LES/PDF Modeling of Turbulent Premixed Flames with Locally Enhanced Mixing by Reaction

Large-eddy simulations (LES) combined with the transported probability density function (PDF) method are carried out for two turbulent piloted premixed methane-air jet flames (flame F1 and flame F3) to assess the capability of LES/PDF for turbulent premixed combustion. The conventionally used model for the sub-filter scale mixing time-scale (or the mixing frequency) fails to capture the premixed flames correctly. This failure is expected to be caused by the lack of the sub-filter scale premixed flame propagation property in the sub-filter scale mixing process when the local flame front is under-resolved. It leads to slower turbulent premixed flame propagation and wider flame front. A new model for specifying the sub-filter scale mixing frequency is developed to account for the effect of sub-filter scale chemical reaction on mixing, based on past development of models for the sub-filter scale scalar dissipation rate in premixed combustion. The new model is assessed in the two turbulent premixed jet flames F1 and F3. Parametric studies are performed to examine the new model and its sensitivity when combined with the different mixing models. Significantly improved performance of the new mixing frequency model is observed to capture the premixed flame propagation reasonably, when compared with the conventional model. The sensitivity of the flame predictions is found be relatively weak to the different mixing models in conjunction with the new mixing frequency model.     

A Non-Adiabatic Flamelet Progress�CVariable Approach for LES of Turbulent Premixed Flames

A progress variable/flame surface density/probability density function method has been employed for a Large Eddy Simulation of a CH₄/Air turbulent premixed bluff body flame. In particular, both mean and variance of the progress variable are transported and subgrid spatially filtered gradient contributes to model the flame surface density (that introduces the effect of the subgrid flame reaction zone) and to presume a probability density function (that introduces the effect of subgrid fluctuations on chemistry). Chemistry is preliminarly tabulated in terms of laminar premixed flames and enthalpy is included as a new coordinate in their tabulation to take into account heat losses in the flowfield. Then, the PDF is used to build a turbulent flamelet library. The filtered mass, momentum, enthalpy and scalar equations mentioned above are integrated by an explicit scheme using finite differences, 2nd?Corder accurate in space and third order in time, over a cylindrical non-uniform grid using a staggered mesh. The bluff-body geometry is modelled by using the Immersed Boundary Method. The numerical predictions are compared with the available experimental data.     

Finite Rate Chemistry Effects in Highly Sheared Turbulent Premixed Flames

Detailed scalar structure measurements of highly sheared turbulent premixed flames stabilized on the piloted premixed jet burner (PPJB) are reported together with corresponding numerical calculations using a particle based probability density function (PDF) method. The PPJB is capable of stabilizing highly turbulent premixed jet flames through the use of a small stoichiometric pilot that ensures initial ignition of the jet and a large shielding coflow of hot combustion products. Four lean premixed methane-air flames with a constant jet equivalence ratio are studied over a wide range of jet velocities. The scalar structure of the flames are examined through high resolution imaging of temperature and OH mole fraction, whilst the reaction rate structure is examined using simultaneous imaging of temperature and mole fractions of OH and CH₂O. Measurements of temperature and mole fractions of CO and OH using the Raman–Rayleigh–LIF-crossed plane OH technique are used to examine the flame thickening and flame reaction rates. It is found that as the shear rates increase, finite-rate chemistry effects manifest through a gradual decrease in reactedness, rather than the abrupt localized extinction observed in non-premixed flames when approaching blow-off. This gradual decrease in reactedness is accompanied by a broadening in the reaction zone which is consistent with the view that turbulence structures become embedded within the instantaneous flame front. Numerical predictions using a particle-based PDF model are shown to be able to predict the measured flames with significant finite-rate chemistry effects, albeit with the use of a modified mixing frequency.     

A Lagrangian-based flame index for the transported probability density function method

We propose a new flame index for the transported probability density function(PDF) method. The flame index uses mixing flux projections of Lagrangian particles on mixture fraction and progress variable directions as the metrics to identify the combustion mode, with the Burke-Schumann solution as a reference. A priori validation of the flame index is conducted with a series of constructed turbulent partially premixed reactors. It indicates that the proposed flame index is able to identify the combustion mode based on the subgrid mixing information. The flame index is then applied the large eddy simulation/PDF datasets of turbulent partially premixed jet flames. Results show that the flame index separate different combustion modes and extinction correctly. The proposed flame index provides a promising tool to analyze and model the partially premixed flames adaptively.     

Flow Physics of a Bluff-Body Swirl Stabilized Flame and their Prediction by Means of a Joint Eulerian Stochastic Field and Tabulated Chemistry Approach

In the frame of this work a transported joint scalar probability density function (PDF) method is combined with the flamelet generated manifolds (FGM) tabulated chemistry approach for large eddy simulation (LES) modeling of a three-dimensional turbulent premixed swirl burner. This strategy accounts for the turbulence-chemistry interaction at reasonable computational costs. At the same time, it allows the usage of detailed chemistry mechanisms for the creation of the chemical database. The simulation results obtained are comparatively assessed along with complementary measurements. Furthermore, transient and time-averaged data are used to provide insight into the flow physics of the bluff-body swirl stabilized flame considered. The sensitivity of the results to different modeling approaches regarding the predicted flame shape and its dynamics is also investigated, where the implemented approach is compared with the well-established artificially thickened flame (ATF) combustion model. Consequently, the investigation conducted in this work aims to provide a complete picture on the ability of the proposed combustion model to reproduce the flow conditions within complex bluff-body swirl stabilized flames.     

Direct measurement of mixture fraction in reacting flow using Rayleigh scattering

The mixture fraction variable, , is very useful in describing reaction zone structure in nonpremixed flames. Extinction limits and turbulent mixing are often described as a function of this variable. Experimental evaluation of is critical for improving our understanding of the influence of turbulent mixing on the chemistry process. Heretofore, the evaluation of mixture fraction in combusting flow required multiple simultaneous concentration measurements. In this paper we present a fuel designed to permit measurements of mixture fraction by Rayleigh scattering technique only. A Rayleigh intensity/mixture fraction correspondence has been obtained experimentally in a laminar coflow flame. The influence of strain rate and differential diffusion effects have been investigated using laminar counterflow diffusion flame and shifting equilibrium chemistry models. The results obtained from comparisons between experiments and these models are very encouraging and suggest that the Rayleigh/mixture fraction correspondence established is valid under both the turbulent mixing and laminar strained flamelet combustion regimes.     

One-Dimensional Modeling of Turbulent Premixed Jet Flames - Comparison to DNS

The one-dimensional turbulence (ODT) model, formulated in an Eulerian reference frame, is applied to a temporally-evolving premixed turbulent hydrogen plane-jet flame and results are compared with direct numerical simulation (DNS) data. This is the first published study to perform direct comparisons of ODT to DNS for premixed flames. The ODT model solves the full set of conservation equations for mass, momentum, energy, and species on a one-dimensional domain corresponding to the transverse jet direction. The effects of turbulent mixing are modeled via a stochastic process, while the full range of diffusive-reactive length and time scales are resolved directly on the one-dimensional domain. A detailed chemical mechanism for hydrogen combustion consisting of 9 species and 21 reactions and a mixture-averaged transport model are used (consistent with the DNS). Cases with two different Damköhler numbers are considered and comparisons between the ODT and DNS data are shown with respect to flow dynamics and thermochemistry. The ODT compared favorably with the DNS in terms of the overall entrainment as judged by the streamwise velocity profile and in terms of local flamelet structure as judged by progress-variable conditional reaction and scalar dissipation rates. While the ODT agreed qualitatively with the overall flame evolution, the net fuel consumption rate was somewhat over-predicted for a brief early period and under-predicted later on, leading to an overly long flame burnout time. It was demonstrated that adjusting a parameter controlling the selection of large eddies improved the prediction of the peak fuel consumption rate and overall reaction progress but worsened the prediction of jet entrainment. An analysis of the 1D nature of ODT is presented that suggests the FSD in ODT needs to be much higher than the FSD in the DNS in order to achieve the same overall burning rate, suggesting that the FSD is under-predicted by a significant fraction. While the success of the ODT in reproducing many of the salient features of nonpremixed flames has been demonstrated, the current study suggests that improvements are needed when applied to premixed flames. It is also important to note that the DNS required approximately 40×10⁶ CPU hours while the ODT required approximately 10³ CPU hours.     

Flow and Mixing Fields for Transported Scalar PDF Simulations of a Piloted Jet Diffusion Flame (‘Delft Flame III’)

Numerical simulation results are presented for ‘Delft Flame III’, a piloted jet diffusion flame with strong turbulence–chemistry interaction. While pilot flames emerge from 12 separate holes in the experiments, the simulations are performed on a rectangular grid, under the assumption of axisymmetry. In the first part of the paper, flow and mixing field results are presented with a non-linear first order k–ε model, with the transport equation for ε based on a modeled enstrophy transport equation, for cold and reactive flows. For the latter, the turbulence model is applied in combination with pre-assumed β-PDF modeling for the turbulence–chemistry interaction. The mixture fraction serves as conserved scalar. Two chemistry models are considered: chemical equilibrium and a steady laminar flamelet model. The importance of the turbulence model is highlighted. The influence of the chemistry model is noticeable too. A procedure is described to construct appropriate inlet boundary conditions. Still, the generation of accurate inlet boundary conditions is shown to be far less important, their effect being local, close to the nozzle exit. In the second part of the paper, results are presented with the transported scalar PDF approach as turbulence–chemistry interaction model. A C₁ skeletal scheme serves as chemistry model, while the EMST method is applied as micro-mixing model. For the transported PDF simulations, the model for the pilot flames, as an energy source term in the mean enthalpy transport equation, is important with respect to the accuracy of the flow field predictions. It is explained that the strong influence on the flow and mixing field is through the turbulent shear stress force in the region, close to the nozzle exit.     

A Combined Experimental and Numerical Study of Laminar and Turbulent Non-piloted Oxy-fuel Jet Flames Using a Direct Comparison of the Rayleigh Signal

In the present study laminar and turbulent oxy-fuel jet flames are investigated both experimentally and numerically with emphasis on the direct comparison of the Rayleigh signal. The Rayleigh signal was measured for both flame setups, correcting for background light appropriately. Two downstream regions were recorded for the laminar flame and three for the turbulent flame. Equivalently, the signal was processed numerically based on the numerical species data and temperature. The laminar flame was used for validating the procedure of processing the Rayleigh signal. Both the numerical species data and the temperature are known from detailed simulations, so a predicted Rayleigh signal can easily be obtained. Further, the influence of the choice of the kinetic mechanism, radiation and diffusion model was investigated. In contrast, in the turbulent Large Eddy Simulation, the Rayleigh signal has to be computed using an appropriate turbulence-chemistry interaction model in order to obtain the Reynolds-filtered Rayleigh signal which is of non-linear nature. In the present investigation, the Rayleigh signal was incorporated in the flamelet/progress variable approach. The statistics of the experimental and numerical Rayleigh signal were then compared. The proposed procedure of directly comparing the experimental and predicted Rayleigh signal was shown to be advantageous in model validation especially in turbulent flame configurations. The procedure enables accurate model validation across an entire 2D field of view whilst using a realistic fuel-oxidizer combination and reducing experimental complexity.     

Large eddy simulation of turbulent premixed and stratified combustion using flame surface density model coupled with tabulation method

Large eddy simulations (LESs) are performed to investigate the Cambridge premixed and stratified flames, SwB1 and SwB5, respectively. The flame surface density (FSD) model incorporated with two different wrinkling factor models, i.e., the Muppala and Charlette2 wrinkling factor models, is used to describe combustion/turbulence interaction, and the flamelet generated manifolds (FGM) method is employed to determine major scalars. This coupled sub-grid scale (SGS) combustion model is named as the FSD-FGM model. The FGM method can provide the detailed species in the flame which cannot be obtained from the origin FSD model. The LES results show that the FSD-FGM model has the ability of describing flame propagation, especially for stratified flames. The Charlette2 wrinkling factor model performs better than the Muppala wrinkling factor model in predicting the flame surface area change by the turbulence. The combustion characteristics are analyzed in detail by the flame index and probability distributions of the equivalence ratio and the orientation angle, which confirms that for the investigated stratified flame, the dominant combustion modes in the upstream and downstream regions are the premixed mode and the back-supported mode, respectively.     

Subgrid Modeling of Turbulent Premixed Flames in the Flamelet Regime

Large eddy simulation (LES) models for flamelet combustion are analyzed by simulating premixed flames in turbulent stagnation zones. ALES approach based on subgrid implementation of the linear eddy model(LEM) is compared with a more conventional approach based on the estimation of the turbulent burning rate. The effects of subgrid turbulence are modeled within the subgrid domain in the LEM-LES approach and the advection (transport between LES cells) of scalars is modeled using a volume-of-fluid (VOF) Lagrangian front tracking scheme. The ability of the VOF scheme to track the flame as a thin front on the LES grid is demonstrated. The combined LEM-LES methodology is shown to be well suited for modeling premixed flamelet combustion. The geometric characteristics of the flame surfaces, their effects on resolved fluid motion and flame-turbulence interactions are well predicted by the LEM-LES approach. It is established here that local laminar propagation of the flamelets needs to be resolved in addition to the accurate estimation of the turbulent reaction rate. Some key differences between LEM-LES and the conventional approach(es) are also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

A Priori Evaluation of the Laminar Flamelet Decomposition Model for Turbulent Premixed Flames using DNS Data

Laminar flamelet decomposition (LFD) is a dynamic approach for modelling sub-filter scale turbulence-chemistry interactions in Large-Eddy Simulations using a stretched flamelet library. In this work, the performance of the LFD model – that was previously used only in non-premixed combustion—is investigated a priori for premixed combustion using positively-strained flamelets in the reactant-to-product configuration. For this purpose, a DNS database of methane-air premixed flames is utilized. The flames are propagating in a rectangular box under homogeneous isotropic turbulence conditions over a wide range of Karlovitz numbers. The results show that the LFD model can correctly account for the sub-filter scale turbulence-chemistry interactions to predict the filtered reaction rates and the filtered scalar field, provided that turbulent and laminar mixing are well predicted. The deviations from the DNS results are attributed to the shortcomings of the strained flamelet library and the non-flamelet effects. Finally, the LFD results are compared with a different sub-filter scale model using the same strained flamlelet library, and the relative performances of the two models are discussed.—

     

Experimental and Theoretical Sensitivity Analysis of Turbulent Flow Past a Square Cylinder

The Siemens SGT-800 3^rd generation DLE burner fitted to an atmospheric combustion rig has been numerically investigated. Pure methane and methane enriched by 80 vol% hydrogen flames have been considered. A URANS (Unsteady Reynolds Averaged Navier-Stokes) approach was used in this study along with the k ? ω SST and the k ? ω SST-SAS models for the turbulence transport. The chemistry is coupled to the turbulent flow simulations by the use of a laminar flamelet library combined with a presumed PDF. The effect of the mesh density in the mixing and the flame region and the effect of the turbulence model and reaction rate model constant are first investigated for the methane/air flame case. The results from the k ? ω SST-SAS along with flamelet libraries are shown to be in excellent agreement with experimental data, whereas the k ? ω SST model is too dissipative and cannot capture the unsteady motion of the flame. The k ? ω SST-SAS model is used for simulation of the 80 vol% hydrogen enriched flame case without further adjusting the model constants. The global features of the hydrogen enrichment are very well captured in the simulations using the SST-SAS model. With the hydrogen enrichment the time averaged flame front location moves upstream towards the burner exit nozzle. The results are consistent with the experimental observations. The model captures the three dominant low frequency unsteady motion observed in the experiments, indicating that the URANS/LES hybrid model indeed is capable of capturing complex, time dependent, features such as an interaction between a PVC and the flame front.     

Statistics and Modelling of Turbulent Kinetic Energy Transport in Different Regimes of Premixed Combustion

The statistical behaviour of turbulent kinetic energy transport in turbulent premixed flames is analysed using data from three-dimensional Direct Numerical Simulation (DNS) of freely propagating turbulent premixed flames under decaying turbulence. For flames within the corrugated flamelets regime, it is observed that turbulent kinetic energy is generated within the flame brush. By contrast, for flames within the thin reaction zones regime it has been found that the turbulent kinetic energy decays monotonically through the flame brush. Similar trends are observed also for the dissipation rate of turbulent kinetic energy. Within the corrugated flamelets regime, it is demonstrated that the effects of the mean pressure gradient and pressure dilatation within the flame are sufficient to overcome the effects of viscous dissipation and are responsible for the observed augmentation of turbulent kinetic energy in the flame brush. In the thin reaction zones regime, the effects of the mean pressure gradient and pressure dilatation terms are relatively much weaker than those of viscous dissipation, resulting in a monotonic decay of turbulent kinetic energy across the flame brush. The modelling of the various unclosed terms of the turbulent kinetic energy transport equation has been analysed in detail. The predictions of existing models are compared with corresponding quantities extracted from DNS data. Based on this a-priori DNS assessment, either appropriate models are identified or new models are proposed where necessary. It is shown that the turbulent flux of turbulent kinetic energy exhibits counter-gradient (gradient) transport wherever the turbulent scalar flux is counter-gradient (gradient) in nature. A new model has been proposed for the turbulent flux of turbulent kinetic energy, and is found to capture the qualitative and quantitative behaviour obtained from DNS data for both the corrugated flamelets and thin reaction zones regimes without the need to adjust any of the model constants.     

Study of a Filtered Flamelet Formulation for Large Eddy Simulation of Premixed Turbulent Flames

Despite significant advances in the understanding and modelling of turbulent combustion, no general model has been proposed for simulating flames in industrial combustion devices. Recently, the increase in computational possibilities has raised the hope of directly solving the large turbulent scales using large eddy simulation (LES) and capturing the important time-dependant phenomena. However, the chemical reactions involved in combustion occur at very small scales and the modelling of turbulent combustion processes is still required within the LES framework. In the present paper, a recently presented model for the LES of turbulent premixed flames is presented, analysed and discussed. The flamelet hypothesis is used to derive a filtered source term for the filtered progress variable equation. The model ensures proper flame propagation. The effect of subgrid scale (SGS) turbulence on the flame is modelled through the flame-wrinkling factor. The present modelling of the source term is successfully tested against filtered direct numerical simulation (DNS) data of a V-shape flame. Further, a premixed turbulent flame, stabilised behind an expansion, is simulated. The predictions agree well with the available experimental data, showing the capabilities of the model for performing accurate simulations of unsteady premixed flames.     

Linear-Eddy Model Formulated Probability Density Function and Scalar Dissipation Rate Models for Premixed Combustion

A tabulated, pseudo-turbulent Probability Density Function (PDF) model for premixed combustion is proposed. The Linear-Eddy Model (LEM) is used to construct the PDFs for a temperature-based progress variable in a premixed, turbulent methane/air V-flame produced by the Cambridge slot burner. As a second case study, the LEM PDFs are similarly compared to PDFs extracted from Direct Numerical Simulations (DNS) of a turbulent premixed flame. LEM demonstrates the ability to reproduce the salient features from experimental and DNS PDFs; moreover, it is able to better capture turbulent effects than previously suggested laminar flamelet PDF models. The Scalar Dissipation Rate (SDR) for premixed combustion is likewise investigated. The stochastic nature of LEM enables it to mimic the overall behaviors of turbulent reactions inexpensively and qualitatively. Crucially, LEM appears to be well suited for the preprocessing tabulation of PDF and SDR models for a number of premixed combustion simulation strategies.     

Linear Eddy Mixing Model Studies of High Karlovitz Number Turbulent Premixed Flames

Turbulent premixed flames exhibit different structural and propagation characteristics with increasing upstream turbulence intensity starting from thin wrinkled flames in the Corrugated Flamelet regimes to a flame with a thicker preheat zone in the Thin Reaction Zone Regime (TRZ) and finally, becoming more disorganized or broken in the Distributed or Broken Reaction Zone (D/BRZ) regimes under intense turbulence. A single comprehensive predictive model that can span all regimes does not currently exist, and in this study we explore the ability of the stand-alone one-dimensional linear-eddy mixing (LEM) model to simulate the flames in all these regimes. Past applications of this 1DLEM model have demonstrated reasonable predictions in the flamelet and TRZ regimes and here, new experiments in the TRZ regime are specifically addressed to evaluate the predictive capability of this model. Additional simulations in the D/BRZ regimes (where no data is currently available) are performed to determine if the model can be extended to the high turbulence regime. Comparison with the data in the TRZ regime shows satisfactory agreement. Analysis suggests varying levels of preheat zone broadening in all the TRZ and D/BRZ cases. While the average heat release distribution for the TRZ cases is nearly identical to the laminar unstrained baseline, changes to the species and heat release distribution are observed only at a high Karlovitz Number K a > 10³. In the D/BRZ regime it is shown that the transition is related to enhanced turbulent diffusion that dominates molecular diffusion effects causing deviations from the laminar baseline.     

Towards an Extension of TFC Model of Premixed Turbulent Combustion

In order to determine the mean rate of product creation within the framework of the Turbulent Flame Closure (TFC) model of premixed combustion, the model is combined with a simple closure of turbulent scalar flux developed recently by the present authors based on the flamelet concept of turbulent burning. The model combination is assessed by numerically simulating statistically planar, one-dimensional, developing premixed flames that propagate in frozen turbulence. The mean rate of product creation yielded by the combined model decreases too slowly at the trailing edges of the studied flames, with the effect being more pronounced at longer flame-development times and larger ratios of rms turbulent velocity u′ to laminar flame speed S _L . To resolve the problem, the above closure of turbulent scalar flux is modified and the combination of the modified closure and TFC model yields reasonable behaviour of the studied rate. In particular, simulations indicate an increase in the mean combustion progress variable associated with the maximum rate by u′/S _L , in line with available DNS data. Finally, the modified closure of turbulent scalar flux is validated by computing conditioned velocities and turbulent scalar fluxes in six impinging-jet flames. The use of the TFC model for simulating such flames is advocated.     

Coupling tabulated chemistry with Large Eddy Simulation of turbulent reactive flows

A new modeling strategy is developed to introduce tabulated chemistry methods in the LES of turbulent premixed combustion. The objective is to recover the correct laminar flame propagation speed of the filtered flame front when the subgrid scale turbulence vanishes. The filtered flame structure is mapped by 1D filtered laminar premixed flames. Closure of the filtered progress variable and the energy balance equations are carefully addressed. The methodology is applied to 1D and 2D filtered laminar flames. These computations show the capability 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 introducing subgrid scale wrinkling effects on the flame front propagation. Finally, the LES of a 3D turbulent premixed flame is performed. To cite this article: R. Vicquelin et al., C. R. Mecanique 337 (2009).