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Combustion and Flame 143 (2005) 491–506www.elsevier.com/locate/combustflam

Lifted methane–air jet flames in a vitiated coflow

R. Cabraa,c, J.-Y. Chena,∗, R.W. Dibblea, A.N. Karpetisb,d, R.S. Barlowb

a Mechanical Engineering Department, University of California, Berkeley, CA 94720, USAb Combustion Research Facility, Sandia National Laboratories, Livermore, CA 94550, USA

c Hamilton-Sundstrand Power Systems, 4400 Ruffin Road, P.O. Box 85757, San Diego, CA 92186-5757, USAd Aerospace Engineering Department, Texas A&M University, College Station, TX 77843-3141, USA

Received 25 February 2005; received in revised form 28 August 2005; accepted 31 August 2005

Available online 10 October 2005

Abstract

The present vitiated coflow flame consists of a lifted jet flame formed by a fuel jet issuing from a cnozzle into a large coaxial flow of hot combustion products from a lean premixed H2/air flame. The fuel streamconsists of CH4 mixed with air. Detailed multiscalar point measurements from combined Raman–Rayleigexperiments are obtained for a single base-case condition. The experimental data are presented and thento numerical results from probability density function (PDF) calculations incorporating various mixing mThe experimental results reveal broadened bimodal distributions of reactive scalars when the probe vin the flame stabilization region. The bimodal distribution is attributed to fluctuation of the instantaneouflame position relative to the probe volume. The PDF calculation using the modified Curl mixing model pwell several but not all features of the instantaneous temperature and composition distributions, time-ascalar profiles, and conditional statistics from the multiscalar experiments. A complementary series of paexperiments is used to determine the sensitivity of flame liftoff height to jet velocity, coflow velocity, and ctemperature. The liftoff height is found to be approximately linearly related to each parameter within thetested, and it is most sensitive to coflow temperature. The PDF model predictions for the corresponding coshow that the sensitivity of flame liftoff height to jet velocity and coflow temperature is reasonably capturedthe sensitivity to coflow velocity is underpredicted. 2005 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Keywords: Laser spectroscopy; Multiscalar measurements; Computational modeling; Reactions in flames; Vitiated flow

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1. Introduction

In practical combustion systems hot combustproducts are often recirculated to enhance flamebility. Prediction of turbulent flames with complerecirculating flows can be a significant challengecurrent combustion models. The vitiated coflow fla

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

0010-2180/$ – see front matter 2005 The Combustion Institutdoi:10.1016/j.combustflame.2005.08.019

is a turbulent reacting flow within a hot environmebut with a simplified geometry. It consists of a fuelissuing into a coflow of hot combustion products froa lean premixed flame. The coflow diameter is mularger than the central jet diameter. This large diaeter isolates the central fuel jet from ambient aira sufficiently long distance so that the computatioproblem may be cast as a two-stream flow. Thefore, the vitiated coflow burner allows detailed expimental and computational investigation of turbule

e. Published by Elsevier Inc. All rights reserved.

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http://dx.doi.org/10.1016/j.combustflame.2005.08.019

492 R. Cabra et al. / Combustion and Flame 143 (2005) 491–506

(a) (b)

Fig. 1. (a) Burner schematic and (b) luminosity image (negative) of a lifted CH4/air jet flame in vitiated coflow.

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mixing and flame stabilization for a fuel flow in hocombustion products, while avoiding the additioncomplexities of recirculating fluid dynamics foundpractical combustors or laboratory-scale swirl buers.

The present investigation of lifted CH4/air jetflames is an extension of previous experimentalcomputational work on a lifted H2/N2 jet flame in vi-tiated coflow[1]. The H2/N2 and CH4/air flames wereselected to provide complementary experimental dto be used for evaluation of combustion models, wthese methane cases following the kinetically spler hydrogen case. As discussed in[1] and in recentcomputational studies of the H2/N2 case by Masriet al. [2] and Goldin[3], the vitiated coflow intro-duces autoignition as an additional possible mecnism of lifted flame stabilization. The liftoff heighwhich nominally corresponds to an average stabiltion position of the flame, is sensitive to several floand flame parameters, especially the coflow temature as illustrated by a recent numerical study[4].Therefore, the measured sensitivity of liftoff heightselected parameters is a useful basis for evaluatiocombustion models, and this approach is used inpresent work to test the probability density functi(PDF) method of combustion modeling. Some fetures of the scalar structure of the H2/N2 flame arecompared to those of the CH4/air flame in the presenpaper.

Within PDF methods the mixing submodel rmains an area in need of improvement (e.g., Pope[5]and Fox[6]). Past studies have examined the permance of available mixing models. For example,

modified Curl (M-Curl) mixing model[7] has per-formed well for turbulent jet flames of H2 [8] and nat-ural gas[9], as well as the H2/N2 lifted flame in viti-ated coflow[1,2]. Subramaniam and Pope[10] foundthat the Euclidean Minimum Spanning Tree (EMSmodel[11] outperformed the Interaction by Exchanwith the Mean (IEM) model[11] for a flow with pe-riodic reaction zones. Additionally, both the EMS[13] and the M-Curl[14] mixing models successfullpredicted the piloted turbulent nonpremixed flamreported by Barlow and Frank[15]. The present studcompares the performance of several mixing modin an environment that exhibits important similaritito practical combustor designs, in that there is mixand flame stabilization of a turbulent fuel flow surounded by lean combustion products. The CH4/airjet flame is modeled by the joint scalar PDF approusing a series of mixing models, and experimentalsults are used to evaluate their relative performan

2. Experimental methods

The vitiated coflow burner is shown schemacally in Fig. 1a. The vitiated coflow was produceusing a perforated plate (brass, 210-mm diamand 12.7-mm thickness) as a premixed flame holA flow blockage of 87% was achieved by drillin2200 holes (1.58-mm diameter) through the plaPremixed H2/air jet flames were stabilized on eahole, and their products mixed to form the vitiatcoflow. An exit collar surrounded the coflow anserved as a barrier that delayed entrainment of am

R. Cabra et al. / Combustion and Flame 143 (2005) 491–506 493

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ent air into the coflow region. Water flowing througa copper coil cooled the stainless-steel exit collar.main jet flowed from a stainless-steel tube (6.35 mo.d./4.57 mm i.d.), which extended 70 mm beyothe perforated plate surface. As will be shownlow, measured profiles of temperature and speciesuniform across this hot coflow, and the flow fieldinterest is unaffected by mixing with the ambient aThis allows the flames to be treated computationas two-stream problems.

Multiscalar point measurements were performin the Turbulent Diffusion Flame (TDF) laboratorySandia National Laboratories. Temperature and mspecies concentrations were measured simultaneoin a single-point fashion, using a Raman–Raylescattering system. Two-photon laser-induced fluocence (LIF) was used for the measurement of CO waccuracy better than was obtainable from the Ramtechnique. A separate LIF system was used for thetermination of OH radical mass fractions in the flamThe spatial resolution of the combined measuremwas 0.75 mm, which corresponds to the length althe laser axis that was imaged onto each detectiontem.

The separate pulsed laser systems were fiwithin an interval of less than 1 µs. At the highest flovelocity (∼100 m/s near the jet exit) this time intervacorresponds to a convective length scale of 100Since this is small compared to the spatial resoluof the multiscalar system, the combined measuments can be considered instantaneous. The precand accuracy of the Raman–Rayleigh–LIF systemdetermined via a series of measurements in flat cbration flames[16]. The measurement precision wdetermined from the standard deviations of theseflame measurements: temperature, 1%; N2, 3%; H2O,5%; CO2, 6%; OH, 10%; and mixture fraction, 6%Detailed documentation of diagnostic methods, stem design, and system uncertainties may be founthe literature[15–19].

Visible chemiluminescence was used as the flafront indicator, and the liftoff height was measurwith a simple digital imaging system. A digital camera (Sony MVC-FD85), with a 1.3 megapixel reslution was mounted on a stand, and its spatial fieldview was calibrated with a target before and after eset of experiments. A long exposure time (1 s atf/2)was necessary to capture the faint flame chemilunescence. For each flame condition 10 to 20 digimages were averaged. An example of an averaimage is shown inFig. 1b. The flame liftoff heightwas determined as the lowest point where luminity from the flame was detected. This definitionthe flame position is expected to underestimate ofaverage liftoff height and yield a result closer to tupstream end of the flame stabilization region. Ho

Table 1Base-case conditions for the vitiated coflow burner

Hydrogen Methane

Jet Coflow Jet Coflow

Re 23,600 18,600 28,000 23,30d (mm) 4.57 210 4.57 210V (m/s) 107 3.5 100 5.4T (K) 305 1,045 320 1,350XO2 0.0021 0.15 0.15 0.12XN2 0.74 0.75 0.52 0.73XH2O 0.0015 0.099 0.0029 0.15XOH (ppm) <1 <1 <1 200XH2 0.25 5× 10−4 100 100XNO (ppm) – – <1 <1XCH4 – – 0.33 0.0003φ – 0.25 – 0.4fs 0.473 0.177

Conditions for both the hydrogen (previous work[1]) and themethane cases (present work) are listed.X, mole fraction;Re, Reynolds number;D, diameter;φ, equivalence ratio;fs ,stoichiometric mixture fraction.

ever, it provides a consistent measure for evaluathe sensitivity of liftoff height to changes in flow parameters.

3. Base-case flame: CH4/air jet into vitiatedcoflow

Multiscalar point measurements were obtaineda single flame (base case), having a fuel jet mixtur33% CH4 and 67% air, by volume. Use of air raththan nitrogen makes a smaller flame and allowshigher Reynolds number flows before blowing off tflame. The bulk velocity of the fuel jet wasVjet =100 m/s. The coflow consisted of products fromlean premixed H2/air flame (φ = 0.40) with a veloc-ity of Vcoflow = 5.4 m/s, which was determined frommeasured flow rates and the equilibrium compositat the measured coflow temperature. Details of eximental conditions are listed inTable 1. The liftoffheight for the base-case condition wasH/d ∼= 35,determined visually. Measurements included a cterline profile extending fromz/d = 1 to z/d = 100downstream of the nozzle exit and radial profilesseveral axial stations (z/d = 1, 15, 30, 40, 50, and 70The radial extent covered by these profiles was fr−3 to 50 mm, with a typical spacing of 2 or 3 mmOn average, 400 samples (laser shots) were colleat each location.

The instantaneous temperature and composdata were processed and the Favre averages anddard deviations were generated. For all comparisthe mixture fraction formulated by Bilger et al.[20]


Fig. 2. Radial profiles of the Favre-averaged temperature and O2 mass fraction atz/d = 1 for the CH4/air jet flame into a vitiatedcoflow. Error bars denote the measured standard deviations.

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The elemental masses,M , and mass fractions,Y , ofcarbon, hydrogen, and oxygen, along with the bouary conditions established at the fuel (subscript 1)coflow (subscript 2) streams, determine the mixtfraction. For the base-case conditions listed inTa-ble 1, the stoichiometric mixture fraction wasfs =0.17.

Two features of the experimental results servesimplify the computational problem for this flamFirst, radial profiles of temperature and oxygen mfraction at z/d = 1 (Fig. 2) exhibit uniform scalarconditions in the jet and coflow, with fluctuation leels comparable to the precision of the measuremsystem. The radial profiles measured farther dostream (and presented in a later section) demonsthat there is no mixing of ambient air into the regiof the developing jet until well downstream of thflame stabilization region. This allows the flame tomodeled as a two-stream problem. Second, anaof the single-shot multiscalar data atz/d = 40 and 50confirmed that elemental mixture fractions basedcarbon and hydrogen are in close agreement, ming that differential diffusion effects are negligiblethis flame, and the computational assumption of unLewis number is appropriate.

3.1. Comparison between CH4/air and H2/N2vitiated coflow flames

Figs. 3 and 4present the scatter data from mesurements of temperature and OH mass fractiontained in the CH4/air and H2/N2 flames[1], respec-tively. The estimated Damköhler numbers areder of unity at the locations where flames stabili

Each of the data ensembles plotted in these figwas formed by combining single-point measuremealong the whole radial profile at each axial locatioThis manner of presentation, namely scattered dof a reactive scalar such as temperatureT againstmixture fractionf , examines the scalar structurethe flame and provides a qualitative representatiothe joint distribution function of the selected scalaThe experimental joint distributions ofFig. 3 exhibita transition from a nonreacting flow (pure mixinto a reacting flow. Atz/d = 30, nearly all the in-stantaneous temperatures (left column) lie alongnonreacting solution, which is labeled as the das“Pure Mixing” line in the figure. Far downstreaat z/d = 70, the measured temperatures are seemove close to the equilibrium limit, marked by thsolid gray line in each graph. A similar transitionseen in the distributions for OH (right column), ait is evident from these scatter data that the flaposition fluctuates widely within the stabilization rgion fromz/d = 30 to at leastz/d = 40 and possiblybeyondz/d = 50. The temperature and OH resuboth show a relaxation of reacted samples towthe equilibrium curves as we move downstream frz/d = 40 toz/d = 70. This reflects decreasing straand increasing residence time as downstream distincreases. Note that there are a few temperaturepoints atz/d = 70 that correspond to mixing of ambient air into the coflow. These events are clearly rand are considered unimportant for the calculationthese lifted flames.

Corresponding results for temperature andfrom the H2/N2 lifted flame[1] are shown inFig. 4.Within their respective stabilization regions, boflames exhibit broadened distributions betweenlimits of pure mixing and full equilibrium, as do previous Raman spectroscopy measurements in liflames[21,22]. However, there are important diffeences between the CH4/air and H2/N2 cases. Thedistributions of temperature andYOH in the methane


Fig. 3. Distributions of instantaneous temperature and OH mole fraction at four axial stations in the lifted CH4/air flame.

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case (Fig. 3) are distinctly bimodal, with the vasmajority of temperature samples lying close tomixing or equilibrium limits. For mixture fractionconditions below 0.2 (lean and near stoichiometthere are very few samples within the interior, ptially reacted part of the distribution. In contrast,z/d = 11 in the H2/N2 flame (Fig. 4) the measuredtemperature samples are spread throughout thetially reacted interior region of the distribution, evfor fuel-lean conditions.

It is expected that some of the partially reacsamples are experimental artifacts resulting from stial averaging when the laser probe volume intsects a thin, partially premixed reaction zone atleading edge of the lifted flame. The probabilitysuch events depends on the PDF of flame positthe thickness of the reaction zone, and the size

the probe volume. In the case of the methane flathere is evidence of reaction already atz/d = 30 andthere are still numerous samples on the pure ming line at z/d = 50. Hence, the lifted flame basfluctuates over a vertical distance of many timesnozzle diameter,d , and most measurement sampare expected to miss the instantaneous flame bThe H2/N2 flame stabilizes much closer to the nozle, with HH2/d ≈ 10 compared toHCH4/d ≈ 35.The fluctuations in the flame liftoff height are propotionally smaller for the hydrogen flame. The transitifrom the pure mixing line to the fully burning condition takes only about 6 diameters in the hydrogflame (8< z/d < 14). This corresponds to a highprobability that the transient reaction zone will itersect the probe volume. However, the distributioof temperature andYOH at z/d = 11 in the H2/N2


Fig. 4. Distributions of instantaneous temperature and OH mole fraction at four axial stations in the lifted H2/N2 flame[1].

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flame cannot be attributed to spatial averaging effeif the reaction zone is thin. The absence of a bimodistribution points to a distributed reaction zone ortoignition kernels or a combination of these phenoena, as discussed in our previous paper[1]. Autoigni-tion may also be important in the lifted CH4/air, asdiscussed below. Nonetheless, the qualitative difences betweenFigs. 3 and 4suggest that there may bdifferences in the structure and stabilization mecnisms for these two flames. The differences cannoconclusively determined from the single-point mesurements alone, and future planar images of scaand velocities would be useful in illuminating the nture of differences.

4. Combustion models

4.1. PDF model calculations

The flow field was computed using a standak–ε model suitable for parabolic flows[7]. Thejoint-scalar PDF approach was used to modelturbulence–chemistry interactions. This approachimplemented in a parabolic marching scheme. Csequently, there is no mechanism for upstream pagation of a turbulent edge flame, and autoignitis the only possible mechanism for flame stabilition within this calculation. Several mixing modewere incorporated into the joint-scalar PDF approto model the lifted CH4/air jet flame under the bas


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condition described above. These mixing modelscluded the modified Curl mixing model[7], the Inter-action by Exchange with the Mean[12], the EuclideanMinimum Spanning Tree mixing model[11], and theone-dimensional (1-D) mixing model[23] which re-sembles the Linear Eddy model[24] without stirring.In addition, the well-mixed reactor (Well-Mixed) ialso included to represent the limit of infinitely famixing within each computational cell.

The radial distribution of velocity atz/d = 0 wasapproximated as uniform in the coflow(r > d/2), andas a fully developed turbulent pipe flow at the nozexit (r � d/2). The initial temperature and compostion distributions were step functions across the nzle inlet diameter ofd = 4.57 mm. Initial concentrations of the major species and OH in the coflow wassigned the values measured atz/d = 1. The equi-librium concentrations of minor species were usfor those species not measured. The equilibrium ccentrations are determined from the measured coequivalence ratio and temperature listed inTable 1.

Other details of the numerical model are givenfollows. The axial domain extended fromz/d = 0 to80, while the radial domain grew asz/d increased.A total of 70 grid cells was used in the radial domaThe Eulerian Monte Carlo PDF used 400 stochaparticles per grid cell. The local mixing frequenwas modeled by the ratio of turbulent time scale toscalar mixing time with a model constant set initiato the “standard” value of 2. For the present reactflows the model constant was adjusted for each ming model to achieve the best centerline distributof both the Favre average and the variance of the mture fraction. The resulting model constant value owas found optimal for all mixing models except fthe EMST model, where a value of 2 was foundgive the best agreement with the experimental res

There is little, if any, offset error in finding the location where light emerges from a flame front. Tpeak of maximum heat release rate and the pealight emitting species, such as CH, C2, or CO∗

2, arewithin a millimeter of each other, which is smasystematic error compared to our measurement.concentrations of the C2H4 and C2H2 intermediatespecies were used in combination to determineflame liftoff height from the PDF calculations. This based on the results from autoignition calculatioshowing that the time at peak heat release is brackby the times at peaks of C2H4 and C2H2. The axiallocations where the mole fraction of C2H4 reached100 ppm and C2H2 reached 2 ppm were recorded, athe liftoff height was then estimated as the averagthe two axial values. This procedure is convenientthe two species are in the reduced chemistry descrbelow) and yields good agreement between the cputationally determined liftoff height, when using t

Fig. 5. Computed temperature (upper graph) versus eqalence ratio for mixing (without reaction) of the fuel acoflow. Comparison of computed ignition delays (lowgraph) with different detailed mechanisms and the 12-reduced chemistry.

modified Curl model, and the experimentally detmined one for the base-case flame.

4.2. Combustion chemistry

The present work implemented a 12-step reduchemical kinetic mechanism developed fromGRI1.2 mechanism for methane combustion[25] thatwas optimized with various flame features incluing autoignition delay times for very lean mixtureDue to the significance of autoignition in the prescontext, it is important to confirm that this reducmechanism accurately reproduces the ignition detimes predicted by the original detailed mechanisThe mixture temperatures resulting from pure mixof the fuel jet and the vitiated coflow are presenin the upper plot ofFig. 5 and show a decreasintrend with equivalence ratio. The lower plot ofFig. 5presents a comparison of predicted ignition delwith GRI1.2 and GRI3.0 mechanisms, the 12-sreduced chemistry, and a high-temperature methmechanism by Warnatz[26]. Because ignition deladepends strongly on temperature, the minimumnition delay occurs in very lean mixtures. With bo


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GRI mechanisms and the 12-step reduced chemithe minimum delay occurs at an equivalence raaround 0.02, which corresponds to∼0.004 in mix-ture fraction. The overall performance of the 12-schemistry is quite satisfactory. In comparison toresults from GRI mechanisms, the detailed mecnism by Warnatz predicts shorter ignition delays athe location of minimum delay is higher at 0.04. Tdifferences are about 20% at the minimum locatioand as large as a factor of 2 near the stoichiomecondition. The sensitivity of predicted ignition delato chemistry model should be considered when coparing model predictions with experimental data.

5. Evaluation of mixing models

PDF calculations were carried out for the bacase condition using each of the five mixing mod(M-Curl, IEM, EMST, 1-D, and Well-Mixed). Resultfrom these calculations are compared below with eother and with experimental results for centerline pfiles of selected scalars, scatter plots of temperatand radial profiles of mixture fraction and tempeture, and conditional statistics (mean and rms) of teperature and the mass fractionsYO2 andYOH.

5.1. Centerline profiles

Centerline profiles provide information on thevolution of the flow that can be used to validatePDF mixing models.Fig. 6 presents the centerlinprofiles of Favre-averaged mixture fraction andfluctuation, temperature and its fluctuation, and mfractions of O2 and OH. The figure includes botexperimental and computational results. All modelsults predict a flow with two stages. The initial stagup toz/d ∼ 25, involves mixing without reaction between the fuel jet and the vitiated coflow. This initimixing stage is characterized by a slow temperarise with relatively low levels of temperature fluctution and negligible OH mass fraction. This is followeby a broad flame stabilization region characterizeda rapid temperature rise, larger temperature fluctions, and the rise ofYOH.

All model results produce the qualitative charateristics of the experimental centerline profiles. Thinclude a moderate temperature increase due toing followed by a rapid temperature increase duecombustion; similar levels for the peak fluctuationsmixture fraction and temperature; slow oxygen dition in the central jet due to entrainment of the coflproducts, followed by rapid consumption of oxygdue to combustion; and similar OH concentration vues downstream in the flame.

As noted earlier, the mixing model constants wadjusted such that the predicted peak fluctuationmixture fraction was about the same for all moels. Under this constraint, the EMST model giveslightly slow decay of mixture fraction in the nefield, in comparison to other models and the msurements, but it predicts reasonable fluctuationmixture fraction and temperature. The predicted teperature rise along the jet centerline gives an indiindication of the flame liftoff height because the ceterline temperature rise will occur downstream offlame stabilization zone. Among the different miximodels, the 1-D model predicts the centerline teperature rise closest to the nozzle exit followed byWell-Mixed model, the EMST, the IEM, and the MCurl model. This trend seems to correlate with thegree of randomness in mixing allowed in each modIn turbulent flows, fluid samples with different proerties are brought together by convection and mivia molecular diffusion. In the 1-D model mixingachieved via diffusion between fluid parcels thatin close proximity to each other in mixture fractiospace. This local treatment tends to inhibit the mixof parcels with substantially different compositionFor particles that are near the condition of minimuignition delay, this localness in mixing could serextended residence times at conditions conducivautoignition, and this may result in the observed sbilization relatively close to the nozzle.

In contrast to the 1-D model, the M-Curl modpicks randomly pairs of particles to mix. Thus flusamples with vastly different properties can be mixand this apparently delays the stabilization offlame by the process of autoignition. The EMSmodel ensures that mixing takes place with the locness property which may allow autoignition to occearlier than with the M-Curl model under the presflame conditions. For brevity and because the moare not commonly used in combustion calculatiofurther details of the results from Well-Mixed and 1-mixing models will not be presented.

5.2. Scatter plots of temperature versus mixturefraction

The predicted scatter plots of temperature vermixture fraction obtained at different axial locatioprovide further metrics for model evaluation. Rsults from the remaining three mixing models (IEMEMST, M-Curl) are contrasted inFig. 7. Results fromthe IEM and EMST models are presented in theand center columns, respectively, for axial locatioz/d = 25, 30, 40, and 50. Distributions computed uing the M-Curl model are plotted in the right-mocolumn for axial locationsz/d = 30, 40, 50, and70. The choice of different axial stations to be pl


l PDF re-ST),

Fig. 6. Comparison of centerline profiles of Favre-averaged temperature and species mass fractions. Numericasults: Modified Curl (M-Curl), Interaction by Exchange with the Mean (IEM), Euclidean Minimum Spanning Tree (EMone-dimensional diffusion (1-D Mix), and the perfectly mixed cells (Well-Mixed). Experimental results (Exp).

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ted is due to the fact that the M-Curl model predia greater liftoff height. The locations are chosenhave similar states in terms of combustion progreAlso plotted are lines for adiabatic equilibrium afor mixing without reaction.

The scatter plots of temperature versus mixtfraction from the three PDF calculations are cosistent with each model’s treatment of mixing. TM-Curl model results exhibit a bimodal distributiofilled with some intermediate states as a resultthe mixing of randomly selected pairings. The IEmodel results are clustered around two bands withpoints scattered in between. The points in the loband gradually react to reach the fully burnt tempatures at the lower axial locations (z/d = 30 and 40).Pure mixing at the lower locations is not well repr

sented by the IEM model. The EMST model resuexhibit a low-variance distribution consistent withmodel that is local in composition space. Since a sliftoff height is predicted, the pure mixing on the fulean side atz/d = 25 is not captured. However, thEMST model does reasonably predict flame broening atz/d = 25. The broad distributions predictewith the M-Curl and EMST mixing models are moconsistent with the experimental results even thothe scatter in the experimental results is due, in pto experimental uncertainty.

5.3. Radial profiles and conditional statistics

Fig. 8 shows radial profiles of Favre-averagmixture fraction and temperature from the measu


esults atuesndition.

Fig. 7. Scatter plots of temperature versus mixture fraction with increased axial distance for IEM and EMST model rz/d = 25, 30, 40, 50, and for M-Curl model results atz/d = 30, 40, 50, and 70. Also plotted are adiabatic equilibrium val(solid line) and nonreacting (dashed line; pure mixing) conditions. The vertical dotted line indicates the stoichiometric co

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ments and from PDF calculations using the modifiCurl mixing model. The outer end of each measuprofile up toz/d = 50 reaches the undiluted coflocondition and shows near-zero temperature fluction. Thus, the experimental jet is isolated from tambient air by the hot coflow for a distance of at lez/d = 50. The elevated temperature fluctuationsthe outer edge of the temperature profile atz/d = 70indicate some degree of mixing of ambient air. Hoever, as noted previously, the temperature scatterfrom this streamwise location (Fig. 3) show only avery small number of points that correspond to su

mixing. Thus, penetration of ambient air into the mesurement region is rare even atz/d = 70.

The radial profiles for temperature inFig. 8 in-dicate no reaction in the first 30 diameters fromexit nozzle. Initially, mixing without reaction occurbetween the vitiated coflow and fuel jet. It is not util z/d = 40 that we see a distinct increase in ttemperature fluctuations and a rise in the mean tperature above the coflow condition. These measments are consistent with visually observed liftheight being nearz/d = 35. Agreement between mesured and modeled profiles of mixture fraction a


erimental
Fig. 8. Radial profiles of Favre-averaged mixture fraction and temperature with increased axial distance. Plotted are expresults (symbols) and PDF with M-Curl mixing results (lines).
delpre-ut-tive

rmsix-owal-enature

ame

re-

and

eentle-

its fluctuation is reasonably good, although the mopredicts somewhat broader profiles. The broaderdicted mixture fraction profiles correspond to an oward shift in the predicted peak temperature relato the measurements atz/d = 40 andz/d = 50. Atz/d = 70, the measured mean temperature and itsat the outer edge of the profile show the effects of ming with air since the mean temperature falls belthat of coflow. Near the jet centerline, the rms vues predicted by the M-Curl mixing model are seto exceed the data. The measured mean temperreaches its maximum at the centerline (f̃ about 0.2)

and the corresponding scatter data show that the flis fully burning. Consequently,T ′′ is expected to belower than those at other locations. The M-Curlsults still show some unburnt samples atz/d = 70(Fig. 7), and hence the predictedT ′′ is higher thandata.

Results for the conditional ensemble averagerms fluctuation of temperature,YO2, and YOH areshown inFigs. 9–11, where computations using thM-Curl model (lines) are compared to the experim(symbols). These conditional statistics are compmentary to the scatter plots (Figs. 3 and 7) in pro-


andl re-s).

iongander-

hedon

an-

ofse-oteresnd

am-rere-ing

ingly

andn-lts

stheug-ionsuel-

m-

rerel-plescurm-msurehetua-eethe

Fig. 9. Evolution of the conditional ensemble averagerms fluctuation of temperature. Plotted are experimentasults (symbols) and PDF with M-Curl mixing results (line

viding insights on the scalar structure and evolutthe lifted CH4/air jet flame, as well as highlightinthe similarities and differences between measuredcalculated results. Considering the conditional avages first (top figures inFigs. 9–11), it is apparentthat the PDF results for temperature andYO2 at verylean conditions tend to follow a trajectory close to tfully reacted (equilibrium) line before deviating ancutting across the interior, partially reacted portiof the domain. Recall from the discussion ofFig. 5that the minimum ignition delay occurs in very lemixtures nearf = 0.004. Therefore, flame stabilization within the calculation occurs by autoignitionthese very lean samples followed by mixing a subquent reaction at other mixture fraction values. Nthat this preference for reaction in very lean mixtuis more obvious in the scatter plots for the IEM aEMST calculations inFig. 7. From Fig. 3 we knowthat the scatter data from measurements of lean sples atz/d = 30 in the flame stabilization region amore obviously bimodal, with many lean samplesmaining near the pure-mixing line. The correspondconditional mean curve forz/d = 40 in Figs. 9–11exhibits a broad peak with the fuel-lean portion beroughly halfway between the mixing-only and ful

Fig. 10. Evolution of the conditional ensemble averagerms fluctuation of O2 mass fraction. Plotted are experimetal results (symbols) and PDF with M-Curl mixing resu(lines).

reacted limits. Farther downstream, atz/d = 50, themajority of samples with fuel-lean mixture fractionare close to the fully reacted curve. Generally,conditional mean results from the PDF model are sgestive of a process that begins at fuel-lean conditand then extends toward stoichiometric and then frich conditions as streamwise distance increases.

With regard to the conditional fluctuations (bottofigures inFigs. 9–11) consider that maximum possible rms levels for temperature andYO2 at a givenmixture fraction correspond to distributions that aperfectly bimodal, with half the samples on the pumixing line and half on the equilibrium curve or, aternatively, a curve representing the reacted samat each downstream location. Lower rms values ocwhen there is a distribution of partially reacted saples in between these limits, and the conditional rbecomes small when all samples at a given mixtfraction are either at the pure-mixing limit or near tsame reacted state. The measured conditional fluctions atz/d = 40 and 50 are roughly 450 K, while thupper limit for a distribution between the mixing linand the reacted state is roughly 600 K. Based onmeasured conditional means inFigs. 9–11, measure-


anden-lts

toi-aythetternalthe

u-

re-thatlarix-

popr-

dvemedi-e-res.om

r the

trem-ricig-iti-n-re-

thee.

wds,tionen-is

dateachwoa-

essi-fbysthe

y.-ed,ty,

gu-.e.,c-

at-

lff

Fig. 11. Evolution of the conditional ensemble averagerms fluctuation of OH mass fraction. Plotted are experimtal results (symbols) and PDF with M-Curl mixing resu(lines).

ments at the average liftoff height ofz/d = 35 shouldyield conditional mean temperatures near the schiometric condition that are approximately halfwbetween the mixing and the reacted state. Due tostrongly bimodal character of the measured scadata, we would expect the corresponding conditiorms temperature fluctuations to be even closer totheoretical upper limit.

The conditional rms results from the PDF calclation show that the peaks in the fluctuations ofT

and YO2 are somewhat below the experimentalsults. This appears to be associated with the factthe prediction shows a significant population of scastates that have moved slightly away from the ming line (e.g., M-Curl results inFig. 7 at z/d = 40),whereas the measurements show the comparableulation staying on the mixing line (within the expeimental uncertainty). InFigs. 9 and 10the predictedcurves for fluctuations ofT andYO2 are also observeto shift to larger mixture fraction values as we modownstream. This trend is consistent with a flastabilization process that begins at very lean contions, which correspond to the minimum ignition dlay times, and then progresses toward richer mixtuThe experiment shows a similar trend for data fr

-

the stabilization region (z/d = 40 and z/d = 50).However, the experimental trend ends beforez/d =70 because the riches samples are already neafully reacted limit.

6. Liftoff height sensitivity

The sensitivity of the flame liftoff height to jevelocity, coflow velocity, and coflow temperatuwas examined by parametric variation, both coputationally and experimentally. In the parametexperiments the liftoff height was determined by dital imaging of the luminous flame base. The vated coflow temperature under different flow coditions was determined by thermocouple measuments. Computations were carried out usingM-Curl model, since it best predicted the base cas

As was shown inFigs. 3 and 7, all chemical ki-netic activity occurs in regions of the flow with a lomixture fraction (f < 0.4) that are also associatewith lower velocities, lower turbulence intensitieand higher temperatures. As such, the combusprocesses of the lifted jet flame should be more ssitive to coflow conditions than jet conditions. This indeed the case shown inFigs. 12 and 13, wherethe sensitivity of liftoff height to jet exit velocity ancoflow velocity is examined. It should be noted ththe two figures are based on the same dataset; incase the liftoff height is plotted against one of the tvelocities (jet/coflow) using the other velocity as a prameter (coflow/jet). A comparison of the two figurmakes it apparent that the liftoff height is very sentive to the coflow velocity. The sensitivity of liftofheight to coflow velocity was also investigatedDahm and Dibble[27], who considered lifted flamein unheated air and developed a model predictingstrong sensitivity of flame blowoff to coflow velocit

Kalghatgi [28] proposed a liftoff height correlation in terms of the maximum laminar flame specoflow density, and jet properties including velociviscosity, and density:

(11)HK = 50

(νjetVjet

S2L,max

)(ρjet

ρcoflow

)1.5.

This correlation was developed using scaling arments for the case of fuel jets into quiescent air (ino coflow). Perhaps fortuitously, the correlation acurately predicted the liftoff height for the H2/N2 jetflame (HK/d = 11.4, Hexp/d ≈ 10) previously pre-sented[1]. In contrast, the CH4/air results plotted inFig. 12a show large discrepancies between Kalghgi’s model and the experimental data.

The PDF model with the M-Curl mixing modepredicts the approximately linear sensitivity of lifto


irclee PDF with

irclee PDF with

Fig. 12. Sensitivity of CH4/air flame liftoff height to jet exit velocity, with coflow velocity as a parameter. The shaded crepresents the base-case liftoff height established by the unaided eye. Plotted are the experimental results (a) and thM-Curl mixing results (b). The thick line shows the prediction from Kalghatgi’s correlation.

Fig. 13. Sensitivity of CH4/air flame liftoff height to coflow velocity, with jet exit velocity as a parameter. The shaded crepresents the base-case liftoff height established by the unaided eye. Plotted are the experimental results (a) and thM-Curl mixing results (b). (The same data as inFig. 12are used here.)

eenom--w

they

lictoea-

rva-vi-lsols inpo-

areus-. As

lin-5%es-si-

DFis

gu-offson-ell-vityply

height to jet velocity reasonably well, as can be sby comparing the slopes of the experimental and cputational results inFig. 12. However, the model underpredicts the sensitivity of liftoff height to coflovelocity, as can be seen inFig. 13, where the linesshowing the measured trend (Fig. 13a) have clearlya steeper slope than the corresponding lines formodeled trend (Fig. 13b). This underprediction mabe due to assumptions inherent in thek–ε turbulencemodel, mixing model, inlet conditions, or paraboflow assumption, and further work will be requiredidentify the reasons for this difference between msured and modeled results.

The sensitivity of liftoff height to coflow scalaconditions was investigated by varying the equilence ratio of the premixed flames that form thetiated coflow. Changing the equivalence ratio achanges the concentrations of oxygen and radicathe coflow. However, since reaction rates are ex

nentially dependent on temperature, while theyonly linearly dependent on composition, the combtion processes are most sensitive to temperatureshown inFig. 14, the sensitivity of liftoff height tocoflow temperature is strong and approximatelyear over the range of conditions considered. Adrop in coflow temperature (60 K) roughly doublthe liftoff height. While the PDF method with MCurl mixing model predicts this temperature sentivity relatively well, Kalghatgi’s model significantlyunderpredicts the sensitivity to temperature. The Pmodeling with well-mixed cells was also tested andshown inFig. 14to do a reasonable job of predictinthe relative change in liftoff height (also nearly dobling with a 60 K decrease), even though the liftheights are themselves under predicted. The reaable approximation by the fast and inexpensive wmixed combustion model suggests that the sensitiof liftoff height to temperature can be captured sim


-sentssults,lshoww

el.m-

isix-h,i-hea-

ana-destim-ifi-

howrt-heral-a-for

re-ns

rebi-er-ure-the

ge

eded.idedf a

hisided

ee.ch

el,resels,e,ess of

ithri-itiv--thea-wb-

hendcat-There-ebi-

e-me.ea-DFbi-

ryhowact

lu-nceion.dif-

nsza-ing

Fig. 14. Sensitivity of liftoff height to measured coflow temperature and equivalence ratio. The shaded circle reprethe base-case condition. Plotted are the experimental rePDF with M-Curl mixing results, PDF with well-mixed celresults, and Kalghatgi’s model. The bottom abscissas sthe variation inφ and oxygen level that resulted in the coflotemperature variation.

by employing the proper chemical kinetics submodTherefore, details of molecular mixing may not be iportant in determining this sensitivity.

An important result from this parametric studythat PDF calculations using the modified-Curl ming model within a parabolic marching approacwhich relies on autoignition for initial flame stablization, do a reasonably good job of predicting teffects of changing coflow conditions on the mesured liftoff height. This might be interpreted asindication that autoignition is the controlling mechnism for stabilization of these lifted flames in vitiatecoflow. However, there is other evidence to suggthat turbulent edge flame propagation may be anportant mechanism in the laboratory flame. Speccally, the computed scatter data for temperature sthat reaction is initiated in very lean mixtures (shoest ignition delay) and progressively spreads to higmixture fractions. The experimental scatter data,though limited with respect to the number of mesured locations, do not show such a preferencereactivity at very lean reactions. The maximum pmixed laminar flame speed for reactant conditioalong the mixing line is about 3.2 m/s and occurson the slightly lean side of the stoichiometric mixtufraction, and this may be sufficient to support stalization by edge flame propagation. Additional expiments beyond the present multiscalar point measments are needed before we can fully understandrelative importance of autoignition and turbulent ed

flame propagation in stabilizing these lifted CH4/airflames in vitiated coflow.

7. Conclusions

Experimental and numerical results on liftflames in a hot (vitiated) coflow were presentLaser-based multiscalar point measurements prova detailed dataset for a base-case condition olifted CH4/air turbulent jet flame in a vitiated coflowof H2/air combustion products. Complementing tbase case, a series of parametric experiments provinformation on sensitivity of the liftoff height to thjet velocity, coflow velocity, and coflow temperaturProbability density function combustion models, eaemploying a different molecular mixing submodwere tested for their capacity to capture the featuof the base-case flame. Each of the mixing modmodified Curl, Euclidean Minimum Spanning Treand IEM, yielded predictions of stable lifted flamand reasonably predicted some qualitative featurethe base-case condition.

The behavior of the PDF combustion model wM-Curl mixing model was further tested by compason with experimental results on the relative sensity of liftoff height to the jet velocity, coflow velocity, and coflow temperature. The model predictedsensitivity to jet velocity and coflow temperature resonably well. However, the sensitivity to the coflovelocity was underpredicted. The liftoff height exhiited the highest sensitivity to coflow temperature.

In the evaluation of the PDF mixing models, tmost compelling argument in favor of the M-Curl aEMST mixing models was the appearance of the stered data of temperature versus mixture fraction.data showed an evolution from a pure mixing (nonacting) condition to a reacting condition. At the flambase, the scatter data distribution was broad andmodal, consistent with a relatively thin turbulent raction zone fluctuating around a laser probe voluAn important difference between modeled and msured results was that the scatter data from the Pcalculations showed clear indications of a flame stalization process that initiates with autoignition in velean mixtures, whereas the measurements do not sany obvious indication that very lean samples refirst. Further work will be needed before firm concsions may be drawn regarding the relative importaof autoignition and turbulent edge flame propagatas stabilization mechanisms for these lifted flames

These methane flames exhibit characteristicsferent from the previously reported H2/N2 liftedflame, particularly with regard to the distributioof scatter data for reactive scalars in the stabilition region. Calculations of both of these flames us


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models that allow for both autoignition and upstreflame propagation should yield interesting insightsthe flame stabilization mechanisms for fuel flowsjected into high-temperature environments.

Acknowledgments

Research at UC Berkeley was supported by NAGlenn Research Center, under Contract NAG3-21Experiments conducted at Sandia were supportethe United States Department of Energy, Office of Bsic Energy Sciences.

References

[1] R. Cabra, T. Myhrvold, J.-Y. Chen, R.W. Dibble, A.NKarpetis, R.S. Barlow, Proc. Combust. Inst. 29 (2001881–1888.

[2] A.R. Masri, R. Cao, S.B. Pope, G.M. Goldin, CombuTheory Model. 8 (2004) 1–22.

[3] G.M. Goldin, AIAA 2005-555 (2005).[4] R. Cao, S.B. Pope, A.R. Masri, Combust. Flame 1

(2005) 438–453.[5] S.B. Pope, Proc. Combust. Inst. 23 (1990) 591–612[6] R.O. Fox, Computational Models for Turbulent Rea

ing Flows, Cambridge Series in Chemical EngineeriCambridge Univ. Press, Cambridge, UK, 2003.

[7] J. Janicka, W. Kolbe, W.J. Kollmann, Non-Equil. Themodyn. 4 (1979) 47–66.

[8] N.S.A. Smith, R.W. Bilger, C.D. Carter, R.S. BarlowJ.-Y. Chen, Combust. Sci. Technol. 105 (1995) 35375.

[9] P.A. Nooren, H.A. Wouters, T.W.J. Peeters,Roekaerts, U. Maas, D. Schmidt, Combust. TheModel. 1 (1997) 79–96.

[10] S. Subramaniam, S.B. Pope, Combust. Flame(1999) 732–754.

[11] S. Subramaniam, S.B. Pope, Combust. Flame(1998) 487–514.

[12] J. Villermaux, J.C. Devillon, in: Proceedings from t2nd International Symposium on Chemical ReactEngineering, Elsevier, New York, 1972, p. 13.

[13] Q. Tang, J. Xu, S.B. Pope, Proc. Combust. Inst.(2000) 133–139.

[14] P.R. Lindstedt, S.A. Louloudi, E.M. Vaos, R.W. BilgeProc. Combust. Inst. 28 (2000) 149–156.

[15] R.S. Barlow, J.H. Frank, Proc. Combust. Inst. 27 (191087–1095.

[16] R.S. Barlow, G.J. Fiechtner, C.D. Carter, J.-Y. ChCombust. Flame 120 (2000) 549–569.

[17] Q.V. Nguyen, R.W. Dibble, C.D. Carter, G.J. FiechtnR.S. Barlow, Combust. Flame 105 (1996) 499–510.

[18] B.B. Dally, A.R. Masri, R.S. Barlow, G.J. FiechtneD.F. Fletcher, Proc. Combust. Inst. 26 (1996) 2192197.

[19] R.S. Barlow, A.N. Karpetis, J.H. Frank, J.-Y. CheCombust. Flame 127 (2001) 2102–2118.

[20] R.W. Bilger, S.H. Stårner, R.J. Kee, Combust. Flame(1990) 135–149.

[21] T.S. Cheng, J.A. Wehrmeyer, R.W. Pitz, CombuFlame 91 (1992) 323–345.

[22] A. Brockhinke, P. Andresen, K. Höinghaus, AppPhys. B 61 (1995) 533–545.

[23] D. Geyer, A. Dreizler, J. Janicka, A.D. Permana, J.Chen, Proc. Combust. Inst. 30 (2005) 711–718.

[24] A.R. Kerstein, J. Fluid Mech. 240 (1992) 289–313.[25] C.J. Sung, C.K. Law, J.-Y. Chen, Combust. Sci. Te

nol. 156 (2000) 201–220.[26] J. Warnatz, private communication (2000).[27] W.J.A. Dahm, R.W. Dibble, Proc. Combust. Inst.

(1988) 801–808.[28] G.T. Kalghatgi, Combust. Sci. Technol. 41 (1984) 1

29.

lifted methane–air jet ﬂames in a vitiated coﬂowperso.crans.org/epalle/m2/ca/combustion and...

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