Liftoff of turbulent jet flames—assessment of edge flame and other concepts using cinema-PIV

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Combustion and Flame 138 (2004) 259–272www.elsevier.com/locate/jnlabr/cn

Liftoff of turbulent jet flames—assessment of edge flamand other concepts using cinema-PIV

Ansis Upatnieksa, James F. Driscolla,∗, Chadwick C. Rasmussena,Steven L. Cecciob

a Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI 48109, USAb Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA

Received 17 August 2003; received in revised form 9 April 2004; accepted 20 April 2004

Available online 19 June 2004

Abstract

Three theories of the liftoff of a turbulent jet flame were assessed using cinema-particle imaging velomovies recorded at 8000 images/s. The images visualize the time histories of the eddies, the flame motioturbulence intensity, and streamline divergence. The first theory assumes that the flame base has a prspeed that is controlled by the turbulence intensity. Results conflict with this idea; measured propagatioremains close to the laminar burning velocity and are not correlated with the turbulence levels. Even wturbulence intensity increases by a factor of 3, there is no increase in the propagation speed. The secoassumes that large eddies stabilize the flame; results also conflict with this idea since there is no significalation between propagation speed and the passage of large eddies. The data do support the “edge flameEven though the turbulence level and the mean velocity in the undisturbed jet are large (at jet Reynolds nu4300 and 8500), the edge flame creates its own local low-velocity, low-turbulence-level region due to strdivergence caused by heat release. The edge flame has two propagation velocities. The actual velocity ofbase with respect to the disturbed local flow is found to be nearly equal to the laminar burning velocity; hothe effective propagation velocity of the entire edge flame with respect to the upstream (undisturbed) flowthe laminar burning velocity. A simple model is proposed which simulates the divergence of the streamconsidering the potential flow over a source. It predicts the well-established empirical formula for liftoff hand it agrees with experiment in that the controlling factor is streamline divergence, and not turbulence intelarge eddy passage. The results apply only to jet flames for Re< 8500; for other geometries the role of turbulencould be larger. 2004 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Keywords:Liftoff; Turbulent jet flame; Nonpremixed; PIV; Edge flame

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1. Introduction

The goal of this work is to use cinema-PIV (paticle imaging velocimetry) diagnostics[1,2] to betterunderstand and measure two parameters that are

* Corresponding author.E-mail address:[email protected] (J.F. Driscoll).

0010-2180/$ – see front matter 2004 The Combustion Institutdoi:10.1016/j.combustflame.2004.04.011

portant in determining the liftoff height of a turbulenonpremixed jet flame—the propagation speed offlame base (Sb) and the gas velocity just ahead of tinstantaneous location of the base (UG). Vanquicken-borne and van Tiggelen[3] proposed that the liftedbase is a premixed flame and the equilibrium requment is that

(1)Sb = UG at x = h.

e. Published by Elsevier Inc. All rights reserved.

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260 A. Upatnieks et al. / Combustion and Flame 138 (2004) 259–272

Nomenclature

fs stoichiometric mixture fraction

h mean liftoff height

Sb propagation speed of the flame base,

relative to the unburned gas, in the−x

direction (Eq. (7))

Seff effective propagation speed of an edge

flame (Eq. (4))

SL,0 unstretched, stoichiometric laminar

burning velocity

UF flame velocity in+x direction, in lab

coordinates, at the instantaneous flame

base location

UG gas velocity in +x direction, in labcoordinates, at the instantaneous flamebase location

UG ensemble average ofUGUP undisturbed mean velocity upstream of

streamline divergence (Fig. 1)U0 jet exit velocityu′ turbulence intensity, root-mean-squared

velocity fluctuations in 3.6 by 3.6 mmregion upstream of instantaneous flamebase

x axial location of the lifted flame base�U velocity change in the incident flow due

to streamline divergence (Eq. (5))

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A second requirement is that the flame remain staso that

(2)dSb/dx > dUG/dx.

If the flame is perturbed to a downstream locatiEq. (2) indicates thatSb will exceed UG, so it willpropagate back upstream to its equilibrium locatatx = h. To model the propagation speed (Sb) severaltheories have been proposed.

1.1. Turbulence intensity theory

Kalghatgi[4] assumed that the intensity of the tubulence controls the propagation speed of the bHe assumed that the base propagates with a tulent burning velocity that is proportional to the squaroot of the local velocity fluctuations (u′), based onthe measurements in Andrews et al.[5], which wereobtained for geometries that are very different fromlifted jet flame. He also assumed that the meanfluctuating velocities are those of a nonreacting tbulent jet, so the effect of the flame on the flowfiewas neglected. It follows that if these assumptionscorrect, there should be a perfect correlation betwthe propagation speed of the base and the rms veity fluctuations (u′) just upstream of the flame basKalghatgi’s analysis[4, Eq. (4)] predicts the follow-ing relation for the liftoff heighth:

(3)h = 50U0(ρF/ρA)3/2/[(SL,0)

2/α].

U0 is the exit velocity of the fuel jet,ρF andρA are thedensities of the fuel and air streams, and(SL,0)

2/α

is the characteristic chemical reaction rate. The thmal diffusivity is α and SL,0 is the stoichiometricunstretched laminar burning velocity.

The problem with the turbulent burning velocimodel is that laboratory-scale jet flames do not appto fall in the regime in which turbulence controls tpropagation speed of the base, even for jet Reynnumbers as large as 29,700.Table 1shows that themeasured mean propagation speed of the flamefor 11 different jet conditions[1,6–9] is not signifi-cantly larger than the laminar value (SL,0). Table 1indicates that laminar processes, rather than tulence intensities, determine the liftoff heights in thecases.

It may seem surprising that the flame base pragates only at the laminar speed, even though thReynolds numbers inTable 1are as large as 29,70The velocity fluctuations near the centerlines of thjets are more than 10 times the laminar burninglocity. However, the lifted base is located at a radlocation that is far from the centerline, where turblence intensities are small, and heat release crenew velocity vectors that point away from the reation zone, which prevents vortices from interactiwith the reaction zone, as described below. Imain Ref. [8] indicate that the reaction zone at the bais not significantly wrinkled by the turbulence; intense wrinkling normally occurs whenever turbulencontrols the propagation speed. Therefore it is notreasonable that the values of propagation speedTable 1are no more than 22% larger than the vaof the laminar flame speed. In the present studycorrelation between the propagation speed andturbulence intensity was measured. If the base dnot propagate faster when subjected to above-aveturbulence levels, then turbulence intensity is nogoverning parameter.

A. Upatnieks et al. / Combustion and Flame 138 (2004) 259–272 261

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Table 1Previous measurements that show that the mean propagspeedSb of the base of a lifted jet flame does not deviasignificantly from the laminar stoichiometric burning veloity SL,0

Mean propagation speeSb/SL,0 of the base of alifted jet flame

Su et al.[7] 0.86, 0.95Re= 2,800–4,000U0 = 10.8–15.3 m/s

Hasselbrink and Mungal[6] 1.2, 1.2Re= 8,700, 29,700U0 = 31–61 m/s

Schefer and Goix[8] 0.20, 0.60,Re= 7,000–19,500 1.20, 1.22U0 = 21–60 m/s

Upatnieks et al.[1] 0.7, 1.2Re= 4,300 (case 1)Re= 8,500 (case 2)U0 = 14–33.2 m/s

Maurey et al.[9] 1.0Re= 4,100,U0 = 16.3 m/s

Note. In all cases, PIV was used to measure the averagvelocity at the baseUG which equalsSb (Eq. (3)).

1.2. Edge-flame theory

The idea that the lifted flame base is an “edflame” has been proposed by Buckmaster and We[11] and others[12–17]. Figs. 1 and 2are schematicof the images of the lifted flames reported by Watset al. [18–20]. The reaction layer normally is nearparallel to the incident stream and the parabola shrepresents the 600 K isotherm. The flowfield is dturbed by the edge flame and these disturbancesbe important for the following reason. If the flow rmained self-similar (and the mean values of mixtfraction andU/U0 were equal everywhere) then thmean gas velocity would be constant along the mstoichiometric contour from the base to the tip. Tconcept would contradict the idea that increasingjet velocity forces the lifted flame base to move tolower velocity region downstream. Therefore sevetheories[14–16]assume that the deviations from sesimilarity caused by an edge flame govern the liflocation.

Fig. 1 illustrates how the effective propagatiospeed of an edge flame can be enhanced by the dgence of the streamlines associated with heat releAt location B the equilibrium condition isEq. (1). Atlocation P, the equilibrium criterion is that the effetive propagation speed of the entire edge flame (Seff)is equal to the undisturbed gas velocity (UP):

(4)Seff = UP.

Fig. 1. Schematic of gas velocities at the base (B) of a liflame and at point P in the undisturbed region upstreamthe streamline divergence.�U is the difference betweethese two velocities.

The streamlines diverge between the upstream pP and the flame base B, causing a gas velocity dience that is defined to be

(5)�U = UP − UG,

whereUG is the mean gas velocity at the base. Cobining Eqs. (1), (4) and (5)yields

(6)Seff = Sb + �U.

Therefore the effective propagation speed of an edgflame is enhanced by�U due to streamline divergence. The edge flame helps to stabilize itself bycelerating the oncoming flow, so it only has to propgate against a reduced gas velocity. Watson et al.[19]showed that the width of the 600 K isotherm increaas the flame rises to greater heights, as is depicteFig. 2. This suggests that as the flame rises to a dostream location, streamline divergence and�U mayincrease. A key issue is the proper modeling of�U term that appears inEq. (6). This requires an understanding of why the streamline divergence vaas the liftoff height changes.

1.3. Large-eddy theory

The analysis of Miake-Lye and Hammer[21] isbased on their assumption that “the flame must pragate from one [large eddy] structure to its upstreneighbor.” Kaplan et al.[22] reported that their numerically simulated flame base sometimes wouldpear to jump upstream to attach to a new large ebut they did not quantify whether these jumps ocurred frequently enough to be a governing meanism. Burgess and Lawn[23] proposed that larg


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Fig. 2. Schematic showing how the width of an edge flacan increase as the liftoff height increases. The schemsummarizes images reported by Watson et al.[20]. As thewidth W increases, the change in velocity�U in the inci-dent flow, as defined inFig. 1, is expected to increase.

eddies create intermittency in the properties of thebulence, which affects the liftoff height. Scheferal. [24], Kelman et al.[25], Tacke et al.[26], andPitts [27] have speculated that large-eddy conceexplain their scalar measurements, but present noticity measurements to confirm these ideas. It is nothat while large eddies may perturb the liftoff heigit has not been demonstrated that large eddies arfundamental reason that the base is stabilized atparticular liftoff height. One goal of the present stuis to quantify the correlation between the passaglarge eddies and the propagation speed of the bas

1.4. Other theories

It has been assumed that the local stretch ratetrols the propagation speed of the base, but thishas been disputed by Hasselbrink and Mungal[6].They find that streamline divergence due to gaspansion reduces the velocity gradients so thatnondimensional stretch rate (Karlovitz number, Kaless than 0.02. The propagation velocity of a stretcflame isSL,0 (1 − Ka Ma), and the Markstein number (Ma) of a stoichiometric methane–air flame1.3[28]. Therefore stretch rates should alter propation speeds by no more than 2.6%. Another concis that excessive values of the scalar dissipationcontrol the liftoff height. However, Watson et al.[20]concluded that “scalar dissipation rates do not relevels thought to cause extinction of the leading ebased on comparison with extinction data for coun

flow diffusion flames.” In a related study, Starner et[29] concluded that heat release caused the scalardients in a flame to be less than those within a cold[30,31].

To assess various flame liftoff concepts, a ndiagnostic technique (cinema-PIV) was operated8000 frames/s to obtain movies showing the turblent eddies as they passed by the base of a lifted flaThe time histories of the propagation speed ofbase (Sb), the rms turbulence intensity (u′), and thepassage of large eddies were recorded. Correlawere measured to determine if the flame base progates faster when it is exposed to larger-than-aveturbulence intensities or to large eddies. Two liftnonpremixed jet flames were operated at Reynonumbers of 4300 and 8500.

2. Experimental arrangement

A lifted turbulent nonpremixed flame was stbilized above a circular fuel tube having an intnal diameter (d) of 5.0 mm and a length of 100d,which provides fully developed turbulent pipe floTable 2lists the operating conditions. The jet was srounded by coaxial laminar airflow having a diameof 170 mm, which eliminates disturbances from roair currents. For Case 1 the jet Reynolds number4300 (U0 = 14.0 m/s), while for Case 2 Re= 8500(U0 = 33.2 m/s). The fuel was 77% methane a23% nitrogen by volume for Case 1 and was 10methane for Case 2. Liftoff heights were 92 mmboth cases.

A detailed description of the cinema-PIV systeis provided in Refs.[1,2]. Ceramic particles having3.5-µm diameter were illuminated in a 48 by 32 mfield of view by a pair of Clark MXR ORC-1000Nd:YAG lasers that operated at 4000 pulses perond. The energy in each 532-nm pulse is 6 mJthe pulse duration is 0.3 µs. A Photec 16-mm cam

Table 2Operating parameters of lifted jet flames

Case 1 Case 2

Jet Reynolds number 4300 8500Jet exit velocityU0 (m/s) 14.0 33.2Coflow air velocity (m/s) 0.26 0.47Lam. burning velocitySL,0 (cm/s) 37 43Liftoff height x (mm) 92 92Integral scalel (mm) 5.5 5.5

Taylor length scale at baseλT (mm) 1.0 0.7PIV spatial resolution (mm) 1.2 1.2Movie (vorticity) resolution (mm) 2.3 2.3Taylor time scaleτT (ms) 1.0 0.40PIV time resolution�t (ms) 0.125 0.125


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recorded images at 8000 images per second. Onlylaser pulse illuminated each frame, so frames wcross-correlated; it was found that illuminating eacframe with two pulses and performing an autocorlation resulted in unacceptable measurement erA Kodak 460C high-resolution 3K by 2K digital camera was used to digitize 4000 images per run. Parseeding density was measured and controlled wilaser attenuation probe. Fiber optics provided aµm-thick crosshair on each image for proper aligment of the frames.

Commercial PIV software (LaVision, Inc., Visflow, Inc.) was used with an interrogation box siof 1.2 mm (64 pixels) near the flame base. Forhigher velocities near the centerline, the interrogabox was 2.3 mm (128 pixels). The spatial resolut(listed inTable 1) is 1.2 mm for all values of velocityreported, since only values near the base are repoFor the movie images of the vorticity field, the resotion is 2.3 mm, since the velocity was averaged o2.3 mm to determine gradients.

The Taylor scale at the liftoff location for Re=4300 was determined to be 1.0 mm, which is apprimately equal to the spatial resolution of 1.2 mm. Tintegral scale[32] is 5.5 mm, and the measured mevalue ofu′ was 12.5 cm/s. The error in measuringu′with a spatial resolution of 1.2 mm was determinto be 1.5%; this is the percentage of the area unthe power spectrum of the velocity fluctuations[33]associated with scales less than 1.2 mm.

The propagation speed of the flame base was msured using the definition

(7)Sb = UG − UF.

The gas velocityUG was interpolated using the velocities on a 3 by 3 grid in the 3.6 by 3.6-mm rgion ahead of the base. Flame velocityUF is definedasdx/dt , wherex is the axial location of the baseA five-point central differencing algorithm was usto determinedx/dt .

The flame base axial location(x) was defined asthe farthest upstream point on the 600-K isothewhich is a definition that was used in previous stuies[6,7,9,10]. To determine the 600-K isotherm it waassumed that the PIV particle density is proportioto the gas density, which is inversely proportionalthe gas temperature. To determine the particle dsity, each image of the particles was subdivided iinterrogation boxes and the particle density in ebox was determined from the fraction of white pixein each box; the isoline for which the particle densis half that of the 300-K incident flow is designatthe 600-K isotherm. Watson et al.[19] have reportedsimultaneous images of the 600-K isotherm andactual flame location, which they identify as the Creaction layer. They show that the base of the

layer is located within 1 mm of the most upstreapoint on the 600-K isotherm in about 90% of their images. This 1-mm distance approximately equalsthickness of the preheat zone of the premixed flaand the present 1.2 mm spatial resolution. Thereforeit is concluded that the location of the flame basethe present work should correspond to the actual bof the CH layers, to within the spatial resolution1.2 mm, for about 90% of the time, based on thesults of Watson et al.

One major advantage of cinema-PIV is that it pvides much a larger dynamic range and signalnoise ratio than conventional PIV. To measurehigh-velocity regions near centerline, the time btween particle images was set to 0.125 ms by crcorrelating adjacent frames of the movie. To msure the lower velocities near the flame base,time between particle images was set to 0.250by cross-correlating frames recorded 0.250 ms apThis ensures that the particle displacement is scient in low-speed regions and is not excessivehigh-velocity regions. Vorticity was determined bcomputing the circulation around each 3× 3-pixelregion. To filter out high-frequency noise, a line3 × 3 smoothing filter and 75% vector overlap weused.

Two movies were produced using the 1097 Pimages recorded at Re= 4300. The first movie vi-sualizes all of the eddies that can be resolved wispatial resolution of 2.3 mm; the second movie vializes only the large eddies that exceed 7 mm in dieter. A spectrally sharp low-pass filter with a cutoff7 mm was applied to the vorticity field to generatelarge-eddy movie.

3. Results

3.1. Correlation between the local turbulenceintensity and the propagation speed of the flame b

Kalghatgi[4] assumed that liftoff is controlled bthe turbulent burning velocity, which he assumedbe proportional to(u′)1/2. For such a theory to bvalid, every time the local turbulence intensity aheof the flame base (u′) increases, the propagation speof the base also must increase, so the following colation should be unity:

(8)RTP = (u′ − u′)(Sb − Sb)

( (u′ − u′)2 (Sb − Sb)2 )1/2.

The cinema-PIV measurements plotted inFig. 3wereused to measure this correlation.Sb is the instanta-neous propagation speed of the base, which isdifference between the flame velocity and the


and
Fig. 3. Time histories of (a) the turbulence intensity at the flame base (u′), (b) the propagation speed of the flame base,(c) the times when large eddies exist near the flame base. The mean values ofu′
rms andSb are 12.5 and 26 cm/s, respectively.Five vertical lines indicate the times when turbulence intensity is largest.

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velocity. The instantaneous turbulence level (u′) isdefined as the rms velocity fluctuations of the nvelocity values measured on a 3× 3 grid in the 3.6by 3.6-mm region just upstream of the flame baOne value ofu′ was determined in this way for eacof the 1097 PIV images, and these values ofu′ areplotted inFig. 3a. The propagation speeds inFig. 3bwere reported previously[1] and are reproduced in oder to provide comparisons to the new measurem(Figs. 3a and 3c).

The correlation coefficientRTP between the curvein Figs. 3a and 3bis 0.34. It is concluded that thpropagation speed of the base is not strongly colated with the local turbulence intensity. Thus, turblence intensity is not the primary factor controllinthe liftoff height in this jet experiment. It is notethat the curves inFig. 3 are sufficiently smooth sthat it is possible to observe the positive and negaoscillations in bothu′ andSb; this is due to the highsampling rate of 8000 PIV images/s that is made possible by cinema-PIV. If the sample rate was 10 timsmaller, there would be insufficient time resolutiondetermine the trends in the data.

The poor correlation betweenu′ andSb can be ob-served by considering the five times that are indicaby the vertical lines inFig. 3awhen the turbulenceintensity is larger than average. They are labeled36, 47, 61, and 89 ms, respectively. At 61 ms thebulence intensity is much higher than at any ottime, yet the propagation speed is only slightly larthan average. At 89 ms the turbulence intensityvery high, yet the propagation speed is slightly lthan average. At 98 ms the propagation speedmaximum, yet the turbulence intensity is not nearmaximum.Fig. 3aalso indicates that the turbulenceintermittent near the base region.

Table 3lists the values ofSb and u′ for the Re=4300 case. The measured value ofSb/SL,0 is 0.7,which is sufficiently close to unity to indicate ththe laminar propagation speed of the base contthe liftoff height. For the higher Reynolds number8500,Sb/SL,0 has a value of 1.2, also close to uniwhich is consistent with the other values inTable 1.

Another assumption made by Kalghatgi[4] is thatthe propagation speed of the lifted flame is givby the turbulent burning velocity relation report


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Table 3Measured velocities at the flame base, case 1 (Re= 4300)

Mean propagation speed Sb 26 cm/sNormalized propagation speed Sb/SL,0 0.7

Mean gas velocity UG 26 cm/sNonreacting mean velocity U∗

G 65 cm/sReacting/nonreacting mean velocityUG/U∗

G 0.40

rms velocity fluctuations u′ 12.5 cm/sNonreacting velocity fluctuations u′ ∗ 63 cm/sReacting/nonreacting fluctuations u′/u′ ∗ 0.20Normalized velocity fluctuations u′/SL,0 0.34

Note.U∗G andu′ ∗ are the mean and fluctuating velocity in

nonreacting jet at the average location of the flame base

by Andrews et al.[5]. However, none of the measurements correlated in Ref.[5] were obtained in alifted flame; instead they were obtained using sphcal chambers, Bunsen burners, and other geomeTo assess if the Andrews et al. formula for burnivelocity accurately represents the present conditionsconsider the measured value ofu′/SL,0 in Table 3,which is 0.34 at the flame base for Re= 4300. At thisturbulence level, the Andrews et al. formula yieldsvalue ofST/SL,0 of 2.6. Yet the present flame bapropagates atSb/SL,0 equal to 0.7, which is aboufour times less than that of the Andrews et al. formuthus Kalghatghi’s assumption is not valid. One reafor this difference is that the lifted flame is nearly vetical and is free to move, so the eddies are obseto pass around the flame and not go through it. Tcauses the lifted flame to be not very wrinkled, as dumented by the images of Watson et al.[19,20], whichcould lead to reduced values of flame surface areapropagation speed.

Table 3also provides evidence that the flame dturbs the flow. The measured mean gas velocity atflame base is 26 cm/s, which is only 40% as largevalue as in a nonreacting jet (65 cm/s) at the same location [32]. The turbulence intensityu′ at the flamebase is 12.5 cm/s, which is only 20% as large as thvalue in a nonreacting jet (63 cm/s) at this location.

3.2. Correlation between eddy passage and thepropagation speed of the flame base

First we define three types of eddies; large eddhave diameters exceeding 6.2 mm, which is the jedius at the liftoff height (i.e., the radial location whethe mean velocity is half the centerline value).termediate eddies are in the range between 2.36.2 mm, and small eddies are smaller than theticity resolution of 2.3 mm.Figs. 4–6show the timehistory of intermediate and large eddies as theyconvected upward past the lifted flame base. Thecenterline is at the left side of each 32 by 48-mm i

age. The average liftoff height is 92 mm. The gre(and blue) eddies induce a clockwise velocity fiewhich is the most probable rotation on the right sof the jet. The red eddies are less common andinduce counterclockwise rotations. The eddy bouaries occur where the vorticity magnitude exce200 s−1, which is the centerline velocity divided bthe jet width. Approximately every 12th image in tmovie is shown.

Fig. 4 indicates that the flame base often remaradially outside of the region where eddies exist ais anchored in a low-turbulence region. The base dnot interact with any eddies in this sequence, yeremains at a constant liftoff height.Fig. 4 indicatesthat the flame base does not need to be in conwith eddies to remain anchored at one fixed lotion. This is consistent with the idea that the laminburning velocity controls liftoff of these jet flamewhich have an average propagation speed thatshown to be approximately equal to the laminar buing velocity.

Fig. 5 shows an intermediate-sized eddy thatteracts with the flame base; the base does notdenly propagate upstream but remains at a fixed lifheight. The 4-mm diameter eddy tends to roll up600-K isotherm and force it to move radially inwarhowever, the liftoff height does not change. The timwhen the intermediate-sized eddies interact withflame correspond to the times when the turbuleintensity (u′) in Fig. 3aare large, as expected. Therfore it follows that when intermediate eddies intact, sometimes the propagation speed increasessometimes it decreases, but its correlation withpresence of intermediate-sized vortices is not laand is approximately 0.34, which is the value ofRTPgiven byEq. (8).

The correlation between the presence of largedies and the propagation speed also was measFigs. 5–8show several large eddies. InFigs. 5d–5fthe liftoff height does not change during large edpassage, while inFigs. 6a–6cthe liftoff height de-creases. InFigs. 6d–6fthe liftoff height increasesHowever, this change in liftoff height is less th5 mm (representing 5% of the average liftoff heigof 92 mm). The changes in liftoff height are entiredue to changes in the gas velocity caused by the leddy, and not to changes in the propagation spFig. 3c is a plot of the times during which large edies overlap the flame base. The correlation coecient between the curves inFigs. 3b and 3cis lessthan 0.1. This indicates that large eddies do not hany significant correlation with the propagation speof the flame base. The flame base was never obseto jump from one large eddy to another, which hbeen suggested as a possible stabilization mechanism[21,22].


in a,y

Fig. 4. Time history of the vorticity field showing that the flamebase often remains radially outside of the region of eddies,low-turbulence region, and at a constant liftoff height. Approximately every 12th image PIV is shown. Re= 4300; (a) 32.75 ms(b) 34.875 ms, (c) 36.875 ms, (d) 37.875 ms, (e) 40.250 ms, (f) 41.875 ms. Solid line= 600-K isotherm. Green/blue: vorticit> 200 s−1 inducing clockwise rotation; red: vorticity< −200 s−1.

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3.3. Streamline divergence due to the edge flame

Fig. 7 shows the divergence of the velocity vetors and the streamlines ahead of the flame bastwo different times. This divergence is consistent wthe observations reported above that both the mgas velocity and the turbulence levels at the basesignificantly less than those of a nonreacting jetthe same location. The thick solid line (the 600isotherm) acts as a bluff body, since the gas dendownstream of the isotherm is less than half ofupstream gas density. The divergence of streamlin a subsonic flow is an indicator that the gaslocity is decreasing, since the mass flowing betwstreamlines is constant. The vectors inFig. 7 indicatethat much of the gas is deflected around the 60isotherm. The velocity field can be considered tothe superposition of two flows: the undisturbedand the dilatation velocity field that is created by tflame.

4. Discussion

4.1. A simple scaling relation to explain liftoff heig

Equation (6)indicates that the effective propagtion speed of an edge flame is increased by the digence of streamlines, which create the velocity dference�U that is shown inFig. 1. It is proposedthat this process can be approximately represeby a source in a uniform stream. The analysis leto a reasonable relation for liftoff height; howevethe analysis is not intended to be quantitative orsimulate all aspects of the problem. The followingsumptions are made:

(a) an edge flame propagates at the effective bing velocity Seff given byEq. (6), and the localpropagation speed of the baseSb is equal toSL,0,which is consistent with the experimental finings listed inTable 1;


otddyyms,

Fig. 5. An intermediate-sized (4-mm) eddy (a–c) and a large eddy (d–f) interacting with flame base, but liftoff height does nchange. For (d–f), the vorticity field has been filtered using a 7-mm low-pass spatial filter to visualize only large eddies. Erotation forces 600-K isotherm to move toward the centerline. Re= 4300; solid line= 600-K isotherm. Green/blue: vorticit> 200 s−1 inducing clockwise rotation; red: vorticity< −200 s−1. (a) 22.3 ms, (b) 25.0 ms, (c) 28.4 ms, (d) 30.0 ms, (e) 31.8(f) 33.6 ms.

theialm

the

anrehe

nbar

es

tedr

(b) the divergence of the streamlines ahead offlame base is similar to that of the 2D potentflow that is created by a source within a uniforstream;

(c) the source is located a distancers from a wall thatsimulates the jet centerline, wherers is the radiusof the stoichiometric contour in a jet;

(d) the strength of the source is proportional toreaction rateS2

L,0/α;(e) in the undisturbed flow the nondimensional me

velocity and mean mixture fraction fields aself-similar and identical everywhere, so tmean velocity on the stoichiometric contour (UP)is U0fs. U0 is the jet exit velocity andfs is thestoichiometric mixture fraction. This assumptiohas been verified by the measurements of Donet al.[34].

Consider a 2D source of strengthλ at (xs, rs) andan image source at(xs,−rs) in a uniform streamof velocity U00. The axial and transverse velocitiare[35]

u/U00 = 1+ (λ/(2π)

)(x − xs)

×[(

(x − xs)2 + (y − rs)

2)−1

+ ((x − xs)

2 + (y + rs)2)−1

],

v/U00 = 1+ (λ/(2π)

)(y − rs)

×[(

(x − xs)2 + (y − rs)

2)−1

(9)+ ((x − xs)

2 + (y + rs)2)−1

].

Fig. 8 is a plot of the streamline pattern generaby Eq. (9); it looks similar to the flow pattern nea


m (d–f).red usingyms,

Fig. 6. Large eddies interacting with flame base, causing the liftoff height to move slightly upstream (a–c) or downstreaHowever, the large eddies do not correlate with the propagation speed of the flame base. Vorticity field has been filtea 7-mm low-pass spatial filter to visualize only large eddies. Re= 4300; solid line= 600-K isotherm. Green/blue: vorticit> 200 s−1 inducing clockwise rotation; red: vorticity< −200 s−1. (a) 15.8 ms, (b) 18.5 ms, (c) 21 ms, (d) 86.5 ms, (e) 88.2(f) 90.8 ms.

he

linetheut-at

thebece

e-m-ne

he.byt-

d

a lifted flame base. The source inFig. 8ais locatedat xs = 22 mm,rs = 2 mm, λ is 120 cm2/s, U00 is60 cm/s. We defineL to be the distance between tflame base and the source. Thus the velocityUB atthe flame base (x − xs = −L, y = rs) is predicted byEq. (9) to beU00 − λ/(2πL), sinceL is sufficientlysmall with respect tors so that the last term inEq. (9)can be ignored. Thus,

(10)�U = U00 − UB = λ/(2πL).

The strength of the sourceλ equals the fluid volume/screated by the heat release, per unit length of thesource. For the actual axisymmetric geometry ofexperiment, the heat is released in the radially oward and inward directions, forming a cylinder thhas the volumeπr2

sL; the reaction rate isS2L,0/α.

The product of these two numbers approximatesvolume/s associated with the source, which shoulddivided by the length of the axisymmetric line sour(2πrs) to provide a value ofλ equal to (1/2)rsL

S2L,0/α. Inserting this value intoEq. (10)yields

(11)�U = (4π)−1rs(S2

L,0/α).

Equation (11)is realistic in that it predicts that thstreamline divergence and�U are increased if the reaction rate(S2

L,0/α) is increased, and that the strealine divergence is zero if there is no reaction. If oconsiders a turbulent jet flow, the radius (rs) of the sto-ichiometric contour is given by Kuo[36, Eq. (6-71)]to bec2x[(c2fsx/d)−1/2 − 1]−1/2. This result is ob-tained from the laminar jet solution by replacing tmolecular diffusivity with the turbulent diffusivityNear the flame base, this result can be simplifiedsettingx/d � 1 so that the radius of the stoichiomeric contour becomes

(12)rs = c3x,

wherec3 is a constant. The left side ofEq. (6) is re-placed withU0fs, according to assumption (e) an


(b)

theer-

n-

ld

n

as

a

tentat

heandtoffat-p-nu-

byloc-es

ed-a-geer-thewn-

Fig. 7. Divergence of velocity vectors (a) and streamlinesnear the lifted edge flame. Re= 4300; solid line= 600-Kisotherm.

Eq. (4). The Sb term in Eq. (6) is set equal toSL,0according to assumption (a). The�U term inEq. (6)is replaced by the right side ofEq. (11). Equation (6)becomes

(13)Seff = U0fs = SL,0 + [c3/(4π)

]x(S2

L,0/α).

This equation for the modeled edge flame hasproper stability characteristics; if the base is pturbed to a larger (downstream)x location,Eq. (13)shows that its effective propagation velocity icreases, which forces it to move upstream. Ifx isreplaced byh, Eq. (13) can be rearranged to yiea liftoff height of

(14)h = c4(U0 − SL,0/fs)/(

S2L,0/α

).

Equation (14)is similar to the empirical relation giveby Eq. (3), since the termSL,0/fs often can be ig-nored with respect toU0. The present approach hthe advantage that not only is the final result (Eq. (14))

Fig. 8. Computed streamlines for a uniform flow oversource located a distancers from a wall. U00 = 60 cm/s,(a) rs = 2 mm, (b)rs = 4 mm, (c)rs = 10 mm.

realistic, the assumptions in the model are consiswith following observations: the base propagatesSL,0 and is not affected by turbulence intensity, tstreamline divergence is an important parameter,the streamline divergence increases with the lifheighth, in agreement with the observations of Wson et al.[19]. While the above analysis is only aproximate, the concepts are consistent with themerical simulations of Boulanger et al.[14]. Theyalso found that the flow deflection that is inducedheat release increases the effective propagation veity of a lifted edge flame. Their computed streamlinand heat release zone (Ref.[14], Fig. 7) look remark-ably similar to those shown inFig. 8.

4.2. Role of eddies in perturbing the flame baselocation

The above results indicate that the passage ofdies is not significantly correlated with the propgation speed (Sb) of the base; however, the passaof eddies was found to be correlated with a diffent parameter: the perturbations in the height offlame base. The base often jumps upstream or do


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stream by 5 mm (5% of the liftoff height) exactwhen a large eddy approaches the flame. These juare expected to occur because the eddy reduceincreases) the local gas velocity, and the flame ispected to move upstream when the approachingvelocity is reduced by the eddy. These jumps doindicate that eddies control the propagation speethe stabilization mechanism.Fig. 6 shows how oneeddy triggers an upstream jump of 5% of the liftoheight (a–c) while another eddy (d–f) triggers a dowstream jump. The base jumps upstream if it iscontact with the side of the eddy that induces anstream gas velocity. Damköhler[37] drew a velocityprofile similar to the one inFig. 6b to show how aneddy wrinkles a flame. He predicted that wherevereddy increases the gas velocity the flame would mdownstream.Fig. 6supports the flame-wrinkling concepts of Damköhler.

Additional research is needed to understand wthe propagation speed of the base has the largeations in time that are seen inFig. 3b. If the base isan unstretched, stoichiometric laminar edge flamewould be expected to propagate at a constant vof SL,0. The flame base may be stretched, althothis is disputed by the data in Ref.[6] that shows thavelocity gradients are reduced by the divergencestreamlines ahead of an edge flame. The base mapropagate exactly along the stoichiometric contbut may find a fuel-lean or a rich pathway. Small sceddies (smaller than 1.2 mm) could not be resolvethis work, but it is not expected that they would cauthe propagation speed to decrease belowSL,0, as isoften seen inFig. 3b. Random measurement uncetainties do not significantly affect the data inFig. 3b,since, the points lie along a relatively smooth curSystematic uncertainties due to out-of-plane moticould contribute some of the variations inFig. 3b, andthey are discussed inAppendix A.

5. Conclusions

1. Cinema-PIV measurements provide the timhistories of three quantities that are important tounderstanding of flame stabilization: the propagationspeed (Sb) of the lifted flame base, the turbulence itensity (u′) just upstream of the moving flame basand the time periods of large eddy passage. Theresolution (8000 PIV images/s) is sufficient to pro-vide smooth curves, so that one can see how ththree time-histories are correlated.

2. The propagation speed of the base is not sigcantly correlated with the local turbulence intensitywith the passage of large eddies. The correlationefficients are 0.34 and less than 0.1, respectively.base does not consistently tend to propagate fa

when the turbulence intensity is larger than averaor when large eddies are present. This indicatesturbulence does not play a major role in determing the liftoff height of these jet flames operated atReynolds numbers of 4300 and 8500. This is content with our previously-reported mean propagatspeeds, which are close to the laminar values (0.7SL,0and 1.2SL,0) for both values of Re. Theories basedturbulent flame propagation do not appear to be vfor these lifted jet flames at Re below 8500. Howevthis does not imply that turbulent flame propagatis not the governing factor for other conditions, suas those within gas turbine combustors.

3. The findings are consistent with the followinflame stabilization concept: even though the turlence level and the mean velocity in the undisturbjet are large, an edge flame exists which createown local low-velocity, low-turbulence level regiodue to streamline divergence. Thus the edge flacan remain nearly laminar, with a propagation velity that is matched to the local gas velocity. A simpmodel of streamline divergence is proposed thabased on the potential flow over a source. It yiea relation for liftoff height that agrees with measuments. The model also agrees with two observatio(a) the base propagates atSL,0 and is not affectedby turbulence intensity, and (b) the width of strealine divergence is important and it increases withliftoff height h [19].

Acknowledgment

This work was supported by National ScienFoundation Grant CTS-9904198 and by OfficeNaval Research Grant N00014-97-1-0302.

Appendix A. Error analysis

Normally the flame base moves upward or dowward, but at times it may have an azimuthal velity component into the laser sheet that contribuan error to the measured propagation velocity. Ithree-dimensional object (such as a sphere) beginmove horizontally into a vertical laser sheet, the loest point where the sphere and sheet intersecterroneously appear to propagate downward; assphere moves out of the sheet, the lowest pointpears to propagate upward. To determine if this souof error is significant, five time periods were selecwhen the flame base was nearly stationary (and msured velocitiesUF were nearly zero). During thesstationary periods the axial velocity of the gasUG isequal to the propagation velocitySb and the out-of-plane error is zero. It was found that the propagat


thatateri-

ap-ord.

toff-theut-

tion

ed,far-notof

ly

stme.tion, as

tyent

that

genmsarti-els.

42

s;ar-

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sordsingi-ofost

ms

on

c.IV/

-

st.

7–

m-

st.

28

98)

ki,

7)

26

st.

,

al,

97)

0)

6–

Fig. 9. Schematic of a severely wrinkled flame basecould produce the apparent negative propagation speeds thare observed about 15% of the time. To avoid this expmental problem, cinema-PLIF diagnostics are needed.

velocity during these five stationary periods hadproximately the same mean value as the entire recFurthermore, it can be argued that any error duemotion of the flame into the laser sheet will be oset by errors of the opposite sign that occur whenflame moves out of the sheet. It is concluded that oof-plane motions do not affect the mean propagaspeed.

Another source of error arises because Refs.[18–20] show that for about 10% of the images reportthe flame base defined in the present work (thethest upstream location of the 600-K isotherm) iswithin 1 mm of the actual flame base (the basethe CH reaction zone).Fig. 9 is a schematic of thehighly wrinkled base that occurs in approximate10% of the images in Refs.[18–20]. If the stoichio-metric contour becomes highly wrinkled, the moupstream location may not be the base of the flaThis can lead to the apparent negative propagaspeeds that are measured about 15% of the timeseen inFig. 3c. PIV errors arise due to uncertain(σx ) in determining the average particle displacemwithin the interrogation box, uncertainty (σC) in reg-istering the cross-hairs on the two particle imagesare to be correlated, uncertainty (σt ) in the time be-tween frames, and velocity errors (σP) due to particlelag. The overall velocity uncertainty (σu) is

(σu/u)2 = (σx/x)2 + (σC/x)2 + (σt /t )2

(15)+ (σP/u)2.

The quantity (σx/x) was measured by considerin100 PIV images of the laminar coflow region takat 0.125-ms intervals during a time period of 1.25that was so short that the flow remained steady. Pcle displacements had an rms variation of 0.64 pix

For flame data, typical particle displacements werepixels, so (σx/x) was 1.5%. The quantityσC is theuncertainty in the alignment of two particle imageit was measured to be 0.23 pixels. For a typical pticle displacement of 42 pixels, (σC/x) is 0.5%. Themaximum variation in the camera framing rate (σt/t )was 0.5%. Particle lag error for the 3.5 µm particwas computed using Ref.[38] to be less than 1.5%Thus the overall uncertainty in the velocity (σu/u)was estimated usingEq. (15)to be 2.2%. The errorwere minimized by using separate frames to recand cross-correlate the particle images and by ua high-resolution 3K by 2K digital camera to digtize the film images. Two indicators of the qualitythe PIV data are the facts that each eddy looks almidentical in any two adjacent frames (taken 0.125apart) and that the curves inFigs. 3a and 3bare rela-tively smooth, indicating that the temporal resolutiwas adequate.

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Liftoff of turbulent jet flames—assessment of edge flame and other concepts using cinema-PIV

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