2703

Proceedings of the Combustion Institute, Volume 29, 2002/pp. 2703–2709

POLARIZED/DEPOLARIZED RAYLEIGH SCATTERING FOR DETERMININGFUEL CONCENTRATIONS IN FLAMES

JOSEPH FIELDING,1 JONATHAN H. FRANK,2 SEBASTIAN A. KAISER,1 MITCHELL D. SMOOKE1 andMARSHALL B. LONG1

1Department of Mechanical EngineeringYale University

New Haven, CT 06520-8284, USA2Combustion Research FacilitySandia National LaboratoriesLivermore, CA 94551, USA

Rayleigh scattering has been shown to be a useful diagnostic technique for two-dimensional imagingstudies of reacting and non-reacting flows. For example, by combining Rayleigh scattering with a simul-taneous measurement of the fuel concentration (e.g., using Raman scattering), mixture fraction and tem-perature can be determined in flames. In this work, it is demonstrated that the fuel concentration can beobtained by measuring the polarized and depolarized components of the Rayleigh signal and taking theirdifference or a suitable linear combination. While the depolarized Rayleigh signal is smaller than thepolarized signal by a factor of �100, this is still a factor of �10 larger than the Raman scattering. Appli-cation of the technique requires that one of the primary constituents of the fuel stream possess a depo-larization ratio sufficiently different from that of the oxidizer. Methane is a convenient candidate as it hasno measurable depolarization. Results are shown for methane flames diluted by argon as well as air.

Introduction

Rayleigh scattering is frequently employed in two-dimensional imaging for temperature and mixturefraction measurements in flames [1–7]. Mixture frac-tion is defined as the mass fraction of all atoms orig-inating from the fuel stream, and it is a quantity ofsignificant interest to turbulent flame modelers. Tocalculate mixture fraction, some measure of fuelconcentration is required along with the Rayleighmeasurement. Species-specific techniques such asRaman scattering or planar laser-induced fluores-cence (PLIF) have been used to determine fuel con-centration; however, each of these approaches hasassociated drawbacks. Raman scattering is muchweaker than Rayleigh scattering (by �103) and themodest signal/noise available often requires inno-vative smoothing approaches [8] and limits the ac-curacy of the derived mixture fraction. PLIF offershigher signal levels, but requires the use of an ad-ditional laser and necessitates tagging the fuelstream with a molecular marker (e.g., acetone). Forderiving mixture fraction, the disappearance of thefuel tag well to the rich side of the stoichiometriccontour makes this fuel measurement technique un-acceptable [3]. This study explores the possibility ofmeasuring the depolarized component of Rayleighscattering (perpendicular to the laser polarization) inconjunction with the polarized component to inferthe fuel concentration in flames. With the larger

cross-section of the depolarized Rayleigh signal(compared to Raman), the combination of thesemeasurements should offer the prospect of im-proved mixture fraction and temperature imaging inturbulent flames. This paper discusses the basis ofthe technique and presents calculated and measuredsignals from laminar flames. Application of the tech-nique to measurements in turbulent flames is dis-cussed in a companion paper [9].

Polarized and DepolarizedRayleigh Scattering

In most Rayleigh experiments, a linearly polarizedlaser is used to illuminate the flow, and the Rayleigh-scattered light is collected normal to the illuminationline or sheet. Nearly all of the scattered light is po-larized parallel to the polarization of the laser withthe intensity, I�, given by the expression

I � KI N r x (1)� 0 � i ii

K is the calibration constant of the collection optics,I0 is the intensity of incident laser light, and N is thetotal number of molecules contained in the probevolume. The summation is over all species with xithe mole fraction and ri the Rayleigh cross-sectionof the ith gas in the mixture.

2704 COMBUSTION DIAGNOSTICS—Diagnostics for Temperature, Mixture Fraction and Species

TABLE 1Depolarization ratios for some common gases at various wavelengths

qp � 102

Gas 444 nm 488 nm 514.5 nm 632.8 nm This work, 532 nm

N2 1.3a 1.08b 0.96 � 0.14d 1.042 � 0.006c 1.02 � 0.02O2 3.6a 2.91b — 3.02 � 0.01e 2.70 � 0.10CO2 — 4.12 � 0.02c 4.085 � 0.02c 4.05 � 0.02c 3.91 � 0.04CO — 0.521 � 0.007c 0.519 � 0.007c 0.48 � 0.005e 0.538 � 0.015H2 — 0.95b — 0.80e —H2O — — 0.0299 � 0.0135d — —C2H2 — 1.897 � 0.005c 1.889 � 0.005c 1.851 � 0.004e —C2H4 — 1.266 � 0.005c 1.247 � 0.005c 1.207 � 0.002c —C2H6 — 0.190 � 0.003c 0.188 � 0.004c 0.166 � 0.001c —C3H8 — 0.214 � 0.003c 0.208 � 0.006c 0.195 � 0.007c 0.181 � 0.015

a Ref. [13].b Ref. [14].c Ref. [15].d Ref. [16].f Ref. [17].

The classical treatment of Rayleigh scattering pre-dicts that a small fraction of polarized incident ra-diation will become depolarized for scattering ob-jects that are not isotropic (i.e., sphericallysymmetric) [10]. The depolarization ratio, qp, is de-fined as the ratio of the radiant intensities scatteredperpendicular (I�) and parallel (I�) to the incomingpolarized source (denoted by the subscript p), andcan be written

2I 3c�q � � (2)p 2 2I 45� � 4c�

where � is the mean value of the polarizability andc is the anisotropy [11]. All components of the po-larizability tensor are frequency dependent, andtherefore, the depolarization ratio will vary with theexcitation wavelength. Equation 2 represents the de-polarization ratio at the exact frequency of the laser;in practice, the measured depolarized signal will alsoinclude contributions from the pure rotational Ra-man spectrum as well (unless high spectral resolu-tion is used) [12]. Table 1 shows literature values ofqp (the total line including rotational Raman lines)for a number of common flame molecules at differ-ent wavelengths [13–17]. It is seen from Table 1 thatdepolarization ratios for most of the major speciesin typical flames are on the order of a few percent.Notable exceptions are some common fuels, whichhave significantly smaller depolarization ratios (or forthe case of methane, essentially zero depolarizationbecause of the spherical-top molecular configura-tion). It is the significantly different depolarizationratio of the fuel that will be exploited in obtainingthe fuel concentration from the difference between

the polarized and depolarized Rayleigh signals. Us-ing the depolarized Rayleigh signal for concentrationmeasurements has previously been demonstrated inplasmas of simple composition [18].

If values of depolarization ratios, Rayleigh cross-sections, and species concentrations are known, it ispossible to predict the signal strength of both thepolarized and the depolarized Rayleigh scattering inflames. Counterflow laminar flame calculations arefrequently used to predict species concentrationsand the results of such calculations can be coupledwith known values of qp and ri to investigate thedetails of the expected signals. As an initial test ofthe idea of obtaining the fuel concentration from thedifference between the polarized and depolarizedRayleigh signals, the case of a fuel mixture of meth-ane and argon is considered. Both methane and ar-gon have zero depolarization and thus represent anideal case for the technique. The predicted polarizedand depolarized Rayleigh signals (plotted as a func-tion of mixture fraction) for a 35% CH4/65% Ar (byvolume) flame are shown in Fig. 1a. While the po-larized Rayleigh signal is maximum at unity mixturefraction, the depolarized signal goes to zero.

The difference (ID) between the parallel and per-pendicular polarization of the Rayleigh signal (nor-malized to values in air) is given by

I I� �I � �D I I�,air �,air

r x r q x� i i � i p,i ii iN

� � (3)� �N I I0 �,air �,air

where ri is the Rayleigh cross-section, xi is the mole

POLARIZED/DEPOLARIZED RAYLEIGH SCATTERING IN FLAMES 2705

Fig. 1. (a) Computed signal profiles for the polarizedand depolarized components of the Rayleigh scattering asa function of mixture fraction in an argon-diluted methanelaminar flame. Signals are scaled to have the same value inair (mixture fraction � 0). (b) Computed signal profiles forthe methane Raman scattering and the difference Rayleighscattering as a function of mixture fraction.

fraction of species i, N is the number density at agiven point in the flame (inversely proportional totemperature), and N0 is the number density at thecalibration temperature and pressure. Predicted dif-ference Rayleigh and fuel concentration profilesshown in Fig. 1b indicate that ID should provide anexcellent fuel tracer for this case (with �10 timesthe signal of the methane Raman in the fuel stream).The calculations include the effect of the changingoverall depolarization qp,mix due to compositionchanges arising from reaction. One primary com-bustion product is CO2, which has the largest qp ap-pearing in Table 1. This is balanced by smaller de-polarization ratios for H2O and other products orintermediates appearing in significant concentra-tions such as CO.

In practice, several factors must be quantified incorrecting the experimentally obtained signal. Thefirst of these is the nonideality of the polarizing filter

used and the accuracy of its orientation relative tothe laser polarization. In the perpendicular imagingmode, some of the parallel polarization signal willpass through the filter element. This effect will becompounded by any depolarization present in thelaser source itself and from background scattering.Thus, the measured signal, S�, is a combination ofthe true depolarization component, I�, backgroundscattering of the same polarization, B� (which mustbe accounted for separately), and some contributionfrom I� arising from the aforementioned factors:

S � I � B � (�I ) (4)� � � �

where � accounts for the parallel polarized Rayleigh‘‘leakage’’ signal or cross-talk. If the background scat-tering, the response of the imaging system, and theleakage of the polarizer are the same for the mea-surements of the polarized and depolarized com-ponents, and if the contribution of leakage from the(small) depolarized to the (large) polarized compo-nent is negligible, the leakage can be expressed as

S � S�,NG1 �,NG2� � (5)S � S�,NG1 �,NG2

where S is the uncorrected, pixelwise intensity asmeasured for two gases NG1 and NG2 with zerodepolarization, such as noble gases. Thus, from im-aging the scattering components of two such gasesat known uniform temperature and pressure, it ispossible to account for the leakage of the polarizedRayleigh and background scattering into the imageof the depolarized scattering. If the background, re-sponse, fixed pattern, or polarizer is different for thetwo images (as is normally the case for simultaneousimaging of the two components), the actual com-putation becomes somewhat more complicated butfollows the same principle. The same calibration im-ages, together with the knowledge of rNG1 and rNG2,also allow for the usual correction of backgroundscattering of the same polarization in each image.

Data on the depolarization ratios of the major spe-cies are not available from literature at 532 nm (sec-ond harmonic of Nd:YAG), which was used in thevalidation experiments described below. Therefore,measurements of these depolarization ratios wereperformed. The second harmonic of a Nd:YAG laserwas focused to a line by a spherical lens with 750 mmfocal length. The beam entered and left a metal sam-ple cylinder (50 mm diameter) through small holes.The gas being measured was fed continuously to thecylinder at ambient temperature and pressure. Theabsence of any laser windows and the use of appro-priate irises provided a field of view that was prac-tically free of stray light. The Rayleigh scattering wasimaged by a cooled CCD camera (Photometrics, 512� 512 pixels) with the polarizer (B � W photo-graphic circular polarizer) mounted in front of theobjective (Nikor 50 mm, f /1.4). The leakage of the

2706 COMBUSTION DIAGNOSTICS—Diagnostics for Temperature, Mixture Fraction and Species

Fig. 2. Experimental measurements of the methane Ra-man and difference Rayleigh signals as a function of non-dimensional radius (D � 16 mm).

polarizer was determined by taking images of scat-tering in argon and helium as outlined above, andthe depolarized scattering was corrected accord-ingly, although the leakage of this specific polarizeris negligible in the context of noisier sheet measure-ments in actual combustion (see below). For the po-larized and depolarized components, 50 and 100shots, respectively, were averaged. The resulting de-polarization ratios are given in Table 1. The uncer-tainty in the depolarization ratios measured has beenassessed by estimating uncertainty in the back-ground and leakage corrections and evaluating thevariations within the image. The underlying cause ofcorrection uncertainties is the drift in laser powerover the time of the measurement series. The mea-surements were taken such that first the polarizedscattering was recorded for all gases, next the polar-izer was rotated, and then the depolarized scatteringwas recorded for all gases. Any error in polarizeralignment is therefore constant within each seriesand is accounted for by the leakage correction. Thescattering from air was measured at the beginningand end of each series to estimate the power drift,which was found to be about 1%. The value for ox-ygen is calculated from the measurements for nitro-gen and air. Values for water vapor and hydrogenwere not measured and are taken to be the valuesavailable from the literature that are closest to532 nm.

Measurements in an Argon-DilutedMethane Flame

The technique was investigated in two differentaxisymmetric laminar diffusion flames using two dif-ferent experimental configurations. In an initial setof experiments, images of an argon-diluted methaneflame (35% CH4/65% Ar, jet diameter D � 16 mm)were taken such that both regions of the undiffused

fuel stream and the air of the coflow were captured.The second harmonic of a Nd:YAG laser (Contin-uum, Powerlite 8000; 260 mJ/pulse) was focusedinto a sheet by a cylindrical lens (250 mm focallength). Scattered light was collected normal to thelaser sheet using a large format f /1.4 camera objec-tive (Nikor 85 mm) and focused onto an unintensi-fied interline transfer CCD camera (PCO/Cooke,SensiCam, 1024 � 1280 pixels). Flame luminositywas suppressed by gating the camera electronicallyfor 2 ls. To further suppress luminosity, an interfer-ence filter (10 nm full width at half-maximum[FWHM] centered at 532 nm) was placed betweenobjective and camera, together with a sheet polarizer(Melles Griot, 003FPG), whose orientation was ro-tated 90� as required. Integration over 12 and 336shots was performed for the polarized and depolar-ized components, respectively. Sufficient suppres-sion of background scattering was achieved by di-recting the laser beam on either side of the flamethrough tubes with staged baffles. As an indepen-dent, direct measurement of the fuel concentration,Raman scattering of methane was imaged succes-sively on the same camera, exchanging polarizer andfilter for the appropriate interference filter (10 nmFWHM centered at 630 nm), integrating �1000shots, and then averaging three images.

Figure 2 shows the measured difference Rayleighand methane Raman signals as a function of radialposition in the 35% CH4/65% Ar flame. As pre-dicted by the calculations, the two measured signalsare essentially identical. The leakage, �, was deter-mined to be 0.82%. The value was determined fromuniform-field images of the scattering from argonand helium and was taken as the mean of the pixel-wise leakage calculated from the calibration images.This yields a parasitic contribution to the measureddepolarized signal that is on the same order as theexpected true depolarized Rayleigh scattering. Thecorrections remove this contribution reasonably wellas verified with images of argon, which should givezero depolarized scattering.

Variations of qp with temperature can be estimatedby evaluating the dependence of the molecular po-larizability and anisotropy in equation 2. For dia-tomic molecules, the mean polarizability (�) in-creases by only 1% for every 1000 K increase intemperature [19,20]. The temperature dependenceof the polarizability anisotropy (c) has not been es-tablished experimentally; however, it is possible touse semitheoretical arguments to assess the appro-priate trend. Ab initio calculations of the polariza-bility of H2 reveal a larger relative increase in theanisotropy than the polarizability with increasing in-ternuclear distance [21]. The increase is estimatedto be on the order of 2% per 1000 K temperatureincrease. Overall, the temperature dependence ofthe depolarization ratio will be approximately 2%per 1000 K or no more than 4% for typical flame

POLARIZED/DEPOLARIZED RAYLEIGH SCATTERING IN FLAMES 2707

Fig. 3. (a) Computed signal profiles for the polarizedand depolarized components of the Rayleigh scattering asa function of mixture fraction in an air-diluted methanelaminar flame. Signals are scaled to have the same value inair (mixture fraction � 0). (b) Computed signal profiles forthe methane Raman scattering, the difference Rayleighscattering (which is multivalued) and a linear combinationof Rayleigh and depolarized Rayleigh, as a function of mix-ture fraction.

temperatures of approximately 2000 K. We there-fore conclude that temperature effects pose no se-rious difficulty for the present purpose as long as thedifference Rayleigh signal exhibits consistent andpredictable behavior through the flame front region.

Calculations and Measurements in anAir-Diluted Methane Flame

For a particular choice of fuel diluent, the detailedbehavior of the difference Rayleigh signal must beconsidered to infer accurately the fuel concentration(i.e., laminar flame calculations should be performedand the signals modeled as described above). Onefuel/diluent mixture of particular interest is the par-tially premixed methane/air ratio of 25% methane/75% air. In a recent series of workshops on turbulentnon-premixed flames [22], considerable work hasbeen done both experimentally and computationally

on flames with this composition. By combining po-larized and depolarized measurements in theseflames, it should be possible to image the mixturefraction (as well as temperature) and hence deter-mine two components of the scalar dissipation,which has not been done in these flames.

Figure 3a shows the calculated Rayleigh and de-polarized Rayleigh signals as a function of mixturefraction for a fuel mixture of 75% air and 25% meth-ane. One notable feature of the calculated signals forthis fuel is that in the mixture fraction range from�0.2 to 0.4, the (normalized) depolarized signal isgreater than the polarized signal. This leads to a neg-ative region in the difference between the two sig-nals as seen in Fig. 3b. The negative value of thedifference signal could be handled by simply addingan offset, but a more significant problem stems fromthe fact that the difference signal is multivalued withrespect to the methane concentration (also shown inFig. 3b). This would make it impossible to assign thedifference signal to a unique value of methane con-centration. This problem can be addressed by form-ing a difference signal based on a different linearcombination of the polarized and depolarized sig-nals. In particular, the signal can be written as.

I I� �I � � a � b (6)LC I I�,air �,air

While the simple difference (i.e., a � 1 and b � 0)worked well for the argon-diluted flame, a value ofa � 1.3 was needed for the air-diluted flame to pro-vide a single-valued function with respect to themethane signal. By choosing an offset of b � 0.065,the resulting linear combination signal becomes neg-ative at nearly the same mixture fraction value thatthe methane concentration goes to zero as seen inFig. 3b. In using the signal then, a unique mappingof the linear combination signal onto the fuel con-centration can be performed.

A second set of experiments was performed tocheck the applicability of the technique for this fuelcomposition. The measurements were performed onthe air-diluted ‘‘flame A’’ of the ‘‘International Work-shop on Measurement and Computation of Turbu-lent Nonpremixed Flames’’ [22] (25% CH4/75% air,jet diameter D � 7.2 mm). The beams of twofrequency-doubled Nd:YAG lasers (560 and 360mJ/Pulse) were combined geometrically and retro-reflected to maximize power. The polarized com-ponent was imaged by the same electronically gatedcamera as above, with the objective (Nikor 50 mm,f /1.4) mounted directly to the camera. The interfer-ence filter was placed in front of the objective. Sincethis imaging train was solely devoted to measuringthe (predominant) polarized component, no polar-izer was used, potentially resulting in an error on theorder of 1% due to the depolarized component, butincreasing the total transmission to the camera sig-nificantly. Imaging of the depolarized component

2708 COMBUSTION DIAGNOSTICS—Diagnostics for Temperature, Mixture Fraction and Species

Fig. 4. Experimental measurements of the methane Ra-man scattering and a linear combination of the polarizedand depolarized Rayleigh signals as a function of non-di-mensional radius (D � 7.2 mm). In the latter, negativevalues are set to zero.

was achieved by optically coupling a similar interlinetransfer CCD camera (PCO/Cooke, SensiCam, 320� 240 pixels after 2 � 2 binning) to an image in-tensifier (ITT Gen III). An interference filter infront of the objective (85 mm f /1.2) and the shortgating time of the intensifier (400 ns) suppressedluminosity. Here, a different polarizer (B � W pho-tographic circular polarizer) was placed in front ofthe objective and could be rotated to be able to takethe necessary calibration images. Synchronizationand registration of the system are described in Ref.[9]. For each image, 80 shots were averaged.

In the second experiment, the leakage was muchsmaller (� � 0.04%), due to the use of the differentpolarizer. Therefore, the parasitic contribution is re-duced to about 4% of the expected true depolarizedRayleigh scattering and was neglected. Omitting thecorrections for cross-talk yields significant simplifi-cation of the data analysis for this two-camera con-figuration.

Figure 4 shows the measured linear combinationof the polarized and depolarized Rayleigh signals asa function of radius in flame A. Also shown in thefigure is the measured fuel concentration obtainedpreviously by single-point Raman scattering [23].For the comparison, the Rayleigh signals have beensmoothed to match the spatial resolution of the Ra-man measurements (0.5 � 0.5 � 0.5 mm3). Onceagain the agreement is extremely good, demonstrat-ing the applicability of the technique even for rela-tively dilute fuel mixtures.

Even with an order of magnitude increase in cross-section of the depolarized Rayleigh over the corre-sponding Raman scattering, the resultant signals arestill relatively weak. For the experimental configu-ration used for measurements in the air-diluted

methane flame, the signal-to-noise ratio of the de-polarized Rayleigh in single-shot images of ambientair was �10. This necessitated some degree ofsmoothing to determine mixture fraction reliablyfrom single-shot images. The application of thistechnique to turbulent flames is described in Ref.[9]. In those experiments, the polarized/depolarizedRayleigh measurements were combined with simul-taneous imaging of OH and CO, which furtherhelped to quantify the mixture fraction near theflame front. However, if the experiment were opti-mized for polarized/depolarized measurement alone(e.g., by using an intracavity configuration providinggreater laser-sheet intensity), it should be possible tofurther improve the signal-to-noise ratio.

Conclusions

The present work establishes depolarization Ray-leigh scattering as a viable diagnostic technique formeasurements of fuel concentration in both argon-diluted (65% by volume) and air-diluted (75% byvolume) laminar methane flames. The differenceRayleigh signal increases the postprocessed signal-to-noise ratio of the effective fuel image by morethan a factor of 3 along the jet centerline. This tech-nique can be applied in situations where one or moreprimary molecular constituents (in this case, meth-ane) possess a significant deviation in depolarizationratio from that of the oxidizer coflow. Table 1 indi-cates that other candidate fuels might include ethaneand propane, which both have small depolarizationratios relative to air. Dilution of the fuel with gasessuch as argon or helium will allow extension of thistechnique to higher qp fuel molecules. Furthermore,such dilution is favorable in that it will increase thedynamic range of the difference signal between thefuel mixture and air coflow. The presence of broad-band fluorescence interferences (which are unpolar-ized and would significantly influence the depolar-ized Rayleigh signal) arising from polycylic aromatichydrocarbons may pose a problem in some flamesand should be examined prior to application.

Acknowledgments

The Yale authors thank the members of the CombustionResearch Facility for their support in doing the experi-ments with special thanks to R. Sigurdsson. The work wassupported by the Department of Energy, Office of BasicEnergy Sciences.

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COMMENTS

Katharina Kohse-Hoeinghaus, Bielefeld University, Ger-many. Your technique offers a better signal-to-noise ratiothan Raman measurements, which would, however, still bepossible in a methane flame and would have the advantageof being direct rather than indirect. Could you commenton the potential of using this approach in flames of, forexample, higher hydrocarbon fuels where Raman mea-surements would not be feasible?

Author’s Reply. We have not done the experiments orlaminar flame calculations for fuels other than methane.However, we believe the technique may indeed work forother fuels. Table 1 shows that the depolarization ratios ofethane and propane, while not zero, are considerably lowerthan that of air, making those good candidates. In addition,if the fuel from the jet contains a significant fraction of anoble gas, then the overall depolarization ratio of the mix-ture will also be small compared to that of air and products,resulting in a difference signal that is representative of thefuel concentration.

●

Yung-Cheng Chen, The University of Sydney, Australia.It was stated in the presentation that the CCD camera forpolarized Rayleigh scattering does not use an image inten-sifier, for better spatial resolution. However, the camera fordepolarized Rayleigh scattering is intensified. Will the finalimage spatial resolution for the mixture fraction improveby using a non-intensified CCD camera for polarized Ray-leigh scattering?

Author’s Reply. Yes. The polarized image, in addition togiving information on the temperature, is used in smooth-ing the depolarized image (Ref. [8] in paper). Therefore,improving the spatial resolution in the polarized image byusing an unintensified camera helps improve the resolutionof both the temperature and the fuel concentration fields,which are needed to derive the mixture fraction.