Quantitative Laser Diagnostic and Modeling Study of C2 and CH

J. Phys. Chem. A 2010, 114, 4719–4734

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Quantitative Laser Diagnostic and Modeling Study of C2 and CH Chemistry in Combustion† Markus Ko¨hler,‡,§ Andreas Brockhinke,‡ Marina Braun-Unkhoff,§ and Katharina Kohse-Hoïnghaus*,‡ Department of Chemistry, Bielefeld UniVersity, UniVersita¨tsstrasse 25, D-33615 Bielefeld, Germany, and Institut fu¨r Verbrennungstechnik, Deutsches Zentrum fu¨r Luft- und Raumfahrt e.V. (DLR), Pfaffenwaldring 38-40, 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 flames of 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 species with high spatial resolution. Previously, CH and C2 chemistry had been studied, predominantly in methane flames, to understand potential correlations of their formation and consumption. For flames of larger hydrocarbon fuels, however, quantitative information on these small intermediates is scarce, especially under fuel-rich conditions. Also, the combustion chemistry of C2 in particular has not been studied in detail, and although it has often been observed, its role in potential build-up reactions of higher hydrocarbon species is not well understood. The quantitative measurements performed here are the first to detect both species with good spatial resolution and high sensitivity in the same experiment in flames of C3 and C5 fuels. The experimental profiles were compared with results of combustion modeling to reveal details of the formation and consumption of these important combustion molecules, and the investigation was devoted to assist the further understanding of the role of C2 and of its potential chemical interdependences with CH and other small radicals. Introduction Small radicals are important intermediates in combustion. Selected diatomic molecules, including, for example, OH and CH, have attracted the interest of combustion chemists and laser diagnosticians for a long time. On the one hand, these species are prominently involved in fuel consumption and oxidation reactions1 and pollutant formation2,3 and, on the other, they are quite readily detected with sensitive laser techniques.4–6 The OH radical is probably the most often detected reactive intermediate in combustion, which is due to its prominent role in the reaction mechanism of hydrocarbon flames, its relatively high concentration and its well-known spectroscopy. CH has been discussed as a marker for the flame front because of its localized occurrence,7,8 and it is also of eminent interest because of its involvement in prompt NO formation.2,3 It has thus been the subject of numerous recent experimental studies,9,10 and its concentration in premixed methane flames can be predicted quite successfully using established flame models.11 In contrast to these often-studied diatomic hydrides, the role of the dicarbon molecule C2 in combustion remains relatively unclear, although its emission has already been described in the 19th century.12 It is readily detected under fuel-rich conditions, and its chemistry and spectroscopy have been discussed in flames13–15 and interstellar media.16,17 It is one of the simplest diatomics, which, unlike N2 or O2, is highly reactive but is not considered particularly important in the main combustion mechanism. †

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

Renewed interest in these two small molecules, CH and C2, is seen for several reasons. Recent results concerning the NCN channel18 have led to new considerations in the NOx formation mechanism, including reactions of the CH radical.19 Furthermore, multiquantity imaging in turbulent flames20,21 has included CH to monitor important features such as local extinction. Regarding the dicarbon molecule, complementary insight into C2 chemistry has originated from studies devoted to the chemical evolution of planetary atmospheres.22–24 While it seems that singlet C2 (X1Σ+g) is a more reactive species than C2 in the (a3Πu) state, reactions of C2 with ethylene, acetylene, methylacetylene, allene, diacetylene, benzene, and other partners have been investigated both theoretically and experimentally.22–26 From the analysis of potential energy surfaces and rate coefficients 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 aromatic compounds (PAHs). For example, butadiynyl radicals can be formed from the C2 (X1Σ+g/a3Πu) reaction with acetylene, and 1,3,5-hexatriynyl from the reaction of C2 (X1Σ+g/a3Πu) with diacetylene,22 while a sequence from the C2 reaction with benzene could lead, for example, to 1,2-didehydronaphthalene.27 These and other reactions are currently not included in combustion mechanisms, and their potential influence on soot precursor chemistry remains elusive. It might also appear reasonable to treat the singlet and triplet forms of the dicarbon molecule as two separate species, acknowledging different dynamics for the singlet and triplet reactions.22 The relative importance of these channels under flame conditions is not evident, however, since both X1Σ+g and a3Πu states, with their small energy difference of about 700 cm-1, are populated at combustion temperatures but may equilibrate rapidly through collisions.

10.1021/jp908242y  2010 American Chemical Society Published on Web 02/05/2010

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The occurrence of excited states of both molecules in combustion, including CH* (A2∆), CH* (B2Σ-), and C2* (d3Πg), introduces additional complexity. The chemistry of these excited-state intermediates is important to understand in order to use their chemiluminescent emissions as intrinsic indicators for the state of combustion, for the measurement of properties such as local stoichiometry and heat release and consequently as low-cost sensors for active combustion control.28–32 The detection of CH and C2 in their ground electronic states and that of chemiluminescent CH* and C2* have been typically discussed independently, and reactions for the formation of the latter are being introduced only recently into current mechanisms.28,33,34 The consumption of these excited-state molecules occurs via chemical reaction as well as collisional deactivation, and groundstate CH and C2 are thus also products of the decay of their chemiluminescent counterparts, CH* and C2*, respectively. Detailed mechanisms describing chemiluminescence emissions should thus include accurate predictions of both the excitedstate and the corresponding ground-state molecules. It may therefore be necessary, with respect to specific questions, to distinguish 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 typically quite small, it may be interesting to discuss the potential thermal population of these excited states. Radiation near 520 nm is needed to excite the C2 d3Πg state, corresponding to 19 500 cm-1. With this, a thermal mole fraction for C2* of about 10-6 can be estimated at 2000 K, higher than the mole fraction of chemiluminescent C2* that was determined to be about 20-30 ppb 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 an insignificant thermal contribution to the chemiluminescent CH* mole fractions of a few ppm.35 An unambiguous assessment of ground- and excited-state concentrations appears thus desirable. The C2 concentration profile is highly localized in flames, similar to that of CH, and C2 might thus also qualify as a flame front marker in fuel-rich combustion, offering a different wavelength range and thus an extended choice of conditions for such measurements. However, C2 signatures have also often been seen as interferences in combustion diagnostics when fuel-rich and sooting flames are probed with high laser intensities, as, e.g., in multiphoton excitation, coherent anti-Stokes Raman scattering (CARS) or laser-induced incandescence (LII) experiments.36–38 To examine the influence of such perturbations and the resulting amount and rate of photolytically produced radicals, an accurate determination of their natural background concentrations would be favorable. From multiple viewpoints, accurate measurements of CH and C2 concentrations and realistic modeling of their occurrence in flames of different fuels are thus considered beneficial. Quantitative concentrations of CH and C2 have been determined in a variety of flames including ref 9, 34, and 38–46. Modeling attempts in methane flames have shown that the prediction quality of C2 profiles may be somewhat less favorable than for CH.34 Specifically, simulated profiles of C2 have been observed to decay less rapidly, as in the experiment, suggesting that C2 consumption reactions may be incompletely included or too slow. Recently, CH and C2 chemistry has been revisited,46 and the striking resemblance of CH and C2 profiles has been discussed from relative measurements in acetylene flames to be a more general motif, which is supposed to be the result of

Ko¨hler et al. a common, rapidly interchanging radical pool. Although different in chemical nature, including formation and consumption pathways, the two molecules seem to be indirectly connected, and earlier observations by different authors are included in this discussion to support the radical pool hypothesis.46 This intriguing behavior is examined here again with measurements of CH and C2 in flames of fuels of higher hydrocarbons that have not been analyzed for this purpose. We have chosen fuel-rich propene-oxygen-argon and cyclopenteneoxygen-argon flames of varied stoichiometry at 50 mbar. Some flames of these fuels had been investigated before,47–49 and they have recently been modeled to study the formation of the first aromatic rings.50–53 Careful quantitative measurements of both intermediates are provided, using cavity ring-down spectroscopy and laser-induced fluorescence, and modeling of their profiles under these conditions is attempted, including a discussion of formation and consumption chemistry. Experiment A combined CRDS and LIF experiment has been set up for the investigations reported here, consisting of the laser and detection systems and a low-pressure burner. Several aspects relevant for quantitative detection of CH and C2 by LIF and CRDS have been described in our previous work;54–56 however, a completely new apparatus has been configured here to allow easy conversion between both techniques. The laser system consists of an injection-seeded Nd:YAG pump laser (Spectra Physics LAB 150-10), which is frequencytripled to pump a dye laser (Coherent ScanMate Pro). The pulseto-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 pulse energy of 195 mJ. Suitable dyes were selected including Coumarin 120 for the CH measurements near 23 000 cm-1 and Coumarin 500 for the C2 experiments near 19 400 cm-1. Absolute wavelength, bandwidth, and pulse energy are controlled with a wavemeter (Burleigh WA 550) and a digital energy detector (Gentec ED100A). For the CRD measurements, the TEM00 mode is predominantly selected using a Kepler telescope with two planar-convex lenses of +100 and +200 mm focal length and a pinhole as spatial filter positioned at the focus of the first lens. The resonator is established between two spherical mirrors (radius 500 mm) of 99.7% reflectivity (Laseroptik Garbsen) at a distance of 700 mm. They are mounted on supports attached to the burner housing, which are adjustable by means of picomotors. The laser diameter in the cavity is less than 0.5 mm. Signals are detected with a photomultiplier (Philips XP2020Q) and analyzed with a 200 MHz digital oscilloscope (CompuScope 12,400). The data acquisition and evaluation is performed with dedicated LabView routines. The system is readily interchangeable to LIF measurements by replacing the mirror supports with conventional ports and quartz windows, and the Kepler telescope by a combination of Rochon and Fresnel prisms (Halle) to control energy and polarization of the exciting laser pulse. The laser beam is focused into the flame with a diameter of 300 µm or less, depending on desired spatial resolution. CH is excited in the B-X transition and the fluorescence in the A-X system is detected at right angles, collected with a spherical mirror (Edmund Optics, f ) 125 mm, d ) 125 mm) and focused onto the entrance slit of a spectrograph (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 radical profiles. To excite CH near 390 nm, Quinolon 390 dye was pumped at 355 nm. The pulse energy was limited to below 130

C2 and CH Chemistry in Combustion

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TABLE 1: Flame Conditionsa fuel

C/O

Φ

fuel flow (slm)

O2 flow (slm)

Ar flow (slm)

propene

0.4 0.5 0.6 0.7 0.77 0.5 0.6 0.7 0.77

1.2 1.5 1.8 2.1 2.3 1.4 1.7 2.0 2.2

0.71 0.84 0.96 1.07 1.14 0.56 0.65 0.73 0.79

2.64 2.51 2.39 2.28 2.21 2.79 2.70 2.62 2.56

1.12 1.12 1.12 1.12 1.12 1.12 1.12 1.12 1.12

cyclopentene

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

µJ to minimize potential saturation effects. This combination of LIF and CRDS is advantageous to profit from the superior spatial resolution of the LIF measurements as well as of the higher sensitivity and more direct absolute calibration of the CRD experiments. A separate LIF setup was used earlier to determine the flame temperature for all flames, doping NO (0.1%) as a tracer into the flame gases. Radiation at 355 nm was generated with a Nd: YAG laser (LOT Oriel/Quantel Brilliant B) used to pump a dye laser (Lambda Physik Scanmate 2E) with Coumarin 120, and NO was excited using the frequency-doubled output (BBO-I) in the range 225.46-225.72 nm, which permits us to access transitions with J′′ ) 12-42. Spectra of CH and C2 were interpreted using LIFBASE simulations,57 and NO spectra for the temperature analysis were fitted using a simulation program provided by Atakan et al.58 Premixed low-pressure flames at 50 mbar were stabilized on a home-built flat flame burner of 63.5 mm diameter placed in a vacuum housing. The burner featured a porous bronze matrix and was kept at 40 °C by means of thermostated water circulation. All flames were diluted with argon at a mole fraction of 0.25. Gases were metered and controlled by mass flow controllers (Mykrolis Tylan FC/DFC 2900/2910), calibrated flows are in slm (standard liters per minute at 1013 mbar and 0 °C). Cyclopentene was delivered using a thermostatted evaporator and flows were controlled with a syringe pump (Teledyne ISCO 500D). Flame conditions are given in Table 1. Simulation. For a simulation of the formation of small aromatic compounds in premixed fuel-rich propene and cyclopentene low-pressure flames, we have recently examined established flame mechanisms and analyzed some of the relevant reaction sequences preceding formation of the first and second ring.53 The mechanisms and approaches provided in that study are used here as a starting point. Mole fractions χi of species i as a function of height h above the burner were calculated using the one-dimensional PREMIX code of the CHEMKIN package,59 thermodynamic data from refs 60 and 61 and transport properties from refs 62 and 63. The temperature profiles taken as input for the calculations are shown in Figure 1. For these simulations, the MIT mechanism of Howard and Richter64,65 already includes a small number of C2 formation and consumption reactions. This mechanism had also been used in ref 55 in an early attempt to model the C2 concentration in a propene-oxygen flame with C/O ) 0.5, where it predicts a later peak and significantly slower decay while overestimating the peak C2 mole fraction. Also, the DLR mechanism (here termed “DLR 2007”) was employed as described in ref 53, with the addition of very few C2 formation and consumption reactions (see Table

Figure 1. Temperature profiles: top, propene; bottom, cyclopentene flames.

TABLE 2: C2 Reactions Included in the DLR 2007 Mechanism Described in Ref 53a no.

reaction

Α

n

Ea

ref

C2 Re001

Formation C2H + OH ) C2 + H2O 4.0 × 107

2

8000

66

Re002 Re003 Re004

Consumption C2 + H2 ) C2H +H 4.0 × 105 C2 + OH ) C2O + H 5.0 × 1013 C2 + O2 ) 2CO 5.0 × 1013

2.4 0 0

1000 0 0

66 66 66

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

2) in analogy to those implemented in the MIT mechanism. The nucleus of the DLR mechanism had been established in ref 67, and it has been continuously updated and improved; relevant literature is given in ref 53. To examine the potential contributions of further reactions concerning C2, CH, C2O, C3, and C3O2, an extended mechanism (termed “DLR 2009”) was developed that includes the reactions provided in Table 3. The following approach was used to compare measured and calculated (total) C2. The experiment detects C2 via the (d-a) transition, and the mole fractions reflect total C2 under the assumption of electronic-state equilibration. The model does not differentiate between singlet and triplet C2 but calculates total C2 as well. Since the more rapid decay of the experimental profiles presented in the results section suggested that fast decay channels are needed in the model, we have also included reactions that consider the rate coefficients for the more reactive

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Ko¨hler et al.

TABLE 3: Reactions added in the DLR 2009 Mechanisma no.

reaction

Α

n

Ea

ref

0 0

17421.8 0

68 46

0 0 0 -0.4 -1.1 -0.9 -0.9 -1.3

0 8087.9 12420.0 25.8 153.0 115.3 87.4 186.8

69 68 70 24 24 24 24 24

0 0 2 0 0 0

21759.8 0 3000.7 0 0 1112.8

46 68 34,11 46,68 46,68 68

-1.4 1.5 0 0 0 0

0 715.4 0 0 0 0

68 68 68 46,34 68 68

0 0 0

46 46,68 46,68

C2 R01 R02

C 2H + H ) C 2 + H 2 C2H + O ) C2 + OH

R03 R04 R05 R06 R07 R08 R09 R10

C2 C2 C2 C2 C2 C2 C2 C2

+ + + + + + + +

H2O ) C2H + OH O 2 ) C2O + O O ) CO + C CH4 ) C3H3 + H C 2H 2 ) C 4H + H C 2H 4 ) C 4H 3 + H C2H6 ) C3H3 + CH3 C 3H 8 ) C 3H 2 + C 2 H 6

Formation 6.2 × 1013 1.1 × 1013 Consumption 3.0 × 1012 1.9 × 1014 7.3 × 1014 6.2 × 1013 1.14 × 1017 3.01 × 1016 1.69 × 1016 2.35 × 1017 CH

R11 R12 R13 R14 R15 R16

C + OH ) CH + O CH2 + H ) CH + H2 CH2 + OH ) CH + H2O CH2 + O ) CH + OH C2H + O ) CH + CO CHCO + O ) CH + CO2

R17 R18 R19 R20 R21 R22

CH CH CH CH CH CH

+ + + + + +

H2O ) H2CO + H CO2 ) CHO + CO H ) C + H2 OH ) HCO + H O2 ) HCO + O O ) CO + H

Formation 2.41 × 1014 1.20 × 1014 1.14 × 107 4.82 × 1013 1.20 × 1013 2.95 × 1013 Consumption 4.58 × 1016 6.63 × 107 1.20 × 1014 3.01 × 1013 8.43 × 1013 3.98 × 1013 C2O

R23 R24 R25

CHCO + H ) C2O + H2 C2H + O ) C2O + H CHCO + O ) C2O + OH

Formation 2.40 × 1012 1.50 × 1013 1.80 × 1013

0 0 0

R26 R27 R28 R29 R30 R31 R32 R33 R34

O + C2O ) 2CO OH + C2O ) H + 2CO O2 + C2O ) CO + CO2 H2 + C2O ) CH2 + CO OH + C2 ) C2O + H C2O + H2O ) HCCO + OH C2O + H ) CH + CO C2O + OH ) CHO + CO C2O ) C + CO2

Consumption 5.0 × 1013 2.0 × 1013 2.0 × 1013 4.0 × 1013 2.0 × 1013 2.4 × 1011 4.8 × 1013 1.98 × 1013 2.4 × 1013

0 0 0 0 0 0 0 0 0

0 0 5365.4 4570.6 0 0 0 0 0

-1 0 2.4 0

0 0 43718.4 0

34 34 34 68,70

0 0 0

0 0 21859.2

34 34 71

0 0 0 0

486.9 10234.1 21819.5 0

72 73 74 75

66 46 34 34 34 46 66 46 46

C3 R35 R36 R37 R38

C + C 2H ) C 3 + H CH + C2 ) C3 + H C3 + H2 ) C3H + H C2 + C2 ) C + C3

Formation 2.0 × 1016 4.0 × 105 4.0 × 105 3.2 × 1014

R39 R40 R41

O + C3 ) CO + C2 OH + C3 ) CO + C2H O2 + C3 ) CO2 + C2

Consumption 5.0 × 1013 2.0 × 1013 9.0× 1012 C 3O 2

R42 R43 R44 R45 a

C 3O 2 C3O2 C3O2 C3O2

) + + +

CO + C2O OH ) CO2 + HCCO H ) CO + HCCO O ) CO2 + C2O

Formation 1.5 × 1015 7.0 × 1012 7.8 × 1012 2.5 × 1010

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

C2 (X1Σ+g) molecules as an upper limit for the triplet C2 species detected in the experiment. The model thus treats total C2 and assumes the faster C2 (X) reaction rates for some consumption

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



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

In an attempt to examine the predictive capability of this DLR 2009 mechanism, most flame conditions were also simulated on the basis of the GRI 3.0 mechanism11 which is considered well-established and validated, especially for methane combustion. The GRI 3.0 mechanism is not suited in its original version to model the combustion chemistry of the propene and cyclopentene flames studied here, and it does also not include dicarbon chemistry. However, the main body of the GRI 3.0 mechanism, 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 considered helpful to use the original GRI 3.0 mechanism for methane flame predictions and to include the additional reactions for propene and cyclopentene combustion as well as dicarbon reactions from the DLR 2009 mechanism. This hybrid GRI-DLR 2009 mechanism is then alternatively used for the prediction of CH and C2 mole fractions in the propene and cyclopentene flames studied here.

neously distributed along the path length d. Mirror losses and scattering appear as the background of the spectrum and are related to the ring-down time τ0. One can therefore directly calculate the absorption coefficient:

Results and Discussion

In this equation B12 is the Einstein coefficient, h is Planck’s constant, ν0 is the transition frequency, f is the oscillator strength, e is the elementary charge, ε0 is the dielectric constant, m is the mass of an electron, and c is the speed of light. The Boltzmann factor fb relates the population in a specific ro-vibronic state to total number densities and is calculated with the commonly known expression. Absolute number densities of C2 were determined using the d3Πg-a3Πu 0-0 P3(25) transition at 19 373 cm-1; the oscillator strength f was taken from ref 76. CH concentrations were measured using the A2∆-X2Πr 0-0 P1(8) transition at 22 967 cm-1 and the Einstein B12 coefficient and spectroscopic constants from ref 57. Quantitative mole fraction profiles as a function of height above the burner derived from CRDS measurements are presented in Figure 2 for the flames

Absolute Concentrations. A monochromatic light pulse coupled into the cavity of a CRDS experiment decreases in intensity because of mirror losses, scattering, and absorption. Light that exits the cavity decays monoexponentially with a ringdown time τ:

τ)

L c(T + σ(ν)Nd)

(1)

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

σ(ν)Nd )

(

L 1 1 c τ τ0

)

(2)

The number density N can be determined calibration-free with known path length d and absorption cross section σ. The path length is given by the diameter of the flame, and the integrated absorption cross section is calculated for the given transition from

σ ) B12hν0 fb ) f

e2 fb 4ε0mc2

(3)

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of both fuels and of varying stoichiometry. The CH mole fractions are on the order of 10-20 ppm, while those of the C2 molecule are, with 100-200 ppb, about 2 orders of magnitude lower. Measurement precision is 10-20% depending on the concentration; the total uncertainty is estimated to be less than a factor of 2. Spatial divergence of the flame and flame curvature effects were not significant under our conditions, as monitored from flame emission and LIF measurements. Both molecules were measured in the same setup and under identical conditions, and the spatial shape of their profiles can thus be compared with high accuracy. In the propene flames, the maximum concentration for both molecules is generally found to coincide spatially, with at most 0.1 mm deviation between CH and C2 peak positions. In contrast, the C2 maximum precedes that of CH by 0.2-0.7 mm in the cyclopentene flames with an increasing difference observed in the richer flames. In agreement with earlier work, the cyclopentene flames are stabilized at a closer distance to the burner surface, with the flame front for the richer flames located at 3-4 mm in the cyclopentene flame, and near 5 mm in the propene flame.53 Consistently, CH and C2 profiles are observed to shift toward higher heights and to broaden with increasing C/O ratio, with this trend being slightly more prominent for C2. Summary of Earlier Work. The general trends observed for the CH and C2 profiles and the absolute magnitude of the concentrations determined here can be compared with previous studies. While CH has been measured quantitatively in premixed and diffusion flames at atmospheric and reduced pressure in flames of several fuels at various stoichiometries, studies that report absolute C2 concentrations are scarce, owed to the higher sensitivity needed for measurements in the ppb range. Some of these experiments have been complemented with modeling. Since the very early investigations, including, for example, those in refs 77–79, both experimental and modeling approaches have come a long way, and we focus therefore on results from about the past decade. Mercier et al.43 have reported mole fractions of about 0.6 ppm of CH in atmospheric pressure methane-air diffusion flames on a Wolfhard-Parker burner, and they have measured C2 in nonsooting and lightly sooting methane-air flames stabilized on the same burner in a later publication,38 with mole fractions of up to 6 ppb. Naik and Laurendeau44 have detected CH in nonpremixed and partially premixed counterflow methane-air flames and have observed levels of about 1 ppm or less, depending on the strain rate; the spatial location of the CH profiles was very well predicted, especially with GRI mechanism 3.0. In slightly rich (Φ ) 1.1 and 1.2) premixed atmospheric-pressure methane-air flames, Evertsen et al.9 have found CH concentrations of the order of (3-4) × 1012 cm-3. The maximum concentration increased slightly for the richer flame, as did the height above the burner at which the peak was observed. Modeling with the GRI 3.0 mechanism (and with the earlier 2.11 version) consistently predicted about a factor of 2 higher CH concentrations at positions distinctly (up to 0.3 mm shift for a peak width of similar magnitude) further away from the burner, and a decay that persisted longer than in the experiments. Careful analysis of temperature and OH profiles showed 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- and propane-doped methane-air flames at 33 Torr, Pillier et al.39 have observed CH levels of 4-10 ppm. The profiles were generally quite well captured by calculations with the GRI mechanism 3.0; a more detailed analysis shows, however, that deviations between experiment and model increase for the richer

Ko¨hler et al. flames, especially when they were doped (up to 1%) with higher hydrocarbons. Thoman and McIlroy41 have investigated several methane-oxygen-argon flames at 31 Torr (Φ ) 1.0, 1.2, 1.4, and 1.6) and used several mechanisms to simulate the experimental CH profiles. Peak CH mole fractions were between 8 and 25 ppm and increased toward the richer flames; similarly, the position of the maximum increased for the richer flames toward larger heights. The greatest discrepancies between experiment and models are seen at the richest stoichiometry where all models predict a wider CH profile shifted further from the burner than experimentally observed. In a study of methane-, ethane-, and ethene-air flames at 25-30 Torr, Smith et al.34 have analyzed absolute CH concentrations, measured by LIF, with the GRI mechanism 3.0. The reported CH profiles in the rich methane flame were from Berg et al.40 Again, CH levels increase from about 10-20 ppm, and profiles widen with richer stoichiometry; these trends are quite well predicted. In some of the same flames, Smith et al.34 have measured C2 concentrations (of ∼30 ppb) along with those of chemiluminescent radicals. This seems to be the first time that profiles of both CH and C2 were given in the same flames for a variety of conditions. CH is seen to precede C2 slightly, and in the richer flames, the C2 profiles widen more substantially in the simulations than in the experiments. Also, the position of the C2 peak is observed later, a trend that is more pronounced in the ethane than in the methane flame. A most recent investigation by Schofield and Steinfeld46 has been devoted to the analysis of the combustion chemistry of both CH and C2. They have found good spatial correlation of the CH and C2 profiles in seven C2H2-O2-N2 flames with equivalence ratio Φ varying from 1.2 to 2.0; the CH profiles are observed to be slightly displaced versus those of C2 to longer reaction times. They state this to be the first consistent study for both molecules, which therefore permits them to perform an in-depth analysis of pertinent kinetic pathways. A quantification of their profiles and a direct comparison with flame modeling are, however, not given. Summarizing previous work with relevance to the study performed here, observations are generally quite consistent. CH and C2 mole fractions under low-pressure premixed flame conditions are, respectively, of similar magnitude in methane, natural gas, ethane, and ethene flames, resembling those seen here for propene and cyclopentene fuels. CH levels are a few to a few tens of ppm, C2 mole fractions are about 2 orders of magnitude lower. The trends in peak positions and profile shapes noted here are also consistent with earlier work. Models are in quite good agreement with experimental results for lean and stoichiometric methane flames; the discrepancies tend to become larger for richer flames, for higher hydrocarbon fuels (even if added in traces), and they are larger for C2 than for CH. Comparison with Models. Before applying the flame models to the propene and cyclopentene flames studied here, we have analyzed the CH and C2 mole fractions in the slightly rich (Φ ) 1.28, corresponding to C/O ) 0.32) low-pressure methane-air flame of Smith et al.34 The CH profile for this flame is also included in ref 34, but the original CH measurement and temperature profile have been obtained about 5 years earlier by Berg et al.40 Figure 3 demonstrates that the modeling results obtained with the DLR 2009 mechanism for both species in this flame agree similarly well with the measurements as the earlier simulations provided by the authors.34 Also, a simulation was performed and included in the top panel of Figure 3 with the original GRI 3.0 mechanism; however, this could not be done for the C2 profile in the center panel, because the GRI


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 mechanism and GRI mechanism for C2. The bottom panel displays the experimental mole fraction (from CRDS, squares) and temperature (from NO-LIF, circles) profiles for a Φ ) 1.60 methane flame; simulations are performed with DLR 2009, GRI, and the hybrid GRI-DLR mechanisms.

mechanism does not include C2. The CH profile from ref 34 is captured quantitatively by both models, and only a very minor displacement to higher heights is seen. Similarly, good agreement of the C2 maximum mole fraction is obtained, but the profile shows a slightly larger deviation in peak position and a somewhat slower decay with a displacement of about 1 mm at half-maximum. In the original work,34 where the model was based upon the GRI mechanism 3.0 with inclusion of some additional C2 reactions, the simulation overpredicts CH marginally, and the peak position is shifted slightly to higher heights. The decay from the model trails about 0.5 mm (at halfmaximum) behind the experimental curve. The C2 profile from the original simulation34 shows good agreement for the peak

J. Phys. Chem. A, Vol. 114, No. 14, 2010 4725 value, but the displacement is again around 0.4 mm at the peak and about 1 mm at half-maximum. To examine the model simulations further, an even richer methane flame (Φ ) 1.6) was analyzed, and the results are included in the bottom panel of Figure 3. Again, temperature was obtained by NO-LIF (open symbols), and the CH mole fractions (full symbols) were determined by CRDS. Simulations with three model variants are displayed, including the original GRI 3.0 mechanism (without C2 chemistry), the DLR 2009 mechanism, and the hybrid GRI-DLR 2009 mechanism, which includes propene, cyclopentene, and C2 chemistry. The maximum temperature in this flame is by about 150 K higher than that of ref 34, originally reported in ref 40. This higher temperature is in line with the discussion in ref 40 that heat release from the oxidation of CO to CO2 under low-pressure conditions is incomplete, and that the CO/CO2 ratio in flames with higher fuel content is nearer to the adiabatic value. The original GRI 3.0 mechanism overpredicts the experimental CH peak by about a factor of 1.7, whereas the DLR 2009 mechanism overpredicts it by about a factor of 2.3; peak positions and profile shapes are in reasonable agreement. The hybrid GRI-DLR 2009 mechanism results are quite similar to those of the original GRI mechanism, with a slight shift in maximum position, however. Since this hybrid mechanism has been constructed to simulate the CH and C2 mole fractions in the propene and cyclopentene flames, this comparison shows that the additions have not significantly affected its capability to predict CH in methane combustion. It should be noted, however, that the agreement in this richer flame is less satisfactory than in the Φ ) 1.28 flame of ref 34. Next we have checked whether inclusion of the reactions in Table 3 has an effect on the general flame structure for the propene and cyclopentene flames, which were analyzed in our previous work.53 Figure 4 shows simulations for several major species, including acetylene, for both flames. For all cases, the DLR 2009 predictions are close to those with the DLR 2007 mechanism. Comparisons of the experimental results for CH and C2 for the propene flames with C/O ) 0.5 and C/O ) 0.7 with the predictions of both DLR mechanisms (DLR 2007 and DLR 2009) are given in Figure 5, and analogous data for the two cyclopentene flames of these stoichiometries are presented in Figure 6; note that all simulated mole fractions are divided by 2. Furthermore, simulations with the hybrid GRI-DLR 2009 mechanism are also included. In spite of the good agreement in the slightly rich methane-air flame presented for the flame from refs 34 and 40 in Figure 3, substantial deviations are now seen for both species in all four flames. Typically, the mole fractions are overpredicted, and the C2 profiles persist longer in the simulations than in the experiments. These general trends are also observed when the MIT mechanism is used (not shown). However, a general recommendation which mechanism performs best is not evident from Figures 5 and 6, regarding positions of the maxima, shapes of the profiles and absolute mole fractions. A closer inspection of Figures 5 and 6 reveals some differences. First, the performance of both DLR mechanisms (DLR 2007 and DLR 2009) will be discussed to examine the effect of the additional reactions from Table 3. In the C/O ) 0.5 propene flame (Figure 5), the DLR 2009 mechanism provides a larger deviation for CH than the DLR 2007 mechanism, and this trend is even more pronounced in the richer propene flame. Specifically, the maximum CH mole fraction in the C/O ) 0.5 flame is about a factor of 3.4 (1.8) higher for the

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Ko¨hler et al.

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

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 calculations have been divided by 2.

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 prediction by the DLR 2009 mechanism; overprediction of the maxima is about 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, the additional reactions in Table 3 that are thought to affect the C2 consumption seem indeed to have a respective effect, although not of the desired magnitude. These reactions certainly affect the predictions of both molecules, although none of the two mechanisms provides completely realistic simulations. The decay of the CH profile is still better represented than that of C2, which is more clearly evident from Figure 7, where the profiles have been normalized to a common maximum.

The analysis for the corresponding cyclopentene flames in Figure 6 reveals that, again, CH is better predicted than C2. Ratios of model versus experiment for CH are within about a factor 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 in parentheses). For C2, the agreement with the absolute maximum mole fraction observed in the experiment is again better for the DLR 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 the predictions is evident from the normalized curves in Figure 7. Generally, the CH profiles are quite well represented in the propene flames of different stoichiometry by both mechanisms, with a slightly improved prediction of the decay by the DLR 2009 mechanism. A less favorable agreement is seen for the



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 from calculations have 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 common maximum value of 1.0 to facilitate comparison of the peak position and width. Symbols are from the experiment, dotted lines simulations with DLR 2007, and solid lines are predictions with the DLR 2009 mechanism.

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shapes of the CH profiles in the cyclopentene flames. The C2 profile peaks persists substantially longer in both models in the C/O ) 0.5 propene flame. This effect is even more visible in the richer propene flame, but the difference between both models is rather small. For C2 in the cyclopentene flames, the trends are quite similar, and in addition, the position of the peak is observed at higher heights. The simulation results exhibit some differences when the hybrid GRI-DLR 2009 mechanism is used. Remember that it was in almost complete agreement with the original GRI 3.0 mechanism when the CH profile is modeled in the Φ ) 1.6 methane flame in Figure 3, exhibiting only a slight shift (∼0.3 mm) in maximum position toward the burner. For CH in the propene flames, the GRI-DLR mechanism overpredicts the maxima by a factor of 2.7 for C/O ) 0.5, and by a factor of 2.5 for C/O ) 0.7; in the cyclopentene flames, the predictions are factors 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-DLR mechanism is thus in slightly better agreement than the DLR 2009 mechanism (both include the additional reactions in Table 3), but overall, the agreement for CH is best for the DLR 2007 mechanism. Furthermore, the prediction of the peak positions in the richer propene and cyclopentene flames with the hybrid GRI-DLR mechanism is not satisfactory and exhibits shifts toward the burner surface of 1.5-2 mm versus the experimental maxima. For the prediction of absolute C2 mole fractions, the hybrid GRI-DLR mechanism performs better than both DLR variants, with ratios of simulated to experimental maxima of 1.5 and 0.6 in 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 cyclopentene flames. Positions of the C2 maxima, however, are less well predicted and precede the experimental one in the richer propene flame and are observed at higher distances for the C/O ) 0.5 propene and cyclopentene flames. Also for this mechanism, the decay of the C2 profile is slower in the simulation than in the experiment. In view of this overall not more convincing performance of the hybrid GRI-DLR mechanism, the further analysis is limited to the DLR 2007 and DLR 2009 mechanisms, with and without the additional reactions in Table 3, because this 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 coefficients for C2 consumption (which were reported for the more reactive singlet and not the experimentally observed triplet state), has no dramatic effect on the width of the C2 profiles. Rather, it has a noticeable influence on the width of the CH profiles and brings them in better agreement with the experiment, at least in the propene flames. In contrast, the maxima for CH show a larger deviation for the mechanism with additional CH, C2, C3, C2O, and C2O3 chemistry, whereas these additional reactions provide a better prediction for the C2 maxima. Remember also that CH and C2 were very well captured in absolute magnitude and profile form by both mechanisms when the Φ ) 1.28 methane flame from ref 34 was modeled (Figure 3). The earlier observation of a strong correlation between CH and C2 chemistry, as discussed by Schofield and Steinberg46 could potentially provide a conceptual explanation, since they argue that several small combustion intermediates including CH and C2 are rapidly interconverted in a common radical pool. To examine the argument of a surprisingly invariant relation of these two species described in ref 46, we have analyzed the ratio of maximum mole fractions of CH and C2, χCH,max/χC2,max, in all investigated flames, expecting it for these reasons to be

Ko¨hler et al.

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

nearly constant. Figure 8 shows these mole fraction ratios as a function of C/O ratio for the experiment and the simulations with DLR 2007, DLR 2009, and MIT mechanisms. Clearly, the experimental ratio is not constant, neither in the propene nor in the cyclopentene flames. Predictions with the MIT and DLR 2007 mechanisms show large differences, and the closest agreement with the experiment for both flames is seen for the DLR 2009 mechanism. Seemingly, the general trends of any potential CH-C2 correlation are quite well represented with this model, with the remaining problem, however, that both intermediate concentrations, especially CH, are overpredicted and that C2 is not removed fast enough. Further removal reactions for C2 could be conceived which would, under these fuel-rich conditions, likely include buildup of larger hydrocarbons rather than oxidation, but so far, the slightly better agreement for C2 with the DLR 2009 mechanism has been paid with larger deviations for CH. Also, such potential further reactions are not needed for the simulation of both species profiles in the methane flame. To examine the influence of these and other reactions in more detail, a reaction flux and sensitivity analysis was performed for all three fuels. With deviations of a factor of 2-3 of the models from the experiment, this analysis is not intended to reveal potential influences of individual reactions, but it is deemed instructive for an overview of the general formation and consumption patterns of the two intermediates. Reaction Path and Sensitivity Analysis. Reaction flux and sensitivity coefficients for CH and C2 are shown in Figures 9-12. They include analysis of the methane-air flame of Smith et al.34 of Φ ) 1.28 (C/O ) 0.32) at h ) 5 mm, the propene-oxygen-argon flame of Φ ) 1.5 (C/O ) 0.5) at h ) 3 mm, and the cyclopentene-oxygen-argon flame with Φ )


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

1.4 (C/O ) 0.5) at h ) 3 mm. Note that the temperatures for these flame conditions are somewhat different with approximately 2000 K in the methane flame and approximately 2200 K in the propene and cyclopentene flames. Figure 9 shows the reaction flux for the formation and consumption of CH to be not very different in the reaction zone in the three flames. CH is primarily formed from CH2 + H T CH + H2 (R12). Among the CH consumption channels, CH + H T C + H2 (R19) and CH + O2 T HCO + O (R21) seem to be of almost similar importance. Other reactions of influence in the propene and cyclopentene flames include CH + C2H2 T C3H2 + H and CH + CO2 T HCO + CO. C2O + H T CH + CO (R32) contributes to CH formation in the cyclopentene flame; reaction numbers refer to Table 3. A direct involvement of the reactions added in the DLR 2009 mechanism is seen. To rationalize the different level of agreement in the rich flames of the three fuels, it can be argued that the formation sequence for CH is much more direct in the methane flame with CH4 f CH3 f 1CH2 f 3CH2 f CH, with quite well-known reaction coefficients for all steps. This is visualized in the top panel of Figure 13 for the Φ ) 1.28 methane flame; the width of the respective arrows and percentages indicated reflect the relative importance of the reactions. For the propene flames, more intermediate species and reactions with lesser well-known rate coefficients are involved, with potential pathways leading from C3H6 via C3H5, C3H4 (propyne), and C3H3 (propargyl) to


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

C3H2 and acetylene (see center panel of Figure 13). Alternative pathways include C2- and C4-intermediates. HCCO and acetylene 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, and some 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 and isomerization reactions, with products C3H3 and C2H2. C3H3 may lead to C3H2, and further intermediate reactions may involve HCCO, C2H2, C2O, and CH2. Alternative routes involve many hydrocarbon intermediates from C1- to C4-species. It is obvious that CH2 is a very important precursor for the CH radical in the flames of all three fuels. The inclusion of higher intermediates in the reaction channels affecting CH in the propene and cyclopentene flames is evident from a sensitivity analysis, with sensitivities >10% given in Figure 10. In the methane flame, prominent reactions of influence on CH formation and consumption include initiation channels such as CH3 + O T CH2O + H and the chainbranching reaction O + H2 T OH + H, the reaction coefficients of which should be quite well-known. The pattern is more complex for the propene and cyclopentene flames where the CH3 + O reaction is of lesser importance and an influence of the chain-branching reaction is not seen. Predominant contributions to CH consumption are seen from CH + H T C + H2 and CH + O2 T HCO + O in all flames. Slightly less influential

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

reactions on CH consumption involve C3H3 and C3H2 in the propene flame, and C3H2 and C2H2 in the cyclopentene flame; the reaction network for CH thus includes species that are not of primary importance in the methane flame. Further reactions with the larger precursors of CH (compare Figure 13) contribute with 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, among others, 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. The sensitive reactions are in good agreement with those seen in the 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 for their methane-air and ethane- and propane-doped methane-air flames. They attribute a slight decrease in CH concentration for the doped flames to be the consequence of the respective decrease in methane and the related C1 pathway. The too high CH concentrations seen in the present work might thus be a result of the less direct formation and consumption pathways and the lesser accuracy for the many involved reaction steps.

Ko¨hler et al.

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

Regarding the simulation of methyl, acetylene, and propargyl in the propene and cyclopentene flames in ref 53, for example, with both DLR and MIT mechanisms, discrepancies in predicting position of the maxima, shape of the respective profiles and absolute mole fractions remain s discrepancies that might also be of importance for some of the reactions identified above that are sensitively involved in predicting the CH profiles. A similar analysis of reaction flux performed for the dicarbon molecule is given in Figure 11. All three flames show the dominant C2 formation pathway to be C2H + O T C2 + OH (Table 3, R02). Reaction R02 is less dominant in the propene and cyclopentene flames, respectively, than in the methane flame. To a lesser extent, O + C3 T C2 + CO is also involved in the propene and cyclopentene flames. Consumption channels for C2 include C2 + O2 T 2CO (Table 2, Re004) as the dominant reaction for all fuels, followed by C2 + O2 T C2O + O (Table 3, R04). Minor contributions are seen from OH + C2 T C2O + H. On first glance, there is no distinct difference for the three fuels. The sensitivity analysis that includes all reactions with sensitivities >10% is reported in Figure 12, and it reveals again a different pattern. Most of the reactions of importance for the C2 formation and consumption do not involve dicarbon directly, with the exception of C2H + O T C2 + OH in all three flames and C2 + O2 T 2CO in the methane and cyclopentene flames. A common sensitive reaction for C2 formation is O + H2 T


J. Phys. Chem. A, Vol. 114, No. 14, 2010 4731 TABLE 4: Reactions Modified in the DLR 2009 Mechanism According to Results of Sensitivity Analysis, for the Propene Flame at C/O ) 0.5 as an Examplea no.

reaction

modification CH

R019 R021

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

R019 R021 R528

DLR 2009 Modification b DLR 2009 × 5 CH + H ) C + H2 CH + O2 ) HCO + O DLR 2009 × 3.75 C 3H 3 + H ) C 3 H 2 + H 2 DLR 2009 × 1.6

R012 R019 R021

DLR 2009 Modification c DLR 2009 × 0.5 CH2 + H ) CH + H2 CH + H ) C + H2 DLR 2009 × 5 CH + O2 ) HCO + O DLR 2009 × 2.92 C2

R02 R012 R019 R021

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

R02 R012 R019 R021 R519

DLR 2009 Modification e C2H + O ) C2 + OH DLR 2009 × 0.5 CH2 + H ) CH + H2 DLR 2009 × 0.5 CH + H ) C + H2 DLR 2009 × 5 CH + O2 ) HCO + O DLR 2009 × 2.92 PC3H4 + H ) C2H2 + CH3 DLR 2009 × 0.5

R02 R012 R019 R021 R452 Re004 R519 R538

DLR 2009 Modification f C2H + O ) C2 + OH DLR 2009 × 0.5 CH2 + H ) CH + H2 DLR 2009 × 0.5 CH + H ) C + H2 DLR 2009 × 5 CH + O2 ) HCO + O DLR 2009 × 2.92 C2H + OH ) HCCO + H DLR 2009 × 2.5 C2 + O2 ) 2CO DLR 2009 × 2 PC3H4 + H ) C2H2 + CH3 DLR 2009 × 0.5 C3H2 + O2 ) HCO + HCCO DLR 2009 × 2

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

Figure 13. Schematic diagram illustrating the formation routes of CH in 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.

OH + H. C2 consumption includes C2H2 + O T HCCO + H, with the strongest influence in the cyclopentene flame. The pattern is different for the remaining reactions, involving species like CH3 and CH4 in the methane flame and C3H3 and C3H4 (propyne) in the propene flame. Further reactions involving C3H2, 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 consumption channels would be likely candidates to achieve a more rapid C2 decay in the propene and cyclopentene flames, as observed in the experiment. Under fuel-rich conditions, one would assume that such reactions might lead to carbon buildup such as tentatively included in R06-R10 (Table 3). To rationalize the

difference in predictive capability for methane versus propene and cyclopentene flames, it is helpful to analyze the main formation pathways toward the dicarbon molecule. In the fuel-rich methane flame, C2 is formed predominantly from C2H with O or from C2 with H2O. C2H results mainly from C2H2 + OH, coming from the decay of C2H3, which is produced via OH/H radical abstraction reactions from C2H4. C2H2, C2H3, and C2H4 can be formed through combinations of C1 species and react with H and OH. CH3, CH2, and CH radicals are involved in these pathways. In the fuel-rich propene flame, the reaction of C2H with O is more dominant, and C2H is mostly formed from C4H2 + H, which results from C4H4 as direct precursor and its decomposition to C4H2 + H2. Various reactions contribute to C4H4 formation, and a larger number of C4, C3, C2, and C1 intermediates are involved in the sequence that eventually yields C2. The general pattern is similarly complex in the fuel-rich cyclopentene flame, involving analogous reactions with, however, quantitatively different contributions. Generally, the fraction of reactions with 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, which is at the origin of the larger deviations of the model from the experimental results. Improvement of the prediction of C2 in the propene and cyclopentene flame will thus probably need

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Figure 14. Comparison of experimental (symbols) CH (top) and C2 (bottom) profiles in propene flames at C/O ) 0.5 with simulation by the DLR 2007 and DLR 2009 mechanisms. Further calculations are included with variants of the DLR 2009 mechanism (modified versions a-f in Table 4). Note that mole fractions from calculations have been divided by 2.

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 both molecules, rate coefficients of several reactions were tentatively modified. Different variants of the DLR 2009 mechanism were used with the modifications a-f identified in Table 4. Groups of reaction coefficients were changed especially for pathways found to be sensitive in CH and C2 formation and removal. The results are shown in Figure 14 for the C/O ) 0.5 propene flame; note that simulated values are divided by 2. Modifications a-c involve CH reactions identified in Figure 10. Significantly increasing the rates for the two most sensitive CH consumption channels (modification a) decreases the CH mole fraction by about a factor of 2, and an additional change of the reaction rate of propargyl with H-atoms (modification b) has only a minor effect. Modification c additionally reduces the rate of the reaction that is most sensitive regarding CH formation, again with a small, but noticeable, improvement. Clearly, these variations for a few sensitive reactions are an improvement, but not sufficient to bring the simulated CH profiles into agreement with the experiment. Similarly, some reactions sensitively involved in C2 formation and consumption have been altered in addition (variants d-f), following the analysis in Figure 12. These results are shown in the bottom panel of Figure 14. Modification d adds a decrease in the rate coefficient for C2H + O T C2 + OH (R02) to the changes in variant c. Reaction R02 is the second most sensitive reaction in C2 formation after O + H2 (the kinetic parameters of which are well-known and should not be varied). Obviously,

Ko¨hler et al. the changes in c, intended to decrease the CH concentration, have not adversely affected the C2 mole fraction, and the addition of R02 has a minor effect on the prediction of C2. Variant e reduces, again in addition to previous changes, the rate coefficient for the reaction of propyne with H-atoms, found to sensitively influence C2 formation in the propene flame. This modification has a slightly more noticeable effect. Further three reactions are added in variant f, which includes the consumption of C2 with O2 to form CO, and two channels that involve HCCO and C3H2 as important species along the reaction sequence. Such combined changes as in modification f do show the potential to decrease the C2 mole fraction in the propene flame, in addition to that of the CH radical. However, even these successive and quite substantial modifications leave some room for further improvement, with the simulations still overpredicting the experimental values by almost a factor of 2. This corroborates the analysis above that the problem is more complex, and that an in-depth analysis along the sequences of reactions leading to CH and C2 in the propene and cyclopentene flames would be necessary. One recent interesting finding has addressed a novel type of “roaming” reaction mechanism80,81 that may lead to lower radical concentrations by providing access to stable products. If this principle were of more general importance, also for some of the many reactions involving radicals in flames, smaller concentrations could be expected for radicals thought to be the result of long, chain-propagating series of reactions. It is not obvious that such reactions might be involved in mechanisms as discussed here, but it might be an interesting hypothesis to pursue further in attempts to improve the predictive capability of combustion models. Conclusions Quantitative mole fractions of two interesting combustion intermediates, CH and C2, were measured in fuel-rich, premixed propene-oxygen-argon and cyclopentene-oxygen-argon flames at low pressure. Although these molecules are often detected in laboratory-scale experiments, details of the chemistry that determines their formation and depletion in flames are not sufficiently studied. Especially for the dicarbon molecule, which is also of astrophysical interest, its low concentration has limited high-precision studies. Previous work has been successful in modeling the profiles of both species quantitatively in methane combustion, with some deviations in very rich flames and for addition of percent levels of C2- and C3-hydrocarbon fuels. Recent interest in C2 chemistry from planetary atmospheres has provided a number of studies of C2 reactions with larger hydrocarbon species that might also be effective in the buildup of polycyclic aromatic hydrocarbons and, eventually, soot, in fuel-rich combustion. The striking similarity of CH and C2 profiles in flames has also inspired a recent investigation46 that concludes that a common radical pool must be the reason for this seeming invariance of the CH-to-C2 relationship with flame condition. The starting point for the present paper was thus an attempt of a better understanding of the elusive role of C2, the smallest all-carbon molecule, in the chemistry of flames and of its relation with CH, which has a key function in NOx formation from combustion processes. Careful examination of the concentration profiles of both molecules with CRDS and LIF has permitted unambiguous assessment of the shapes and positions of maxima. Combustion modeling was performed to analyze the underlying flame chemistry in detail. Several conclusions can be drawn from this work.

C2 and CH Chemistry in Combustion •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 excellent agreement with the present model. •Mole fractions of CH in a Φ ) 1.60 methane flame are overpredicted by the GRI mechanism, the DLR 2009 mechanism and a hybrid GRI-DLR 2009 mechanism that includes C2, propene, and cyclopentene chemistry. •Mole fractions of CH and C2 in fuel-rich propene and cyclopentene flames are also overpredicted. The location of the maxima and the decay of the C2 profiles are not well captured by the model. Inclusion of a number of CH- and C2-related reactions (DLR 2009 mechanism) has improved the predicted profile shape for CH, but not influenced the too slow C2 consumption. Results are generally not more satisfying with the hybrid GRI-DLR 2009 mechanism. Potentially, a more rapid consumption of precursors of C2 would assist in bringing the prediction closer to the experiment. •Ratios of CH versus C2 maxima are not constant and are best predicted by the DLR 2009 model. •Reaction flux and sensitivity analyses reveal a more complex pattern of CH and C2 formation in the flames of higher hydrocarbons than for methane. CH is formed in the methane flame through a C1-species sequence, and kinetic expressions for most of the sensitive reactions in the methane flame are quite well known. This is not the case for the C3 and C5 fuels where many intermediates are of importance for the pathways toward both molecules. Unless the species that precede the formation of these small intermediates are quantitatively captured by combustion models, a more complete understanding of the present discrepancies between experiment and models cannot be expected. Because of the eminent role of CH in the NOx reaction network, the results suggest that increased attention should be devoted to improve the accuracy of many reaction coefficients for small intermediate species if a similar predictive capability is needed as in methane combustion. Acknowledgment. K.K.H., A.B., and M.K. gratefully acknowledge partial support of this work by Deutsche Forschungsgemeinschaft within SFB 686 TP B3 and under contract Ko 1363/18-3. They also thank Patrick Nau for his valuable contributions to part of the data evaluation. Furthermore, helpful assistance of Xing Xu with some model calculations is gratefully acknowledged. Finally, K.K.H. thanks Ju¨rgen Troe and Ralf Kaiser for helpful discussions on C2 chemistry; she is further grateful to Hanna Reisler and Curt Wittig for directing her to some earlier work on C2. References and Notes (1) Miller, J. A.; Troe, J.; Pilling, M. J. Proc. Combust. Inst. 2005, 30, 43–88. (2) Miller, J. A.; Bowman, C. T. Prog. Energy Combust. Sci. 1989, 15, 287–338. (3) Dagaut, P.; Glarborg, P.; Alzueta, M. U. Prog. Energy Combust. Sci. 2008, 34, 1–46. (4) Kohse-Hoïnghaus, K. Prog. Energy Combust. Sci. 1994, 20, 203– 279. (5) Kohse-Hoïnghaus, K.; Barlow, R. S.; Aldeń, M.; Wolfrum, J. Proc. Combust. Inst. 2005, 30, 89–123. (6) Smyth, K. C.; Crosley, D. R. Detection of minor species with laser techniques. In Applied Combustion Diagnostics; Kohse-Hoïnghaus, K., Jeffries, J. B., Eds.; Taylor and Francis: New York, 2002; pp 9-68. (7) Vagelopoulos, C. M.; Frank, J. H. Proc. Combust. Inst. 2005, 30, 241–249. (8) Donbar, J. M.; Driscoll, J. F.; Carter, C. D. Combust. Flame 2000, 122, 1–19. (9) Evertsen, R.; van Oijen, J. A.; Hermanns, R. T. E.; de Goey, L. P. H.; ter Meulen, J. J. Combust. Flame 2003, 132, 34–42. (10) Lamoureux, N.; El-Bakali, A.; Gasnot, L.; Pauwels, J. F.; Desgroux, P. Combust. Flame 2008, 153, 186–201.

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