Quantitative Laser Diagnostic and Modeling Study of C 2 and CH Chemistry in Combustion †

Quantitative Laser Diagnostic and Modeling Study of C2 and CH Chemistry inCombustion†

Markus Kohler,‡,§ Andreas Brockhinke,‡ Marina Braun-Unkhoff,§ andKatharina Kohse-Hoinghaus*,‡

Department of Chemistry, Bielefeld UniVersity, UniVersitatsstrasse 25, D-33615 Bielefeld, Germany, andInstitut fur Verbrennungstechnik, Deutsches Zentrum fur Luft- und Raumfahrt e.V. (DLR), Pfaffenwaldring38-40, D-70569 Stuttgart, Germany

ReceiVed: August 26, 2009; ReVised Manuscript ReceiVed: January 15, 2010

Quantitative concentration measurements of CH and C2 have been performed in laminar, premixed, flat flamesof propene and cyclopentene with varying stoichiometry. A combination of cavity ring-down (CRD)spectroscopy and laser-induced fluorescence (LIF) was used to enable sensitive detection of these specieswith high spatial resolution. Previously, CH and C2 chemistry had been studied, predominantly in methaneflames, to understand potential correlations of their formation and consumption. For flames of largerhydrocarbon fuels, however, quantitative information on these small intermediates is scarce, especially underfuel-rich conditions. Also, the combustion chemistry of C2 in particular has not been studied in detail, andalthough it has often been observed, its role in potential build-up reactions of higher hydrocarbon species isnot well understood. The quantitative measurements performed here are the first to detect both species withgood spatial resolution and high sensitivity in the same experiment in flames of C3 and C5 fuels. Theexperimental profiles were compared with results of combustion modeling to reveal details of the formationand consumption of these important combustion molecules, and the investigation was devoted to assist thefurther understanding of the role of C2 and of its potential chemical interdependences with CH and othersmall radicals.

Introduction

Small radicals are important intermediates in combustion.Selected diatomic molecules, including, for example, OH andCH, have attracted the interest of combustion chemists and laserdiagnosticians for a long time. On the one hand, these speciesare prominently involved in fuel consumption and oxidationreactions1 and pollutant formation2,3 and, on the other, they arequite readily detected with sensitive laser techniques.4–6 The OHradical is probably the most often detected reactive intermediatein combustion, which is due to its prominent role in the reactionmechanism of hydrocarbon flames, its relatively high concentra-tion and its well-known spectroscopy. CH has been discussedas a marker for the flame front because of its localizedoccurrence,7,8 and it is also of eminent interest because of itsinvolvement in prompt NO formation.2,3 It has thus been thesubject of numerous recent experimental studies,9,10 and itsconcentration in premixed methane flames can be predicted quitesuccessfully using established flame models.11 In contrast tothese often-studied diatomic hydrides, the role of the dicarbonmolecule C2 in combustion remains relatively unclear, althoughits emission has already been described in the 19th century.12

It is readily detected under fuel-rich conditions, and its chemistryand spectroscopy have been discussed in flames13–15 andinterstellar media.16,17 It is one of the simplest diatomics, which,unlike N2 or O2, is highly reactive but is not consideredparticularly important in the main combustion mechanism.

Renewed interest in these two small molecules, CH and C2,is seen for several reasons. Recent results concerning the NCNchannel18 have led to new considerations in the NOx formationmechanism, including reactions of the CH radical.19 Further-more, multiquantity imaging in turbulent flames20,21 has includedCH to monitor important features such as local extinction.Regarding the dicarbon molecule, complementary insight intoC2 chemistry has originated from studies devoted to the chemicalevolution of planetary atmospheres.22–24 While it seems thatsinglet C2 (X1Σ+

g) is a more reactive species than C2 in the(a3Πu) state, reactions of C2 with ethylene, acetylene, methyl-acetylene, allene, diacetylene, benzene, and other partners havebeen investigated both theoretically and experimentally.22–26

From the analysis of potential energy surfaces and rate coef-ficients at room temperature and below, it is reasoned that C2

could also be involved in molecular build-up reactions in flames,leading to polyacetylene radicals or to small polycyclic aromaticcompounds (PAHs). For example, butadiynyl radicals can beformed from the C2 (X1Σ+

g/a3Πu) reaction with acetylene, and1,3,5-hexatriynyl from the reaction of C2 (X1Σ+

g/a3Πu) withdiacetylene,22 while a sequence from the C2 reaction withbenzene could lead, for example, to 1,2-didehydronaphthalene.27

These and other reactions are currently not included in combus-tion mechanisms, and their potential influence on soot precursorchemistry remains elusive. It might also appear reasonable totreat the singlet and triplet forms of the dicarbon molecule astwo separate species, acknowledging different dynamics for thesinglet and triplet reactions.22 The relative importance of thesechannels under flame conditions is not evident, however, sinceboth X1Σ+

g and a3Πu states, with their small energy differenceof about 700 cm-1, are populated at combustion temperaturesbut may equilibrate rapidly through collisions.

† Part of the special section “30th Free Radical Symposium”.* Corresponding author. E-mail: [email protected].‡ Bielefeld University.§ Deutsches Zentrum fur Luft- und Raumfahrt e.V. (DLR).

J. Phys. Chem. A 2010, 114, 4719–4734 4719

10.1021/jp908242y 2010 American Chemical SocietyPublished on Web 02/05/2010

The occurrence of excited states of both molecules incombustion, including CH* (A2∆), CH* (B2Σ-), and C2* (d3Πg),introduces additional complexity. The chemistry of theseexcited-state intermediates is important to understand in orderto use their chemiluminescent emissions as intrinsic indicatorsfor the state of combustion, for the measurement of propertiessuch as local stoichiometry and heat release and consequentlyas low-cost sensors for active combustion control.28–32 Thedetection of CH and C2 in their ground electronic states andthat of chemiluminescent CH* and C2* have been typicallydiscussed independently, and reactions for the formation of thelatter are being introduced only recently into currentmechanisms.28,33,34

The consumption of these excited-state molecules occurs viachemical reaction as well as collisional deactivation, and ground-state CH and C2 are thus also products of the decay of theirchemiluminescent counterparts, CH* and C2*, respectively.Detailed mechanisms describing chemiluminescence emissionsshould thus include accurate predictions of both the excited-state and the corresponding ground-state molecules. It maytherefore be necessary, with respect to specific questions, todistinguish and consider six CH and C2 species, namely CH*(A2∆), CH* (B2Σ-), CH (X2Πr), C2* (d3Πg), C2 (a3Πu), and C2

(X1Σ+g), in combustion chemistry.

Since concentrations of chemiluminescent species are typi-cally quite small, it may be interesting to discuss the potentialthermal population of these excited states. Radiation near 520nm is needed to excite the C2 d3Πg state, corresponding to19 500 cm-1. With this, a thermal mole fraction for C2* of about10-6 can be estimated at 2000 K, higher than the mole fractionof chemiluminescent C2* that was determined to be about 20-30ppb in a low-pressure methane flame.34 By the same argument,thermal formation of excited-state CH (A2∆) with 23 000 cm-1

would be of the order of 10-8, which would represent aninsignificant thermal contribution to the chemiluminescent CH*mole fractions of a few ppm.35 An unambiguous assessment ofground- and excited-state concentrations appears thus desirable.The C2 concentration profile is highly localized in flames, similarto that of CH, and C2 might thus also qualify as a flame frontmarker in fuel-rich combustion, offering a different wavelengthrange and thus an extended choice of conditions for suchmeasurements. However, C2 signatures have also often beenseen as interferences in combustion diagnostics when fuel-richand sooting flames are probed with high laser intensities, as,e.g., in multiphoton excitation, coherent anti-Stokes Ramanscattering (CARS) or laser-induced incandescence (LII) experi-ments.36–38 To examine the influence of such perturbations andthe resulting amount and rate of photolytically produced radicals,an accurate determination of their natural background concen-trations would be favorable.

From multiple viewpoints, accurate measurements of CH andC2 concentrations and realistic modeling of their occurrence inflames of different fuels are thus considered beneficial. Quan-titative concentrations of CH and C2 have been determined ina variety of flames including ref 9, 34, and 38–46. Modelingattempts in methane flames have shown that the predictionquality of C2 profiles may be somewhat less favorable than forCH.34 Specifically, simulated profiles of C2 have been observedto decay less rapidly, as in the experiment, suggesting that C2

consumption reactions may be incompletely included or tooslow. Recently, CH and C2 chemistry has been revisited,46 andthe striking resemblance of CH and C2 profiles has beendiscussed from relative measurements in acetylene flames tobe a more general motif, which is supposed to be the result of

a common, rapidly interchanging radical pool. Although dif-ferent in chemical nature, including formation and consumptionpathways, the two molecules seem to be indirectly connected,and earlier observations by different authors are included in thisdiscussion to support the radical pool hypothesis.46

This intriguing behavior is examined here again with mea-surements of CH and C2 in flames of fuels of higher hydrocar-bons that have not been analyzed for this purpose. We havechosen fuel-rich propene-oxygen-argon and cyclopentene-oxygen-argon flames of varied stoichiometry at 50 mbar. Someflames of these fuels had been investigated before,47–49 and theyhave recently been modeled to study the formation of the firstaromatic rings.50–53 Careful quantitative measurements of bothintermediates are provided, using cavity ring-down spectroscopyand laser-induced fluorescence, and modeling of their profilesunder these conditions is attempted, including a discussion offormation and consumption chemistry.

Experiment

A combined CRDS and LIF experiment has been set up forthe investigations reported here, consisting of the laser anddetection systems and a low-pressure burner. Several aspectsrelevant for quantitative detection of CH and C2 by LIF andCRDS have been described in our previous work;54–56 however,a completely new apparatus has been configured here to alloweasy conversion between both techniques.

The laser system consists of an injection-seeded Nd:YAGpump laser (Spectra Physics LAB 150-10), which is frequency-tripled to pump a dye laser (Coherent ScanMate Pro). The pulse-to-pulse stability is 99% at the Nd:YAG fundamental frequency,and a bandwidth of 0.25 cm-1 is reached at 355 nm with a pulseenergy of 195 mJ. Suitable dyes were selected includingCoumarin 120 for the CH measurements near 23 000 cm-1 andCoumarin 500 for the C2 experiments near 19 400 cm-1.Absolute wavelength, bandwidth, and pulse energy are con-trolled with a wavemeter (Burleigh WA 550) and a digitalenergy detector (Gentec ED100A).

For the CRD measurements, the TEM00 mode is predomi-nantly selected using a Kepler telescope with two planar-convexlenses of +100 and +200 mm focal length and a pinhole asspatial filter positioned at the focus of the first lens. Theresonator is established between two spherical mirrors (radius500 mm) of 99.7% reflectivity (Laseroptik Garbsen) at a distanceof 700 mm. They are mounted on supports attached to the burnerhousing, which are adjustable by means of picomotors. The laserdiameter in the cavity is less than 0.5 mm. Signals are detectedwith a photomultiplier (Philips XP2020Q) and analyzed with a200 MHz digital oscilloscope (CompuScope 12,400). The dataacquisition and evaluation is performed with dedicated LabViewroutines. The system is readily interchangeable to LIF measure-ments by replacing the mirror supports with conventional portsand quartz windows, and the Kepler telescope by a combinationof Rochon and Fresnel prisms (Halle) to control energy andpolarization of the exciting laser pulse. The laser beam is focusedinto the flame with a diameter of 300 µm or less, depending ondesired spatial resolution. CH is excited in the B-X transitionand the fluorescence in the A-X system is detected at rightangles, collected with a spherical mirror (Edmund Optics, f )125 mm, d ) 125 mm) and focused onto the entrance slit of aspectrograph (Acton Research, SpectraPro 300i, 1800 lines/mm);it is registered with an intensified CCD camera (Theta Systems).Both LIF and CRDS were combined to measure the CH radicalprofiles. To excite CH near 390 nm, Quinolon 390 dye waspumped at 355 nm. The pulse energy was limited to below 130

4720 J. Phys. Chem. A, Vol. 114, No. 14, 2010 Kohler et al.

µJ to minimize potential saturation effects. This combinationof LIF and CRDS is advantageous to profit from the superiorspatial resolution of the LIF measurements as well as of thehigher sensitivity and more direct absolute calibration of theCRD experiments.

A separate LIF setup was used earlier to determine the flametemperature for all flames, doping NO (0.1%) as a tracer intothe flame gases. Radiation at 355 nm was generated with a Nd:YAG laser (LOT Oriel/Quantel Brilliant B) used to pump a dyelaser (Lambda Physik Scanmate 2E) with Coumarin 120, andNO was excited using the frequency-doubled output (BBO-I)in the range 225.46-225.72 nm, which permits us to accesstransitions with J′′ ) 12-42.

Spectra of CH and C2 were interpreted using LIFBASEsimulations,57 and NO spectra for the temperature analysis werefitted using a simulation program provided by Atakan et al.58

Premixed low-pressure flames at 50 mbar were stabilized ona home-built flat flame burner of 63.5 mm diameter placed ina vacuum housing. The burner featured a porous bronze matrixand was kept at 40 °C by means of thermostated watercirculation. All flames were diluted with argon at a mole fractionof 0.25. Gases were metered and controlled by mass flowcontrollers (Mykrolis Tylan FC/DFC 2900/2910), calibratedflows are in slm (standard liters per minute at 1013 mbar and0 °C). Cyclopentene was delivered using a thermostattedevaporator and flows were controlled with a syringe pump(Teledyne ISCO 500D). Flame conditions are given in Table1.

Simulation. For a simulation of the formation of smallaromatic compounds in premixed fuel-rich propene and cyclo-pentene low-pressure flames, we have recently examinedestablished flame mechanisms and analyzed some of the relevantreaction sequences preceding formation of the first and secondring.53 The mechanisms and approaches provided in that studyare used here as a starting point. Mole fractions �i of species ias a function of height h above the burner were calculated usingthe one-dimensional PREMIX code of the CHEMKIN pack-age,59 thermodynamic data from refs 60 and 61 and transportproperties from refs 62 and 63. The temperature profiles takenas input for the calculations are shown in Figure 1. For thesesimulations, the MIT mechanism of Howard and Richter64,65

already includes a small number of C2 formation and consump-tion reactions. This mechanism had also been used in ref 55 inanearlyattempt tomodel theC2 concentrationinapropene-oxygenflame with C/O ) 0.5, where it predicts a later peak andsignificantly slower decay while overestimating the peak C2

mole fraction. Also, the DLR mechanism (here termed “DLR2007”) was employed as described in ref 53, with the additionof very few C2 formation and consumption reactions (see Table

2) in analogy to those implemented in the MIT mechanism.The nucleus of the DLR mechanism had been established inref 67, and it has been continuously updated and improved;relevant literature is given in ref 53. To examine the potentialcontributions of further reactions concerning C2, CH, C2O, C3,and C3O2, an extended mechanism (termed “DLR 2009”) wasdeveloped that includes the reactions provided in Table 3. Thefollowing approach was used to compare measured and calcu-lated (total) C2. The experiment detects C2 via the (d-a)transition, and the mole fractions reflect total C2 under theassumption of electronic-state equilibration. The model does notdifferentiate between singlet and triplet C2 but calculates totalC2 as well. Since the more rapid decay of the experimentalprofiles presented in the results section suggested that fast decaychannels are needed in the model, we have also includedreactions that consider the rate coefficients for the more reactive

TABLE 1: Flame Conditionsa

fuel C/O Φfuel flow

(slm)O2 flow

(slm)Ar flow

(slm)

propene 0.4 1.2 0.71 2.64 1.120.5 1.5 0.84 2.51 1.120.6 1.8 0.96 2.39 1.120.7 2.1 1.07 2.28 1.120.77 2.3 1.14 2.21 1.12

cyclopentene 0.5 1.4 0.56 2.79 1.120.6 1.7 0.65 2.70 1.120.7 2.0 0.73 2.62 1.120.77 2.2 0.79 2.56 1.12

a All flames were investigated at 50 mbar and exhibited an argonmole fraction of 0.25 and a cold gas velocity of 50 cm/s.

Figure 1. Temperature profiles: top, propene; bottom, cyclopenteneflames.

TABLE 2: C2 Reactions Included in the DLR 2007Mechanism Described in Ref 53a

no. reaction Α n Ea ref

C2

FormationRe001 C2H + OH ) C2 + H2O 4.0 × 107 2 8000 66

ConsumptionRe002 C2 + H2 ) C2H +H 4.0 × 105 2.4 1000 66Re003 C2 + OH ) C2O + H 5.0 × 1013 0 0 66Re004 C2 + O2 ) 2CO 5.0 × 1013 0 0 66

a Rate coefficients are given as k ) ATn exp(-Ea/RT); units aregiven in cm, s, K; Ea is in cal mol-1.

C2 and CH Chemistry in Combustion J. Phys. Chem. A, Vol. 114, No. 14, 2010 4721

C2 (X1Σ+g) molecules as an upper limit for the triplet C2 species

detected in the experiment. The model thus treats total C2 andassumes the faster C2 (X) reaction rates for some consumption

reactions. This has been deemed attractive in view of additionalconsumption pathways which may lead to the formation ofhigher-molecular species.

TABLE 3: Reactions added in the DLR 2009 Mechanisma

no. reaction Α n Ea ref

C2

FormationR01 C2H + H ) C2 + H2 6.2 × 1013 0 17421.8 68R02 C2H + O ) C2 + OH 1.1 × 1013 0 0 46

ConsumptionR03 C2 + H2O ) C2H + OH 3.0 × 1012 0 0 69R04 C2 + O2 ) C2O + O 1.9 × 1014 0 8087.9 68R05 C2 + O ) CO + C 7.3 × 1014 0 12420.0 70R06 C2 + CH4 ) C3H3 + H 6.2 × 1013 -0.4 25.8 24R07 C2 + C2H2 ) C4H + H 1.14 × 1017 -1.1 153.0 24R08 C2 + C2H4 ) C4H3 + H 3.01 × 1016 -0.9 115.3 24R09 C2 + C2H6 ) C3H3 + CH3 1.69 × 1016 -0.9 87.4 24R10 C2 + C3H8 ) C3H2 + C2H6 2.35 × 1017 -1.3 186.8 24

CH

FormationR11 C + OH ) CH + O 2.41 × 1014 0 21759.8 46R12 CH2 + H ) CH + H2 1.20 × 1014 0 0 68R13 CH2 + OH ) CH + H2O 1.14 × 107 2 3000.7 34,11R14 CH2 + O ) CH + OH 4.82 × 1013 0 0 46,68R15 C2H + O ) CH + CO 1.20 × 1013 0 0 46,68R16 CHCO + O ) CH + CO2 2.95 × 1013 0 1112.8 68

ConsumptionR17 CH + H2O ) H2CO + H 4.58 × 1016 -1.4 0 68R18 CH + CO2 ) CHO + CO 6.63 × 107 1.5 715.4 68R19 CH + H ) C + H2 1.20 × 1014 0 0 68R20 CH + OH ) HCO + H 3.01 × 1013 0 0 46,34R21 CH + O2 ) HCO + O 8.43 × 1013 0 0 68R22 CH + O ) CO + H 3.98 × 1013 0 0 68

C2O

FormationR23 CHCO + H ) C2O + H2 2.40 × 1012 0 0 46R24 C2H + O ) C2O + H 1.50 × 1013 0 0 46,68R25 CHCO + O ) C2O + OH 1.80 × 1013 0 0 46,68

ConsumptionR26 O + C2O ) 2CO 5.0 × 1013 0 0 66R27 OH + C2O ) H + 2CO 2.0 × 1013 0 0 46R28 O2 + C2O ) CO + CO2 2.0 × 1013 0 5365.4 34R29 H2 + C2O ) CH2 + CO 4.0 × 1013 0 4570.6 34R30 OH + C2 ) C2O + H 2.0 × 1013 0 0 34R31 C2O + H2O ) HCCO + OH 2.4 × 1011 0 0 46R32 C2O + H ) CH + CO 4.8 × 1013 0 0 66R33 C2O + OH ) CHO + CO 1.98 × 1013 0 0 46R34 C2O ) C + CO2 2.4 × 1013 0 0 46

C3

FormationR35 C + C2H ) C3 + H 2.0 × 1016 -1 0 34R36 CH + C2 ) C3 + H 4.0 × 105 0 0 34R37 C3 + H2 ) C3H + H 4.0 × 105 2.4 43718.4 34R38 C2 + C2 ) C + C3 3.2 × 1014 0 0 68,70

ConsumptionR39 O + C3 ) CO + C2 5.0 × 1013 0 0 34R40 OH + C3 ) CO + C2H 2.0 × 1013 0 0 34R41 O2 + C3 ) CO2 + C2 9.0× 1012 0 21859.2 71

C3O2

FormationR42 C3O2 ) CO + C2O 1.5 × 1015 0 486.9 72R43 C3O2 + OH ) CO2 + HCCO 7.0 × 1012 0 10234.1 73R44 C3O2 + H ) CO + HCCO 7.8 × 1012 0 21819.5 74R45 C3O2 + O ) CO2 + C2O 2.5 × 1010 0 0 75

a Rate coefficients are given as k ) ATn exp(-Ea/RT); units are given in cm, s, K; Ea is in cal mol-1.


In an attempt to examine the predictive capability of this DLR2009 mechanism, most flame conditions were also simulatedon the basis of the GRI 3.0 mechanism11 which is consideredwell-established and validated, especially for methane combus-tion. The GRI 3.0 mechanism is not suited in its original versionto model the combustion chemistry of the propene and cyclo-pentene flames studied here, and it does also not includedicarbon chemistry. However, the main body of the GRI 3.0mechanism, including the C1- and C2-chemistry submechanisms,exhibits some differences from that of the DLR mechanism,and it is widely used in the community. It was thus consideredhelpful to use the original GRI 3.0 mechanism for methane flamepredictions and to include the additional reactions for propeneand cyclopentene combustion as well as dicarbon reactions fromthe DLR 2009 mechanism. This hybrid GRI-DLR 2009 mech-anism is then alternatively used for the prediction of CH andC2 mole fractions in the propene and cyclopentene flamesstudied here.

Results and Discussion

Absolute Concentrations. A monochromatic light pulsecoupled into the cavity of a CRDS experiment decreases inintensity because of mirror losses, scattering, and absorption.Light that exits the cavity decays monoexponentially with a ring-down time τ:

where L is the cavity length, c is the speed of light, T refers tomirror and scattering losses, and σ(ν) is the absorption crosssection of the absorber with the number density N, homoge-

neously distributed along the path length d. Mirror losses andscattering appear as the background of the spectrum and arerelated to the ring-down time τ0. One can therefore directlycalculate the absorption coefficient:

The number density N can be determined calibration-free withknown path length d and absorption cross section σ. The pathlength is given by the diameter of the flame, and the integratedabsorption cross section is calculated for the given transitionfrom

In this equation B12 is the Einstein coefficient, h is Planck’sconstant, ν0 is the transition frequency, f is the oscillator strength,e is the elementary charge, ε0 is the dielectric constant, m is themass of an electron, and c is the speed of light. The Boltzmannfactor fb relates the population in a specific ro-vibronic state tototal number densities and is calculated with the commonlyknown expression. Absolute number densities of C2 weredetermined using the d3Πg-a3Πu 0-0 P3(25) transition at 19 373cm-1; the oscillator strength f was taken from ref 76. CHconcentrations were measured using the A2∆-X2Πr 0-0 P1(8)transition at 22 967 cm-1 and the Einstein B12 coefficient andspectroscopic constants from ref 57. Quantitative mole fractionprofiles as a function of height above the burner derived fromCRDS measurements are presented in Figure 2 for the flames

Figure 2. CH and C2 mole fractions in propene and cyclopentene flames.

τ ) Lc(T + σ(ν)Nd)

(1)

σ(ν)Nd ) Lc (1

τ- 1

τ0) (2)

σ ) B12hν0 fb ) fe2

4ε0mc2fb (3)


of both fuels and of varying stoichiometry. The CH molefractions are on the order of 10-20 ppm, while those of the C2

molecule are, with 100-200 ppb, about 2 orders of magnitudelower. Measurement precision is 10-20% depending on theconcentration; the total uncertainty is estimated to be less thana factor of 2. Spatial divergence of the flame and flame curvatureeffects were not significant under our conditions, as monitoredfrom flame emission and LIF measurements. Both moleculeswere measured in the same setup and under identical conditions,and the spatial shape of their profiles can thus be comparedwith high accuracy. In the propene flames, the maximumconcentration for both molecules is generally found to coincidespatially, with at most 0.1 mm deviation between CH and C2

peak positions. In contrast, the C2 maximum precedes that ofCH by 0.2-0.7 mm in the cyclopentene flames with anincreasing difference observed in the richer flames. In agreementwith earlier work, the cyclopentene flames are stabilized at acloser distance to the burner surface, with the flame front forthe richer flames located at 3-4 mm in the cyclopentene flame,and near 5 mm in the propene flame.53 Consistently, CH andC2 profiles are observed to shift toward higher heights and tobroaden with increasing C/O ratio, with this trend being slightlymore prominent for C2.

Summary of Earlier Work. The general trends observedfor the CH and C2 profiles and the absolute magnitude of theconcentrations determined here can be compared with previousstudies. While CH has been measured quantitatively in premixedand diffusion flames at atmospheric and reduced pressure inflames of several fuels at various stoichiometries, studies thatreport absolute C2 concentrations are scarce, owed to the highersensitivity needed for measurements in the ppb range. Some ofthese experiments have been complemented with modeling.Since the very early investigations, including, for example, thosein refs 77–79, both experimental and modeling approaches havecome a long way, and we focus therefore on results from aboutthe past decade. Mercier et al.43 have reported mole fractionsof about 0.6 ppm of CH in atmospheric pressure methane-airdiffusion flames on a Wolfhard-Parker burner, and they havemeasured C2 in nonsooting and lightly sooting methane-airflames stabilized on the same burner in a later publication,38

with mole fractions of up to 6 ppb. Naik and Laurendeau44 havedetected CH in nonpremixed and partially premixed counterflowmethane-air flames and have observed levels of about 1 ppmor less, depending on the strain rate; the spatial location of theCH profiles was very well predicted, especially with GRImechanism 3.0. In slightly rich (Φ ) 1.1 and 1.2) premixedatmospheric-pressure methane-air flames, Evertsen et al.9 havefound CH concentrations of the order of (3-4) × 1012 cm-3.The maximum concentration increased slightly for the richerflame, as did the height above the burner at which the peakwas observed. Modeling with the GRI 3.0 mechanism (and withthe earlier 2.11 version) consistently predicted about a factorof 2 higher CH concentrations at positions distinctly (up to 0.3mm shift for a peak width of similar magnitude) further awayfrom the burner, and a decay that persisted longer than in theexperiments. Careful analysis of temperature and OH profilesshowed that this was not due to experimental uncertainties.

In an extensive study of 12 lean (Φ ) 0.7), stoichiometric(Φ ) 1.0), and rich (Φ ) 1.25) methane-air and ethane- andpropane-doped methane-air flames at 33 Torr, Pillier et al.39

have observed CH levels of 4-10 ppm. The profiles weregenerally quite well captured by calculations with the GRImechanism 3.0; a more detailed analysis shows, however, thatdeviations between experiment and model increase for the richer

flames, especially when they were doped (up to 1%) with higherhydrocarbons. Thoman and McIlroy41 have investigated severalmethane-oxygen-argon flames at 31 Torr (Φ ) 1.0, 1.2, 1.4,and 1.6) and used several mechanisms to simulate the experi-mental CH profiles. Peak CH mole fractions were between 8and 25 ppm and increased toward the richer flames; similarly,the position of the maximum increased for the richer flamestoward larger heights. The greatest discrepancies betweenexperiment and models are seen at the richest stoichiometrywhere all models predict a wider CH profile shifted further fromthe burner than experimentally observed. In a study of meth-ane-, ethane-, and ethene-air flames at 25-30 Torr, Smithet al.34 have analyzed absolute CH concentrations, measuredby LIF, with the GRI mechanism 3.0. The reported CH profilesin the rich methane flame were from Berg et al.40 Again, CHlevels increase from about 10-20 ppm, and profiles widen withricher stoichiometry; these trends are quite well predicted. Insome of the same flames, Smith et al.34 have measured C2

concentrations (of ∼30 ppb) along with those of chemilumi-nescent radicals. This seems to be the first time that profiles ofboth CH and C2 were given in the same flames for a variety ofconditions. CH is seen to precede C2 slightly, and in the richerflames, the C2 profiles widen more substantially in the simula-tions than in the experiments. Also, the position of the C2 peakis observed later, a trend that is more pronounced in the ethanethan in the methane flame.

A most recent investigation by Schofield and Steinfeld46 hasbeen devoted to the analysis of the combustion chemistry ofboth CH and C2. They have found good spatial correlation ofthe CH and C2 profiles in seven C2H2-O2-N2 flames withequivalence ratio Φ varying from 1.2 to 2.0; the CH profilesare observed to be slightly displaced versus those of C2 to longerreaction times. They state this to be the first consistent studyfor both molecules, which therefore permits them to performan in-depth analysis of pertinent kinetic pathways. A quantifica-tion of their profiles and a direct comparison with flamemodeling are, however, not given.

Summarizing previous work with relevance to the studyperformed here, observations are generally quite consistent. CHand C2 mole fractions under low-pressure premixed flameconditions are, respectively, of similar magnitude in methane,natural gas, ethane, and ethene flames, resembling those seenhere for propene and cyclopentene fuels. CH levels are a fewto a few tens of ppm, C2 mole fractions are about 2 orders ofmagnitude lower. The trends in peak positions and profile shapesnoted here are also consistent with earlier work. Models are inquite good agreement with experimental results for lean andstoichiometric methane flames; the discrepancies tend to becomelarger for richer flames, for higher hydrocarbon fuels (even ifadded in traces), and they are larger for C2 than for CH.

Comparison with Models. Before applying the flame modelsto the propene and cyclopentene flames studied here, we haveanalyzed the CH and C2 mole fractions in the slightly rich (Φ) 1.28, corresponding to C/O ) 0.32) low-pressure methane-airflame of Smith et al.34 The CH profile for this flame is alsoincluded in ref 34, but the original CH measurement andtemperature profile have been obtained about 5 years earlier byBerg et al.40 Figure 3 demonstrates that the modeling resultsobtained with the DLR 2009 mechanism for both species inthis flame agree similarly well with the measurements as theearlier simulations provided by the authors.34 Also, a simulationwas performed and included in the top panel of Figure 3 withthe original GRI 3.0 mechanism; however, this could not bedone for the C2 profile in the center panel, because the GRI


mechanism does not include C2. The CH profile from ref 34 iscaptured quantitatively by both models, and only a very minordisplacement to higher heights is seen. Similarly, good agree-ment of the C2 maximum mole fraction is obtained, but theprofile shows a slightly larger deviation in peak position and asomewhat slower decay with a displacement of about 1 mm athalf-maximum. In the original work,34 where the model wasbased upon the GRI mechanism 3.0 with inclusion of someadditional C2 reactions, the simulation overpredicts CH margin-ally, and the peak position is shifted slightly to higher heights.The decay from the model trails about 0.5 mm (at half-maximum) behind the experimental curve. The C2 profile fromthe original simulation34 shows good agreement for the peak

value, but the displacement is again around 0.4 mm at the peakand about 1 mm at half-maximum.

To examine the model simulations further, an even richermethane flame (Φ ) 1.6) was analyzed, and the results areincluded in the bottom panel of Figure 3. Again, temperaturewas obtained by NO-LIF (open symbols), and the CH molefractions (full symbols) were determined by CRDS. Simulationswith three model variants are displayed, including the originalGRI 3.0 mechanism (without C2 chemistry), the DLR 2009mechanism, and the hybrid GRI-DLR 2009 mechanism, whichincludes propene, cyclopentene, and C2 chemistry. The maxi-mum temperature in this flame is by about 150 K higher thanthat of ref 34, originally reported in ref 40. This highertemperature is in line with the discussion in ref 40 that heatrelease from the oxidation of CO to CO2 under low-pressureconditions is incomplete, and that the CO/CO2 ratio in flameswith higher fuel content is nearer to the adiabatic value.

The original GRI 3.0 mechanism overpredicts the experi-mental CH peak by about a factor of 1.7, whereas the DLR2009 mechanism overpredicts it by about a factor of 2.3; peakpositions and profile shapes are in reasonable agreement. Thehybrid GRI-DLR 2009 mechanism results are quite similar tothose of the original GRI mechanism, with a slight shift inmaximum position, however. Since this hybrid mechanism hasbeen constructed to simulate the CH and C2 mole fractions inthe propene and cyclopentene flames, this comparison showsthat the additions have not significantly affected its capabilityto predict CH in methane combustion. It should be noted,however, that the agreement in this richer flame is lesssatisfactory than in the Φ ) 1.28 flame of ref 34.

Next we have checked whether inclusion of the reactions inTable 3 has an effect on the general flame structure for thepropene and cyclopentene flames, which were analyzed in ourprevious work.53 Figure 4 shows simulations for several majorspecies, including acetylene, for both flames. For all cases, theDLR 2009 predictions are close to those with the DLR 2007mechanism.

Comparisons of the experimental results for CH and C2 forthe propene flames with C/O ) 0.5 and C/O ) 0.7 with thepredictions of both DLR mechanisms (DLR 2007 and DLR2009) are given in Figure 5, and analogous data for the twocyclopentene flames of these stoichiometries are presented inFigure 6; note that all simulated mole fractions are divided by2. Furthermore, simulations with the hybrid GRI-DLR 2009mechanism are also included. In spite of the good agreementin the slightly rich methane-air flame presented for the flamefrom refs 34 and 40 in Figure 3, substantial deviations are nowseen for both species in all four flames. Typically, the molefractions are overpredicted, and the C2 profiles persist longerin the simulations than in the experiments. These general trendsare also observed when the MIT mechanism is used (not shown).However, a general recommendation which mechanism per-forms best is not evident from Figures 5 and 6, regardingpositions of the maxima, shapes of the profiles and absolutemole fractions.

A closer inspection of Figures 5 and 6 reveals somedifferences. First, the performance of both DLR mechanisms(DLR 2007 and DLR 2009) will be discussed to examine theeffect of the additional reactions from Table 3. In the C/O )0.5 propene flame (Figure 5), the DLR 2009 mechanismprovides a larger deviation for CH than the DLR 2007mechanism, and this trend is even more pronounced in the richerpropene flame. Specifically, the maximum CH mole fraction inthe C/O ) 0.5 flame is about a factor of 3.4 (1.8) higher for the

Figure 3. Simulation of CH (top) and C2 profiles (center) in Φ )1.28 methane flame from Smith et al.34 with the DLR 2009 mechanismand GRI mechanism for C2. The bottom panel displays the experimentalmole fraction (from CRDS, squares) and temperature (from NO-LIF,circles) profiles for a Φ ) 1.60 methane flame; simulations areperformed with DLR 2009, GRI, and the hybrid GRI-DLR mechanisms.


DLR 2009 mechanism than in the experiment, and for the C/O) 0.7 flame it is about 2.8 (1) times that of the experiment;values in parentheses are for DLR 2007 mechanism.

The deviations for C2 are reversed, with the better predictionby the DLR 2009 mechanism; overprediction of the maxima isabout a factor of 2.6 (3.5) for the C/O ) 0.5 propene flame,and 2.3 (2.6) for the richer flame (Figure 5). Interestingly, theadditional reactions in Table 3 that are thought to affect the C2

consumption seem indeed to have a respective effect, althoughnot of the desired magnitude. These reactions certainly affectthe predictions of both molecules, although none of the twomechanisms provides completely realistic simulations. Thedecay of the CH profile is still better represented than that ofC2, which is more clearly evident from Figure 7, where theprofiles have been normalized to a common maximum.

The analysis for the corresponding cyclopentene flames inFigure 6 reveals that, again, CH is better predicted than C2.Ratios of model versus experiment for CH are within about afactor of 2; specifically 1.7 (1) for the C/O ) 0.5 flame and 2(0.7) in the C/O ) 0.7 flame (DLR 2007 mechanism inparentheses). For C2, the agreement with the absolute maximummole fraction observed in the experiment is again better for theDLR 2009 model (as for propene), with a factor of about 3.6(4.8) in the C/O ) 0.5 flame and 2 (2.5) in the richer flame.

Regarding the shapes of the profiles, the quality of thepredictions is evident from the normalized curves in Figure 7.Generally, the CH profiles are quite well represented in thepropene flames of different stoichiometry by both mechanisms,with a slightly improved prediction of the decay by the DLR2009 mechanism. A less favorable agreement is seen for the

Figure 4. Some stable species profiles in propene (a) and cyclopentene (b) flames at C/O ) 0.7 predicted using DLR 2007 and DLR 2009mechanisms.

Figure 5. Comparison of experimental (symbols) CH (top) and C2 (bottom) profiles in propene flames at C/O ) 0.5 (left) and C/O ) 0.7 (right)with simulation by DLR 2007 (dotted lines), DLR 2009, and hybrid GRI-DLR mechanisms (solid lines). Note that mole fractions from calculationshave been divided by 2.


Figure 7. Profiles of CH and C2 mole fractions in the C/O ) 0.5 and C/O ) 0.7 propene and cyclopentene flames, normalized to a commonmaximum value of 1.0 to facilitate comparison of the peak position and width. Symbols are from the experiment, dotted lines simulations with DLR2007, and solid lines are predictions with the DLR 2009 mechanism.

Figure 6. Comparison of experimental (symbols) CH (top) and C2 (bottom) profiles in cyclopentene flames at C/O ) 0.5 (left) and C/O ) 0.7(right) with simulation by DLR 2007 (dotted lines), DLR 2009, and hybrid GRI-DLR mechanisms (solid lines). Note that mole fractions fromcalculations have been divided by 2.


shapes of the CH profiles in the cyclopentene flames. The C2

profile peaks persists substantially longer in both models in theC/O ) 0.5 propene flame. This effect is even more visible inthe richer propene flame, but the difference between both modelsis rather small. For C2 in the cyclopentene flames, the trendsare quite similar, and in addition, the position of the peak isobserved at higher heights.

The simulation results exhibit some differences when thehybrid GRI-DLR 2009 mechanism is used. Remember that itwas in almost complete agreement with the original GRI 3.0mechanism when the CH profile is modeled in the Φ ) 1.6methane flame in Figure 3, exhibiting only a slight shift (∼0.3mm) in maximum position toward the burner. For CH in thepropene flames, the GRI-DLR mechanism overpredicts themaxima by a factor of 2.7 for C/O ) 0.5, and by a factor of 2.5for C/O ) 0.7; in the cyclopentene flames, the predictions arefactors of 1.3 and 1.5 higher for C/O ) 0.5 and C/O ) 0.7,respectively. From the absolute values, the hybrid GRI-DLRmechanism is thus in slightly better agreement than the DLR2009 mechanism (both include the additional reactions in Table3), but overall, the agreement for CH is best for the DLR 2007mechanism. Furthermore, the prediction of the peak positionsin the richer propene and cyclopentene flames with the hybridGRI-DLR mechanism is not satisfactory and exhibits shiftstoward the burner surface of 1.5-2 mm versus the experimentalmaxima.

For the prediction of absolute C2 mole fractions, the hybridGRI-DLR mechanism performs better than both DLR variants,with ratios of simulated to experimental maxima of 1.5 and 0.6in the C/O ) 0.5 and C/O ) 0.7 propene flames, respectively,and 2 and 0.85 in the C/O ) 0.5 and C/O ) 0.7 cyclopenteneflames. Positions of the C2 maxima, however, are less wellpredicted and precede the experimental one in the richer propeneflame and are observed at higher distances for the C/O ) 0.5propene and cyclopentene flames. Also for this mechanism, thedecay of the C2 profile is slower in the simulation than in theexperiment. In view of this overall not more convincingperformance of the hybrid GRI-DLR mechanism, the furtheranalysis is limited to the DLR 2007 and DLR 2009 mechanisms,with and without the additional reactions in Table 3, becausethis enables us to assess their effect more directly.

It is intriguing that the addition of the reactions in Table 3,especially with some potentially overestimated rate coefficientsfor C2 consumption (which were reported for the more reactivesinglet and not the experimentally observed triplet state), hasno dramatic effect on the width of the C2 profiles. Rather, ithas a noticeable influence on the width of the CH profiles andbrings them in better agreement with the experiment, at leastin the propene flames. In contrast, the maxima for CH show alarger deviation for the mechanism with additional CH, C2, C3,C2O, and C2O3 chemistry, whereas these additional reactionsprovide a better prediction for the C2 maxima. Remember alsothat CH and C2 were very well captured in absolute magnitudeand profile form by both mechanisms when the Φ ) 1.28methane flame from ref 34 was modeled (Figure 3).

The earlier observation of a strong correlation between CHand C2 chemistry, as discussed by Schofield and Steinberg46

could potentially provide a conceptual explanation, since theyargue that several small combustion intermediates including CHand C2 are rapidly interconverted in a common radical pool.To examine the argument of a surprisingly invariant relation ofthese two species described in ref 46, we have analyzed theratio of maximum mole fractions of CH and C2, �CH,max/�C2,max,in all investigated flames, expecting it for these reasons to be

nearly constant. Figure 8 shows these mole fraction ratios as afunction of C/O ratio for the experiment and the simulationswith DLR 2007, DLR 2009, and MIT mechanisms. Clearly,the experimental ratio is not constant, neither in the propenenor in the cyclopentene flames. Predictions with the MIT andDLR 2007 mechanisms show large differences, and the closestagreement with the experiment for both flames is seen for theDLR 2009 mechanism. Seemingly, the general trends of anypotential CH-C2 correlation are quite well represented with thismodel, with the remaining problem, however, that both inter-mediate concentrations, especially CH, are overpredicted andthat C2 is not removed fast enough. Further removal reactionsfor C2 could be conceived which would, under these fuel-richconditions, likely include buildup of larger hydrocarbons ratherthan oxidation, but so far, the slightly better agreement for C2

with the DLR 2009 mechanism has been paid with largerdeviations for CH. Also, such potential further reactions arenot needed for the simulation of both species profiles in themethane flame. To examine the influence of these and otherreactions in more detail, a reaction flux and sensitivity analysiswas performed for all three fuels. With deviations of a factorof 2-3 of the models from the experiment, this analysis is notintended to reveal potential influences of individual reactions,but it is deemed instructive for an overview of the generalformation and consumption patterns of the two intermediates.

Reaction Path and Sensitivity Analysis. Reaction flux andsensitivity coefficients for CH and C2 are shown in Figures9-12. They include analysis of the methane-air flame of Smithet al.34 of Φ ) 1.28 (C/O ) 0.32) at h ) 5 mm, thepropene-oxygen-argon flame of Φ ) 1.5 (C/O ) 0.5) at h )3 mm, and the cyclopentene-oxygen-argon flame with Φ )

Figure 8. Ratio of peak mole fraction of CH versus peak mole fractionof C2 as a function of C/O ratio: top, propene flames; bottom,cyclopentene flames.


1.4 (C/O ) 0.5) at h ) 3 mm. Note that the temperatures forthese flame conditions are somewhat different with approxi-mately 2000 K in the methane flame and approximately 2200K in the propene and cyclopentene flames.

Figure 9 shows the reaction flux for the formation andconsumption of CH to be not very different in the reaction zonein the three flames. CH is primarily formed from CH2 + H TCH + H2 (R12). Among the CH consumption channels, CH +H T C + H2 (R19) and CH + O2 T HCO + O (R21) seem tobe of almost similar importance. Other reactions of influencein the propene and cyclopentene flames include CH + C2H2TC3H2 + H and CH + CO2 T HCO + CO. C2O + H T CH +CO (R32) contributes to CH formation in the cyclopenteneflame; reaction numbers refer to Table 3. A direct involvementof the reactions added in the DLR 2009 mechanism is seen.

To rationalize the different level of agreement in the richflames of the three fuels, it can be argued that the formationsequence for CH is much more direct in the methane flame withCH4 f CH3 f

1CH2 f3CH2 f CH, with quite well-known

reaction coefficients for all steps. This is visualized in the toppanel of Figure 13 for the Φ ) 1.28 methane flame; the widthof the respective arrows and percentages indicated reflect therelative importance of the reactions. For the propene flames,more intermediate species and reactions with lesser well-knownrate coefficients are involved, with potential pathways leadingfrom C3H6 via C3H5, C3H4 (propyne), and C3H3 (propargyl) to

C3H2 and acetylene (see center panel of Figure 13). Alternativepathways include C2- and C4-intermediates. HCCO and acety-lene precede CH2 as predominant source for CH. The C3O2/C2O route is of minor influence under these conditions (C/O )0.5). The reaction network might be even more complex, andsome rate coefficients are less well-established for the rich (C/O) 0.5) cyclopentene flame (see bottom panel of Figure 13),where intermediate steps may start from C5H6 f C5H5 andisomerization reactions, with products C3H3 and C2H2. C3H3 maylead to C3H2, and further intermediate reactions may involveHCCO, C2H2, C2O, and CH2. Alternative routes involve manyhydrocarbon intermediates from C1- to C4-species. It is obviousthat CH2 is a very important precursor for the CH radical in theflames of all three fuels.

The inclusion of higher intermediates in the reaction channelsaffecting CH in the propene and cyclopentene flames is evidentfrom a sensitivity analysis, with sensitivities >10% given inFigure 10. In the methane flame, prominent reactions ofinfluence on CH formation and consumption include initiationchannels such as CH3 + O T CH2O + H and the chain-branching reaction O + H2T OH + H, the reaction coefficientsof which should be quite well-known. The pattern is morecomplex for the propene and cyclopentene flames where theCH3 + O reaction is of lesser importance and an influence ofthe chain-branching reaction is not seen. Predominant contribu-tions to CH consumption are seen from CH + H T C + H2

and CH + O2T HCO + O in all flames. Slightly less influential

Figure 9. Reaction flux analysis for CH in rich methane (a),34 propene(b), and cyclopentene (c) flames, predicted using the DLR 2009mechanism.

Figure 10. Sensitivity analysis for CH in rich methane (a),34 propene(b), and cyclopentene (c) flames, predicted using the DLR 2009mechanism.


reactions on CH consumption involve C3H3 and C3H2 in thepropene flame, and C3H2 and C2H2 in the cyclopentene flame;the reaction network for CH thus includes species that are notof primary importance in the methane flame. Further reactionswith the larger precursors of CH (compare Figure 13) contributewith sensitivities of a few percent (not shown in Figure 10).For the propene flame, these include, e.g., C2H2, HCCO, C3H4

(propyne), and C3H2 reactions, and for the cylcopentene flame,sensitivities toward further reactions with C3H3, C2H2, and C5H5

are seen above the 5% level.It is interesting to compare the analysis of the original authors

for the methane flame. Berg et al.40 have identified, amongothers, sensitivities of CH formation and consumption to CH+ H2 T H + CH2, CH + O2 T O + HCO, CH3 + O T H +CH2O, CH + H T C + H2, and O + H2 T H + OH. Thesensitive reactions are in good agreement with those seen inthe present work and again, mostly C1 species are involved.The same general conversion chain through the C1 route CH4

f CH3 f CH2 f CH is also discussed by Pillier et al.39 fortheir methane-air and ethane- and propane-doped methane-airflames. They attribute a slight decrease in CH concentrationfor the doped flames to be the consequence of the respectivedecrease in methane and the related C1 pathway. The too highCH concentrations seen in the present work might thus be aresult of the less direct formation and consumption pathwaysand the lesser accuracy for the many involved reaction steps.

Regarding the simulation of methyl, acetylene, and propargylin the propene and cyclopentene flames in ref 53, for example,with both DLR and MIT mechanisms, discrepancies in predict-ing position of the maxima, shape of the respective profiles andabsolute mole fractions remain s discrepancies that might alsobe of importance for some of the reactions identified above thatare sensitively involved in predicting the CH profiles.

A similar analysis of reaction flux performed for the dicarbonmolecule is given in Figure 11. All three flames show thedominant C2 formation pathway to be C2H + O T C2 + OH(Table 3, R02). Reaction R02 is less dominant in the propeneand cyclopentene flames, respectively, than in the methaneflame. To a lesser extent, O + C3 T C2 + CO is also involvedin the propene and cyclopentene flames. Consumption channelsfor C2 include C2 + O2 T 2CO (Table 2, Re004) as thedominant reaction for all fuels, followed by C2 + O2T C2O +O (Table 3, R04). Minor contributions are seen from OH + C2

T C2O + H. On first glance, there is no distinct difference forthe three fuels.

The sensitivity analysis that includes all reactions withsensitivities >10% is reported in Figure 12, and it reveals againa different pattern. Most of the reactions of importance for theC2 formation and consumption do not involve dicarbon directly,with the exception of C2H + OT C2 + OH in all three flamesand C2 + O2 T 2CO in the methane and cyclopentene flames.A common sensitive reaction for C2 formation is O + H2 T

Figure 11. Reaction flux analysis for C2 in rich methane (a),34 propene(b), and cyclopentene (c) flames, predicted using the DLR 2009mechanism.

Figure 12. Sensitivity analysis for C2 in rich methane (a),34 propene(b), and cyclopentene (c) flames, predicted using the DLR 2009mechanism.


OH + H. C2 consumption includes C2H2 + O T HCCO + H,with the strongest influence in the cyclopentene flame. Thepattern is different for the remaining reactions, involving specieslike CH3 and CH4 in the methane flame and C3H3 and C3H4

(propyne) in the propene flame. Further reactions involvingC3H2, C3H4 (propyne), and C3H5 show sensitivities of 4-7%.For the cyclopentene flame, further reactions with sensitivities>5% include species such as C3H3, C3H2, C4H4, C4H3, and C5H5.

It is not evident from this analysis that direct C2 consumptionchannels would be likely candidates to achieve a more rapidC2 decay in the propene and cyclopentene flames, as observedin the experiment. Under fuel-rich conditions, one would assumethat such reactions might lead to carbon buildup such astentatively included in R06-R10 (Table 3). To rationalize the

difference in predictive capability for methane versus propeneand cyclopentene flames, it is helpful to analyze the mainformation pathways toward the dicarbon molecule.

In the fuel-rich methane flame, C2 is formed predominantlyfrom C2H with O or from C2 with H2O. C2H results mainlyfrom C2H2 + OH, coming from the decay of C2H3, which isproduced via OH/H radical abstraction reactions from C2H4.C2H2, C2H3, and C2H4 can be formed through combinations ofC1 species and react with H and OH. CH3, CH2, and CH radicalsare involved in these pathways.

In the fuel-rich propene flame, the reaction of C2H with O ismore dominant, and C2H is mostly formed from C4H2 + H,which results from C4H4 as direct precursor and its decomposi-tion to C4H2 + H2. Various reactions contribute to C4H4

formation, and a larger number of C4, C3, C2, and C1 intermedi-ates are involved in the sequence that eventually yields C2. Thegeneral pattern is similarly complex in the fuel-rich cyclopenteneflame, involving analogous reactions with, however, quantita-tively different contributions. Generally, the fraction of reactionswith less well-known kinetic parameters involved in the C2

formation process is larger for the higher hydrocarbon fuels,and it is seemingly not a well-defined subset of reactions, whichis at the origin of the larger deviations of the model from theexperimental results. Improvement of the prediction of C2 inthe propene and cyclopentene flame will thus probably need

Figure 13. Schematic diagram illustrating the formation routes of CHin C/O ) 0.32 methane (top), C/O ) 0.5 propene (center), and C/O )0.5 cyclopentene (bottom) flames, following DLR 2009 mechanism.pC3H4 is propyne; C5H5 (oc) refers to open-chain isomers.

TABLE 4: Reactions Modified in the DLR 2009 MechanismAccording to Results of Sensitivity Analysis, for the PropeneFlame at C/O ) 0.5 as an Examplea

no. reaction modification

CH

DLR 2009 Modification aR019 CH + H ) C + H2 DLR 2009 × 5R021 CH + O2 ) HCO + O DLR 2009 × 3.75

DLR 2009 Modification bR019 CH + H ) C + H2 DLR 2009 × 5R021 CH + O2 ) HCO + O DLR 2009 × 3.75R528 C3H3 + H ) C3H2 + H2 DLR 2009 × 1.6

DLR 2009 Modification cR012 CH2 + H ) CH + H2 DLR 2009 × 0.5R019 CH + H ) C + H2 DLR 2009 × 5R021 CH + O2 ) HCO + O DLR 2009 × 2.92

C2

DLR 2009 Modification dR02 C2H + O ) C2 + OH DLR 2009 × 0.5R012 CH2 + H ) CH + H2 DLR 2009 × 0.5R019 CH + H ) C + H2 DLR 2009 × 5R021 CH + O2 ) HCO + O DLR 2009 × 2.92

DLR 2009 Modification eR02 C2H + O ) C2 + OH DLR 2009 × 0.5R012 CH2 + H ) CH + H2 DLR 2009 × 0.5R019 CH + H ) C + H2 DLR 2009 × 5R021 CH + O2 ) HCO + O DLR 2009 × 2.92R519 PC3H4 + H ) C2H2 + CH3 DLR 2009 × 0.5

DLR 2009 Modification fR02 C2H + O ) C2 + OH DLR 2009 × 0.5R012 CH2 + H ) CH + H2 DLR 2009 × 0.5R019 CH + H ) C + H2 DLR 2009 × 5R021 CH + O2 ) HCO + O DLR 2009 × 2.92R452 C2H + OH ) HCCO + H DLR 2009 × 2.5Re004 C2 + O2 ) 2CO DLR 2009 × 2R519 PC3H4 + H ) C2H2 + CH3 DLR 2009 × 0.5R538 C3H2 + O2 ) HCO + HCCO DLR 2009 × 2

a Rate coefficients are given relative to those of basis mechanism(DLR 2009).


attention to the reaction kinetics of most common HxCyOz

intermediates in fuel-rich combustion.To provide some perspective on potentially effective changes

that might decrease the absolute concentrations of bothmolecules, rate coefficients of several reactions were tentativelymodified. Different variants of the DLR 2009 mechanism wereused with the modifications a-f identified in Table 4. Groupsof reaction coefficients were changed especially for pathwaysfound to be sensitive in CH and C2 formation and removal. Theresults are shown in Figure 14 for the C/O ) 0.5 propene flame;note that simulated values are divided by 2. Modifications a-cinvolve CH reactions identified in Figure 10. Significantlyincreasing the rates for the two most sensitive CH consumptionchannels (modification a) decreases the CH mole fraction byabout a factor of 2, and an additional change of the reactionrate of propargyl with H-atoms (modification b) has only a minoreffect. Modification c additionally reduces the rate of the reactionthat is most sensitive regarding CH formation, again with asmall, but noticeable, improvement. Clearly, these variationsfor a few sensitive reactions are an improvement, but notsufficient to bring the simulated CH profiles into agreement withthe experiment.

Similarly, some reactions sensitively involved in C2 formationand consumption have been altered in addition (variants d-f),following the analysis in Figure 12. These results are shown inthe bottom panel of Figure 14. Modification d adds a decreasein the rate coefficient for C2H + O T C2 + OH (R02) to thechanges in variant c. Reaction R02 is the second most sensitivereaction in C2 formation after O + H2 (the kinetic parametersof which are well-known and should not be varied). Obviously,

the changes in c, intended to decrease the CH concentration,have not adversely affected the C2 mole fraction, and theaddition of R02 has a minor effect on the prediction of C2.Variant e reduces, again in addition to previous changes, therate coefficient for the reaction of propyne with H-atoms, foundto sensitively influence C2 formation in the propene flame. Thismodification has a slightly more noticeable effect. Further threereactions are added in variant f, which includes the consumptionof C2 with O2 to form CO, and two channels that involve HCCOand C3H2 as important species along the reaction sequence.

Such combined changes as in modification f do show thepotential to decrease the C2 mole fraction in the propene flame,in addition to that of the CH radical. However, even thesesuccessive and quite substantial modifications leave some roomfor further improvement, with the simulations still overpredictingthe experimental values by almost a factor of 2. This cor-roborates the analysis above that the problem is more complex,and that an in-depth analysis along the sequences of reactionsleading to CH and C2 in the propene and cyclopentene flameswould be necessary.

One recent interesting finding has addressed a novel type of“roaming” reaction mechanism80,81 that may lead to lower radicalconcentrations by providing access to stable products. If thisprinciple were of more general importance, also for some ofthe many reactions involving radicals in flames, smallerconcentrations could be expected for radicals thought to be theresult of long, chain-propagating series of reactions. It is notobvious that such reactions might be involved in mechanismsas discussed here, but it might be an interesting hypothesis topursue further in attempts to improve the predictive capabilityof combustion models.

Conclusions

Quantitative mole fractions of two interesting combustionintermediates, CH and C2, were measured in fuel-rich, premixedpropene-oxygen-argon and cyclopentene-oxygen-argon flamesat low pressure. Although these molecules are often detectedin laboratory-scale experiments, details of the chemistry thatdetermines their formation and depletion in flames are notsufficiently studied. Especially for the dicarbon molecule, whichis also of astrophysical interest, its low concentration has limitedhigh-precision studies. Previous work has been successful inmodeling the profiles of both species quantitatively in methanecombustion, with some deviations in very rich flames and foraddition of percent levels of C2- and C3-hydrocarbon fuels.Recent interest in C2 chemistry from planetary atmospheres hasprovided a number of studies of C2 reactions with largerhydrocarbon species that might also be effective in the buildupof polycyclic aromatic hydrocarbons and, eventually, soot, infuel-rich combustion. The striking similarity of CH and C2

profiles in flames has also inspired a recent investigation46 thatconcludes that a common radical pool must be the reason forthis seeming invariance of the CH-to-C2 relationship with flamecondition. The starting point for the present paper was thus anattempt of a better understanding of the elusive role of C2, thesmallest all-carbon molecule, in the chemistry of flames and ofits relation with CH, which has a key function in NOx formationfrom combustion processes.

Careful examination of the concentration profiles of bothmolecules with CRDS and LIF has permitted unambiguousassessment of the shapes and positions of maxima. Combustionmodeling was performed to analyze the underlying flamechemistry in detail. Several conclusions can be drawn from thiswork.

Figure 14. Comparison of experimental (symbols) CH (top) and C2

(bottom) profiles in propene flames at C/O ) 0.5 with simulation bythe DLR 2007 and DLR 2009 mechanisms. Further calculations areincluded with variants of the DLR 2009 mechanism (modified versionsa-f in Table 4). Note that mole fractions from calculations have beendivided by 2.


•Mole fractions of CH and C2 in a fuel-rich (Φ ) 1.28)methane flame of Smith et al.34 and Berg et al.40 are in excellentagreement with the present model.

•Mole fractions of CH in a Φ ) 1.60 methane flame areoverpredicted by the GRI mechanism, the DLR 2009 mechanismand a hybrid GRI-DLR 2009 mechanism that includes C2,propene, and cyclopentene chemistry.

•Mole fractions of CH and C2 in fuel-rich propene andcyclopentene flames are also overpredicted. The location of themaxima and the decay of the C2 profiles are not well capturedby the model. Inclusion of a number of CH- and C2-relatedreactions (DLR 2009 mechanism) has improved the predictedprofile shape for CH, but not influenced the too slow C2

consumption. Results are generally not more satisfying with thehybrid GRI-DLR 2009 mechanism. Potentially, a more rapidconsumption of precursors of C2 would assist in bringing theprediction closer to the experiment.

•Ratios of CH versus C2 maxima are not constant and arebest predicted by the DLR 2009 model.

•Reaction flux and sensitivity analyses reveal a more complexpattern of CH and C2 formation in the flames of higherhydrocarbons than for methane. CH is formed in the methaneflame through a C1-species sequence, and kinetic expressionsfor most of the sensitive reactions in the methane flame arequite well known. This is not the case for the C3 and C5 fuelswhere many intermediates are of importance for the pathwaystoward both molecules. Unless the species that precede theformation of these small intermediates are quantitativelycaptured by combustion models, a more complete understandingof the present discrepancies between experiment and modelscannot be expected. Because of the eminent role of CH in theNOx reaction network, the results suggest that increased attentionshould be devoted to improve the accuracy of many reactioncoefficients for small intermediate species if a similar predictivecapability is needed as in methane combustion.

Acknowledgment. K.K.H., A.B., and M.K. gratefully ac-knowledge partial support of this work by Deutsche For-schungsgemeinschaft within SFB 686 TP B3 and under contractKo 1363/18-3. They also thank Patrick Nau for his valuablecontributions to part of the data evaluation. Furthermore, helpfulassistance of Xing Xu with some model calculations is gratefullyacknowledged. Finally, K.K.H. thanks Jurgen Troe and RalfKaiser for helpful discussions on C2 chemistry; she is furthergrateful to Hanna Reisler and Curt Wittig for directing her tosome earlier work on C2.

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Quantitative Laser Diagnostic and Modeling Study of C 2 and CH Chemistry in Combustion †