multiscalar imaging in partially premix ed jet ßames with argon...

Combustion and Flame 143 (2005) 507–523www.elsevier.com/locate/combustflame

Multiscalar imaging in partially premixed jet flames withargon dilution

J.H. Frank a,∗, S.A. Kaiser a, M.B. Long b

a Combustion Research Facility, Sandia National Laboratories, Livermore, CA 94551-0969, USAb Department of Mechanical Engineering, Yale University, New Haven, CT 06520-8284, USA

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

Available online 14 October 2005

Abstract

Simultaneous imaging of depolarized and polarized Rayleigh scattering combined with OH-LIF and two-photonCO-LIF provides two-dimensional measurements of mixture fraction, temperature, scalar dissipation rate, and theforward reaction rate of the reaction CO+ OH = CO2 + H in turbulent partially premixed flames. The conceptof the three-scalar technique for determining the mixture fraction using CO-LIF with depolarized and polarizedRayleigh signals was previously demonstrated in a partially premixed CH4/air jet flame [J.H. Frank, S.A. Kaiser,M.B. Long, Proc. Combust. Inst. 29 (2002) 2687–2694]. In the experiments presented here, we consider a similarjet flame with a fuel-stream mixture that is better suited for the diagnostic technique. The contrast between thedepolarized and the polarized Rayleigh signals in the fuel and air streams is improved by partially premixingwith an argon/oxygen mixture that has the same oxygen content as air. The substitution of argon, which has a zerodepolarization ratio, for the nitrogen in air decreases the depolarized Rayleigh signal in the fuel stream and therebyincreases the contrast between the depolarized and the polarized Rayleigh signals. We present a collection ofinstantaneous 2-D measurements and examine conditional means of temperature, scalar dissipation, and reactionrates for two downstream locations. The emphasis is on the determination of the scalar dissipation rate from themixture-fraction images. The axial and radial contributions to scalar dissipation are measured. The effects of noiseon the scalar dissipation measurements are determined in a laminar flame, and a method for subtracting the noisecontribution to the scalar dissipation rates is demonstrated. 2005 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Keywords: Turbulent flames; Imaging diagnostics; Mixture fraction; Scalar dissipation; Rayleigh scattering; Laser-inducedfluorescence

1. Introduction

Mixture fraction (ξ), scalar dissipation (χ), andreaction rate are fundamental quantities in the study

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

of turbulent combustion but are particularly challeng-ing to measure. Multidimensional measurements ofthese quantities are needed to improve our under-standing of flow–flame interactions in turbulent non-premixed and partially premixed combustion. The de-termination of mixture fraction requires simultaneousmeasurements of all major species and temperature.For multidimensional measurements, it is not fea-

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508 J.H. Frank et al. / Combustion and Flame 143 (2005) 507–523

sible to measure all of these quantities, so mixturefraction must be determined from a reduced set ofmeasurements. Over the past 23 years, the diagnosticcapabilities for measuring mixture fraction in turbu-lent nonpremixed flames have evolved from single-point Raman/Rayleigh [1–3], UV-Raman [4,5], andRaman/Rayleigh/LIF ([6–9] and references therein)measurements to 1-D [10–16] and 2-D [17–23] tech-niques. The single-point measurements have providedinsights into turbulent nonpremixed flames, and well-documented data sets are currently used for the devel-opment of turbulent combustion models via the TNFWorkshop [24].Scalar dissipation, which is defined as χ =

2D(∇ξ · ∇ξ), where D is the mass diffusivity, re-quires multidimensional measurements to determinethe gradient of mixture fraction. One-dimensionalmeasurements of mixture fraction provide only a sin-gle component of the mixture-fraction gradient [10,16]. To improve on this limitation, the projectionof the mixture-fraction gradient onto the flame nor-mal can be determined using simultaneous flame-orientation measurements [11,12]. However, this ap-proach does not provide a direct measurement of thefull scalar dissipation rate, and the determination ofthe flame orientation over a wide range of mixturefractions is challenging. Two-dimensional mixture-fraction imaging affords wide-field measurements oftwo components of the scalar dissipation and can pro-vide intuitive physical insight into the flame structure.Each image of mixture fraction or scalar dissipationcontains on the order of 104–105 point measure-ments.

1.1. Reduced schemes for determining mixturefraction

Schemes for determining mixture fraction in twodimensions involve the measurement of two or threejudiciously selected scalars. Ideally, the measuredquantities provide good sensitivity to variations inmixture fraction and have high signal-to-noise ratios.A two-scalar method, which is based on fuel massfraction (Yfuel) and sensible enthalpy (h = cpT ), canbe derived by simplifying the chemistry to a one-step reaction between fuel and oxidizer and assumingunity Lewis number [25,26]. In this formulation, theconserved scalar is β = Yfuel + cpT /q , and the mix-ture fraction is given by

ξ2 scalar =β − β2β1 − β2

(1)= Yfuel + (cpT − cp,2T2)/qYfuel,1 + (cp,1T1 − cp,2T2)/q

,

where q is the lower heat of combustion per unit massof fuel, and subscripts 1 and 2 designate the fuel and

oxidizer streams, respectively. This formulation hasbeen used for mixture-fraction imaging in both H2/air[21] and CH4/air jet flames [17,18,21]. An iterativeprocedure is used to determine fuel mass fraction andtemperature from measurements of fuel concentrationand Rayleigh scattering. In this procedure, laminarflame calculations are used to tabulate the temperatureand mixture-fraction-dependent auxiliary variables,which include cp , the effective Rayleigh cross sec-tion, σRay, and the mixture molecular weight, Wmix.Within the iteration, a “reactedness” can be computedfrom the local Rayleigh temperature, and the values ofcp , σRay, and Wmix are linearly interpolated betweentheir values in a laminar flame and in a nonreact-ing flow [19]. Thus nonequilibrium behavior is takeninto account in an approximate fashion for these vari-ables. However, the two-scalar approach has furtherlimitations that stem from the assumption of one-stepchemistry. This issue is most prominent in fuel-richregions where rich-side chemistry converts the par-ent fuel into intermediate species, which are not ac-counted for in a one-step reaction. In flames with asignificant likelihood of local extinction, one singlereaction step is a particularly poor approximation.These inherent errors in the two-scalar approach

can be reduced by measuring an intermediate speciesand constructing a conserved scalar from three mea-sured quantities. Carbon monoxide is a key intermedi-ate species that can be measured by two-photon LIF.A conserved scalar can be constructed from sensibleenthalpy, fuel and CO mass fractions by consideringthe two-step chemical mechanism for methane oxida-tion,

(2)CH4 + 32O2 = CO+ 2H2O+ Q1,(3)CO+ 12O2 = CO2 + Q2,

where Q1 and Q2 are the heat released per mole ofconsumed CH4 and CO, respectively. The expressionfor a new conserved scalar is derived from the Shvab–Zel’dovich formalism of coupling functions [27]. Thesimplified unsteady species conservation equation isL(Yi) = wi , where the operator L is given by L ≡ρ ∂∂t + ρv · ∇ − ∇ · (ρD∇), and wi is the rate ofproduction of species i by chemical reaction. By de-finition, a conserved scalar has no chemical sourceterm, and therefore L(β) = 0. The two-step mecha-nism in Eqs. (2) and (3) can be rewritten on a massbasis as

(4)CH4 + 3O2 = 74CO+94H2O+ q1,

(5)CO+ 47O2 =117 CO2 + q2,

where q1 and q2 are the heat released per unit massof consumed CH4 and CO, respectively. To derive aconserved scalar, we set β = Yfuel + aYCO + bcpT ,

J.H. Frank et al. / Combustion and Flame 143 (2005) 507–523 509

apply L(β) = 0 using Eqs. (4) and (5), and solve forthe coefficients a and b. From Eqs. (4) and (5),

L(β) = w1(−1+ 7/4a + bq1) + w2(−a + bq2)(6)= 0,

wherew1 andw2 are the rates for the first (4) and sec-ond (5) reaction steps, respectively. If the two termsin parentheses are set equal to zero, then the coeffi-cients a and b are independent of the reaction ratesfor the two reaction steps. The resulting coefficientsare a = q2/q and b = 1/q , and the conserved scalaris β = Yfuel + q2/qYCO + cpT /q . The three-scalarmixture fraction is given by

ξ3 scalar =β − β2β1 − β2

(7)= Yfuel + q2/qYCO + (cpT − cp,2T2)/q

Yfuel,1 + (cp,1T1 − cp,2T2)/q,

where q2/q = 0.20 according to the heat-release ratesfor the two-step mechanism. The mixture fraction,temperature, fuel, and CO mass fractions are deter-mined by an iterative routine that uses the Rayleighand the CO-LIF signals. Conversion of the CO-LIFsignal to CO mass fraction requires an estimate ofthe variations in Boltzmann fraction and quenchingrates. The variations in Boltzmann fraction are deter-mined from the temperature measurements, and thequenching rates are estimated from laminar flame cal-culations. In the present experiments, we found thatusing q2/q = 0.27 in the iterative algorithm for de-termining mixture fraction produced results that weremost consistent with detailed point measurements ofturbulent jet flames [6,24]. In the remainder of thispaper, we will refer to the measured mixture fractionsimply as ξ with the subscript “3 scalar” implied.

1.2. Considerations for mixture-fraction imaging

The fuel concentration is central to the reducedformulations of mixture fraction and has previouslybeen measured by LIF of fuel tracers [17], Ra-man scattering from the fuel [17–19,22], and differ-ence Rayleigh scattering [23,28]. Difference Rayleighscattering provides the most promising method forimaging the fuel concentration since fuel Ramansignals are comparatively weak, and LIF from fueltracers is plagued by pyrolysis of the tracer [17]. Indifference Rayleigh scattering, the polarized and de-polarized components of Rayleigh scattering from apolarized laser beam are simultaneously recorded onseparate detectors. Rayleigh scattering from isotropicmolecules, such as CH4, contains no measurable de-polarized component. In contrast, Rayleigh scatteringfrom anisotropic molecules, such as N2, O2, CO2,

H2O, H2, and CO, contains both depolarized and po-larized components. The methane concentration canbe related to the difference between the polarizedand depolarized Rayleigh signals when these signalsare normalized to their respective values in air. Toensure that the difference signal is not multivaluedwith respect to the methane concentration, a linear,or nonlinear, combination of the polarized and de-polarized signals can be used instead of the simpledifference [23,28].Fuel mixtures that have no depolarized compo-

nent provide optimal contrast between the differenceRayleigh signal in the fuel mixture and the air coflow.The use of anisotropic diluent gases, such as nitrogenand oxygen, in the fuel mixture decreases the dynamicrange of the difference Rayleigh signal. Partial pre-mixing of methane with air, however, produces morerobust flames and significantly reduces broadband flu-orescence interference from polycyclic aromatic hy-drocarbons. For partially premixed flames, the dy-namic range of the difference Rayleigh signal can besignificantly improved by replacing the nitrogen in airwith a noble gas, which has zero depolarization ratio.In the present study, we consider a fuel mixture thatis similar to the Sandia piloted methane/air jet flamesA–F in the Turbulent Nonpremixed Flame Workshop(TNF) [6,24] but has argon instead of nitrogen as theinert part of the diluent. The new fuel mixture hasthe same methane/diluent ratio (1/3 by volume) asthe original series of jet flames, but the dilution airis replaced by a mixture of argon and oxygen withthe same oxygen content as air. Flames with this newfuel mixture are designated “4Ar” flames to reflectthe argon/oxygen ratio (3.76/1 by volume). Pilotedjet flames with this fuel composition were previouslyused for combined Rayleigh/CH4-Raman/N2-Ramanimaging by Fielding et al. [22]. The argon-dilutedflames have a stoichiometric mixture fraction, ξst, of0.41, and the air-diluted flames have ξst = 0.35. Tomatch the air-dilution value of ξst with an argon–oxygen mixture would require an argon/oxygen ra-tio of 13/1. However, highly turbulent flames withthis diluent could not be stabilized on the piloted jetburner.The increase in air–fuel contrast that is provided

by argon dilution is demonstrated in Fig. 1 usingcalculated Rayleigh signals. The Rayleigh signals inFigs. 1a and 1b were computed from counterflow–flame calculations with air-diluted and argon/oxygen-diluted fuel mixtures, respectively [29,30]. The mix-ture fraction in these plots was determined froma linear combination of the hydrogen and carbonmass fractions [6]. The oxidizer stream containedroom-temperature air, and the global strain rate was200 s−1. The depolarization ratios for computingthe depolarized Rayleigh signals are from Fielding


Fig. 1. Predicted polarized and depolarized Rayleigh signalsare shown with CO and OH concentrations in air-diluted (a)and argon/oxygen-diluted (b) methane flames with a strainrate of 200 s−1.

et al. [28]. Fig. 1 includes plots of the CO and OHconcentrations that are normalized with respect totheir peak values. A previous study demonstrated thatdifference Rayleigh scattering can provide a measure-ment of fuel concentration in an air-diluted methanejet flame, and the result was used for determining themixture fraction via a three-scalar approach [23]. Inthe present analysis, emphasis was placed on optimiz-ing the signal-to-noise ratio of 2-D mixture-fractionmeasurements in flames with a relatively low proba-bility of local extinction. Consequently, the fuel con-centration was derived from the polarized Rayleighsignal, which had the largest signal-to-noise ratio ofall the measured scalars. A surrogate signal, S′fuel,for the fuel concentration was constructed by sub-tracting an offset from the polarized Rayleigh signaland normalizing with respect to the signal in thefuel stream (S′fuel = (SPol − SPolmin)/(SPol,fuel −SPolmin), where SPolmin is the minimum polarizedRayleigh signal). Fig. 2 shows a laminar flame cal-culation of the methane concentration and the pre-dicted fuel surrogate signal normalized to their re-spective values in the fuel stream. This calculationhas a global strain rate of 200 s−1. The variationsin SPolmin for strain rates between 100 and 600 s−1are within the noise of the measured Rayleigh sig-nal. On the rich side of ξst, the curves for S′fuel andthe normalized methane concentration show excel-lent overlap. The polarized Rayleigh signal, however,

Fig. 2. Comparison of predicted fuel concentration, NCH4 ,and surrogate fuel concentration, S′fuel, derived from the po-larized Rayleigh signal in an argon/oxygen-diluted methaneflame. The mask signal, Smask, eliminates the ambiguity ofthe multivalued Rayleigh signal.

is multivalued with respect to mixture fraction, andan additional measurement is needed to eliminate theambiguity between the rich and the lean regions ofthe flame. A linear or nonlinear combination of thepolarized and depolarized Rayleigh signals can beused to identify the rich and lean regions. This iden-tification is significantly enhanced by the increasedcontrast between the depolarized and the polarizedRayleigh signals that is afforded by the presence ofargon in the diluent. We used the linear combinationSmask = SPol − 2SDep + 0.077 to determine a masksignal, Smask, which was negative for lean conditionsand positive for rich conditions. This particular linearcombination did not scale with the fuel concentrationbut instead was chosen to provide a larger slope nearstoichiometric conditions to improve the sensitivity ofthe mask. A binary mask was created by thresholdingSmask at 0, and S′fuel was multiplied by the mask toeliminate the ambiguity. The increased contrast pro-vided greater certainty about the local presence orabsence of fuel. Alternative schemes for exploitingthis increased contrast to determine fuel concentra-tion and mixture fraction in flames with arbitrarydegrees of local extinction are under development.These approaches involve a more integrated use of allthe measured scalars but may result in larger noisecontributions to the measured scalar dissipation rates.In the present analysis, the surrogate for fuel concen-tration becomes less accurate in regions of localizedextinction.The experimental methods are described below

followed by a presentation of results using the three-scalar technique for determining mixture fractionin argon/oxygen-diluted laminar and turbulent jetflames. Mixture-fraction images are used to determinethe axial and radial components of the scalar dissipa-tion rate in a turbulent partially premixed methane


jet flame. Images of mixture fraction, scalar dissipa-tion, temperature, and the forward reaction rate forthe reaction CO+OH= CO2+H are presented. Thereaction rate is determined from the OH-LIF and two-photon CO-LIF signals, whose excitation–detectionscheme is chosen such that the pixel-by-pixel prod-uct is proportional to the forward rate of the reactionCO+OH= CO2+H over the relevant range of mix-ture fractions [23,31]. We estimate the noise contribu-tion to scalar dissipation measurements in a laminarflame and use these results to provide a first-ordernoise correction for scalar dissipation measurementsin a turbulent flame. Conditional means of reactionrate and temperature are presented as a function ofscalar dissipation rate.

2. Experimental methods

2.1. Laser and detector arrangement

The experiments were performed in the AdvancedImaging Laboratory at Sandia National Laborato-ries. Single-shot images of polarized and depolarizedRayleigh scattering, two-photon CO-LIF, and single-photon OH-LIF were simultaneously collected. Theexperimental facility was similar to that used by Franket al. [23] and Fielding et al. [28], and is shownschematically in Fig. 3. The beams from five lasersat three wavelengths were combined and focusedinto a sheet by a fused-silica cylindrical lens (f.l. =500 mm). Sequential timing of the lasers and detec-tors eliminated the possibility of crosstalk betweenthe diagnostics. For the Rayleigh measurements, theoutputs of two frequency-doubled Nd:YAG lasers at532 nm were combined by stacking the beams on topof each other at a location 15 m away from the testsection. The beams propagated at slightly differentangles with respect to the horizontal and merged intoa single sheet in the test section. Typical combinedenergies were approximately 1.7 J/shot. Two-photonCO-LIF was excited by pumping overlapped tran-sitions in the B–X(0,0) bandhead of the Hopfield–Birge system at 230.1 nm. The frequency-doubledoutputs of two Nd:YAG-pumped optical parametricoscillators (OPO) were combined to a typical com-bined energy of 30–35 mJ/shot at 230.1 nm. TheOH-LIF was excited at 285 nm using a frequency-doubled, Nd:YAG-pumped dye laser that was tunedto the Q(12) transition of the A–X(1,0) band. The285-nm beam was combined with the 230-nm beamsby using a dichroic mirror that reflected 230 nm andpartially transmitted 285 nm. The associated energyloss in the 285-nm beam was inconsequential becauseonly a small fraction (0.3 mJ/shot) of the output of

the dye laser was used to excite OH-LIF. The over-lap of the sheets and each sheet’s intensity profilewere checked and documented for each experimentby inserting a beam-splitting wedge after the sheet-forming lens and recording the profiles at various dis-tances from the lens. The overall sheet thickness wasapproximately 200 µm in the center of the imaged re-gion and 250 µm at the edges.Rayleigh scattering from the probe volume was

imaged onto an unintensified interline-transfer cam-era (640 × 512 pixels after 2 × 2 binning) by acommercial camera lens (f/1.2, f.l. = 50 mm) cou-pled with a 500-mm achromatic close-up lens. The600-ns exposure time of the Rayleigh camera sup-pressed luminous background radiation. On the op-posite side of the burner, the depolarized componentof the Rayleigh scattering was isolated by a commer-cial photographic polarizer and a high-throughput in-terference filter (λc = 532 nm, (λFWHM = 10 nm,τmax = 87%) and imaged onto an ICCD camera(512 × 512 pixels, GenIII intensifier) with a cameralens (f/1.2, f.l. = 85 mm) coupled with a 500-mmachromatic close-up lens. The depolarized and polar-ized Rayleigh images were corrected for shot-to-shotfluctuations in the laser beam profiles. For this pur-pose, the Nd:YAG beam profiles were recorded foreach shot by including a region of ambient air in thepolarized Rayleigh image. On the same side as thepolarized Rayleigh camera, the OH-LIF signal fromthe A–X(0,0) and (1,1) bands was reflected by adichroic mirror and imaged onto an ICCD camera(512× 512, GenII) through suitable color glass filters(UG-11 andWG-295) using a UV-camera lens (Cerco45 mm, f/1.8) with a 500-mm close-up lens. Theaverage beam profile of the dye laser and the through-put of the imaging optics were measured by recordingfluorescence from acetone that was uniformly seededinto an air flow.The CO fluorescence from the B–A(0,1) band

was detected at 483.5 nm on the same side as thedepolarized Rayleigh detection. The CO-LIF signalwas separated from the depolarized Rayleigh scat-tering by a dichroic mirror and was imaged onto anICCD camera (512 × 512, GenII) by a commercialcamera lens (f/1.2, f.l. = 85 mm + 500-mm achro-matic close-up lens) with a partially blocked inter-ference filter (λc = 484 nm, (λFWHM = 10 nm) tominimize out-of-band interference. Two-photon CO-LIF is particularly sensitive to variations in the laserbeam profile because the LIF signal has a nonlineardependence on laser intensity. The average variationsin the OPO laser-sheet intensity were corrected usingCO-LIF measurements from a uniform cold flow ofdilute CO in N2 and from the exhaust-gas region of apremixed flat-flame burner. To correct for shot-to-shotfluctuations, Rayleigh scattering from the combined


Fig. 3. Experimental configuration for multiscalar imaging measurements. Simultaneous 2-D measurements of depolarized andpolarized Rayleigh scattering are combined with OH-LIF and two-photon CO-LIF.

230-nm beams was measured in the air coflow with afifth ICCD camera (512× 512, GenII).This multiscalar imaging facility was modified

from previous studies to improve the measurements.The availability of higher energy lasers for Rayleighscattering and optimized detection optics improvedthe signal-to-noise ratio (SNR) of the depolarizedRayleigh signal from 10 to 33 in air. The SNR ofthe polarized Rayleigh signal in air was 70. Theeffects of beam steering were significantly reducedby eliminating a retro-reflector and using a singlepass of the Rayleigh laser beam. The SNR for theCO-LIF signal was increased from 15 to 23 by im-proved detection and higher sheet energy. The spa-tial resolution of the measurements was enhancedby more closely matching the area projected ontoeach of the detectors. The use of commercial close-up lenses on the Rayleigh, depolarized Rayleigh,and CO-LIF detectors was found to measurably in-crease the contrast in those images. This enhancedcontrast was most evident for the Rayleigh channel,which used an unintensified camera. Finally, the over-lapping and characterization of the laser sheets wasimproved through extensive profiling during align-ment.

2.2. Flow conditions

The flow facility, which is identical to that ofRefs. [23,28], included a piloted burner that was

developed at Sydney University. A set of well-doc-umented point measurements for methane/air jetflames in this burner is available via the TNF Work-shop [6,24]. The burner consisted of a 7.2-mm-diameter jet and a 18.2-mm-diameter pilot surroundedby a coflow of filtered air with a mean velocity of0.9 m/s. For the air-diluted flames, the jet and pi-lot flows were identical to those in Ref. [6]. For theargon-diluted flames, the lean premixed pilot flameburned a mixture of C2H2, H2, O2, CO2, N2, andAr having the same equilibrium composition and en-thalpy as a premixed mixture of the methane/argon/oxygen fuel mixed with air at an equivalence ratioof 0.68. The argon-diluted flames, Flame A4Ar andD4Ar, had the same flow rates as their air-dilutedcounterparts, namely the nonpiloted laminar Flame A(Re = 1100) and the turbulent, piloted Flame D (Re= 22,400). Both Flame D and D4Ar have a rela-tively low probability of extinction. Argon has a lowerspecific heat than nitrogen, resulting in higher flametemperatures, and the difference in the stoichiomet-ric mixture fraction (ξst,air = 0.35, ξst,4Ar = 0.41)shifts the stoichiometric contour slightly closer tothe jet axis. A series of 150 images was acquired forFlames D and D4Ar at axial locations of x/d = 7.5and 15. In the laminar Flames A and A4Ar, 50-shotdatasets were recorded at a height above burner ofx/d = 5.


2.3. Interferences, image registration, and beamsteering

To correct the Rayleigh signals for backgroundscattering and crosstalk between the polarized and de-polarized signals, images were taken with the field ofview flooded by argon, helium, and nitrogen. In thedetection of the depolarized Rayleigh signal, a por-tion of the much stronger polarized Rayleigh com-ponent “leaked” into this channel. The correspond-ing crosstalk factor λ was quantified as described inFielding et al. [28], and the depolarized images werecorrected by subtracting the pixel-by-pixel productof λ and the polarized Rayleigh signal. The cameraused for polarized Rayleigh imaging captured a smallamount of interference from flame luminosity, dueto the limited extinction ratio in the masked regionof the interline-transfer CCD chip. It was possible toaccount for this effect by subtracting an average lu-minosity image, which was acquired with the gateshifted off the 532-nm laser pulses. Interference fromPAH-LIF excited at 532 nm was negligible.Images from the four scalar channels were reg-

istered by imaging a transparent random-dot target,which allowed for checking the mismatch at subpixelresolution using routines from cross-correlation parti-cle image velocimetry (PIV), and then adjusting theregistration parameters accordingly. The maximumresidual mismatch as determined from the target shotswas 2 pixels, occurring in a region near the edge ofthe images. This region corresponded to pure air inalmost all of the shots. The average mismatch towardthe center of the images, where the highest scalar gra-dients are to be expected, was in the subpixel range.Based on the vectors obtained from random-dot PIV,bilinear warping [23] could be employed for furtherimprovement, but this was deemed unnecessary inthe current data set. Images from the beam-profilingRayleigh channel at 230 nm were vertically registeredwith the CO-LIF images. This was accomplished byinserting an array of thin wires into the beam, cre-ating a suitable intensity pattern in both the 230-nmRayleigh images and the CO-LIF signal from a uni-form flow of nitrogen-diluted CO.Beam steering due to index-of-refraction gradients

is a potential problem for laser measurements in tur-bulent flames. The effects of such beam steering pro-duced stripes in the Rayleigh images. These stripescould not be corrected using a single beam profileacross the entire imaged region because the stripeswere inherently not parallel. However, correctionsfor beam steering were possible with a ray-tracingmethod, which was based on using the Rayleigh im-ages as an approximate measure of the index-of-refraction field [32]. This ray-tracing technique wasapplied to the polarized and depolarized Rayleigh im-

ages. The effects of beam steering on the scalar sta-tistics presented below were further reduced by onlyconsidering data from the side of the flame closestto the lasers and thereby avoiding the region of theworst beam steering. Consequently, the statistical re-sults presented here were not significantly affected bythe beam-steering correction. The ray-tracing tech-nique was also used to estimate the effects of beamsteering on the scattered light as it traversed the re-gion of the flame between the probe volume and thecollection optics. The results indicated that the spreadof rays in the image plane was on the subpixel scaleand was therefore negligible [32].

3. Results and discussion

3.1. Imaging results from turbulent flames

We first consider a comparison of measurementsin the air-diluted and argon/oxygen-diluted turbulentflames. Fig. 4 shows an example of simultaneoussingle-shot measurements of polarized and depolar-ized Rayleigh scattering as well as CO-LIF and OH-LIF signals in Flame D. The imaged region is centered15 diameters downstream of the nozzle exit and spans4 diameters in the radial direction. The images in thefigure have not been smoothed, and the LIF signalshave not been corrected for variations in quenchingrates or Boltzmann-fraction population. The superiorsignal-to-noise ratio of the polarized Rayleigh imageis apparent. Near the jet centerline, Rayleigh scatter-ing from the low-temperature fuel/air mixture pro-duces a significant signal on the depolarized Rayleighchannel because of the premixing with air. In contrast,images from Flame D4Ar in Fig. 5 show a signifi-cantly reduced depolarized Rayleigh signal on the jetcenterline due to the substitution of argon for nitro-gen. According to the predicted signals in Fig. 1, thedifference between the polarized and the depolarizedRayleigh signals in the fuel mixture is a factor of 1.7greater for the argon/oxygen-diluted fuel mixture thanfor the air-diluted fuel. This improved contrast signif-icantly enhances the ability to identify the rich andlean regions of the flame.Fig. 6 shows the mixture-fraction, temperature,

and reaction-rate measurements that were deter-mined from the four images in Fig. 5. The mixture-fraction and temperature images were smoothed witha Gaussian smoothing kernel (σ = 0.57 pixels). Thissmoothing is advantageous for determining scalar dis-sipation rates and will be discussed in Section 3.2.The largest mixture-fraction gradients are observedin the fuel-rich region and are indicative of highscalar dissipation rates. The sensitivity of the polar-ized Rayleigh signal to changes in mixture fraction


Fig. 4. Sample images of the four measured scalars forFlame D at x/d = 15. The Rayleigh signals are normal-ized by the corresponding values in air. The LIF signalsare not corrected for variations in quenching rates or Boltz-mann-fraction population.

Fig. 5. Sample images for Flame D4Ar at x/d = 15. Colorscales are the same as in Fig. 4.

is apparent. Near the jet centerline, the polarizedRayleigh image in Fig. 5 shows a pocket with sig-nificantly decreased signal where hot gases are en-trained into the fuel mixture (indicated by arrow inthe figure). The corresponding region in the mixture-fraction image of Fig. 6, however, exhibits a relativelymodest decrease in mixture fraction. This sensitivityof the polarized Rayleigh signal is evident from thecalculations in Fig. 1b. As the mixture fraction variesfrom 1.0 to 0.8, the predicted polarized Rayleigh sig-nal decreases by 70%. Similarly, for the lean side, thepolarized Rayleigh signal decreases by 78% as themixture fraction changes from 0 to 0.2. This lean-sidesensitivity can be seen by comparing the significant

Fig. 6. Single-shot measurements of mixture fraction, tem-perature, and reaction rate in Flame D4Ar at x/d = 15.

change in Rayleigh signal with the modest variationin mixture fraction at the interface between the hotgases and the surrounding air stream on the left-handside of the images, where large-scale structures en-train air. In the high-temperature regions of the flame,the sensitivity of the Rayleigh signal to mixture frac-tion decreases. To determine mixture fraction in theseregions, it is essential to optimize the signal-to-noiseratio of the Rayleigh measurements, and it is advan-tageous to have simultaneous CO-LIF measurements.The CO-LIF signal spans a large portion of the

rich region with a packet of CO penetrating into thelow-temperature rich region near the jet axis (indi-cated by arrow in Fig. 5). The reaction-rate imageis determined from the pixel-by-pixel product of theCO-LIF and OH-LIF signals without requiring anycorrection for the variation in the quenching rates andBoltzmann-fraction population. In Fig. 6, the regionof appreciable reaction rate spans a relatively broadhigh-temperature zone and has a width of approxi-mately 3.8 mm at the bottom of the image. In Sec-tion 3.3, the reaction-rate images are used to evaluatecorrelations between reaction rate and scalar dissipa-tion rate.To appreciate the spatial structures in the turbulent

flame, we consider a selection of temperature, scalardissipation, and reaction-rate images at x/d = 7.5 and15 in Figs. 7 and 8, respectively. The scalar dissi-pation was determined from the mixture-fraction im-ages by χ = 2D((∂ξ/∂r)2 + (∂ξ/∂x)2). The imagesin each figure were selected from the full datasetsby sampling every 10th image from the first 100shots. The images were cropped to a 15.1× 5.7-mmsubregion and expanded to better show the detailedflame structures. The right side of each image co-incides with the jet centerline. Contours of mixturefraction were superimposed onto each of the imagesin Figs. 7 and 8. The mixture-fraction and tempera-ture images were smoothed with a Gaussian smooth-ing kernel (σ = 0.57 pixels) before evaluating the


Fig. 7. Single-shot measurements of temperature, scalar dissipation, and reaction rate in Flame D4Ar at x/d = 7.5. The superim-posed contours of mixture fraction indicate ξ = 0.21 (blue), 0.41= ξst (red), 0.61 (white). Image dimensions are 15.1×5.7 mm,and the jet axis is located at the right edge of each image.

scalar dissipation rate, and the same smoothing wasapplied to the reaction-rate images. The scalar dissi-pation rate was determined using fourth-order centraldifferencing to calculate the radial and axial compo-nents of the mixture-fraction gradient. The diffusiv-ity, D, was determined from the temperature imagesusing the following fit to the mixture-averaged diffu-sivity in a counterflow flame calculation with a strainrate of 200 s−1:D = −0.04992+ 0.4939(T /1000)+

1.2539(T /1000)2 (cm2/s). This expression providesa reasonable approximation to the mixture-averageddiffusivity which predominantly depends on tempera-ture. Laminar flame calculations for a range of strainrates indicate that the temperature dependence of thediffusivity is relatively insensitive to the strain rate.We first consider some general observations from

the measurements at x/d = 7.5 shown in Fig. 7. Theregions of high scalar dissipation rate occur in thin


Fig. 8. Single-shot measurements of temperature, scalar dissipation, and reaction rate in Flame D4Ar at x/d = 15. The superim-posed contours of mixture fraction indicate ξ = 0.21 (blue), 0.41= ξst (red), 0.61 (white). Image dimensions are 15.1×5.7 mm,and the jet axis is located at the right edge of each image.

filaments that are frequently aligned with the richmixture-fraction contours. The instantaneous reactionzones are relatively closely aligned with the jet axis,and the peak reaction rates occur slightly to the richside of the stoichiometric contours. In cases where thereaction zone is more convoluted (shots 1, 4, 5, 7, 8,10), the rich mixture-fraction contour is considerablymore distorted than the lean or stoichiometric con-tours, and in some cases the rich contour extends to-

ward the jet axis well beyond the edge of the reactionzone (shots 1, 4, 5, 8, 10). There is a very low prob-ability of localized extinction at x/d = 7.5, as is evi-dent by the continuity of the reaction zones in Fig. 7.However, there are cases where the reaction rate andtemperature are locally depressed or the reaction zoneis thinner (shots 2, 4, 7, 8). These locations frequentlycorrespond to regions where the rich and stoichio-metric mixture-fraction contours are closer together,


and the filaments of high scalar dissipation rate aremore likely to overlap with the stoichiometric con-tour. When there is a local decrease in the temperaturenear stoichiometric conditions, we expect that the fuelconcentration will be overestimated by the surrogatefuel signal. This overestimate will artificially increasethe measured mixture fraction at stoichiometric andslightly rich conditions. However, the reaction rateand temperature measurements are expected to re-main relatively accurate.The images in Fig. 8 show that the reaction zones

are considerably more convoluted at x/d = 15, andthe discontinuities in the reaction zones indicate re-gions of localized extinction. These results are consis-tent with point measurements that show an increasedprobability of extinction at the “neck” of the pilotedjet flames near x/d = 15 for jet flames with a rangeof Reynolds numbers [6]. The thickness of the re-action zones spans a wider range at x/d = 15 thanat x/d = 7.5. The relatively wide reaction zones ob-served in several of the reaction-rate images may inpart be the result of larger angles between the flamenormal and the plane of the laser sheet (shots 1, 2,3, 5). The filaments of high scalar dissipation are in-clined at a steeper angle with respect to the jet axisthan at x/d = 7.5. The thin and extinguished reactionzones show the same trend as in Fig. 7, such that atthese locations the filaments of high scalar dissipationtend to overlap the stoichiometric contour (shots 3,4, 6, 7, 8, 10). The increased probability of thesehigh-dissipation zones overlapping the stoichiometriccontour at x/d = 15 is likely to contribute to differ-ences in the conditional mean of scalar dissipation atx/d = 7.5 and 15. As will be seen in Section 3.3, thedecrease in the rich peak of the scalar dissipation ismuch more significant than the decrease in the peaknear stoichiometric conditions. This difference couldin part be explained by an increased occurrence of theoverlap between the scalar dissipation filaments andthe stoichiometric contour.Several shots at x/d = 15 show a substantial

gap between the reaction zone and the lean mixture-fraction contour (shots 5, 7, 8, 9). The images inshot 10 of Fig. 8 are particularly notable since theycapture the pinch-off of a fuel-rich pocket as tworeaction zones come in close proximity. The lowerleft face of the pocket is aligned with a filament ofhigh scalar dissipation with the rich and stoichiomet-ric contours close together. This region also exhibitsa depressed temperature and reaction rate. These ob-servations represent an initial sampling of the in-terrelationship between the mixture fraction, scalardissipation, reaction rate, and temperature fields thatresult from flow–flame interactions in turbulent jetflames.

Fig. 9. Conditional scalar dissipation rates in Flame D4Ar atx/d = 15 (a) and 7.5 (b) evaluated from mixture-fractionand temperature images that are smoothed by symmetricGaussian kernels with different widths.

3.2. Noise and resolution

The measurement of scalar dissipation is particu-larly sensitive to noise in the mixture-fraction imagesbecause the scalar dissipation is proportional to thesquare of the mixture-fraction gradient. Smoothingcan reduce the noise at the expense of spatial reso-lution. We consider the tradeoff between noise reduc-tion and spatial averaging in conditional mean scalardissipation measurements from 150 shots at two axiallocations in Flame D4Ar. The results of smoothingwith Gaussian kernels having σ = 0.57, 1.14, 2.28pixels are shown in Fig. 9 for x/d = 7.5 and 15.The differences in the magnitude and the shape ofthe scalar dissipation plots result from the combinedeffects of noise reduction and spatial averaging. Asthe width of the smoothing kernel is increased, thenoise contribution to the scalar dissipation decreases.Spatial averaging is significant when the resolution istoo coarse to accurately sample the mixture-fractiongradients. To demonstrate the effects of spatial aver-aging, we applied the Gaussian smoothing kernels to1-D laminar counterflow flame calculations [29] withthe same CH4/O2/Ar fuel-stream mixture as the ex-periments. While there are limitations to the compari-son between laminar flame calculations and turbulentjet flames, it is instructive to consider the effects of


Fig. 10. Laminar flame calculations with the CH4/O2/Ar fuel mixture show the effects of spatial averaging on scalar dissipationmeasurements in flames with strain rates of 30, 200, 700, and 1300 s−1. The spatial averaging is varied by smoothing withGaussian kernels having σ = 0.57, 1.14, and 2.28 pixels.

spatial averaging on a laminar flamelet as the strainrate is increased. The original and smoothed resultsare shown in Fig. 10 for four strain rates ranging from30 to 1300 s−1. The spacing between the symbolsin the plot corresponds to the 58-µm pixel spacingin the experiments. At the two lower strain rates, thespatial scales are well resolved, and smoothing has anegligible impact on the scalar dissipation, with theexception of a minor deviation occurring at a strainrate of 200 s−1 and a kernel with σ = 2.28 pixels. Atthe two larger strain rates, smoothing with the largestkernel further reduces the peak scalar dissipation andeliminates the trough near stoichiometric conditions.The results for the narrowest kernel (σ = 0.57 pix-els) indicate that smoothing has minor effects even atstrain rates of 1300 s−1. The width of this smooth-ing kernel is comparable to the width of the measured

line spread function for the polarized Rayleigh imag-ing system.The noise contribution in the scalar dissipation

measurements after Gaussian smoothing with a ker-nel of σ = 0.57 pixels can be estimated by consid-ering a laminar flame in which one component ofthe mixture-fraction gradient is negligible. Fig. 11shows single-shot Gaussian-smoothed measurementsof mixture fraction, temperature, and scalar dissipa-tion rate at x/d = 5 in Flame A4Ar. Over the im-aged area, the average mixture-fraction gradient in theaxial direction is negligible. Consequently, the axialcomponent of the scalar dissipation determined froman average mixture-fraction image, 2D(∂〈ξ〉/∂x)2,is approximately zero. However, the measured ax-ial component of scalar dissipation in a single-shotmeasurement is nonzero because it is dominated by


Fig. 11. Single-shot measurements of mixture fraction,temperature, and scalar dissipation from Flame A4Ar atx/d = 5.

the noise in the mixture-fraction and temperature im-ages. The conditional mean noise contribution to thescalar dissipation measurements can be determinedin the laminar flame by 〈χnoisex |ξ〉 = 2D(∂ξ/∂x)2.Fig. 12 shows the conditionally averaged axial andradial components of the scalar dissipation, whichwere evaluated from a series of 50 shots in FlameA4Ar. The slight “shoulder” around ξ = 0.15 (indi-cated by the arrow) is attributable to a minor lean-sideartifact introduced in the calculation of mixture frac-tion. The mean radial component of scalar dissipation,〈χmeasr |ξ〉 = 2D(∂ξ/∂r)2, is the sum of the actualscalar dissipation and the noise contribution, χnoiser .In principle, if the conditional mean noise con-

tribution, 〈χnoiser |ξ〉, is known, then it can be sub-tracted from 〈χmeasr |ξ〉 to obtain an improved mea-surement of the conditional mean scalar dissipation.If the noise statistics are comparable in the axial andradial directions, then 〈χnoiser |ξ〉 = 〈χnoisex |ξ〉, andthe corrected mean scalar dissipation can be deter-mined by 〈χcorrr |ξ〉 = 〈χmeasr |ξ〉 − 〈χnoisex |ξ〉. Thisnoise-corrected scalar dissipation is shown by the dot-ted curve in Fig. 12. To verify the validity of thiscorrection in the laminar flame, we compared thenoise-corrected scalar dissipation with the scalar dis-sipation obtained from a mixture-fraction image thatwas smoothed to the point of having negligible noise,〈χ smo|ξ〉. This more extensive smoothing was per-formed using an elliptical Gaussian kernel (σr = 1.7pixels, σx = 10 pixels), which preserved the radialgradients while significantly reducing the noise. Thepreservation of the gradients was verified by com-paring radial profiles of mixture fraction from thesmoothed and unsmoothed images. In Fig. 12, theexcellent agreement between 〈χcorrr |ξ〉 and 〈χ smo|ξ〉indicates that the noise correction works quite well inFlame A4Ar.In turbulent flames, we performed a similar cor-

rection to the scalar dissipation using the laminar

Fig. 12. Conditional means of radial and axial componentsof scalar dissipation in laminar Flame A4Ar at x/d = 5 af-ter smoothing the mixture-fraction and temperature imagesby a symmetric Gaussian kernel (σr = σx = 0.57 pixels).The axial component represents the noise contribution. Thedifference between the radial and axial components (dottedline) is the noise-corrected scalar dissipation. The solid lineis the best estimate of the true scalar dissipation based onsmoothing with an elliptical Gaussian kernel (σr = 1.7 pix-els, σx = 10 pixels).

flame results as a first-order estimate of the noisecontribution to the scalar dissipation. The total noisecontribution to the scalar dissipation, χnoise, is thesum of the axial and radial contributions, χnoise =χnoisex +χnoiser . If the noise statistics of scalar dissipa-tion are comparable in the axial and radial directions,then the total noise can be estimated as twice the axialnoise contribution, and the noise-corrected scalar dis-sipation is given by χcorr = χmeas − 2χnoisex , whereχnoisex is determined from Flame A4Ar. This first-order estimate of the noise contribution to the scalardissipation assumes that χnoise is only dependent onmixture fraction. Higher order corrections that wouldaccount for variations in χnoise as a function of χ arecurrently under investigation.Fig. 13 shows the measured and noise-corrected

conditional scalar dissipation at x/d = 7.5 and 15.The slight dip in the noise-corrected dissipation atξ = 0.15, which also will be discernible in someof the subsequent figures, is caused by the artifactthat was discussed for Fig. 12. At both downstreamlocations, the measured scalar dissipation exhibitspeaks at lean and rich conditions. The noise correc-tion slightly shifts the lean peak toward the stoichio-metric mixture fraction. For the rich peaks, the noisecorrection is 16 and 24% of the scalar dissipationmeasured at x/d = 7.5 and 15, respectively. Fromx/d = 7.5 to 15, the noise-corrected rich scalar dis-sipation peak decreases by 43%, and the lean peakdecreases by 25%. The magnitude, shape, and axialprogression of the scalar dissipation plots agree wellwith line measurements in Flame D [11]. The line


Fig. 13. Measured and noise-corrected conditional meanscalar dissipation rates in Flame D4Ar at x/d = 15 (a) and7.5 (b) with Gaussian smoothing (σ = 0.57 pixels) of themixture-fraction images.

measurements, however, show a single peak in thescalar dissipation on the rich side and a plateau, orshoulder, near stoichiometric conditions. These dif-ferences may result from a combination of factors,including a lower spatial resolution in the line mea-surements, the substitution of Ar for N2 in flamesconsidered here, and the different definitions of mix-ture fraction.The ability to subtract the noise contribution from

the measured scalar dissipation rates makes it possi-ble to isolate the effects of spatial averaging in theturbulent flame data. The spatial resolution was artifi-cially reduced by sampling the unsmoothed mixture-fraction and temperature images with a coarser pixelspacing, and the resulting scalar dissipation rates werecorrected for the noise contribution at the respec-tive resolution. Fig. 14 compares the noise-correctedscalar dissipation rates using the native pixel spacingas well as every second and fourth pixel, correspond-ing to pixel spacings of 58, 116, and 232 µm, re-spectively. In general, degrading the resolution yieldsa decrease in the peaks of the scalar dissipation,which is consistent with the results of the laminarflame calculations shown in Fig. 10 and discussedabove. The local minimum in the scalar dissipationbecomes less prominent as the resolution is degraded.At x/d = 7.5 the trough in the scalar dissipation

Fig. 14. Noise-corrected conditional mean of scalar dissi-pation determined from unsmoothed mixture-fraction andtemperature images with the pixel spacing increased to 116and 232 µm by sampling every second and fourth pixel, re-spectively. Data are from x/d = 15 (a) and 7.5 (b).

plot is eliminated at a resolution of 232 µm. How-ever, at x/d = 7.5, the dissipation values near therich peak are lower at the native pixel spacing thanthey are with 116-µm spacing, indicating the limita-tions of this noise correction scheme for high lev-els of noise. For the rich peak in scalar dissipa-tion, the noise correction with the native pixel spac-ing is 〈χnoisex |ξ〉 = 57 s−1, which is approximately30% of the uncorrected scalar dissipation. For re-duced resolutions, the noise correction decreases asthe inverse square of the pixel spacing. A compari-son of Figs. 13 and 14 indicates good agreement be-tween the noise-corrected scalar dissipation rates withGaussian smoothing (σ = 0.57 pixels) and 116-µmsampling. Further smoothing is likely to eliminatefeatures that contribute to the local minimum in scalardissipation near ξ = 0.5, which is slightly on therich side of the peak reaction rate for CO + OH.These results suggest that Gaussian smoothing withσ = 0.57 pixels is a reasonable compromise betweenretaining the best resolution possible and suppressingnoise.In general, the appropriate degree of smoothing

will depend on the spatial scales present within theflame and will vary with axial location. The Batche-lor scale, λB, is commonly used as an estimate for the


resolution requirements. In the self-similar region ofjet flows that are dominated by mixing, the Batchelorscale can be evaluated as λB = CδRe−3/4 Sc−1/2,where Re and Sc are the Reynolds and Schmidt num-bers, respectively, and C is an empirical constant thatdepends on the flow configuration and the defini-tion of the characteristic velocity and length scale, δ.While this expression may be applicable in the farfield of a reacting jet where the flow is dominated bymixing, the determination of λB is ambiguous in thenear field of a jet flame where reactions affect the flowscales. Estimates of λB in Flame D at x/d = 15 us-ing single-point measurements of the temperature andmajor species [6] span an order of magnitude whenC = 1–2 and the temperature that is used for deter-mining the flow properties is varied between the jetcenterline value and the maximum in the mean radialprofile. This uncertainty indicates that alternative ap-proaches to determining resolution requirements areneeded.A unique aspect of 2-D scalar dissipation measure-

ments is the ability to examine the contribution of twodifferent components of scalar dissipation. The noise-correction technique can be applied separately to theconditional mean of the axial and radial componentsof scalar dissipation in the turbulent flame. Figs. 15aand 15b compare the axial and radial components ofscalar dissipation at two downstream locations. Eachcomponent has been corrected for the conditionalmean noise contribution by subtracting 〈χnoisex |ξ〉,which was determined from Flame A4Ar, as previ-ously described. The scalar dissipation is dominatedby the radial component. At the rich peak, the radialcomponent is a factor of 4.0 and 2.9 greater than theaxial component for x/d = 7.5 and 15, respectively.From x/d = 7.5 to 15, the radial and axial compo-nents of the rich peak decrease by 50 and 33%, re-spectively. In principle, the imaging data could alsobe used to determine the projection of the axial andradial components of ∇ξ onto the flame-normal co-ordinates, where the local flame normal is specifiedfrom the mixture-fraction contours.

3.3. Reaction rate and temperature vs scalardissipation

Turbulent diffusion flame theory predicts the scal-ing of reaction rate with scalar dissipation rate, thusrelating the reaction rate to the molecular mixingrates [33]. It is therefore of great interest to measurereaction-rate statistics conditioned on scalar dissipa-tion rate and mixture fraction. The results of the imag-ing measurements can provide such statistics. As anexample, the conditional means of temperature andreaction rate as a function of scalar dissipation rate areshown in Figs. 16a and 16b, respectively. The results

Fig. 15. Noise-corrected conditional mean of axial and ra-dial components of scalar dissipation at x/d = 15 (a) and7.5 (b) with Gaussian smoothing (σ = 0.57 pixels) of themixture-fraction images.

are doubly conditioned on scalar dissipation rate anda mixture-fraction interval of 0.4 < ξ < 0.5, whichapproximately corresponds to the region of peak re-action rate for the CO + OH reaction. The con-ditional mean temperature monotonically decreaseswith increasing scalar dissipation rate. The reactionrate shows a slight increase at low scalar dissipationrates and then decays for χ > 100 s−1. At the highestscalar dissipation rates, the depressed temperaturesand reaction rates are the result of an increased prob-ability of localized extinction. The images in Figs. 7and 8, which were described in Section 3.1, show thetypes of flame structures that contribute to localizeddecreases in reaction rate and temperature.Fig. 16 includes results from a set of laminar

flame calculations with strain rates ranging from 50to 1370 s−1 in increments of 10 s−1. At each strainrate, the temperature, reaction rate, and scalar dissi-pation rate were averaged over the mixture-fractioninterval of 0.4< ξ < 0.5. The reaction rate was com-puted by k(T )[OH][CO], where the rate constant,k(T ), was specified by Gri-Mech 3.0 [30]. The lami-nar flame calculations indicate trends similar to thoseof the measurements for both the temperature and thereaction rate. Detailed agreement between the calcu-lations and measurements is not expected since the


Fig. 16. Conditional mean and standard deviation of tem-perature (a) and reaction rate (b) at x/d = 15 and 7.5. Thevalues are doubly conditioned on scalar dissipation rate andthe mixture-fraction interval of 0.4–0.5.

calculations do not capture unsteady effects, such asextinction or ignition.The reaction CO+OH= CO2 +H is the primary

pathway for CO2 production in CH4/air flames, andthe reaction-rate results presented here indicate thebehavior of only one portion of the full reaction mech-anism. In the future, it would be interesting to com-pare reaction rates from different parts of the reactionmechanism. For example, the addition of formalde-hyde LIF coupled with OH-LIF imaging could pro-vide a measure of a reaction rate that may be moreclosely correlated with the local heat release rates[34,35].

4. Conclusions

Multiscalar imaging of depolarized and polarizedRayleigh scattering combined with OH-LIF and two-photon CO-LIF provided simultaneous measurementsof temperature, mixture fraction, scalar dissipationrate, and the forward reaction rate of the reactionCO + OH = CO2 + H. The technique was demon-strated in a partially premixed turbulent jet flame witha CH4/O2/Ar fuel-stream mixture. The flame consid-ered here (Flame D4Ar) had the same fuel/diluent ra-tio (1/3 by vol) and jet velocity as the air-diluted San-dia Flame D investigated by Barlow and Frank [6].

In the modified fuel mixture, the N2 from air wasreplaced with Ar to enhance the contrast of the de-polarized and polarized Rayleigh signals between thefuel and air streams. The enhanced contrast facilitatedthe identification of the rich and lean regions of theflame, which improved the mixture-fraction measure-ments.The mixture fraction was determined by a three-

scalar formulation using the depolarized and polar-ized Rayleigh signals combined with the CO-LIFsignal. The emphasis here was on providing mea-surements of mixture fraction and its gradient withimproved signal-to-noise ratios compared to previ-ous experiments [23]. The radial and axial compo-nents of the scalar dissipation were determined fromthe mixture-fraction images. Analysis of the tradeoffbetween noise reduction and spatial averaging withimage smoothing showed that a Gaussian smooth-ing kernel (σ = 0.57 pixels) significantly reduced thenoise contribution to the scalar dissipation measure-ments and that more significant smoothing eliminateddetails in the conditional mean of scalar dissipationrate at x/d = 7.5. The noise contribution to the scalardissipation measurements was evaluated in a steadylaminar flame (Flame A4Ar), and the results wereused to perform a first-order correction for the noisecontribution in a turbulent flame.A collection of instantaneous 2-D measurements

of mixture fraction, temperature, scalar dissipationrate, and reaction rate was presented. The regions ofhigh scalar dissipation rate were confined to thin fil-aments. At x/d = 7.5, these filaments were primarilyaligned with a rich mixture-fraction contour of ξ =0.61, which approximately corresponded to the peakin the conditional mean scalar dissipation rate. Re-gions with depressed temperatures and reaction ratesfrequently coincided with filaments of high scalar dis-sipation overlapping the stoichiometric contour as therich and stoichiometric contours came in close prox-imity. These events were more frequent at x/d = 15,where extinction events were more probable and thereaction zone was more convoluted. This increasedoverlap between the scalar dissipation filaments andthe stoichiometric contour was likely a factor in theobserved differences in conditional means of scalardissipation rate at x/d = 7.5 and 15. Overestimates ofthe fuel concentration in regions of depressed temper-ature are expected to introduce localized errors in themixture fraction, while the reaction rate and temper-ature measurements are expected to remain relativelyaccurate.The imaging results presented here provide an

initial glimpse into the spatial relationships of themixture fraction, scalar dissipation, temperature, andreaction-rate fields. We anticipate that a great dealmore will be learned from further studies of the data,


including an analysis of correlations of scalar dissipa-tion rate and reaction rate with flame curvature. Thedevelopment of the diagnostic technique for applica-tion to flames with considerably higher probabilitiesof localized extinction is ongoing. Comparisons ofmultiscalar imaging measurements with single-pointand 1-D measurements will provide a more completeunderstanding of flow–flame interactions in turbu-lent nonpremixed and partially premixed flames. Theavailability of two-dimensional measurements is ex-pected to help advance modeling efforts and is par-ticularly well suited for comparisons with large-eddysimulations.

Acknowledgments

This research was supported by the U.S. Depart-ment of Energy, Office of Basic Energy Sciences, Di-vision of Chemical Sciences, Geosciences, and Bio-sciences. Sandia National Laboratories is a multi-program laboratory operated by Sandia Corporation,a Lockheed Martin Company, for the United StatesDepartment of Energy under contract DE-AC04-94-AL85000. The authors thank R. Sigurdsson for assis-tance during the experiments. The work on imagingof mixture fraction in turbulent flames has gone on inone form or another for more than 10 years. Whilethe problem remains a very difficulty one, significantstrides have been made. This progress is closely tiedto Professor Bilger’s pioneering ideas, ready encour-agement, and guidance. Two of the authors (J.H.F.and M.B.L.) have been privileged to work in his labsin Sydney and to benefit from his deep understand-ing and enthusiasm for the subject, his quick wit, aswell as his generous hospitality. For this we are deeplygrateful.

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