Numerical Study on Flame-Front Characteristics of Conical Turbulent

Nov 21, 2008 - Premixed turbulent methane/air flames with conical (or Bunsen) configuration are computed in two stages for selected equivalence ratios...
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Energy & Fuels 2009, 23, 1843–1848

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Numerical Study on Flame-Front Characteristics of Conical Turbulent Lean Premixed Methane/Air Flames† Baris Yilmaz,*,‡,§ Sibel Ozdogan,‡ and Iskender Go¨kalp§ Faculty of Engineering, Mechanical Engineering Department, Marmara UniVersity, Kuyubasi-Kadikoy, Istanbul 34722, Turkey, and Institut de Combustion Ae´rothermique Re´actiVite´ et EnVironnement (ICARE)-Centre National de la Recherche Scientifique (CNRS), 1c, AV. de la Recherche Scientifique 45071, Orle´ans Cedex 2, France ReceiVed May 15, 2008. ReVised Manuscript ReceiVed September 30, 2008

Premixed turbulent methane/air flames with conical (or Bunsen) configuration are computed in two stages for selected equivalence ratios. First, the turbulent cold-flow field inside the combustion chamber is modeled, and turbulence characteristics are computed using the k-ε turbulence model and its variants. Second, the flame-front properties are investigated by two different turbulent premixed combustion models, namely, the Zimont model and the coherent flame model. All computations are performed with the Fluent software. The computations are confronted to the experimental data corresponding to turbulent flames in the corrugated flamelet regime. Experimental results concern turbulent premixed methane/air flames stabilized on a Bunsentype burner; they are obtained mainly by LDA for the cold- and hot-flow velocity statistics and by laserinduced Mie and Rayleigh scattering techniques for flame-front statistics. The computations are in agreement with the experimental data; in particular, the decrease of both the flame height and the flame brush thickness with the increase of the equivalence ratio is well-reproduced by the computations.

1. Introduction The non-premixed mode of combustion is traditionally preferred in gas turbine combustors because of safety and stability reasons. Lean premixed combustion (LPC) has been recently developed along with other methods to achieve lower level NOx emissions. In LPC, fuel and air are premixed before entering the combustor, and the flame temperature, hence, thermal NOx formation, is reduced because of operation under lean mixture conditions. The operation near the lean flammability limit may, however, lead to local and global flame extinction or increased flame instabilities. The control of such flames necessitates the knowledge of both their chemical kinetics and flame propagation properties at the desired equivalence ratio. Fuel and oxidizer are mixed at a molecular level in premixed flames. If the mixture lies within flammability limits, a local increase in temperature initiates the combustion process. The chemical reactions are typically very fast, so that the instantaneous flame-front thickness is of the order of 0.1-1 mm in the case of hydrocarbon fuels.1 The flame-front propagation toward the unburnt reactants is the key feature of premixed combustion. Premixed combustion usually takes place within turbulent environments. Turbulence increases the mixing processes and thereby enhances combustion. On the other hand, combustion releases heat and generates flow instability because of gas expansion. Therefore, the interaction between turbulence and combustion has a coupled and complex behavior.1,2 Turbulent combustion is characterized by a wide range of time and length scales.1,2 In turbulent premixed flames, turbu†

From the Conference on Fuels and Combustion in Engines. * To whom correspondence should be addressed. Telephone: (90) 2163480292. Fax: (90) 2163480293. E-mail: [email protected]. ‡ Marmara University. § ICARE-CNRS. (1) Poinsot, T.; Veynante, D. Theoretical and Numerical Combustion; R.T. Edwards Publications: Philadelphia, PA, 2001.

lence wrinkles and stretches the propagating laminar flame sheet, increasing the flame surface area and thus the overall flame speed. The large turbulent eddies tend to wrinkle and corrugate the flame sheet, while the small turbulent eddies, if smaller than the laminar flame thickness, may penetrate the flame sheet and modify the laminar flame structure by enhancing heat and mass transport, mainly in the preheating zone.1-3 The interaction of the chemistry with the turbulent flow fluctuations is another source of complexity. A number of approaches have been proposed to treat chemical reactions in turbulent flow.4 The most common one is the fast chemistry approach, which neglects the chemical kinetic limitations on flame propagation. It assumes instantaneous chemical reactions, which are only limited by turbulent mixing.4 There are several premixed combustion models developed using the fast chemistry assumption.2 Computer modeling is currently playing a key role for the design of gas turbine combustors.4 Major gas turbine manufacturers use computational fluid dynamics (CFD)-based turbulent combustion modeling as part of their design procedure. Modeling of premixed turbulent flames has been carried out on several levels. At the lowest level, the RANS equations for turbulent reactive flows are solved for the mean fields. At the next level, a transport equation derived from the Navier-Stokes equations is solved for the joint PDF of composition and velocity, providing a complete statistical description. The third level of modeling is large eddy simulation (LES), where the large scales (2) Peters, N. Turbulent Combustion; Cambridge University Press: Cambridge, U.K., 2000. (3) Veynante, D.; Vervisch, L. Turbulent Combustion; Von Karman Institute for Fluid Dynamics Lecture Series Notes 2006-2007; Vervisch, L.; Veynante, D.; van Beeck, J. P. A. J., Eds.; Von Karman Institute for Fluid Dynamics: Sint-Genesius-Rode, Belgium, 2007. (4) Brewster, B. S.; Cannon, S. M.; Farmer, J. R.; Meng, F. Prog. Energy Combust. Sci. 1999, 25, 353–385.

10.1021/ef8003587 CCC: $40.75  2009 American Chemical Society Published on Web 11/21/2008

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of the turbulent flow field are resolved explicitly, while the small scales are modeled. The highest level of modeling is direct numerical simulation (DNS), where the NS equations are solved directly without any modeling assumption. Although the k-ε model is categorized at the lowest level of the modeling approaches, it is widely used in CFD-based industrial design applications.2,4,5 Comprehensive modeling of gas turbine combustion has been an active area of research for the last few decades, and numerous models and computation results have been reported in the literature. A summary of this literature is reviewed by Brewster et al.4 In this list, the majority of computations have been carried out for jet engine combustors operated in the non-premixed mode and the k-ε model has been universally used for turbulent closure. Modeling gas turbine combustors operating in the LPC mode is of current interest.4,6 Recently, lean premixed turbulent Bunsen flames of various hydrocarbon fuels at ambient pressure conditions are modeled with three different flame surface density (FSD) models by Aluri et al.7 The computed average flame-front positions of the flames were compared to the available experimental data. In a similar vein, the present study aims to model and compute the global features of turbulent lean premixed methane-air flames experimentally investigated at ICARE, Orle´ans, France. These flames are stabilized on a Bunsen-type burner for several equivalent ratios and chamber pressures.8,9 The turbulent premixed flames are computed using the Zimont model10-12 and the coherent flame model (CFM).1,7,13-15 Both models are based on the assumption of infinitely thin flame front or fast chemistry assumptions. These models are applicable for the present experimental data because it is confirmed by Halter9 that the flames are located within the flamelet regime region.9 A one-step global methane/air reaction is considered for turbulence-chemistry interactions. However, the laminar flame speeds at various flame conditions are derived from a CHEMKIN II package with the GRI-Mech 3.0 detailed reaction mechanism. 2. Experimental Setup The experimental setup consists of a stainless-steel cylindrical combustion chamber with an inner diameter of 300 mm,8,9 operated up to 1 MPa. The chamber consists of two 600 mm water-cooled vertical cylindrical sections. In each section, there are four windows for optical diagnostics, as shown in Figure 1. The internal walls of the chamber are painted in black with a laser light absorbing paint, resistant to temperature. The laser light traverses the combustion chamber through two opposite windows. The windows are electri(5) Herrmann, M. Numerical simulation of turbulent Bunsen flames with a level set flamelet model. Combust. Flame 2006, 145, 357–375. (6) Sankaran, R.; Hawkes, E. R.; Chen, J. H.; Lu, T.; Law, C. K. Proc. Combust. Inst. 2007, 31, 1291–1298. (7) Aluri, N. K.; Sha, Q.; Muppala, S. P. R.; Dinkelacker, F. Flame surface density modelssA numerical evaluation. Proceedings of the ECM2005, Brussels, Belgium, 2005; p 132. (8) Lachaux, T. Etude des effets de la haute pression sur la structure et la dynamique des flammes turbulentes de pre´me´lange pauvre de me´thaneair. Ph.D. Thesis, Universite d’Orleans, Orleans, France, 2004. (9) Halter, F. Caracterisation des effets de l’ajout d’ajout d’hydrogene et de la haute pression dans les flammes turbulentes de premelange methane/ air. Ph.D. Thesis, Universite d’Orleans, Orleans, France, 2005. (10) Zimont, V.; Polifke, W.; Bettelini, M.; Weisenstein, W. J. Eng. Gas Turbines Power 1998, 120, 526–532. (11) Zimont, V. L. Exp. Therm. Fluid Sci. 2000, 21, 179–186. (12) Fluent 6.2 Users Manual, Fluent, Inc., Lebanon, NH, 2005. (13) Duclos, J. M.; Veynante, D.; Poinsot, T. Combust. Flame 1993, 95, 101–117. (14) Prasad, R. O. S.; Gore, J. P. Combustion and Flame 1999, 116, 1–14. (15) Muppala, S. P. R.; Aluri, N. K.; Dinkelacker, F.; Leipertz, A. Combust. Flame 2005, 140, 257–266.

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Figure 1. Combustion chamber setup (left) and the schematic view of the burner (right) (PF, pilot flame flow channel; PP, perforated plate; MF, main premixed flow). Table 1. Modifications Proposed for the Constants of the k-ε Turbulence Modela standard k-ε model (Std k-ε) Turpin and Troyes16 (Mod. k-ε 1) Morgans et al.17 (Mod. k-ε 2) a

Cε1

Cε2

σk

σε

1.44 1.5 1.6

1.92 1.82 1.92

1.0 1.0 1.0

1.3 1.7 1.3

Parentheses represent the names in the figures.

Figure 2. Mean velocity distributions along the normalized symmetry axis (inner chamber diameter, D, is 25 mm). Table 2. CFM Modelled Source Terms of Eq 8 κm Aik

∂uk ∂xi

D

κt Ro

ε k

βo

SL + C√k 2 Σ Y/Yu

cally heated to avoid water condensation, and a nitrogen flow dries the windows during measurements if necessary. The internal pressure is set manually; a pressure gauge and a thermocouple are used to check burned gas pressure and temperature. The burner is an axisymmetric Bunsen-type burner placed at the bottom of the chamber. It can be moved vertically. The inner diameter of the burner is 25 mm. A perforated plate is located 50 mm upstream of the burner exit to generate the required turbulence. A stoichiometric methane/air pilot flame is used to stabilize the lean premixed flame. The experimental results concern the flow velocity field obtained by LDA and the flame-front statistics obtained by laser-induced Mie scattering.8,9 The experimental conditions are chosen to be close to the gas turbine combustor operating conditions by applying constant average burner exit velocity.9 Air is used as the working fluid in cold-flow measurements. A 15 Hz pulsed Nd:YAG laser (Spectra Physics GCR 130) at 532.5 nm is used for Mie scattering flame tomography. The pulse energy is 270 mJ. The laser beam passing through two spherical lenses produces a light sheet 200 µm thick and approximately 90

Lean Premixed Methane/Air Flames

Figure 3. Turbulent kinetic energy distributions along the normalized symmetry axis.

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Figure 6. Comparison of the average progress variable distribution along the symmetry axis for three different equivalence ratios (ER ) equivalence ratio) for two combustion models.

regions far from the burner exit to reduce the computational time. The computations are performed in cold and reactive cases separately using the Fluent software. 3.1. Cold-Flow Case. The conical jet flow becomes turbulent mainly by the effect of the turbulence grid used in the burner section and the shear forces between the main flow and the surrounding air inside the combustion chamber. This turbulence field is modeled by the k-ε turbulence model. In this model, the flow field is described by Favre-averaged Navier-Stokes equations in the conservative form. Besides the continuity and momentum equations, two more scalar equations are solved which are defined in the following form:

Figure 4. Turbulent dissipation rate distributions along the normalized symmetry axis.

(( ) ) (( ) )

µt ∂k ∂ ∂ ∂Fk + (Fkui) ) µ+ + Gk - Fε ∂t ∂xi ∂xi σk ∂xi µt ∂ε ∂Fε ∂ ε ∂ ε2 + (Fεui) ) µ+ + Cε1 Gk - Cε2F ∂t ∂xi ∂xi σε ∂xi k k

(1) (2)

The turbulent viscosity is defined as k2 (3) ε In these equations, Gk represents turbulence generation because of the mean velocity gradients. The constants of this model are Cε1 ) 1.44, Cε2 ) 1.92, Cµ ) 0.09, σk ) 1.0, and σε ) 1.3. Several variants of the k-ε model provided by the Fluent library, such as RNG and realizable k-ε models,12 are also examined. Moreover, the model constants of the standard k-ε turbulence model are proposed to be modified for conical flames in several works.16,17 The model constants and their modified versions are presented in Table 1. Pope18 proposes the addition of an extra term to the ε equation of the standard k-ε turbulence model to resolve round jetplane jet anomaly. This correction is also applied to Fluent by means of user-defined function utilities.12 3.2. Reactive Flow Case. The premixed flame-front statistics are investigated by means of two turbulent premixed combustion models, namely, the Zimont model10,11 and the CFM model.1,7,13-15 Both models assume infinitely fast chemistry and propose an extra scalar transport equation besides the mean flow governing equations. The laminar flame speed is the key parameter in the algebraic closure of these equations. It is µt ) FCµ

Figure 5. Comparison of the computed average progress variable distribution to the experiments along symmetry axis.

mm high. The flow is seeded by olive oil droplets. The Mie scattered light is collected at 90° to the sheet by a CCD camera. The overall resolution is 0.11 mm/pixel. More details about the experimental techniques can be found in previous publications.8,9

3. Numerical Studies The numerically computed results of this study are to be compared to the experimental data obtained using the ICARE high-pressure combustion facility described above. First, an axisymmetric and two-dimensional model of the chamber geometry is generated. The chamber space is meshed with structured fine meshes near the burner exit as well as in the mixing regions, where the gradients of the reactive flow parameters are expected to be high. Coarse meshes are used in

(16) Turpin, G.; Troyes, J. AIAA-2000-3463, 36th AIAA/ASME/SAE/ ASEE, Joint Propulsion Conference and Exhibit, Huntsville, AL, 2000. (17) Morgans, R. C.; Dally, B. B.; Nathan, G. J.; Lanspeary, P. V.; Fletcher, D. F. In the 2nd International Conference on CFD in the Minerals and Process Industries, Melbourne, Australia, 1999. (18) Pope, S. B. AIAA J. 1978, 16 (3), 279–281.

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Figure 7. Average progress variable contour plots. Left and right parts in each graph indicate the results obtained by computations and experiments, respectively (first row, the Zimont model; second row, the MCFM model).

flame front moves toward the unburnt mixture. In this approach, the flame-front propagation is modeled by solving a transport equation for the Favre-averaged reaction progress variable, c, represented by

( )

∂ ∂Fc ∂ µt ∂c + (Fuc) ) + FSc ∂t ∂xi ∂xi Sct ∂xi

(4)

where Sct and Sc are the turbulent Schmidt number and the reaction progress source term, respectively. The progress variable is defined as the normalized sum of the mass fractions of the product species as given in eq 5. Hence, it is 0 and 1 in the fresh and burned gases, respectively n

Figure 8. Species mass fraction distribution along the normalized axial direction for ER ) 0.6.

c)

⁄

n

∑Y ∑Y i

i)1

i,eq

(5)

i)1

An algebraic closure for the source term in eq 4 is proposed by Zimont and his co-workers10,11 as FSc ) FuUt|∇c|

(6)

and turbulent flame speed Ut is expressed by the following relation:11 Ut ) A(u′)3/4Ul1/2R-1/4lt1/4

Figure 9. Comparison of FSD distributions obtained by the CFM model, modified CFM, and experiment versus the progress variable.

computed in this study by the PREMIX code of the CHEMKIN II software package.19 In many industrial premixed combustion devices, combustion takes place in a thin flame sheet, which separates unburnt premixed reactants and burnt products. The Zimont model considers that the reaction takes place in this sheet only and (19) Kee, R. J.; Rupley, F. M.; Miller, J. A. CHEMKIN II Users Manual. Report SAND89-8009, Sandia National Laboratories, Livermore, CA, 1989.

(7)

where A is the model constant proposed to be 0.52 for methane/ air mixtures.11 Ul is the laminar flame speed, R is the thermal diffusivity of the unburnt mixture, and lt is the integral turbulent length scale. To take the stretch effects into account, the source term for the progress variable is multiplied by a factor that controls the quenching probability of the flame.10-12 An alternative method to model thin premixed flames is the FSD approach.1,7,13-15 In this approach, the FSD transport equation given in the following form is solved:

( )

∂ ∂Σ ∂ νt ∂Σ + (FuΣ) ) + κmΣ + κtΣ - D ∂t ∂xi ∂xi σc ∂xi

(8)

The first term on the right-hand side of the equation represents the variation of flame surface by turbulent diffusion. The second and third terms indicate the production of the flame surface by mean flow gradients and local turbulence conditions, respectively. The last term represents the destruction of the flame

Lean Premixed Methane/Air Flames

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surface. There are several approaches to model production and destruction terms.1,13-15 In the present study, a well-known version of the FSD model, namely, the CFM model, is also studied. The assumptions for the source terms in the CFM approach are given in Table 2. The κm term is often neglected compared to the κt term.1,7 The model constants, Ro, βo and C, are defined as 1.7, 1.0, and 0.5, respectively.13-15 We added the CFM model to the Fluent software by means of user-defined functions. Both the analysis of the flame properties and the prediction of the consumption/production rates of species become possible when using this model. Species equations for a one-step methane/air global reaction are solved together with the flame surface transport equation. The source terms of the species equations are closed by the computed FSD. This closure is defined as w˙F ) -FoIoSLYoΣ

(9)

where Fo and Yo represent the unburnt fuel density and mass fraction, respectively. SL is the laminar flame speed. Io represents the stretch factor set to 1.1 A modification for the preconstant of the κt term is proposed in ref 7, where the average flame position is investigated numerically and the turbulent flame speed parameters are compared to measured data. It is reported that the tuning of this term leads to relatively well-predicted flame shapes in comparison to the experiments. Aluri et al.7 also observed that the CFM model with original constants underestimates the reaction rate. This modified version of the CFM model, abbreviated as the MCFM model in this paper, is also tested. In the next few paragraphs, the used premixed combustion models are tested for various equivalence ratios to predict the average flame position, which is characterized by the progress variable distribution along the symmetry axis. 3.3. Boundary Conditions. Boundary and initial conditions are determined according to the experimental conditions. The mean axial velocity profile measured at 5 mm downstream of the burner exit8 is considered to be the initial velocity profile. Grid-generated turbulence conditions are introduced using the turbulent kinetic energy and dissipation rate profiles extracted from measured data. To add 3D effects of the turbulence to the 2D measurements, w′ velocity is assumed to be equal to V′. The profile of the initial turbulent kinetic energy is therefore obtained from the following relation: 1 (10) k ) (u′2 + 2V′2) 2 and the turbulent dissipation rate is calculated by the following equation: ε)

u′3 lt

(11)

where u′, V′, and w′ represent fluctuation velocities and lt is the integral length scale. The pilot flame velocity is adjusted to satisfy the mass flow rate ratio of 13% of the main flow rate condition dictated by the experiments.9 All of the computations are performed at atmospheric pressure conditions and at 300 K. 4. Results and Discussion 4.1. Cold-Flow Case. The turbulent characteristics of the inchamber flow field are examined by cold-flow simulations. In this case, air is assumed to be the working fluid in line with the experiments.

A comparison of the mean velocity distributions in the normalized axial direction shows that the modified versions of the k-ε turbulence model result in better agreement with experiments than the standard one, as shown in Figure 2. The Cε1 modification (abbreviated as Mod. k-ε 1 in the figures) gives the most satisfactory result for the mean velocity profile within the domain of available experimental data. The RNG version of the k-ε model shows slightly better agreement in the mean velocity profile up to four diameters downstream compared to the other modified versions. However, this version predicts steeper decay beyond that region. The turbulence decay, which starts about three diameters after the burner exit is also well-predicted by simulations in line with the experiments. All versions except for the standard k-ε model are in accordance with the experimental data in the whole computational domain. Turbulent kinetic energy profiles are compared to the experiments in Figure 3. It is observed that all of the variants of the k-ε model predict almost the same profiles up to the onset of the turbulence core decay region. Downstream, the standard k-ε model and modified Cε1 version profiles deviate more than the profiles predicted by the other versions. All of the modified versions, except for modified Cε1, predict the turbulent kinetic energy distribution in accordance with the experiment up to four diameters downstream. The RNG version begins to deviate from the experiments at that region. The modified Cε2 (abbreviated as Mod. k-ε 2 in the figures), Pope-corrected (abbreviated as Pope k-ε in the figures), and the realizable k-ε model versions predict the turbulent kinetic energy profile slightly better than the other versions in the whole domain of experiments. The deviations of the realizable k-ε version increase toward the end of the domain. All models predict a maximum near the end of the computational domain, which cannot be verified because of the lack of additional experimental data. A similar tendency is also observed for the turbulent dissipation rate profiles in Figure 4. When turbulence begins to decay, the predictions of computations become different than measurements. However, the predictions of both the RNG and the Pope-corrected versions are in accordance with the experiments up to four diameters after the burner exit. The RNG version shows good agreement up to five diameters downstream, while the Pope-corrected version resembles the modified Cε2 version and deviates from the experiments. The modified Cε1 version results in the worst turbulent dissipation rate prediction compared to the other versions. The standard k-ε model shows a steeper turbulent dissipation rate profile compared to the other versions. Although experimental data are no more available, all models predict a maximum turbulent kinetic energy after five diameters downstream, which cannot be verified because of the lack of experimental data in that region. 4.2. Reactive Flow Case. The reactive case studies presented in this study are based on cold-flow standard k-ε results. The premixed methane/air flow at a 0.6 equivalence ratio is computed initially. In Figure 5, results using the Zimont model and two versions of the CFM models are presented. When the progress variable computations are compared to the experiments, it is observed that the CFM model locates the flame front further downstream from the burner exit. In addition, it predicts a wider progress variable profile, hence a thicker flame brush than experiments. The Zimont model predicts a progress variable profile similar to the experiments. However, it locates the flame front slightly downstream. The MCFM model results in the best agreement with experiments for the average progress variable profile along the symmetry axis. This model

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predicts the average flame position very close to the measured data. However, it gives a steeper profile for the average progress variable, which means a faster chemical production rate than the experiments; thus, the flame brush thickness is smaller. The effect of the equivalence ratio on the flame-front position and average thickness is also investigated in the present work. The computational results for the equivalence ratio values at 0.6, 0.7, and 0.8 are performed using the Zimont model and the MCFM combustion model, presented in Figure 6. The comparison of the average progress variable distributions along the normalized symmetry axis indicates that the increase of the equivalence ratio results in steeper progress variable distributions. The average progress variable axial profile is shifted upstream by increasing the equivalence ratio. These computations confirm the early experimental results obtained in Orle´ans with a similar burner configuration.20,21 Consequently, the flame heights and the flame brush thicknesses decrease when the fuel mass fraction in the mixture is increased. Similar tendencies on the average flame structure have also been reported in several other works.7,15,20,21 The Zimont model predicts more decrease in flame tip position than in the MCFM model, with an increasing equivalence ratio. It is also observed that both combustion models predict relatively closer flame tips at higher equivalence ratios. The average progress variable contour plots are directly compared to those of experiments in Figure 7. Both models predict relatively well global tendencies when the equivalence ratio is varied. However, there are significant differences between model results when compared to experiments. Both models predict thinner flame brush thicknesses. The distributions of the reactant and product mass fractions predicted by the MCFM model are presented in Figure 8. These distributions are obtained for a one-step global methane/air reaction. The reactants are totally consumed within the reaction region, which is between two and three diameters downstream of the burner exit. Figure 9 represents the FSD distributions computed by the CFM, MCFM, and Zimont models and the relevant experimental data. In the CFM model, the FSD is directly computed by solving an extra transport equation besides the turbulent mean flow and species equations as discussed in section 3.2. However, the FSD distribution versus progress variable predicted by the Zimont model is derived from post-processing of the progress variable data by using the following relation: Σ)

gcj(1 - jc) |σy|Ly

(12)

where σy, Ly and g represent the flamelet orientation factor, the wrinkling integral length scale of the flame front, and a model constant with an order of unity,1,9 respectively. σy is computed as 0.59, and Ly/g is estimated as 1.5 based on experiments at atmospheric pressure and 0.6 equivalence ratio conditions by Halter.9 The derived FSD distribution indicates that the Zimont model overestimates the FSD compared to the MCFM model and experiments (Figure 9). The maximum FSD is located at 0.5 as expected from eq 12. The CFM model underestimates the FSD as reported previously.7 The MCFM model locates the FSD (20) Boukhalfa, A.; Go¨kalp, I. Proc. Combust. Inst. 1989, 22 (1), 755– 761. (21) Deschamps, B.; Boukhalfa, A.; Chauveau, C.; Go¨kalp, I.; Shepherd, I. G.; Cheng, R. K. Proc. Combust. Inst. 1992, 24 (1), 469–475.

profile in the best agreement with the experiments compared to the other models. The average progress variable for the maximum FSD is determined as 0.58 by MCFM. This value is reported as 0.59 in the experimental study of Halter.9 5. Conclusion The numerical simulations of data obtained on ICARE experimental setup concerning the turbulent premixed flame structure are performed in this study. They are realized for both the cold-flow and reactive-flow cases. The turbulence core decay, at three diameters downstream, is well-predicted by all versions of the k-ε turbulence in coldflow computations. The RNG version of the k-ε model predicts relatively better cold-flow field profiles for this geometry. The modified Cε1 version predicts the best mean velocity profile, however, the worst turbulence kinetic energy and dissipation rate profiles. The standard k-ε model computations show steeper and relatively deviating flow field profiles. In general, turbulent field simulations with the RNG version are in better agreement with the experiments compared to the other versions. All models predict a maximum in both turbulence kinetic energy and dissipation rate profiles near the end of the computational domain. For a more precise evaluation and a comprehensive understanding of the turbulent flow field, more experimental data are required in both the radial direction at several axial stations, only available 5 mm downstream, and the axial direction, mainly around five and six diameters downstream from the burner exit. The reactive case computations are performed in two stages. Initially, the equivalence ratio is kept constant at 0.6, and the methane/air flame front structure is examined by Zimont, CFM, and MCFM models. The MCFM model results in the best agreement with experiments for the average progress variable profile along the symmetry axis. However, it gives a slightly steeper profile for the average progress variable and a faster chemical production rate than the experiments; thus, the flame brush thickness is smaller. The Zimont model predicts a progress variable profile similar to the experiments. However, it locates the flame front slightly downstream. The CFM model locates the flame front further downstream. This model predicts a wider progress variable profile and, hence, a thicker flame brush than experiments. At the second stage, the influence of the equivalence ratio on the flame structure is investigated with the Zimont and MCFM models. It is observed that the average progress variable axial distribution is shifted upstream when the equivalence ratio is increased. The flame brush thicknesses are also decreased at higher equivalence ratios. On the other hand, the Zimont model predicts further decrease in the flame-front positions and the flame brush thicknesses than in the MCFM model. The FSD distribution versus progress variable is also examined. The MCFM model computations show the best agreement with the experiment. The CFM model underestimates the FSD; however, the Zimont model overestimates the FSD. Acknowledgment. This work is supported within the international joint research project program between CNRS and TUBITAK (Project MAG-104M330). Baris Yilmaz is supported within the joint Ph.D. Grant by the French Embassy in Ankara, as well as by the Ph.D. support project (FEN-DKR-181005-0215) of BAPKOMarmara University, Istanbul, Turkey. EF8003587