Nitric oxide formation in premixed flames of H2+CO+CO2 and air

Proceedings of the Combustion Institute, Volume 29, 2002/pp. 2171–2177

NITRIC OXIDE FORMATION IN PREMIXED FLAMES OF H2 ⴐ CO ⴐ CO2 AND AIR ALEXANDER A. KONNOV, IGOR V. DYAKOV and JACQUES DE RUYCK Department of Mechanical Engineering Vrije Universiteit Brussel Brussels, Belgium

Burning velocity and probe sampling measurements of the concentrations of O2, CO2, CO, and NO in the postflame zone of the flames of H2 Ⳮ CO Ⳮ CO2 and air are reported. The heat flux method was used for stabilization of laminar, premixed, non-stretched flames on a perforated plate burner at 1 atm. Axial profiles of the concentrations of major species were used to evaluate the influence of the ambient air entrainment and downstream heat losses. The influence of the downstream heat losses to the environment has been included in the modeling. The numerical predictions of the concentrations of O2, CO2, and CO in the postflame zone are in a good agreement with the experiment. The amount of the NO formed in the adiabatic flame front is significantly higher than that formed downstream. It is shown that in rich mixtures, where the NNH route forming NO is dominant, the heat losses do not affect significantly the calculated [NO]. The comparison of the experimental data with the detailed flame structure modeling strongly suggests a reduced value of the rate constant k1 for the reaction NNH Ⳮ O ⳱ NH Ⳮ NO. The calculations with k1 ⳱ (1 Ⳳ 0.5) ⳯ 1014exp(ⳮ16.75 Ⳳ 4.2 kJ/mol/RT) cm3/mol s bring the modeling close to the measurements not only in rich but also in stoichiometric and lean flames. The rate constant proposed in the present study is consistent with earlier evaluations within uncertainty limits.

Introduction After massive research efforts carried out in the past two to three decades, important reaction routes that lead to NO formation in flames are thought to be well understood. However, an agreement between measurements of emitting NOx and model predictions is often only qualitative. For instance, measurements and modeling of nitric oxide formation in atmospheric and high-pressure laminar flames of methane and ethane [1–3] suggest problems in the NO prediction. It was argued that discrepancies between NO concentrations measured by laser-induced fluorescence (LIF) and calculated ones might be explained by the uncertainties in the new route forming NO via NNH radicals [2–5]. The oxidation of NNH radicals in reaction NNH Ⳮ O ⳱ NH Ⳮ NO

(1)

is a key step in this route proposed by Bozzelli and Dean [6]. They suggested that significant amounts of nitric oxide can be produced in flames from N2 via NNH, formed in N2 Ⳮ H ⳱ NNH

(2)

Miller and Melius [7] apparently were the first to suggest a high value of k1 ⳱ 5 ⳯ 1013 cm3/mol s for T ⬎ 2000 K. This appears to be reasonably consistent with subsequent QRRK analysis [6,8]. Experiments, aimed at corroborating the formation of

NO from the NNH route, have been performed by Harrington et al. [9]. Although agreement between measurements in low-pressure hydrogen/air flames and modeling employing GRI-MECH 2.11 [10] was imperfect, it was concluded that the NNH route is a viable explanation for the presence of ppm levels of [NO] in these flames. Assuming that the NH radicals formed in reaction 1 are totally converted into NO, and that reaction 2 is equilibrated, the rate of NO formation is proportional to the concentration of N2, O atoms, H atoms, and (k1Kp2), where Kp2 is the equilibrium constant of reaction 2. Effective values of (k1Kp2) have been obtained by Hayhurst and Hutchinson [11] at 1800–2500 K in rich flames of H2 Ⳮ O2 Ⳮ N2 and CH4 Ⳮ O2 Ⳮ N2 burning at 1 atm. Konnov et al. [12] extended the temperature range for measuring (k1Kp2) down to 1400 K by modeling experiments on the lean combustion of hydrogen and air in a stirred reactor [13]. Subsequent evaluation of the NNH route forming NO in hydrogen combustion in stirred reactors showed that this pathway is important at short residence times from 1000 to 2200 K in rich, stoichiometric, and lean mixtures [14,15]. Recently, the rate constant of reaction 1 has been derived by comparing experiments in hydrogen/air flames at ⬃1200 K [9] with modeling, employing an updated detailed H/N/O kinetic scheme [16]. To match calculations with experimental profiles of [NO] in these flames, the rate constant of this reaction is found to be reduced significantly

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(by ⬃50%) below values adopted earlier [6–8]. Combination of the adjusted rate constant with measurements in the range 1800–2500 K [11] strongly suggested a non-zero activation energy of reaction 1. The rate constant derived from 1200 to 2500 K was k1 ⳱ (2 Ⳳ 1) ⳯ 1014exp(ⳮ16.75 Ⳳ 4.2 kJ/mol/RT) cm3/mol s [16]. Accurate determination of the rate constant k1 was hampered by unavoidable uncertainties in temperature measurements and by the presence of other sources of NO. For instance, in the lean combustion of hydrogen and air in a stirred reactor [13], a significant part of NO is formed via nitrous oxide route [15]. In rich flames of H2 Ⳮ O2 Ⳮ N2, nitric oxide formed via the thermal Zeldovich mechanism had to be taken into account, while in rich flames of CH4 Ⳮ O2 Ⳮ N2 potential prompt NO might also interfere [11]. Finally in low-pressure hydrogen/air flames [9], both the NNH route and the reactions of N2Hx species were shown to contribute to the formation of NO [16]. The present study has been devoted therefore to measuring the concentrations of NO in adiabatic laminar premixed flames where the NNH route forming NO is dominant. In the following, an experimental installation is shortly described. Burning velocity measurements and axial profiles of the concentrations of major species and NO in the postflame zone are then presented. Finally the NO concentration measurements are compared with the detailed flame modeling. Experimental Premixed flames of H2 Ⳮ CO Ⳮ CO2 and air were stabilized at 1 atm over the burner plate of 30 mm in diameter perforated with small holes using the heat flux method introduced by de Goey et al. [17]. The experimental setup for the adiabatic flame stabilization and determination of the flame burning velocity were described elsewhere [18–21]; however, the most relevant details are repeated shortly here. Initial mixture temperature was 298 K. Concentration measurements of stable species were made using non-cooled quartz probes. The probes had an inlet diameter of 0.9 mm, an external diameter of 6 mm, and 1 mm walls. The sampling gas line was connected to the gas analyzers via a conditioning unit, membrane pump, and filter. The conditioning unit removes the water (dew point 5 ⬚C) by rapid chilling, without allowing dissolution of gas components in the liquid phase. To compare the measured concentrations with the predicted by the modeling ones, the last were recalculated to the dry basis. To measure concentrations of the different components, several gas analyzers from Fisher Rosemount Gmbh were used. Oxygen concentration was measured by the Oxynos 100 paramagnetic analyzer. Carbon monoxide and carbon dioxide concentrations were detected by the Binos 1000 analyzer. For

the concentrations of CO higher than 1000 ppm, the Binos 100 analyzer was used. The model 951A NO/ NO2 chemiluminescence analyzer was used for measurements of NO and NOx (the sum of NO and NO2). In the present work, the measurements of NO or NOx were indistinguishable within the experimental accuracy. The flame modeling described below confirms that in the postflame zone of interest, the concentration of NO2 was always below 1% of that of NO. Before each series of measurements, the gas analyzers were calibrated with calibrating mixtures. The calibrating mixtures and pure gases were used as delivered by the supplier. The stated purity of the gases was 99.99% and better; the total amount of hydrocarbons in the mixtures studied never exceeded 40 ppm. The calibrating mixtures of CO, CO2, and NO diluted by pure nitrogen were prepared with the stated accuracy of 3, 2, and 5%, respectively. The oxygen analyzer was calibrated by the ambient air. Error Assessment The flames stabilized employing the heat flux method resemble steady one-dimensional adiabatic free flames as soon as the heat flux from the flame to the burner is zero. However, due to finite size of the flame, the influence of ambient conditions is not negligible. The flat flame non-idealities have been examined elsewhere [18,19] and are shortly summarized below. The analysis was based on the previous numerical and experimental flame characterization performed by LDV, LIF, and CARS [20–22]. A development and testing of the installation used in the present study was described earlier [18]. An overall accuracy of the burning velocity measurements was estimated to be better than Ⳳ0.8 cm/s (double standard deviation with 95% confidence level) in the whole range of velocities from about 10 to 40 cm/s. It should be noted that in the downstream region of the flat flame, the effects of the buoyancy, flow expansion, and heat loss to the environment disturb significantly an idealized one-dimensional structure of the flame. Due to the heat losses to the environment, temperature gradients as large as 100 K/cm have been observed experimentally [22]. The postflame zone cooling is of particular importance for the formation of nitrogen oxides because of the strong temperature impact in the thermal NO mechanism. The cooling of the postflame gases has been modeled and its consequences are discussed below. The perturbation of the flame by the probe also causes changes in the temperature profile. This can modify the apparent location of the species’ profiles and their peak concentrations. In the present experiments, the cooling of the flame front was observed when the probes were introduced into the flame at

NO IN FLAMES OF H2 Ⳮ CO Ⳮ CO2 AND AIR

Fig. 1. Adiabatic burning velocities in flames of H2 Ⳮ CO Ⳮ CO2 and air. Two series of symbols represent dayto-day repeatability of measurements; solid line, modeling.

distances below about 10 mm. Hence, measurements are to be performed at longer distances, and the comparison of the measured [NO] with the modeling is then only meaningful when the amount of the NO formed in the unperturbed flame front is significantly higher than that formed downstream where the probe perturbation is present. In the present work, the probe dimensions were comparable or larger than the flame front thickness. Therefore, no attempts to resolve spatial concentration profiles in the region of the steep gradients were made. The spatial resolution of the probes was estimated to be about 1 mm [19]. The influence of the probe position relative the flame front and other errors introduced by the probe were assessed experimentally [19]. The uncertainty of the concentration measurements includes the instrumental accuracy of the gas analyzers, the accuracy of preparation of the calibrating mixtures, and possible modification of the sample composition in the non-cooled probes. The CO–CO2 conversion may occur in the probes at moderate temperatures. An agreement between calculated and measured concentrations of the major species was always better than 10% [19]; therefore, this conversion is probably of minor importance. The NO–NO2 conversion may also occur in the probes; however, its effect was compensated in this work by the measurements of the total [NOx] that was attributed to the NO concentration in the postflame zone. An overall accuracy of 10% is also assumed in the measurements of the nitric oxide concentrations presented below. Modeling Details A detailed C/H/N/O reaction mechanism for the combustion of small hydrocarbons is used for the

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modeling [23,24]. The H/N/O submechanism is listed elsewhere [15]. The current version of the mechanism (Release 0.5) consists of 1200 reactions among 127 species. This mechanism has been validated with experimental data available for oxidation, ignition, and flame structure of hydrogen, carbon monoxide, formaldehyde, methanol, methane, ethane, propane, and some of their mixtures. The CHEMKIN-II collection of codes [25–27], including transport properties [28] from Sandia National Laboratories, were used. Multicomponent diffusion and thermal diffusion options were taken into account. Adaptive mesh parameters were GRAD ⳱ 0.1 and CURV ⳱ 0.5. To include the downstream heat losses, the following procedure has been used. The structure of the adiabatic flame was first modeled. The calculated adiabatic temperature profile was next modified downstream the flame front assuming a temperature gradient of 100 K/cm [22]: T ⳱ Tad ⳮ100X, where X is the axial distance from the burner surface in centimeters. Finally, the flame structure modeling was performed with the given temperature profile using the burner-stabilized flame option of the CHEMKIN code.

Results and Discussion The present measurements were performed in the mixtures of H2 Ⳮ CO Ⳮ CO2 and air. Fuel was used as delivered from the purification and mixing plant with the following composition: hydrogen (5.05 Ⳳ 0.15%), carbon dioxide (50.2 Ⳳ 1%), and carbon monoxide (44.75%). This mixture has been chosen to stabilize relatively cold flames having burning velocities from 10 to 50 cm/s that is within working range of the present experimental rig [18]. Air was mixed on-line in the mixing panel of the experimental rig from pure oxygen and nitrogen with the dilution ratio O2/(O2 Ⳮ N2) equal to 0.209. Adiabatic burning velocities in flames of H2 Ⳮ CO Ⳮ CO2 and air are shown in Fig. 1. Two series of symbols represent day-to-day repeatability, which is better than the error of the method (Ⳳ0.8 cm/s). Modeling of the adiabatic burning velocities at 298 K agrees well with the experiments. Yet the calculations are somewhat lower than measurements in lean, stoichiometric, and moderately rich mixtures. This may indicate some uncertainties in the rate coefficients of some key reactions and/or in the transport properties used in the flame calculations as suggested by Paul and Warnatz [29]. A luminous flame front was stabilized at distances smaller than about 1 mm from the burner. Probe sampling was taken at distances from 10 to 20 mm from the burner. At smaller distances, the influence of the probe on the adiabaticity of the flames was observed. To reveal the range of the flames not disturbed by the air entrainment, the axial profiles of

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Fig. 2. Concentrations of CO, O2, and CO2 in flames of H2 Ⳮ CO Ⳮ CO2 and air at different distances from the burner. Points, measurements; lines, calculations. Crosses, open diamonds, and open squares, [CO] at 10, 15, and 20 mm from the burner, respectively; solid diamonds, solid squares, and solid circles, [CO2] at 10, 15, and 20 mm; open circles, open triangles, and solid triangles, [O2] at 10, 15, and 20 mm. Solid lines, model prediction in adiabatic flame at 10 mm; dashed lines, model prediction in adiabatic flame with downstream heat losses at 10 mm.

Fig. 3. Axial profiles of NO concentration and temperature in the flame of H2 Ⳮ CO Ⳮ CO2 and air, ␾ ⳱ 1.2. Points, measurements; lines, calculations. Solid lines, temperature and [NO] in the adiabatic flame; dashed lines, temperature and [NO] in the flame with downstream heat losses; dash-dotted line, [NO] in the flame with downstream heat losses and reduced k1; dash-double-dot line, [NO] in the adiabatic flame and k1 ⳱ 0.

the major gas components were measured and compared with the model predictions. In the experiments presented below, the probe was introduced perpendicular to the flame front at the axis of the burner. Figure 2 shows concentrations of O2, CO2, and CO in the flames of H2 Ⳮ CO Ⳮ CO2 and air measured at different distances from the burner. The measurements are compared with the model prediction for two types of flame: an adiabatic flame and a flame with downstream heat losses. The calculated axial profiles of major components, O2, CO2, and CO, are almost perfectly flat in lean and rich mixtures; only small changes are observed in flames close to the stoichiometric one. The experimental concentrations of the major species are very close at different distances from the burner; that is, axial profiles are also flat in all flames except in very rich and very lean mixtures. The dilution of the burned gases by the ambient air is seen in Fig. 2 in the mixture with equivalence ratio ␾ ⳱ 0.8. The comparison of experiments and calculations also shows that the air penetrates rich flames, dilutes burned gases, and oxidizes carbon monoxide into carbon dioxide at ␾ ⬎ 2. One can thus conclude that the flames in the range of equivalence ratios from 0.9 to 1.8 are not significantly affected by the air entrainment. Calculated concentrations of the major species in the adiabatic flames and in the flames with downstream heat losses are slightly different; however, this difference is within the uncertainty of measurements. In agreement with the earlier observations in methane/air flames [19], the burning velocity measurements (Fig. 1) in conjunction with major species concentrations (Fig. 2) clearly show that disturbances of the flame structure due to the ambient air are observed only in slowly burning mixtures. Selected axial profiles of NO concentrations measured in the flames of H2 Ⳮ CO Ⳮ CO2 and air are shown in Figs. 3–6. The sizes of the symbols correspond to the estimated uncertainties in the spatial resolution of the probe sampling and in the absolute concentrations. The calculated adiabatic flame temperature profiles and assumed temperature profiles in the flames with downstream heat losses of 100 K/cm are also shown. The measured [NO] are compared with calculated concentrations in the adiabatic flames and in the flames with heat losses. All mixture compositions from ␾ ⳱ 0.8 to ␾ ⳱ 2.3 have been modeled. Figs. 3–6 show, however, only rich flames where the NNH route forming NO is dominant. To illustrate the importance of the NNH mechanism in these flames, the modeling has been also performed in adiabatic flames with this route suppressed by setting the rate constant of the reaction 1 to zero. It is seen from Figs. 3–6 that the NNH route is indeed dominant in the rich mixtures. It forms from 70% of the total NO in the flame with ␾ ⳱ 1.2 up

NO IN FLAMES OF H2 Ⳮ CO Ⳮ CO2 AND AIR

Fig. 4. Axial profiles of NO concentration and temperature in the flame of H2 Ⳮ CO Ⳮ CO2 and air, ␾ ⳱ 1.3. Points, measurements; lines, calculations. Solid lines, temperature and [NO] in the adiabatic flame; dashed lines, temperature and [NO] in the flame with downstream heat losses; dash-dotted line, [NO] in the flame with downstream heat losses and reduced k1; dash-double-dot line, [NO] in the adiabatic flame and k1 ⳱ 0.

Fig. 5. Axial profiles of NO concentration and temperature in the flame of H2 Ⳮ CO Ⳮ CO2 and air, ␾ ⳱ 1.4. Points, measurements; lines, calculations. Solid lines, temperature and [NO] in the adiabatic flame; dashed lines, temperature and [NO] in the flame with downstream heat losses; dash-dotted line, [NO] in the flame with downstream heat losses and reduced k1; dash-double-dot line, [NO] in the adiabatic flame and k1 ⳱ 0.

to 90% in the flame with ␾ ⳱ 1.55. It is also important that the heat losses downstream do not affect significantly the calculated [NO]. Calculations with even higher rates of cooling give very close results because of the relatively low temperatures in the flames studied. The amount of the NO formed in

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Fig. 6. Axial profiles of NO concentration and temperature in the flame of H2 Ⳮ CO Ⳮ CO2 and air, ␾ ⳱ 1.55. Points, measurements; lines, calculations. Solid lines, temperature and [NO] in the adiabatic flame; dashed lines, temperature and [NO] in the flame with downstream heat losses; dash-dotted line, [NO] in the flame with downstream heat losses and reduced k1; dash-double-dot line, [NO] in the adiabatic flame and k1 ⳱ 0.

the flame front is significantly higher than that formed downstream; thus the comparison of the measured [NO] with the modeling is meaningful even in the absence of the direct measurement of the temperature profiles modified by the probe and/ or due to heat losses. The model predicts roughly twice as high the concentration of NO compared to the measured values in all rich flames despite of the adiabatic temperature variation from 1800 down to 1600 K. One can assume therefore that the model overpredicts [NO] due to an overestimation of the pre-exponential factor of the rate constant k1. The modeling with k1 ⳱ 1 ⳯ 1014 exp(ⳮ16.75 kJ/mol/ RT) cm3/mol s and with downstream heat losses is shown in Figs. 3–6. The calculated [NO] are found then in good agreement with the measurements. The concentrations of NO measured in these flames are summarized in Fig. 7. Calculated [NO] at 10 mm from the burner in the adiabatic flames, in the flames with downstream heat losses, and in the flames with downstream heat losses and reduced k1 are shown. It is remarkable that reduction of the rate constant k1 by 50% brings the modeling close to the measurements not only in rich but also in stoichiometric and lean flames. This indicates that variation in the key rate constants of other routes forming NO, such as thermal NO in near-stoichiometric mixtures and nitrous oxide mechanism in lean mixtures, cannot compensate the disagreement observed in rich mixtures where the NNH route is dominant. It should be noted as well that the flame structures calculated for pure gas components and for real gas composition with contaminants reported

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Fig. 7. Concentrations of NO in flames of H2 Ⳮ CO Ⳮ CO2 and air at different distances from the burner. Points, measurements. Crosses, 10 mm from the burner; diamonds, 15 mm; squares, 20 mm. Lines, calculations at 10 mm from the burner. Dash-dotted line, [NO] in the adiabatic flame; dashed line, [NO] in the flame with downstream heat losses; solid line, [NO] in the flame with downstream heat losses and reduced k1.

Fig. 8. Arrhenius plot of k1. Squares and dash-triple-dot line, [16]; dashed line, GRI-MECH [10]; dash-dot line, derived from the QRRK analysis [8]; dash-double dot line with error bars and dotted line, calculated from the measurements of (k1Kp6) [11]; solid line, this work.

by the supplier were indistinguishable in terms of concentrations of major components and NO. It is concluded therefore that comparison of the new experimental data presented in this work with the detailed flame structure modeling strongly suggests a reduced value of the rate constant k1.

The available data for k1 are summarized in Fig. 8. Two expressions for (k1Kp2) have been obtained in the range 1800–2500 K [11]; the first one was the best fit to the experimental values, and the second one was derived assuming that the rate constant k1 is not very sensitive to temperature. The rate constants were calculated from these expressions using thermodynamic data [30] adopted in the present study. It should be noted that the experimental values [11] have uncertainties as large as a factor of 5. Error bars are shown for the extremes of temperature. The rate constant derived in the range 1200– 2500 K [16] was actually considered as an upper limit. Thus, the rate constant proposed in the present study is consistent with earlier evaluations [7,11,16] within uncertainty limits. Many parameters affect accuracy of determination of the rate constant k1 by comparison of a predicted species profiles with the measurements. They include accuracy of the key rate constants of H2 Ⳮ CO oxidation that control the concentration of radicals and of other important reactions for NO formation, heats of formation of the key species, equilibrium constant of reaction 2, and temperature profiles in the flames. In the present study, the flames were adiabatic with respect to the burner, while heat losses downstream were quantified and modeled. The detailed reaction mechanism used in the present work has been extensively validated. It predicts accurately major species concentrations and flame burning velocities of the mixtures studied. Also, good performance of this mechanism has been demonstrated in the flame modeling and prediction of NO formation in methane flames [18,19]. This suggests that rate constants of the key reactions, such as chain branching H Ⳮ O2 ⳱ OH Ⳮ O, propagation CO Ⳮ OH ⳱ CO2 Ⳮ H and termination H Ⳮ O2 Ⳮ M ⳱ HO2 Ⳮ M as well as key reactions of the thermal NO and nitrous oxide mechanisms are relatively well known. A combined uncertainty of these key rate constants together with their sensitivities gives an overall error of the rate constant k1 of about 50%. Significant uncertainty of the heat of formation of NNH would imply much higher error limits in the pre-exponential factor and activation energy of reaction 1. Burcat and McBride [30] cited DHf(NNH) with an uncertainty of 13.6 kJ/mol; the enthalpy change of reaction 2 was derived to within 7 kJ/mol [11] or 5 kJ/mol [12]. A change of 6.3 kJ/ mol in the DHf(NNH) altered predicted [NO] by a factor of 2 [9]. This has a direct bearing on the uncertainty of the reported k1 value since the rate of NO formation via NNH route is proportional to the (k1Kp2), as mentioned above. One can conclude therefore that any modification of the heat of formation of NNH would cause inversely proportional change of the rate constant k1 derived in the present work.

NO IN FLAMES OF H2 Ⳮ CO Ⳮ CO2 AND AIR

Conclusions Burning velocity and probe sampling measurements of the concentrations of O2, CO2, CO, and NO in the postflame zone of the flames of H2 Ⳮ CO Ⳮ CO2 and air are reported. Axial profiles of the concentrations of major species were used to evaluate the influence of the ambient air entrainment and downstream heat losses. In the very lean mixtures, ambient air dilutes the burned gases, while in the very rich mixtures it causes oxidation of the combustion products. The numerical predictions of the concentrations of O2, CO2, and CO in the postflame zone are in a good agreement with the experiment. The amount of the NO formed in the adiabatic flame front is significantly higher than that formed downstream; thus the one-dimensional modeling can be directly compared with experimental axial profiles. The influence of the downstream heat losses to the environment was modeled. It is shown that in rich mixtures, where the NNH route forming NO is dominant, the heat losses do not affect significantly the calculated [NO]. The comparison of the new experimental data presented in this work with the detailed flame structure modeling strongly suggests a reduced value of the rate constant k1. The calculations with k1 ⳱ (1 Ⳳ 0.5) ⳯ 1014 exp(ⳮ16.75 Ⳳ 4.2 kJ/mol/RT) cm3/mol s brings the modeling close to the measurements not only in rich but also in stoichiometric and lean flames. The rate constant proposed in the present study is consistent with earlier evaluations within uncertainty limits. Acknowledgments The Government of Brussels is acknowledged for the financial support of this work through the ‘‘Research in Brussels’’ grant to I.V.D. The help of K. J. Bosschaart, E. C. M. Brock, and L. P. H. de Goey (TU/Eindhoven) in the design and construction of the installation is gratefully acknowledged. REFERENCES 1. Reisel, J. R., Combust. Flame 120:233 (2000). 2. Thomsen, D. D., Kuligowski, F. F., and Laurendeau, N. M., Combust. Flame 119:307 (1999). 3. Thomsen, D. D., and Laurendeau, N. M., Combust. Flame 124:350 (2001). 4. Charlston-Goch, D., Chadwick, B. L., Morrison, R. J. S., Campisi, A., Thomsen, D. D., and Laurendeau, N. M., Combust. Flame 125:729 (2001). 5. Hughes, K. J., Tomlin, A. S., Hampartsoumian, E., Nimmo, W., Zsely, I. G., Ujvari, M., Turanyi, T., Clague, A. R., and Pilling, M. J., Combust. Flame 124:573 (2001). 6. Bozzelli, J. W., and Dean, A. M., Int. J. Chem. Kinet. 27:1097 (1995). 7. Miller, J. A., and Melius, C. F., Proc. Combust. Inst. 24:719 (1992).

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