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Favre- and Reynolds-averaged velocity measurements: Interpreting PIV and LDA measurements in combustion M. Mustafa Kamal , Ruigang Zhou, Saravanan Balusamy, Simone Hochgreb Department of Engineering, University of Cambridge, CB2 1PZ, UK Available online 4 July 2014 Abstract Previous studies using particle image velocimetry (PIV) and laser Doppler anemometry (LDA) have raised the question of how these measurements should be compared. This study reports on the difference between Favre-averaged and Reynolds-averaged velocity statistics for a turbulent burner using PIV and LDA for unconditional and conditional velocity measurements. The experimental characterization of flow fields of premixed and stratified methane/air flames is carried out under globally turbulent lean conditions (global equivalence ratio at 0.75), over a range of stratifications and swirl numbers. Unconditioned velocity data was acquired using aluminium oxide to seed the flow field. Conditioned measurements were performed using vegetable oil aerosol as seed, which burns through the flame front, thus allowing only the non-reacting flow velocities to be obtained. A critical comparison of unconditioned velocity profiles measured using both PIV and LDA, including axial, radial, and tangential components is made against conditioned and reconstructed mean velocities at different cross-sections of the flame. The comparison reveals how the differences between the Favre-averaged (unconditioned) and the Reynolds-averaged (con- ditioned) velocity measurements in the flame brush region can be accounted for using the mean progress of reaction, and highlights the limits of the accuracy and agreement between PIV and LDA measurements. Ó 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Turbulent flame; Premixed flame; LDA; PIV; Favre averaging 1. Introduction Recent progress towards the understanding of premixed turbulent combustion and validation of numerical simulation models has relied on detailed databases for a variety of scalar and velocity measurements in premixed and stratified flames [1–5]. Recent work by Zhou et al. [4] directly compared low speed measurements of velocities and their statistical moments in a strat- ified swirl burner using laser Doppler anemometry (LDA) and low speed particle image velocimetry (PIV). Unlike prior work (Nomura et al. [6] and Seffrin et al. [1]), both the velocities, their moments and the integral length scales measured with both techniques were in excellent agreement, http://dx.doi.org/10.1016/j.proci.2014.06.061 1540-7489/Ó 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Corresponding author. Fax: +44 (0) 1223 764311. E-mail address: [email protected] (M.M. Kamal). Available online at www.sciencedirect.com ScienceDirect Proceedings of the Combustion Institute 35 (2015) 3803–3811 www.elsevier.com/locate/proci Proceedings of the Combustion Institute

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Page 1: Favre- and Reynolds-averaged velocity measurements ...Favre- and Reynolds-averaged velocity measurements: Interpreting PIV and LDA measurements in combustion M. Mustafa Kamal⇑, Ruigang

Available online at www.sciencedirect.comProceedings

ScienceDirect

Proceedings of the Combustion Institute 35 (2015) 3803–3811

www.elsevier.com/locate/proci

of the

CombustionInstitute

Favre- and Reynolds-averaged velocitymeasurements: Interpreting PIV and LDA

measurements in combustion

M. Mustafa Kamal ⇑, Ruigang Zhou, Saravanan Balusamy,Simone Hochgreb

Department of Engineering, University of Cambridge, CB2 1PZ, UK

Available online 4 July 2014

Abstract

Previous studies using particle image velocimetry (PIV) and laser Doppler anemometry (LDA) haveraised the question of how these measurements should be compared. This study reports on the differencebetween Favre-averaged and Reynolds-averaged velocity statistics for a turbulent burner using PIV andLDA for unconditional and conditional velocity measurements. The experimental characterization of flowfields of premixed and stratified methane/air flames is carried out under globally turbulent lean conditions(global equivalence ratio at 0.75), over a range of stratifications and swirl numbers. Unconditioned velocitydata was acquired using aluminium oxide to seed the flow field. Conditioned measurements wereperformed using vegetable oil aerosol as seed, which burns through the flame front, thus allowing onlythe non-reacting flow velocities to be obtained. A critical comparison of unconditioned velocity profilesmeasured using both PIV and LDA, including axial, radial, and tangential components is made againstconditioned and reconstructed mean velocities at different cross-sections of the flame. The comparisonreveals how the differences between the Favre-averaged (unconditioned) and the Reynolds-averaged (con-ditioned) velocity measurements in the flame brush region can be accounted for using the mean progress ofreaction, and highlights the limits of the accuracy and agreement between PIV and LDA measurements.� 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Keywords: Turbulent flame; Premixed flame; LDA; PIV; Favre averaging

1. Introduction

Recent progress towards the understanding ofpremixed turbulent combustion and validationof numerical simulation models has relied ondetailed databases for a variety of scalar and

http://dx.doi.org/10.1016/j.proci.2014.06.0611540-7489/� 2014 The Combustion Institute. Published by El

⇑ Corresponding author. Fax: +44 (0) 1223 764311.E-mail address: [email protected] (M.M. Kamal).

velocity measurements in premixed and stratifiedflames [1–5]. Recent work by Zhou et al. [4]directly compared low speed measurements ofvelocities and their statistical moments in a strat-ified swirl burner using laser Doppler anemometry(LDA) and low speed particle image velocimetry(PIV). Unlike prior work (Nomura et al. [6] andSeffrin et al. [1]), both the velocities, theirmoments and the integral length scales measuredwith both techniques were in excellent agreement,

sevier Inc. All rights reserved.

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Fig. 1. Radial profiles of mean axial velocity forunconditioned PIV and LDA, extracted at z = 30 mm.

3804 M.M. Kamal et al. / Proceedings of the Combustion Institute 35 (2015) 3803–3811

as shown in Fig. 1. Although such concordance isgenerally considered a success, the agreementbetween measurements was puzzling: as explainedfurther on, LDA relies on local time-based burstsof particle passage, in proportion to the particle(and gas) density, whereas PIV measurementsare number averaged images. Therefore, LDAmeasurements have in general been consideredFavre (density) averaged [7,8], whilst PIV mea-surements should be Reynolds (number) aver-aged. There should therefore be an observabledifference within the flame brush. We have there-fore undertaken a set of experiments using aero-sols to generate velocity measurements in theunreacted zone only, in order to clarify the differ-ences and understand under what conditions PIVand LDA measurements should agree.

In the following sections, we describe the mea-surement principles and how they were executed,the comparison between LDA and PIV condi-tioned and unconditioned measurements, andconnect the various measurements using whatwould be expected using a thin flame model.

1.1. Velocity measurements

Measurements of velocity in flames rely chieflyon optical methods such as LDA and PIV. In

both cases, sufficiently small particles or aerosolsare used to seed the mixture, which can followthe relevant turbulent frequencies. In LDA, veloc-ities are determined from the signal produced byMie scatter of a particle travelling through amillimetre-long laser light fringe volume. The fre-quency of the bursts is therefore proportional tothe number of particles crossing the probe volumeper unit time, and thus to the density of the gasand the velocity of the particles. If the particleseeding is uniform, the probability of crossing isinversely proportional to the velocity, thus LDAmeasurements are routinely corrected for thevelocity bias by the transit time between particles[9,10]. However, the expansion of gases in flamesmeans that in the region of the flame brush, theparticle density is proportional to the gas density,so that the measurements will be weighted accord-ingly, in what is called density or Favre weighting.

In PIV, a twin set of images of the Mie scatteris taken spaced by time, and the displacementsand velocities are obtained via spatial correlationof the two images. Measurements in a particularregion are averaged over a spatial interrogationwindow, typically of the order of 16–32 pixelssquare, often corresponding to sub-millimetre res-olutions. Ensembles of measurements are aver-aged, yielding an equally weighted measurementfor each sample set of images, in what is callednumber or Reynolds averaging.

Most common flames are thin relative to theoverall domain, with typical thicknesses under0.5 mm at atmospheric conditions. The flamethickness is comparable or slightly smaller thanthe spatial resolution of LDA and PIV. Therefore,most measurements are made either in the reac-tant or product zones, with very low probabilityof measurements within the flame zone itself.Measurements within the narrow flame zonewould be automatically weighted by density forinterrogation windows of the same order of mag-nitude as the thickness of the flame, thus averag-ing velocities according to the number of particleand autocorrelation pairs in the image set. Wecan therefore say that for measurements aroundthe flame brush of turbulent flames, we expectPIV measurements to be Reynolds averaged andLDA measurements to be Favre averaged. Underwhat conditions would the averages of velocitycomponents be similar or identical? We addressthis question in the following section.

1.2. Averaging in the thin flame limit

In the thin flame or BML model [11,12], wehave a description of the flame in two zones forreactant and product, corresponding to a progressvariable c, where c = 0 in the reactants and unityin the products. The local probability of c isdenoted p(c), and the corresponding average or

density averaged values of a scalar �w or ~w can

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M.M. Kamal et al. / Proceedings of the Combustion Institute 35 (2015) 3803–3811 3805

be correspondingly calculated as �w ¼R 1

0 wðcÞpðcÞdc ¼ ð1� �cÞwr þ �cwp , and ~w ¼ 1=�q

R 1

0wðcÞ

qðcÞpðcÞdc ¼ ð1� �cÞwr þ �cwp, where the sub-scripts r and p indicate reactant and product,respectively, q is the density, and the mean density

is �q ¼R 1

0qðcÞwðcÞpðcÞdc ¼ ð1� �cÞqrwr þ �cqpwp.

Following the original model, we use a tempera-ture rise ratio s = (Tp � Tr)/Tr to quantify thedensity difference. The Favre-averaged progressof reaction thus follows as ~c ¼ �c=ððsþ 1Þ � s�cÞ.Now we are ready to express the Favre averagedvelocity components ~ui as a function of theReynolds average values of the properties in thereactant and product regions, and the meanprogress of reaction as:

~u ¼ ð1� ~cÞ�ur þ ~c�up ð1aÞ�u ¼ ð1� �cÞ�ur þ �c�up ð1bÞ

Subtracting Eq. (1b) from (1a), we have:

�u� ~u ¼ ð�c� ~cÞð�up � �urÞ ð2ÞWe therefore have the result that the differencebetween the Favre and Reynolds averaged veloci-ties should be proportional to the difference in localvelocities of the reactants and products, weightedby the difference between Reynolds and Favreaveraged progress of reaction. The latter termcan be determined from the definition of the pro-gress of reaction in the limit of a thin flame as:

ð�c� ~cÞ ¼ scð1� �cÞ=ðsð1� �cÞ þ 1Þ ð3ÞFigure 2 shows that the difference peaks at avalue of around 0.4 at a progress of reaction

Fig. 2. Difference between Reynolds- and Favre-averaged progress of reaction values in the thin flamelimit, as a function of progress of reaction and normal-ized flame temperature rise. The values for s = 3.6 and6.5 are based on the equilibrium temperatures associatedwith the minimum and maximum equivalence ratios instratified cases, and s = 6.0 refers to the equivalenceratio for the premixed case.

approximately 0.7 towards the product zone fora range of values of s compatible with the presentexperiments and flames in general. This meansthat even if there are significant velocity differ-ences between reactants and products, the differ-ence between Favre and Reynolds averagedvelocities should be smaller than 0.4 times therespective value, particularly at the edges of theflame brush.

In what follows, we test the hypothesis aboveby comparing measurements obtained within aflame brush using particle-seeded flows withLDA and PIV to obtain the unconditioned veloc-ity components ~ui and �ui, and aerosol seeded flowsusing PIV to obtain the conditioned reactantvelocity ~uri ¼ �uri. This allows us to obtain �upi fromEq. (1b) and the right and left hand sides ofEq. (2) for comparison, if the local pdf of progressof reaction is available.

2. Experimental setup and methods

2.1. Cambridge/Sandia Stratified Swirl Burner(SwB)

The SwB burner was designed to generate react-ing flow conditions representative of turbulentflows in practical systems, including sufficientlyhigh turbulence levels, swirl, and operation underpremixed and stratified conditions. The swirl bur-ner geometry is described in [3,13], and a cross sec-tion and top view are shown in Fig. 3.

The burner consists of co-annular tubes with adevelopment length exceeding 25 hydraulic diame-ters to ensure well developed turbulent flow. Aceramic central bluff body is used to stabilize theflame with minimal heat loss. Mass flow controllersare used to control the inner annulus equivalenceratio (/i) and the outer annulus equivalence ratio(/o) independently, allowing the stratification ratio(SR = /i//o) to be easily varied, for a fixed globalstratification ratio (/g). In the present paper, onlycases without swirl have been considered.

2.2. Operating conditions

The operating conditions for the present studyare shown in Table 1. The generalized notationSwBNz is used to denote the test cases, where Nis the case number and z is the downstream dis-tance in millimetres. The bulk velocity in the outerannulus, Uo = 18.7 m/s, was set at more thantwice the value of the velocity in the inner annulus,Ui = 8.3 m/s, in order to generate substantial lev-els of shear and thus turbulence between the twoflows. Co-flow air was supplied around the outerannulus with a bulk velocity Uco = 0.4 m/s to pro-vide well-characterized boundary conditions. TheReynolds numbers derived from the bulk veloci-ties at the exit geometry are Rei = 5960 for the

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Fig. 3. Burner geometry. Top: top view, bottom: exit geometry. The arrows indicate the direction of flow and swirl.

Table 1Operating conditions, for global /g = 0.75.

Case /i /o SR

SwB1 0.75 0.75 1SwB5 1 0.5 2SwB9 1.125 0.375 3

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inner flow and Reo = 11500 for the outer flow. Thestratification ratio was varied from unity for pre-mixed cases to 3 for the most stratified cases.The inner, outer, and co-flow were each seededwith 1 lm calcined aluminium oxide particles incase of unconditioned measurements, and withvegetable oil aerosol in case of conditioned mea-surements. The solid particle seeding was achieved

by passing a portion of each air flow through sim-ple turbulent fluidized seeders, and adjusting thefraction of the total flow through each seeder usingneedle valves to ensure similar seed density ininner, outer and co-flow streams. For the aerosol,a high air velocity atomizer was used to produce amonodisperse mist of aerosol droplets with a meandiameter of about 1 lm as measured by an elec-tronic low pressure impactor. The characteristictime scale for drag on a particle in Stokes flow issp ¼ qpd2

p=18la, where qp and dp are the particledensity and diameter, respectively, and la is thedynamic viscosity of the surrounding fluid, the cal-culated time scale sp is of the order of 10�5 s, indi-cating for this particle size, velocity fluctuationfrequencies of up to tens of kHz can be followed.

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2.3. PIV measurements

The PIV system consists of a double-pulsedNd:YAG laser (Litron Nano PIV) operating at532 nm and 100 mJ/pulse shaped into an expand-ing beam. The time delay between each pulse wasoptimised to 10 ls based on the interrogation win-dow size and the maximum displacement of parti-cle pairs to be within 1/4 of the interrogationwindow size. The light scattered by the seed parti-cles was imaged using a CCD camera (LaVisionImager Pro X 4M) fitted with a Nikon AF MicroNikkor 60 mm lens (f/4) and a 50 mm interferencefilter centred about 532 nm, at 90 degrees to thelaser sheet. The 2048 � 2048 pixels imaged fieldwas 60.3 mm wide by 60.3 mm tall, yielding apixel resolution of 29.4 lm. The PIV system wasoperated at 7 Hz and 2000 images were recordedfor each condition.

All PIV images were processed using LaVisionsoftware (Davis 7.4). For the two-componentPIV, raw images were pre-processed by subtract-ing a sliding background (3 pixel scale length)and normalizing the particle intensity using amin/max filter (3 pixel scale length). Vectors werecalculated using multi-pass cross-correlation withan initial window size of 64 � 64, decreasing toa 32 � 32 window size in the final three passes.The window overlap was held constant at 50%in each pass. This gives a vector spatial resolutionof 0.47 mm/vector. All vector fields were filteredvia rejection for a Q-factor (ratio of highest to sec-ond highest peaks in the displacement correlationmap) below 1.2, and the resulting fields were med-ian filtered. Isolated regions with fewer than fivevectors were removed. No interpolation was doneto for missing vectors. The full scale velocity mea-surement error can be determined by the ratio ofthe nominal correlation peak value (0.1 pixel forwindow of 32 � 32 pixels) to the maximum dis-placement permitted, namely 1/4 of the final inter-rogation window. Thus the measurement error forthe two-component PIV (32 � 32) is calculated tobe ±1.3% of full scale.

2.4. Pairwise LDA configuration

The LDA used is a Dantec two-componentsystem. The laser used is an Ar-ion continuouswave laser (Spectra-Physics Stabilite 2017) operat-ing at 514.5 nm and 488 nm with power set to1.5 W. The signals generated by scattering aretransferred to the burst spectrum analyser proces-sor through a Nikon Micro Nikkor 105 mm lens(f/2.8), a pinhole, a Dantec colour separator andphotodetectors, for measurements of two velocitycomponents. The receiving optics collect light atan off-axis forward position at an angle of 30�.The calculated dimensions of the LDA probe vol-ume are 3.40 mm length � 0.14 mm width � 0.14mm height, which yields an effective probe volume

of 0.91 � 0.14 � 0.13 mm after considering themagnification of the lens (determined by focallength and focusing distance), and the angle. Apairwise LDA setup was achieved by rotatingthe system by 90 degrees and scanning along thesame positions to obtain the third velocity compo-nent. As a result, all three velocity components areresolved at the measurement locations with atleast 10 kHz data rate. Transit time weighting isapplied to minimize the velocity bias due torandom sampling. Radial symmetry of the flowis verified by acquiring full radial scans. The mea-surements were taken at multiple axial locations,corresponding to previous scalar measurements[3,13]. The sampling spatial resolution (spatialinterval between each measurement point) is1 mm. The random errors introduced for themean and RMS velocity measurements in LDAare 0.7% and 1.4% corresponding to the finitesample size of LDA data (�10,000 data per mea-surement point). Further details of the LDA pro-cessing and optimization are available in [4].

2.5. Progress of reaction measurements

Measurements of progress of reaction weremade by considering the Mie scatter signal of atotal of 2000 images of vegetable oil droplets usedin the PIV. Vegetable oil evaporates and burns attemperature above about 600 K. The evaporationtime of the aerosol droplets (15 s) is very largecompared to the time step between two laserpulses (10 ls) and the time needed for a dropletto travel through the field of view (3 ms). TheMie signal interface marks an approximate iso-thermal contour (around 650 K) [14] and, in thethin flame approximation, also separates productsand reactants. The flame thickness is of the orderof 0.2 mm [3], thus sufficiently thin for the presentapproximation. A low luminosity signal arisingfrom the filtered flame emission marks the prod-uct region present near the interface. In order todetermine the appropriate flame interface, ahistogram-based thresholding method is adoptedfor each Mie scattered image. As signal-to-noiseratios in images vary due to beam profile inhomo-geneities and variations in seeding concentration,a modified algorithm based on the work of Weißet al. [15] is employed, such that the interface isdetermined as the position of the maximum gradi-ent in the Mie scattering intensity field. A preli-minary threshold calculated from the globalintensity histogram, coupled with a ridge findingalgorithm is implemented to detect the maximumgradient. The algorithm showed little sensitivity tothe threshold value over a wide range, and theresults for the progress of reactions are robustcompared to measurements based on temperature[3]. The ensemble of thresholded and binarisedimages is averaged to construct a mean flamebrush.

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3. Results and discussion

3.1. Conditioned measurements

Figure 4 presents radial profiles of mean axialvelocity for all the three cases at z = 30 mmobtained from conditioned (aerosol only) PIVand LDA measurements. As expected, the condi-tioned PIV results are in excellent agreement withthe conditioned LDA measurements.

The mean progress of reaction obtained fromthe aerosol measurements is shown in Fig. 5.The flame region widens with the expansion ofthe flame products, and the flame brush regionwidens due to the action of turbulence furtherdownstream in all cases. The effect of stratificationfrom the premixed (SwB1) to the most stratified(SwB9) flame is to widen the flame due to higherinner temperatures and overall rate of heatrelease.

3.2. Conditioned and unconditioned velocities

Radial profiles of the mean velocity compo-nents from both the conditioned and uncondi-tioned LDA measurements are shown for allcases in Fig. 6. The mean progress variable is alsooverlaid on the same figure for individual cases.The velocity profiles have been discussed in [4]:the flow leaves the annular channels as fullydeveloped flow, and a shear layer emerges anddevelops. The flame stabilizes at the edge of the

Fig. 4. Radial profiles of conditioned reactant meanaxial velocity PIV and LDA, extracted at z = 30 mm.

bluff body and develops in a projected triangularcross section emerging from the bluff body vertex,as shown in Fig. 5 and highlighted in the shadedarea in Fig. 6. The conditioned and unconditioned

Fig. 5. Mean progress of reaction �c. Linear gray scalefrom black: product; white: reactant.

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Fig. 6. Radial profiles of LDA measurements of mean conditioned reactant velocities u, v, w representing axial, radial,and tangential directions (solid lines), the unconditioned LDA measurements (symbols), and progress of reaction (solidblack line) for three different axial positions (rows) for case SwB1 (left), SwB5 (middle) and SwB9 (right).

Fig. 7. Radial profiles of calculated product and measured conditioned reactant axial velocities extracted at threedifferent axial positions (rows) in the flame brush region for all the three cases.

M.M. Kamal et al. / Proceedings of the Combustion Institute 35 (2015) 3803–3811 3809

profiles for the radial and tangential velocities areindistinguishable from the conditioned measure-ments within the accuracy of the present measure-ments. Since the non-axial velocity component

values are very low in the present non-swirlingflows, they are not considered further. The axialmeasurements are in agreement except within theflame brush and product region, where they

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Fig. 8. LHS=ð�u� ~uÞ, and RHS = ð�c� ~cÞð�ur � �upÞ from Eq. (2) as a function of progress of reaction, extracted at threedifferent axial positions (rows) for all the three cases.

3810 M.M. Kamal et al. / Proceedings of the Combustion Institute 35 (2015) 3803–3811

depart. The discrepancy is particularly large in theregion near the burner, where the conditionedvelocity at the edge of the flame brush is almosttwice the value of the unconditioned velocity.Further downstream however, the axial velocitymeasurements of conditioned and unconditionedvelocities are closer, within approximately 10–20percent.

The conditioned and unconditioned velocitiesobtained from aerosol and particle seeding canbe used to determine the conditioned productvelocity via Eq. (1), as a function of the progressof reaction, as shown in Fig. 7. The productvelocity is much lower than the reactant velocitieswithin the flame brush. This is a result of thelower unconditioned velocity within the region.The effect is more pronounced in the cases withhigher heat release rate (SwB9), and furtherdownstream.

The calculated difference between the PIV-derived Reynolds averaged unconditioned mea-surements for axial velocities �u, and the Favreaveraged unconditioned velocities ~u (Fig. 1), herecalled left hand side, LHS (of Eq. (2)), can be plot-ted against the progress of reaction along with theexpected difference of these two quantities fromthe right hand side (RHS) of Eq. (2). The RHS isthe product of the difference in Favre averagedand Reynolds averaged progress of reaction (fromEq. (3) and Fig. 6) times the difference in Reynoldsaveraged velocities of product and reactant from

Fig. 7. Figure 8 shows the outcome: despite the sig-nificant differences between the product and reac-tant velocities, the difference in the Reynolds andFavre averages is indeed very small, and explainsthe surprising agreement between the LDA andPIV measurements.

4. Conclusions

We have shown the reason why PIV and LDAmeasurements within the flame brush may notdiffer significantly in the approximation of thinflames, and demonstrated the principle for aparticular case, in which there are significant dif-ferences between reactant and product velocitiesand densities.

Unless there are very large differences in veloc-ities in the middle region of the flame brush wherethe density-weighted progress of reaction is high-est, the difference is minimized because it is pro-portional to the gap between averaged progressof reaction and its density weighted version, whichis a small number. Exceptions of course must bemade for situations where the thin flame modeldoes not apply. We suggest that in general LDAand PIV measurements in flame brushes will leadto somewhat different results, and the experi-menter should be aware of what conditions applyin the particular situation. The present data can bemade available by contacting the authors.

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Acknowledgments

The authors would like to thank the Universityof Engineering and Technology Peshawar (Paki-stan) and the University of Cambridge for theirfinancial contributions to this work.

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