study on laminar burning characteristics of premixed high...

965r 2009 American Chemical Society pubs.acs.org/EF

Energy Fuels 2010, 24, 965–972 : DOI:10.1021/ef901117dPublished on Web 12/03/2009

Study on Laminar Burning Characteristics of Premixed High-Octane Fuel-Air

Mixtures at Elevated Pressures and Temperatures

Jing Gong, Chun Jin, Zuohua Huang,* and Xuesong Wu

State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an, People’s Republic China

Received October 1, 2009. Revised Manuscript Received November 11, 2009

Laminar burning characteristics of high-octane fuel-air premixed mixtures (ETBE, TBA, and ethanol)were studied in a constant-volume bomb at various equivalence ratios, initial temperatures, and initialpressures by using outwardly propagating spherical flames with a high-speed schlieren imaging system.The flame propagation speed, the laminar burning velocity, the Markstein length, the adiabatic flametemperature, the flame thickness, and the density ratio were obtained and the influence of equivalenceratio, initial temperature, and initial pressure on these parameters was analyzed. The experimentalresults show that both the unstretched flame propagation speed and unstretched laminar burningvelocity increase with the increase of initial temperature and decrease with the increase of initial pressure.Thermal-diffusive instabilities (Markstein length) decrease at higher initial temperature and/or at lowerinitial pressure. Meanwhile, the unstretched flame propagation speed and the unstretched laminarburning velocity give maximum values on the rich mixture side. The onset of cellular instability wasevaluated in terms of the hydrodynamic and diffusional-thermal instabilities, and the reasons for theonset of the cellular structure were analyzed. The results indicate that the propensity for cellularstructure is enhanced due to the increase in hydrodynamic and diffusional-thermal instabilities at highinitial pressure. Moreover, the flame instability is more sensitive to initial pressure compared to initialtemperature.

1. Introduction

Nowadays, our society faces the problems of energy short-age and environmental pollution. To solve these problems,many efforts have been undertaken. One is to improvecombustion efficiency and reduce emissions of traditionalinternal combustion engines. The other is to develop therenewable energy and alternative fuels. The research onalternative fuel has made great development in recent years.Gasoline additives are always used to improve the perfor-mance and reduce the emissions of automotive vehicles.1,2

Ethyl tert-butyl ether (ETBE) is one kind of octane improver.The demandofETBEhas increased rapidly in place ofMethyltert-butyl ether (MTBE) in recent years3 because MTBE willcontaminate the groundwater whereas ETBE will not.4-7

Many reports concentrated on the production of ETBE using

the method of liquid phase synthesis from ethanol andisobutylene (IB).8-10 However, IB sources are limited tocatalytic cracking and steam cracking fractions,11 and thecost of this kind of production method is high due to thepurification process of high purity ETBE. These restrictthe wide application of ETBE as the octane enhancer. Froman economic and technological aspect, an alternative route tosynthesis ETBE from tert-butyl alcohol (TBA) and ethanol isintroduced.3 Without separating ETBE from others, thereaction product is a blend composed of ETBE, unreactedTBA, and unreacted ethanol. All three compounds (ETBE,TBA, and ethanol) are gasoline boosters. They not onlyimprove the octane ratings12 but also reduce the emissionof carbon monoxide, unburned hydrocarbons, and otherexhaust emissions.13 It is predictable that the substitution ofthis high-octane mixture (ETBE, TBA, and ethanol) insteadof ETBE can decrease the cost of octane improver, withoutlowering the engine performance. As the fundamentalcombustion characteristics are strongly related to enginecombustion, it is necessary to understand the fundamentalcombustion characteristics and provide the guidance onengine operation.

Laminar burning velocity is a fundamental characteristic ofa mixture and is always used to validate the chemical kineticsmechanism and predict the performance and emissions ofan internal combustion engine.14 There are various flameconfigurations inmeasuring the laminar burning velocity, such

*To whom correspondence should be addressed. Telephone: þ008629 82665075.Fax:þ0086 29 82668789. E-mail: [email protected].(1) Al-Hasan, M. Energy Convers. Manage. 2003, 44 (9), 1547–1561.(2) Rosell, M.; Lacorte, S.; Ginebreda, A.; Barcel, D. J. Chromatogr.

A 2003, 995 (1-2), 171–184.(3) Yang, B. L.; Yang, S. B.; Yao, R. Q.React. Funct. Polym. 2000, 44

(2), 167–175.(4) Squillace, P. J.; Zogorski, J. S.;Wilber,W.G.; Price,C.V.Environ.

Sci. Technol. 1996, 30 (5), 1721–1730.(5) da Silva, R.; Cataluna, R.; Menezes, E. W. d.; Samios, D.;

Piatnicki, C. M. S. Fuel 2005, 84 (7-8), 951–959.(6) Caprino, L.; Togna, G. I. Environ. Health Persp. 1998, 106 (3),

115–125.(7) Shih, T.; Rong, Y.; Harmon, T.; Suffet, M. Environ. Sci. Technol.

2004, 38 (1), 42–48.(8) de Menezes, E. W.; Cataluna, R. Fuel Process. Technol. 2008, 89

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Eng. Chem. Res. 1997, 36 (11), 4756–4762.

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Woolley, R. Combust. Flame 1998, 115 (1-2), 126–144.

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Energy Fuels 2010, 24, 965–972 : DOI:10.1021/ef901117d Gong et al.

as the stagnation plane flame,15,16 the heat flux method,17,18

and the outwardly propagating spherical flame.19-22 Stagna-tion plane flame method is difficult to draw a clear flame frontand to stabilize the flame under the high-pressure conditions.The heat flux method needs interpolation to determine theadiabatic burning velocity.23 For outwardly propagating sphe-rical flame, the stretch is well-defined and there is a linearrelationship between flame speeds and flame stretches. Mean-while, the Markstein length, which characterizes the effect ofstretch on flame propagation and reflecting the flame stability,can be obtained easily. For this reason, the outwardly propa-gating spherical flame has been widely used to measure thelaminar burning velocity.24-27 In this study, the laminar burn-ing velocity of the premixed high-octane fuel composing of65.3% ethanol, 11.9%TBA, and 22.8%ETBE bymass (resultof reaction with an EtOH/TBA molar ratio of 2) and airmixture was measured at various initial temperatures andpressures over a wide range of equivalence ratios by using theoutwardly propagating spherical flames.

Many previous researches concentrated on combustioncharacteristics of ethanol and/or ETBE air mixtures, respec-tively. Egolfopoulos et al.28 measured the laminar burningvelocities of ethanol-air mixture at atmospheric pressure,different equivalence ratios, and temperatures ranging from363 to 453K in the counter-flow flames. Liao et al.29 obtainedthe laminar burning velocity of ethanol-air mixtures atatmospheric pressure and at temperatures between 358 and480 K over a wide range of equivalence ratios in a cuboidbomb. According to Liao, there existed a power law correla-tion between the unstretched laminar burning velocity andinitial temperature and/or equivalence ratio over the rangesstudied. More recently, Bradley et al.30 studied the laminarburning velocities and Markstein numbers of ethanol-airmixtures using a spherical explosion bomb at pressures upto 1.4 MPa. The results showed that the occurrence ofunstable flame was more possible with the increase of initialpressure and the flame speed was enhanced by the flamewrinkling arising from the instabilities. For ETBE-air

mixtures, Yahyaoui et al.31 studied the laminar burningvelocities in a spherical bomb at room temperature andatmospheric pressure over wide range of equivalence ratios(0.5-1.5), and experimental results from both shock tube andspherical bomb were compared to those computed using adetailed chemical kinetic reaction mechanism.

2. Experimental Setup and Procedures

In this experiment, a constant-volume bomb (a cylinder-typevessel 180 mm in diameter and 210 mm in length) is used, of whichthe two sides have quartz windows to make the inside observableand to provide optical access. The details of the experimental setuphavebeen reported in ref 32.When the initial pressure is less than theatmosphericpressureaU-tubemercurymanometer isused toensurethe initial pressure with high precision, and a pressure transmitter isused when the initial pressure is higher than the atmosphericpressure. The measuring accuracy of the U-tube mercury man-ometer is 66 Pa. The high-octane fuel-air mixture is ignited bycentrally located electrodes and a standard capacitive dischargeignition system. A high-speed digital camera (HG-100K) operatingat 10000 frames/s is employed to record the flame picture, and aKistler pressure transducer is used to record the pressure with aresolution of 0.01 KPa during combustion process. In the presentexperiment, themixturesofoxygenandnitrogen (molar ratio1:3.76)are employed to simulate “dry air”. The liquid fuel mixtures areinjected into the chamber by a microliter syringe through the liquidfuel injection valve, and gases are introduced into the chamberthrough the inlet/outlet valve by the calculation in advance accord-ing to the designed equivalence ratio, initial temperature, and initialpressure. Then, waiting for 10min before the ignition is necessary toensure thewell-mixedandmotionlessmixture.On theotherhand, toescape from the influence of wall temperature on mixture tempera-ture, a sufficient interval is set between two experiments to cooldown and preserve the same initial temperature.

In the experiment, the initial temperature is set at 373, 423, and473 K; the initial pressures are 0.10, 0.25, 0.50, and 0.75MP; andthe equivalence ratios ranges from 0.7 to 1.4. The total equiva-lence ratio (φ) is defined as φ = (F/A)/(F/A)st, where F/A isthe fuel-air ratio and (F/A)st refers to the stoichiometric valueof F/A.

3. Determination of the Laminar Burning Velocity

For the spherically propagating flame, the stretched flamepropagation speed,Sn, is derived from the flame radius versustime:33-36

Sn ¼ dru

dtð1Þ

where ru is the radius of the flame in schlieren photograph andt is the elapsed time from spark ignition.

The flame stretch rate,R, indicates the expending rate of theflame front area. In aquiescentmixture, a general definitionofstretch at any point on the flame surface is shown in eq 2,

R ¼ dðln AÞdt

¼ 1

A

dA

dtð2Þ

(15) Chao, B. H.; Egolfopoulos, F. N.; Law, C. K. Combust. Flame1997, 109 (4), 620–638.(16) Yu, G.; Law, C. K.;Wu, C. K.Combust. Flame 1986, 63 (3), 339–

347.(17) Hermanns, R. T. E.; Konnov, A. A.; Bastiaans, R. J. M.; de

Goey, L. P. H.; Lucka, K.; Kohne, H. Fuel 2010, 89 (1), 114–121.(18) Vanmaaren, A.; Thung, D. S.; Degoey, L. P. H. Combust. Sci.

Technol. 1994, 96 (4-6), 327–344.(19) Gu, X. J.; Haq, M. Z.; Lawes, M.; Woolley, R. Combust. Flame

2000, 121 (1-2), 41–58.(20) Marley, S.K.; Roberts,W. L.Combust. Flame 2005, 141 (4), 473–

477.(21) Miao, H. Y.; Ji, M.; Jiao, Q.; Huang, Q.; Huang, Z. H. Int. J.

Hydrogen Energy 2009, 34 (7), 3145–3155.(22) Law, C. K.; Jomaas, G.; Bechtold, J. K. Proc. Combust. Inst.

2005, 30, 159–167.(23) Bosschaart, K. J.; de Goey, L. P. H. Combust. Flame 2004, 136

(3), 261–269.(24) Tang, C.; Huang, Z.; Jin, C.; He, J.; Wang, J.; Wang, X.; Miao,

H. Int. J. Hydrogen Energy 2008, 33 (18), 4906–4914.(25) Lamoureux, N.; Djebaili-Chaumeix, N.; Paillard, C. E. Exp.

Therm. Fluid Sci. 2003, 27 (4), 385–393.(26) Vu, T. M.; Park, J.; Kwon, O. B.; Kim, J. S. Int. J. Hydrogen

Energy 2009, 34 (16), 6961–6969.(27) Tseng, L. K.; Ismail, M. A.; Faeth, G. M. Combust. Flame 1993,

95 (4), 410–426.(28) Egolfopoulos, F. N.; Du, D. X.; Law, C. K. In Twenty-Fourth

Symp. (Int) on Combust., 1992; The Combustion Institute: Pittsburgh,1992; pp 833-841.(29) Liao, S. Y.; Jiang, D. M.; Huang, Z. H.; Zeng, K.; Cheng, Q.

Appl. Therm. Eng. 2007, 27 (2-3), 374–380.(30) Bradley, D.; Lawes, M.; Mansour, M. S. Combust. Flame 2009,

156 (7), 1462–1470.

(31) Yahyaoui, A.; Djebaili-Chaumeix,N.;Dagaut, P.; Paillard, C. E.Energy Fuels 2008, 22 (6), 3701–3708.

(32) Zhang, Z.Y.;Huang, Z.H.;Wang,X.G.;Xiang, J.;Wang,X. B.;Miao, H. Y. Combust. Flame 2008, 155 (3), 358–368.

(33) Bradley, D.; Gaskell, P. H.; Gu, X. J. Combust. Flame 1996, 104(1-2), 176–198.

(34) Huang, Z. H.; Wang, Q.; Yu, J. R.; Zhang, Y.; Zeng, K.; Miao,H. Y.; Jiang, D. M. Fuel 2007, 86, 2360–2366.

(35) Serrano, C.; Hernandez, J. J.; Mandilas, C.; Sheppard, C. G.W.;Wbolley, R. Int. J. Hydrogen Energy 2008, 33 (2), 851–862.

(36) Huang, Z.; Zhang, Y.; Zeng, K.; Liu, B.; Wang, Q.; Jiang, D.Combust. Flame 2006, 146 (1-2), 302–311.

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where A is the area of flame. For an outwardly propagatingspherical flame, the flame stretch rate can be simplified as,

R ¼ 1

A

dA

dt¼ 2

ru

dru

dt¼ 2

ruSn ð3Þ

And a linear correlation is occurred between the flame speedand the flame stretch rate with respect to the early stage offlame propagation,33 that is,

Sl -Sn ¼ LbR ð4Þwhere Sl is the unstretched flame propagation speed and Lb isthe Markstein length of burned gas. The unstretched flamespeed,Sl, can be obtained as the intercept value atR=0 in theplot ofSn againstR. The burned gasMarkstein lengthLb is thenegative value of the slope of a Sn-R curve according to eq 4.Positive values of Lb demonstrate that the flame speed de-creases with the increase of flame stretch rate and the flame isstable to diffusional-thermal instability. In this case, theflame speed in the flame protruding position will be sup-pressed if any kinds of protuberances appear at the flamefront.On the contrary, negative values ofLb indicate the flamespeed is increasedwith the increase of the flame stretch rate. Inthis case, the flame speed in the flame protruding position willbe creased if any kinds of protuberances appear at the flamefront, and the instability of the flame front will be increased.37

When Lb is positive and the absolute value is small, the localflame speed in the flame protruding position will not besuppressed effectively if any kinds of protuberances appearat the flame front (stretch rate is increased). This is attributedto the weak influence of stretch rate on flame speed. Thus, theflame instability in this case is more obvious compared withthat of positive Lb with large absolute value.

The laminar burning velocity can be obtained by thefollowing equation,

ul ¼ FbSl=Fu ð5Þwhere Fb and Fu are the densities for burned gas and unburnedgas, which can be received from initial state and thermalequilibrium calculation, respectively; and density ratio, σ, isdefinedasσ=Fu/Fb.Massburning flux is definedas f0=Fuul.38

Owing to the finite thickness, there exist two possibledefinitions for the stretched laminar burning velocity.14 Oneis the stretched laminar burning velocity un, which is defined atthe unburned gas side and related to the entrainment of theunburned gas. The other is stretched mass burning velocityunr, which is involved in the production of the burned gas.

un ¼ S SnFbFu

" #ð6Þ

unr ¼ FbFb -Fu

ðun -SnÞ ð7Þ

where S is a rectified function depending on the flame radiusand the density ratio and accounting for the effect of the flamethickness on the mean density of the burned gas. Bradley etal.14 provided a formula for S,

S ¼ 1þ 1:2δlru

FuFb

!2:224

35-0:15

δlru

FuFb

!2:224

352

ð8Þ

Here, δl is laminar flame thickness achieved by δl = ν/ul,39

where ν is the kinetic viscosity of the unburned mixtures.

4. Results and Discussions

4.1. Flame Propagation Speed and Markstein Length.

During the early stage of flame propagation, there exists atendency for the flame to quench due to the high stretch rate.A spark produces a flame kernel and results in a veryapparent flame expansion. Then, there is a limitation ofminimum ignition energy for the continuous propagationof the flame. The introduction of the minimum ignitionenergy can influence the measured value. Bradly et al.,33

Figure 1. Stretched flame propagation speed vs stretch rate atdifferent equivalence ratios, initial temperatures, and pressures.

(37) Liao, S. Y.; Jiang, D. M.; Gao, J.; Huang, Z. H. Energy Fuels2004, 18 (2), 316–326.(38) Law, C. K., Combustion Physics; Cambridge University Press:

New York, 2006; pp 275-283.(39) Bradley, D.; Lawes, M.; Liu, K.; Verhelst, S.; Woolley, R.

Combust. Flame 2007, 149 (1-2), 162–172.

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Liao et al.,40 and Lamoureux et al.41 indicated that the flamespeeds were independent of the ignition energy when flameradius is beyond 6 mm.With respect to the isobaric combus-tion, the maximum flame radius is limited to 25 mm, wherethe variation of the pressure can be discounted.42 Thus, thefollowing study uses the flame radius between 6 mm and25 mm to avoid the influence of ignition energy and pressurevariation, which has been testified suitably for the constant-volume combustion chamber used in this study.32,36,43,44

Figure 1 shows the stretched flame propagation speed (Sn)versus the stretch rate (R) at different equivalence ratios,initial temperatures, and pressures. There exists a linearrelationship between the stretched flame propagation speedsand flame stretch rates. The stretched flame propagationspeed is decreased with the increase of stretch rate in all thecases, indicating a positive value of Lb. In Figure 1a, Sn givesits maximum value at the stoichiometric equivalence ratioand the slope of the Sn-R curve is increased with the increaseof equivalence ratio, indicating the decrease of Lb. Thatmeans the instability of the flame front is increased at richmixture side. As shown in Figure 1b, stretched flame propa-gation speed is increased with the increase of initial tempera-

ture. Increasing initial temperature will promote the mixturecombustion and chemical reaction rate. Figure 1c shows theinfluence of initial pressure on stretched flame propagationspeed. The stretched flame propagation speed is decreasedwith the increase of initial pressure. The slopes of Sn-R linespresent the negative values, reflecting the positive values ofMarkstein lengths. This indicates that the flame front isstable to the diffusional-thermal instability.

Figure 2 illustrates the Markstein length and unstretchedflame propagation speed versus equivalence ratio at differentinitial temperatures. The Markstein length decreases mono-tonously with the increase of equivalence ratio and thedecrease of initial temperature. Markstein length reflectsthe influence of diffusional-thermal and flame stretch onthe explosion flame front, which results from the competingeffects of heat conduction from the flame and reactantdiffusion toward the flame.43 Thus, it reveals that leanmixtures and/or high initial temperature mixtures are morestable to diffusional-thermal instability. The unstretchedflame propagation speed increases with the increase of initialtemperature due to the increase of chemical reaction rate.The peak value of the unstretched flame propagation speedappears at an equivalence ratio between 1.0 and 1.1, and itshifts to the rich mixture side slightly as the increase of theinitial temperature.

Figure 3 gives Markstein length and unstretched flamepropagation speed versus equivalence ratio at differentinitial pressures. The Markstein length decreases with theincrease of initial pressure, and this indicates the flamebecomes more unstable with the increase of initial pressure.

Figure 2. Markstein length and unstretched flame propagationspeed versus equivalence ratio at different initial temperatures. Figure 3. Markstein length and unstretched flame propagation

speed vs equivalence ratio at different initial pressures.

(40) Liao, S. Y.; Jiang, D. M.; Gao, J.; Huang, Z. H.; Cheng, Q. Fuel2004, 83 (10), 1281–1288.(41) Lamoureux, N.; Djebaili-Chaumeix, N.; Paillard, C. E. Exp.

Therm. Fluid Sci. 2003, 27 (4), 385–393.(42) Hu, E.; Huang, Z.; He, J.; Jin, C.; Zheng, J. Int. J. Hydrogen

Energy 2009, 34 (11), 4876–4888.(43) Hu, E.; Huang, Z.; He, J.; Zheng, J.; Miao, H. Int. J. Hydrogen

Energy 2009, 34 (13), 5574–5584.(44) Chen, Z.; Wei, L.; Huang, Z.; Miao, H.; Wang, X.; Jiang, D.

Energy Fuels 2009, 23 (2), 735–739.

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The unstretched flame propagation speed decreases with theincrease of initial pressure, and the maximum value is pre-sented near the equivalence ratio of 1.1.

Figure 4 shows the adiabatic temperature versus equiva-lence ratio at different initial temperatures and pressures.Adiabatic temperature, a parameter that characterizes thethermodynamic behavior of the combustible mixture, isdeduced from combustion equilibrium. The peak value ofTad is presented at the equivalence between 1.0 and 1.1 in allcases, and the trend is similar to the unstretched flamepropagation speed. For a given equivalence ratio, Tad

increases with the increase of initial temperature. Thisphenomenon results from the enhancement of chemicalreaction rate as initial temperature increases, leading tothe increase of intermediate radicals such as OH, andultimately increases the Tad. In case of specified initialtemperature and equivalence ratio, Tad shows little varia-tion at different initial pressures except for stoichiometricmixtures. Tad is increased obviously with the increase ofinitial pressure at equivalence ratios from 0.9 to 1.2. This isattributed to the reduced thermal dissociation at higherinitial pressure.45 This behavior was also reported byAnupam et al.46 in methane-air flame and Di et al.47 indiethyl ether-air flame.

4.2. Laminar Burning Velocity and Mass Burning Flux.

Figure 5 shows the stretched laminar burning velocity (un)versus stretched mass burning velocity (unr) at differentequivalence ratios, initial temperatures, and initial pressures.The stretched laminar burning velocity based on the rate ofdisappearance or entrainment of cold unburned gas, in-creases with the increase of stretch rate except for leanmixtures (φ = 0.8) at the reference condition, Pu = 0.10MP, andTu=373K. In contrast, the stretchedmass burningvelocity, unr, related to the rate of appearance of burned gas,decreases as stretch rate increases. The difference between unand unr is clearly illustrated in Figure 5, and this results fromthe influence of flame thickness on burning velocity. The

Figure 4. Adiabatic flame temperature vs equivalence ratio atdifferent initial temperatures and pressures.

Figure 5. Stretched laminar burning velocity and stretched massburning velocity vs stretch rate at different equivalence ratios, initialtemperatures, and initial pressures (un: soild point; unr: hollowpoint).

(45) Law, C. K.; Makino, A.; Lu, T. F.Combust. Flame 2006, 145 (4),808–819.(46) De, A.; Ting, D.; Checkel, M. D. SAE Tech. Paper,

2006-01-0494, 2006.(47) Di,Y.G.;Huang, Z.H.; Zhang,N.; Zheng, B.;Wu,X. S.; Zhang,

Z. Y. Energy Fuels 2009, 23, 2490–2497.

970


difference is more obvious at small radius (corresponding tolarge stretch rate), and it reflects the large influence of flamethickness on burning velocity. As flame radius approaches toinfinity and/or flame stretch rate becomes infinitesimal, theeffect of flame thickness can be neglected, that is, un and unrtend toward a identical value, the unstretched laminarburning velocity. As shown in Figure 5a, at Pu = 0.10 MPand Tu =373 K, the value of un-unr is larger at φ=1.0 andφ=1.2 comparedwith that atφ=0.8.This suggests the effectof flame thickness on burning velocity is decreased at leanmixture combustion. Figure 5, panels b and 5c, illustrates theeffect of initial temperature and initial pressure on un and unr.They all increase with the increase of initial temperature andthe decrease of initial pressure. These variation tendenciesare similar to those of Sn and Sl. Although these parametersare defined from different respects, they will reflect the samecombustion characteristics. Therefore, they present the si-milar variation tendencies with the variation of initial tem-perature and pressure.

Figure 6 gives the unstretched laminar burning velocityversus equivalence ratio at different initial temperatures andinitial pressures. The unstretched laminar burning velocity isincreased as initial temperature increases and initial pressuredecreases. The peak value of unstretched laminar burningvelocity occurs near φ=1.0 in the mixtures. This behavior issimilar to that of unstretched flame propagation speed.

Figure 7 gives the mass burning flux (f0) versus equiva-lence ratio at different initial temperatures and initialpressures. The value of f0 is increased with the increaseof initial temperature and initial pressure. This is different

to unstretched laminar burning velocity, which is in-creased with the increase of initial temperature and de-creased with the increase of initial pressure. For a specifiedinitial pressure, the enhanced chemical reaction ratecaused by increasing initial temperature leads to theincrease of flame propagation speed and laminar burningvelocity. The density of combustible mixture is decreased,and this also results from the increased initial temperature.However, the rate of decreasing in density is less than theincreasing in laminar burning velocity. This combinedeffect leads to the increase of f0 as initial temperatureincreases. For a given initial temperature, with the increaseof initial pressure, the unstretched laminar burning velo-city is decreased and the density of mixture is increased. Asthe increase rate in density of mixture is larger than thedecrease rate in laminar burning velocity, f0 is ultimatelyincreased at an elevated initial pressure as shown inFigure 7b. The different trend between f0 and ul reflectsthe influence of unburned mixture density at differentinitial pressures.38

4.3. Flame Stability andCellular Structure.The occurrenceof flame front instability depends on the combined influenceof hydrodynamic and thermal-diffusive instabilities.Marksteinlength is employed to represent the thermal-diffusive in-stability, which is the dominant factor leading to theunstable flame front at the early stage of flame propagation.Hydrodynamic instability is originated from gas thermalexpansion, and this instability becomes more obviouslyas the flame propagates outwardly and is characterizedby density ratio, σ, and flame thickness, δl. Generally,

Figure 6. Unstretched laminar burning velocity versus equivalenceratio at different initial temperatures and initial pressures.

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

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hydrodynamic instability is enhancedwith increasing densityratio and decreasing flame thickness.48

For a specified equivalence ratio, the flame front instabil-ity is affected by initial temperature and initial pressure.Figure 8 shows the schlieren images of flame front at flameradius of 30 mm at different initial pressures and initialtemperatures. The flame front maintains a smooth surfaceat initial pressure of 0.10 MP, and no crack or cellularstructure is observed. At the initial pressure of 0.25 MP,the image of the flame front shows some cracks, and one ofthe possible reasons for these cracks is the influence ofignition and the centrally located electrodes at the earlystage of flame propagation. At the elevated pressure (Pu =0.50 MP), cellular structure is clearly presented and thisreflects the occurrence of the unstable flame. These beha-viors indicate that, at a specified equivalence ratio and initialtemperature, the cellular flame structure will occur moreeasily with the increase of initial pressure. In other words, theinstability of the flame front is increased as initial pressureincreases. This is consistent to the analysis inLb and δl shownin Table 1. As shown in Table 1, Fu/Fb varies little and δl isdecreased with the increase of initial pressure, and thisindicates an increase in hydrodynamic instability at elevated

initial pressure. In respect to thermal-diffusive instability,the flame is highly unstable with the increase of initialpressure. Schlieren images clearly show the instability ofthe flame front at Pu = 0.50 MP. The correspondingMarkstein length gives the negative value.

At different initial temperatures, as shown in data of table2, both Fu/Fb and δl are decreased with the increase of initialtemperature. The decrease of Fu/Fb results in the decrease ofhydrodynamic instability and the decrease of δl signifies theincrease of hydrodynamic instability. As thermal-diffusiveinstability (Markstein length) has little variation and main-tains positive value, the flame front instability is insensitiveto the initial temperature under the combined effects ofhydrodynamic and thermal-diffusive instabilities. The ana-lysis is consistent with the results demonstrated in schlierenimages. This is also consistent with the results obtained byother researchers.43

Figure 9 shows the development of cellular flame structurewith the expansion of the spherical flame at different equiva-lence ratios, an initial pressure of 0.25 MPa, and initialtemperature of 373 K. A smooth flame front is presentedat the equivalence of 0.7, even at large radius. With theincrease of equivalence ratio, the cellular structure is ob-served, and the structure is developed gradually as the flamepropagates, when the stretch is lessened (corresponding to

Figure 8. Schlieren images of flame front at flame radius of 30mmatdifferent initial pressures and initial temperatures (φ = 1.0).

Table 1. Markstein Length, Flame Thickness, and Density Ratio at

Different Initial Pressures (Tu = 473 K, φ = 1.0)

initialpressure Pu (MPa)

Marksteinlength Lb (mm)

flamethickness δl (mm)

densityratio Fu/Fb

0.10 1.3700 0.0441 5.31030.25 0.3920 0.0193 5.36520.50 -0.1910 0.0105 5.3899

Table 2. Markstein Length, Flame Thickness, and Density Ratio at

Different Initial Temperatures (Pu = 0.1 MP, φ = 1.0)

initialtemperature Tu (K)

Marksteinlength Lb (mm)

flamethickness δl (mm)

densityratio Fu/Fb

373 0.5960 0.0497 6.5826423 1.0000 0.0470 5.8707473 1.3700 0.0441 5.3103 Figure 9. Schlieren images of flame front at different equivalence

ratios and flame radius. (Pu = 0.25 MP, Tu = 373 K).

(48) Wu,X.; Huang, Z.; Jin, C.;Wang,X.; Zheng, B.; Zhang,Y.;Wei,L. Energy Fuels 2009, 23 (9), 4355–4362.

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the increase of flame radius) the cellular instability can nolonger be suppressed. Consequently, the cellular structurequickly cracks and develops over the entire flame surface.This phenomenon is more obvious and the onset of cellularflame structure becomes advancing at large equivalence ratio(φ=1.3) compared with that at φ=1.0. The results suggestthat flame instability is sensitive to equivalence ratio. In-creasing equivalence ratio leads to an increased instability ofthe flame. This is in consistentwith the result of analysis fromthe Markstein length.

5. Conclusions

Combustion characteristics of outwardly spherical laminarpremixed flame of high-octane fuel-airmixtures were studiedby a high-speed schlieren photography system in a constant-volume bomb at elevated temperatures and pressures. Flamefront instability and laminar burning velocity were analyzed.

The main results are summarized as follows: (1) Unstretchedflame propagation speed and unstretched laminar burningvelocity are increased as initial temperature increases andinitial pressure decreases. (2) Markstein length decreases withthe increase of equivalence ratio and initial pressure, and itincreases with the increase of initial temperature. This indi-cates that flame is stable at high initial temperature and lowinitial pressure at the early stage of flame propagation. (3)Hydrodynamic instability is influenced by density ratio andflame thickness. Hydrodynamic instability is increased withthe increase of initial pressure. (4) Flame front instability isdecreased with the decrease of equivalence ratio and initialpressure. The cellular flame structure advances with theincrease of initial pressure and equivalence ratio. Flameinstability is insensitive to initial temperature.

Acknowledgment. This study is supported by NationalScience Foundation of China (Nos. 50636040, 50821604).

study on laminar burning characteristics of premixed high...

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