Proceedings

Proceedings of the Combustion Institute 31 (2007) 901–908

www.elsevier.com/locate/proci

of the

CombustionInstitute

Effect of velocity gradient on propagation speedof tribrachial flames in laminar coflow jets

M.K. Kim, S.H. Won, S.H. Chung *

School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-742, Republic of Korea

Abstract

The effect of velocity gradient on the propagation speed of tribrachial flame edge has been investigatedexperimentally in laminar coflow jets for propane fuel. It was observed that the propagation speed of tri-brachial flame showed appreciable deviations at various jet velocities in high mixture fraction gradientregime. From the similarity solutions, it was demonstrated that the velocity gradient varied significantlyduring the flame propagation. To examine the effect of velocity gradient, detail structures of tribrachialflames were investigated from OH LIF images and Abel transformed images of flame luminosity. It wasrevealed that the tribrachial point was located on the slanted surface of the premixed wing, and this slantedangle was correlated with the velocity gradient along the stoichiometric contour. The temperature field wasvisualized qualitatively by the Rayleigh scattering image. The propagation speed of tribrachial flame wascorrected by considering the direction of flame propagation with the slanted angle and effective heat con-duction to upstream. The corrected propagation speed of tribrachial flame was correlated well. Thus, themixture fraction gradient together with the velocity gradient affected the propagation speed.� 2006 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Keywords: Tribrachial flame; Edge flame; Velocity gradient; Mixture fraction gradient

1. Introduction

Tribrachial (or Triple) flames have drawnattention recently with regard to the issues relatedto their unique propagation behavior in fuel/airmixing layers and to flame stabilization in bothlaminar and turbulent jets [1–7]. The edge of alaminar lifted flame demonstrated a tribrachialstructure, which consists of a lean and a rich pre-mixed flame wings and a trailing diffusion flame,all extending from a single location. The coexis-tence of these three types of flames ensures thatthe edge is located along the stoichiometric con-

1540-7489/$ - see front matter � 2006 The Combustion Institdoi:10.1016/j.proci.2006.07.238

*Corresponding author. Fax: +82 2 883 0179.E-mail address: shchung@snu.ac.kr (S.H. Chung).

tour in a jet [1] and the presence of premixed flamewings could exhibit a unique propagation speed[3].

When the propagation speed of tribrachialflame is balanced with the local flow velocityalong the stoichiometric contour in a jet, the flamecan be stably lifted. Based on the similarity solu-tions of velocity and concentration in jets, a corre-lation of lift-off height, jet velocity, and nozzlediameter was derived and experimentally substan-tiated for its validity [1–3].

The characteristics of the propagation speed oftribrachial flame have been extensively analyzedtheoretically and numerically in mixing layersconsidering such effects as heat generation [3,4],mixture fraction gradient [5–7], Lewis number[8,9], and buoyancy [10]. The dominant factors

ute. Published by Elsevier Inc. All rights reserved.

902 M.K. Kim et al. / Proceedings of the Combustion Institute 31 (2007) 901–908

affecting the propagation speed have been identi-fied as the mixture fraction gradient in front of atribrachial edge and the flow redirection effectresulting from heat generation along the curvedpremixed flame wings. Predictions show that thepropagation speed decreases with increasing mix-ture fraction gradient and the ratio of maximumpropagation speed to the stoichiometric laminarburning velocity in the limit of small mixture frac-tion gradient is proportional to the square root ofthe density ratio of unburned to burnt gases [3].

Experiments on the propagation speed havealso been conducted for methane and propanefuels [11,12]. The propagation speed has beendetermined from the unsteady propagation behav-ior of tribrachial flames in free jets from the mea-sured displacement speed and the predicted localaxial velocity. The results confirmed the inversedependence on fuel mixture fraction gradientand the maximum propagation speed in the limitof small mixture fraction gradient.

The analytical studies and the experimentshave several limitations. Many of the previoustheoretical studies on the propagation speed of tri-brachial flames have been conducted assuminguniform velocity field in the upstream region ofa tribrachial flame. The experiments for propanejets have been performed only for relatively smallmixture fraction gradient fields, in such a way thatthe extrapolated minimum propagation speed inthe limit of large mixture fraction gradient waslarger than the stoichiometric laminar burningvelocity, which is in contradiction with the theo-retical prediction [7], where it has been predictedthat the propagation speed can be smaller thanthe stoichiometric laminar burning velocity.

To resolve these issues, the present study isfocused on the propagation speed of tribrachialedge for relatively large mixture fraction gradient,from which the effect of velocity gradient at theupstream of a tribrachial flame will be examined.

2. Experiment

The apparatus consisted of a coflow burnerand flow controllers, an ignition system, and avisualization setup. The coflow burner systemwas adopted to minimize outer disturbances, thusto obtain relatively more stable lifted flames ascompared to free jets.

It has a central fuel nozzle with 0.254 mm i.d.and 10 cm in length to ensure the fully developedvelocity profiles at the exit for the jet velocitysmaller than 10 m/s. Coflow air was supplied froma coaxial nozzle with 90 mm i.d. through glassbeads and a ceramic honeycomb to obtain uni-form flow. The tip of the fuel nozzle protruded10 mm above the honeycomb.

The fuel was chemically pure grade propaneand compressed air was used as the oxidizer.

The flow rates of fuel and air were controlled bymass flow controllers which were calibrated by awet-test gas meter. The coflow velocity Vco wasfixed at 3 cm/s. The test section was confined withan acrylic cylinder with 90 mm i.d. and 20 cm inlength to prevent ambient disturbances and tomaintain uniform coflow in the test region [13].

Flames were ignited at 10 cm downstreamfrom the nozzle by an electric spark and the trajec-tory of propagating flames was traced by a highspeed camera with 500 fps. To understand thestructure of tribrachial flame, a planar laser-in-duced fluorescence (PLIF) technique for OH rad-icals and the Abel transformed images from directphotographs were utilized. Qualitative tempera-ture fields near a tribrachial flame were visualizedfrom the Rayleigh scattering signal. Details of thePLIF setup and the Rayleigh scattering measure-ment were described previously [13,14].

3. Results and discussion

3.1. Propagating edge

Previous studies on the propagation speed oftribrachial flame demonstrated that it is inverselyproportional to the mixture fraction gradient infront of the flame edge [3,5–7]. Due to the flowredirection effect from gas expansion, the propa-gation speed of tribrachial flame edge Se can belarger than the stoichiometric laminar velocitySo

Ljst with its maximum value proportional to theratio of the densities of unburned to burnt gasesffiffiffiffiffiffiffiffiffiffiffiffi

qu=qb

pmultiplied by the stoichiometric laminar

burning velocity. The propagation speed has alsobeen investigated experimentally in laminar freejets for both methane and propane fuels [11,12].In these studies, the propagation speed was deter-mined from the transient behavior of propagatingedge after ignition. The flame displacement speedSd, which is the time derivative of edge height oftribrachial flame He from a fuel nozzle, was mea-sured. The local flow velocities along the stoichi-ometric contour ust have been calculated fromthe similarity solutions for velocity and concentra-tion, whose validity has been substantiated fromLDV and Raman measurements. Then, the prop-agation speed of tribrachial edge was determinedfrom Se = Sd + ust [11].

Similar method was adopted for the presentexperiment in the coflow with propane fuel. Figure 1shows the propagation speed of tribrachial edge Se

in terms of the fuel mass fraction gradient dYF/dR|st

along the stoichiometric contour [13], which is anindication of the mixture fraction gradient. Here,YF is the mass fraction of fuel, R = r/r0, r is theradial coordinate, and r0 is the nozzle radius. Inthe previous experiment in free jets with propane[11], the range of dYF/dR|st was smaller than0.008. It reported the inverse proportionality of Se

Fig. 2. Velocity and mass fraction gradients in terms ofnon-dimensional axial distance along the stoichiometriccontour for U0 = 6, 8, and 10 m/s.

Fig. 1. Propagation speed of tribrachial flame edge withmass fraction gradient for U0 = 6, 8, and 10 m/s.

M.K. Kim et al. / Proceedings of the Combustion Institute 31 (2007) 901–908 903

to the mass fraction gradient. The data in the rangeof dYF/dR|st < 0.002 was discarded, since the rangecorresponds to initial ignition transient by flamekernel growth in spark ignition. In case of the pro-pane in free jets, the cold jet flow-field especiallynear the nozzle can be influenced by the buoyancyinduced air entrainment near the nozzle, as theflame edge approaches the nozzle. Thus, to ensurethe experimental repeatability, only the data forlarge He, that is for small dYF/dR|st, were analyzed.In the present experiment with the coflow, theexperimental repeatability was maintained satisfac-torily such that the range of the mass fraction gra-dient can be extended up to 0.03, however, thedata of initial transient for dYF/dR|st < 0.002 wasdiscarded.

The present data in Fig. 1 shows several inter-esting features. First, the propagation speed offlame edge depends sensitively on the jet velocityU0 especially for large dYF/dR|st. Second, thereexists a range of dYF/dR|st where Se increases withdYF/dR|st, for example, dYF/dR|st > 0.012 forU0 = 10 m/s.

To elucidate these characteristics of Se with U0

in the range of high mass fraction gradient, detailsof the cold jet flow are first examined based on thesimilarity solutions, which accounted for the vir-tual origins for their accuracy and the effect ofcoflow [13]. The mass fraction gradient dYF/dR|st

and the velocity gradient du/dr|st along the stoichi-ometric contour of the coflow jets are plotted inFig. 2 in terms of the non-dimensional axial dis-tance X = (x/d)/Re, where x is the axial distancefrom the nozzle, d is the nozzle diameter, Re isthe Reynolds number defined as Re = dU0,m/m,U0,m is the maximum velocity at the nozzle exit(2U0) assuming the Poiseuille flow, and m is thekinematic viscosity.

The result shows that the mass fraction gradi-ent is minimally affected by the jet velocity of fuel.Note that dYF/dR|st along the stoichiometric con-tour in free jets depends only on X by the similar-ity. In a coflow with the strong jet condition of

Vco/U0� 1 [13], the effect of coflow velocity ondYF/dR|st is weak. Thus, the three cases of U0

are indistinguishable in the figure. The normalizedvelocity gradient d(u/U0)/dR|st also depends on Xonly in free jets and the effect of coflow velocity issmall for the strong jet condition. Since thedimensional velocity gradient du/dr|st could affectthe propagation speed, we have plotted du/dr|st inFig. 2. The dimensional velocity gradient dependssensitively on U0, that is, it is nearly linear with U0

at a specified X. Moreover, there exist significantvariations near the nozzle region. The range ofdYF/dR|st < 0.008 in the previous experiment [11]corresponds to X > 0.58, where the variation ofdu/dr|st is small. In the present range of dYF/dR|st < 0.03, the velocity gradient becomes appre-ciably larger than the range of the previous exper-iment. Thus, the behavior of Se for large dYF/dR|st shown in Fig. 1 may be attributed to theeffect of velocity gradient on tribrachial flameedge, which will be discussed in detail in thefollowing.

3.2. Effect of velocity gradient

To investigate the effect of velocity gradient onthe propagation speed of tribrachial flame edge,detail structures of tribrachial flames were firstinvestigated from the instantaneous images takenduring the edge propagation using the ICCDcamera. The premixed flame wings of tribrachialflame were determined by tracing the local maxi-mum luminosity across the premixed wings fromthe Abel transformed images.

Figure 3 shows the Abel transformed imagesand the traces of premixed flame wings forU0 = 6 m/s, typically for small (a) and large (b)cases of the velocity gradient, corresponding toHe = 53 and 31 mm, respectively. The stoichiome-tric contours evaluated from the similarity solu-tions are also plotted in the dotted lines. Theresult shows that the stoichiometric contour cross-es the premixed flame wing and the premixed

Fig. 3. Abel transformed flame luminosity and trace ofpremixed flame wing together with stoichiometric con-tour for U0 = 6 m/s during unsteady propagation for (a)He = 53 and (b) 31 mm.

904 M.K. Kim et al. / Proceedings of the Combustion Institute 31 (2007) 901–908

flame wing is appreciably slanted at the cross-point with the angle h. In the previous studies,the tribrachial point is assumed to be locatedalong the stoichiometric contour due to the coex-istence of three different types of flames. This hasbeen substantiated from the Raman measure-ments [15] that the tribrachial edge determinedexperimentally is located very closely to the theo-retically predicted stoichiometric contour.

The detailed structure of tribrachial flame edgewas further analyzed for stationary lifted flamesfrom the OH PLIF images and the Abel-trans-formed images of flame luminosity, as shown inFig. 4, for U0 = 12.7 (a and c) and 9.56 m/s (band d). Flame luminosity and OH LIF signal havebeen reported to be reasonable flame markers forpremixed and diffusion flames, respectively[4,13,14], for a tribrachial flame. The Abel trans-formed images clearly shows the lean premixedflame (LPF) and rich premixed flame (RPF) wings

Fig. 4. Images of OH PLIF and Abel transformed luminosityedge for U0 = 12.7 m/s (a and c) and 9.56 m/s (b and d).

of the tribrachial structure. The trailing diffusionflame (DF) can also be identified. The OH LIFimages further clarify the locations of trailing dif-fusion flames. In the close-ups near the flame edg-es (c and d), the OH LIF signal with its localmaximum trace marked with the open squares isexhibited, together with the trace of the premixedflame wings marked with the open circles. Thecross-point of these two traces can be regardedas the tribrachial point. However, note that thereexists an ambiguity of the local maximum OHLIF very near the premixed flame wing. The pre-dicted stoichiometric contours are representedwith the dashed lines. The stoichiometric contourspass through the tribrachial points reasonablyclosely for both cases. Note that the premixedflame wings at the tribrachial points are apprecia-bly slanted. This slantedness causes problems inthe determination of Se, since it was determinedfrom Se = Sd + ust, where, Sd and ust are the axialcomponents not normal to the premixed flamewings.

In the previous studies on the measurement ofthe propagation speed of tribrachial flame, it wasassumed that Sd and ust in front of the flame edgeare normal to the flame edge [11–13]. This couldbe reasonably acceptable, since the ranges of du/dr|st and dYF/dR|st were relatively small. Howev-er, in the present study, both the fuel mass frac-tion and the velocity gradients are relativelylarge, especially near the nozzle.

In this regard, the slanted angle h of the pre-mixed flame wing with horizontal direction atthe tribrachial point has been measured duringthe transient flame propagation at several jetvelocities. The identification of exact tribrachialpoint may require OH LIF images and Abel trans-formed direct photographs during the flame prop-agation. However, as mentioned previously, thereexist ambiguities in pinpointing the tribrachial

for stationary lifted flames and close-ups near the flame

Fig. 6. Corrected propagation speed of tribrachial flamewith mass fraction and velocity gradients.

M.K. Kim et al. / Proceedings of the Combustion Institute 31 (2007) 901–908 905

point even using OH LIF image. Since the resultsfor the stationary lifted flames demonstrated closeagreement between the cross-point determinedfrom the predicted stoichiometric contour andthe cross-point determined from the OH LIF withthe Abel transformed premixed flame wings, thestoichiometric contours were used in determiningthe slanted angles for the transient cases. As canbe seen in Fig. 4, this angle could somewhat over-estimate the angle determined from the OH LIFand the maximum error is estimated to be 20�for high velocity gradient conditions.

The slanted angle h of the premixed flame wingis plotted in Fig. 5 with the velocity gradient alongthe stoichiometric contour. The result shows a sat-isfactory correlation between h and du/dr|st. Todeduce the relation between them, it has beenassumed as follows. The sensitivity of the laminarburning velocity to the fuel mass fraction gradientdetermines the curvature of the premixed flamewing [12] and the velocity gradient is simply to tiltthe premixed flame surface near the tribrachialpoint. Then, the slanted angle can be expressedas h = tan�1(C · du/dr|st), where C is a constant.The dotted line is the best fit with the correlationcoefficient R of 0.96 and C = 0.00481 [s]. Since theslanted angle is significantly large for large veloc-ity gradients, it should be considered in the deter-mination of Se from Sd + ust.

3.3. Propagation speed of tribrachial flame

Since the tribrachial flame edge during thepropagation was measured experimentally in theaxial direction, the balance mechanism betweenthe local flow velocity and propagation speed oftribrachial flame requires to be corrected byaccounting for the slanted angle of the flamesurface. In this regard, the displacement speed oftribrachial flame edge and the local flow velocityneed to be corrected in the normal directionfrom the flame surface, in such a way thatS�e ¼ ðSd þ ustÞ � cos h.

Fig. 5. Slanted angle of premixed flame wing withvelocity gradient along stoichiometric contour.

The corrected propagation speed S�e of tribra-chial flame is plotted with the fuel mass fractiongradient dYF/dR|st in Fig. 6. There are severalpoints to be noted from the comparison betweenthe original data in Fig. 1 and the corrected data.First, the increasing behavior of Se for large dYF/dR|st disappears in S�e . Second, the divergence inSe for large dYF/dR|st for the different U0 disap-pears. Third, the overall trend of the propagationspeed shows the inverse proportionality with themass fraction gradient, having agreement withthe theoretical prediction, which will be furtherdiscussed later. Fourth, the propagation speed oftribrachial flame becomes smaller than the lami-nar burning velocity, which is reported to be40 cm/s for propane [16], for dYF/dR|st approxi-mately larger than 0.007.

We have also plotted S�e in terms of the velocitygradient du/dr|st. The result demonstrated a satis-factory correlation for all U0 tested. Note, howev-er, that the correlation of S�e with du/dr|st is due tothe nature of the relation between du/dr|st anddYF/dR|st in jets as demonstrated in Fig. 2. Sincethe dominant factor influencing the propagationspeed is identified to be dYF/dR|st, we will furtherinvestigate the effect of dYF/dR|st later.

Even considering the possible overestimationof h, having the maximum error of about 20� ascompared to that determined from the OH LIFas mentioned previously, it can be safely conclud-ed that S�e is smaller than So

Ljst for large dYF/dR|st.To further examine this propagation speed small-er than the stoichiometric laminar burning veloc-ity, the radius of flame curvature rcurv at thetribrachial point during unsteady propagationwas measured by tracing the premixed flamewings. The curvature is plotted in terms of themass fraction gradient in Fig. 7. It was reportedthat the flame curvature has a linear correlationwith the mass fraction gradient, considering thevariation of laminar burning velocity around thetribrachial point [12]. The present result confirms

Fig. 8. Rayleigh scattering image indicating temperatureand fuel concentration fields for U0 = 9 m/s andHL = 25 mm.

Fig. 7. Measured curvature with mass fraction gradient.

906 M.K. Kim et al. / Proceedings of the Combustion Institute 31 (2007) 901–908

that the flame curvature is correlated linearly withthe mass fraction gradient as represented by thesolid line with the correlation coefficient of 0.92,even though the tribrachial point is located alonga slanted surface of the premixed flame wings.

Note that the typical preheat zone thickness ofa premixed flame is O (1 mm). The criteria of theradius of curvature rcurv smaller than 1 mm isdYF/dR|st J 0.006, which is in reasonable agree-ment with the mass fraction gradient where thepropagation speed of tribrachial flame becomessmaller than the stoichiometric laminar burningvelocity in Fig. 6. Since the radius of curvatureof tribrachial edge is comparable to the laminarpremixed flame thickness, the upstream heatingeffect at the edge may not be effective by the defo-cusing effect of the thermal conduction toupstream. Thus, the flow redirection effect maynot be effective, such that S�e can be smaller thanSo

Ljst, substantiating the theoretical prediction [6].In the curvature measurements for stationary

lifted flame edges, the tribrachial structure wasconfirmed up to rcurv � 0.8 mm, having distinctlean and rich premixed flame wings. The tribrachi-al structure for rcurv < 0.8 mm in the transientexperiment cannot be confirmed. The structuremay change to a bibrachial flame, where one ofthe premixed flame wings becomes indistinguish-able with the trailing diffusion flame. This struc-tural change was reported in the numerical study[6,7,17,18] when the radius of curvature becomessufficiently small.

3.4. Heat conduction effect

It has been previously shown that the fuel massfraction gradient is the dominant factor affectingthe propagation speed. The modified propagationspeed in Fig. 6, however, exhibited appreciableinfluence of U0 on S�e , especially for relativelysmall dYF/dR|st. Note that the mass fraction gra-dient controls the radius of curvature of the edge,as was shown in Fig. 6. This can be understoodfrom the fact that the mass fraction gradient is

an indication of the thickness of flammable regionin mixing layers. The flow redirection effect can beaffected by the radius of curvature, through theheating to the upstream. This implies that the flowredirection effect can also be influenced by theheat conduction characteristics from the flameedge to the upstream.

To characterize the behavior of heat conduc-tion from a tribrachial flame edge, the tempera-ture field was measured qualitatively by usingthe Rayleigh scattering technique. Figure 8 showsthe Rayleigh image for the stationary lifted flamewith U0 = 9 m/s, whose liftoff height HL is 25 mm.The lower part of the image represents the fuelconcentration field due to the difference in theRayleigh cross-sections between propane and air.The upper part is a qualitative temperature distri-bution, since the Rayleigh signal is proportionalto the number density of molecules, whichdepends on temperature.

The heat flux q from the flame surface will beperpendicular to an iso-temperature contour.Although not shown, the qualitative iso-tempera-ture contour from Rayleigh scattering has almostthe same slanted angle as the flame surface at thetribrachial point, as expected. The flow redirectioncan be controlled by the preheating toward theupstream in the streamwise direction, that is, theaxial direction, which can be estimated to beqcosh. Consequently, the flow redirection effectcould be mitigated with the slanted angle of flamesurface.

This argument leads to the following. Thepropagation speed of tribrachial flame edge canbe controlled by the mass fraction gradienttogether with the effective heat flux normal tothe axial direction, that is, (qcosh) (dYF/dR|st)

�1.In this regard, the corrected propagation speed S�eis plotted in terms of (dYF/dR|st)/cosh. From therelation of tan h = C · du/dr|st in Fig. 5, 1/coshcan be expressed as {1 + (C · du/dr|st)

2}0.5 whereC = 0.00481 [s]. The relation of S�e with dYF/dR|st · {1 + (C · du/dr|st)

2}0.5 is shown in Fig. 9.As compared to the result in Fig. 6, the deviation

Fig. 9. Corrected propagation speed of tribrachial flameedge with mass fraction gradient accounting for heatconduction.

M.K. Kim et al. / Proceedings of the Combustion Institute 31 (2007) 901–908 907

of S�e for small dYF/dR|st when varying the jetvelocity, appreciably suppressed by consideringthe effective heat flux to the streamwise direction.The corrected propagation speed correlated wellwith the mass fraction gradient multiplied by theeffective heat flux factor, regardless of the jetvelocity.

By considering the effects of both the fuel massfraction gradient and the effective heat flux, thepropagation speed of flame edge can be correlatedas follows when using So

Ljst ¼ 40 cm=s [16]

S�eSo

Ljst

¼ 0:02018

��0:0077155þ dY F=dRjst

�n

1þ ð0:00481� du=drjstÞ2o0:5�

þ 0:155196 ð1Þ

with the correlation coefficient of 0.99 and du/dr|st

in [1/s]. Note that the term {1 + (0.00481 · du/dr|st)

2}0.5 is in the range of 1 to 10, meaning thatthe velocity gradient significantly affects the mea-surement in the propagation speed. When both ofthe gradients approach zero, the maximum limit-ing value of the propagation speed of the edgeis extrapolated to be 1.11 m/s. This value isin good agreement with the predicted value

offfiffiffiffiffiffiffiffiffiffiffiffiqu=qb

p� So

Ljst which is calculated to be

1.10 m/s with SoLjst ¼ 40 cm=s.

For large dYF/dR|st, the edge flame cannotmaintain the tribrachial structure [17]. From thenumerical study [18], it has been suggested thatthe propagation speed of bibrachial flamedecreased linearly with dYF/dR|st. The inset inFig. 9 for large dYF/dR|st also shows the lineardecreasing trend when the radius of curvature atthe edge becomes even smaller than the preheatzone thickness.

Further research is needed on the propagationcharacteristics of such edge flames for largedYF/dR|st.

4. Concluding remarks

The characteristics of propagation speed of tri-brachial flame have been investigated experimen-tally for propane fuel in the coflow jets. Byextending the range of the fuel mass fraction gra-dient in the present experiment, the propagationspeed in terms of the fuel mass fraction gradientshowed appreciable dependence on the fuel jetvelocity, especially in the large velocity gradientregime.

From the detailed visualizations of tribrachialstructure, the tribrachial point was observed tobe located along the slanted premixed flamewings. The measured slanted angle was successful-ly correlated with the velocity gradient.

The measured propagation speed of tribrachialflame in the axial direction was corrected consid-ering the direction of flame propagation with theslanted angle and the effective heat conductionto the upstream. The corrected propagation speedof tribrachial flame correlated well with the massfraction gradient when the effective heat conduc-tion to streamwise direction was accounted for.

When the mass fraction gradient becomeslarge, the propagation speed of the edge wasobserved to be smaller than the stoichiometriclaminar burning velocity, which substantiatedthe theoretical predictions.

Acknowledgment

This work was supported by CERC throughIAMD.

References

[1] S.H. Chung, B.J. Lee, Combust. Flame 86 (1991)62–72.

[2] B.J. Lee, S.H. Chung, Combust. Flame 109 (1997)163–172.

[3] G.R. Ruetsch, L. Vervisch, A. Linan, Phys. Fluids 7(1995) 1447–1454.

[4] T. Plessing, P. Terhoeven, N. Peters, M.S. Man-sour, Combust. Flame 115 (1998) 335–353.

[5] J.W. Dold, Combust. Flame 76 (1989) 71–88.[6] L.J. Hartley, J.W. Dold, Combust. Sci. Technol. 80

(1991) 23–46.[7] S. Ghosal, L. Vervisch, J. Fluid Mech. 415 (2000)

227–260.[8] J. Buckmaster, M. Matalon, Proc. Combust. Inst. 22

(1988) 1527–1535.[9] V.N. Kurdyumov, M. Matalon, Proc. Combust.

Inst. 29 (2002) 45–52.[10] J.Y. Chen, T. Echekki, Combust. Theory Model. 5

(2001) 499–515.[11] J. Lee, S.H. Won, S.H. Jin, S.H. Chung, O. Fujita,

K. Ito, Combust. Flame 134 (2003) 411–420.[12] Y.S. Ko, S.H. Chung, Combust. Flame 118 (1999)

151–163.

908 M.K. Kim et al. / Proceedings of the Combustion Institute 31 (2007) 901–908

[13] J. Lee, S.H. Won, S.H. Jin, S.H. Chung, Combust.Flame 135 (2003) 449–462.

[14] S.H. Won, S.H. Chung, M.S. Cha, B.J. Lee, Proc.Combust. Inst. 28 (2000) 2093–2099.

[15] Y.S. Ko, S.H. Chung, G.S. Kim, S.W. Kim,Combust. Flame 123 (2000) 430–433.

[16] S.G. Davis, C.K. Law, Combust. Sci. Technol. 140(1998) 427–449.

[17] P.N. Kioni, B. Rogg, K.N.C. Bray, A. Linan,Combust. Flame 95 (1993) 276–290.

[18] S.H. Won, J. Kim, K.J. Hong, M.S. Cha, S.H.Chung, Proc. Combust. Inst. 30 (2005) 339–347.