from the unburnt to burnt side across the flame brush. A consistent correlation exists between the Favre-averaged scalar dissipation and progress variable variance. This implies that small-scale scalar dissipation of local flame-fronts is linked to large-scale scalar fluctuations. Sub- or super-flamelet OH concentration is found in lean LPG/air or CNG/air premixed flames, respectively, and occurs in line with a positive or negative correlation between OH concentrations and magnitudes of the progress variable gradient.     

Characterization of the effects of hydrogen addition in premixed methane/air flames

The use of hydrogenated fuels shows considerable promise for applications in gas turbines and internal combustion engines. In the present work, the effects of hydrogen addition in methane/air flames are investigated using both a laminar flame propagation facility and a high-pressure turbulent flame facility. The aim of this research is to contribute to the characterization of lean methane/hydrogen/air premixed turbulent flames at high pressures, by studying the flame front geometry, the flame surface density and the instantaneous flame front thermal thickness distributions. The experiments and analyses show that a small amount of hydrogen addition in turbulent premixed methane–air flames introduces changes in both instantaneous and average flame characteristics.     

LES of a premixed jet flame DNS using a strained flamelet model

Turbulent premixed flames in the thin and broken reaction zones regimes are difficult to model with Large Eddy Simulation (LES) because turbulence strongly perturbs subfilter scale flame structures. This study addresses the difficulty by proposing a strained flamelet model for LES of high Karlovitz number flames. The proposed model extends a previously developed premixed flamelet approach to account for turbulence’s perturbation of subfilter premixed flame structures. The model describes combustion processes by solving strained premixed flamelets, tabulating the results in terms of a progress variable and a hydrogen radical, and invoking a presumed PDF framework to account for subfilter physics. The model is validated using two dimensional laminar flame studies, and is then tested by performing an LES of a premixed slot-jet direct numerical simulation (DNS). In the premixed regime diagram this slot-jet is found at the edge of the broken reaction zones regime. Comparisons of the DNS, the strained flamelet model LES, and an unstrained flamelet model LES confirm that turbulence perturbs flame structure to leading order effect, and that the use of an unstrained flamelet LES model under-predicts flame height. It is shown that the strained flamelet model captures the physics characterizing interactions of mixing and chemistry in highly turbulent regimes.     

Validation of leading point concept in RANS simulations of highly turbulent lean syngas-air flames with well-pronounced diffusional-thermal effects

While significant increase in turbulent burning rate in lean premixed flames of hydrogen or hydrogen-containing fuel blends is well documented in various experiments and can be explained by highlighting local diffusional-thermal effects, capabilities of the vast majority of available models of turbulent combustion for predicting this increase have not yet been documented in numerical simulations. To fill this knowledge gap, a well-validated Turbulent Flame Closure (TFC) model of the influence of turbulence on premixed combustion, which, however, does not address the diffusional-thermal effects, is combined with the leading point concept, which highlights strongly perturbed leading flame kernels whose local structure and burning rate are significantly affected by the diffusional-thermal effects. More specifically, within the framework of the leading point concept, local consumption velocity is computed in extremely strained laminar flames by adopting detailed combustion chemistry and, subsequently, the computed velocity is used as an input parameter of the TFC model. The combined model is tested in RANS simulations of highly turbulent, lean syngas-air flames that were experimentally investigated at Georgia Tech. The tests are performed for four different values of the inlet rms turbulent velocities, different turbulence length scales, normal and elevated (up to 10 atm) pressures, various H₂/CO ratios ranging from 30/70 to 90/10, and various equivalence ratios ranging from 0.40 to 0.80. All in all, the performed 33 tests indicate that the studied combination of the leading point concept and the TFC model can predict well-pronounced diffusional-thermal effects in lean highly turbulent syngas-air flames, with these results being obtained using the same value of a single constant of the combined model in all cases. In particular, the model well predicts a significant increase in the bulk turbulent consumption velocity when increasing the H₂/CO ratio but retaining the same value of the laminar flame speed.     

Capabilities and limitations of multi-regime flamelet combustion models

Flamelet combustion models typically assume that burning occurs in either a fully premixed or a fully non-premixed mode. These assumptions tend to limit the applicability of the models to single-regime combustors. Efforts aimed at reducing this limitation have introduced multi-regime approaches that account for different types of mixing and chemistry interactions. In this study a multi-regime model is applied to two laminar n-heptane flames in an effort to characterize the capabilities and limitations of the approach. Both a 2-D laminar triple flame and a 2-D laminar counter-flow diffusion flame are numerically simulated using the multi-regime model. Data for comparison is generated by additionally simulating the flames using finite rate chemistry, a purely premixed flamelet model, and a purely non-premixed flamelet model. Simulations demonstrate that the multi-regime approach functions as desired, and tends to access flamelets from the appropriate regime under both non-premixed and premixed conditions. Some important differences between the flamelet solutions and finite rate solution are observed, however. These differences are caused by the finite rate solution deviating away from the assumed flamelet manifolds, rather than by inadequate regime predictions. In the analyses of these simulations, an emphasis is placed on understanding the formation of the pollutant species NO. It is shown that even when the local combustion regime is correctly predicted, small deviations from an assumed flamelet manifold can lead to changes in the NO production rate. The simulation results confirm that multi-regime flamelet models are applicable to a wide variety of reacting flows, but the results also help to characterize the limitations of these models.     

Modeling ignition and chemical structure of partially premixed turbulent flames using tabulated chemistry

Correctly reproducing the autoignition and the chemical composition of partially premixed turbulent flames is a challenge for numerical simulations of industrial applications such as diesel engines. A new model DF-PCM (diffusion flame presumed conditional moment) is proposed based on a coupling between the FPI (flame prolongation of ILDM) tabulation method and the PCM (presumed conditional moment) approach. Because the flamelets used to build the table are laminar diffusion flames, DF-PCM cannot be used for industrial applications like Diesel engines due to excessive CPU requirements. Therefore two new models called AI-PCM (autoignition presumed conditional moment) and ADF-PCM (approximated diffusion flames presumed conditional moment) are developed to approximate it. These models differ from DF-PCM because the flamelet libraries used for the table rely on PSR calculations. Comparisons between DF-PCM, AI-PCM, and ADF-PCM are performed for two fuels, n-heptane, representative of diesel fuels, and methane, which does not exhibit a “cool flame” ignition regime. These comparisons show that laminar diffusion flames can be approximated by flamelets based on PSR calculations in terms of autoignition delays and steady state profiles of the progress variable. Moreover, the evolution of the mean progress variable of DF-PCM can be correctly estimated by the approximated models. However, as discussed in this paper, errors are larger for CO and CO₂ mass fractions evolutions. Finally, an improvement to ADF-PCM, taking into account ignition delays, is proposed to better reproduce the ignition of very rich mixtures.     

Direct comparison of turbulent burning velocity and flame surface properties in turbulent premixed flames

Direct comparison of the turbulent burning velocity (obtained from flame speeds) to the flame perimeter ratio has been made in turbulent premixed flames propagating freely downward for propane/air mixtures at various equivalence ratios, with u′/S_L of ranging from 1.4 to 5.3. The turbulent flame speed ranged from 2.6 to about 7 times the laminar flame speed at high turbulence intensities, while the flame perimeter ratio ranges from 1.4 to 3.3. In the current freely propagating flames, the global flame curvature can lead to an enhancement of the flame speed by a factor of up to 3.5. This global flame curvature is attributable to the wall heat loss in the current burner configuration, and flame brush thickness has been used as a measure of the global flame curvature. For flames involving coupling of the globally curved flame geometry with flow divergence or any flow non-uniformity, correcting for this geometrical effect requires a careful consideration of the flame topology and flow field. The difference between the observed flame speed and the 2-D flame perimeter ratio, after correcting for the global flame curvature effect, is attributed to the fact that the flame wrinkles in three-dimensions are associated with a larger flame surface area than that determined from the flame perimeter ratio data. This also points to a need to better understand the 3-D geometrical effects including the global flame curvature and the local flame wrinkle structure in turbulent premixed flames. The observed turbulent flame speed data for the most part follow the flame speed models of Bray and Damkohler, wherein the flame surface area increase is modeled as a function of turbulence and thermochemical properties. The above results, taken together, indicate that the fundamental assumption that the turbulent flame speed depends primarily on the increased flame surface area is valid. This concept can be used to estimate the turbulent flame speed within reasonable accuracy provided that the 3-D flame effects associated with the global flame curvature and local flame wrinkle structure are considered.Keywords: Turbulent premixed flames, Flame speed, Flame surface, Burning velocity     

Effects of Lewis number on turbulent scalar transport and its modelling in turbulent premixed flames

The behaviour of the turbulent scalar flux in premixed flames has been studied using Direct Numerical Simulation (DNS) with emphasis on the effects of Lewis number in the context of Reynolds-averaged closure modelling. A database was obtained from DNS of three-dimensional freely propagating statistically planar turbulent premixed flames with simplified chemistry and a range of global Lewis numbers from 0.34 to 1.2. Under the same initial conditions of turbulence, flames with low Lewis numbers are found to exhibit counter-gradient transport, whereas flames with higher Lewis numbers tend to exhibit gradient transport. The Reynolds-averaged transport equation for the turbulent scalar flux is analysed in detail and the performance of existing models for the unclosed terms is assessed with respect to corresponding quantities extracted from DNS data. Based on this assessment, existing models which are able to address the effects of non-unity Lewis number on turbulent scalar flux transport are identified, and new or modified models are suggested wherever necessary. In this way, a complete set of closure models for the scalar flux transport equation is prescribed for use in Reynolds-Averaged Navier-Stokes simulations.     

Molecular transport effects on turbulent flame propagation and structure

Various experimental and DNS data show that premixed combustion is affected by the differences between the coefficients of molecular transport of fuel, oxidant, and heat not only at weak but also at moderate and high turbulence. In particular, turbulent flame speed increases with decreasing the Lewis number of the deficient reactant, the effect being very strong for lean hydrogen mixtures. Various concepts; flame instability, flame stretch, local extinction, leading point, that aim at describing the effects of molecular transport on turbulent flame propagation and structure are critically discussed and the results of relevant studies of perturbed laminar flames (unstable flames, flame balls, flames in vortex tubes) are reviewed. The crucial role played by extremely curved laminar flamelets in the propagation of moderately and highly turbulent flames is highlighted and the relevant physical mechanisms are discussed.     

Influence of evaporation on spray flamelet structures

The structure of laminar spray flames considerably differs from their gaseous counterpart. However, most often flamelet models employed in the simulation of turbulent spray combustion are based on laminar gas flame structures neglecting the influence of spray evaporation in the laminar spray flamelets. In this work, a combined theoretical and numerical study of the impact of spray evaporation on the structure of laminar spray flames is presented. Spray flamelet equations are derived, which explicitly take into account evaporation effects – the classical gas flamelet equations are recovered for non-evaporating conditions. Two new terms accounting for evaporation and for combined mixing and evaporation, respectively, are identified, and their relative importance is evaluated by means of numerical simulations of an axisymmetric laminar mono-disperse ethanol/air counterflow spray flame. The results show that the distribution of the spray evaporation rate plays a key role in the characterization of the spray flame structure. The new source terms overweigh the dissipation term of the gas phase in most situations even for non-evaporating species. Therefore, spray evaporation should always be considered. The relevance of the present formulation for turbulent spray modeling is evaluated and discussed, and a novel spray flamelet formulation is suggested.     

Basic considerations in the turbulent flame propagation in premixed gases

A general discussion is given of some fundamental problems of turbulent flame propagation in premixed gases. The following subjects are considered in greater detail: Stability of laminar flames in turbulent flow, shear wave-flame interaction, flame generated turbulence, influence of small scale turbulence on flame propagation and structure of turbulent flames at high Reynolds numbers. The principal object of this study is to describe the basic physical facts which have to be taken into consideration in the modeling of turbulent flames in gases without giving a detailed survey of all the research that has been carried out in the field.