Fuel 87 (2008) 3123–3131

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Large-eddy simulation of turbulent combustion using different combustion models

L.X. Zhou a,*, L.Y. Hu a,b, F. Wang a,c

a Department of Engineering Mechanics, Tsinghua University, Beijing 100084, Chinab School of Power Engineering, Shanghai Jiaotong University, Shanghai 200400, Chinac Department of Thermal Engineering, Beihang University, Beijing 100083, China

a r t i c l e i n f o a b s t r a c t

Article history:Received 21 May 2007Received in revised form 19 April 2008Accepted 29 April 2008Available online 23 May 2008

Keywords:Large-eddy simulationTurbulent combustionCombustion models

0016-2361/$ - see front matter � 2008 Elsevier Ltd. Adoi:10.1016/j.fuel.2008.04.025

* Corresponding author.E-mail address: zhoulx@mail.tsinghua.edu.cn (L.X.

The second-order moment (SOM) combustion model proposed by the present authors is compared witheddy-break-up (EBU) and presumed probability density function (PDF) combustion models in large-eddy simulation of jet diffusion combustion, swirling diffusion combustion and premixed combustionbehind a bluff body. The statistical results for time-averaged and RMS fluctuation temperatures are val-idated by experimental results. It is seen that the SOM model can always give good statistical results inLES of both non-premixed and premixed combustion, whereas the EBU and presumed PDF models can-not always do. The instantaneous results indicate that organized large vortex and thin flame surfacestructures are observed in jet diffusion combustion and bluff-body stabilized premixed combustion,whereas no organized vortex and thin flame surface structures are observed in swirling diffusioncombustion.

� 2008 Elsevier Ltd. All rights reserved.

1. Introduction

Large-eddy simulation (LES) of turbulent combustion attractsmore and more attention, since it can give the instantaneous flowand flame structures leading to a better understanding to the tur-bulence-chemistry interaction; give the statistical results, betterthan the Reynolds-averaged N–S (RANS) modeling results. In LESdifferent sub-grid-scale (SGS) stress models and combustion mod-els are used. The most popular SGS stress models are the Smagorin-sky eddy-viscosity model [1], the Germano dynamic model [2] andthe dynamic kinetic energy model [3]. Various combustion modelsare proposed. For nonpremixed combustion, the laminar–flameletmodel [4] is frequently used and for the premixed combustionthe G-equation model [5] and the linear-eddy model [6] areadopted. Besides, the rather complex probability density function(PDF) equation model [7] and the simple eddy-break-up (EBU)model [8] are also used for both premixed and nonpremixed com-bustion. However, these combustion models either cannot alwaysgive satisfactory results, or are insufficiently validated by experi-ments. Jones [9] and Mare et al. [10] simulated the nonpremixedcombustion in can-type gas-turbine combustors using a Smagorin-sky SGS stress model and a laminar flamelet combustion model.The simulated flow pattern and the temperature are in reasonable

ll rights reserved.

Zhou).

agreement with those observed in experiments, but the agreementbetween the predicted and measured species concentrations (par-ticularly CO) is not satisfactory. Zhao et al. [11] simulated pre-mixed combustion in an afterburner using the EBU combustionmodel and only the predicted temperature profile at the exit iscompared with the measurement results. Therefore, the combus-tion models for LES need to be further studied and validated byexperiments.

Recently, a second-order moment (SOM) model for LES is pro-posed by the present authors [12]. In this paper, this SOM com-bustion model for LES will be validated by experiment resultsof jet diffusion combustion, swirling diffusion combustion andpremixed combustion behind a bluff body. Meanwhile, differentSGS stress models, including the Smagorinsky–Lilly’s model andthe dynamic kinetic energy model, and different combustionmodels, including the EBU model, the presumed PDF model andSOM model are used. The statistical results for time-averagedvariables are compared with each other and validated by experi-mental results for four different cases to further assess the SOMmodel. Furthermore, the flame structures of the jet diffusionflame, swirling diffusion flame and the premixed flame behind abluff body are studied.

2. The LES governing equations and SGS models

The filtered continuity, momentum, species and energy equa-tions for LES can be given as

Nomenclature

a,c empirical model constantsB pre-exponential factord distance to the closest wall Sc Schmidt numberE activation energyg SGS mass fluxh enthalpyk turbulent kinetic energyK reaction rate constantLs mixing length for subgrid scalesp pressurePr Prandtl numberq SGS heat fluxR gas-law constantSc Schmidt numberS strain-rate tensort timeT temperatureu velocity componentV volume of the computational cellw reaction ratex,y,z space coordinateY mass fraction

Greek alphabetsb stoichiometric coefficiente dissipation rate

j Von Kármán constantl dynamic viscositylt subgrid-scale turbulent viscositym kinematic viscosityq densityrY, rT model constantss subgrid-scale stresssC reaction timesT turbulent diffusion time

SubscriptsFu fueli,j,k components; coordinatesox oxygenp products speciessgs sub-grid-scale valuet turbulent

Superscripts- filtered value’ sub-grid-scale value

3124 L.X. Zhou et al. / Fuel 87 (2008) 3123–3131

oqotþ o

oxiðq�uiÞ ¼ 0 ð1Þ

o

otðq�uiÞ þ

o

oxjðq�ui�ujÞ ¼

o

oxjl o�ui

oxj

� �� o�p

oxi� osij

oxjð2Þ

oq�Ys

otþ o

oxjðq�uj

�YsÞ ¼o

oxj

lSc

o�Ys

oxj

� �� �ws �wsgs �

ogjsgs

oxjð3Þ

oqhotþ o

oxjðqh�ujÞ ¼

o

oxj

lPr

ohoxj

!�

oqjsgs

oxjð4Þ

The sub-grid-scale stress sij is defined by

sij � quiuj � q�ui�uj ð5Þ

For the SGS stress, two models are adopted. The first one is theSmagorinsky–Lilly (SL) eddy-viscosity model, which gives

sij �13skkdij ¼ �2lt

�Sij; �Sij �12

o�ui

oxjþ o�uj

oxi

� �; lt ¼ qL2

s j�Sj;

j�Sj � ð2�Sij�SijÞ1=2 ð6Þ

where Ls = min (jd, CsV1/3).

The second one is the dynamic kinetic energy (DKE) model,where the sub-grid-scale kinetic energy is defined asksgs ¼ 1

2 ðu2i � �u2

i Þ. The sub-grid-scale eddy viscosity, lt, is computedusing ksgs as lt ¼ Ckk1=2

sgs Df , where Df is the filter size computedfrom Df � V1/3. The sub-grid-scale stress can then be written as:sij � 2

3 ksgsdij ¼ �2Ckk1=2sgs Df

�Sij. ksgs is obtained by solving its transportequation:

o�ksgs

otþ o�uj

�ksgs

oxj¼ �sij

o�ui

oxj� Ce

k3=2sgs

Dfþ o

oxj

lt

rk

oksgs

oxj

� �ð7Þ

In the above-stated equations, the model constants, Ck and Ce,are determined dynamically and rk is taken as 1.0.

The sub-grid scale mass flux and heat flux are closed by gradi-ent modeling as

gjsgs ¼ qðujYs � �uj�YsÞ ¼

lt

rY

o�Ys

oxjð8Þ

qjsgs¼ qðujT � �uj

�TÞ ¼ lt

rT

o�Toxj

ð9Þ

where rY and rT are model constants, rY = rT = 1.0. The widelyused Germano dynamic stress model is not adopted here, becausethe comparison between the SL model and the DKE model is suffi-cient. �ws;wsgs are the filtered reaction rate and the SGS reactionrate of s species, respectively.

Three combustion models are used. The first one is the second-order moment (SOM) combustion model, proposed by the presentauthors [12] The Arrhenius expression of the chemical reactionrate of a global one-step reaction is

ws ¼ Bq2Y fuYox expð�E=RTÞ

and we have

�ws ¼ q2 �K �Yox�Y fu; �K ¼ B

Zexpð�E=R�TÞpð�TÞd�T ð10Þ

The SOM SGS combustion model, using a gradient modeling andexpressing the effect of small-scale temperature and species fluc-tuations on the SGS reaction rate, is given by

wsgs ¼ q2½�KðYoxY fu � �Yox�Y fuÞ þ �YoxðKY fu � �Y fu

�KÞþ �Y fuðKYox � �Yox

�K�

and the sub-grid scale correlation terms are given by the algebraicexpressions

UW� �U �W ¼ clto�Uoxj

� �o �Woxj

� ��q

asTþ ð1� aÞ

sC

� �� �ð11Þ

L.X. Zhou et al. / Fuel 87 (2008) 3123–3131 3125

where U and W denote Y1 or Y2 or K, sC is the chemical reactiontime, sT is the turbulent fluctuation time, a and c are model con-stants, taken as a = 0.9, c = 2.0 for swirling flames and c = 0.5 forjet and bluff-body flames. The reaction time and fluctuation timeare given by

sC ¼ Bqð�YO2 þ b�YCH4 Þ exp � ER�T

� �� ��1

; sT ¼ 1=j�Sj

where b is the stoichiometric coefficient.The second one is the fast-chemistry-presumed PDF combus-

tion model [13], in which a mixture fraction equation is used in-stead of Eq. (3) and Eq. (4), so we have

o

otðq�f Þ þ o

oxjðq�uj

�f Þ ¼ o

oxj

lSc

o�foxj

!� omjsgs

oxjð12Þ

where

mjsgs ¼ qðujf � �uj�f Þ ¼ lt

rf

o�foxj

; ff � f f ¼ 12

L2s jrf j2

A b-function PDF is taken for the p (f). All of the speciesconcentration and enthalpy are determined by the mixture fractionbased on local chemical equilibrium.

The third combustion model is the EBU combustion model [13],in which the reaction rate is given by

�ws þwsgs ¼ c1qek

min YCH4 ;YO2

b; c2

YP

1þ b

( )ð13Þ

where c1 = 4.0, c2 = 0.5. For LES, the turbulent fluctuation frequency

e/k is taken as a subgrid-scale one, e=k ¼ffiffiffiffiffiffiffiffiffiffiffiffi2SijSij

q. So we have

Fig. 1. A swirl combu

Fig. 2. A piloted jet flame (Sa

�ws þwsgs ¼ c1qjSjmin YCH4 ;YO2

b; c2

YP

1þ b

( )ð14Þ

where b = 4.For the methane–air and propane–air reaction mechanisms, the

global one-step reaction rates are given [14] as

wfu ¼ 2:119� 1011Y1:3ox Y0:2

fu expð�2:027� 108=RTÞ ð15Þwfu ¼ 1:0� 1010q2YoxY fu expð�1:84� 104=TÞ ð16Þ

In Eq. (15) for methane–air reaction, R is the universal gas constant,R = 8.32 KJ/kmol K.

3. Simulated combustors and numerical methods

The large-eddy simulation of turbulent diffusion and premixedcombustion was carried out for four different cases. Case 1 is themethane-air swirling diffusion combustion in a swirl combustorwith a central fuel inlet, measured in the Department of Engineer-ing Mechanics, Tsinghua University [15]. The geometrical configu-ration of this swirl combustor is shown in Fig. 1. Its sizes are:D1 = 8 mm, D2 = 10 mm, D3 = 30 mm, Df = 80 mm, Dout = 110 mm,Lf = 500 mm. The swirl number is 0.43; the air and methane inletflow rates are 8.9 m3/h and 0.8932 m3/h, respectively. The inlettemperature is 300 K. The grid sizes in x, y and z directions are1–2 mm. The total number of cells is 523,328. The mesh type ishexagonal. The time step is taken as 0.005 s. For the numerical pro-cedure, the pressure-implicit split-operator (PISO) algorithm isused for p-v corrections, the second order implicit differencescheme for the time-dependent term, and the central differencing

stor for Case 1.

ndia Flame C) for Case 3.

0 800 16000

1

2

3

4

R(c

m)

0 800 1600 0 800 1600 0 800 1600 0 800 1600

X=50 (cm)X=40X=27.5X=17.5X=10X=5

T(K)0 800 1600

EXP RANS-SOM LES-EBU LES-SOM

Fig. 3. Time-averaged temperature (Case1).

3126 L.X. Zhou et al. / Fuel 87 (2008) 3123–3131

difference scheme for the convection and diffusion terms areadopted.

Case 2 is the methane–air swirling diffusion combustion mea-sured in Ref. [16]. The shape and sizes of this swirl combustor canbe found in [16]. It has a bluff body of 50-mm-diameter(DB = 50 mm) with a central fuel jet of 3.6-mm diameter. Sur-rounding the bluff body is an annular tube of 60-mm-diameter

Fig. 4. Time-averaged temperature (Case 2).

for supplying the primary swirling air stream. Swirl is introducedinto the primary-air stream by three tangential inlets, each ofthem is 7 mm in diameter, and is located at 300 mm upstreamof the burner exit plane and inclined 15� upward to the horizon-tal plane. The burner assembly is mounted in a wind tunnel pro-viding a co-flowing secondary air stream of 20 m/s with a freestream turbulence level of around 2%. Pure CH4 is supplied fromthe central jet. The methane inlet velocity is 32.7 m/s. The axialannular air velocity is 38.2 m/s. The tangential annular air veloc-ity is 19.1 m/s. The central inlet Reynolds number is 7200. Theannular inlet Reynolds number is 75,900. The swirl number, de-fined as the ratio of the tangential momentum to the axialmomentum, is 0.5. The co-flow air velocity is 20 m/s. The inletair and fuel temperature is 300 K. The diameter is 100 mm andthe length is 250 mm for the three-dimensional computation do-main. The largest computational grid sizes in x, y and z directionsare 1.6 mm, and the smallest grid size in the reaction zone is0.5 mm. The mesh type is hexagon. The total number of grids is931,010. The time step is taken as 0.02 ms. The numerical proce-dure is the same as that for Case 1.

Case 3 is the piloted jet methane–air diffusion flame measuredin the Sandia Laboratory (Sandia Flame C) [17]. The geometricalconfiguration and sizes of the piloted jet flame are shown inFig. 2. The main jet is a mixture of 25% methane and 75% air in vol-ume and the bulk velocity is 29.7 m/s. The Reynolds number basedon the main jet is 13,400. The pilot nozzle diameter is 18.2 mm andthe pilot flow velocity is 6.8 m/s. The co-flow air velocity is 0.9 m/s.The grid sizes are taken as 0.5 mm near the nozzle (diameter7.2 mm) and the pilot (diameter 18.2) inlets, smaller than 2 mmin the reaction zone and 4 mm in other regions. The time step istaken as 0.001 ms for non-reacting flows and 0.0001 ms for react-ing flows. The numerical procedure is the same as that for Case 1.

Case 4 is the premixed propane–air combustion behind a bluffbody measured in Ref. [18]. The combustor geometry is shown inFig. 1 in Ref. [18]. The inlet velocity is 17 m/s, the inlet tempera-ture is 288 K, and the equivalence ratio of the propane-air mix-ture is 0.65. The maximum grid size is 0.5 mm, and the timestep is taken as 0.1 ms. The numerical procedure is the same asthat for Case 1.

Running the cases for swirling flames of Cases 1 and 2 usingSOM, simplified PDF and EBU combustion models in a 3G-CPU PCtakes about 40 days, 50 days and 35 days, respectively. For thejet flame using SOM combustion model, it takes about 20 days.For the bluff-body flame using SOM combustion model, it takesabout 60 days.

Fig. 5. RMS temperature fluctuation (K) (Case 2).

0

2

0 1000 20000

2

0 1000 20000

2

0 1000 20000

2

0 1000 20000

2

0 1000 20000

2

4

0 1000 20000

2

4

0 1000 20000

2

4

0 1000 20000

2

4

6

0 1000

x=1d

r/d

T (K)

x=2d x=75dx=60dx=3d x=7.5d x=15d x=30d x=45d EXP LES-SOM RANS-SOM

Fig. 6. Time-averaged temperature (Case 3).

L.X. Zhou et al. / Fuel 87 (2008) 3123–3131 3127

4. Statistical results and their experimental validation

Fig. 3 gives the time-averaged temperature for methane–airswirling combustion in Case 1, using both LES–SOM and LES–EBUcombustion models and also RANS–SOM modeling results in com-parison with experimental results. It is seen that both LES–SOMand RANS–SOM results are in good agreement with the experimen-tal results, and the LES–SOM results are better than the RANS–SOMresults at the cross sections of x = 5 and x = 10. Obviously, in mostregions the LES–SOM model is much better than the LES–EBU mod-el, which remarkably over-predicts the temperature. The reasonthat the EBU model gives bad results is that for most high temper-

ature regions it actually does not take the chemical kinetics intoaccount, and the reaction rate is determined only by turbulence.In case of not high velocities as for Case 1, the chemical kineticsplays important role. There are still some discrepancy betweenthe modeling results and the experiments near the inlet, whichmay be caused by the over-simplified one-step global chemicalkinetics.

Figs. 4 and 5 give the time-averaged temperature and RMS tem-perature fluctuation profiles for Case 2, respectively. It is seen thatin general the agreement is obtained between the LES results usingdifferent SGS models and the experiments. The reason is that forhigh velocity cases the chemical kinetics plays minor role, so

0

2

0 4000

2

0 5000

2

0 5000

2

4

0 5000

2

4

0 5000

2

4

6

0 5000

2

4

6

0 5000

2

4

6

0 5000

2

4

6

0 500

x=1d

r/d

Trms (K)

x=2d x=75dx=60dx=3d x=7.5d x=15d x=30d x=45d

EXP LES-SOM RANS-SOM

Fig. 7. RMS Temperature Fluctuation (K) (Case 3).

500 1000 1500

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

500 1000 1500

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

y

EXP

LES

T(K)

x=0.350x=0.150

Fig. 8. Time-averaged temperature (Case 4).

3128 L.X. Zhou et al. / Fuel 87 (2008) 3123–3131

different combustion models lead to smaller differences. However,among them, the KE+SOM model still gives better results thanother models and the SL+PDF model gives worst results.

The predicted statistically averaged temperature and RMStemperature fluctuation for the methane–air jet flame (Case 3)using LES–SOM and RANS-SOM models are given in Figs. 6 and7 respectively. It is seen that better agreement is obtained be-tween LES–SOM results and experiments. For the averaged tem-perature, at first five cross sections the RANS–SOM modelingresults are near to the LES–SOM and experimental results, butin the downstream region, the LES–SOM results are better thanRANS–SOM results. RANS–SOM modeling gives more uniform dis-tribution and faster temperature reduction than the measurementdoes, while the LES–SOM modeling gives obviously better results.

For RMS temperature fluctuation, the LES–SOM modeling resultsare in better agreement than the RANS–SOM modeling results.Two peaks can be correctly predicted by LES–SOM modeling, asshown in Fig. 7. The RANS–SOM modeling can predict the magni-tude of RMS values of temperature, but fails to give two peaks. Ingeneral, for using the same combustion model, the LES results arebetter than the RANS modeling results, so as for simulation ofnon-combusting turbulent flows. The reason is that the energy-carrying large eddies are more exactly simulated by LES thanthose simulated by RANS modeling.

Finally, the predicted time-averaged temperature for the pro-pane–air premixed combustion behind a bluff body (Case 4) usingthe LES–SOM model and its comparison with experiments is givenin Fig. 8. One can make the judgment that even for the premixed

Fig. 9. Instantaneous vorticity and temperature maps (Case 1).

L.X. Zhou et al. / Fuel 87 (2008) 3123–3131 3129

combustion behind a bluff body the LES–SOM model can still workvery well.

All of the above-stated examples of experimental validation ofLES statistical results convince us that generally speaking, theSOM combustion model can always give better results in LES ofboth non-premixed and premixed combustion, while the EBUand presumed PDF combustion models cannot always do. The rea-son is that the SOM combustion model can better account for boththe effect of turbulence and chemical kinetics, whereas other mod-els cannot well account for chemical kinetics.

5. Instantaneous results and discussion

Fig. 9 shows the instantaneous vorticity and temperature mapsfor methane–air swirling combustion of Case 1. It is seen that theoncoming flow from the central and annular inlets forms a strongshear layer. Many small vortices are formed around this shearlayer. The shear layer diffuses quickly; the vorticity is largest nearthe inlet and the large vortex structures formed in the upstream re-gion are quickly broken up. Comparison of the instantaneous tem-perature maps with the vortex structures shows that the flame islocated in the region of high shear. Obviously, the chemical reac-

Fig. 10. Instantaneous vorticity an

tion is intensified by the large-eddy structures in swirling flows.However, no distinct thin flame surface is observed. This impliesthat swirl thickens the flame front. Fig. 10 shows the instantaneousvorticity and temperature maps for methane–air swirling combus-tion of Case 2. In this case the large-size vortex structures are muchstronger than that in Case 1 due to the existence of a central bluffbody at the inlet. The flame structure is entirely different from thatof Case 1. The flame contracts to a neck region just near the exit ofthe swirl burner before its propagation. The combustion tempera-ture behind the neck region is the highest. Combustion occurs atthe outer edges of the shear layers. Fig. 11 gives the instantaneousvorticity surface and temperature map for methane-air piloted jetcombustion of Case 3. The typical strong coherent structures of jetflows are observed. For jet combustion, unlike swirling combus-tion, a thin flame-front structure is obvious. In the upstream re-gion, there is a thin flame front, whereas the vortices are rathersmall, and in the downstream region the large-size vortices areformed where the reaction is completed. Fig. 12 gives the instanta-neous vorticity and temperature isolines for propane–air premixedcombustion behind a bluff body of Case 4. The unsteady large-sizevortices behind the bluff body are observed; the vortex formationand shedding are clearly seen. Accordingly, combustion takes place

d temperature maps (Case 2).

Fig. 12. Instantaneous vorticity and temperature isolines (Case 4).

Fig. 11. Instantaneous vorticity surface and temperature map (Case 3)).

3130 L.X. Zhou et al. / Fuel 87 (2008) 3123–3131

at the edge of these vortices. The thin flame surface can also beseen here.

6. Conclusions

(1) Validation by experimental results shows that the SOM com-bustion model can always give better statistical results inLES of both non-premixed and premixed combustion,whereas the EBU and presumed PDF combustion modelscannot always give good results.

(2) Organized large vortex and thin flame surface structures areobserved in jet diffusion combustion and bluff-body stabi-lized premixed combustion.

(3) No organized vortex and thin flame surface structures areobserved in swirling diffusion combustion.

Acknowledgement

This study was sponsored by the National Natural ScienceFoundation of China under the Grant 50606026 and50736006.

References

[1] Smagorinsky J. General circulation experiments with the primitive equations. I.The basic experiment. Monthly Weather Rev 1963;91:99–164.

[2] Germano M, Piomelli U, Moin P, Cabot WH. A dynamic sub-grid-scale eddyviscosity model. Phys Fluids A 1991;3:1760–5.

[3] Kim WW, Menon S, Mongia HC. Large-eddy simulation of a gas turbinecombustor flow. Combust Sci Technol 1999;143:25–62.

[4] DesJardin PE, Frankel SH. Two-dimensional large eddy simulation of sootformation in the near-field of strongly radiating nonpremixed acetylene–airturbulent jet flame. Combust Flame 1999;119:121–3.

[5] Park N, Kobayashi T, Taniguchi N. Application of flame-wrinkling LEScombustion models to a turbulent premixed combustion around bluff body.In: Nagano Y, Hanjialic K, Tsuji T (editors), Proceedings of 3rd InternationalSymposium on Turbulence, Heat and Mass Transfer, Nagoya, Japan; 2000. p.847–54.

[6] McMurtry PA, Menon S, Kerstein AR. Linear eddy modeling of turbulentcombustion. Energy Fuels 1993;7:817–26.

[7] Renfro MW, Chaturvedy A, King GB. Comparison of OH time-seriesmeasurements and large-eddy simulations in hydrogen jet flames. CombustFlame 2004;139:142–51.

[8] Fureby C, Lokstrom C. Large-eddy simulation of bluff-body stabilized flames.In: Proceedings of 25th Symposium (International) on Combustion, TheCombustion Institute, Pittsburgh, PA; 1994. p. 1257–64.

[9] Jones WP. Large eddy simulation of turbulent combustion processes. ComputPhys Commun 2002;147:533–7.

[10] Mare FD, Jones WP, Menzies KR. Large eddy simulation of a model gas turbinecombustor. Combust Flame 2004;137:278–94.

L.X. Zhou et al. / Fuel 87 (2008) 3123–3131 3131

[11] Zhao JX, Yan YW. Large-eddy simulation of combusting flow field in anafterburner. J Eng Thermophys (in Chinese) 2004;25(Suppl.):237–9.

[12] Hu LY, Zhou LX, Zhang J. Large-eddy simulation of a swirling diffusion flameusing a SOM SGS combustion model. Numer Heat Transfer 2006;B50:41–58.

[13] Zhou LX. Theory and numerical modeling of turbulent gas-particle flows andcombustion. Florida: CRC Press; 2003. p. 165–76.

[14] Westbrook CK, Dryer FL. Simplified reaction mechanisms for the oxidation ofhydrocarbon fuels in flames. Combust Sci Technol 1981;27:31–43.

[15] Zhou LX, Chen XL, Zhang J. Studies on the effect of swirl on NO formation inmethane–air turbulent combustion. Proc Combust Inst 2003;29:2235–42.

[16] Masri AR, Kalt PAM, Barlow RS. The compositional structure of swirl-stabilizedturbulent nonpremixed flames. Combust Flame 2004;137:1–37.

[17] http://www.ca.sandia.gov/TNF/pilotedjet.html; 2003.[18] Giacomazzi E, Battaglia V, Bruno C. The coupling of turbulence and chemistry

in a premixed bluff-body flame as studied by LES. Combust Flame2004;138:320–35.