Experimental Investigation on Laminar Burning Velocities and

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Experimental Investigation on Laminar Burning Velocities and Markstein Lengths of Premixed Methane−n‑Heptane−Air Mixtures Gesheng Li,* Junjie Liang, Zunhua Zhang, Le Tian, Yi Cai, and Linyuan Tian Key Laboratory of High Performance Ship Technology of Ministry of Education, School of Energy and Power Engineering, Wuhan University of Technology, Wuhan, Hubei 430063, People’s Republic of China ABSTRACT: Laminar burning velocities and Markstein lengths of premixed methane−n-heptane−air mixtures were experimentally investigated at an initial pressure of 0.1 MPa, initial temperatures of 358, 393, and 428 K, and equivalence ratios of 0.7−1.5. The methane content in the methane−n-heptane mixtures ranges from 0 to 1. The experiments were conducted in a combustion chamber with central ignition. In the present study, the difference between the linear and nonlinear extrapolation methods was analyzed quantitatively for methane−n-heptane−air flames. Comparisons of the laminar burning velocities of methane−air and n-heptane−air flames were conducted, respectively, between the present and other studies. Subsequently, effects of the initial temperature and methane content on the laminar burning velocity and flame instability of methane−n-heptane−air mixtures were analyzed. Then, the critical methane content at which the laminar burning velocity and flame instability of methane−n-heptane−air flames start to change relatively significantly was explored. The results show that the laminar burning velocities of methane−air and n-heptane−air flames measured in the present study are in good agreement with the data available in the literature. Laminar burning velocities and flame instabilities of methane−n-heptane−air flames seem to be less sensitive to the methane content when the methane content is below 0.75. The change in the initial temperature tends to diminish the difference in the laminar burning velocity between methane−air and n-heptane−air flames and only has weak effects on the flame instability of methane−n-heptane−air mixtures. According to variations of the laminar burning velocities and Markstein lengths of methane−n-heptane−air flames with the methane content, the value of 0.75 can be treated preliminarily as the critical methane content. the cylinder pressure,9 premixed combustion characteristics for mixtures of natural gas and diesel need to be taken into account to design and optimize the natural gas−diesel dual-fuel engines. Laminar burning velocity is one of the important parameters involved in laminar premixed combustion, and it plays an important role in turbulent combustion simulation and validation of chemical kinetic mechanisms. Natural gas and diesel are both complex mixtures containing many different species. The main component of natural gas is methane, and diesel mainly consists of alkanes, cycloalkanes, and aromatics.13,14 With respect to natural gas, its laminar combustion characteristics, including laminar burning velocity and flame instability, have been studied by some researchers.15−19 The compositions of the natural gas used in these studies are dependent upon the origins. As for diesel, studies on premixed combustion characteristics of diesel mainly focus on its surrogate fuels because of the complex composition of the diesel.13,20,21 Methane and n-heptane can be treated preliminarily as representatives of natural gas and diesel, respectively, for simplicity.13,14,22 Respective laminar premixed combustion characteristics, including laminar burning velocity and flame instability, for methane and n-heptane have been investigated experimentally and numerically (e.g., refs 22−52). Among these studies, the experimental methods employed include outwardly

1. INTRODUCTION As a clean alternative transportation fuel, natural gas has drawn increasing attention for its potential in relieving the dependence upon petroleum-based fuels and reducing the environmental pollutants. Natural gas has a higher octane number, and therefore, the natural-gas-fueled engines can operate with larger compression ratios, indicating that a higher thermal efficiency will be achieved. The mole ratio of C/H in natural gas is close to 1:4 because the main component of natural gas is methane, implying a potential to significantly reduce the CO2 emission from the engines fueled with natural gas.1,2 Besides, natural gas has economic advantages because of its abundant reserve and low price. At present, studies have been extensively performed on applications of natural gas to spark and compression ignition engines. (e.g., refs1−12) For compression ignition engines fueled with natural gas, generally a certain amount of diesel will be injected into the cylinder to ignite the natural gas because it is difficult to ignite the natural gas directly through compression.2,3,8−12 A typical operation mode of natural gas− diesel dual-fuel engines is that natural gas is injected into the intake manifold and the diesel fuel is injected into the cylinder directly.2 Thus, premixed natural gas−air mixtures are produced. During the ignition delay period, the diesel vaporizes and mixes with the premixed natural gas−air mixtures, generating a certain amount of premixed natural gas−diesel− air mixtures. During the initial stage of the in-cylinder combustion process, premixed combustion of natural gas− diesel−air mixtures dominates. Considering the significant influence of premixed combustion on the parameters, such as the maximum heat release rate and the maximum rise rate of © XXXX American Chemical Society

Received: February 13, 2015 Revised: May 30, 2015

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DOI: 10.1021/acs.energyfuels.5b00355 Energy Fuels XXXX, XXX, XXX−XXX

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Energy & Fuels expanding spherical flames,22−24,26,28,29,33,39,40,45,49,50 heat flux method,27,31,37,51,52 Bunsen flames,30,41 counterflow twin flames,42−44,46−48 etc. In the studies on laminar premixed combustion characteristics of methane, the species added into the methane include hydrogen,28,31,32,35,36,40 nitrogen,27,33,34 carbon dioxide,30,33,34,39,40 water,33,35 etc. For n-heptane, species such as iso-octane43,45 and nitrogen44 are mixed with it, and the combustion characteristics of the mixtures are investigated. According to the previous studies, methane (natural gas) burns at a relatively slow rate and its flame tends to be more instable when the equivalence ratio is increasing. However, in comparison to methane (natural gas), n-heptane (diesel surrogate fuels) burns at a faster rate, and the variation of the flame instability of n-heptane with the equivalence ratio is opposite to that of methane. If methane (natural gas) is blended with n-heptane (diesel surrogate fuels), the combustion characteristics of the mixtures cannot be deduced accurately from linear combination of the individual combustion characteristics of methane (natural gas) and nheptane (diesel surrogate fuels) because of the strong nonlinearity of the chemical reaction process.36 To the knowledge of the authors, less information on the premixed combustion characteristics of methane (natural gas)−n-heptane (diesel surrogate fuels) mixtures is available in the literature. Therefore, the objective of the present study is to investigate the laminar premixed combustion characteristics of methane− n-heptane mixtures, which are treated preliminarily as the representatives of the mixtures of natural gas and diesel. In this paper, outwardly expanding spherical flames are employed to determine the laminar burning velocities and Markstein lengths of methane−n-heptane−air mixtures at an initial pressure of 0.1 MPa, initial temperatures of 358, 393, and 428 K, and equivalence ratios ranging from 0.7 to 1.5. The methane content in the mixtures covers a range from 0 to 1. Besides, the critical value for the methane content, at which the laminar burning velocity and Markstein length of methane−n-heptane− air mixtures start to change relatively significantly, will be explored.

Figure 1. Schematic of the experimental setup. Then, the respective partial pressures of methane and air were derived through the ideal gas state equation. For n-heptane, its liquid volume at the ambient temperature and pressure was calculated because it was at the ambient temperature and pressure that the required amount of n-heptane was determined. At the start of experiments, the initial temperatures inside the combustion chamber were stabilized at the desired values by means of the heating system and the thermal insulation materials mounted outside the combustion chamber. Then, a vacuum pump was used to vacuum the combustion chamber. After that, a certain volume of liquid n-heptane, the value of which had been derived, was injected into the combustion chamber. Then, the injected n-heptane started to vaporize, and the pressure inside the combustion chamber began to increase. When the reading of the pressure transducer did not change, methane and air were introduced into the combustion chamber according to their respective partial pressures. To ensure homogeneity and motionless of the reactants inside the combustion chamber, the reactants would not be ignited by the electrical spark until about 10 min passed after the preparation of the reactants was completed. In the course of experiments, each experiment is repeated at least 3 times under the same experimental conditions and a good repeatability was reached. The laminar burning velocity determined in the present study has an absolute error of 1.5 cm/s and relative error of 5% approximately. The methane content involved in the study is defined as the mole fraction of methane in the methane−n-heptane mixture at the initial experimental conditions, and it varies from 0 to 1 in the present study. The initial temperature covers a range of 358−428 K, and the equivalence ratio ranges from 0.7 to 1.5. The initial pressure is fixed at 0.1 MPa. 2.2. Data Processing. The schlieren flame images obtained using the above experimental setup were processed to derive the parameters, including unstretched flame speed, laminar burning velocity, etc. A computer program was written with MATLAB in the laboratory of the authors to complete the data processing. In the program, the Canny edge detection method was applied to the schlieren flame images to derive the edge pixels of the spherical flame fronts.55 A flame image processed by the Canny edge detection method is shown in Figure 2a, and the yellow points denote the edge pixels of the flame front. The radius of the flame front, R, was derived in terms of the area of the flame front bounded by the edge pixels. The comparison between the circle with a radius of R and the flame front is shown in Figure 2b. It is seen that the circle with a radius of R fits the flame front well. Through the computer program, the profile of flame radius with time, t, was obtained. During the subsequent process of data processing, a range of 6−25 mm was imposed on the flame radius.53 Avoiding the disturbances caused by the transient ignition process was responsible for the selection of the lower limit. The upper limit was

2. EXPERIMENTAL SECTION 2.1. Experimental Setup. In the present work, the experimental method used to investigate the premixed laminar combustion characteristics of methane−n-heptane−air mixtures was outwardly expanding spherical flames. Detailed information on the experimental setup has been shown in ref 53. The related experimental error analysis can be referred to refs 43, 53, and 54. Only a brief description is presented here. Shown in Figure 1 is the schematic of the experimental setup employed in the present study. The experimental setup mainly consists of a cylindrical constant-volume combustion chamber, a heating system, an electrical spark generator, a system for data acquisition, and a schlieren optical system for observing flame propagation with a highspeed digital camera. The cylindrical combustion chamber is made of stainless steel, and its inner diameter and volume are 174 mm and 5.86 L, respectively. Two quartz optical windows of 80 mm diameter are mounted in the cylindrical combustion chamber to provide optical access for viewing the spherical flames. Two electrodes of 1.5 mm diameter are fitted in the combustion chamber to produce electrical sparks in the center of the combustion chamber. The high-speed digital camera operates at the capture rate of 10 000 frames per second in the current study. During the process of preparing the reactants, a pressure transducer was used to monitor the pressure inside the combustion chamber. The respective mole numbers of methane, n-heptane, and air were computed at first according to the initial experimental conditions. B

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equivalence ratios. In comparison to the linear fitting lines, the nonlinear fitting cures are in better agreement with the experimental data points. For the situation that Sn varies nonlinearly with α, there are significant differences in the unstretched flame speeds and Markstein lengths between the linear and nonlinear extrapolation methods. Taking the n-heptane−air flames as an example, the differences in the unstretched flame speed and Markstein length between the linear and nonlinear methods reach their peaks at the equivalence ratio of 0.8 and the values of the differences are 0.18 m/s and 0.946 mm, respectively. If the parameters derived from the nonlinear method are treated as the benchmarks, thus the linear method overestimates the unstretched flame speed and Markstein length by 6.9 and 97.5%, respectively, for the n-heptane−air flames at the equivalence ratio of 0.8. When the equivalence ratio is increasing, the differences in the unstretched flame speed and Markstein length for the n-heptane−air flames are reduced. Nevertheless, there is still a remarkable difference in the Markstein length between the linear and nonlinear methods. For the n-heptane−air flames at the equivalence ratio of 1.5, although the difference in the unstretched flame speed between the linear and nonlinear methods is only 0.04 m/s, the difference in the Markstein length between the linear and nonlinear methods is still up to 0.28 mm, which is 31.4% of the value of the Markstein length derived from the nonlinear method. When the methane content is 0.5, the methane−n-heptane−air flames behave similar to the n-heptane−air flames at various equivalence ratios. However, for the methane−air flames, an opposite phenomenon is observed that the differences in the unstretched flame speed and Markstein length of methane−air flames between the linear and nonlinear methods increase gradually with the increasing equivalence ratio. At the equivalence ratio of 1.4, the linear method overestimates the unstretched flame speed and Markstein length of methane−air flames by 14.2 and 151.1%, respectively. Therefore, in the subsequent study, the nonlinear relationship between Sn and α expressed by eq 4 is selected to derive the unstretched flame speed. The laminar burning velocity, ul, is computed from Sl using

Figure 2. Spherical flame images processed by the written computer program. chosen to ensure that the pressure inside the combustion chamber remains nearly constant, and thus, the flame propagation taking place in the combustion chamber could be treated as a quasi-isobaric process. Subsequently, the stretched flame speed, Sn, for the outwardly expanding spherical flames can be computed according to R−t via Sn =

dR dt

(1)

The relative rate of change of the flame surface area is defined as the stretch rate, α, i.e. α≡

1 dA 2 dR 2 = = Sn A dt R dt R

(2)

where A is the flame surface area. To derive the unstretched flame speed, Sl, two different relationships between Sn and α are used. They are26,56,57 Sn = S l − L bα

(3)

ul =

and ⎛ Sn ⎞2 ⎛ Sn ⎞2 2L α ⎜ ⎟ ln⎜ ⎟ = − b S S Sl ⎝ l⎠ ⎝ l⎠

ρb ρu

Sl

(5)

where ρu is the density of the unburned gas at initial conditions and ρb is assumed to be the density of the burned gas in the chemical equilibrium state.58 The thermal radiation is not considered when evaluating ρb.59

(4)

where Lb is the Markstein length. Variations of Sn with α for methane−n-heptane−air flames at 393 K and 0.1 MPa are shown in Figure 3. From the figure, it is observed that the stretched flame speed Sn of methane−n-heptane−air flames varies either nonlinearly or linearly with the stretch rate α at various

3. RESULTS AND DISCUSSION 3.1. Validation of the Experimental Setup. To validate the experimental setup mentioned above, the laminar burning

Figure 3. Variations of the stretched flame speeds for methane−n-heptane−air flames with the stretch rate at various equivalence ratios. C

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Figure 4. Comparisons of laminar burning velocities and Markstein lengths for methane−air flames between the present and other studies. The light green symbols denote error bars.

In the study by Akram et al.,38 GRI-Mech 3.061 is used to compute the laminar burning velocities of methane−air mixtures. The reaction mechanism involved in the study by Dirrenberger et al.52 is a chemical scheme for the oxidation of the mixture of n-heptane, iso-octane, and toluene, and this mechanism is developed by the authors themselves. For methane−air flames, it is interesting to note that, as the equivalence ratio is below about 1.1, the laminar burning velocities determined by different researchers tend to converge to a fixed value at each of the equivalence ratios. While at equivalence ratios above 1.1, scatter in data of the laminar burning velocity is observed. The laminar burning velocities for methane−air flames measured in the present study are in good agreement with the experimental values obtained by other researchers, except the data obtained by Bradley et al.,23 which is higher at the lean-fuel side and lower at the rich-fuel side than other data. Furthermore, a good agreement in the laminar burning velocity is also observed between the present study and the modeling study by Akram et al.38 With regard to the Markstein length, it is observed from Figure 4b that the values measured in the present study agree well with the data obtained by Halter et al.,57 Miao et al.,60 and Chen et al.62 For n-heptane−air flames, from Figure 5, it is seen that the values of the laminar burning velocity measured in the present study are in close agreement with most data points extracted from the literature, except those obtained by Kumar et al.,44 which is higher than all other data at most equivalence ratios. However, the agreement in the laminar burning velocity between the present study and the modeling study by Dirrenberger et al.52 seems not to be good. In comparison to the majority of the experimental results, at the rich-fuel side, the reaction mechanism underestimates the laminar burning velocity, while at the lean-fuel side, the laminar burning velocity is overestimated slightly. Through the above comparisons, the accuracy of the experimental facility used in the present study is validated. Meanwhile, considering that the parameters including the laminar burning velocity and Markstein length are derived through the computer program written for data processing of outwardly expanding spherical flames, thus the accuracy of the computer program is also validated to some extent.

velocities of methane−air mixtures at 0.1 MPa and 298 K and n-heptane−air mixtures at 0.1 MPa and 358 K were determined, respectively, at different equivalence ratios, and the values obtained were compared to the corresponding data extracted from the literature. The result is shown in Figures 4 and 5.

Figure 5. Comparisons of laminar burning velocities for n-heptane−air flames between the present and other studies. The light green symbols denote error bars.

The experimental values of laminar burning velocities of methane and n-heptane presented in Figures 4 and 5 are derived from different experimental methods. For example, the technique used in the studies by Dyakov et al.27 and Dirrenberger et al.18,52 is the heat flux method. The counterflow twin-flame technique is used by Kumar et al.,44 Smallbone et al.,46 and Ji et al.47 to measure the laminar burning velocity of nheptane−oxidizer mixtures. The rest of the experimental values are measured using the outwardly expanding spherical flames, except the data obtained by Vagelopolous et al.25 The experimental data extracted from the papers by Halter et al.57 and Miao et al.60 were derived using the nonlinear extrapolation method. The modeled values of laminar burning velocities of methane−air and n-heptane−air mixtures come from the studies by Akram et al.38 and Dirrenberger et al.,52 respectively. D

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al.32 and Chong et al.,63 although the initial temperature in these studies was lower than that in the study by Hu et al.22 Kumar et al.44 measured the laminar burning velocities of nheptane−O2−N2 mixtures using the counterflow twin-flame technique, and the sensitivity analysis of the laminar burning velocity was also performed at the initial pressure of 1 atm, the initial temperatures of 298 and 470 K, and the equivalence ratio of 1.0. The mechanism proposed by Seiser et al.64 was used in the study. From the study by Kumar et al.,44 it was observed that the elementary reactions, including H + O2 = O + OH, CO + OH = CO2 + H, and O + H2 = H + OH, have significant influence on the laminar burning velocity of n-heptane−air mixtures, and the result is independent of the initial temperature. Via the comparison of the sensitivity analysis of the laminar burning velocity between methane and n-heptane, it can be found that some elementary reactions, such as H + O2 = O + OH and CO + OH = CO2 + H, are always limiting steps in the combustion processes of methane and n-heptane. It is a common phenomenon that the elementary reactions involving H, O, and OH have significant influence on the combustion of hydrocarbon fuels, as summarized by Kuo.65 The similarity in the dependence of the laminar burning velocity upon the elementary reactions should be responsible for the less obvious variation in the laminar burning velocity of methane−n-heptane mixtures when changing the methane content. 3.3. Flame Instability of Methane−n-Heptane Mixtures. Through observing the trend of the Markstein length, the variation of the flame instability of methane−n-heptane−air mixtures is obtained. The variation of the Markstein length with the increasing equivalence ratio at 428 K is presented in Figure 8. Because of the similar dependence of the Markstein length upon the methane content at different initial temperatures, the profiles of the Markstein length for methane−n-heptane−air mixtures with the equivalence ratio at 358 and 393 K are not shown here, except a few data points. Similar to the dependence of the laminar burning velocity upon the methane content, the Markstein length for methane− n-heptane−air mixtures only decreases slightly when the methane content reaches 0.5, as shown in Figure 8, indicating that the flame instability of methane−n-heptane−air mixtures is less sensitive to the methane content when the methane content is below 0.5. Only a slight change occurs in the Markstein length as the methane content is up to 0.75. The variation of the Markstein length for pure methane with the equivalence ratio is significantly different from that for methane−n-heptane−air mixtures, implying the opposite trend in the flame instability between pure methane and methane−n-heptane mixtures. From another perspective, that is to say that the flame instability of pure methane will be altered even when a tiny amount of n-heptane is added to methane. Besides, from Figure 8, it is observed that the Markstein lengths of methane and n-heptane decrease slightly when the initial temperature is elevated, implying that their flame instabilities enhance when increasing the initial temperature. 3.4. Critical Value of the Methane Content. Although laminar burning velocities and Markstein lengths for methane− n-heptane−air mixtures have been obtained at methane contents of 0, 0.25, 0.5, 0.75, and 1, it is still difficult to determine a critical methane content at which the laminar burning velocity and Markstein length of methane−n-heptane− air flames start to change significantly. To derive the critical value of the methane content, laminar burning velocities and Markstein lengths for methane−n-

3.2. Laminar Burning Velocities of Methane−nHeptane Flames. Experiments of spherical flames for methane−n-heptane mixtures at an initial pressure of 0.1 MPa and initial temperatures of 358, 393, and 428 K were conducted using the above experimental setup, and the result is as follows. Variations of the unstretched flame speed and laminar burning velocity of the combustible mixtures of methane, nheptane, and air with the equivalence ratio at different initial temperatures are shown in Figures 6 and 7, respectively.

Figure 6. Unstretched flame speeds of methane−n-heptane−air flames at different equivalence ratios at the initial temperature of 428 K.

Because of the similar trend of the unstretched flame speed with the equivalence ratio at different initial temperatures, only the variation of the unstretched flame speed with the equivalence ratio at 428 K is presented, as shown in Figure 6. The value of the equivalence ratio is about 1.1, at which the unstretched flame speed reaches its maximum. It is observed that the unstretched flame speed of methane−n-heptane−air mixtures remains nearly constant, even when the methane content is up to 0.5, and as the methane content reaches 0.75, a slight change occurs in the unstretched flame speed. The overall trend of the laminar burning velocity of the methane−n-heptane−air flames with the equivalence ratio at various initial temperatures, as shown in Figure 7, is similar to that of the unstretched flame speed presented in Figure 6. At the initial temperature of 428 K, even when the methane content is up to 0.75, the laminar burning velocity just has an imperceptible decrease. It is also seen that, as the initial temperature increases, the difference in the laminar burning velocity between methane and n-heptane tends to diminish and the laminar burning velocity for the mixture of methane, nheptane, and air remains unchanged when varying the methane content. With respect to the less obvious change in the laminar burning velocity of methane−n-heptane−air mixtures when varying the methane content, it can be interpreted from the point of view of chemical kinetics. In the study by Hu et al.,22 the sensitivity analysis of the laminar burning velocity of pure methane−air flames was performed at the initial pressure of 0.1 MPa, the initial temperature of 373 K, and the equivalence ratio of 0.8. GRI-Mech 3.061 was used in the study. It was found that the laminar burning velocity is sensitive to the elementary reactions H + O2 = O + OH, OH + CO = H + CO2, etc. Similar results were also obtained in the studies by Bougrine et E

DOI: 10.1021/acs.energyfuels.5b00355 Energy Fuels XXXX, XXX, XXX−XXX

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Figure 7. Variations of the laminar burning velocities for methane−n-heptane−air flames with the equivalence ratio at different initial temperatures.

flames is less dependent upon the methane content. At the equivalence ratio of 1.1, changes in both the laminar burning velocity and Markstein length are imperceptible. While at the equivalence ratios of 0.8 and 1.3, slight and significant changes occur in the laminar burning velocity and Markstein length, respectively. As shown in the figure, when the methane content in the methane−n-heptane mixtures is up to 0.75, the laminar burning velocity and Markstein length start to change relatively obviously. Then, the methane content of 0.75 can be treated preliminarily as the critical methane content at which the laminar burning velocity and Markstein length of methane−nheptane−air flames start to change significantly. The methane content mentioned above denotes the mole fraction of methane in the methane−n-heptane mixture, and it can be converted into the mass fraction or energy fraction. According to the molecular weights and higher heating values of methane and n-heptane,66 when the mole fraction of methane is equal to 0.75, the corresponding mass and energy fractions of methane in the methane−n-heptane mixture are 0.324 and 0.355, respectively. It means that, when the mass (or energy) fraction of methane is larger than 0.324 (or 0.355), the combustion characteristics of methane−n-heptane−air mixtures will change significantly. It is seen that the proportion of methane in the methane−n-heptane mixture is relatively low from the point of view of mass or energy when the mole fraction of methane reaches the critical value. In the study by Papagiannakis et al.,9 which is associated with the natural gas− diesel dual-fuel engines, the mass fraction of natural gas in the

Figure 8. Variations of the Markstein lengths for methane−nheptane−air flames with the equivalence ratio.

heptane−air flames were measured at equivalence ratios of 0.8, 1.1, and 1.3 and an initial temperature of 393 K, with the increment of the methane content being reduced to be 0.1. The result is shown in Figure 9. From the figure, it is seen that laminar burning velocities and Markstein lengths do not vary linearly with the methane content for methane−n-heptane−air flames. In comparison to the variation of the Markstein length with the methane content, the laminar burning velocity for methane−n-heptane−air F

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Figure 9. Laminar burning velocities and Markstein lengths for methane−n-heptane−air flames at various methane contents.

natural gas−diesel mixture is up to 0.86. Thus, in the present study, if the mass fraction of methane in the methane−nheptane mixture is equal to 0.86, the corresponding mole and energy fractions of methane are 0.975 and 0.876, respectively. That is to say that, at this point, the heat release mainly comes from the combustion of methane rather than n-heptane. Meanwhile, the combustion characteristics of methane−nheptane mixtures are more similar to those of methane rather than n-heptane.

Notes

4. CONCLUSION Laminar burning velocities and Markstein lengths for methane−n-heptane−air mixtures at an initial pressure of 0.1 MPa and initial temperatures of 358, 393, and 428 K were experimentally determined at various methane contents using outwardly expanding spherical flames. A computer program was written with MATLAB to complete the data processing. The difference between the linear and nonlinear extrapolation methods is discussed in detail for methane−n-heptane−air mixtures, and the nonlinear method is selected. To validate the accuracy of the experimental setup and the computer program, comparisons of the laminar burning velocities of methane−air and n-heptane−air mixtures between the present and other studies were performed, respectively, and the agreement is good. On this basis, through the spherical flame experiments of methane−n-heptane−air mixtures, it is seen that the laminar burning velocities of methane−n-heptane−air mixtures are less dependent upon the methane content compared to the Markstein lengths. The increase of the initial temperature tends to diminish the difference in the laminar burning velocity between methane and n-heptane and only has weak effects on the flame instability of the methane−n-heptane mixtures. At last, according to variations of the laminar burning velocities and Markstein lengths of methane−n-heptane−air mixtures with the methane content, the value of 0.75 can be treated preliminarily as the critical methane content at which the laminar burning velocity and Markstein length of methane−nheptane−air flames start to change significantly.

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the Natural Science Foundation of China (Grant 51479149) and the Fundamental Research Program of Application of Ministry of Transport of the People’s Republic of China (Grant 2015329811130). The authors appreciate the “Alternative Fuel Research Group of WUT” for assistance in setting up and testing the experimental facilities. REFERENCES

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DOI: 10.1021/acs.energyfuels.5b00355 Energy Fuels XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.energyfuels.5b00355 Energy Fuels XXXX, XXX, XXX−XXX