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MBMS analysis of a fuel-lean ethylene flame
MBMS Analysis of a Fuel-Lean Ethylene Flame ANUJ BHARGAVA and PHILLIP R. WESTMORELAND*
Chemical Engineering Department, University of Massachusetts Amherst, Amherst, MA 01003-3110 A one-dimensional laminar C2H4/O2/Ar flame was analyzed with a molecular-beam mass spectrometer (MBMS) system. Profiles of concentration, area expansion ratio and temperature were measured for a C2H4/O2/56.9% Ar (f 5 0.75) flame at 4.000 6 0.001 kPa (30.00 Torr) and 30.0 cm/s burner velocity (at 300K). Full concentration profiles were mapped for 22 stable and radical species, while point measurements were made for seven other species. These mole fraction data are valuable for inference of kinetics and testing of reaction mechanisms. Elemental flux deviations were less than 15% in the flame zone and less than 4% in the post-flame zone supporting the data’s accuracy and reliability. Flux balance calculations were also used to obtain the net rate of destruction for C2H4 and C2H3. New values of the rate constants for C2H4 1 H 3 C2H3 1 H2, C2H4 1 OH 3 C2H3 1 H2O and C2H3 3 C2H2 1 H were supported by the agreement between measured rates and the rates predicted from measured temperatures, measured mole fractions, and the new rate constants. © 1998 by The Combustion Institute
INTRODUCTION Understanding C2H4 and C2H3 chemistry is important from the point of predicting combustion chemistry of higher hydrocarbons. Hydrogen abstraction from C2H4, forming vinyl radical, is of great importance in the combustion process. At the same time, reaction with O and OH radicals can also be significant in the consumption of the fuel C2H4. Overall rate constants for these reactions are available for a wide range of temperatures, but for data on branching ratios, one has to rely on low-temperature measurements. Destruction of vinyl is not well understood either. Vinyl may decompose to C2H2 1 H, or it may react with H, O, OH or O2 [1– 4]. The present work maps a lean ethylene flame to an extensive level of detail, valuable for flame modeling. Several researchers have carried out other MBMS studies of C2H4 flames under different conditions, including Peeters and Mahnen [5], Peeters and Vinckier [6], and Homann et al. [7]. Except for the very lean flame (f 5 0.21) of Peeters and Mahnen [5], each of these data sets is missing some measurement valuable for modeling (e.g., measured temperature profile). Harris et al. [8] and Cool et al. [9] have carried out measurements of some species *Corresponding author. Anuj Bhargava is now at United Technologies Research Center, MS 129-30, 411 Silver Lane, East Hartford, CT 06108. 0010-2180/98/$19.00 PII S0010-2180(98)00018-2
in ethylene flames with species-specific laser techniques like laser-induced fluorescence (LIF) and resonance-enhanced multiphoton ionization (REMPI). While valuable, these measurements are likewise insufficient to characterize a flame fully. In the present work, a fuel-lean ethylene flame (f 5 0.75) has been mapped with MBMS for mole fractions, thermocouples for temperature, and hot-wire anemometry for area expansion ratio. This data set has been used in conjunction with recent rich-flame data [10] to obtain and test rate constants for reactions at flame conditions. While the rich flame gives valuable information on molecular-weightgrowth chemistry, the lean flame provides more insight into oxidation chemistry. EXPERIMENTAL APPARATUS AND PROCEDURE Experiments were carried out in an apparatus originally built by Biordi et al. [11] and modified for this work (Fig. 1). Details about the experimental apparatus have been described by Biordi et al. [11–13] and Thomas [14]. Gas flow rates were metered with mass flow controllers (MKS Instruments, Inc., Andover, MA) and mixed. The mixed gases were fed through a 9.91-cm-diameter, sintered-bronze, internally cooled flat-flame burner (Thermet Inc., Gloucester, MA and this laboratory). The flame was ignited by a spark from a Tesla coil and COMBUSTION AND FLAME 115:456 – 467 (1998) © 1998 by The Combustion Institute Published by Elsevier Science Inc.
MBMS ANALYSIS OF A LEAN ETHYLENE FLAME
457
burgh) and collected with a Channeltron electron multiplier (Galileo Electro-optics 4816, Sturbridge, MA). Signal was then measured either as a continuous, modulated current with a lock-in amplifier (EG&G PARC Model 5301 with Model 5317 Differential Preamplifier, Princeton, NJ) or as pulses corresponding to individual ions (PARC/SSR Instruments Model 1110, Princeton, NJ). This mass-spectrometer chamber was pumped with a 4 in. diffusion pump with a liquid-N2-cooled baffle. Both diffusion pumps in the system use low-vaporpressure polyphenylether oil (Santovac-5, Monsanto, St. Louis). A cold finger filled with liquid N2 was also used as a cryopump for the massspectrometer chamber.
Fig. 1. Schematic of the molecular-beam mass spectrometry (MBMS) system.
stabilized by heat transfer to the burner. The bottom of the luminous flame was approximately 5 mm from the burner. Gases were pumped from the burner chamber through two 3.8 cm diam. ports to a 15.2 cm diam. pipe and a gate valve into a 300 cfm mechanical pump (Stokes Microvac 412H-10, Pennwalt Corp., Philadelphia). The burner chamber was isolated from any downstream pressure variations by the gate valve used to set critical flow. Pressure was maintained constant within 0.01 mm Hg by an automatically controlled ballast flow of air (MKS Instruments, Inc., Andover, MA). The molecular beam was formed with a hybrid quartz probe (180 mm orifice, 45° tip) followed by an aluminum skimmer cone (2 mm orifice, included angle of 80°). The chamber between the two was pumped to a pressure of about 1024 to 1025 Torr with a 6 in. diffusion pump. A water-cooled baffle before the diffusion pump minimized backstreaming. After the skimmer, the beam was modulated at 560 Hz with a toothed-wheel chopper and was ionized with a tungsten-filament electronimpact (EI) ionizer. Ions were resolved by a quadrupole mass spectrometer (Extranuclear Laboratories Model 240, Extrel Corp., Pitts-
Methods of Measuring Mole Fractions First, ionization efficiency curves (signal vs ionizing-electron voltage) were measured for the molecular weight of interest at several positions in the flame. These curves were used to identify flame species by their ionization potentials, for indirect calibration, and to determine the ionizer voltage to be used in mapping. Ionizing voltage was kept low, lower than that causing any ion fragmentation effects. Major stable species to be mapped were directly calibrated before and after concentration profiles were measured. A calibration gas mixture of H2, CH4, C2H4, CO, Ar, C3H6, 1-butene, CO2, and toluene was mixed with the flame gas mixture, fed to the burner, and sampled at 6.00 Torr and 298 K, reproducing flame molecular weight and density at 30.00 Torr and 1500 K. Minor and radical species were calibrated from ionization efficiency curves by the method of relative ionization cross-sections (RICM) [13], which is estimated to have a factor-of-2 uncertainty. H, O, and OH calibration coefficients were obtained by assuming that the fast bimolecular reactions H 1 O2 7 OH 1 O,
(Rxn. 1)
O 1 H2 7 OH 1 H,
(Rxn. 2)
OH 1 H2 7 H2O 1 H,
(Rxn. 3)
O 1 H2O 7 OH 1 OH,
(Rxn. 4)
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A. BHARGAVA AND P. R. WESTMORELAND
attain partial equilibrium in the post-flame zone (37 and 46.5 mm from the burner surface). Any one of these reactions is considered to have reached a partial or dynamic equilibrium if its equilibrium-constant concentration ratio, calculated from experimental concentrations, is equal to its reaction equilibrium constant, calculated from thermodynamics. Expressions for K eqR, the equilibrium constant for reaction R fitted over a temperature range of 300 –2300 K, are K eq1 5
S
X OX OH X HX O2
D
5 2.60 3 102T20.354 eq
exp(217.111 kcal/mol/RT),
K eq2 5
S
X HX OH X OX H2
D
(1)
5 2.225 3 eq
exp(21.86 kcal/mol/RT),
K eq3 5
S
X HX HO2 XOHXH2
D
(2)
5 2.118 3 1021 eq
exp(15.182 kcal/mol/RT).
(3)
The fits are within 3% of values calculated from NASA coefficients by Burcat [15] and Westmoreland [16]. Equations 1, 2, and 3 were solved for the mole fraction ratios of H, O, and OH to Ar in terms of the mole fraction ratios of the stable species H2, H2O, and O2. Calibration factors become
F
X H2 X O2 X OH 5 K eq1K eq2 X Ar X Ar X Ar
G
1/ 2
,
(4)
X H2 X O2 X Ar XO 5 K eq1K eq3 , X Ar X Ar X Ar X H2O
(5)
S D S D S D
XH2 XH 1/2 5 Keq3K1/2 eq1Keq2 XAr XAr
3/ 2
XH2O X Ar
21
X O2
X Ar
1/2
. (6)
These above three equations are combined with an H or O elemental balance in the post-flame zone (37 and 46.5 mm from the burner surface) to give four equations and four unknowns, namely, X O/X Ar, X OH/X Ar, X H/X Ar, and X H2O/ X Ar. The final calibration coefficients, (Xi/XAr)/ (Ii/IAr) where I is the measured signal, were determined as the average of the values at 37.0
and 46.5 mm (the coefficients for the radicals were 0.9316 and 0.8898 for H, 1.8652 and 1.9831 for O atom, and 3.1874 and 3.2315 for OH at 37 and 46.5 mm, respectively). These calibration coefficients indicate that if H, O, and OH had been calibrated by the ionization cross-section method (relative to H2, O2, and CH4, respectively), the mole fraction values would have been off by 222%, 1120%, and 165%, respectively. These results are consistent with earlier observations that O atom is particularly difficult to calibrate by the relative ionization crosssection method [17–19]. The calibration coefficients found from reactions 1–3 were used in reaction 4 to find if it was at equilibrium or not. The reaction does reach equilibrium. This result indicates that the partial equilibrium assumption used to calculate calibration coefficients for H, O, and OH is valid. H2O was calibrated by an overall elemental balance on O, while Ar was obtained by an overall mole balance. Isotopic interferences in the raw signals were corrected by calculated signal strengths for (M-1) and (M-2) ions. The mole fraction data were smoothed using a cubic-spline routine. Profiles of species fluxes, elemental fluxes, and reaction rates were also calculated from the data at each position using standard methods [20]. Temperatures Accurate temperature measurements are essential to interpret and model data. Pt/Pt-13% Rh thermocouples, 0.076 cm in diameter, were used to measure temperatures. These thermocouples were coated with a Y2O3/4.5% BeO glass to avoid catalytic effects [21, 22]. Radiative losses were calibrated as a function of resistive-heating current, using a vacuum chamber to eliminate convective effects. In the flame, the current flowing through the thermocouple was varied until the temperature matched the calibration curve (i.e., T TC 5 T gas), hence eliminating convective heat transfer. An emissivity of 0.55 6 0.2 was calculated for the coated thermocouple. Area Expansion Ratio Area expansion ratio, A( z) 5 r ( z) n ( z)/ r 0n o , was measured with hot-wire anemometry using
MBMS ANALYSIS OF A LEAN ETHYLENE FLAME
459
TABLE 1 List of Species Examined Along With Their IP and Mass Spectrometer Conditions for Fuel-Lean Flame Ionization Potential (eV) Species H atom H2 CH*2 CH3 CH4 O OH H2O C2H2 C2H3 C2H4 CO C2H5 HCO C2H6 CH2O O2 HO2 H2O2 Ar C3H5 HCCO C3H6 CH2CO C3H7 CH2CHO C3H8 CH3CHO CO2 C3H2O* C3H3O* C3H4O* C3H5O* C3H6O* C6H6* a b
Mass 1 2 14 15 16 16 17 18 16 27 28 28 29 29 30 30 32 33 34 40 41 41 42 42 43 43 44 44 44 54 55 56 57 58 78
Literaturea 13.598 15.43 10.396 9.84 12.71 13.62 12.94 12.62 11.41 8.94 10.53 14.01 8.40 9.93 11.55 10.88 12.07 11.53 10.92 15.76 8.07 9.50 9.74 9.60 8.10 10.85 11.07 10.22 13.80 10.0 6 0.5b 8.4 6 0.5b 10.18 8.9 to 9.3 9.96 9.25
Concentration measurement
Measured IP, Position (mm) 13.75 6 0.2, 10.0 15.66 6 0.2, 5.50 Not measured 10.06 6 0.2, 4.0 12.86 6 0.1, 4.0 13.66 6 0.1, 10.0 13.11 6 0.2, 10.0 12.55 6 0.2, 15.5 11.30 6 0.2, 4.15 9.03 6 0.2, 4.15 10.65 6 0.1, 1.0 and 5.5 14.16 6 0.1, 5.5 and 7.0 Not detected 9.90 6 0.2, 3.0 Not detected 10.95 6 0.1, 3.0 11.95 6 0.1, 2.5 11.86 6 0.2, 2.5 10.76 6 0.2, 2.5 Reference Not detected 9.24 6 0.3, 3.0 Not detected 9.38 6 0.2, 3.0 Not detected 10.71 6 0.2, 2.25 Not detected 10.11 6 0.2, 2.25 13.90 6 0.1, 18.0 9.88 6 0.2, 1.15 8.80 6 0.5, 1.15 9.81 6 0.2, 1.15 9.11 6 0.3, 1.15 9.86 6 0.2, 1.15 9.46 6 0.3, 1.15
EI (eV)
Calibration type
15.60 16.95 12.70 12.70 14.20 15.60 15.60 15.60 12.35 10.85 12.40 16.40
Partial equilibrium Direct Ionization cross-section Ionization cross-section Direct Partial equilibrium Partial equilibrium H atom balance Ionization cross-section Ionization cross-section Direct Direct
11.50
Ionization cross-section vs C2H4
12.85 14.00 14.00 14.00 18.00
Ionization cross-section vs C2H4 Direct Ionization cross-section vs O2 Ionization cross-section vs O2 Direct
11.50
Ionization cross-section vs CO2
11.50
Ionization cross-section vs CO2
11.50
Ionization cross-section vs CO2
11.50 16.60 10.86 10.86 10.86 10.86 10.86 10.86
Ionization Direct Ionization Ionization Ionization Ionization Ionization Ionization
vs CH4 vs CH4
vs C2H4 vs C2H4
cross-section vs CO2 cross-section cross-section cross-section cross-section cross-section cross-section
vs vs vs vs vs vs
Ar Ar Ar Ar Ar Ar
Rosenstock et al. [45] except as noted otherwise. Estimated by Thomas [14]; *Upper-bound measurements.
cold gases. The anemometer was made of a 23 mm long, 0.076 mm diam. platinum wire supported by 0.381 mm diam. platinum wire. The wire was supported normal to the flow direction and operated at 570 K (determined by the resistance of the wire). The measurements were fitted by the expression A~ z! 5 ~0.9941 2 0.0076z!/~1 2 0.0122z! with z in mm. Details of the experimental procedure are presented in [10].
RESULTS Mole fraction profiles were measured for 22 stable and radical species in a C2H4/O2/56.9% Ar (f 5 0.75) flame at 4.000 6 0.001 kPa (30.00 Torr) and 30.0 cm/s burner velocity (based on 300K). Upper bound measurements were also made for seven other species. A list of all the species measured along with their mass spectrometer conditions is presented in Table 1. The concentration profiles for the 22 species are given in Figs. 2 to 6, while upper bounds for the
460
A. BHARGAVA AND P. R. WESTMORELAND TABLE 2 Species for Which Point Measurements Were Made
Mass
Species
Mole fraction at 1.15 mm from the burner surface
Mole fraction at 3.10 mm from the burner surface
14 54 55 56 57 58 78
CH2 C3H2O C3H3O C3H4O C3H5O C3H6O C6H6
2.8 3 1025 2.6 3 1026 2.0 3 1026 1.26 3 1025 8.1 3 1026 1.06 3 1025 7.6 3 1026
1.8 3 1025 1.9 3 1026 4.0 3 1026 9.9 3 1026 4.4 3 1026 9.6 3 1026 6.0 3 1026
seven species are given in Table 2. Results are discussed in the following order: correction for sampling perturbations, temperature profiles, major species, the major radicals, other C1 and C2 hydrocarbons, oxygenates, and point measurements. Correction for Sampling Perturbations In MBMS sampling, the quartz probe and the thermocouple induce some perturbations in the measured concentration and temperature profiles. Several researchers have studied the distortions that are caused by the probe and thermocouple. Biordi et al. [23] measured the CH4 concentration profile in a low-pressure methane flat flame. They found that the profile measured by MBMS using a hybrid quartz probe was shifted towards the burner by about 5 orifice diameters as compared to a more spatially precise microprobe measurement. Stepowski et al. [24] measured OH profiles at 0.033 atm with both MBMS and laser-induced fluorescence (LIF), finding a shift of 2 orifice diameters in the MBMS data beyond the flame zone. They further found that the quartz probe reduces the OH concentration measured with a MBMS in the preheating zone as compared to the measurements made with LIF. This effect was attributed to a perturbation of the diffusion field by the probe. The authors suggested that the OH concentration measured by MBMS is the actual value in the sample (post-flame zone). Cattolica et al. [25] measured OH profile in flames at 1 atm with MBMS and LIF and found a shift upstream for MBMS of about 2 orifice diameters. For modeling purposes, the measured temperature profile was lowered by 100 K to ac-
count for the cooling effect of the probe and moved 0.5 mm away from the burner surface to account for perturbations caused by the thermocouple [20]. The concentration profile was moved by 0.9 mm (5 times the orifice diameter) towards the burner surface in order to account for perturbations caused by the quartz probe. Temperature Profiles The corrected temperature profile is shown in Fig. 2. Burner temperature was measured as 440 K with the thermocouple touching the burner surface. A maximum temperature of 2025 K was recorded at 9.5 mm above the burner surface. With the standard correction applied, the maximum became 1925 K at 10 mm.
Fig. 2. Mole fraction data and smoothed profiles for major stable species, C2H4 (*), O2 (D), CO (•), H2O (O), CO2 (3), Ar (◊), and the smoothed temperature profile (solid line with no points shown).
MBMS ANALYSIS OF A LEAN ETHYLENE FLAME
Fig. 3. Mole fraction data and smoothed profiles for H (3), H2 (O), O (D), and OH (•).
Species Profiles Among the major stable species, C2H4 is fully consumed by 5 mm, as shown in Fig. 2. The O2 mole fraction falls rapidly in the first 6 mm before settling down to a final value of 0.11. The intermediate species H2 and CO form near the burner and then are consumed. H2 rises to a maximum value of 6.70 3 1023 at 4.3 mm, as shown in Fig. 3. It declines rapidly to approximately 3 3 1023 by 15 mm and then declines only slightly further. CO rises rapidly to a mole fraction of 7.92 3 1022 by 2.8 mm. Beyond its maximum, it decreases sharply to about 3.03 3 1023 at 9 mm, thereafter declining slowly. H2O and CO2 are the products of H2 and CO oxidation, respectively. H2O shows a local maximum of 0.185 at 12 mm before settling down to 0.173 mole fraction. CO2 rises to a mole fraction of 0.10 at 8 mm and then gradually increases to 0.13 by 51 mm, the largest distance where measurements were made. The major radicals H, O, and OH are shown in Fig. 3, with H2 also shown for comparison. H atom rises to a maximum value of 2.68 3 1023 at 15.75 mm, while OH rises higher to a maximum value of 9.90 3 1023 at 18 mm. Like most radicals, their concentrations decrease slowly in the post-flame zone, reaching 1.02 3 1023 and 6.51 3 1023 by 51 mm, respectively. Signal measured for mass 16 was analyzed as CH4 at distances close to the burner, but at distances above 8 mm it was assigned to O atom. The mole fraction of O atom has a maximum of 6.20 3 1023 at 11.9 mm and then decreases
461
Fig. 4. Mole fraction data and smoothed profiles for HCO (O), CH2O (D), HO2 (3), and H2O2 (◊).
gradually, to 2.56 3 1023 at 51.32 mm. An O atom profile between 0 and 8 mm was estimated by extrapolation. The other oxidizing radical that was detected and measured was HO2. HO2 peaks at a value of 4.27 3 1024 at 2.79 before decreasing gradually to 2.63 3 1025 at 12.57 mm. The coupled molecule H2O2 peaks at 3.79 3 1024 at 2.8 mm and then declines to 1.18 3 1025 at 12.57 mm (see Fig. 4). Among the hydrocarbon radicals, C2H3 and CH3 are thought to be especially important in the combustion process. C2H3 radical attains a maximum mole fraction of only 4.99 3 1025 at 4.1 mm and then comes down sharply, reaching a mole fraction of 4.61 3 1026 at 8.13 mm (Fig. 5). On the other hand, the much less reactive CH3 peaks at 4.3 mm at a much higher mole fraction of 7.77 3 1023. Its mole fraction then decreases steadily to 1.44 3 1025 at 8.13 mm.
Fig. 5. Mole fraction data and smoothed profiles for CH3 (3), CH4 (O), C2H3 (◊), C2H2 (D), and C2H4 (•).
462
Fig. 6. Mole fraction data and smoothed profiles for CHCO (3), CH2CO (O), CH2CHO (D), and CH3CHO (◊).
The other C1 and C2 species that were detected were CH4 and C2H2, shown in Fig. 5. As mentioned earlier, signal at mass 16 was a combination of O atom and CH4. The ionization efficiency measurements indicated that the signal closer to the burner was predominantly CH4, while further away from the burner, the signal was dominated by O atom. The CH4 signal rises rapidly to 7.27 3 1026 at 3.13 mm. Following its maximum, the methane mole fraction decreased slowly to 3.3 3 1023 at 6.6 mm. Beyond 7.6 mm, the signal increases, indicating that the signal in this region is dominated by O atom. The C2H2 mole fraction profile rises to 9.51 3 1024 at 4.83 mm from the burner surface and then decreases more rapidly. Mass 29 and mass 30 were identified as the C1 oxygenates, HCO and CH2O, respectively (Fig. 4). The signal for mass 29, which had an ionization potential of 9.85 6 0.20 eV at 3.0 mm, is strongly dominated by HCO (IP 5 9.90 eV) but also includes any C2H5 (IP 5 8.40 eV). By the same reasoning, mass 30 was strongly dominated by CH2O rather than C2H6. HCO shows a peak mole fraction value of 9.4 3 1025 at 3.3 mm, while CH2O peaks at a mole fraction of 5.6 3 1024 at 3 mm. Among the C2 oxygenated species, mass 42 (CH2CO) and mass 43 (C2H3O) are highest in concentration. The mole fraction profiles for the different C2 oxygenates are shown in Fig. 6. The ionization potentials of the two mass 42 species C3H6 and CH2CO are so close that it is not possible to distinguish between the two. Because the preliminary modeling suggested that the signal is strongly dominated by the
A. BHARGAVA AND P. R. WESTMORELAND oxygenate, it was interpreted as CH2CO. Its mole fraction has a maximum of 2.6 3 1024 at 3.05 mm. For mass 43, the appearance potential of 10.71 6 0.20 eV at 2.25 mm implies that the signal at that position is from CH2CHO, which has an ionization potential value of 10.85 eV, rather than from C3H4 or the less stable CH3CO. A C2H3O1 fragment of CH3CHO would be formed near this potential, but the shape difference of the mass 43 profile relative to CH3CHO implies that CH2CHO dominates. The mass 43 signal was corrected for isotopic contribution from the mass 42 (CH2CO) signal and converted to mole fraction. The mole fraction then displays a maximum of 2.04 3 1024 at 2.54 mm. The other C2 oxygenates detected were mass 41 (HCCO) and mass 44 (CH3CHO), shown in Fig. 6. Mass 41 signal could also be from C3H5 (IP 5 8.07 eV), but the ionization potential measurement of 9.24 6 0.30 eV at 3.0 mm implies that the mass 41 signal at that point is dominated by HCCO (IP 5 9.50 eV). Its mole fraction rose to a maximum of 9.56 3 1026 at 3.56 mm. The ionization efficiency curve for mass 44 measured at 2.25 mm showed two distinct linear regions. The species at higher electron energy (IP 5 13.90 6 0.1) was CO2 (ionization potential of 13.8 eV). The species occurring at lower eV (10.11 6 0.2) was acetaldehyde (IP of 10.22 eV) rather than propane (IP of 11.07 eV), attaining a maximum mole fraction of 8.57 3 1025 at 2.03 mm from the burner. Point measurements were also made for CH2; C3 oxygenates C3H2O, C3H3O, C3H4O, C3H5O, C3H6O; and C6H6. As the concentrations of these species were too low for full profile measurements, upper bound measurements were made for the seven species at two distances. “Upper bound” means that the signal detected and measured was a sum of the signal from the species from the molecular beam and background signal, which included signal from the species in the background and noise. The mole fractions (upper limit) thus obtained are shown in Table 2. All seven species were calibrated by the method of relative ionization cross-section with respect to argon. Signal for masses 54 –58 may instead have been from the pure hydrocarbon species (C4H6 to C4H10) but were treated as being from oxygen-containing species. For some
MBMS ANALYSIS OF A LEAN ETHYLENE FLAME
Fig. 7. Overall elemental flux balance for C, H, O, and Ar.
masses the assignments were made due to modeling considerations, while in other cases it was possible to distinguish the species (C3H3O, C3H5O, C3H6O) with the help of ionization efficiency curves. For some of the species, literature ionization potential values were not available (e.g., C3H2O, C3H3O). Ionization potentials for these species were obtained by analogies to acrolein as suggested by Thomas (1992). Flux Balances The calculation of elemental fluxes from smoothed data profiles is a good test for internal consistency of the MBMS data. Because atoms are conserved in chemically reacting systems, the mass flux of each element should be constant throughout the flat flame. Elemental fluxes not only test elemental balances in the post-flame zone where concentration gradients are small and convective fluxes dominate, but they also test the shapes of data profiles in the preheat and primary reaction zones where large thermal and concentration gradients cause diffusive fluxes as large as convective fluxes. For details on the calculation procedure, refer to [10]. The elemental fluxes (g-atom cm22 s21) calculated from burner feeds were 1.67 3 1025 for H, 1.20 3 1023 for C, 8.66 3 1023 for O, and 4.41 3 1022 for Ar with a total molar flux of 1.76 3 1023 mol s21 cm22 at the burner surface. The percent deviations from these elemental fluxes are shown in Fig. 7. The magnitude of elemental deviations were as good or better than seen in other MBMS flame studies [14, 26]. Deviations in the post-flame-zone balances
463
Fig. 8. Reaction rates for C2H4 kinetics with new rate coefficients for C2H4 1 OH 5 C2H3 1 H2O and C2H4 1 H 5 C2H3 1 H2 reactions.
were 12.75% for C, 24.25% for H, 11.50% for O, and 22.25% for Ar. The larger deviations in elemental fluxes between 0 and 15 mm were probably due to uncertainties of shapes for the mole fraction profiles, which affect the species diffusion velocities. DISCUSSION C2H4 Kinetics From the molar flux balances, net rates of reaction were obtained for C2H4. By analyzing the rates based on measured concentration profiles and temperature [25] and literature kinetics, it becomes possible to identify the key destruction reactions of C2H4. On comparing the net rates obtained from flux balances and rates obtained from data and literature kinetics, improved rate coefficients for reactions involving C2H4 can be tested. The net rate of destruction of C2H4 is shown in Fig. 8. The overall experimental rate curve in the figure is the net rate obtained from flux balance while the overall predicted rate curve is the sum total of all the key formation and destruction channels. Included in the figure are the new rate coefficients for C2H4 1 OH 5 C2H3 1 H2O and C2H4 1 H 5 C2H3 1 H2 that were obtained from analysis of a rich ethylene flame [10]. It was not possible to decouple the different destruction reactions in order to predict new rate coefficients by comparing with the experimental net rate, although it had been possible in the rich ethylene flame [10]. The overall predicted rate was obtained as the sum of the net rates of the four key reactions (C2H4 1 H 5 C2H3 1 H2,
464
A. BHARGAVA AND P. R. WESTMORELAND
Fig. 9. Reaction kinetics for C2H3.
C2H4 1 OH 5 C2H3 1 H2O, C2H4 1 O 5 C2H3 1 OH, and C2H4 1 O 5 CH3 1 HCO). Other C2H4 consumption channels (C2H4 1 O 5 H 1 CH2CHO, C2H4 1 O2 5 C2H3 1 HO2, etc.) were also included but had negligible contribution. The rate coefficients used for the C2H4 1 H 5 C2H3 1 H2 and C2H4 1 OH 5 C2H3 1 H2O reaction channels are k 5 4.49 3 10 7 3 T 2.12 exp(213366/RT), and k 5 (5.53 6 0.14) 3 10 5 3 T (2.31060.004) exp(2(2900 6 60)/RT), respectively [10]. For the C2H4 1 O reaction channel, an overall rate coefficient k ` 5 1.88 3 10 8 3 T 1.60 3 exp(21020/RT) was used along with branching ratio estimations for the different reaction channels from Smalley et al. [27]. As seen in Fig. 8, the overall predicted rate compared excellently with the predicted net rate of C2H4 consumption. Uncertainties should be due primarily to calibration and to the C2H4 1 O kinetics. C2H3 Kinetics After having done C2H4 analysis, rates of vinyl reactions were studied in further detail. As seen in Fig. 9, the experimental net rate of vinyl formation/consumption is about 2 orders of magnitude less than the overall rate predicted with older literature rate constants. This difference suggested that the vinyl destruction chemistry was incomplete because the vinyl formation chemistry is well defined [10]. This discrepancy between the predicted and measured rates is less but is consistent with the observations made in a rich ethylene flame [10]. Examining the dominant reactions tells which reactions can be the cause of this deviation. Under the present fuel-lean conditions, vinyl is
primarily formed by H-abstractions from ethylene by H, OH, and O. Most of the vinyl destruction takes place by C2H3 decomposition reaction at high temperatures or by O2 attack on C2H3 at lower temperatures. The reaction C2H3 1 H 5 C2H2 1 H2 also contributes to vinyl destruction. To improve the kinetics, rate constants were examined and revised. The new rate coefficient suggested by Knyazev and Slagle [28] was used for vinyl decomposition. For C2H3 1 O2, the low-pressure experimental rate constant of 4.0 3 1012 3 exp(1125/T) cm3mol21s21 [29] was used, linearly extrapolating the Arrhenius fit for estimating the rate at higher temperatures. Note that theory [1, 2] indicates this rate constant should decrease dramatically at high temperatures. For C2H3 1 H 5 C2H2 1 H2, a rate coefficient of k 5 1 3 10 14 [30] was used. The destruction rate still appears to be underpredicted, but the deviation seems most consistent with C2H3 calibration uncertainty by the relative ionization cross-section method (RICM). At least two explanations seem possible. First, the rate constants could be incorrect, in particular for C2H3 1 O2 or for C2H3 decomposition reactions [10]; rate constants for the other reactions are known better and have less effect on the destruction rate here. The rate constant for either C2H3 oxidation or decomposition would need to be higher by a factor of 10 –20 relative to the rate constants proposed in the literature in the 300 –2000 K temperature range. A more plausible explanation is the uncertainty in the experimental mole fractions and temperatures. Among the experimental parameters, the RICM-based C2H3 calibration factor is most suspect. RICM calibration factors are normally credited with better than a factorof-two accuracy, mainly based on uncertainties in measuring cross-sections and on comparison to other measurements of H and OH [13]. If the C2H3 calibration factor is only slightly greater, a factor of 3.2 rather than the usually assumed 2, then the corrected rate constants come into good agreement with the falloff expression of Knyazev and Slagle [28]. Uncertainty in the C2H3 calibration factor was then treated as the most likely explanation, lending support to the higher C2H3 decomposition rate constants reported by Knyazev and Slagle [28].
MBMS ANALYSIS OF A LEAN ETHYLENE FLAME Calculations With Flame Mechanisms The temperature and area expansion ratio measurements have been used to model the flames with different reaction sets (Dagaut et al.) [31, 32], Wilk et al. [33], and a reaction set developed in our group [34]. C1 and some C2 hydrocarbon reactions were taken from the GRIMech 1.2 reaction set [35]. New reaction kinetics involving C2 to C6 hydrocarbons have been added from several different sources (30 – 33, 36 and other studies) in order to predict concentration profiles for these species. The NIST Kinetics Database 3.6 [37] was used extensively as a source for rate constants for different reactions. More oxidation chemistry has also been incorporated into the reaction set from the mechanism by Wilk et al. [33]. For modeling, PREMIX/Chemkin codes written at Sandia National Laboratories [38 – 41] have been used. The predictions were then compared with the data. Detailed discussion and presentation of the mechanism will be presented in a subsequent paper. The models are able to predict the magnitude (to within an order of magnitude of the experimental data) and the shape of the mole fraction profiles to a reasonable level. A shift in the position of the profiles measured experimentally and model predictions was observed with the literature reaction sets. This shift could be due to experimental uncertainty (measured temperatures may be too high in regions close to the burner), missing reactions, incorrect thermochemistry and rate constants, and extrapolations of rate parameters beyond the temperature and pressure range where they have been tested or measured. The changes in reaction kinetics corrected nearly all the shift between the data and the predictions with previous sets, indicating important improvement in the rate constants and that uncertainties in the temperature profile were not the cause of error. Predictions with the new reaction set are quite good for most of the lower hydrocarbon species [34], but they fail to predict the shape and magnitude of higher hydrocarbon species. More work needs to be done on the reaction set to get even better comparisons between the predictions and experimental data, especially for higher hydrocarbon species.
465
Reaction Path Analysis The sequence and relative importance of reactions in this flame were examined with reaction path analysis. Reaction path analysis [42, 43] uses a reaction set to analyze the predicted flame structure (mole fraction profiles) it has yielded, distinguishing contributions of individual reactions to formation or consumption of a given species at each position. For reversible reactions, forward and reverse rates are treated separately. Note that this approach is different from linear sensitivity analysis, which establishes the impact of rate-constant uncertainty using differential changes (in effect, perturbation of the Arrhenius pre-exponential factor). Note also that both methods interpret the predictions of the reaction set used, giving the mechanism of steps only if the reaction set used is correct. Nevertheless, using the reaction sets tested here reveals a fairly consistent picture of the chemistry in this flame. Ethylene is destroyed mainly by abstraction C2H4 1 (OH, H, O) 3 C2H3 1 (H2O, H2, OH)
(R1, 2, 3)
to form vinyl; O here is the ground-state O(3P). The low-barrier, chemically activated O-addition channels C2H4 1 O 3 CH3 1 HCO,
(R4)
C2H4 1 O 3 CH2CHO 1 H
(R5)
are secondary channels in this high-temperature flame because the higher energy barrier for abstraction is easily overcome. Vinyl destruction is predicted to occur by three main channels: C2H3 (1M) 3 C2H2 1 H (1M),
(R6)
C2H3 1 O2 3 CH2O 1 HCO,
(R7)
C 2H 3 1 H 3 C 2H 2 1 H 2,
(R8)
in order of decreasing importance, making C2H2 the dominant product. The present modeling and modeling of a fuel-rich C2H4 flame [10] indicate that a recent, faster rate constant for R6 [28] is necessary to predict the measured C2H3 profiles consistently. This change greatly reduces the need for a fast rate constant for R7.
466
A. BHARGAVA AND P. R. WESTMORELAND
Acetylene is then destroyed mainly by Oatom reactions:
CH4 1 (OH, H, O) 3 CH3 1 (H2O, H2, OH)
C2H2 1 O 3 HCCO 1 H,
completely consume the CH4.
(R9)
C2H2 1 O 3 Triplet CH2 1 CO,
(R10)
where ketyl is converted to CO: HCCO 1 H 3 Singlet CH2 1 CO,
(R11)
HCCO 1 O 3 CO 1 HCO,
(R12)
(where HCO also goes rapidly to CO) and to CO2: HCCO 1 O2 3 CO2 1 HCO.
(R13)
Singlet CH2 relaxes collisionally to the groundstate triplet CH2, which is destroyed by reaction with O2. Near the burner, C2H4 is rapidly converted to C2H5, C2H2 1 H (1M) 3 C2H5 1(M),
(R14)
but at higher temperatures, nearly all of the thermal C2H5 reverts to C2H4, C2H5 1(M) 3 C2H4 1 H (1M).
(R-14)
The reason is that H addition to the fuel is fast near the burner where H has back-diffused and falloff of the rate constant is least important (low temperatures). Falloff in R14 and fast rates in both directions R14 and R-14 leave only a small net formation of C2H5. Ethyl is destroyed mainly by reaction with H,
CONCLUSIONS Concentration measurements have been made for 22 species, along with upper-bound measurements for seven species, in a fuel-lean flame with a molecular-beam mass spectrometry (MBMS) system. Temperature measurements were made with a Pt/Pt-13% Rh thermocouple, while the area expansion ratio was measured with a hot-wire anemometer. Flux balance calculations for the four elements involved in the combustion indicate deviations of less than 20%. This result indicates that the data are complete and reliable. The data have been analyzed to give C2H4 and C2H3 chemistry at high temperatures (1500 –2200 K). Preliminary modeling indicated discrepancies between the modeling predictions and experimental data with respect to the position of the profiles. Future work will focus on development of a reaction set that makes predictions consistent with these and other flame data. This work was supported by the U.S. Department of Energy Contract DE-FG02-91ER14192, which is gratefully acknowledged. REFERENCES
(R15)
1.
and CH3 is then oxidized by the well-known sequence [44],
2.
C2H5 1 H 3 CH3 1 CH3,
CH3 1 O 3 CH2O 1 H,
(R16)
3. 4. 5.
CH2O 1 (OH, H, O) 3 HCO 1 (H2O, H2, OH),
(R17, 18, 19)
HCO 1 (M, O2) 3 CO 1 (H, HO2), (R20, 21)
6.
CO 1 OH 3 CO2 1 H,
7.
(R22)
8.
with some formation of CH4 by CH3 1 H (1M) 3 CH4 (1M), although later in the flame
(R24, 25, 26)
(R23) 9.
Westmoreland, P. R., Combust. Sci Tech., 82:151 (1992). Bozzelli, J. W., and Dean, A. M., J. Phys. Chem., 97:4427 (1993). Carpenter, B. K., J. Am. Chem. Soc., 115:9806 (1993). Mebel, A. M., Diau, E. W. G., Lin, M. C., and Morokuma, K., J. Am. Chem. Soc., 118:9759 (1996). Peeters, J., and Mahnen, G., First European Symposium on Combustion, Sheffield, England, 1973, p. 245; Mahnen, G., Ph.D. dissertation, University of Louvain, 1973. Peeters, J., and Vinckier, C., Fifteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1975, p. 969. Homann, K. H., Mochizuki, M., and Wagner, H. Gg., Z. Phys. Chem N. F., 37:299 (1963). Harris, S. J., Weiner, A. M., Blint, R. J., and Goldsmith, J. E. M., Twenty-First Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1986, p. 1033. Cool, T. A., Bernstein, J. S., Song, X. M., and Good-
MBMS ANALYSIS OF A LEAN ETHYLENE FLAME
10. 11. 12.
13. 14.
15.
16.
17.
18.
19. 20. 21. 22. 23. 24.
25. 26.
27. 28. 29. 30. 31. 32. 33. 34.
win, P. M., Twenty-Second Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1988, p. 1421. Bhargava, A., and Westmoreland, P. R., Combust. Flame, 113:338 (1998). Biordi, J. C., Lazzara, C. P., and Papp, J. F., U.S. Bureau of Mines RI 7723, 1973, p. 39. Biordi, J. C., Lazzara, C. P., and Papp, J. F., Fifteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1975, p. 917. Biordi, J. C., Prog. Energy Combust. Sci., 3:151 (1977). Thomas, S. D., Ph.D. dissertation, Department of Chemical Engineering, University of Massachusetts Amherst, Amherst, MA, 1992. Burcat, A., and Radhakrishnan, K., Table of Coefficient Sets for NASA Polynomials in Combustion Chemistry (W. C. Gardiner, Jr., Ed.), Springer-Verlag, New York, 1984. Westmoreland, P. R., Ph. D. dissertation, Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 1986. Bittner, J. D., and Howard, J. B., Eighteenth Symposium (International on Combustion, The Combustion Institute, Pittsburgh, 1981, p. 1105. Westmoreland, P. R., Howard, J. B., and Longwell, J. P., Twenty-first Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1986, p. 773. Thomas, S. D., and Westmoreland, P. R., Combust. Flame, submitted. Fristrom, R. M., Flame Structure and Processes, Oxford University Press, New York, 1995. Kent, J. H., Combust. Flame, 14:279 (1970). Shandross, R. A., Longwell, J. P., and Howard, J. B., Combust. Flame, 85:282 (1991). Biordi, J. C., Lazzara, C. P., and Papp, J. F., Combust. Flame, 23:73 (1974). Stepowski, D., Puechberty, D., and Cottereau, M. J., Eighteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1981, p. 1567. Cattolica, R. J., Yoon, S., and Knuth, E. L., Combust. Sci. Tech., 28:225 (1982). Shandross, R. A., Ph.D. dissertation, Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 1995. Smalley, J. F., Nesbitt, F. L., and Klemm, R. B., J. Phys Chem., 90:491 (1986). Knyazev, V. D., and Slagle, I. R., J. Phys. Chem., 100:16899 (1996). Slagle, I. R., Park, J. Y., Heaven, M. C., and Gutman, D., J. Am. Chem. Soc. 108:4356 (1984). Tsang, W., and Hampson, R. F., J. Phys. Chem. Ref Data, 15:1087 (1986). Dagaut, P., Cathonnet, M., Boettner, J. C., and Gaillard, F., Combust. Flame, 71:295 (1988). Dagaut, P., Cathonnet, M., Boettner, J. C., Combust. Sci. and Tech., 83:167 (1992). Wilk, W. J., Cernansky, N. P., Pitz, W. J., and Westbrook, C. K., Combust. Flame, 77:145 (1989). Bhargava, A., Ph.D. dissertation, Department of Chem-
467
ical Engineering, University of Massachusetts Amherst, Amherst, MA, 1997. 35. M. Frenklach, H. Wang, C.-L. Yu, M. Goldenberg, C. T. Bowman, R. K. Hanson, D. F. Davidson, E. J. Chang, G. P. Smith, D. M. Golden, W. C. Gardiner and V. Lissianski, http://www.me.berkeley.edu/ gri_mech/; M. Frenklach, H. Wang, M. Goldenberg, G. P. Smith, D. M. Golden, C. T. Bowman, R. K. Hanson, W. C. Gardiner and V. Lissianski, GRIMech - An Optimized Detailed Chemical Reaction Mechanism for Methane Combustion, Report No. GRI-95/0058, November 1, 1995. 36. Baulch, D. L., Cobos, C. J., Cox, R. A., Esser, C., Frank, P., Just, Th., Kerr, J. A., Pilling, M. J., Troe, J., Walker, R. W., and Warnatz, J., Evaluated Kinetic Data for Combustion Modeling, J. Phys. Chem. Ref. Data, 21:411 (1992). 37. Lias, S. G., Liebman, J. F., Levin, R. D., and Kafafi, S. A., NIST Standard Reference Database 25, Version 2.01, National Institute of Standard and Technology, 1994. 38. Kee, R. J., Miller, J. A., and Jefferson, T. H., CHEMKIN II version 2.5: A General-Purpose, Problem Independent, Transportable, Fortran Chemical Kinetics Code Package, SAND80-8003, Sandia National Laboratories, Livermore, California, 1980. Modification of CHEMKIN version 3.9, 1992. 39. Kee, R. J., Grcar, J. F., Smooke, M. D., and Miller, J. A., A Fortran Program for Modeling Steady Laminar One-Dimensional Premixed Flames, SAND 858240, Sandia National Laboratories, Livermore, California, 1985. Modifications of PREMIX version 2.5, 1991. 40. Kee, R. J., Dixon-Lewis, G., Warnatz, J., Coltrin, M. E., and Miller, J. A., A Fortran Computer Package for the Evaluation of Gas-Phase, Multicomponent Transport Properties, SAND87-8246, Sandia National Laboratories, Livermore, California, 1986. Modification of TRANLIB version 1.6, 1990. 41. Kee, R. J., Rupley, F. M., and Miller, J. A., The CHEMKIN Thermodynamic Data Base, SAND 878215, Sandia National Laboratories, Livermore, California, 1987. 42. Westmoreland, P. R., Howard, J. B., and Longwell, J. P., Twenty-First Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1986, p. 773. 43. Burgess, D. R. F., Jr., Program Senk3plot, National Institute of Science and Technology, Gaithersburg MD, 1993. 44. Warnatz, J., Eighteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1981, p. 369. 45. Rosenstock, H. M., Draxl, K., Steiner, B. W., and Herron, J. T., J. Phys. Chem. Ref Data Supplement, 6:1 (1977).
Received 26 August 1997; revised 22 January 1998; accepted 26 January 1998.
Chemical Engineering Department, University of Massachusetts Amherst, Amherst, MA 01003-3110 A one-dimensional laminar C2H4/O2/Ar flame was analyzed with a molecular-beam mass spectrometer (MBMS) system. Profiles of concentration, area expansion ratio and temperature were measured for a C2H4/O2/56.9% Ar (f 5 0.75) flame at 4.000 6 0.001 kPa (30.00 Torr) and 30.0 cm/s burner velocity (at 300K). Full concentration profiles were mapped for 22 stable and radical species, while point measurements were made for seven other species. These mole fraction data are valuable for inference of kinetics and testing of reaction mechanisms. Elemental flux deviations were less than 15% in the flame zone and less than 4% in the post-flame zone supporting the data’s accuracy and reliability. Flux balance calculations were also used to obtain the net rate of destruction for C2H4 and C2H3. New values of the rate constants for C2H4 1 H 3 C2H3 1 H2, C2H4 1 OH 3 C2H3 1 H2O and C2H3 3 C2H2 1 H were supported by the agreement between measured rates and the rates predicted from measured temperatures, measured mole fractions, and the new rate constants. © 1998 by The Combustion Institute
INTRODUCTION Understanding C2H4 and C2H3 chemistry is important from the point of predicting combustion chemistry of higher hydrocarbons. Hydrogen abstraction from C2H4, forming vinyl radical, is of great importance in the combustion process. At the same time, reaction with O and OH radicals can also be significant in the consumption of the fuel C2H4. Overall rate constants for these reactions are available for a wide range of temperatures, but for data on branching ratios, one has to rely on low-temperature measurements. Destruction of vinyl is not well understood either. Vinyl may decompose to C2H2 1 H, or it may react with H, O, OH or O2 [1– 4]. The present work maps a lean ethylene flame to an extensive level of detail, valuable for flame modeling. Several researchers have carried out other MBMS studies of C2H4 flames under different conditions, including Peeters and Mahnen [5], Peeters and Vinckier [6], and Homann et al. [7]. Except for the very lean flame (f 5 0.21) of Peeters and Mahnen [5], each of these data sets is missing some measurement valuable for modeling (e.g., measured temperature profile). Harris et al. [8] and Cool et al. [9] have carried out measurements of some species *Corresponding author. Anuj Bhargava is now at United Technologies Research Center, MS 129-30, 411 Silver Lane, East Hartford, CT 06108. 0010-2180/98/$19.00 PII S0010-2180(98)00018-2
in ethylene flames with species-specific laser techniques like laser-induced fluorescence (LIF) and resonance-enhanced multiphoton ionization (REMPI). While valuable, these measurements are likewise insufficient to characterize a flame fully. In the present work, a fuel-lean ethylene flame (f 5 0.75) has been mapped with MBMS for mole fractions, thermocouples for temperature, and hot-wire anemometry for area expansion ratio. This data set has been used in conjunction with recent rich-flame data [10] to obtain and test rate constants for reactions at flame conditions. While the rich flame gives valuable information on molecular-weightgrowth chemistry, the lean flame provides more insight into oxidation chemistry. EXPERIMENTAL APPARATUS AND PROCEDURE Experiments were carried out in an apparatus originally built by Biordi et al. [11] and modified for this work (Fig. 1). Details about the experimental apparatus have been described by Biordi et al. [11–13] and Thomas [14]. Gas flow rates were metered with mass flow controllers (MKS Instruments, Inc., Andover, MA) and mixed. The mixed gases were fed through a 9.91-cm-diameter, sintered-bronze, internally cooled flat-flame burner (Thermet Inc., Gloucester, MA and this laboratory). The flame was ignited by a spark from a Tesla coil and COMBUSTION AND FLAME 115:456 – 467 (1998) © 1998 by The Combustion Institute Published by Elsevier Science Inc.
MBMS ANALYSIS OF A LEAN ETHYLENE FLAME
457
burgh) and collected with a Channeltron electron multiplier (Galileo Electro-optics 4816, Sturbridge, MA). Signal was then measured either as a continuous, modulated current with a lock-in amplifier (EG&G PARC Model 5301 with Model 5317 Differential Preamplifier, Princeton, NJ) or as pulses corresponding to individual ions (PARC/SSR Instruments Model 1110, Princeton, NJ). This mass-spectrometer chamber was pumped with a 4 in. diffusion pump with a liquid-N2-cooled baffle. Both diffusion pumps in the system use low-vaporpressure polyphenylether oil (Santovac-5, Monsanto, St. Louis). A cold finger filled with liquid N2 was also used as a cryopump for the massspectrometer chamber.
Fig. 1. Schematic of the molecular-beam mass spectrometry (MBMS) system.
stabilized by heat transfer to the burner. The bottom of the luminous flame was approximately 5 mm from the burner. Gases were pumped from the burner chamber through two 3.8 cm diam. ports to a 15.2 cm diam. pipe and a gate valve into a 300 cfm mechanical pump (Stokes Microvac 412H-10, Pennwalt Corp., Philadelphia). The burner chamber was isolated from any downstream pressure variations by the gate valve used to set critical flow. Pressure was maintained constant within 0.01 mm Hg by an automatically controlled ballast flow of air (MKS Instruments, Inc., Andover, MA). The molecular beam was formed with a hybrid quartz probe (180 mm orifice, 45° tip) followed by an aluminum skimmer cone (2 mm orifice, included angle of 80°). The chamber between the two was pumped to a pressure of about 1024 to 1025 Torr with a 6 in. diffusion pump. A water-cooled baffle before the diffusion pump minimized backstreaming. After the skimmer, the beam was modulated at 560 Hz with a toothed-wheel chopper and was ionized with a tungsten-filament electronimpact (EI) ionizer. Ions were resolved by a quadrupole mass spectrometer (Extranuclear Laboratories Model 240, Extrel Corp., Pitts-
Methods of Measuring Mole Fractions First, ionization efficiency curves (signal vs ionizing-electron voltage) were measured for the molecular weight of interest at several positions in the flame. These curves were used to identify flame species by their ionization potentials, for indirect calibration, and to determine the ionizer voltage to be used in mapping. Ionizing voltage was kept low, lower than that causing any ion fragmentation effects. Major stable species to be mapped were directly calibrated before and after concentration profiles were measured. A calibration gas mixture of H2, CH4, C2H4, CO, Ar, C3H6, 1-butene, CO2, and toluene was mixed with the flame gas mixture, fed to the burner, and sampled at 6.00 Torr and 298 K, reproducing flame molecular weight and density at 30.00 Torr and 1500 K. Minor and radical species were calibrated from ionization efficiency curves by the method of relative ionization cross-sections (RICM) [13], which is estimated to have a factor-of-2 uncertainty. H, O, and OH calibration coefficients were obtained by assuming that the fast bimolecular reactions H 1 O2 7 OH 1 O,
(Rxn. 1)
O 1 H2 7 OH 1 H,
(Rxn. 2)
OH 1 H2 7 H2O 1 H,
(Rxn. 3)
O 1 H2O 7 OH 1 OH,
(Rxn. 4)
458
A. BHARGAVA AND P. R. WESTMORELAND
attain partial equilibrium in the post-flame zone (37 and 46.5 mm from the burner surface). Any one of these reactions is considered to have reached a partial or dynamic equilibrium if its equilibrium-constant concentration ratio, calculated from experimental concentrations, is equal to its reaction equilibrium constant, calculated from thermodynamics. Expressions for K eqR, the equilibrium constant for reaction R fitted over a temperature range of 300 –2300 K, are K eq1 5
S
X OX OH X HX O2
D
5 2.60 3 102T20.354 eq
exp(217.111 kcal/mol/RT),
K eq2 5
S
X HX OH X OX H2
D
(1)
5 2.225 3 eq
exp(21.86 kcal/mol/RT),
K eq3 5
S
X HX HO2 XOHXH2
D
(2)
5 2.118 3 1021 eq
exp(15.182 kcal/mol/RT).
(3)
The fits are within 3% of values calculated from NASA coefficients by Burcat [15] and Westmoreland [16]. Equations 1, 2, and 3 were solved for the mole fraction ratios of H, O, and OH to Ar in terms of the mole fraction ratios of the stable species H2, H2O, and O2. Calibration factors become
F
X H2 X O2 X OH 5 K eq1K eq2 X Ar X Ar X Ar
G
1/ 2
,
(4)
X H2 X O2 X Ar XO 5 K eq1K eq3 , X Ar X Ar X Ar X H2O
(5)
S D S D S D
XH2 XH 1/2 5 Keq3K1/2 eq1Keq2 XAr XAr
3/ 2
XH2O X Ar
21
X O2
X Ar
1/2
. (6)
These above three equations are combined with an H or O elemental balance in the post-flame zone (37 and 46.5 mm from the burner surface) to give four equations and four unknowns, namely, X O/X Ar, X OH/X Ar, X H/X Ar, and X H2O/ X Ar. The final calibration coefficients, (Xi/XAr)/ (Ii/IAr) where I is the measured signal, were determined as the average of the values at 37.0
and 46.5 mm (the coefficients for the radicals were 0.9316 and 0.8898 for H, 1.8652 and 1.9831 for O atom, and 3.1874 and 3.2315 for OH at 37 and 46.5 mm, respectively). These calibration coefficients indicate that if H, O, and OH had been calibrated by the ionization cross-section method (relative to H2, O2, and CH4, respectively), the mole fraction values would have been off by 222%, 1120%, and 165%, respectively. These results are consistent with earlier observations that O atom is particularly difficult to calibrate by the relative ionization crosssection method [17–19]. The calibration coefficients found from reactions 1–3 were used in reaction 4 to find if it was at equilibrium or not. The reaction does reach equilibrium. This result indicates that the partial equilibrium assumption used to calculate calibration coefficients for H, O, and OH is valid. H2O was calibrated by an overall elemental balance on O, while Ar was obtained by an overall mole balance. Isotopic interferences in the raw signals were corrected by calculated signal strengths for (M-1) and (M-2) ions. The mole fraction data were smoothed using a cubic-spline routine. Profiles of species fluxes, elemental fluxes, and reaction rates were also calculated from the data at each position using standard methods [20]. Temperatures Accurate temperature measurements are essential to interpret and model data. Pt/Pt-13% Rh thermocouples, 0.076 cm in diameter, were used to measure temperatures. These thermocouples were coated with a Y2O3/4.5% BeO glass to avoid catalytic effects [21, 22]. Radiative losses were calibrated as a function of resistive-heating current, using a vacuum chamber to eliminate convective effects. In the flame, the current flowing through the thermocouple was varied until the temperature matched the calibration curve (i.e., T TC 5 T gas), hence eliminating convective heat transfer. An emissivity of 0.55 6 0.2 was calculated for the coated thermocouple. Area Expansion Ratio Area expansion ratio, A( z) 5 r ( z) n ( z)/ r 0n o , was measured with hot-wire anemometry using
MBMS ANALYSIS OF A LEAN ETHYLENE FLAME
459
TABLE 1 List of Species Examined Along With Their IP and Mass Spectrometer Conditions for Fuel-Lean Flame Ionization Potential (eV) Species H atom H2 CH*2 CH3 CH4 O OH H2O C2H2 C2H3 C2H4 CO C2H5 HCO C2H6 CH2O O2 HO2 H2O2 Ar C3H5 HCCO C3H6 CH2CO C3H7 CH2CHO C3H8 CH3CHO CO2 C3H2O* C3H3O* C3H4O* C3H5O* C3H6O* C6H6* a b
Mass 1 2 14 15 16 16 17 18 16 27 28 28 29 29 30 30 32 33 34 40 41 41 42 42 43 43 44 44 44 54 55 56 57 58 78
Literaturea 13.598 15.43 10.396 9.84 12.71 13.62 12.94 12.62 11.41 8.94 10.53 14.01 8.40 9.93 11.55 10.88 12.07 11.53 10.92 15.76 8.07 9.50 9.74 9.60 8.10 10.85 11.07 10.22 13.80 10.0 6 0.5b 8.4 6 0.5b 10.18 8.9 to 9.3 9.96 9.25
Concentration measurement
Measured IP, Position (mm) 13.75 6 0.2, 10.0 15.66 6 0.2, 5.50 Not measured 10.06 6 0.2, 4.0 12.86 6 0.1, 4.0 13.66 6 0.1, 10.0 13.11 6 0.2, 10.0 12.55 6 0.2, 15.5 11.30 6 0.2, 4.15 9.03 6 0.2, 4.15 10.65 6 0.1, 1.0 and 5.5 14.16 6 0.1, 5.5 and 7.0 Not detected 9.90 6 0.2, 3.0 Not detected 10.95 6 0.1, 3.0 11.95 6 0.1, 2.5 11.86 6 0.2, 2.5 10.76 6 0.2, 2.5 Reference Not detected 9.24 6 0.3, 3.0 Not detected 9.38 6 0.2, 3.0 Not detected 10.71 6 0.2, 2.25 Not detected 10.11 6 0.2, 2.25 13.90 6 0.1, 18.0 9.88 6 0.2, 1.15 8.80 6 0.5, 1.15 9.81 6 0.2, 1.15 9.11 6 0.3, 1.15 9.86 6 0.2, 1.15 9.46 6 0.3, 1.15
EI (eV)
Calibration type
15.60 16.95 12.70 12.70 14.20 15.60 15.60 15.60 12.35 10.85 12.40 16.40
Partial equilibrium Direct Ionization cross-section Ionization cross-section Direct Partial equilibrium Partial equilibrium H atom balance Ionization cross-section Ionization cross-section Direct Direct
11.50
Ionization cross-section vs C2H4
12.85 14.00 14.00 14.00 18.00
Ionization cross-section vs C2H4 Direct Ionization cross-section vs O2 Ionization cross-section vs O2 Direct
11.50
Ionization cross-section vs CO2
11.50
Ionization cross-section vs CO2
11.50
Ionization cross-section vs CO2
11.50 16.60 10.86 10.86 10.86 10.86 10.86 10.86
Ionization Direct Ionization Ionization Ionization Ionization Ionization Ionization
vs CH4 vs CH4
vs C2H4 vs C2H4
cross-section vs CO2 cross-section cross-section cross-section cross-section cross-section cross-section
vs vs vs vs vs vs
Ar Ar Ar Ar Ar Ar
Rosenstock et al. [45] except as noted otherwise. Estimated by Thomas [14]; *Upper-bound measurements.
cold gases. The anemometer was made of a 23 mm long, 0.076 mm diam. platinum wire supported by 0.381 mm diam. platinum wire. The wire was supported normal to the flow direction and operated at 570 K (determined by the resistance of the wire). The measurements were fitted by the expression A~ z! 5 ~0.9941 2 0.0076z!/~1 2 0.0122z! with z in mm. Details of the experimental procedure are presented in [10].
RESULTS Mole fraction profiles were measured for 22 stable and radical species in a C2H4/O2/56.9% Ar (f 5 0.75) flame at 4.000 6 0.001 kPa (30.00 Torr) and 30.0 cm/s burner velocity (based on 300K). Upper bound measurements were also made for seven other species. A list of all the species measured along with their mass spectrometer conditions is presented in Table 1. The concentration profiles for the 22 species are given in Figs. 2 to 6, while upper bounds for the
460
A. BHARGAVA AND P. R. WESTMORELAND TABLE 2 Species for Which Point Measurements Were Made
Mass
Species
Mole fraction at 1.15 mm from the burner surface
Mole fraction at 3.10 mm from the burner surface
14 54 55 56 57 58 78
CH2 C3H2O C3H3O C3H4O C3H5O C3H6O C6H6
2.8 3 1025 2.6 3 1026 2.0 3 1026 1.26 3 1025 8.1 3 1026 1.06 3 1025 7.6 3 1026
1.8 3 1025 1.9 3 1026 4.0 3 1026 9.9 3 1026 4.4 3 1026 9.6 3 1026 6.0 3 1026
seven species are given in Table 2. Results are discussed in the following order: correction for sampling perturbations, temperature profiles, major species, the major radicals, other C1 and C2 hydrocarbons, oxygenates, and point measurements. Correction for Sampling Perturbations In MBMS sampling, the quartz probe and the thermocouple induce some perturbations in the measured concentration and temperature profiles. Several researchers have studied the distortions that are caused by the probe and thermocouple. Biordi et al. [23] measured the CH4 concentration profile in a low-pressure methane flat flame. They found that the profile measured by MBMS using a hybrid quartz probe was shifted towards the burner by about 5 orifice diameters as compared to a more spatially precise microprobe measurement. Stepowski et al. [24] measured OH profiles at 0.033 atm with both MBMS and laser-induced fluorescence (LIF), finding a shift of 2 orifice diameters in the MBMS data beyond the flame zone. They further found that the quartz probe reduces the OH concentration measured with a MBMS in the preheating zone as compared to the measurements made with LIF. This effect was attributed to a perturbation of the diffusion field by the probe. The authors suggested that the OH concentration measured by MBMS is the actual value in the sample (post-flame zone). Cattolica et al. [25] measured OH profile in flames at 1 atm with MBMS and LIF and found a shift upstream for MBMS of about 2 orifice diameters. For modeling purposes, the measured temperature profile was lowered by 100 K to ac-
count for the cooling effect of the probe and moved 0.5 mm away from the burner surface to account for perturbations caused by the thermocouple [20]. The concentration profile was moved by 0.9 mm (5 times the orifice diameter) towards the burner surface in order to account for perturbations caused by the quartz probe. Temperature Profiles The corrected temperature profile is shown in Fig. 2. Burner temperature was measured as 440 K with the thermocouple touching the burner surface. A maximum temperature of 2025 K was recorded at 9.5 mm above the burner surface. With the standard correction applied, the maximum became 1925 K at 10 mm.
Fig. 2. Mole fraction data and smoothed profiles for major stable species, C2H4 (*), O2 (D), CO (•), H2O (O), CO2 (3), Ar (◊), and the smoothed temperature profile (solid line with no points shown).
MBMS ANALYSIS OF A LEAN ETHYLENE FLAME
Fig. 3. Mole fraction data and smoothed profiles for H (3), H2 (O), O (D), and OH (•).
Species Profiles Among the major stable species, C2H4 is fully consumed by 5 mm, as shown in Fig. 2. The O2 mole fraction falls rapidly in the first 6 mm before settling down to a final value of 0.11. The intermediate species H2 and CO form near the burner and then are consumed. H2 rises to a maximum value of 6.70 3 1023 at 4.3 mm, as shown in Fig. 3. It declines rapidly to approximately 3 3 1023 by 15 mm and then declines only slightly further. CO rises rapidly to a mole fraction of 7.92 3 1022 by 2.8 mm. Beyond its maximum, it decreases sharply to about 3.03 3 1023 at 9 mm, thereafter declining slowly. H2O and CO2 are the products of H2 and CO oxidation, respectively. H2O shows a local maximum of 0.185 at 12 mm before settling down to 0.173 mole fraction. CO2 rises to a mole fraction of 0.10 at 8 mm and then gradually increases to 0.13 by 51 mm, the largest distance where measurements were made. The major radicals H, O, and OH are shown in Fig. 3, with H2 also shown for comparison. H atom rises to a maximum value of 2.68 3 1023 at 15.75 mm, while OH rises higher to a maximum value of 9.90 3 1023 at 18 mm. Like most radicals, their concentrations decrease slowly in the post-flame zone, reaching 1.02 3 1023 and 6.51 3 1023 by 51 mm, respectively. Signal measured for mass 16 was analyzed as CH4 at distances close to the burner, but at distances above 8 mm it was assigned to O atom. The mole fraction of O atom has a maximum of 6.20 3 1023 at 11.9 mm and then decreases
461
Fig. 4. Mole fraction data and smoothed profiles for HCO (O), CH2O (D), HO2 (3), and H2O2 (◊).
gradually, to 2.56 3 1023 at 51.32 mm. An O atom profile between 0 and 8 mm was estimated by extrapolation. The other oxidizing radical that was detected and measured was HO2. HO2 peaks at a value of 4.27 3 1024 at 2.79 before decreasing gradually to 2.63 3 1025 at 12.57 mm. The coupled molecule H2O2 peaks at 3.79 3 1024 at 2.8 mm and then declines to 1.18 3 1025 at 12.57 mm (see Fig. 4). Among the hydrocarbon radicals, C2H3 and CH3 are thought to be especially important in the combustion process. C2H3 radical attains a maximum mole fraction of only 4.99 3 1025 at 4.1 mm and then comes down sharply, reaching a mole fraction of 4.61 3 1026 at 8.13 mm (Fig. 5). On the other hand, the much less reactive CH3 peaks at 4.3 mm at a much higher mole fraction of 7.77 3 1023. Its mole fraction then decreases steadily to 1.44 3 1025 at 8.13 mm.
Fig. 5. Mole fraction data and smoothed profiles for CH3 (3), CH4 (O), C2H3 (◊), C2H2 (D), and C2H4 (•).
462
Fig. 6. Mole fraction data and smoothed profiles for CHCO (3), CH2CO (O), CH2CHO (D), and CH3CHO (◊).
The other C1 and C2 species that were detected were CH4 and C2H2, shown in Fig. 5. As mentioned earlier, signal at mass 16 was a combination of O atom and CH4. The ionization efficiency measurements indicated that the signal closer to the burner was predominantly CH4, while further away from the burner, the signal was dominated by O atom. The CH4 signal rises rapidly to 7.27 3 1026 at 3.13 mm. Following its maximum, the methane mole fraction decreased slowly to 3.3 3 1023 at 6.6 mm. Beyond 7.6 mm, the signal increases, indicating that the signal in this region is dominated by O atom. The C2H2 mole fraction profile rises to 9.51 3 1024 at 4.83 mm from the burner surface and then decreases more rapidly. Mass 29 and mass 30 were identified as the C1 oxygenates, HCO and CH2O, respectively (Fig. 4). The signal for mass 29, which had an ionization potential of 9.85 6 0.20 eV at 3.0 mm, is strongly dominated by HCO (IP 5 9.90 eV) but also includes any C2H5 (IP 5 8.40 eV). By the same reasoning, mass 30 was strongly dominated by CH2O rather than C2H6. HCO shows a peak mole fraction value of 9.4 3 1025 at 3.3 mm, while CH2O peaks at a mole fraction of 5.6 3 1024 at 3 mm. Among the C2 oxygenated species, mass 42 (CH2CO) and mass 43 (C2H3O) are highest in concentration. The mole fraction profiles for the different C2 oxygenates are shown in Fig. 6. The ionization potentials of the two mass 42 species C3H6 and CH2CO are so close that it is not possible to distinguish between the two. Because the preliminary modeling suggested that the signal is strongly dominated by the
A. BHARGAVA AND P. R. WESTMORELAND oxygenate, it was interpreted as CH2CO. Its mole fraction has a maximum of 2.6 3 1024 at 3.05 mm. For mass 43, the appearance potential of 10.71 6 0.20 eV at 2.25 mm implies that the signal at that position is from CH2CHO, which has an ionization potential value of 10.85 eV, rather than from C3H4 or the less stable CH3CO. A C2H3O1 fragment of CH3CHO would be formed near this potential, but the shape difference of the mass 43 profile relative to CH3CHO implies that CH2CHO dominates. The mass 43 signal was corrected for isotopic contribution from the mass 42 (CH2CO) signal and converted to mole fraction. The mole fraction then displays a maximum of 2.04 3 1024 at 2.54 mm. The other C2 oxygenates detected were mass 41 (HCCO) and mass 44 (CH3CHO), shown in Fig. 6. Mass 41 signal could also be from C3H5 (IP 5 8.07 eV), but the ionization potential measurement of 9.24 6 0.30 eV at 3.0 mm implies that the mass 41 signal at that point is dominated by HCCO (IP 5 9.50 eV). Its mole fraction rose to a maximum of 9.56 3 1026 at 3.56 mm. The ionization efficiency curve for mass 44 measured at 2.25 mm showed two distinct linear regions. The species at higher electron energy (IP 5 13.90 6 0.1) was CO2 (ionization potential of 13.8 eV). The species occurring at lower eV (10.11 6 0.2) was acetaldehyde (IP of 10.22 eV) rather than propane (IP of 11.07 eV), attaining a maximum mole fraction of 8.57 3 1025 at 2.03 mm from the burner. Point measurements were also made for CH2; C3 oxygenates C3H2O, C3H3O, C3H4O, C3H5O, C3H6O; and C6H6. As the concentrations of these species were too low for full profile measurements, upper bound measurements were made for the seven species at two distances. “Upper bound” means that the signal detected and measured was a sum of the signal from the species from the molecular beam and background signal, which included signal from the species in the background and noise. The mole fractions (upper limit) thus obtained are shown in Table 2. All seven species were calibrated by the method of relative ionization cross-section with respect to argon. Signal for masses 54 –58 may instead have been from the pure hydrocarbon species (C4H6 to C4H10) but were treated as being from oxygen-containing species. For some
MBMS ANALYSIS OF A LEAN ETHYLENE FLAME
Fig. 7. Overall elemental flux balance for C, H, O, and Ar.
masses the assignments were made due to modeling considerations, while in other cases it was possible to distinguish the species (C3H3O, C3H5O, C3H6O) with the help of ionization efficiency curves. For some of the species, literature ionization potential values were not available (e.g., C3H2O, C3H3O). Ionization potentials for these species were obtained by analogies to acrolein as suggested by Thomas (1992). Flux Balances The calculation of elemental fluxes from smoothed data profiles is a good test for internal consistency of the MBMS data. Because atoms are conserved in chemically reacting systems, the mass flux of each element should be constant throughout the flat flame. Elemental fluxes not only test elemental balances in the post-flame zone where concentration gradients are small and convective fluxes dominate, but they also test the shapes of data profiles in the preheat and primary reaction zones where large thermal and concentration gradients cause diffusive fluxes as large as convective fluxes. For details on the calculation procedure, refer to [10]. The elemental fluxes (g-atom cm22 s21) calculated from burner feeds were 1.67 3 1025 for H, 1.20 3 1023 for C, 8.66 3 1023 for O, and 4.41 3 1022 for Ar with a total molar flux of 1.76 3 1023 mol s21 cm22 at the burner surface. The percent deviations from these elemental fluxes are shown in Fig. 7. The magnitude of elemental deviations were as good or better than seen in other MBMS flame studies [14, 26]. Deviations in the post-flame-zone balances
463
Fig. 8. Reaction rates for C2H4 kinetics with new rate coefficients for C2H4 1 OH 5 C2H3 1 H2O and C2H4 1 H 5 C2H3 1 H2 reactions.
were 12.75% for C, 24.25% for H, 11.50% for O, and 22.25% for Ar. The larger deviations in elemental fluxes between 0 and 15 mm were probably due to uncertainties of shapes for the mole fraction profiles, which affect the species diffusion velocities. DISCUSSION C2H4 Kinetics From the molar flux balances, net rates of reaction were obtained for C2H4. By analyzing the rates based on measured concentration profiles and temperature [25] and literature kinetics, it becomes possible to identify the key destruction reactions of C2H4. On comparing the net rates obtained from flux balances and rates obtained from data and literature kinetics, improved rate coefficients for reactions involving C2H4 can be tested. The net rate of destruction of C2H4 is shown in Fig. 8. The overall experimental rate curve in the figure is the net rate obtained from flux balance while the overall predicted rate curve is the sum total of all the key formation and destruction channels. Included in the figure are the new rate coefficients for C2H4 1 OH 5 C2H3 1 H2O and C2H4 1 H 5 C2H3 1 H2 that were obtained from analysis of a rich ethylene flame [10]. It was not possible to decouple the different destruction reactions in order to predict new rate coefficients by comparing with the experimental net rate, although it had been possible in the rich ethylene flame [10]. The overall predicted rate was obtained as the sum of the net rates of the four key reactions (C2H4 1 H 5 C2H3 1 H2,
464
A. BHARGAVA AND P. R. WESTMORELAND
Fig. 9. Reaction kinetics for C2H3.
C2H4 1 OH 5 C2H3 1 H2O, C2H4 1 O 5 C2H3 1 OH, and C2H4 1 O 5 CH3 1 HCO). Other C2H4 consumption channels (C2H4 1 O 5 H 1 CH2CHO, C2H4 1 O2 5 C2H3 1 HO2, etc.) were also included but had negligible contribution. The rate coefficients used for the C2H4 1 H 5 C2H3 1 H2 and C2H4 1 OH 5 C2H3 1 H2O reaction channels are k 5 4.49 3 10 7 3 T 2.12 exp(213366/RT), and k 5 (5.53 6 0.14) 3 10 5 3 T (2.31060.004) exp(2(2900 6 60)/RT), respectively [10]. For the C2H4 1 O reaction channel, an overall rate coefficient k ` 5 1.88 3 10 8 3 T 1.60 3 exp(21020/RT) was used along with branching ratio estimations for the different reaction channels from Smalley et al. [27]. As seen in Fig. 8, the overall predicted rate compared excellently with the predicted net rate of C2H4 consumption. Uncertainties should be due primarily to calibration and to the C2H4 1 O kinetics. C2H3 Kinetics After having done C2H4 analysis, rates of vinyl reactions were studied in further detail. As seen in Fig. 9, the experimental net rate of vinyl formation/consumption is about 2 orders of magnitude less than the overall rate predicted with older literature rate constants. This difference suggested that the vinyl destruction chemistry was incomplete because the vinyl formation chemistry is well defined [10]. This discrepancy between the predicted and measured rates is less but is consistent with the observations made in a rich ethylene flame [10]. Examining the dominant reactions tells which reactions can be the cause of this deviation. Under the present fuel-lean conditions, vinyl is
primarily formed by H-abstractions from ethylene by H, OH, and O. Most of the vinyl destruction takes place by C2H3 decomposition reaction at high temperatures or by O2 attack on C2H3 at lower temperatures. The reaction C2H3 1 H 5 C2H2 1 H2 also contributes to vinyl destruction. To improve the kinetics, rate constants were examined and revised. The new rate coefficient suggested by Knyazev and Slagle [28] was used for vinyl decomposition. For C2H3 1 O2, the low-pressure experimental rate constant of 4.0 3 1012 3 exp(1125/T) cm3mol21s21 [29] was used, linearly extrapolating the Arrhenius fit for estimating the rate at higher temperatures. Note that theory [1, 2] indicates this rate constant should decrease dramatically at high temperatures. For C2H3 1 H 5 C2H2 1 H2, a rate coefficient of k 5 1 3 10 14 [30] was used. The destruction rate still appears to be underpredicted, but the deviation seems most consistent with C2H3 calibration uncertainty by the relative ionization cross-section method (RICM). At least two explanations seem possible. First, the rate constants could be incorrect, in particular for C2H3 1 O2 or for C2H3 decomposition reactions [10]; rate constants for the other reactions are known better and have less effect on the destruction rate here. The rate constant for either C2H3 oxidation or decomposition would need to be higher by a factor of 10 –20 relative to the rate constants proposed in the literature in the 300 –2000 K temperature range. A more plausible explanation is the uncertainty in the experimental mole fractions and temperatures. Among the experimental parameters, the RICM-based C2H3 calibration factor is most suspect. RICM calibration factors are normally credited with better than a factorof-two accuracy, mainly based on uncertainties in measuring cross-sections and on comparison to other measurements of H and OH [13]. If the C2H3 calibration factor is only slightly greater, a factor of 3.2 rather than the usually assumed 2, then the corrected rate constants come into good agreement with the falloff expression of Knyazev and Slagle [28]. Uncertainty in the C2H3 calibration factor was then treated as the most likely explanation, lending support to the higher C2H3 decomposition rate constants reported by Knyazev and Slagle [28].
MBMS ANALYSIS OF A LEAN ETHYLENE FLAME Calculations With Flame Mechanisms The temperature and area expansion ratio measurements have been used to model the flames with different reaction sets (Dagaut et al.) [31, 32], Wilk et al. [33], and a reaction set developed in our group [34]. C1 and some C2 hydrocarbon reactions were taken from the GRIMech 1.2 reaction set [35]. New reaction kinetics involving C2 to C6 hydrocarbons have been added from several different sources (30 – 33, 36 and other studies) in order to predict concentration profiles for these species. The NIST Kinetics Database 3.6 [37] was used extensively as a source for rate constants for different reactions. More oxidation chemistry has also been incorporated into the reaction set from the mechanism by Wilk et al. [33]. For modeling, PREMIX/Chemkin codes written at Sandia National Laboratories [38 – 41] have been used. The predictions were then compared with the data. Detailed discussion and presentation of the mechanism will be presented in a subsequent paper. The models are able to predict the magnitude (to within an order of magnitude of the experimental data) and the shape of the mole fraction profiles to a reasonable level. A shift in the position of the profiles measured experimentally and model predictions was observed with the literature reaction sets. This shift could be due to experimental uncertainty (measured temperatures may be too high in regions close to the burner), missing reactions, incorrect thermochemistry and rate constants, and extrapolations of rate parameters beyond the temperature and pressure range where they have been tested or measured. The changes in reaction kinetics corrected nearly all the shift between the data and the predictions with previous sets, indicating important improvement in the rate constants and that uncertainties in the temperature profile were not the cause of error. Predictions with the new reaction set are quite good for most of the lower hydrocarbon species [34], but they fail to predict the shape and magnitude of higher hydrocarbon species. More work needs to be done on the reaction set to get even better comparisons between the predictions and experimental data, especially for higher hydrocarbon species.
465
Reaction Path Analysis The sequence and relative importance of reactions in this flame were examined with reaction path analysis. Reaction path analysis [42, 43] uses a reaction set to analyze the predicted flame structure (mole fraction profiles) it has yielded, distinguishing contributions of individual reactions to formation or consumption of a given species at each position. For reversible reactions, forward and reverse rates are treated separately. Note that this approach is different from linear sensitivity analysis, which establishes the impact of rate-constant uncertainty using differential changes (in effect, perturbation of the Arrhenius pre-exponential factor). Note also that both methods interpret the predictions of the reaction set used, giving the mechanism of steps only if the reaction set used is correct. Nevertheless, using the reaction sets tested here reveals a fairly consistent picture of the chemistry in this flame. Ethylene is destroyed mainly by abstraction C2H4 1 (OH, H, O) 3 C2H3 1 (H2O, H2, OH)
(R1, 2, 3)
to form vinyl; O here is the ground-state O(3P). The low-barrier, chemically activated O-addition channels C2H4 1 O 3 CH3 1 HCO,
(R4)
C2H4 1 O 3 CH2CHO 1 H
(R5)
are secondary channels in this high-temperature flame because the higher energy barrier for abstraction is easily overcome. Vinyl destruction is predicted to occur by three main channels: C2H3 (1M) 3 C2H2 1 H (1M),
(R6)
C2H3 1 O2 3 CH2O 1 HCO,
(R7)
C 2H 3 1 H 3 C 2H 2 1 H 2,
(R8)
in order of decreasing importance, making C2H2 the dominant product. The present modeling and modeling of a fuel-rich C2H4 flame [10] indicate that a recent, faster rate constant for R6 [28] is necessary to predict the measured C2H3 profiles consistently. This change greatly reduces the need for a fast rate constant for R7.
466
A. BHARGAVA AND P. R. WESTMORELAND
Acetylene is then destroyed mainly by Oatom reactions:
CH4 1 (OH, H, O) 3 CH3 1 (H2O, H2, OH)
C2H2 1 O 3 HCCO 1 H,
completely consume the CH4.
(R9)
C2H2 1 O 3 Triplet CH2 1 CO,
(R10)
where ketyl is converted to CO: HCCO 1 H 3 Singlet CH2 1 CO,
(R11)
HCCO 1 O 3 CO 1 HCO,
(R12)
(where HCO also goes rapidly to CO) and to CO2: HCCO 1 O2 3 CO2 1 HCO.
(R13)
Singlet CH2 relaxes collisionally to the groundstate triplet CH2, which is destroyed by reaction with O2. Near the burner, C2H4 is rapidly converted to C2H5, C2H2 1 H (1M) 3 C2H5 1(M),
(R14)
but at higher temperatures, nearly all of the thermal C2H5 reverts to C2H4, C2H5 1(M) 3 C2H4 1 H (1M).
(R-14)
The reason is that H addition to the fuel is fast near the burner where H has back-diffused and falloff of the rate constant is least important (low temperatures). Falloff in R14 and fast rates in both directions R14 and R-14 leave only a small net formation of C2H5. Ethyl is destroyed mainly by reaction with H,
CONCLUSIONS Concentration measurements have been made for 22 species, along with upper-bound measurements for seven species, in a fuel-lean flame with a molecular-beam mass spectrometry (MBMS) system. Temperature measurements were made with a Pt/Pt-13% Rh thermocouple, while the area expansion ratio was measured with a hot-wire anemometer. Flux balance calculations for the four elements involved in the combustion indicate deviations of less than 20%. This result indicates that the data are complete and reliable. The data have been analyzed to give C2H4 and C2H3 chemistry at high temperatures (1500 –2200 K). Preliminary modeling indicated discrepancies between the modeling predictions and experimental data with respect to the position of the profiles. Future work will focus on development of a reaction set that makes predictions consistent with these and other flame data. This work was supported by the U.S. Department of Energy Contract DE-FG02-91ER14192, which is gratefully acknowledged. REFERENCES
(R15)
1.
and CH3 is then oxidized by the well-known sequence [44],
2.
C2H5 1 H 3 CH3 1 CH3,
CH3 1 O 3 CH2O 1 H,
(R16)
3. 4. 5.
CH2O 1 (OH, H, O) 3 HCO 1 (H2O, H2, OH),
(R17, 18, 19)
HCO 1 (M, O2) 3 CO 1 (H, HO2), (R20, 21)
6.
CO 1 OH 3 CO2 1 H,
7.
(R22)
8.
with some formation of CH4 by CH3 1 H (1M) 3 CH4 (1M), although later in the flame
(R24, 25, 26)
(R23) 9.
Westmoreland, P. R., Combust. Sci Tech., 82:151 (1992). Bozzelli, J. W., and Dean, A. M., J. Phys. Chem., 97:4427 (1993). Carpenter, B. K., J. Am. Chem. Soc., 115:9806 (1993). Mebel, A. M., Diau, E. W. G., Lin, M. C., and Morokuma, K., J. Am. Chem. Soc., 118:9759 (1996). Peeters, J., and Mahnen, G., First European Symposium on Combustion, Sheffield, England, 1973, p. 245; Mahnen, G., Ph.D. dissertation, University of Louvain, 1973. Peeters, J., and Vinckier, C., Fifteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1975, p. 969. Homann, K. H., Mochizuki, M., and Wagner, H. Gg., Z. Phys. Chem N. F., 37:299 (1963). Harris, S. J., Weiner, A. M., Blint, R. J., and Goldsmith, J. E. M., Twenty-First Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1986, p. 1033. Cool, T. A., Bernstein, J. S., Song, X. M., and Good-
MBMS ANALYSIS OF A LEAN ETHYLENE FLAME
10. 11. 12.
13. 14.
15.
16.
17.
18.
19. 20. 21. 22. 23. 24.
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Received 26 August 1997; revised 22 January 1998; accepted 26 January 1998.