Article pubs.acs.org/EF
Measurements of Laminar Burning Velocities above Atmospheric Pressure Using the Heat Flux MethodApplication to the Case of n-Pentane Patricia Dirrenberger, Hervé Le Gall, Roda Bounaceur, Pierre-Alexandre Glaude, and Frédérique Battin-Leclerc* Laboratoire Réactions et Génie des Procédés, Université de Lorraine, CNRS, ENSIC, BP 20451, 1 rue Grandville, 54001 Nancy, France S Supporting Information *
ABSTRACT: A new adiabatic burner allowing the measurement of burning velocities at high pressure with the heat flux method has been developed. Experimental measurements of laminar burning velocities of methane and n-pentane were performed for pressures up to 6 atm at 298 K and at atmospheric pressure for temperatures from 298 to 398 K. Equivalence ratios varied from 0.6 to 1.9. The results for methane flames are in good agreement with the only results of literature obtained above atmospheric pressure using the heat flux method; those for n-pentane are to our knowledge the first application of this method to a flame of a liquid fuel above atmospheric pressure. Based on these measurements, empirical correlations of the variation of the measured laminar flame velocities with pressure and temperature have been proposed for methane and n-pentane. In the case of methane, these correlations lead to a satisfactory prediction of literature measurements made using constant volume bombs.
1. INTRODUCTION
2. EXPERIMENTAL FACILITY All the measurements made in this study are based on the heat flux method proposed first by de Goey and co-workers1 in order to stabilize adiabatic flat flames using a heat loss compensation and to derive adiabatic burning velocities directly from inlet gas flow rate measurements. With this method, contrary to the measurements performed using a constant volume bomb or a counterflow-flame burner, there is no need for afterward correction to take into account the stretch effect.12 Two burners have been used in this study: the atmospheric burner described by Dirrenberger et al.2,3 and a new one, specifically designed for higher pressures. This design of the second burner was close to that used by Dirrenberger et al.2,3 at atmospheric pressure, with a few changes. In the two cases, the burner head was a perforated 30 mm diameter brass plate. As shown in Figure 1a, the high-pressure burner was enclosed in a chamber, the pressure of which was regulated by a pneumatic valve. Pressure was measured using a manometer, the accuracy of which was 0.5% for the zero of the apparatus (i.e., about 0.05 atm) and 1% in the reading of the pressure (e.g., about 0.1 at 5 atm). The pressure chamber included a water cooled jacket to cool the hot flame gases and a quartz window to visualize the flame. A noticeable amount of water was formed by the flame and led to condensation. The water was continuously drained from the chamber and evacuated toward two metallic tanks, which were regularly emptied. Due to its enclosure in a closed vessel, the burner could not be ignited directly by the user as the atmospheric pressure burner but required the use of a stationary high voltage electrode allowing the formation of an electric arc
1
Since its introduction by de Goey and co-workers in 1993, the heat flux method has been used to measure adiabatic burning velocities for a wide range of gaseous and liquid fuel components at atmospheric pressure (e.g., natural gas components,2 gasoline components3,4) but very rarely at lower5 or higher6 pressures. Since adiabatic burning velocity is an important parameter to design internal combustion engines, it is important to have reliable measurements at pressures approaching the elevated values (from 7 to 20 bar7) observed in actual combustion chambers. This should be performed especially for liquid components of fuels. Here, we present a new experimental device built to measure adiabatic burning velocities using the heat flux method above atmospheric pressure. Measurements using the new experimental setup have been made up to 6 atm for methane and burning velocities compared satisfactorily with the data of Goswami et al.6 New measurements have then been made in the case of n-pentane, a liquid linear alkane representative of those present in gasoline, up to 4.2 atm. Experiments for both fuels have also been made at atmospheric pressure at temperatures up to 398 K. Comparisons between experimental results for n-pentane and simulations using a detailed kinetic model of literature are shown. From these measurements, empirical correlations reproducing the variations of adiabatic burning velocities with temperature and pressure have been derived and used to make comparisons with recent literature measurements8−11 involving pressures up to 18 bar for the same reactants using another technique, the constant volume bomb, which is usually used to measure laminar burning velocities at high pressure. © 2014 American Chemical Society
Received: September 11, 2014 Revised: December 15, 2014 Published: December 16, 2014 398
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Figure 1. Scheme of the apparatus used at high pressure: (a) scheme of the full setup, (b) view of the burner head and the pressure chamber.
lighting the flame. Being located relatively far from the burner, this electrode did not disturb the thin flat flame. The two burner heads were mounted on two mixing chambers enclosed in thermostatic oil jackets, the temperature of which was set to the desired initial temperature of the fresh gas mixture. The circumference of the burner plate was heated with thermostatic oil set to around 50 K above the temperature of the unburned gas mixture. In practice, if an initial temperature of 398 K was desired, the temperature of the mixing chamber was set to 398 K and that of the burner plate to 448 K. Thus, the heat flux from the burner to the unburned gas mixture could compensate for the heat flux from the flame toward the burner necessary for stabilizing the flame. Eight type K thermocouples were inserted into holes of the burner plate and positioned at different distances and angles from the center to the periphery of the burner. If the unburned gas velocity was lower than the adiabatic flame burning velocity, the
sum of the heat loss and heat gain by the burner was higher than zero. Then, the center of the burner plate was hotter than the periphery, and the flame was stabilized under subadiabatic conditions. On the other hand, if the unburned gas velocity was higher than the adiabatic burning velocity, the center of the burner plate was cooler than the periphery and the flame was stabilized under superadiabatic conditions. Thus, when the temperature profile was flat, it means that no heat was globally lost or gained by the flame so that the flame became adiabatic with respect to the burner.1 The adjustment of the flow rate of the gas mixture made it possible to find the appropriate gas velocity, which canceled out the net heat flux so that the radial temperature distribution in the burner plate was uniform. The flow rate at which the net heat flux was zero corresponded to the adiabatic flame burning velocity.13 For both the atmospheric and high pressure burners, gas flows were regulated by Bronkhorst High-Tech Mass Flow Controllers 399
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Energy & Fuels (MFC). For compounds liquid at room temperature, liquid flow rates were measured using Bronkhorst mini-CORI-FLOW mass flow controller. Gases were delivered by Messer and Air Liquide (purity > 99.95% for methane and purity > 99.995% for oxygen and nitrogen) and n-pentane by Sigma-Aldrich (purity > 99%). Note that, in order to reach a larger range of equivalence ratios toward rich mixtures with the high pressure burner, we have attempted to use higher range MFCs (e.g., 19.6 nL/min of methane instead of 2 nL/min) in the lower part of their range since flow rates were enhanced due to the increase of pressure. The accuracy in the obtained results was alas too low and led to strong uncertainties in the measurements. Consequently, the range of equivalence ratios studied at high pressure, as described hereafter, has been limited by the range of available MFCs. The burner head used for high pressures was slightly different from that used at atmospheric pressure as shown in Figure 1b. Due to an increase of the gas flow rates when increasing pressure, the diameter of the holes of the perforated plate has been reduced to 0.3 compared to 0.5 mm for the atmospheric pressure burner. This reduction aims at minimizing the possible local stretch due to flame curvature nearby the holes.14 Consequently, the pitch between the holes is 0.4 instead of 0.7 mm for the atmospheric pressure burner, and the diameter of the thermocouples has also been reduced from 0.5 mm to 0.25 mm. To facilitate the drilling of these more numerous smaller holes, the thickness of the plate of the high pressure burner has been reduced from 2 to 1.5 mm. Note that while thermocouples were firmly plugged in the case of the atmospheric pressure burner, the thinner thermocouples could slightly move with time inside the holes and induce a source of uncertainty since the location of the thermocouples relative to the burner plate surface influence the accuracy of the measurements. To avoid that water condensation perturbed the flame and eventually extinguished it, small gutters have been dug in the metallic ring holding the burner head to allow easy water evacuation. The reproducibility of the measurements at high pressure, shown by repeating several times a same measurement under the same conditions, was between 4 and 8%. As the adiabatic laminar flame velocity is obtained when the net heat loss is zero, the error depends on only a few factors.2 The error in the laminar flame velocity can be attributed to the error in the mass flow measurements (around 0.5% for each MFC), which can lead to a global error of 1.5% in the laminar flame velocity, the error in the reading of the temperature with thermocouples, which could lead to an error of around 0.2 cm/s in the laminar flame velocity, and errors due directly to flame distortions, such as edge effects for example (around 0.2 cm/s). Concerning the determination of equivalence ratios, note that the main error is due to the error in the mass flow measurements, which leads to an error of about 1%. Note also that the previously mentioned errors in pressure measurements can lead to errors in burning velocity and volumetric flow rate determinations.
MFCs. In Figures 2−6, the error bars correspond to the uncertainties evaluated, as described previously. 3.1. Evolution of the Laminar Flame Velocities of Methane with Pressure at 298 K. Figures 2 and 3 present the variation of our
Figure 2. Methane burning velocity at 298 K and 1, 1.5, 2, and 3 atm vs equivalence ratio.
Figure 3. Methane burning velocity vs pressure up to 6 atm at 298 K and at equivalence ratios of 0.7, 0.8, 0.9, and 1 and comparison with literature. measurements of methane flame velocity at 298 K with equivalence ratio and with pressure, respectively. Measurements have been made in equivalence ratio ranges 0.7−1.7 at 1 atm, 0.7−1.45 at 1.5 atm, 0.7−0.95 at 2 atm, and 0.7−0.8 at 3 atm. Figure 2 shows measurements made with both burners at 1 atm. A very good agreement was obtained, demonstrating that the enclosure of the flame in the pressure chamber did not perturb the measurements. At 1.5 atm, the shape of the evolution curve obtained versus equivalence ratio remains the same as at 1 atm, with the maximum being still at 1.1. However, the maximum velocity decreases significantly, from 38.1 at 1 atm to 31.3 cm/s at 1.5 atm. Figure 3 displays the exponential decrease obtained when increasing pressure for different lean mixtures. Many studies (e.g., refs 6, 10, 15−28) present measurements of laminar flame velocities of methane at 298 K above atmospheric pressures. Figure 3 shows that our measurements at 1.5, 2, and 3 atm are in very good agreement with those of Goswami et al.6 obtained using the
3. EXPERIMENTAL RESULTS The apparatuses above-described have been used to study the evolution with pressure and with temperature of the laminar flame velocities of methane and n-pentane. When comparing with literature, we will use only the measurements made after 1995, since the measurements made in bomb or stagnation plate flame before that time were based on a linear extrapolation on the flame speed at zero stretch, leading to inaccurate stretch corrections,12 and at pressure below 6 atm, as in the present study. The data corresponding to new measurements with their associated uncertainties are given in a file in Supporting Information. Note that, as explained previously in this text, the range of equivalence ratios studied at high pressure was limited by the range of available 400
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Energy & Fuels same heat flux method. The agreement is also satisfactory with measurements made at 2 atm by Hassan et al.21 and Rozenchan et al.24 in constant volume bombs. 3.2. Evolution of the Laminar Flame Velocities of Methane with Temperature at Atmospheric Pressure. Figure 4 presents the
Figure 5. n-Pentane burning velocity at 298 K and equivalence ratios of 0.7, 0.8, 0.9, and 1 for pressures up to 4.2 atm. Symbols are experiments, and lines are simulations. for three temperatures, 298, 358, and 398 K. As for methane, the increasing temperature maintains the shape of the evolution curve obtained versus equivalence ratio, with the maximum burning velocity at ϕ = 1.1 but with larger values. The maximum burning velocity is 38.8 cm/s at 298 K, 51.4 cm/s at 358 K, and 60.8 cm/s at 398 K. A few other studies about measurements of laminar flame velocities of n-pentane have been performed at atmospheric pressure and elevated temperature (e.g., refs 31−33). To our knowledge, no previous study was performed on this compound using the heat flux method. Our measurements are in good agreement with most of these previous data. At 298 K, good agreement is observed with those of Davis and Law31 obtained using a stagnation flame. At 358 K, our data are in good agreement with the measurements of Ji et al.32 obtained using a stagnation flame for equivalence ratios lower than 1.4, with some deviations observed for richer mixtures, and with the data of Kelley et al.33 using a constant volume bomb over the full equivalence ratio range. Note that Ji et al.32 and Kelley et al.33 performed also measurements for n-heptane, as did Dirrenberger et al.:3 larger deviations were obtained between measurements made using the different methods for this heavier alkane. No data have been found in literature at 398 K. Simulations have also been performed using the detailed kinetic model previously described and are plotted in Figure 6. A good agreement between experiments and simulations can be observed for the three studied temperatures, with a slight underprediction for equivalence ratios above 1.2.
Figure 4. Methane burning velocity vs equivalence ratio at atmospheric pressure and 298, 318, 358, and 398 K (black symbols) and comparison with literature: gray symbols are data obtained using heat flux method; blue crosses are data obtained using constant volume bombs. variation of laminar flame velocity of methane at atmospheric pressure for four temperatures, 298, 318, 358, and 398 K. In order to give a complete picture, we remind here the measurements made at 298 K by Dirrenberger et al.2 When increasing temperature, the shape of the evolution curve obtained versus equivalence ratio remains the same, with the maximum being still at 1.1. However, the maximum velocity increases significantly with temperature: 41.2 cm/s at 318 K, 50.3 cm/s at 358 K and 58.9 cm/s at 398 K. Methane is the most studied hydrocarbon concerning burning velocity measurements (see ref 2). The results obtained with our atmospheric pressure apparatus at 298 K are in good agreement with previously published data, particularly for lean mixtures.2 Several studies concerning measurements of laminar flame velocities of methane have also been performed at atmospheric pressure and elevated temperature (for example, refs 10, 13, 28). Our measurements are in good agreement with literature data, particularly with those of Hermanns et al.29 obtained using the same method but also with those of Gu et al.10 obtained using a constant volume bomb. 3.3. Evolution of the Laminar Flame Velocities of n-Pentane with Pressure at 298 K. Figure 5 presents the variation of measurements of n-pentane flame velocity at 298 K with pressure at four equivalence ratios, 0.7, 0.8, 0.9, and 1. At an equivalence ratio of 1, measurements have only been possible at 1.2 atm. At higher pressures, flame oscillations due to thermodiffusive or acoustic instabilities were observed which prevent flame stabilization. As for methane, an exponential decrease was obtained when increasing the pressure. Note that the only measurement that can be found in literature for n-pentane flame velocity above atmospheric pressure is that of Farrell et al.9 performed at 450 K and 3 atm. To compare with these new experimental data, simulations have been performed using the publically available version of software EXGAS, which automatically generates detailed kinetic models for the oxidation of alkanes.30 These results are presented in Figure 5 and show that the shape of the curves of the evolution of laminar flame velocities with pressure is well predicted by the model, with, however, an overestimation, which is limited at atmospheric pressure but increases for the highest pressures. 3.4. Evolution of the Laminar Flame Velocities of n-Pentane with Temperature at Atmospheric Pressure. Figure 6 presents the variation of laminar flame velocity of n-pentane at atmospheric pressure
Figure 6. n-Pentane burning velocity vs equivalence ratio at atmospheric pressure and 298, 358, and 398 K (black symbols) and comparison with literature: blue crosses are data obtained using constant volume bombs, and green symbols are data obtained using stagnation stabilized flames. Symbols are experiments and lines simulations. 401
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4. CORRELATIONS By considering the previous experimental results, it was possible to propose temperature and pressure correlations for the laminar flame velocities of methane and n-pentane. As proposed for a long time in literature (e.g., refs 34 and 35), power law correlations can represent the dependence of burning velocities on temperature and pressure: SL = SL0(T /T0)α (P /P0)β
(1)
where SL is the burning velocity in air, T0 = 298 K, P0 = 1 atm (the reference conditions), SL0 is the burning velocity in air under reference conditions, α and β are constant for a given fuel and a given equivalence ratio. Using the previously shown measurements, we have determined α and β values for methane and npentane and then used eq 1 for the prediction of burning velocities under conditions slightly outside those of this study. 4.1. Correlations for Methane. Figure 7 plots the measured laminar burning velocities of methane flames as a function of log
Figure 8. Evolution of the values of (a) the α and (b) the β constants versus equivalence ratio for methane and comparison with literature.
the case of methane. As shown in Figure 8a, all the values calculated in this study and those of Hermanns et al.29 and Yan et al.36 are between 1.4 and 2.2, with globally a good agreement. As shown in Figure 8b, the present values of the β constant are in good agreement (less than 10% deviation) with those obtained by Goswami et al.6 using the same method, but more deviation is observed with those obtained by other methods.10,23 For a stoichiometric flame, our results can then be correlated by eq 2: SL = SL0(T/T0)1.58 (P/P0)−0.38
(2)
As shown in Figures 9 and 10, eq 2 can be used to simulate laminar burning velocities in temperature and pressure ranges slightly outside those of this study. Figure 9 shows that this equation can well reproduce the evolution of burning velocities from the literature (constant volume bomb data) for temperatures up to 400 K (the highest temperature of this study), under pressures from 2 to 15 atm. Elia et al.8 have performed measurements at 2, 3.5, and 15 atm for temperatures up to 550 K, but for temperatures between 480 and 550 K, the extrapolation of eq 2 leads to significantly deteriorated simulations at 2 and 3.5 atm. Figure 10 displays the prediction of eq 2 for the evolutions of flame velocity as a function of pressure at temperature of 350, 400, and 470 K. Literature results are well predicted for pressure up to 18 atm, while the highest pressure studied here was 6 atm. Sensible predictions of flame velocity using eq 2 outside the range of its validations are possible but only in the case of extrapolating pressure.
Figure 7. Laminar flame velocities of methane versus log T/T0 and log P/P0 and correlations for the different studied equivalence ratios.
T/T0 (at 1 atm) and log P/P0 (at 298 K) for the different equivalence ratios. For both the variation with temperature and with pressure, Figure 7 well shows that straight lines are obtained. The corresponding slopes are respectively the α and β constants in eq 1 related to methane for each equivalence ratio. Figure 8 presents the evolution of the values of the α and β constants versus equivalence ratio obtained for methane with their associated error bars, as well as a comparison with values of the literature. Using the same method as in this work, Hermanns et al.29 and Yan et al.36 obtained also values for the α constants in 402
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Figure 9. Comparison between the evolutions of burning velocities of methane with temperature predicted by the present correlations and literature values (equivalence ratio of 1).
Figure 11. Laminar burning velocities of n-pentane versus log T/T0 and log P/P0 and correlations for the different studied equivalence ratios. Figure 10. Comparison between the evolutions of burning velocities of methane with pressure predicted by the present correlations and literature values (equivalence ratio of 1).
apparatus has been used at 298 K in the case of methane up to 6 atm and in that of n-pentane up to 4.2 atm. The data for methane are in good agreement with those obtained by Goswami et al.6 using the same method. For the moment, flame instabilities limit the range of accessible equivalence ratios to lean mixtures for n-pentane. A previously developed burner has also been used at atmospheric pressure to perform measurements of laminar flame velocities for methane and n-pentane for temperatures up to 398 K. Correlations of the variation of the measured laminar flame velocities with pressure and temperature have been proposed based on these data. In the case of methane, the correlation simulates well literature burning velocities for pressure up to 18 atm. If constant volume bombs remain the most valuable tool to study laminar burning velocities at high pressure, the present results show that burners based on the heat flux method are on their way to provide measurements for pressures up to 10 bar, with possible limitations for heavy hydrocarbon rich mixtures which have to be more thoroughly investigated. Simulations of the present experimental results on n-pentane using a literature detailed kinetic model show increasing deviations when increasing pressure. This demonstrates the interest of developing new types of setup to increase the range of available data for model validations.
4.2. Correlations for n-Pentane. Figure 11 plots the measured laminar burning velocities of n-pentane versus log T/T0 and log P/P0 for the different studied equivalence ratios. For both temperature and pressure, straight lines are obtained. The corresponding slopes are respectively the α and β coefficients related to n-pentane for each equivalence ratio. The values of α are larger for methane than for n-pentane in lean mixtures and smaller in rich mixtures. The values of β are larger for methane than for n-pentane in the range of equivalence ratio studied (0.7−0.9). When using these values in eq 1 to reproduce the values measured in a constant volume bomb by Farrell et al.9 at 450 K, 3 atm and for equivalence ratios from 0.7 to 0.9, deviations up to 30% are observed, the simulations being significantly lower than the experimental data. Figure 12 presents the evolution of the values of the α and the β constants versus equivalence ratio obtained for n-pentane with their associated error bars. The values obtained for these two constants for npentane are close to those presented for methane, except at the ends of the studied equivalence ratio ranges.
5. CONCLUSION A new burner based on the heat flux method was developed to perform measurements of laminar burning velocities at subatmospheric pressures for both gaseous and liquid fuels. This 403
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Figure 12. Evolution of the values of (a) the α and (b) the β constants versus equivalence ratio for n-pentane.
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ASSOCIATED CONTENT
S Supporting Information *
Data corresponding to new measurements with their associated uncertainties. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This study was supported by SAUDI-ARAMCO. REFERENCES
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