Transported PDF modelling with detailed chemistry of pre- and auto-ignition in CH 4 /air mixtures K. Gkagkas, R.P. Lindstedt * Department of Mechanical Engineering, Imperial College London, Exhibition Road, London SW7 2AZ, UK Abstract The pre- and auto-ignition behavior of methane under varying levels of preheat in a turbulent flow field has been studied through the combination of detailed chemistry with a transported PDF approach closed at the joint-scalar level. The study considers the Cabra Burner configuration, which consists of a central methane/air jet issuing into a vitiated co-flow. The aim of the work is to explore the detailed thermochem- ical flow structure and to substantially reduce uncertainties associated with the chemical kinetics. The applied chemistry features 44 solved species and 256 reactions and includes low temperature oxygen adducts. The mechanism has, in related work, been shown to reproduce the spontaneous temperature limit for methane and ethane along with ignition delays times at higher temperatures. Radiation is accounted for through the RADCAL method and the inclusion of enthalpy into the joint-scalar PDF. Molecular mixing is closed using the modified Curl’s model and a set of time–scale ratios (C / = 2.3, 2.5, 3.0 and 4.0) have been used to explore the model sensitivity. The impact on predictions of variations in the pilot stream com- position have been explored by varying concentrations of OH and H 2 over a wide range. A detailed anal- ysis of the flame structure, focusing on the chemical processes occurring before and during the ignition, suggests that the burner conditions lead to a classical auto-ignition pattern with the early formation of HO 2 and CH 2 O prior to ignition. The work suggests that, under the current conditions, flame stabilization is dominated by turbulence–chemistry interactions rather than by specific modes of flame propagation. The work shows a significant sensitivity to the pilot stream composition and that residual H 2 acts as an ignition promoter. However, the sensitivity to the time–scale ratio C / is shown to be less than can be expected from studies of flame extinction using the same methodology. Ó 2006 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Flame structures; PDF calculations; Detailed chemistry; Auto-ignition 1. Introduction The ability of calculation methods to repro- duce pre- and auto-ignition phenomena in turbu- lent flow fields is of fundamental importance in the context of flame stabilization and emerging technologies such as HCCI engines. Mastorakos et al. [1] performed DNS of auto-ignition in tur- bulent flows and compared the properties of the corresponding turbulent and laminar flames. Dif- ferences in the trends of auto-ignition were explained using the turbulent time- and length- scales along with partial premixing. Cabra et al. [2,3] introduced a simple burner geometry that permits the experimental study of auto-ignition and flame lift-off in a well-defined flow configura- tion. The burner consists of a co-axial fuel jet 1540-7489/$ - see front matter Ó 2006 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.proci.2006.08.078 * Corresponding author. Fax: +44 20 7589 3905. E-mail address: [email protected](R.P. Lindstedt). Proceedings of the Combustion Institute 31 (2007) 1559–1566 www.elsevier.com/locate/proci Proceedings of the Combustion Institute
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Proceedings
Proceedings of the Combustion Institute 31 (2007) 1559–1566
www.elsevier.com/locate/proci
of the
CombustionInstitute
Transported PDF modelling with detailed chemistryof pre- and auto-ignition in CH4/air mixtures
K. Gkagkas, R.P. Lindstedt *
Department of Mechanical Engineering, Imperial College London, Exhibition Road, London SW7 2AZ, UK
Abstract
The pre- and auto-ignition behavior of methane under varying levels of preheat in a turbulent flow fieldhas been studied through the combination of detailed chemistry with a transported PDF approach closedat the joint-scalar level. The study considers the Cabra Burner configuration, which consists of a centralmethane/air jet issuing into a vitiated co-flow. The aim of the work is to explore the detailed thermochem-ical flow structure and to substantially reduce uncertainties associated with the chemical kinetics. Theapplied chemistry features 44 solved species and 256 reactions and includes low temperature oxygenadducts. The mechanism has, in related work, been shown to reproduce the spontaneous temperature limitfor methane and ethane along with ignition delays times at higher temperatures. Radiation is accounted forthrough the RADCAL method and the inclusion of enthalpy into the joint-scalar PDF. Molecular mixingis closed using the modified Curl’s model and a set of time–scale ratios (C/ = 2.3, 2.5, 3.0 and 4.0) havebeen used to explore the model sensitivity. The impact on predictions of variations in the pilot stream com-position have been explored by varying concentrations of OH and H2 over a wide range. A detailed anal-ysis of the flame structure, focusing on the chemical processes occurring before and during the ignition,suggests that the burner conditions lead to a classical auto-ignition pattern with the early formation ofHO2 and CH2O prior to ignition. The work suggests that, under the current conditions, flame stabilizationis dominated by turbulence–chemistry interactions rather than by specific modes of flame propagation. Thework shows a significant sensitivity to the pilot stream composition and that residual H2 acts as an ignitionpromoter. However, the sensitivity to the time–scale ratio C/ is shown to be less than can be expected fromstudies of flame extinction using the same methodology.� 2006 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
Keywords: Flame structures; PDF calculations; Detailed chemistry; Auto-ignition
1. Introduction
The ability of calculation methods to repro-duce pre- and auto-ignition phenomena in turbu-lent flow fields is of fundamental importance inthe context of flame stabilization and emerging
1540-7489/$ - see front matter � 2006 The Combustion Institdoi:10.1016/j.proci.2006.08.078
technologies such as HCCI engines. Mastorakoset al. [1] performed DNS of auto-ignition in tur-bulent flows and compared the properties of thecorresponding turbulent and laminar flames. Dif-ferences in the trends of auto-ignition wereexplained using the turbulent time- and length-scales along with partial premixing. Cabra et al.[2,3] introduced a simple burner geometry thatpermits the experimental study of auto-ignitionand flame lift-off in a well-defined flow configura-tion. The burner consists of a co-axial fuel jet
ute. Published by Elsevier Inc. All rights reserved.
1560 K. Gkagkas, R.P. Lindstedt / Proceedings of the Combustion Institute 31 (2007) 1559–1566
issuing into hot combustion products from a leanpremixed hydrogen flame. The subsequent igni-tion occurs in the shear layer and the geometrypermits the detailed study of turbulence–chemis-try interactions.
Extensive measurements of H2/N2 jet flames inthe Cabra burner configuration [3–5] and relatedcalculations using transported PDF-based clo-sures have been performed by Masri et al. [6],Cabra et al. [3] and Cao et al. [7]. A range of mix-ing models and detailed or reduced chemicalkinetic mechanisms have been applied. Goodagreement between experimental and computa-tional results has been achieved and the studiessuggest that the flames are largely controlled bychemical kinetics. The transported PDF approachhas been shown to be able to capture extinctionand re-ignition processes in hydrocarbon flames[6,9–11]. However, Cao and Pope [13] have showna significant sensitivity to the applied chemistry aspart of a study of a range of piloted turbulent dif-fusion flames. Past studies of methane flames inthe Cabra configuration include that of Cabraet al. [8] who explored the influence of mixingmodels and boundary conditions. A perhaps sur-prising result was that the modified Curl’s model[12] was found to perform comparatively well.
The focus of the current study is on a detailedexamination of the thermochemical flow structureof methane/air flames in a vitiated co-flow [8]using a comprehensive detailed reaction mecha-nism that includes low-temperature chemistry.The sensitivity of predictions to boundary condi-tions, chemical rate constants and the time scaleratio are also explored.
2. The Cabra burner
The Cabra burner [3] consists of a fuel jet noz-zle and a surrounding perforated disk. The fuel jethas an inner diameter of D = 4.57 mm and a wallthickness of 0.89 mm. The disk has a diameter of210 mm and 2200 holes with a diameter of1.58 mm. Each hole stabilizes a premixed flameand thus provides a hot co-flowing stream. Thecentral fuel jet nozzle extends 70 mm downstreamof the plane of the perforated disk to ensureuniform co-flow properties.
The boundary conditions are presented inTable 1 along with other properties. Detailed singlepoint measurements of temperature and composi-tion were performed using the Raman–Rayleigh-LIF technique and mass fractions of CH4, N2, O2,H2O, OH, CO and CO2 were measured [2,8].
3. Computational details
The transported PDF approach of Lindstedtand co-workers [10,11,20] is used in the present
work. The joint-scalar PDF may be written asthe following random vector
~f /ð/a; f ;H ; xÞ ð1Þwhere /i with i = 1, . . .,a are the species massfractions of the gas phase and H is the enthalpyof the mixture. In the current hybrid approach,the flow field is closed at the second moment le-vel, using the pressure strain correlation fromSpeziale et al. [14]. A transport equation forthe composition PDF is coupled and solvedusing a Langrangian particle-based Monte Carlomethod [21].
A full detailed mechanism that includes low-temperature chemistry capable of reproducingthe spontaneous ignition of methane is used.The chemistry is based on the work of Lindstedtand Meyer [15] and extended by Rizos [16]. Themechanism consists of 256 reactions and the fol-lowing 44 species: CH4, H, H2O, O2, H2O2, O,OH, HO2, CO, CO2, C2H4, CH3, C2H2, CH3OH,C2H6, H2, CH2O, C2O, H2C2, CH3CHO, CH3CO,CH3OO, C2H4O, CH2CHO, C2H5OO, CH3O,CHO, 1CH2, CH2OH, C2H5OOH, CH3OOH,C2H5, C2H4OOH, C2H5O, CH, 3CH2, C2H,HCCO, CH2CO, C2H3, C1, C2, CH2CHO andN2 [17].
The radiative loss term is expressed on thebasis of the optically thin assumption [18] as out-lined by Lindstedt and Louloudi [19]. The turbu-lent transport of the PDF is modelled through agradient diffusion approximation with the ‘‘turbu-lent Prandtl number’’ (rt) set to unity. The secondmoment closure provides the scalar mixing timescale (s/) used in the transported PDF solutionprocedure via the modified Curl’s model [12]applied here.
s�1/ ¼
e�/g/002¼ C/
2
~�~k¼ C/
2s�1
T ð2Þ
In the above equation, e�/ is the scalar dissipationrate and g/002 the corresponding scalar variance. In
0
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T [
K]
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6040200 80 100x/D [-]
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0.8
1
f [-
]
20 40 60 80 100x/D [-]
0
0.05
0.1
0.15
0.2
T" [K
]f" [-]
Fig. 1. Temperature and mixture fraction statisticsalong the centerline. Lines correspond to computationsand symbols to measurements.
0
0.05
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0.25
YC
H4 [
-]
0
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YC
O [
-]
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0.08
YO
2 [-]Y
CO
2 [-]K. Gkagkas, R.P. Lindstedt / Proceedings of the Combustion Institute 31 (2007) 1559–1566 1561
the present work, C/ = 2.3 [11] is retained as abase case with 2.3 6 C/ 6 4.0 also explored.
3.1. Boundary conditions and solution details
The flow is treated as axi-symmetric and theboundary conditions were based on experimentaldata [2,4] as shown in Table 1. Boundary valuesfor minor species concentrations were computedbased on chemical equilibrium. For H2, the con-centration was set to correspond to the measure-ments taken one diameter downstream from thejet exit plane. The axial domain extends fromx/D = 0 to x/D = 100 and the (adaptive) radialdomain from r/D = 5 to approximately r/D = 15.A uniform velocity was used for the co-flow(r > D/2). The initial velocity profile (r < D/2) forthe fuel jet was derived by assuming a fully devel-oped turbulent pipe flow. The velocity co-variancewas specified via the correlation coefficient (quv).The values from Cao et al. [7], defined in termsof R ” D/2, were used. Between 0 6 r/R 6 1 a lin-ear variation of quv from 0 to 0.4 was assumed andfollowed by quv = 0.4 for 1 6 r/R 6 2.87 andquv = 0 for r/R > 2.87. The temperature and com-position profiles were set as step functions acrossthe inner diameter (D = 4.57 mm) of the nozzle.
0
600 20 4020 40 80 100
x/D [-]
0
0.001
0.002
0.003
YO
H [
-]
60 80 100
x/D [-]
0
0.001
0.002
0.003
0.004
YH
2 [-]
Fig. 2. Species mass fractions along the centerline. Linescorrespond to computations and symbols tomeasurements.
4. Computational results
Computations were performed with 80 and 140computational cells (Nc) in the radial direction,�1900 axial steps and with 120, 200 and 400expected stochastic particles (Np) per cell. No sig-nificant differences were observed as a result ofincreased refinement. The results shown belowcorrespond to Nc = 80 and Np = 120 unless other-wise indicated.
4.1. Centerline profiles
Comparisons between measurements and cal-culations of temperature, mixture fraction andvarious scalars along the central axis of the jetare shown in Figs. 1 and 2.
The centerline profiles of the Favre-averagedtemperature, mixture fraction and their fluctua-tions are shown in Fig. 1. Predictions of mean val-ues generally agree well with measurements andscalar fluctuations also show a satisfactory trend.The mean values for the mass fractions of CH4,O2, CO, CO2, H2 and OH along the centerlineare shown in Fig. 2. It can be seen that there argu-ably is an under-prediction of CO and an over-prediction of OH. However, the discrepanciesremain within experimental error.
The flow studied exhibits a two-stage behavior.Initially, the mixing process is dominant and thereis no apparent effect of chemical reaction. Thetemperature at the centre line is rising slowly, with
low levels of fluctuations, whereas the concentra-tions of CO, CO2 and OH remain negligible. Asthe flow progresses downstream, the first stage isfollowed by an ignition region, which is accompa-nied by strong temperature fluctuations and rap-idly increasing radicals concentrations. Theeffects of ignition become obvious at the centerlineat the axial position of x/D � 45.
4.2. Radial profiles
A better understanding of the ignition processrequires examination of the radial profiles of thevarious scalars. The radial profiles of the Favre-averaged temperature are shown in Fig. 3. Theagreement obtained for mean and rms values isgenerally good. It is obvious from the rise in tem-perature that ignition occurs between the axialdistances of x/D = 30 and x/D = 40. Untilx/D = 30 the effects of mixing dominate, whereasat x/D = 40 there is a distinct rise in the meantemperature above the co-flow level, as well asan increase in fluctuations.
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2000
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2000
T [
K]
4 60 2 2 48
r/D
0
500
1000
1500
2000
2500
6 8
r/D
x/D=1 x/D=15
x/D=30 x/D=40
x/D=50 x/D=70
Fig. 3. Radial profiles of Favre-averaged temperatureand temperature fluctuations with increased axial dis-tance. Solid lines correspond to calculated mean values,dashed lines to calculated RMS values, circles tomeasured mean values and squares to measured RMSvalues.
0.002
0.004
0.006
PDF
[-]
1000 1500 2000 2500 3000
T [K]
0
0.002
0.004
0.006
1000 1500 2000 2500 3000
T [K]
x/D=30 x/D=40
x/D=50 x/D=70
Fig. 5. The downstream evolution of the conditionaPDF of temperature. Lines correspond to calculationsand symbols to measurements (Np = 400).
0.0001
0.0002
0.0003
0.0005
0.001
0.0015
0.002
YO
H [
-]
r/D
0
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0.002
0.003
0 2 4 6 8 2 4 6 8
r/D
x/D=1 x/D=15
x/D=30 x/D=40
x/D=50 x/D=70
Fig. 6. Radial profiles of Favre-averaged OH massfractions with increased axial distance. Lines and sym-bols as in Fig. 3 (Np = 400).
1562 K. Gkagkas, R.P. Lindstedt / Proceedings of the Combustion Institute 31 (2007) 1559–1566
The radial profiles of the mixture fraction areshown in Fig. 4. The level of agreement betweenthe simulation and the experiment indicates agood representation of the mixing process. Theradial profiles generally show acceptable agree-ment at most axial positions. However, significantdifferences are observed for molecular hydrogenaround the point of ignition. The current calcula-tions do not account for upstream diffusion of H2
and an elliptic study of the flame could provehelpful. Nevertheless, the downstream evolutionof the conditional PDF of temperature is satisfac-torily predicted as shown in Fig. 5. The corre-sponding radial profiles for the hydroxyl radicalare shown in Fig. 6, where the scale is changedto more clearly show the level of agreementobtained. The OH radical is a good indictor of
0.2
0.4
0.6
0.8
1
0.1
0.2
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0.4
f [-
]
60 2 4 8 62 4 8
r/D
0
0.1
0.2
0.3
r/D
x/D=1 x/D=15
x/D=30 x/D=40
x/D=50 x/D=70
Fig. 4. Radial profiles of Favre-averaged mixture frac-tion and mixture fraction fluctuations with increasedaxial distance. Lines and symbols as in Fig. 3.
l
post-ignition chemical activity. In the calcula-tions, the maximum OH concentration appearsslightly shifted towards the co-flow region. Theimplication is that ignition appears to occur underslightly leaner conditions than recorded experi-mentally. It is also obvious that the OH levelsare somewhat higher than those measured but,as shown for the centerline, the discrepancies areprobably within experimental uncertainties.
4.3. Scatter and conditional plots in mixturefraction space
Scatter plots of temperature versus mixturefraction (Fig. 7) show the state of particles duringthe evolution of the flow and provide furtherinsight into the ignition process. At x/D = 30most particles reside on the mixing line betweenthe fuel and the oxidizer stream, with a fewparticles on the lean side indicating the onset of
500
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3000
T [
K]
0 0.2 0.4 0.6 0.8 1
f [-]
0
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1500
2000
2500
30000
0.2 0.4 0.6 0.8 1
f [-]
x/D=30
x/D=50
x/D=40
x/D=70
Fig. 7. Scatter plots of temperature versus mixturefraction with increased axial distance. The lines corre-spond to chemical equilibrium.
K. Gkagkas, R.P. Lindstedt / Proceedings of the Combustion Institute 31 (2007) 1559–1566 1563
chemical reaction. At x/D = 40, ignition is obvi-ous, with particles on the lean side reaching adia-batic temperatures. Further downstream, themajority of the particles have been fully burnt.
The conditional statistics can be very useful todepict the evolution of the ignition process by pro-viding insight into the scalar structure. Generallythe agreement obtained mirrors that shown inphysical space. However, the results for theensemble averages of YOH, shown in Fig. 8, doillustrate an interesting point. It can be seen thatimmediately after ignition, the computationalresults suggest that ignition initially occurs forlean to stoichiometric mixtures.
4.4. Sensitivity analysis
The base case simulation outlined above sug-gests that overall good agreement can be
0.0005
0.001
0.0015
0.002
YO
H [
-]
0 0.1 0.2 0.3 0.4 0.5 0.6
f [-]
0
0.001
0.002
0.003
0.004
0 0.1 0.2 0.3 0.4 0.5
x/D=30 x/D=40
x/D=50 x/D=70
Fig. 8. Evolution of the conditional ensemble average ofOH mass fraction. Solid lines correspond to calculationswith Np = 120, dashed lines to Np = 400 and circles tomeasurements.
obtained. However, it is also useful to investigatekey parametric sensitivities. In the present work,the effects of changes in the chemical compositionof the co-flow, variations of the co-flow tempera-ture and a variation in the time–scale ratio con-stant C/ are explored. Values of C/ = 2.3, 2.5,3.0 and 4.0 yield the corresponding H/D = 35.0,34.7, 34.0 and 31.2 at ignition. By increasing thevalue of C/, the mixing of the two streams isincreased, therefore leading to a shorter lift-offheight. However, the magnitude of change is suchthat it would appear that ignition is mainly chem-ically controlled with a comparatively modest sen-sitivity to changes in the time–scale ratio. Thisfinding is notably different from studies of flamesundergoing extinction where comparatively smallchanges can have a significant impact [9–11].
A sensitivity analysis was also performed onthe effect of the co-flow temperature on the lift-off height. Several criteria were used in order todefine the ignition point, including reference con-centrations of species like OH, CH2O and HO2.The results can be seen in Fig. 9, where compari-sons are made to the measurements of Cabra et al.[8]. The trend is arguably captured satisfactorilyand the choice of indicator does not affect therecorded ignition point strongly, especially forhigher initial temperatures. The different co-flowtemperatures can also be expected to impact theboundary conditions on species concentrations.
The effects of increasing concentrations of H2
and OH in the co-flow were investigated systemat-ically. Boundary condition values ofX H2
= 8.5 · 10�7, 1.4 · 10�4, 1.4 · 10�3 and1.4 · 10�2 yield the corresponding H/D = 49.0,44.0, 35.0 and 1.5 at ignition. Similarly, boundarycondition values of XOH = 2.0 · 10�5, 2.0 · 10�4
and 2.0 · 10�3 yield the corresponding H/D =35.0, 32.0 and 20.0. It is obvious that the ignitionpoint is very sensitive to OH and H2 concentra-tions in the co-flow.
1260 1280 1300 1320 1340 1360 1380
T [K]
10
20
30
40
50
60
70
80
H/D
Fig. 9. Effect of co-flow temperature on lift-off height asobtained with different indicator species: �: CH2O, � � �:OH, + ÆÆ +: HO2, �: measurements.
2.0E-051.6E-051.2E-058.0E-064.0E-060.0E+00
r/D
x/D
5 -10 -5 0 5 10 150
10
20
30
40
50
60
70
80
90
100
7.0E-045.6E-044.2E-042.8E-041.4E-040.0E+00
YCH2O
YHO2
-1
Fig. 11. Computed CH2O (left plot) and HO2 (rightplot) mass fractions (Np = 400).
1564 K. Gkagkas, R.P. Lindstedt / Proceedings of the Combustion Institute 31 (2007) 1559–1566
5. Analysis of pre- and auto-ignition chemistry
Species of particular relevance to ignitioninclude intermediates such as CH2O, HO2 andH2O2. The temperature is shown in Fig. 10 andthe HO2 radical field is shown in Fig. 11. Thebuild up of the latter species in the mixing regionis obvious, with the peak occurring in the area ofthe initial ignition position. The mass fraction issubsequently quickly reduced and it is obviousthat HO2, and H2O2, which has a similar concen-tration pattern, are crucial during the pre-ignitionphase. Their subsequent decomposition leads tothe formation of the hydroxyl radical, which trig-gers the high temperature chemistry. It can beseen from Fig. 10 that the concentration of theOH radical has a similar pattern to the tempera-ture field, shifted upstream and towards thecentreline.
The formation of formaldehyde is characteris-tic of the conversion of methane at lower temper-atures as shown in Fig. 11. It can be seen that themaximum concentration of CH2O is reached justbefore the flame front, and then quickly dropsas the high temperature burning process develops.It is evident that HO2 and CH2O play a crucialrole during the pre-ignition stage and create theproper conditions for the initiation of the hightemperature chemistry.
3.0E-032.4E-031.8E-031.2E-036.0E-040.0E+00
r/D
x/D
-15 - 10 -5 0 5 10 150
10
20
30
40
50
60
70
80
90
100
2100174013801020660300
T [K]
YOH
Fig. 10. Computed temperature (left plot) and OH(right plot) mass fraction (Np = 400).
5.1. Reaction path analysis
The pattern discussed above is consistent witha classical auto-ignition behavior and a study ofthe reaction paths and key sensitivities was per-formed to investigate the critical reactions con-trolling the pre- and auto-ignition process. Therelevant reaction rate constants are shown inTable 2.
In the pre-ignition region (20 6 x/D 6 50) theHO2 radical is formed mainly by reactions (5)and (34) with relative contributions of 47% and37%, respectively.
O2 + H (+ M) �HO2ðþMÞ ð5Þ
CHO + O2 �COþHO2 ð34Þ
Consumption of the HO2 radical is mainlythrough reactions (6) , (8) and (74) which contrib-ute 14%, 51% and 20%.
HO2 + H �OHþOH ð6Þ
HO2 + OH �H2OþO2 ð8Þ
CH3 + HO2 �CH3OþOH ð74Þ
Formaldehyde is formed via reactions (67),(81) and (85) which contribute 28%, 26% and17%. Reaction (81) is the dominant channel forCH3O decomposition.
17 CO + OH � CO2 + H 6.32E+03 1.5 -2.079 [24]34 CHO + O2 � CO + HO2 1.20E+07 0.807 �3.043 [26]35c CHO + M � CO + H + M 1.86E+14 �1.0 71.128 [27]60 CH2O + H � CHO + H2 1.26E+05 1.62 9.063 [24]62 CH2O + OH � CHO + H2O 3.43E+06 1.18 �1.87 [28]67 CH3 + O � CH2O + H 8.43E+10 0 0 [23]74 CH3 + HO2 � CH3O + OH 1.80E+10 0 0 [23]81 CH3O + M � CH2O + H + M 5.45E+10 0 56.5 [23]85 CH2OH + O2 � CH2O + HO2 4.56E�09 5.94 �18.99 [29]90 CH4 + OH � CH3 + H2O 1.56E+04 1.83 11.6 [28]
a Units are kmol, m3, s, K and kJ/mol.b Chaperon efficiencies are 2.0 for H2, 11.0 for H2O, 1.9 for CO, 3.8 for CO2, 0.4 for N2 and 1.0 for all other species.
Troe parameter is Fc = 0.5.c Chaperon efficiencies are 1.89 for H2, 6.5 for H2O, 2.5 for CO, 2.5 for CO2 and 1.0 for all other species.
K. Gkagkas, R.P. Lindstedt / Proceedings of the Combustion Institute 31 (2007) 1559–1566 1565
CH3 + O �CH2OþH ð67Þ
CH3O + M �CH2OþHþM ð81Þ
CH2OH + O2 �CH2OþHO2 ð85Þ
In the second region (30 6 x/D 6 60), wherethe maximum concentration of CH2O can befound, HO2 is consumed mainly by reactions (6),(8) and (74) which contribute 27%, 35% and 21%.
HO2 + H �OHþOH ð6Þ
HO2 + OH �H2OþO2 ð8Þ
CH3 + HO2 �CH3OþOH ð74Þ
Consumption of CH2O is mainly via reactions(60) and (62) which contribute 12% and 75%.Lindstedt and Meyer [15] found in their study ofCH3OH oxidation that reactions (60) and (62)exhibited similar sensitivities, but with oppositesigns.
CH2O + H �CHOþH2 ð60Þ
CH2O + OH �CHOþH2O ð62Þ
The OH radical is formed predominantly byreactions (1) and (4) which contribute 37% and22%.
H + O2 �OþOH ð1Þ
OH + OH �H2OþO ð4Þ
Finally, in the high temperature region(45 6 x/D 6 80) CO is formed through reactions(34) and (35) which contribute 12% and 53%.Reaction (17) is virtually the only consumptionpath.
CO + OH �CO2 þH ð17Þ
CHO + O2 �COþHO2 ð34Þ
1566 K. Gkagkas, R.P. Lindstedt / Proceedings of the Combustion Institute 31 (2007) 1559–1566
CHO + M �COþHþM ð35Þ
The main reaction paths indicate the crucialrole of CH2O and HO2 at the different pre-igni-tion stages.
A sensitivity analysis was performed by multi-plying and dividing the key reaction rate constantsidentified above by a factor of 5. The results areshown in Fig. 12. It is evident that the ignitionpoint is particularly sensitive to reactions (6), (8)and (62).
6. Conclusions
In the present work, a transported PDFapproach, closed at the joint-scalar level, is coupledwith a second moment closure for the velocity fieldand a detailed chemical mechanism featuring 44independent scalars to compute a CH4/air liftedflame. Extensive comparisons of the computedresults with experimental data illustrate the abilityof the current modeling approach to accuratelypredict the detailed thermochemical structure ofthe flame studied and the potential to predictauto-ignition phenomena. A comprehensive exam-ination of the different scalar fields was conducted,providing useful insight on the processes occurringduring the different stages of the flow. The mostimportant minor species during the pre-ignitionphase were identified and the crucial role of theH2, HO2 and CH2O chemistry was illustrated.The current approach is using a parabolic formula-tion and hence there is no mechanism for upstreampropagation of a turbulent edge flame. The resultsthus indicate that under the current conditions theflow may be described as a classical auto-ignitionevent in a turbulent flow field. The sensitivity ofresults to parametric variations in modeling con-stants and boundary conditions reveal a sensitivityto the latter. In particular, it appears that the pres-ence of H2 in the shear layer has a significant role inpromoting the onset of ignition.
Acknowledgment
The authors acknowledge the financial supportof BP Global Fuels Technology and are gratefulfor the interest shown by Dr C. Goodfellow, DrJ.T. Joseph, Dr R. Kay, Dr D.B. McLeary, DrI.A.B. Reid and Dr J.S. Rogerson.
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