2687

Proceedings of the Combustion Institute, Volume 29, 2002/pp. 2687–2694

REACTION-RATE, MIXTURE-FRACTION, AND TEMPERATURE IMAGING INTURBULENT METHANE/AIR JET FLAMES

JONATHAN H. FRANK,1 SEBASTIAN A. KAISER2 and MARSHALL B. LONG2

1Combustion Research FacilitySandia National LaboratoriesLivermore, CA 94551, USA

2Department of Mechanical EngineeringYale University

New Haven, CT 06520, USA

Instantaneous two-dimensional measurements of reaction rate, mixture fraction, and temperature aredemonstrated in turbulent partially premixed methane/air jet flames. The forward reaction rate of thereaction CO � OH ⇒ CO2 � H is measured by simultaneous OH laser-induced fluorescence (LIF) andtwo-photon CO LIF. The product of the two LIF signals is shown to be proportional to the reaction rate.Temperature and fuel concentration are measured using polarized and depolarized Rayleigh scattering. Athree-scalar technique for determining mixture fraction is investigated using a combination of polarizedRayleigh scattering, fuel concentration, and CO LIF. Measurements of these three quantities are coupledwith previous detailed multiscalar point measurements to obtain the most probable value of the mixturefraction at each point in the imaged plane. This technique offers improvements over two-scalar methods,which suffer from decreased sensitivity around the stoichiometric contour and biases in fuel-rich regionsdue to parent fuel loss. Simultaneous reaction-rate, mixture-fraction, and temperature imaging is dem-onstrated in laminar (Re � 1100) and turbulent (Re � 22,400) CH4/air (1/3 by volume) jet flames. Theturbulent jet flame is the subject of multiple numerical modeling efforts. A primary objective for developingthese imaging diagnostics is to provide measurements of fundamental quantities that are needed to ac-curately model interactions between turbulent flows and flames.

Introduction

The development of multiscalar imaging diagnos-tics for turbulent flames is essential to understandingthe interaction of turbulent flows and flames. A cen-tral objective in diagnostic research is to developtechniques for instantaneous multidimensional mea-surements of fundamental quantities, such as reac-tion rate and mixture fraction. These quantities ofinterest can be determined at a single point usingmultiscalar measurements, which are widely avail-able [1–3] and can provide as many as 10 simulta-neous measurements, including temperature andnine species [1]. However, only a subset of thesescalars can be measured simultaneously in two di-mensions. The challenge in imaging diagnostics is tomeasure fundamental quantities of interest by com-bining a judicious choice of laser-based imagingtechniques. In the present work, we focus on com-bined laser-induced fluorescence (LIF) and Ray-leigh measurements to determine the reaction rateand mixture fraction in two dimensions.

Reaction-Rate Imaging

Recently, the feasibility of reaction-rate imaginghas been demonstrated in laminar premixed flames

by combining two LIF measurements [4–6]. The ba-sic concept is described here using the reaction CO �OH ⇒ CO2 � H, which is the dominant reactionpathway for CO2 production in CH4/air flames andis a focus of the present work. The forward reactionrate, RR, is given by RR � k(T)[CO][OH], wherek(T) is the forward rate constant and T is the tem-perature. The basis of this diagnostic involves usingthe product of simultaneous OH LIF and two-pho-ton CO LIF measurements to obtain a signal that isproportional to the reaction rate. The product ofLIF signals from CO and OH can be approximatedby fCO(T)fOH(T)[CO][OH], where the temperaturedependence of the LIF signals is represented byf(T). The exact functional dependence of f(T) de-pends on the particular transition(s) employed, thespectral characteristics of the detection system, andthe temperature dependence of the quenchingcross section. For reaction-rate imaging, the strategyis to select pump/detection schemes such thatfOH(T)fCO(T) � k(T). When this relationship isachieved, the product of CO and OH LIF signals isproportional to k(T)[CO][OH].

Previously, reaction-rate imaging was applied toOH/CH2O [6,7] and CO/OH [4,5] combinations.

2688 COMBUSTION DIAGNOSTICS—Diagnostics for Temperature, Mixture Fraction and Species

Fig. 1. Predicted profiles of signal versus mixture frac-tion for polarized and depolarized Rayleigh scattering, OHLIF, and two-photon CO LIF in a partially premixed CH4/air flame with a strain rate of 100 s�1.

Fig. 2. Comparison of normalized reaction rate and theproduct of predicted OH LIF and CO LIF signals as afunction of mixture fraction.

The previous demonstrations of CO � OH reaction-rate imaging were limited to repeatable flow-flameinteractions in laminar premixed flames. In thosestudies, phase averaging was used to improve thesignal-to-noise ratios of two-photon CO LIF, whichis a relatively weak process compared to single-pho-ton LIF. Attempts to increase the CO LIF signal forimaging include the use of a multipass cell [8] andbroadband collection [5]. Multipass cells are subjectto beam-steering effects and are not conducive tocombining multiple imaging diagnostics. Broadbandcollection proved to be problematic because of laser-generated interference from C2* emission [5]. Sub-traction of this interference required a separate off-resonance measurement. This approach is notpractical for instantaneous measurements in turbu-lent flames. In the broadband detection scheme, theC2* emission can be a significant fraction of the totalCO LIF signal in rich premixed flames and can over-whelm the CO LIF signal in nonpremixed or par-tially premixed flames.

In the present work, we investigate reaction-rateimaging of CO � OH in partially premixed CH4/airjet flames using a narrow bandpass filter to eliminateC2* emission. Fig. 1 shows predicted profiles of COLIF and OH LIF as a function of mixture fractionfor a partially premixed laminar CH4/air (1/3 by vol-ume) flame using a laminar flame calculation with astrain rate of 100 s�1 [9]. In partially premixed andnonpremixed methane flames, the OH peaks on thelean side of the reaction zone, and the CO peaks onthe rich side. In Fig. 1, the two profiles overlap fora narrow range of mixture fraction bracketing thestoichiometric value of fst � 0.351.

First, we examine the feasibility of choosing apump/detection scheme for OH and CO LIF suchthat fOH(T)fCO(T) � k(T). Ideally, the two-photonCO LIF should be excited near the peak of the ex-citation spectrum in the flame of interest since it isa relatively weak scattering process. Calculations forthe partially premixed flames considered hereshowed that optimal pumping is achieved for over-lapping Q-branch transitions in the B-X(0,0) Hope-field-Birge system. The OH pumping scheme wassubsequently chosen to best obtain the proportion-ality, fOH(T)fCO(T) � k(T). This was achieved by ex-citation of the Q1(12) transition of the A-X(1,0)band. The temperature dependence of the productfOH(T)fCO(T) for these pump schemes was comparedwith k(T), using k(T) � BTMe�E/RT, where T is tem-perature, B � 4.76 � 107 mol/cm3, M � 1.23, andE � �293 J/mol (GRI-Mech 2.11). Over the tem-perature range of significant CO � OH reaction(1600–1950 K), the rate constant, k(T), is not astrong function of temperature and only varies byslightly more than �10%.

The proportionality of fOH(T)fCO(T) to k(T) is ex-cellent between 1600 and 1800 K, but the value offOH(T)fCO(T) deviates from k(T) by as much as 12%at temperatures above 1800 K and becomes a dual-valued function of temperature. In nonpremixed orpartially premixed flames, fOH(T)fCO(T) is dual val-ued because of different quenching environmentsfor lean and rich mixture fractions. In general, thispresents a challenge when trying to attain the nec-essary proportionality with k(T). Fortunately, this isnot a significant limitation for the CO � OH reac-tion-rate diagnostic since k(T) is not a strong func-tion of temperature, and pumping schemes can bechosen such that fOH(T)fCO(T) also has a relativelyweak temperature dependence over the relevantrange of temperature.

Figure 2 shows a comparison of predicted profilesof reaction rate and the product of CO LIF and OHLIF. Both profiles have been normalized to theirpeak values. The figure demonstrates that the prod-uct of LIF signals quite accurately represents thereaction rate. The bounds on the predicted system-atic error in using the product of LIF signals to mea-sure reaction rate are approximately 8.1% on the

REACTION-RATE, MIXTURE-FRACTION, AND TEMPERATURE IMAGING 2689

lean side and �5.5% on the rich side. The lean-sideerrors are greater because of the larger temperaturerange over which the CO � OH reaction is signifi-cant. For this same reason, the lean side is moresensitive to systematic errors introduced by less op-timal choices of CO and OH excitation schemes.

Mixture-Fraction Imaging

The mixture fraction can be determined by mea-suring all major species. However, it is impracticalto do this in two dimensions. Mixture-fraction im-aging thus requires the identification of a subset ofthese measurements that can provide an accuratemeasure of the mixture fraction with enough signalfor two-dimensional measurements. Previous effortshave focused on a two-scalar approach that com-bines Rayleigh scattering and fuel concentrationmeasurements. A fundamental difficulty with thisapproach is that it is not very sensitive near stoichio-metric conditions, where the fuel signal disappearsand the Rayleigh signal does not vary greatly as afunction of mixture fraction. Methods for obtainingfuel concentration have included LIF of fuel tracers[10,11], Raman scattering from fuel [10–13], anddifference Rayleigh scattering [14]. The most prom-ising of these techniques is difference Rayleigh scat-tering, which is used in the present experiments.

In difference Rayleigh scattering, temperatureand fuel measurements are taken by simultaneouslyrecording polarized and depolarized components ofRayleigh scattering. The details of this technique aredescribed elsewhere [14], and only a brief overviewis provided here. The depolarized Rayleigh scatter-ing is a function of the effective depolarization ratiofor the local composition. Isotropic molecules, suchas methane, have an extremely small depolarizationratio. In a methane/air flame, regions containingmethane have a reduced depolarization ratio. Whennormalized to the signal in air, the difference be-tween the polarized and depolarized signal providesa measure of fuel concentration.

In the present work, we investigate the use of athree-scalar technique to obtain the mixture frac-tion. The third scalar, CO, is a relatively strong func-tion of mixture fraction near stoichiometric condi-tions and provides improved sensitivity fordetermining the mixture fraction (Fig. 1). Previously,one other three-scalar technique has been investi-gated using N2 Raman imaging [15]. This methodprovided relatively modest signal-to-noise ratios andrequired the substitution of argon for N2 in partiallypremixed fuel/air mixtures to obtain sensitivity nearthe stoichiometric contour.

Experimental Methods

Experiments were performed in the AdvancedImaging Laboratory at Sandia’s Combustion Re-search Facility using the experimental apparatus

shown in Fig. 3. A combination of four lasers andfive cameras was used to simultaneously image OHLIF, two-photon CO LIF, and polarized and depo-larized Rayleigh scattering.

OH and CO Measurements

Two-dimensional measurements of OH and two-photon CO LIF were performed simultaneously.For OH LIF, the frequency-doubled output from aNd:YAG-pumped dye laser was tuned near 285 nmto pump the Q1(12) transition of the A-X(1,0) band.The OH fluorescence from the (0,0) and (1,1) bandswas reflected by a dichroic beam splitter with a re-flective coating from 300 to 350 nm and imaged ontoan intensified CCD camera (Andor Technology,512 � 512 pixels) with an f/1.8 Cerco quartz cameralens. The projected pixel size was 67 lm � 67 lm.The image intensifier was gated for 400 ns, brack-eting the dye laser pulse and eliminating any inter-ference from the other lasers. The OH LIF imageswere corrected for spatial variations in the lasersheet using acetone LIF to record the beam profile.

Two-photon excitation of overlapping transitionsin the B-X(0,0) Hopefield-Birge system of CO wasachieved using the frequency-doubled output froma Nd:YAG-pumped optical parametric oscillator(OPO) (22 mJ) near 230.1 nm. The laser was tunedto maximize the CO LIF signal in a laminar partiallypremixed CH4/air (1/3 by volume) flame. Sheet-forming optics were used to form a 6-mm high lasersheet. The two-photon excitation scheme for CO re-quired a high-intensity laser sheet to maximize theCO LIF signal. The average laser beam profile wasmeasured using CO LIF from a dilute mixture ofCO in N2 (0.3% CO by volume). Shot-to-shot fluc-tuations in the laser sheet profile were recorded onan unintensified CCD camera. The OPO beam pro-file was sampled by a fused silica wedge positionedafter the sheet-forming optics. Filters placed in frontof the beam-profile camera transmitted the 230-nmbeam while blocking light from the other lasers. Cor-rections for shot-to-shot fluctuations were importantfor the CO LIF measurements because of the sen-sitivity of two-photon CO LIF to variations in beamintensity.

Timing of the laser pulses was controlled with dig-ital delay generators. The lasers fired sequentially,with the dye laser firing first and the OPO followingafter a 470-ns delay. The sequential timing of thelasers and intensifiers eliminated the possibility ofcross talk between the two diagnostics. The jointCO/OH LIF measurements were essentially instan-taneous because the elapsed time for a single mea-surement was orders of magnitude less than the flowtimescales.

The CO fluorescence was reflected by a dichroicbeam splitter and imaged onto an intensified CCDcamera (Andor Technology, 512 � 512 pixels). The

2690 COMBUSTION DIAGNOSTICS—Diagnostics for Temperature, Mixture Fraction and Species

Fig. 3. Experimental setup for simultaneous imaging of polarized and depolarized Rayleigh scattering, OH LIF, andtwo-photon CO LIF.

imaging system included an f/1.2 camera lens and anarrow bandpass interference filter (kcenter � 484 nm,Dk � 10 nm), which transmitted fluorescence fromthe B-A(0,1) transition at 483.5 nm and blocked la-ser-generated Swan band emission from C2*. Theprojected pixel size was 71 lm � 71 lm. The imageintensifier for the CO LIF camera was gated for400 ns, bracketing the OPO laser pulse. The single-shot signal-to-noise ratio in the jet flames was ap-proximately 15 for the unsmoothed CO LIF signal.A Gaussian smoothing kernel (rx � ry � 90 lm)was used to further improve the signal-to-noise ratioin the data analysis.

Temperature and Fuel Measurements

Temperature and fuel measurements were per-formed using joint polarized/depolarized Rayleighscattering. The depolarized component of Rayleighscattering is typically 2 orders of magnitude smallerthan polarized Rayleigh scattering. To provide suf-ficient signal for depolarized Rayleigh imaging, twovertically polarized Nd:YAG lasers (360 and 560 mJ/pulse at 532 nm) were spatially overlapped and sepa-rated temporally by 110 ns. The first of the Nd:YAGlasers was fired 416 ns prior to the dye laser usedfor OH LIF. The two Nd:YAG beams were formedinto coaligned sheets within the imaged region. Aretroreflection of both beams was used to furtherincrease signal. After the first pass through the test

section, the beams were collimated with a cylindricallens and retroreflected by a flat mirror. On the returnpath, the beams were focused to a sheet by a secondpass through the cylindrical lens.

Vertically polarized Rayleigh scattering was im-aged onto an unintensified interline transfer CCDcamera (Sensicam, 640 � 512 pixels after 2 � 2binning) with a projected pixel dimension of 53 lm� 53 lm and an exposure period of 600 ns, brack-eting both Nd:YAG lasers. Rayleigh scattering wastransmitted through a dichroic beamsplitter and col-lected with an f/1.4 50-mm focal length camera lens.On the opposite side of the burner, the horizontalcomponent of Rayleigh scattering was imaged ontoan intensified CCD camera (Sensicam, 320 � 240pixels after 2 � 2 binning) with a projected pixeldimension of 90 lm � 90 lm. Rayleigh scatteringwas transmitted through a dichroic beamsplitterand collected with an f/1.2 85-mm focal lengthcamera lens. A polarizer (B�W photographic cir-cular polarizer) transmitted the horizontally po-larized Rayleigh scattering and blocked the verti-cally polarized component. A narrow bandpass filter(kcenter � 532 nm, Dk � 10 nm) eliminated broad-band laser-generated interference. The intensifierwas gated for 400 ns, bracketing both Nd:YAG laserpulses. The single-shot signal-to-noise ratios in am-bient air were approximately 10 and 75 for the un-smoothed depolarized and polarized Rayleigh sig-nals, respectively. Contour-aligned smoothing was

REACTION-RATE, MIXTURE-FRACTION, AND TEMPERATURE IMAGING 2691

Fig. 4. Simultaneous measurements of CO LIF, OHLIF, reaction rate (RR), temperature (T), and mixture frac-tion (f) in a laminar CH4/air jet flame. Images are centeredat x/d � 5 and are 40-shot averages.

used to further improve the signal-to-noise ratio ofthe depolarized Rayleigh signal.

Image Matching and Stripe Corrections

A precise image-matching technique was devel-oped to obtain accurate registration between theCCD cameras. The polarized Rayleigh camera,which had the highest spatial resolution, was used asthe reference to which the other three images werematched. The relative displacement between cam-eras was determined at 200 locations throughout theimaged region using a cross-correlation analysis oftarget images. Images were matched with an eight-parameter bilinear geometric warping algorithm.The eight parameters were determined from a re-gression of the 200 displacement vectors. The resid-ual matching error was in the subpixel range.

When laser beams propagate through flames,beam steering can be noticeable over extended pathlengths. The dual-pass arrangement used for Ray-leigh scattering was sensitive to beam-steering ef-fects, which arose from gradients in the index of re-fraction associated with density variations in theflame. Beam steering introduced stripes in the laser-beam profile, and these stripes fluctuated from shotto shot as the temperature profile varied in the tur-bulent flame. To correct for these stripes, theNd:YAG beam profile was recorded for each shot byincluding a region of ambient air in the polarizedRayleigh image. However, a correction with a single-beam profile did not sufficiently remove stripes

across the entire imaged region because the stripeswere inherently not parallel. Residual stripes wereidentified using an image analysis algorithm, and asecond stage of correction significantly reduced theimpact of beam steering.

Results and Discussion

Simultaneous two-dimensional measurements ofreaction rate, temperature, and fuel are demon-strated in laminar and turbulent axisymmetric jetflames. These flames correspond to flames A and Din the TNF Workshop library and are the subject ofmultiple numerical modeling efforts [16]. Detaileddescriptions, including single-point measurementsof species, temperature, and velocity, are availablevia the internet [16] and in Refs. [1,17,18].

Laminar Flame

A partially premixed axisymmetric laminar flamewith the same fuel composition as the turbulentflame was used as a test case for verifying the mix-ture-fraction and reaction-rate measurement tech-niques. A steady laminar CH4/air (1/3 by volume)jet flame with Re � 1100 was stabilized on a 7.2-mmdiameter nozzle. Fig. 4 shows results of simultane-ous two-dimensional measurements over a 21-mmwide region centered on the jet axis at x/d � 5. Theimages are an average of 40 single shots and havebeen cropped to show only the region that is com-mon to all four imaging diagnostics. The CO and OHLIF signals are displayed without any corrections forcollisional quenching or Boltzmann fraction varia-tions because the main focus here is to use the LIFsignals for determining the reaction rate. The rela-tively broad CO profile peaks in the fuel-rich regionand is surrounded by a layer of OH, which peaks tothe lean side of stoichiometric and slightly overlapsthe region of CO. The reaction-rate image was de-termined from the pixel-by-pixel product of the COand OH LIF images, and the reaction-rate peak isobserved to coincide with the location of maximumtemperature. The mixture-fraction and temperatureimages indicate a 3.3-mm wide potential core of un-diluted fuel/air mixture near the jet axis.

The mixture fraction was determined using a com-bination of depolarized and polarized Rayleigh scat-tering and CO LIF. The functional dependence ofeach signal on mixture fraction was determined fromdetailed single-point measurements [1]. The polar-ized Rayleigh signal has the highest signal-to-noiseratio and provides the best measure of the mixturefraction at both extremes of mixture fraction (below�0.2 and above �0.5). However, the Rayleigh signalis a relatively weak function of mixture fraction nearstoichiometric, where CO can provide improvedsensitivity. In addition, the Rayleigh signal by itself

2692 COMBUSTION DIAGNOSTICS—Diagnostics for Temperature, Mixture Fraction and Species

Fig. 5. Comparison of radial profiles from imaging (line)and multiscalar single-point measurements (circles) of mix-ture fraction (top) and reaction rate (bottom) in a laminarCH4/air jet flame at x/d � 5.

cannot be used to determine the mixture fractionbecause it is a dual-valued function of mixture frac-tion, as seen in Fig. 1. This ambiguity can be elimi-nated by using measurements of CO LIF and dif-ference Rayleigh imaging to identify the lean andrich regions of the jet flame. Difference Rayleighmeasurements were used to identify fuel-rich re-gions with a mixture fraction greater than 0.5. Formixture fraction values between 0.5 and 0.2, the COLIF was used to indicate whether the local mixturewas fuel rich or lean. Regions with a mixture fractionless than 0.2 were identified by the lack of both fueland CO.

Detailed single-point measurements of speciesand temperature in this laminar flame provide ameans to validate the mixture-fraction and reaction-rate imaging techniques [1]. The top panel of Fig. 5shows a comparison of radial profiles of mixture frac-tion. The solid line shows the radial profile of themixture fraction from Fig. 4. The profile has beenaveraged in the axial direction over a 5-mm regioncentered at x/d � 5. The circles indicate values ofthe mixture fraction determined from multiscalarpoint measurements using the following more com-plete formulation of mixture fraction [1,19]:

2(Y � Y )/w � (Y � Y )/2wC C,2 C H H,2 Hf �2(Y � Y )/w � (Y � Y )/2wC,1 C,2 C H,1 H,2 H

(1)

where Y’s are elemental mass fractions, w’s areatomic weights, and subscripts 1 and 2 refer to themain jet and coflowing air stream, respectively. Themixture-fraction imaging technique shows excellent

agreement with the point measurements and dem-onstrates the successful implementation of thescheme for determining the mixture fraction.

A comparison of the radial profiles of reaction-rateis shown in the bottom panel of Fig. 5. The solid lineis a radial profile of the normalized product of COand OH LIF shown in the reaction-rate image ofFig. 4. The circles show the reaction rate determinedfrom RR � k(T)[OH][CO], where the temperatureand OH and CO concentrations from the multiscalarpoint measurements are used and the rate constantparameters are taken from GRI-Mech 2.11. Overall,the reaction-rate profiles match quite well, indicat-ing that reaction-rate imaging is quite accurate inthese partially premixed jet flames. The reaction-rateimaging shows too high a reaction rate on the fuel-rich side for radial locations between approximately4.0 and 5.0 mm. This location corresponds to mix-ture fraction values between 0.5 and 0.6, where poly-cyclic aromatic hydrocarbon interference has beenobserved in single-point Raman measurements [20].The addition of a narrow bandpass filter could re-duce the interference.

Turbulent Flame Results

The turbulent flame considered here is a turbulentCH4/air (1/3 by volume) piloted jet flame withRe � 22,400. The 7.2-mm diameter main jet wassurrounded by an 18.2-mm diameter pilot, whichhelped anchor the turbulent flame. The pilot flamewas comprised of a mixture of C2H2, H2, air, CO2,and N2 with the same enthalpy and equilibriumcomposition as a CH4/air flame with an equivalenceratio of 0.77. Detailed single-point measurementswere used to determine the functional dependenceof each measured signal on the mixture fraction [1].The point measurements indicate that at stoichio-metric conditions, the root mean square fluctuationsof the Rayleigh signal are approximately 7%.

The images in Fig. 6 show two separate instanta-neous measurements of CO and OH LIF, reactionrate, temperature, and mixture fraction at a down-stream location of x/d � 15. The jet centerline islocated on the right side of each image, where thesmallest scale turbulent structures are seen in theunreacted fuel/air mixture. The reaction zone is athin strip located near the stoichiometric mixture-fraction contour.

The temperature and mixture-fraction measure-ments provide a means to verify the reaction-ratediagnostic technique, since the reaction rate can bedetermined by k(T)[OH][CO] and compared withthe product of the LIF signals. For this purpose, theOH and CO LIF images were converted to concen-trations by using species and temperature data fromsingle-point measurements to determine quenchingrates as a function of mixture fraction [1]. Quenchingcross sections for OH were obtained from Ref. [21].

REACTION-RATE, MIXTURE-FRACTION, AND TEMPERATURE IMAGING 2693

Fig. 6. Simultaneous single-shot measurements of OH LIF, CO LIF, reaction rate (RR), temperature (T), and mixturefraction (f) in a turbulent CH4/air jet flame. Images are centered at x/d � 15.

Fig. 7. Correlation of OH LIF � CO LIF with reactionrate determined from k(T)[OH][CO] in turbulent partiallypremixed CH4/air jet flame.

Recent measurements of temperature-dependentquenching cross sections of two-photon CO LIF[22] were used to determine CO concentrations.

As a check on the diagnostic technique, the reac-tion rate was determined both by multiplying COand OH LIF signals and by k(T)[OH][CO] for shot2 in Fig. 6. Fig. 7 shows the excellent correlationbetween the two methods, indicating that the prod-uct of LIF signals provides a good measure of thereaction rate in these flames.

ConclusionsSimultaneous two-dimensional measurements of

reaction rate, temperature, and fuel were demon-strated in laminar and turbulent partially premixed

CH4/air jet flames using a combination of two-pho-ton CO LIF, OH LIF, and depolarized and polarizedRayleigh scattering. The instantaneous forward re-action rate for CO � OH ⇒ CO2 � H was deter-mined from the pixel-by-pixel product of CO andOH LIF images.

The CO LIF combined with depolarized and po-larized Rayleigh scattering provided a three-scalartechnique for unambiguously determining the mix-ture fraction. Multiscalar single-point measurementswere used to determine the functional dependenceof polarized Rayleigh scattering and CO LIF on mix-ture fraction. These functions were then used to de-termine the instantaneous mixture fraction. The dif-ference Rayleigh and CO LIF were used to identifyfuel-rich and fuel-lean regions. This eliminated theambiguity of using the dual-valued Rayleigh signalalone to determine the mixture fraction. The three-scalar mixture-fraction imaging technique is an im-provement to two-scalar methods, which suffer fromdecreased sensitivity near the stoichiometric contourand biases in fuel-rich regions due to parent fuelloss.

Acknowledgments

This research was supported by the U.S. Department ofEnergy, Office of Basic Energy Sciences, Division ofChemical Sciences. The authors thank R. Sigurdsson forvaluable assistance in the laboratory.

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