Thermally assisted fluorescence oflaser-excited OH A 2S1 as a flame diagnostic tool

A. A. Neuber, J. Janicka, and E. P. Hassel

A simple laser-induced-fluorescence measurement technique for turbulent flame temperature and OHconcentration measurement is proposed and successfully tested. The main idea is that a narrow-bandtunable excimer laser beam 1l 5 308 nm2 is focused into a turbulent atmospheric-pressure nonpremixedflame. The OH molecule Q1132 1X 2P v9 5 0, A 2S1v8 5 02 transition is excited. By subsequentvibrational energy transfer, the distribution in the molecules’ upper electronic energy level 1excited S1

state2 is redistributed. By evaluating the spectrum of the broadband emission from the v8 5 1= v9 5 0and v8 5 2= v9 5 1 bands with a full spectral fit, we were able to evaluate the temperature and the OHmolecule density. The concurrent processes of quenching, vibrational energy transfer, and rotationalenergy transfer were taken into account in the evaluation process. The results were compared withnumerical flame calculations and revealed good agreement. One problem with this new proposedapplication of laser-induced fluorescence is the self-absorption of the emitted light. This, however, isshown not to be serious, but it has to be checked carefully. The main advantages are a simpleexperimental setup and procedure, high signal intensity, and a simple and straightforward dataevaluationmethod. Thus this measurement technique is suitable for turbulent flame temperature andOH concentration measurement, and it is an alternative to other well-established techniques that aremuch more complicated.Key words: Laser-induced fluorescence, turbulent combustion, diffusion flame, OH concentration.

r1996 Optical Society of America

1. Introduction

The modeling of turbulent combustion is still anobjective of extensive research. Appropriate de-signed experiments provide the means to addressmany of the questions not yet answered. Laser-induced fluorescence 1LIF2 is, among other recentlydeveloped and promising laser spectroscopic tech-niques such as degenerate four-wave mixing,1,2 suit-able for measuring the concentrations of minor spe-cies and radicals and the temperature. Thesequantities are important to the formation of pollut-ants. In the past two decades many researchershave been concerned with various subdomains ofLIF.3–7 All of them encounter, at least at pressuresequal to or higher than atmospheric pressure, seri-ous problems with electronic quenching. Therefore

The authors are with the Technische Hochschule Darmstadt,Energie-undKraftwerkstechnik, Petersenstrasse 30, 64287Darm-stadt, Germany.Received 19 December 1995; revised manuscript received 11

March 1996.0003-6935@96@214033-08$10.00@0r 1996 Optical Society of America

the correction of the measured LIF signals or spe-cially designed experimental approaches are neces-sary.8–13Modeling of the complete LIF process, including

all intermediate subprocesses such as photon absorp-tion, stimulated and spontaneous emission, molecu-lar electronic quenchingQ, vibrational energy trans-fer 1VET2, and rotational energy transfer14–17 1RET2,is another promising method. The principal phys-ics of the coupling between radiation and atoms ormolecules is well understood. This allows us tocalculate thermalized spectra of many combustion-relevant molecular species. The major problem isthe understanding of the interaction of the excitedmolecules with their neighboring molecules. Theoccurring energy transfer can be calculated if thesurrounding major species concentrations ci andtemperature T are known. To do this, the rates ofquenching, VET, and RET as functions of ci and Tmust be known. Unfortunately these rates are notyet available from the literature for the entire tem-perature range and all possible mixtures of thesurrounding gas. Considering the work alreadydone, these data for CH4–air combustion may be

20 July 1996 @ Vol. 35, No. 21 @ APPLIED OPTICS 4033

available in a few years.18–23 Thus a method that isnot strongly dependent on quenching, VET, and RETwould be useful.Thermally assisted fluorescence of laser-excited

OH A 2S1 based on VET seems promising. Theusefulness of this approach was shown by Joklik24 bymeasurements in the postflame regions of variouslaminar premixed flames. In this paper the evalua-tion theory is based on a two-level model that takesinto account quenching and VET. The presentedexperimental data are spectrally and temporallyaveraged. The accuracy of the temperature mea-surements is given by 650 K, and the variation ofQ@V 1Q is the electronic quenching rate in inverseseconds, and V is the VET rate in inverse seconds2 ofthe first vibrational state for a wide range of equiva-lence ratios and fuels is reported.Applying a comparable excitation and detection

scheme, Crosley and Smith25 have already donesome fundamental work. They excited the X 2P1v8 5 02 = A 2S 1v8 5 02 transition in single-shot mea-surements and detected the intensities of the 10, 02and 11, 02 bands by using two photomultipliers.Spectral separation was done by a spectrometer.Data analysis was done with the steady-state as-sumption, neglecting the influence of rotation on thevibrational transfer from v8 5 0 into v8 5 1. Anerror of 660 K for temperature and an uncertaintyof 633% in theQ1@V10 ratio were given.In 1984, Dyer and Crosley26 reported more de-

tailed temperature measurements based on VET inthe burnt gases of premixed CH4@O2@N2 flames.Again, only the VET of v8 5 0 into v8 5 1 and viceversa is considered. The excitation was kept in thelinear regime. Spectrally integrated intensities ofthe single bands were detected. Q@V ratios werecalculated from the band ratios, with an averagevalue of the Q@V parameter obtained by comparisonwith thermocouple temperature measurements.Thermocouple temperatures and VET temperatureswere consistent within 5%.In the research described here, the laser is tuned

to a wavelength that corresponds to the Q1132 10, 02transition of the A–X system of OH. The spectralpower is chosen to be high enough to saturate thistransition. As a consequence of VET, a LIF signalarises from the 11, 02 and 12, 12 bands. This signal isdetected with a camera spectrometer system in orderto get full spectral information in a single shot.Because the main aim of this research is the investi-gation of turbulent combustion, it is necessary to getall information with one single shot. The proposedmethod reduces the dependence of the evaluationquality on the exact knowledge of the absolute valueof the Q@V ratio. The influence of errors arisingfrom the calculation of the quite uncertain Q andVET rates, taken from literature, is minimized.

2. Experimental Setup

The radiation for the excitation of OH molecules isgenerated by a narrow-band tunable XeCl excimer

4034 APPLIED OPTICS @ Vol. 35, No. 21 @ 20 July 1996

laser 1Lambda Physics2 that produces UV light 1308nm, bandwidth 0.3 cm21, 130 mJ, 20-ns pulse dura-tion2. The main beam is focused by a 1000-mm lensinto the flame 1Fig. 12. Tilting of the lens avoidsoptical break-down. The resulting focus is approxi-mately rectangular 1height 1.0 mm, depth 0.4 mm2.LIF photons are collected by a camera lens 1NikonUV-1052, which is mounted with the front pointing tothe spectrometer in order to minimize lens aberra-tions. The spectrometer 1Spex, f 5 500 mm, singlegrating 600 lines@mm, f-number 4.62 is mountedsuch that the entrance slit 10.3 mm 3 1.7 mm2 isparallel to the focused laser beam direction. Fromgeometric optic calculations of the signal receivingoptics with a measured magnification of the cameralens of 1.7, the measurement volume Vm dimensionsare 0.7 mm 3 0.24 10.4 mm3 1length times heighttimes depth2. Because the receiving optics thusgives smaller dimensions of the measurement vol-ume than the laser focus does, the collection ofnonsaturated fluorescence from the wings of thefocused laser beam is minimized.27The spectrally resolved LIF signal is detected by

an intensified diode array 1Spectroscopy Instru-ments, 700 intensified channels, each 0.025mm 3 2.5mm, gate time 50 ns2. The signal may be referencedby a synchronized measurement of the laser pulseenergy by the use of a photodiode 1EG&G FND-100Q2in connection with a boxcar integrator. The mea-sured pulse energy fluctuation is 61.7% of the meanvalue. Thus, for the most part, no reference ismade. For some parts of the described experi-ments, the spectrometer is replaced by another onewith a higher spectral resolution 1Spex, f 5 1000mm, single grating 2400 lines@mm, f-number 92.The burner of the free turbulent H2@N2 jet diffu-

sion flame28 consists of a tube with a diameter of 6mm and a coflowing air stream of 0.2 m@s. The fuelstream exit parameters of the two test flames aremass fraction H2 5 5%, Reynolds numberRe 5 8600,and mass fraction H2 5 20%, Re 5 8600, which arecalled flame 1 and flame 2, respectively. A statisti-cal description of the data is essential to obtain fullinformation about the strong fluctuations caused byturbulence.To obtain reasonable mean values and standard

deviations, it is necessary to take at least 100single-shot spectra, i.e., at least 100 single tempera-ture and concentration values at each particularspatial position. These data are to be compared

Fig. 1. Experimental setup used in the broadband LIF experi-ments. The OH LIF signal is collected by an UV camera lens.

with results from combustionmodel predictions 1withReynolds-stress model and equilibrium chemistry292,which give the results in the form of averaged valuesand standard deviations or turbulence levels asfunctions of the spatial flame coordinates, axis, andradius. Few turbulent combustion models use com-plete probability density functions.30 Thus, in Ref.29, it is sufficient to restrict the description of theturbulence to the first- and the second-order statisti-cal moments needed for a comparison with thecommon first- and second-order closure models.

3. Results

In Fig. 2 an OH LIF spectrum that is recorded withthe high-resolution spectrometer in second order isshown. The excited Q1132 transition is indicated asQ11 1308.17 nm2, and all other transitions are wellseparated with the exceptions of the P21132 and theP11112 lines. The laser linewidth is smaller than thespectral resolution of the spectrometer, and thecalculated spectral line positions of these three tran-sitions are within a width of 1.3 cm21. Because theabsorption cross section of the P21132 transition is by afactor 4 or 5 lower than that of the excited Q1132 line,the laser is closely tuned to this transition 1Dn , 0.3cm212. When the spectral overlap integrals are cal-culated for this tuning position, it is found that theabsorption cross section is more than 190 cm2 cm21@Jfor all three transitions. The Rayleigh signal de-tected with a rotated polarization of the excitinglaser beam and the same spectral resolution revealsnot only the main line but also a satellite line that iscaused by the incomplete spectral suppression of theexcimer laser’s broadband amplified spontaneousemission, which is due to the high gain of the lasermedium.30 It was carefully checked that this is thebest spectral position that coincides with a mol-ecule’s transition. It can be seen that the satelliteline falls in the gap between the Q1112 and the Q1122transition; thus its influence is negligible. Another

Fig. 2. OH LIF spectrum from a diffusion flame and the laserline spectrum taken by the use of Rayleigh scattering from roomair. The main laser line at 308.17 nm excites simultaneously theQ11132, QP21132, P11112OH lines with a sufficient spectral overlap andpower to saturate all of them. Fortunately, the satellite laserline at 307.9 nm falls in the gap between the Q11112 and Q11122transitions.

method to determine the coincidence between laserline and OH molecular lines is an excitation scan.But one disadvantage of this method is that theinfluence of the laser satellite lines cannot be de-tected. At the adjusted tuning position of the laser,the spectral intensity of the main laser line is 5.4 3109 W@cm2 cm21 in the focal region. Thus thesaturation parameter for the three excited transi-tions, which is defined as the ratio of the absorptionrate coefficient to the effective quenching rate,8 is,500, and the three transitions in the 10–02 band aresaturated.The measurement signal is the spectrum of the

broadband thermally assisted LIF emission of the11–02 and 12–12 bands recorded with the low-resolu-tion spectrometer 1Fig. 32. These two bands overlapspectrally. The 2–1 band with a slight greaterFranck–Condon factor30 has a lower intensity thanthe 1–0 band because the number of molecules in thev 5 1 level is greater than in the v 5 2 level becauseof thermalization of the state densities of the uppervibrational levels.31

4. Analysis

It is assumed that the rotational distribution in thevibrational levels v8 5 1 and 2 of the A 2S1 state iscompletely thermalized.32 Additionally, in the firststep, it is assumed that the ratio of the densities ofthe vibrational states v8 5 1 and 2 is thermalized.From these assumptions, the OH LIF spectra caneasily be calculated as thermal emission for the twobands populated by VET.Figure 3 shows a measured single-shot spectrum

from flame 1 and a corresponding calculated one.The calculated spectra temperatures are varied asT0 5 1939 K, T1 5 1739 K, and T2 5 2139 K. Thisresults in least-squares sums of S0 5 0.243, S1 50.410, and S2 5 0.409, respectively. This shows thesensitivity and convergence of the evaluation proce-dure because the least-squares sums are quite differ-ent, and so the fit gives a clear minimum for the

Fig. 3. Single-shot broadband OH LIF spectrum in the freeturbulent H2@N2 diffusion flame 1solid curve2. The spectra werecalculated with T 5 1939 6 200 K. Compared with the experi-mental data, the spectrum with T 5 1939 K has the lowestleast-squares sum, which is half of the value of the others.

20 July 1996 @ Vol. 35, No. 21 @ APPLIED OPTICS 4035

least-squares sum. The temperature T0 is the re-sult of a full spectral fit that is similar to thatdescribed in Refs. 33 and 34 for fitting of coherentanti-Stokes Raman spectroscopy andRaman spectra.All experimental spectra are fitted by theoreticalspectra when the least-squares sum is minimized;the main fit parameters are the OH concentrationcOH, the temperature T, and the spectral shift. Totest the assumptions, the influence of the VET on thefitted temperatures is investigated with a simplethree-level model to describe the thermally assistedfluorescence.A scheme of the transfer rates in the A 2S1 state is

shown in an energy-level diagram in Fig. 4. Thevarious processes are described by rate equations35:

dN2@dt 5 N0V02 2 N21A2 1 Q2 1 V20 1 V212 1 N1V12,

11a2

dN1@dt 5 N0V01 2 N11A1 1 Q1 1 V10 1 V122 1 N2V21,

11b2

dN0@dt 5 N1V10 2 N01A0 1 Q0 1 V02 1 V012

1 N2V20 1 pump 2 loss, 11c2

where Ni is the state density of level i, Qi is theelectronic quenching rate 1in inverse seconds2, andVi j is the VET rate from level i to level j 1in inverseseconds2. Pump and loss refer to absorption andstimulated emission, respectively, and are deter-mined by the intense laser radiation that couples thelower X 2P 1v9 5 02 and the upper A 2S1 1v8 5 02electronic levels. These rates are some orders ofmagnitude higher than the others. The time con-stant to reach steady state in the N0 state is esti-mated to be of the order of 10212 s. Thus, after <2.5ns the rotational distribution will reach steady statetoo. Under these conditions, steady state can beassumed. The stationary solution of the rate equa-tions gives the ratios of the state densities:

N2@N1 5 C exp32hc1E2 2 E12@kT4, 122

Fig. 4. Schematic energy-level diagram of the A 2S1 state, thefirst excited electronic state of the OH molecule. The first threevibrational levels 1v 5 0, 1, 22 and the occurring collision or radia-tion transfer rates are shown. The rotational levels are notshown. V symbolizes the VET, Q the quenching processes.Pump and loss are determined by the intense laser radiation thatforces the level to saturate.

4036 APPLIED OPTICS @ Vol. 35, No. 21 @ 20 July 1996

with

C 5 3V201A1 1 Q1 1 V10 1 V122 1 V10V214

@3V101A2 1 Q2 1 V20 1 V212 1 V20V124. 132

Ei is the energy of level i 1in inverse meters2, h isPlanck’s constant 1in joules times seconds2, c is thespeed of light 1in meters per second2, k is Boltzmann’sconstant 1in joules per degree Kelvin2, and T is thetemperature 1in degrees Kelvin2. Detailed balanc-ing of the VET rates,

V12@V21 5 exp32hc1E2 2 E12@kT4, 142

and neglect of the exponential terms as well as thespontaneous emission result in a simple dependenceon the rates for C:

C 5 1V20Q1 1 V10V20 1 V10V212

@1V10Q2 1 V10V20 1 V10V212. 152

The two vibrational levels are thermalized andC5 1if the identity V20@V10 5 Q2@Q1 is valid.Table 1 gives the influence of variations ofC on the

temperatures resulting from full spectral fits. Thespectra are calculated with a fixed temperature forvarious values of C and then fitted to experimentalspectra. C 5 1 means that the A 2S1 state is fullythermalized. It is to be seen that deviations fromthe thermal equilibrium 1C 5 12 gives erroneous re-sults in temperature. Therefore C must be knownfor the evaluation of the spectra or has to be cali-brated. During the presented evaluations it is as-sumed that C 5 1, and this assumption is discussedbelow during the comparison of the experimentaland the numerical turbulent flame temperatures.In Fig. 5a the measured mean temperature of

flame 2 is plotted as a function of radial position.The downstream level is 20 in normalized units ofthe nozzle diameter 1x@D 5 202, and the radial posi-tion r 5 0 is on the flame symmetry axis. The solidcurve is a simulation with a Reynolds-stress modelfor the flow field and with chemical equilibriumassumption for the reaction.36 Extensive tempera-ture measurements with spontaneous Raman spec-troscopy37 and coherent anti-Stokes Raman spectros-copy38,39 in the same turbulent diffusion flames showthat the simulation gives the correct temperaturewithin a bandwidth of 100 K maximum.The LIF temperatures also lie within this band-

width for those flame locations that give more than75% of valid spectra 1that is, at a radius from 11 to 15mm2; otherwise the statistic is biased too much 1Fig.

Table 1. Influence of Nonthermalized Vibrational State Distribution

Ttheo C 5 0.7 C 5 0.8 C 5 0.9 C 5 1.0 C 5 1.1 C 5 1.2 C 5 1.3

1600 1504 1536 1568 1600 1632 1666 16991900 1750 1800 1849 1900 1951 2003 20562200 1991 2059 2129 2200 2272 2344 2434

5b2 because there is simply not enough OH in themeasurement volume. This biasing is a commonproblem of all spectroscopic temperature measure-ment techniques that rely strongly on nonuniformdistributed species. It does not occur in the laminarpremixed flames of Refs. 24–26. OH mole fractionshigher than <10 parts in 106 1ppm2 exist in atmo-spheric flames for only temperatures above 1000 K.40So it is not surprising that the measured tempera-tures in flame regions with low mean OH concentra-tion are too high.In contrast, there is no biasing of theOH concentra-

tion because in the averaging procedure mole frac-tions lower than 10 ppm; that is, the detection limit,can be set to zero with a small error only. Peakvalues of the OH concentration are estimated to beas high as 15,000 ppm.40The mean OH concentration profiles, shown in

Fig. 5c, differ clearly in position and spatial width.This is because the combustion model assumption ofchemical equilibrium is valid only for the majorspecies but not for the radicals like OH.40 Bothconcentrations, experimental and theoretical, arenormalized at maximum value and therefore give noinformation about the absolute OH concentration.As a rough estimation the estimation the simulatedequilibrium OH concentration is approximately 5 31014 cm23 maximum. Nevertheless a comparison ofthe relative values is still interesting.In Fig. 6 the OH concentrations of flame 1 and

flame 2 are compared at the downstream positionx@D 5 20. The theoretical and the experimentalOH concentrations of flame 1 are normalized asdescribed in Fig. 5; that is, the maxima of theexperimental and the theoretical OH curves forflame 2 1only flame 22 are set to 100. So one experi-

Fig. 5. a, open circles, variation of experimental mean tempera-ture with the flame radius at the flame level x@D 5 20 of flame 2;solid curve, calculatedmean temperature; filled circles, experimen-tal standard deviation of the temperature caused by turbulentfluctuations; dashed curve, calculated standard deviation. b,fraction of spectra with high enough intensity for a successfulevaluation 1in percentage2. c, open circles, experimental meanOH concentration in molecules per volume, normalized to 100;solid curve, calculated mean OH concentration, normalized to100; filled circles, experimental standard deviation of the OHconcentration.

mental and one theoretical calibration factor are set.The results from the other flame, flame 1, are correctin absolute relation to the 1calibrated2 results fromflame 2. Flame 1 is smaller in shape than flame 2because flame 1 ismore diluted with N2, and thus theaverage line of stoichiometric mixture is nearer tothe axis than that in flame 2. The experimentalmaximum OH levels for flame 1 and 2 are quitesimilar, although the stoichiometric mixture fractionfst is quite different, with fst@1 5 0.367 and fst@2 50.127 for flame 1 and flame 2, respectively. Thecombustion model simulation of flame 1 predicts anOH level much lower than that of flame 2. This isan obvious sign that the combustion model chemicalequilibrium assumption fails to predict correct OHconcentrations, which is known in the literature assuperequilibrium OH concentration 1see, e.g., Refs.13 and 342.From the experimental data 3solid angle of detec-

tion 0.007, transmission of receiving optics 0.86,sensitivity of the camera system 0.2 counts@photon,measurement volume 0.7 mm 3 0.24 mm 3 0.4 mm,Einstein coefficient 11–0 band2 0.3 3 106 s21, laserpulse duration 25 ns2, the detection limit is esti-mated with the following assumptions. The statedensity in the levels v8 5 1 and v8 5 0 are assumed tobe in thermal equilibrium. The temperature isassumed to be 2300 K. Molecular density for allspecies is 3.3 3 1018@cm3. Because of saturation,the density in levels v8 5 0 and v9 5 0 are equal.It is further assumed that ,50 detector counts are avalid signal that is separated from the background1,5 counts2. From these data the detection limitfollows to be 10 ppmOH.41 From the literature, oneobtains a sense of the same order of magnitude forLIF measurements in the 0–0 band.41

Fig. 6. Open circles, variation of experimental OH concentrationwith the flame radius at the flame level x@D 5 20 of flame 2;dashed curve, calculated OH concentration of flame 2; filledcircles, experimental flame 1; solid curve, calculated flame 1.The numerical and the experimental results from flame 2 arenormalized to 100, and the values of flame 1 are normalized by thefactor resulting from the normalizing procedure applied to flame2. The variation of OH concentration with the fuel mixture canbe directly compared.

20 July 1996 @ Vol. 35, No. 21 @ APPLIED OPTICS 4037

5. Discussion

A. Temperature

The main systematic uncertainty in the experimen-tal results originates from the unknown value of C.The rates that determine this value are rarelyknown for two reasons. First, one cannot find verymuch quantitative data on VET in the literature.Second, if it would be possible to calculate completelycross sections of the VET and all other collisionalprocesses, a lack of information about the composi-tion of the neighboring molecules remains, whichalso influences the rates. That problem can besolved by simultaneous measurement of the majorspecies, e.g., with spontaneous Raman spectroscopy.34The first problem is still severe, even if the majorspecies are known. In spite of this, for the workdescribed here the value of C is estimated indepen-dently of flame conditions.The literature contains much information about

RET42–50 and quenching18,20,23,46,49–57 but less aboutVET,22,50,51 and unfortunately much less with respectto higher vibrational levels.21 No values could befound for the quenching rate Q2, but some of Q1 1Ref.502 and Q0 1Ref. 492 and the VET rates V21, V20, andV10 1Ref. 222 were found. For lack of better informa-tion we assumed the ratios Q2@Q1 and Q1@Q0 to beequal. Data on electronic quenching as well as VETare available only for the thermodynamic state ofpure N2 at T 5 300 K.22 For this state, with Eq. 112,C becomes ,0.9. This corresponds to a tempera-ture of error of ,3% at temperatures above 1000 K.TheOH formation is strongly exponential tempera-

ture dependent, and thus OH exists mainly above,1000 K. C is determined mainly by the ratio ofthe vibrational and the electronic quenching rates.The ratio has values of approximately 5 to 10, withN2 molecules as collider. So a factor of 3 in the VETrates is of little influence in the presented context.The temperature measurements are accurate within100 K. From this it is concluded that for collidermolecules other than N2, e.g., the H2O molecule, theequation V20@V10 5 Q2@Q1 approximately is valid.From the temperature measurements, which appearto be accurate within 100 K, it is concluded thatcollider molecules other than N2 e.g. the H2O mol-ecule, which has 1 order of magnitude higher elec-tronic quenching rate,20 must have approximatelyequal ratios of V20@V10 and Q2@Q1. The influence ofRET is neglected by the assumption of a completelythermalized rotational distribution in the v8 5 1, 2levels. There are no detailed investigations of VETthat would include initial and final vibrational rota-tional levels. Lengel and Crosley found some chan-neling of energy into rotation with the 1 = 0vibrational transfer of the OH A 2S1 state.22 Thiscan hardly be transferred to the presented condi-tions in detail because here an upward VET happensin which the OH gains energy from a collisionpartner. Further investigations with higher spec-tral resolution are needed to resolve the rotationallines spectrally. This can be done only in stationary

4038 APPLIED OPTICS @ Vol. 35, No. 21 @ 20 July 1996

flames by the use of time averages because otherwisethe signal intensity in atmospheric flames will not besufficient.Self-absorption of the LIF signal, which is possible

mainly in the 11–02 band because of the most denselypopulation v9 5 0 level in the X 2P state, is estimatedto have a low error potential. It is shown by numeri-cal emission and absorption calculations that a sheetof OH molecules 1mole fraction 1000 ppm, tempera-ture T 5 1300 K, thickness 16 mm2 shifts the result-ing temperature by 140 K if the detected OH is at1600 K. This case is a safe limit because in mostflames the product of concentration and momentarysheet thickness is much lower. That the influenceof self-absorption is small results only from the ratioof the Franck–Condon factor of the 11–02 band to thatof the 10–02 band, which is 0.25.30

B. OH Concentration

The temperature determination error also affectsthe OH concentration measurement. Additionally,the quenching rate values influence the LIF signalintensity directly, even if C 5 1. The absolutequenching cross sections are linear to the OH concen-trations. Cattolica and Mataga found a very strongdependence of quenching on temperature for the v8 50 and v8 5 1 levels with H2O molecules as collider.20The overall quenching cross section s1v8 5 02 of col-lider H2O decreases from 90 Å2 at T 5 300 K to 26 Å2

at T 5 1075 K and s1v8 5 12 from 80 to 35 Å2. Thiswould result in an OH concentration error of nearly100% by an overestimation of the OH concentrationat high temperatures. The flames investigated con-tain OH concentrations of a sufficient level only attemperatures higher than <1000 K, so the results ofPaul23 have to be considered. In this paper a muchlower temperature dependence of s0 for most colli-sion partners in the higher temperature range ispresented. The harpooned model for temperature-dependent quenching gives a maximum variation of33% with H2O as collision partner for the crosssection T 5 1000 K to 2000 K. The referencedmeasurements therein23 even show a lower tempera-ture dependence of the cross section. In addition,the other potential collision partners such as N2, O2,and H2 also have a lower quenching cross section.Thus the maximum estimated error in the measuredrelative OH concentrations is 33%.

6. Conclusion

The experimental results presented demonstratethat thermally assisted fluorescence of laser-excitedOH is a tool, easy to apply, to measure temperatureand OH concentration in turbulent atmosphericdiffusion flames.58 The discussion revealed that themain uncertainty in the temperature determinationwith full spectral fit arises from the assumption ofthermal equilibrium of the collision populated levelsv8 5 1, v8 5 2. The error is estimated to be 3% withN2 as the collider molecule. More general, a com-parison with flame-modeling temperature data

showed the error in the mean temperature value tobe lower than 100 K. One should keep in mind thatthis good agreement in temperature between experi-ment and simulation holds only if there is a sufficientOH concentration in the measurement volume witheach laser shot. If electronic quenching is the domi-nant collision process compared with VET, the ratiosof the vibrational rates V20@V10 and the electronicquenching rates Q2@Q1 are nearly equal. The OHconcentration detection limit is approximately 10ppm, and the error caused directly by quenching inthe v8 5 1, 2 levels is lower than 33%. The unknownenergy transfer rates 1Q, VET, RET2 influence theoverall measurement error. To reduce the errorbelow the limits given, future research must concen-trate on combined techniques that yield the concen-tration of the major species and OH simultaneouslyand on the determination of energy-transfer crosssections in a wider parameter 1temperature, rota-tional and vibrational quantum number, collisionalspecies2 range. Because the detected radiationwave-length is shorter than the excitation wavelength, thepresented diagnostic tool is quite insensitive tointerfering radiation, so there is a good chance ofmeasuring successfully in CH4 flames, which are ofgreat technical interest.

This research is supported by theDeutsche Forsch-ungsgemeinschaft, contract number Ja 544@4-1.We thank Stephan Wegscheider, who worked hardfor the evaluation of the experimental data. Nu-merical simulations of the flame were done by DirkPfuderer.

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