Measurement of Laminar Burning Velocities and Markstein Lengths for

Apr 3, 2009 - ... and the Markstein lengths are also decreased with the increase of the equivalence ratio. On the basis of the experimental data, a co...
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Energy & Fuels 2009, 23, 2490–2497

Measurement of Laminar Burning Velocities and Markstein Lengths for Diethyl Ether-Air Mixtures at Different Initial Pressure and Temperature Yage Di, Zuohua Huang,* Ni Zhang, Bin Zheng, Xuesong Wu, and Zhiyuan Zhang State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong UniVersity, Xi’an, People’s Republic China ReceiVed January 7, 2009. ReVised Manuscript ReceiVed March 18, 2009

Measurement of laminar burning velocities and Markstein lengths were made for the diethyl ether-air mixtures at different equivalence ratios, initial temperatures, and pressures by using spherically propagating flame and schlieren photography method. The results show that the stretched flame propagation speeds, the unstretched flame propagation speeds, the stretched laminar burning velocities, the stretched mass burning velocities, and the unstretched laminar burning velocities increase with the increase of the initial temperature. Although the Markstein lengths decreases with the increase of the initial temperature. The stretched flame propagation speeds, the unstretched flame propagation speeds, the stretched laminar burning velocities, the stretched mass burning velocities, the unstretched laminar burning velocities and the Markstein lengths are decreased with the increase of the initial pressure, and the Markstein lengths are also decreased with the increase of the equivalence ratio. On the basis of the experimental data, a correlation is obtained for the unstretched laminar burning velocity versus the initial temperature and pressure over wide range of equivalence ratios.

1. Introduction Laminar burning velocity is an important and fundamental parameter of fuels that has attracted more investigation in fuel and combustion communities. Laminar burning velocities are the basic data in combustion and engine simulation,1 which influence the performance and emissions of the combustion process in many combustion devices.2,3 Meanwhile, laminar burning velocity can be used for the kinetic mechanism validation because it is a basic physiochemical property of the premixed combustible gases.4 Thus, various flame configurations have been employed in determining the laminar burning velocity, such as the stagnation plane flame,5 the heat flux method,6 and the outwardly propagating spherical flames.7,8 Besides the measurement, some researchers determined the laminar burning velocity using combustion pressure informa* Corresponding author: phone: +0086 29 82665075; fax: +0086 29 82668789; e-mail: [email protected]. (1) Farrell, J. T.; Weissman, W.; Johnston, R. J.; Nishimura, J.; Ueda, T.; Iwashita, Y. Fuel effects on SIDI efficiency and emissions. SAE Tech. Paper 2003-01-3186; 2003. (2) Bayraktar, H.; Durgun, O. Energ. ConVers. Manage. 2005, 46, 2317– 2333. (3) Anupam, D.; David, S. K. T.; Checkel, M. D. The effects of temperature and pressure on stretched, freely propagating, premixed, laminar methane-air-flame. SAE Tech. Paper 2006-01-0494; 2006. (4) Huzayyin, A. S.; Moneib, H. A.; Shohatta, M. S.; Attia, A. M. A. Fuel 2008, 87, 39–57. (5) Chao, B. H.; Egolfopoulos, F. N.; Law, C. K. Combust. Flame 1997, 109, 620–638. (6) Bosschaart, K. J.; Goy, L. P. H. D. Combust. Flame 2004, 136, 261– 269. (7) Dowdy, D. R.; Smith, D. B.; Taylor, S. C. Laminar burning velocities and stretch effects in hydrogen/air mixtures , 23rd International Symposium on Combustion; The Combustion Institute: 1990; pp 325-332. (8) Bradley, D.; Hicks, R. A.; Lawes, M.; Sheppard, C. G. W.; Woolley, R. Combust. Flame 1998, 115, 126–144.

tion.4,9-11 The stagnation plane flame method is difficult to draw a clear flame front and to stabilize the flame under high-pressure conditions. The heat flux method needs to determine the heat loss as a function of inlet velocity and to extrapolate the results to zero heat loss to get the adiabatic burning velocity. When the combustion pressure is employed to determinate the laminar burning velocity, the influence of stretch is ignored. For the spherically expanding flame, the effect of stretch is well-defined, and the unstretched laminar burning velocity can be determined by the means of an extrpolation at zero stretch. The understanding and quantifying of the effect of stretch is important not only for laminar flames, which occur in some practical burners, but also for the modeling of turbulent flames in SI engines.12 Meanwhile, the Markstein length, which is an important parameter that reflects the flame stabilities, can easily be obtained. Thus, the method of outwardly propagating spherical flames has been widely used in the measurement of laminar burning velocity. Using the spherically propagating flame and high-speed schlieren photography method, Dowdy et al.7 measured the laminar burning velocities and analyzed the stretch effects in hydrogen-air mixtures. Bradley et al.8 measured the laminar burning velocities and Markstein lengths for the iso-octane-air and the iso-octane-n-heptane-air mixtures. Gu et al.13 measured the laminar burning velocity of methane-air mixtures. (9) Dahoe, A. E.; Goey, L. P. H. D. J. Loss. PreVent. Proce. 2003, 16, 457–478. (10) Takizawa, K.; Takahashi, A.; Tokuhashi, K.; Kondo, S.; Sekiya, A. Flame 2005, 141, 298–307. (11) Razus, D.; Oancea, D.; Movileanu, C. J. Loss. PreVent. Proce. 2006, 19, 334–342. (12) Davis, S. G.; Quinard, J.; Searby, G. Combust. Flame 2002, 130, 112–122. (13) Gu, X. J.; Haq, M. Z.; Lawes, M.; Woolley, R. Combust. Flame 2000, 121, 41–58.

10.1021/ef900015k CCC: $40.75  2009 American Chemical Society Published on Web 04/03/2009

Laminar Burning Velocities of Diethyl Ether-Air

Radwan et al.14 measured the laminar burning velocities of some coal derived fuels. Huang et al.15 measured the laminar burning velocity of natural-hydrogen mixtures. Liao et al.16 measured the laminar burning velocities for the ethanol-air mixtures at elevated temperature, Tang et al.17 measured the laminar burning velocity for the propane-air mixtures, and Zhang et al.18 measured the laminar burning velocity for the methanol-air mixtures. Additionally, Davis et al.,12 Gu et al.,13 Tseng et al.,19 and Bradley et al.20 have measured the Markstein length to quantify the flame stretch considering the effects of both strain and flame curvature and attempted to incorporate these effects in numerical simulations of turbulent premixed flames. Diethyl ether (DEE) is a new type of engine alternative fuel and can be used as the oxygenate additive to decrease engine PM emission.21-23 However, there is no report on the laminar burning velocity of DEE, thus the measurement of the laminar burning velocity of DEE becomes the importance in the understanding of DEE combustion and will provide data for DEE chemical kinetics validation. The objective of this paper is to measure the laminar burning velocity and Markstein lengths for the DEE-air mixtures at different initial temperature and pressure over a wide range of equivalence ratios and to summarize the correlation for the laminar burning velocity versus initial pressure and temperature based on the experimental data. 2. Experimental Setup and Procedures A cylinder-type vessel with 180 mm in diameter and 210 mm in length is used in this study. A pressure transmitter is used to measure the initial and partial pressures for the case of initial pressure larger than the atmospheric pressure, and a mercury manometer is used to regulate the initial and partial pressures in the case of initial pressures less than the atmospheric pressure. A pressure transducer is used to record the combustion pressure, and a thermocouple is employed to measure the initial temperature. Two sides of vessel are transparent to make the inside observable and provide optical access. A high-speed digital camera (Redlake HG100K) operating at 5000 frames per second will record the flame propagation during the combustion. A standard capacitive discharge ignition system is used to initialize a flame kernel. Experimental setup is the same as that in ref 18. The amount of DEE is calculated in advance according to the designed equivalence ratio, initial pressure, and temperature, and then it is injected into the constant vessel with a microliter syringes. Finally, air is introduced to the vessel according to its partial pressure. DEE-air mixture is heated and evaporates in the vessel and waits for 10 min before ignition start to ensure a well-mixed and motionless mixture. The laminar burning velocity is derived from the well-established method as described by Dowdy et al.7 and Bradley et al.,8 which is (14) Radwan, M.; Ismail, M.; Selim, M. Y.; Saleh, H. Energ. Sources 2001, 23, 345–361. (15) Huang, Z. H.; Zhang, Y.; Zeng, K.; Liu, B.; Wang, Q.; Jiang, D. M. Combust. Flame 2006, 146, 302–311. (16) Liao, S. Y.; Jiang, D. M.; Huang, Z. H.; Zeng, Ke.; Cheng, Q. Appl. Therm. Eng. 2007, 27, 374–380. (17) Tang, C. L.; Huang, Z. H.; Jin, C.; He, J. J.; Wang, J. H.; Wang, X. B.; Miao, H. Y. Int. J. Hydrogen. Energ. 2008, 33, 4906–4914. (18) Zhang, Z. Y.; Huang, Z. H.; Wang, X. G.; Xiang, J.; Wang., X. B.; Miao, H. Y. Flame 2008, 155 (3), 358–368. (19) Tseng, L. K.; Ismail, M. A.; Faeth, G. M. Combust. Flame 1993, 95, 410–426. (20) Bradley, D.; Gaskell, P. H.; Gu, X. J. Combust. Flame 1996, 104, 176–198. (21) Anand, R.; Mahalakshmi, N. V. Proc. Inst. Mech. Eng., Part D 2007, 221, 109–116. (22) Mack, J. H.; Flowers, D. L.; Buchholz, B. A.; Dibble, R. W. P. Combust. Inst. 2005, 30, 2693–2700. (23) Jothi, N. K. M.; Nagarajan, G.; Renganarayanan, S. Renew. Energ. 2007, 32, 1583–1593.

Energy & Fuels, Vol. 23, 2009 2491 widely used in the research.13,16-18,24,25 For an outwardly propagating spherical flame, the stretched flame speed is the velocity of the flame front relative to a fixed position, which can be derived from the radius versus time:

Sn )

dru dt

(1)

where ru is the radius of the flame in schlieren photograph, and t is the elapsed time from spark ignition. As described in previous research,8 a general definition of stretch at any point on flame surface is the Lagrangian time derivative of the logarithm of the area A of any infinitesimal element of the surface shown in eq 2:

R)

1 dA d(ln A) ) dt A dt

(2)

For the outwardly propagating spherical flame, the flame stretch rate can be simplified as

R)

2 dru 2 1 dA ) ) Sn A dt ru dt ru

(3)

For the weakly stretched flame expansion, there exists a linear relationship between the flame speeds and the flame stretch rate,13

Sn ) Sl - LbR

(4)

where Sl is the unstretched flame propagation speed, obtained as the intercept value of Sn at R ) 0 in the plot of Sn against R. Burned gas Markstein length Lb is the negative value of the slope of Sn versus R. Positive Lb corresponds to Lewis numbers larger than unity, and the flame speed will decrease with the increase of the stretch rate, and vice versa. It is well recognized that the negative Lb corresponds to Lewis numbers less than unity and that flame speed will increase with the increase of the stretch rate. Negative values of Lb are associated with a more unstable flame.26,27 If the pressure change is negligible, a simple relationship links the Sl to the unstretched laminar burning velocity ul is shown in eq 5, in which Fb and Fu are the densities for burned and unburned gases, respectively.

ul ) FbSl/Fu

(5)

Laminar burning velocity represents the rate at which the flame front propagates into the unburned gases. Due to the finite flame thickness, there exist two possible definitions for the stretched laminar burning velocity on the two sides of flame fronts.8 One is the stretched laminar burning velocity un shown in eq 6, and the other is stretched mass burning velocity unr as expressed in eq 7.

[ ]

(6)

Fb (u - unr) Fb - Fu n

(7)

un ) S Sn unr )

Fb Fu

where S is a function that depends upon the flame radius and density ratio.20 Bradley et al.8 provided an expression for S, shown in eq 8.

S ) 1 + 1.2

[()] δl Fu ru Fb

2.2

[()]

- 0.15

δl Fu ru Fb

2.2 2

(8)

(24) Kwon, O. C.; Faeth, G. M. Combust. Flame 2001, 124, 590–610. (25) Verhelst, S.; Woolley, R.; Lawes, M.; Sierens, R. Combust. Inst. 2005, 30, 209–216. (26) Law, C. K.; Sung, C. J. Prog. Energ. Combust. 2000, 26, 459– 505. (27) Bradley, D.; Sheppard, C. G. W.; Woolley, R.; Greenhalgh, D. A.; Lockett, R. D. Combust. Flame 2000, 122, 195–209.

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Here δl is the characteristic laminar flame thickness, obtained by δl ) ν/ul, in which ν is the kinetic viscosity of the unburned mixture. As the data is unavailable, pure gas viscosities are determined theoretically using the method given by Chung et al.28 Viscosities of the unburned gas mixtures are deduced from the equation derived by Wilke.29

3. Results and Discussions 3.1. Flame Propagation Speeds and Markstein Length. 3.1.1. Stretched Flame Propagation Speed. The previous researchers supplied a linear relationship between the stretched laminar flame speed (Sn),8,30-33,37 and the stretch rate (R) in certain range of flame radii by removing the spark ignition influence at small radius and pressure rising influence at large radus. The slope of the Sn-R curve indicates the burned gas Markstein length (Lb), which can reflect the stability of flame. The negative value of the slope of the Sn-R curve corresponds to the positive value of Lb. Positive values of Lb indicate that the flame speed decreases with the increase of flame stretch rate. In this case, if any kinds of protuberances appear at the flame front, the flame speed in the flame protruding position will be suppressed, and this makes the flame stability. In contrast to this, a negative value of Lb means that the flame’s speed increases with the increase of flame stretch rate. In this case, if any kinds of protuberances appear at the flame front, the flame speed in the flame protruding position will be increased, and this will increase the instability of the flame.15 Figure 1a shows the relationship between the stretched flame speed Sn and stretch rate R at different equivalence ratios. Except for φ ) 1.4, Sn is decreased with the increase of R, indicating a positive value of Lb and a stable flame front. In the case of φ ) 1.4, Sn shows a slight increasing with the increase of the stretch rate and this gives a negative value of Lb, reflecting the instability trend of the flame front, as described in Bradley et al.8 and illustrated in Zhang et al.18 The figure shows that the slope of Sn-R is larger in the case of lean mixture combustion, and this indicates that the lean mixture flame has the more stable flame front than that of the rich mixture flame. This has been verified by Bradley et al.8 and Zhang et al.18 in their study of iso-octane and methanol fuels. The phenomena are also illustrated later in Figure 4, in which the value of Lb is deceased with the increase of equivalence ratio. In the case of φ ) 0.8, there is a sharp fall in Sn with the stretch rates at the point A. Bradley et al.8 regarded that the fully developed flame is not yet established in this regime. Thus, the data in such regime, where stretch rate is larger than that for position A, can not be used in the calculation. In the case of φ ) 1.2 and φ ) 1.4, the figure shows a remarkable increasing at positions B and C, respectively. This reflects the occurrence of flame front instability where the cellular structure of the flame front increases the flame front surface area and makes a remarkable increase in Sn. As low value of Lb for rich mixture combustion, the propagating flame will develop into a cellular structure flame front as flame is propagating. In order to minimize the influences of flame thickness variations, curvature, and unsteadiness caused by flame propagation with (28) Chung, T. H.; Ajlan, M.; Lee, L. L.; Starling, K. E. Eng. Chem. Res. 1988, 27 (4), 671–679. (29) Wilke, C. R. J. Chem. Phys. 1950, 18, 517–519. (30) Sivashinsky, G. SIAM J. Appl. Math. 1981, 40 (3), 432–438. (31) Matkowsky, B. J.; Olagunju, D. O. SIAM J. Appl. Math. 1982, 42 (5), 1138–1156. (32) Clavin, P.; Williams, F. A. J. Fluid. Mech. 1982, 116, 251–282. (33) Bechtold, J. K.; Matalon, M. Combust. Flame 1987, 67, 77–90. (34) Aung, K. T.; Hassan, M. I.; Faeth., G. M. Combust. Flame 1997, 109, 1–24.

Figure 1. Stretched flame speed versus stretch rates at different equivalence ratio, initial temperatures, and pressures.

flame radius, the flame conditions should be conservatively selected, where the ratio of characteristic flame thickness to flame radius is less than 0.02.19,34,35 In addition, the value of Sn is higher at φ ) 1.0 and φ ) 1.2 at the same stretch rate. Faster flame speed corresponds to the higher flame temperature because the laminar flame speed is highly sensitive to the small changes in the flame temperature profile.36 Anupam et al.3 reported that the higher flame temperature was also observed at φ ) 1.0 and φ ) 1.2, which is consistent with our measurement of Sn. Figure 1b shows the stretched flame propagation speed versus flame stretch rate at different initial temperatures at the (35) Hassan, M. I.; Aung, K. T.; Kwon, O. C.; Faeth, G. M. J Propul. Power. 1998, 14, 479–488. (36) Maaren, A. V. One-step chemical reaction parameters for premixed laminar flames. Ph.D Thesis, Eindhoven University of Technology: 1994.

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Figure 2. Unstretched flame speeds versus equivalence ratio at different initial temperatures and pressures.

Figure 3. Adiabatic flame temperatures versus equivalence ratio at different initial temperatures and pressures.

stoichiometric equivalence ratio. Sn is increased with the increase of initial temperature. The studies in literature3,8,13-18 reported the similar phenomenon with the variation of the initial temperature. This is reasonable since increasing the initial temperature will promote the mixture combustion and chemical reaction rate. Relatively large variation in Sn is presented at small stretch rate. Such phenomenon was also observed by Bradley et al.8 It is unlikely to be caused by radiant loss from the hot gas, but it is likely that Lb is very sensitive at small stretch rate or large flame radius.8 This phenomenon still needs further investigation to make the mechanism clarification. Figure 1c shows the relationship of Sn-R at different initial pressures for the stoichiometric DEE-air mixture. Sn is decreased with the increase of the initial pressure. The similar results were reported in refs 3, 8, 13, and 16-18. High ambient

pressure slows down the flame propagation speed and results in this phenomenon. 3.1.2. Unstretched Flame Propagation Speed. Figure 2 gives the variation of unstretched flame speeds with the equivalence ratio at different initial temperatures and pressures. With the increase of equivalence ratio, φ, the unstretched flame speeds, Sl, will increase for the lean mixture combustion but will decrease for the rich mixture combustion. Maximum value of Sl is presented at φ ) 1.1. Huang et al.15 measured the unstretched flame speeds for natural-hydrogen-air mixture combustion and found the maximum value of Sl was also presented at φ ) 1.1. Zhang et al.18 showed that the maximum value of Sl was presented at φ ) 1.1 for the methanol-airnitrogen mixture combustion. However, Tang et al.17 reported that the maximum value of Sl for the propane-air mixture

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Figure 4. Burned gas Markstein length versus equivalence ratio at different initial temperatures and pressures.

combustion was presented at φ ) 1.2. It can be concluded that the maximum flame propagation speed is presented at the mixtures that are slightly richer than stoichiometry. It is likely that the slightly richer mixtures can compensate the thermal dissociation due to the higher flame temperature as shown in Figure 3, leading to the more completed combustion compared with that for the stoichiometric mixture. Figure 2 shows the effect of initial temperature and pressure on the unstretched flame propagation speed. As shown in Figure 2a, for a specific equivalence ratio, the unstretched flame propagation speed is increased with the increase of initial temperature due to the enhanced chemical reaction rate. In fact, H and OH radical production and transport have strong correlation with burning velocities.35 Kwon and Faeth24 believed that the increased temperature leaded to radical concentrations, particularly the major radicals H, OH, and O, in the reaction zone to increase, which increases the reaction rates and flame speed. Figure 2b shows that the unstretched flame propagation speed is decreased with the increase of the initial pressure. Hassan et al.35 explained that the increased rates of the threebody recombination reactions at elevated pressures caused the significant reductions of all radical concentrations in the highpressure flame. The influence of initial temperature and pressure on unstretched flame propagation speed is also related to the variations of adiabatic flame temperature, Tad. The adiabatic flame temperature deduced from the combustion equilibrium is plotted in Figure 3a. For a specific equivalence ratio, Tad is increased with the increase of initial temperature. The trend is similar to the stretched flame speed and the unstretched flame speed, and this is due to the enhanvement of chemical reaction rate as initial temperature increased, leading to the increase of intermediate radicals like OH, and finally increases the Tad. The influence of initial pressure on Tad at initial temperature of 323 k is plotted in Figure 3b. The results show that the changes in initial pressure have negligible effect on Tad except for mixtures near stoichiometry. Anupam et al.3 reported the similar behavior in the methane-air flame. For the equivalence ratios of 1.0 and 1.1, Tad is increased with the increase of the initial pressure, and this is attributed to the reduced thermal dissociation.35 3.1.3. Markstein Lengths. Figure 4 shows the burned gas Markstein length, Lb, versus equivalence ratio, φ, at different initial temperatures and initial pressures. Lb is increased with the increase of equivalence ratio, indicating that the flame front instability is increased with the increase of equivalence ratio. The similar results were presented in refs 8 and 16-18. Previous studies showed that Lb is decreased with the increase of

Di et al.

equivalence ratio for heavy hydrocarbon fuels and oxygenates, but it is increased with the increase of equivalence ratio for light hydrocarbon fuel like methane. The oxygenate fuel DEE demonstrates the behavior of heavy hydrocarbon fuels. In addition, Markstein length can be normalized by the characteristic flame thickness as Markstein number.8 Bechtold and Matalon37 reviewed the Markstein number for the mixtures of hydrogen-air, methane-air, methanol-air, ethanol-air, propane-air, and octane-air, and the results showed an increase in Markstein number with the increase of equivalence ratio for the hydrogen-air and the methane-air flames and an opposite trend for the heavier hydrocarbons and alcohols. The results in this study are consistent with those reported in Bechtold and Matalon.37 Markstein length shows the decreasing trend with the increase of the initial temperature. The behavior becomes more obviously at lean mixture combustion. This means that the flame front stability will be decreased with the increase of the initial temperature. Meanwhile, Lb is decreased with the increase of the initial pressure, and this suggests that the flame front stability will be decreased with the increase of the initial pressure. Hassan et al.35and Zhang et al.18 demonstrated the similar results. 3.2. Laminar Burning Velocities. 3.2.1. Stretched Laminar Burning Velocity. Bradley defined two burning velocities due to the existing of finite flame thickness.8 One is stretched laminar burning velocity, un, based on the rate of disappearance or entrainment of cold unburned gas. The other is stretched mass burning velocity, unr, based on the rate of appearance of burned gas. Bradley et al.8 believed that unr is the pertinent property of engine dynamic performance because it governs the pressure development in cylinder. Analogously, un is the possible property of engine economic performance, which has much connection with the rate of fuel consumption. Thus, it is necessary to investigate the characteristics of un and unr. In addition, the influence of flame thickness is more significant at the smaller radius and is less at the larger radius. Both un and unr tend toward the identical value of the unstretched laminar burning velocity ul when the radius approach to infinity and/or flame stretch rate becomes zero. Figure 5, panels a-c, gives the stretched laminar burning velocity un and the stretched mass burning velocity unr versus the stretch rate at different equivalence ratios, initial temperature, and initial pressures, respectively. The difference between un and unr is clearly illustrated in Figure 5, where un is increased as the stretch rate increases, and unr is decreased as the stretch rate increases. The difference of (un - unr) is larger at high stretch rate, and this is attributed to the influence of flame thickness.8 Bradley et al.,8 Huang et al.,15 and Zhang et al.18 reported the similar trends for different fuels. Figure 5a shows the variations of un and unr with the equivalence ratio at the reference conditions, Pu ) 0.10 MPa and Tu ) 323 K. The values of un and unr are larger at the φ ) 1.2 compared with that at φ ) 0.8, 1.0, and 1.4, and this is consistent to that of Sn as shown in Figure 1a. When the stretch rate tends to zero, the line of un will intersect that of unr, and the vertical value of the intersection is the value of the unstretched laminar burning velocity ul. Figure 5, panels b and c, illustrates the effect of initial temperature and initial pressure on un and unr. The values of un and unr are increased with the increase of the initial temperature, but they are decreased with the increase of the initial pressure. The trends are similar with that of Sn and Sl. The possible explanation is that Sn, Sl, un, and unr are the apparent

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to propagate at high speed.37 As illustrated in Figure 6, the unstretched laminar burning velocity ul is increased with the increase of the initial temperature and is decreased with the increase of the initial pressure. Similar results were reported in the previous research.8,14,15,18,39 As discussed above, the increased initial temperature increases the intermediate radical concentrations, particularly the major radicals H, OH, and O in the reaction zone, leading to the increasing of reaction rates and laminar burning velocities.24 In addition, high adiabatic temperature also promotes the laminar burning velocity.37 An increase in initial pressure will enhance the rate of three-body recombination reaction and decreases the intermediate radical concentration and laminar burning velocity.35,36 Law38 gave the different explanation. Since the eigenvalue for flame propagation is the laminar mass burning flux f 0 ) Fuul, instead of ul alone, the data of mass burning flux are also plotted in Figure 7. The value of f 0 is increased with the increase of the initial pressure. The decreasing of ul shown in Figure 6b and an increase of f 0 illustrated in Figure 7 lead to the conclusion that the decreasing trend of ul as initial pressure increases is actually caused by the increase of the density of unburned mixture.38 3.2.3. Laminar Burning Velocity Correlation. On the basis of the experimental data, the exponents R and β in the following universal formula are correlated as follows: ul ) ul0(Tu/Tu0)R(Pu/Pu0)β

(9)

where the subscript 0 represents the reference condition, that is, Tu0 ) 323 K and Pu0 ) 0.10 MPa in the formula. The unstitched laminar burning velocity at reference condition, ul0, at different equivalence ratio, φ, is correlated in eq 10. ul0 ) -1.009φ2 + 2.109φ - 0.652

Figure 5. Stretched laminar burning velocity and stretched mass burning velocity vs stretch rate for different equivalence ratio, initial temperatures, and pressures.

representation of the combustion that are defined from different standpoints, but they are controlled by the same original combustion. 3.2.2. Unstretched Laminar Burning Velocities. Figure 6 shows the unstretched laminar burning velocities as a function of φ at different initial temperatures and pressures, which is shown in the solid lines. The unstretched laminar burning velocities, ul, gives its maximum value at an equivalence ratio of 1.1, and this is consistent to the results in other fuels,3,4,15 where the maximum adiabatic flame temperature is presented at this equivalence ratio as shown in Figure 3 and ref 4. This is because that the adiabatic flame temperature through the Arrhenius kinetics exerts a dominant influence on the laminar burning velocity. Since the adiabatic flame temperature is related to combustion-released heat, fuels with large heat release tend

(10)

The maximum burning velocity in eq 10 is about 0.449 m/s at the equivalence ratio of 1.05, corresponding to 0.467 m/s by experiment. In general, the results show that the correlated burning velocities are in good agreement with the results of experiment over a wide range of equivalence ratios. Figure 8 shows the variation of exponent R, given by R ) ln(ul/ul0)/ln(Tu/Tu0), at the initial pressure of 0.10 MPa. The temperature exponent gives its minimum value at the equivalence ratio slightly larger than the stoichiometric equivalence ratio, and the values of exponent are increased in both lean and rich mixtures. The similar trends were reported by Verhelst et al.25 The results show that the temperature exponents give less variation at initial temperatures of 343 and 363 K, and this may reveal the fact that the temperature exponent is a temperatureinsensitive parameter. To obtain an universal polynomial formula for simulation utilization, the values at initial temperature of 343 and 363 K are averaged and plotted in Figure 8. On the basis of the averaged values, a polynomial is fitted for the temperature exponent in the following as the function of equivalence ratio. (11) R ) 6.461φ2 - 13.070φ + 7.901 This correlation is valid for Pu ) 0.10 MPa, and 343 K e Tu e U363 K. In the previous study, Liao et al.16 also believed (37) Bechtold, J. K.; Matalon, M. Combust. Flame 2001, 127, 1906– 1913. (38) Law, C. K. Combustion Physics; Cambridge University Press: New York, 2006; pp 275-283. (39) Metghalchi, M.; Keck, J. Combust. Flame 1982, 48, 191–210. (40) Iijima, T.; Takeno, T. Combust. Flame 1986, 65, 35–43. (41) Gu¨lder, O. L. Laminar burning velocities of methanol, ethanol and isooctane mixture. 19th Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, PA, 1982; pp 275-281. (42) Milton, B. E.; Keck, J. C. Combust. Flame 1984, 58 (1), 13–22.

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Figure 6. Unstretched laminar burning velocities vs equivalence ratios.

Figure 7. Mass burning flux vs equivalence ratio at different initial pressures.

that R was affected by φ, and proposed a first-order polynomial shown in eq 12, for the ethanol-air mixture combustion. R ) 1.783 - 0.375(φ - 1) (12) Iijima and Takeno40 proposed an equivalence ratio dependence, eq 13, for the methane-air mixtures. R ) 1.60 + 0.22(φ - 1) (13) Anupam et gave that value of 1.8-2.5 for R, Gu¨lder et al.41 reported a constant of 1.75. For the stoichiometric flame, Milton and Keck42 reported the value of 1.26, Verhelst et al.25 gave the value of 1.32, and the values are approximate to the value in this study (R ) 1.292). However, Stone et al.,43 Iijima and Takedo,40 Liao et al.16 and Hill and Hung44 gave the values of 1.42, 1.60, 1.783, and 1.80, respectively, for temperature exponent in their studies. In addition, Rallis and Grforth45 gave the temperature exponents ranging from 1.37 to 2.33. It is al.3

(43) Stone, R.; Clarke, A.; Beckwith, P. Combust. Flame 1998, 114, 546–555. (44) Rallis, C. J.; Grforth, A. M. Prog. Energ. Combus. 1980, 6, 303– 329. (45) Hill, P. G.; Hung, J. Combust. Sci. Technol. 1988, 60 (1-3), 7– 30.

Figure 8. Temperature exponent R vs equivalence ratio at 0.10 MPa and different initial temperatures.

believed that the difference in temperature exponent is attributed to the difference of the fuel molecular structure and the experimental method. The pressure exponent, at Tu ) 323 K, is correlated in the same way as temperature exponent, given in β ) ln(ul/ul0)/ln(Pu/ Pu0). As shown in Figure 9, the pressure exponent strongly depends on initial pressure but has less dependence on equivalence ratio. The dot line is the averaged value of β within the concerned equivalence ratio for a specified initial pressure. The values of β are -0.13, -0.18, -0.41, and -0.50 for initial pressure of 0.25, 0.50, 0.75, and 1.0 MPa, respectively. These values are replotted in Figure 10. Thus, a third-order polynomial as the function of initial pressure is correlated for β. β ) 3.413P3u + -6.560P2u + 3.227Pu - 0.580

(14)

This equation is valid for: 0.25 MPa e UPu e U1.0 MPa, Tu ) 323 K. The results show that the pressure exponent β is a pressure-sensitive parameter. The decrease of the pressure exponent with the increase of initial pressure also indicates the increase of the initial pressure will decrease the laminar flame velocity. Gu¨lder et al.41 gave the similar explanation in their study.

Laminar Burning Velocities of Diethyl Ether-Air

Energy & Fuels, Vol. 23, 2009 2497

LPG-air mixture and propane-air mixtures and proposed a second-order polynomial formula as the function of φ for β. On the basis of the analysis and correlation from the previous studies and this study, it can be seen that the values of R and β depend on the type of fuel besides the influence of equivalence ratio, initial temperature, and pressure. 3.2.4. Comparison between Experimental and Calculated Laminar Burning Velocities. As shown in Figure 6, the dotted line indicates the calculated unstretched laminar burning velocities, which are in good line with experimental ones illustrated in solid lines. The maximum deviation is corresponding to the equivalence ratio of 0.7 and the initial pressure of 0.50 MPa, and the value is 18.6%. For other flames, the maximum deviation is not more than 10%. Figure 9. Pressure exponent β vs equivalence ratio at 323 K and different initial pressures.

Figure 10. Pressure exponent β vs initial pressures.

In the previous studies, Iijima and Takedo40 and Stone et al.43 reported that the pressure exponent depended on the initial pressure and the equivalence ratio. Anupam et al.3 correlated the value of β between -0.59 and -0.45. Hill and Hung44 suggested a pressure exponent of -0.299 for the pressures ranging from 0.2 to 1 bar. Rallis and Garforth45 analyzed the pressure dependency for the stoichiometric methane/air flames and gave the value of -0.3 for the pressure exponent when the initial pressure is above 1 bar. Gu¨lder et al.41 provided a polynomial formula for β, which has less dependence on the equivalence ratio. Takizawa et al.10 measured the laminar burning velocity of fluorinated compounds and fitted a firstorder polynomial formula for β. Huzayyin et al.4 investigated

4. Conclusions The unstretched laminar burning velocities and Markstein lengths were measured for the DEE-air mixtures at different equivalence ratios, initial temperatures, and pressures using a cylindrical-type bomb and schlieren photography method. The main results are summarized as follows. (1) The stretched flame propagation speeds, the unstretched flame propagation speeds, the stretched laminar burning velocities, the stretched mass burning velocities, and the unstretched laminar burning velocities increase with the increase of the initial temperature, and they decrease with the increase of the initial pressure. The unstretched flame propagation speed and unstretched laminar burning velocity present the maximum values at the equivalence ratio of 1.1. (2) The Markstein lengths decrease with the increase of the equivalence ratio, the initial temperature, and the initial pressure. The flame front instability decreases with the increase of the equivalence ratio, the initial temperature, and the initial pressure. (3) A formula for the unstretched laminar burning velocity is correlated based on the experimental data for the DEE-air premixed mixture combustion. The temperature exponent is a second-order polynomial as the function of equivalence ratio, and the pressure exponent is a third-order polynomial as the function of initial pressure. Both temperature exponent and pressure exponent may depend on fuel type. The correlated unstretched laminar burning velocitis are in good line with experimental results. Acknowledgment. The authors express their thanks to the National Natural Science Fund of China (50576070, 50821604) for supporting this project. EF900015K