Quantitative species measurements inmicrogravity flames with near-IR diode lasers

Joel A. Silver, Daniel J. Kane, and Paul S. Greenberg

Absolute concentrations of water vapor are measured in microgravity 1µ-g2, nonpremixed methane, andpropane jet flames with diode-laser wavelength modulation spectroscopy. These experiments areperformed in the 2.2-s µ-g drop facility at the NASALewis Research Center. Abel inversion methods areused to determine time-dependent radial profiles from eight line-of-sight projections across theflames. At all measured heights above the nozzle, water vapor spatial distributions in µ-g flames aremuch wider than their 1-g counterparts. Radial growth of the water signal continues throughout thedrop, verifying earlier suggestions that a steady state is not reached during the duration of the test,despite a quasi-steady flame shape. Large amounts of water vapor are observed at larger radii, at oddswith visual 1video2 observations and numerical predictions.Key words: Microgravity, combustion, diode laser, wavelength modulation spectroscopy.

1. Introduction

A low-gravity environment, in space or in ground-based facilities such as drop towers, provides a noveland unique setting for the fundamental study ofcombustion mechanisms that are normally obscuredby buoyancy effects. There is a widely acknowledgedneed for advanced diagnostic techniques inmicrograv-ity combustion research.1 When the demands ofspace flight are considered, the need for improveddiagnostic systems that are rugged, compact, reliable,and have low power demand becomes apparent. Formeasurement of species concentrations or tempera-ture, nonintrusive laser diagnostics are normally themethods of choice. However, most laser diagnosticmethods in use today 1laser-induced fluorescence,spontaneous Raman or Rayleigh scattering, coherentanti-Stokes Raman scattering, two-dimensional imag-ing, etc.2 rely on bulky and expensive lasers thatusually have substantial power or cooling require-ments and may exhibit quirky operating characteris-tics. In addition, these laser methods are, at best,poorly suited or, at worst, not applicable at all, to the

J. A. Silver and D. J. Kane are with Southwest Sciences, Inc.,1570 Pacheco Street, Suite E-11, Santa Fe, New Mexico 87505.P. S. Greenberg is with the NASA Lewis Research Center, Cleve-land, Ohio 44135.Received 2August 1994; revised manuscript received 5 December

1994.0003-6935@95@152787-15$06.00@0.

r 1995 Optical Society of America.

measurement of fuel, oxidizer, and major productspecies.We describe a prototype instrument for nonintru-

sive measurement of concentration and temperatureprofiles of species that are important in microgravitycombustion research. The system combines the useof near-infrared diode lasers with high-frequencywavelength modulation spectroscopy 1WMS2 to mea-sure gas phase species in high-temperature systems,permitting the development of a monitoring systemwith a wide dynamic range and a fast time response.Fiber optics direct the diode-laser radiation alongeight lines of sight. Abel inversion techniques areused to extract axially symmetric mole-fraction pro-files from these projections. These spatial, tempo-ral, and spectral profiles can be used to determineimportant parameters such as the flame-front loca-tion, the extent of diffusional mixing, and local tem-peratures. This research focuses on detection ofwater vapor and methane. Water vapor mole frac-tions were successfully measured in zero-gravityflames. Methane, although observed in normal grav-ity, was insufficiently free of background effects to beuseful. To our knowledge, these experiments repre-sent the first quantitative measurements of chemicalspecies under microgravity combustion conditions.

2. Experimental

The diode-laser-based detection system is designed tomeasure molecular absorption along eight lines ofsight across microgravity flames. The key to thisapproach is to separate the laser, detector, and elec-

20 May 1995 @ Vol. 34, No. 15 @ APPLIED OPTICS 2787

tronics from the experimental drop package, whichencounters severe deceleration loading. This is ac-complished by piping the laser radiation to and fromthe drop rig by the use of optical fibers. The detailsof the apparatus are presented in this section.

A. Microgravity Combustion Apparatus

Experiments are performed in the NASA Lewis 2.2-smicrogravity drop tower.2 This facility and the ex-perimental apparatus are shown in Fig. 1. In brief, aself-contained test rig holding the fuel supply, nozzle,igniter, and optical fiber frame is suspended above a27-m shaft by a piano wire. On receiving an electri-cal trigger, the wire is sheared, and the package freefalls for 2.2 s. Gravity levels of 1024 g are typical.At the end of the drop, the assembly decelerates in apit of aerated sand. Deceleration forces on the flamenozzle and the optical fiber frame are approximately100 g. A drag shield surrounding the experimentalpackage minimizes air resistance during the fall andprotects the system from contamination by the sand.Anonpremixed flame is generated from ignition of a

regulated flow of propane or methane that issues froma stainless-steel tube, 0.0825 cm in radius. Flowrates monitored with an in-line flowmeter rangedfrom 1.5 to 3.0 scc@s, with no coflow of air. A coiledKanthal filament located 1 mm above the nozzle tip isused to ignite the flame. This coil is attached to anarm that is swung out of the optical path by anelectromagnetic switch. At the start of the free fall,a solenoid valve turns on the gas flow, and the flameignites within 200 ms, then the heater arm is swungaway. For some experiments, the flame was ignitedand allowed to stabilize in 1 g before free fall. Igniterand gas-flow functions are controlled with an on-board microcontroller.The entire measurement system, except for the

optical frame, sits on a table at the top of the tower.The optical frame is mounted above the nozzle tip andholds eight pairs of fiber-optic collimating lenses that

Fig. 1. Schematic of microgravity 1µ-g2 drop experiment.

2788 APPLIED OPTICS @ Vol. 34, No. 15 @ 20 May 1995

pitch and catch the laser beam across the flame atdifferent distances from the flame center. A 30-m-long, 12-conductor, single-mode optical cable connectsthe laser and the detection electronics to the drop rig.The fiber cable is tied to a cross beam above the shaftand is slung halfway down and then up to a second tiepoint on the drop rig cover. This approach mini-mizes any chance of snagging the fiber cable duringthe drop as well as reducing any torque to the rig,which might cause it to fall unevenly. The totalsuspended weight of this cable is ,3 kg.One fiber in the cable transmits the laser radiation

to a wideband fiber-optic 1 3 8 splitter that dividesthe light into eight channels. Each channel fiber isterminated by a gradient index 1GRIN2 lens collimatorof a diameter of 1.8 mm. Each collimated beamtraverses the flame region and is collected by a returncollimator that focuses the light into a return fiber.The light in these eight lines is transmitted backthrough the cable to individually fiber-pigtailedInGaAs photodetectors mounted on the detection–demodulation circuit boards. The advantage of thisapproach is that there are no electronics or movingparts on the drop rig.The design of the optical frame is critical to the

operation of the system. Although the light is easilycollimated into a narrow beam by the input lens,collecting and focusing the light into the return fiberis most challenging because of the small acceptanceangle of the collection optic. The square opticalframe is mounted rigidly to the aluminum plate thatholds the fuel jet and can be adjusted in height inincrements of 2 mm relative to the nozzle tip.The frame used in preliminary experiments has a

4.0-mm spacing between adjacent lines of sight and isconstructed from aluminum. It consists of two pieces:a main section having V grooves to locate the lensesaccurately and a cover that has springs to hold thelenses in place. This design functions quite well, androtation of the fibers in their grooves, repeated disas-sembly, and externalmechanical vibrations have littleor no effect on the measured efficiencies of lightcollection across the flame region.Various types of optical fibers were evaluated for

the detection leg of this frame. 1The laser comespigtailed with a single-mode fiber, so the input leg tothe optical frame is predetermined.2 These includeda single-mode fiber with a 9.5-µm-diameter core, a50-µm-core multimode fiber, and a 200-µm-core mul-timode fiber. Our experience with fiber optics leadsus to be cautious when using multimode fibers be-cause of the possible introduction of interferencefringes or fiber noise into the absorption spectrum.However, a larger-core fiber makes it easier to collectthe light into the fiber after it traverses the flame.The fractional laser powers measured for these threefibers show collection efficiencies across a 12-cm airpath that range from 19% for the single-mode fiber to75% for the larger-core multimode fiber. Our conclu-sion from these tests is that it is best to use thesingle-mode-fiber collection scheme, trading off some

signal loss to avoid the noise inherent in the multi-mode fibers. Only very weak etalons are observedwhen this frame is used.After preliminary drop tests, it appeared that the

4.0-mm spacing of this frame was too large to providesufficient spatial resolution near the flame center, so anew fiber frame with 3.0-mm-spaced lines of sightwas designed and constructed from annealed toolsteel. Unlike the earlier aluminum frame, this de-sign is more rigid and does not exhibit any flexing.The open path across the frame is only 5.7 cm, andstrong etalons, which are due to backreflections offeither the GRIN lens front surface or the fiber–GRINlens interface, were observed. To eliminate this prob-lem, we used beveled 14.5°2, antireflection-coatedGRINlens collimators fabricated by Oz Optics on the inputlines to the frame. Backreflections do not focus ontothe fiber, and thus etalon formation is reduced.Unfortunately this requires a more complicated fiber-mounting design, because the beam exits the collima-tor not along the lens axis, but at an angle equal tothat of the bevel. Thus the lens must be set at ,4.5°,and its rotational angle must be adjusted so that itstrikes the center of the opposite 1detector-side2 colli-mator. Despite the additional design complication,the alignment of the optics is fairly simple andrequires only minimal, if any, readjustment after adrop. The collection efficiency for this frame is,50%when single-mode collection fibers are used. Thisimprovement over the larger frame is due to a combi-nation of a shorter open path and more degrees offreedom in alignment.

B. Laser Detection System

High-frequency laser WMS is used to measure theweak absorption signals observed in these experi-ments. The usefulness of this method is its highsensitivity and large bandwidth 1which are limitedonly by the modulation frequency2. Unlike directabsorption, the detection sensitivity is limited bydetector quantum noise and not by laser 1@f noise.This can improve the detection sensitivity by 3 to 4orders of magnitude. We described this technique inconsiderable detail in two recent publications, includ-ing comparisons with other high-frequency diode-laser detection methods 1e.g., one- and two-tone fre-quency modulation spectroscopy2.3,4Briefly, this method, which is an extension of diode-

laser derivative spectroscopy techniques widely usedat kilohertz frequencies,5 involves adding a sinusoidalmodulation at frequency f to the diode-laser injectioncurrent. Typically the amplitude of this currentmodulation is characterized by the dimensionlessWMS modulation index m, which reflects the magni-tude of frequency excursion induced by the modula-tion relative to the absorption linewidth. Phase-sensitive electronics demodulate the detectorphotocurrent at the second harmonic of modulationfrequency, 2f. In the small modulation limit theWMS line shape is the second derivative of theoriginal molecular absorption line shape. In prac-

tice the modulation index is set at a value thatmaximizes the signal level at which induced wave-length modulation is comparable with the width ofthe spectral feature, and, in this regime, line shapesare only derivativelike but can be readily calculated.3Diode lasers used in this study include standard

commercial InGaAsP devices used in optical commu-nications 11316–1345 nm; Toshiba, Mitsubishi, andFujitsu2 as well as new custom devices availablethrough Sensors Unlimited 11393 and 1659 nm2. Thelatter are superior because they are designed toaccess the strong near-infrared bands of methane andwater. The laser wavelength can be coarsely tuned ifthe laser temperature is varied 1tuning rate of approxi-mately 20.5 cm21 °C212. High-resolution tuning ofthe laser wavelength is accomplished by variation ofthe laser diode injection current 1,0.03 cm21 mA212.The laser controller 1ILX Lightwave Model LDX-27222has an adjustable current resolution of 0.01 mA.Short-term 110-min2 stability of the controller is 5 mK1temperature2. The laser linewidth 1,100 MHz, or0.003 cm212 is small compared with the spectral widthof the absorption lines 10.05–0.1 cm21 HWHM2. Thispermits full resolution of the detailed molecular lineshape and also allows the selective measurement ofan individual line without spectral interferences.The laser packages have a single in-line or butterfly

pin configuration and contain the laser, a photodiodepower monitor, and an integrated thermoelectric cool-er–heater for controlling the laser temperature. Thelaser output is coupled directly into a single-mode19.5-µm core diameter2 optical fiber with an ST-styleconnector on its end. An optical isolator 1.35-dBrejection2 prevents feedback of light into the laserfrom the optical fiber ends or other optical components.In most of the devices we use, the isolator is integralto the laser package 1between the laser and the fiber2,but an in-line fiber package downstream from thelaser is used for the 1345-nm device. The 1393-nmlaser, which is suitable for temperature determina-tions 1see Section 32 was not obtained until after thelast round of drop experiments. Subsequent micro-gravity measurements were not possible because of ashutdown of the drop tower for an extended period ofrenovation.The laser wavelength is calibrated with a Michel-

son interferometer wavelength meter 1Burleigh2.Wavelength meter readings, combined with compari-sons of measured and tabulated water and methanespectra, are sufficient to permit unambiguous identifi-cation of the absorption lines. A confocal etalon1TecOptics SA300, free spectral range 300MHz2 estab-lishes a frequency scale for measurement of absorp-tion linewidths and is also used to calibrate the1nonlinear2 laser tuning response.The spectral region of water that was studied by

the use of these near-infrared diode lasers containsmany water vapor absorption bands that are over-tones and combinations of fundamental modes.Absorption bands of moderate strength occur in the

20 May 1995 @ Vol. 34, No. 15 @ APPLIED OPTICS 2789

regions covered by the commercially available commu-nications InGaAsP diode lasers 1n1 1 2n2 and n1 1 n32.Water line strengths 1mostly the n1 1 n3 band2 be-tween 1340 and 1395 nm are only a factor of 5 weakerthan the strongest infrared fundamental lines.6Until recently, however, no lasers that operated inthis spectral region were available. We note thatroom-temperature measurements of water have beenreported when GaAlAs diode lasers operating near820 nm were used.7 However, the intensity of theseshorter-wavelength water bands is too weak for use inthis project.Methane has two bands accessible in the near

infrared. A weak n2 1 2n3 band lies near 1310 nmand was used in the earliest stages of this research.Little published data on this band exist,8 and weobtained room-temperature line strengths at the LosAlamos National Laboratory Fourier Transform Spec-trometer Facility. A stronger 2n3 band of methanenear 1659 nm is accessible with recently availablelasers.Table 1 lists the absorption lines used in this study,

where the spectroscopic parameters listed are ob-tained from the U.S. Air Force Geophysics Labora-tory HITRAN compilation.6 In the 1393-nm region, apair of closely spaced water lines of significantlydifferent ground rotational energies occurs, permit-ting the measurement of local gas temperatures.During the microgravity drop experiments, the1345-nm laser was used for detection of water vapor,and the 1659-nm laser was used for detection ofmethane.

C. Instrumental Components

The overall system comprises six units: the laser, amodulation source, the laser controller, a detection–demodulation unit, the computer, and the opticalframe. The diode laser is housed in a small boxhaving connections for input current, laser tempera-ture control, and an optional second-stage tempera-ture control. A separate isolated BNC connector isused for the RF input modulation signal. The laseroutput fiber, as well as all other optical fiber ends,terminates in ST-style connectors. This permitsrapid and reliable exchange and connection of alloptical components.

2790 APPLIED OPTICS @ Vol. 34, No. 15 @ 20 May 1995

A block diagram of the electronics is shown in Fig.2. The collected light impinges onto fiber-pigtailedphotodiodes 1Epitaxx2. The photocurrent is dividedinto ac- and dc-coupled legs. The dc-coupled signal islow-pass filtered 16.25 kHz2 and conditioned to providea voltage proportional to the laser intensity 1I02 strik-ing the detector. Amplified and filtered 2f ac-coupledsignals are demodulated by the local oscillator andare then normalized by the detector dc outputs withfast analog divider chips. These normalized signalsare directly proportional to absorbance and are sentto the A@D system described below for digitization,signal averaging, and storage. The normalization ofthe 2f signals by transmitted laser power corrects forsuch effects as variation in the laser power as afunction of wavelength, differences in laser power inthe eight channels, and changes in transmitted laserpower that are due to beam-steering effects, fiberlosses, or particulates in the flow.In the present paper, we use 500-kHz modulation

with second-harmonic detection. For each of theeight channels the detector ac output is bandpassfiltered, amplified, and sent to the RF input of adouble-balancedmixer 1Mini-Circuits2. A2-MHz tran-sistor transistor logic 1TTL2 oscillator serves as themaster clock. Its frequency is divided by 4 to providethe 500-kHz sinewave for laser current modulationthat is fed to the external modulation input of thelaser through a bias-T network that isolates the lasergrounds. A 0° phase, 1-MHz TTL reference output isobtained when the master clock output is divided by2; a 90° phase, 1-MHz reference is similarly obtainedfrom an inverted master clock signal. The mixer IFoutput is amplified and low-pass filtered before digiti-zation. All electronics are assembled on customprinted circuit boards. One board contains all themodulation circuitry, and eight receiver boards per-form all the demodulation and signal conditioning.The ac and dc gains of each channel can be indepen-dently varied.WMS signal processing uses an AM demodulation.

The phase of the local oscillator 1relative to the RFinput2must compensate for electronic phase delays inthe filters and other components. A priori, we didnot know how stable the phase would be for each of

Table 1. Spectral Parameters of Water Vapor and Methane Lines Studied

Parameter H2O H2O H2O CH4 Units

Nominal laser wavelength 1345 1393 1393 1659 nmAbsorption frequency 7435.6162a 7179.74a 7181.1719 6026.2275 cm21

296 K line strengthb 8.8 12232 3.22 12222 1.80 12202 5.7 12222 cm2 molecules21 cm21

N2 broadening coefficient 0.0504 0.0525 0.1031 0.0660 cm21 atm21 1HWHM2Self-broadening coefficient 0.2373 0.2850 0.4630 0.079 cm21 atm21 1HWHM2Broadening T dependence 0.68 0.68 0.73 0.75Rotational energy 1557.85 1216.189 136.726 10.4816 cm21

Vibrational transition n1 1 n3 n1 1 n3 n1 1 n3 2n3Rotational transition 13, 0, 13 ; 12, 0, 12 7, 6, 1 ; 7, 6, 2 3, 0, 3 ; 2, 0, 2 R1121J8, K8, N8 ; J9, K9, N92 3, 1, 13 ; 12, 1, 12 7, 6, 2 ; 7, 6, 1

aBlended line.bExponents in parentheses 1102XX2.

Fig. 2. Block diagram of electronics: BP’s, bandpass filters; LP’s, low-pass filters; I and Q, in-phase and quadrature signals, respectively.

the eight detection channels or how much the phasewould vary from channel to channel. Thus a flexibleapproach is used in which both in-phase and quadra-ture signals of each channel are obtained. Eachdetector’s photocurrent is split into two detection legs;one leg goes to amixer with a local oscillator at 0°, andthe other is fed to amixer with a local oscillator at 90°.The signal at any arbitrary phase can be recon-structed 1in postdrop computer analyses2 by selectionof the phase angle u,

S1u2 5 S10°2cos1u2 1 S190°2sin1u2. 112

As a result we collect data from 16 rather than 8channels. The selection of the optimum phase isdiscussed below.The data-acquisition system uses a 33-MHz 80486-

based microcomputer 1Dell2 and includes a 2048-pointarbitrary waveform synthesizer 1QuaTech WSB-102and a 16-channel, 200-kHz, 12-bit A@D converter1Analog Devices RTI-8602 that are used to sweep thelaser wavelength and to digitize the demodulatedsignals, respectively. The laser wavelength isscanned repetitively with an analog voltage rampgenerated by the waveform synthesizer. The ramp isrounded at the edges, where it resets to the startingvoltage, and also includes a dead time 1flat output2that allows the laser wavelength to stabilize betweenramps. Data are collected during the linear portionof the ramp periods.With an A@D dwell time of 5 µs, all 16 inputs are

sequentially sampled over 80 µs. The laser is thenstepped in wavelength, and this process is repeated

for 128 spectral samples, equivalent to a total spectralrange of 0.35 cm21. Including a 12.5% dead time, acomplete spectrum of all spatial lines is completed in11.5 ms 187 Hz2. Typically, eight such spectra arecoadded to provide an overall data bandwidth of 10.9Hz. A cyclical data buffer in the computer permitsthe storage of a selected number of predrop andpostdrop spectra as well.

3. Data Analysis

In this section we follow the path of analyzing the rawWMS signal to compute mole fractions in the flame asa function of position and drop time. The flames areaxially symmetric, thus species properties along aradial coordinate are desired. The raw WMS volt-ages 1spectra2 are first conditioned and reconstructedto their optimal detection phase. They are thentransformed from line-of-sight projections to radialspectra with anAbel inversion. Finally, the data aretransformed to number densities and mole fractionsas a function of radial position and drop time.We start withWMS signals in 16 data channels as a

function of drop time. Sample water vapor data at1345 nm for the center channel are shown in Fig. 3.These data, which are typical of most experiments,exhibit a peak fractional absorbance of approximately1%. The fiber-splitter etalons are visible in thesespectra, as are curved baselines. The noisy scansnear 2.2 s denote the deceleration of the package atthe end of the drop. During the predrop time period1t , 02, virtually no signal is observed because theroom-temperature water vapor cross section at 1345

20 May 1995 @ Vol. 34, No. 15 @ APPLIED OPTICS 2791

nm is small compared with the cross section at flametemperatures and because the ambient mole fractionof water is ,0.015. Baseline effects that might arisefrom etalons, residual amplitude modulation, or othersources, as well as high-frequency noise, are removedfrom the raw data by a combination of low-passfiltering and subtraction of the predrop baselinesfrom all subsequent scans. More sophisticated tech-niques are also available for measurements wherespecies absorption is present before the drop.After baseline removal, selected channel and time

spectra are displayed on the computer screen. Thephase is chosen by adjustment of the S1u2 signal 3Eq.1124 to optimize the 2f line shape and minimize thequadrature component. The span of phase settingsover the eight channels is typically 20°, but thepattern of values among the channels is consistentand shows only a few degrees of variation from run torun. These interchannel differences arise from thevariation in phase delays of the passive electronicbandpass filters. Absorption peaks for individualscans and channels are then aligned at a predeter-mined wavelength bin to account for any jitter in thescan starting current. Figure 4 shows three chan-nels of filtered, phased, and background-free datafrom the same experiment as in Fig. 3. Postdrop

Fig. 3. Example of raw WMS data versus drop time 1propane–airflame, 16.2-mm height2 for in-phase and quadrature channels aty 5 0 mm 1across the flame center2.

Fig. 4. Optimized WMS projection spectra versus drop time forchannels 1, 3, and 7 1 y 5 0, 6, and 18 mm, respectively2.

2792 APPLIED OPTICS @ Vol. 34, No. 15 @ 20 May 1995

data have no significance and are set to zero. Noticethat these spectra have excellent signal-to-noise ra-tios, with very symmetric line shapes and no baselinecurvatures.

A. Abel Transformation of Projections to Radial Distributions

The tomography of cylindrical objects was solvedanalytically by Abel.9 For a cylindrically symmetricfield distribution F1r2, and an infinitesimally narrowprobe, the line-of-sight integral projections P1r2 aregiven by

P1r2 5 2 e0

`

F31r2 1 y221@24dy, 122

where y is the radial coordinate along the direction ofthe projection. The inversion of these projectiondata is

F1r2 5 21

p er

` dP1r82@dr8

1r82 2 r221@2dr, 132

where y 5 1r82 2 r221@2. A schematic representation ofthese functions is shown in Fig. 5. The length of thearrows in Fig. 5 represents the optical path length ofthe system that lies between the fiber collimatorpairs. Because a derivative of the projection data isneeded and the integrand diverges at r 5 r8, the use ofAbel transforms has been restricted. Dasch10 re-cently compared simple numerical approaches to per-form this transform and showed that it can be accom-plished with the formula

F1ri2 51

Dr oj50

`

Di jP1rj2, 142

where Di j is an operator matrix that depends only onthe number of projections and ri 5 iDr is the distancefrom the center of the object for projections evenly

Fig. 5. Schematic representation of the projection and the radialfunctions.

Fig. 6. Correction of Abel transforms for outlying signals: 1a2 added radial function; 1b2 projection of this function; 1c2 added projection1dashed curve2 scaled to the measured projection 1solid curve2; the portion beyond r8 is catenated onto the measured values to form the fullextended projection; 1d2 complete radial transformation of the experimental data.

spaced at Dr. Based on this study, a three-pointAbeltransformation is chosen for our analyses.With this approach, an inversion of the observed

projections to radial distributions is performed foreach wavelength in the measured spectra. Becauseeach wavelength is an independentmeasurement, thecomplete spectrum at each radial position is recon-structed. One property of the Abel inversion is thatthe noise in the interior channels is noticeably largerthan at larger radii. To reduce uncertainties in theanalysis, and because we are not using the fullspectral line shapes at this point, peak–trough spec-tral heights 1which are linearly proportional to concen-tration2 are found before transformation, and theseheights 1rather than the full spectra2 are transformedto radial heights. This reduces the error in theinterior channels. Although this height method isused for all subsequent data analysis below, fullytransformed spectra produce essentially the sameresults.The general assumption in the inversion of 1mea-

sured2 projection data to radial profiles is that theconcentration beyond the outermost projection 1ra-dius2 is zero. Unfortunately this is not true for ourcurrent experiments. All the water vapor signallying outside of channel i 5 8 1but still between thefiber collimators2 is inherently measured as part ofeach projection 1see Fig. 52. The transform, how-ever, assumes that all this signal lies within ri58.Thus this additional signal incorporated into theprojection is incorrectly attributed to radial intensitywithin ri58. What must be done, therefore, is toassume a functional form for these outlying data 1inradial coordinates2 and create projection data for theoutside region ri.8. We do this by invoking a simplefunctional form for the outlying data 1linear or qua-dratic decay to zero signal or a constant value equal tothe ri58 signal, over a distance of j additional chan-nels2. This is illustrated in Fig. 6, in which r8denotes the value of r in the eighth channel. Thisradial function shown in Fig. 61a2 is transformed to

projection data 3Fig. 61b24 and scaled such that itequals the measured signal at P1ri582, as shown in Fig.61c2. The projection for ri.8 1dashed curves2 is ap-pended to the measured data for ri51–8 1the projectionof the added function for i # 8 is inherently a part ofthe measured data2, and the Abel transform to thefinal radial profile is shown in Fig. 61d2. This profilesatisfies the requirement of zero signal at the largestradial position ri1j. An example of radially trans-formed spectra is shown in Fig. 7. As compared withthe data in Fig. 4, the inversion process has intro-duced much more variation in the channel 1 data, butthe outer channels retain good signal structure.For the microgravity measurements, a quadratic

form for the outlying data is used, being perhapsmorephysically realistic than a linear decay, althougheither function produces essentially the same results.The constant-value outlying signal model is appropri-ate when significant signals of the measured gas areexpected outside the rmax position, e.g., to account forroom air humidity when a spectral line having signifi-cant absorbance at room temperature is used.Numerical simulations by the use of this approach

validate its applicability. Computed radial mole-

Fig. 7. Computed Abel-inverted radial spectra as a function ofdrop time for channels 1, 3, and 7.

20 May 1995 @ Vol. 34, No. 15 @ APPLIED OPTICS 2793

fraction profiles of water vapor11 are used to constructprojections that simulate the experimental setup andare used as input to the radial inversion routine.Our method of accounting for the signal outside of theeight lines of sight recovers the full radial distributionquite well. Although the best way to avoid thisproblem is to space the lines of sight across a wideenough region to cover all areas where signal mightexist, the preliminary video data and the theoreticalpredictions suggested that the flame width would bewithin a 6-mm radius. Thus the 21-mm outer posi-tion seemed sufficient. This turned out to be incor-rect. Although more widely spaced sight lines solvethe coverage problem, they reduce spatial resolution,which is critical near the flame center. Clearly, morelines of sight are desirable.

B. Conversion of Radial WMS Signals to Mole Fractions

Radial WMS spectral or peak height profiles, as afunction of drop time, are converted to mole-fractionprofiles for water and methane. As presented above,the WMS line-shape signal W 1already normalized toI02 is linearly proportional to absorbance 1i.e., concen-tration2,3

W 5 Caf 1m, f2, 152

where C is the electronic calibration constant thatconverts volts to absorbance a. The factor f 1m, f2can be viewed as an efficiency factor of the WMSmethod, defined as the relative height of a WMSfeature 1peak–trough or peak–baseline2 to its directabsorbance height 1I 2 I02. This term is dependenton the magnitude of the modulation index m and onthe absorption line-shape function f1n2. In generalf 1m, f2 is insensitive to both of these terms 1hence it isinsensitive to temperature and mole fraction2 near itsoptimal value. The modulation index is set at ,2.5so that f 1m, f2 encompasses values between 0.56 and0.29 for the full range of conditions expected.When Eq. 152 is combined with Beer’s law a 5

e sNdr and the ideal gas law N 5 P@KT, the meanmole fraction xi at each radial position ri is

7xi8 5WK

PC e s0 f 1m, f2

Tdr

, 162

where N is the number density, P is the pressure, T isthe temperature, K is the gas constant, s0 is theabsorption cross section at the peak center, and Dr isthe absorption path length. In this case the absor-bance is integrated over the radial distance dr fromri 2 Dr@2 to ri 1 Dr@2. The cross section at linecenter s0 is related to the temperature-dependentabsorption line strength S1T2 by

s0 5 S1T2f1n02, 172

The line shape is a Voigt profile. The temperature

2794 APPLIED OPTICS @ Vol. 34, No. 15 @ 20 May 1995

dependence of the line strength, S1T2, can be readilycalculated to high accuracy at any temperature, pro-vided it has been accuratelymeasured at one tempera-ture. We have conducted laboratory measurementsof the relevant line strengths and broadening coeffi-cients at room temperature to verify the accuracy ofthe HITRAN6 numbers used in the analysis.Examination of Eq. 162 shows that the 1spatially

dependent2 temperature comes into play in the cross-section and the modulation correction terms as wellas in the density term. In addition, Eq. 162 is paramet-ric, in that the absorption linewidth 1which affectsboth the absorption cross-section and modulationcorrection terms2 has a small dependence on the molefraction of the measured gas. This arises becausethe Lorentzian 1pressure-broadening2 component ofthe line shape is a mole-fraction-weighted average ofindividual broadening coefficients, which vary foreach collision partner in the gas mixture. For watervapor, self-broadening coefficients are much largerthan those from differing gases, so that the variationin broadening is mostly dependent on the mole frac-tion of water. Fortunately, high-temperature linesin the near infrared, even those at atmospheric pres-sure, are predominantly Doppler broadened. None-theless, we account for the mole fraction of water inour computations and perform a parametric analysisto compute the exact xi. Figure 8 is a contour plot ofthe temperature-dependent terms 1those inside theintegral2 in Eq. 162 as a function of T and xH2O, with themodulation index value used in the water vapormeasurements performed in the microgravity droptower. The product of these terms is relatively insen-sitive to mole fraction and shows a great sensitivity totemperature only near 300 K.Good temperature profiles are required for accu-

rate mole fractions to be determined. In the presentcase, because gas temperature is itself a measure-ment objective, this information can be obtained bythe use of techniques described below. When gastemperatures are not well known,mole-fraction uncer-tainties can be minimized by selection of an absorp-tion line with a cross-section-to-temperature ratiothat is relatively insensitive to temperature over therange of temperatures expected 3see Eq. 1624.

Fig. 8. Contour plot of temperature- andmole-fraction-dependentcorrection terms for water vapor 11345 nm, 10.0-mAmodulation; inunits of 10223 cm2 K212.

Flame temperatures can be determined bymeasure-ment of the ratio of absorption signals for two absorp-tion lines that have different ground-state energies.12This ratio is proportional to the ratio of line strengths,which depends only on temperature and known mo-lecular constants. The line-strength ratio for twoabsorption lines is simply

S1

S25S11T02

S21T02exp32hcDErot

k 11T 21

T024 , 182

where T0 is a reference temperature 1typically 296 K ifone is using the HITRAN compilation2 and DErot is thedifference in the lower-state rotational energy for thetwo lines. For the line pair at 1393 nm listed inTable 1, the computed signal ratio varies by almost afactor of 30 between 300 and 1800 K. A spectrum ofthese lines near 1393 nm, taken in a nonpremixedatmospheric-pressure methane jet flame, is shown inFig. 9. This spectrum is the result of the Abelinversion process described above. The temperaturederived from this spectrum is 1650 6 150 K, wherethe major portion of the error is due to uncertaintiesin the 1estimated2 broadening coefficients for theselines and a smaller contribution that arises from thelimited resolution of the Abel inversion. With accu-rately measured broadening parameters and with thesame signal to noise observed in Fig. 9, a temperatureaccuracy of approximately 675 K is possible.In the absence of adjacent line pairs, one might

attempt to fit the WMS line shape to extract the localtemperature. However, for the lines used in thesestudies, the line shapes are not sufficiently sensitiveto temperature to achieve this goal. As a result, localtemperature profiles are obtained from numericalcomputations,11,13 which include hydrodynamics,14 fi-nite-rate chemistry, soot formation, and radiativetransfer effects. This model assumed a nozzle diam-eter, flow rates, and fuels that mimic the presentexperiments. Temperature and species-concentra-tion spatial profiles predicted by the model for normalgravity agree well with thermocouple measurementsin our laboratory and with videotape data of flameshapes. For microgravity flames, the model predic-tions of flame shape agree well with observed pro-

Fig. 9. Radial spectrum of water vapor in methane–air flameobtained with the 1393-nm laser.

files.15–17 Themodel also predicts that the maximumin water vapor mole fractions should occur just out-side of the loci of maximum temperatures, which issimilarly observed in 1-g flames. However, the loca-tion and the shape of these temperature and watervapor profiles appear to be somewhat insensitive tothe heat-transfer parameters, so that the maximumtemperature value is only weakly dependent on theinputs of the model. As a result, we estimated themaximum flame temperature in microgravity as 1500K and scaled the model temperature fields to accom-modate this choice. This value is consistent withfilmed flame colors and uncorrected thermocouplemicrogravity measurements.15

4. Calibrations

In addition to the experiments and measurementsdiscussed above, which related to the instrumentdesign and construction, a variety of calibrations arerequired for quantification of the WMS signals.These include characterization of spectral line param-eters, relative channel gains, overall electronic calibra-tion, and laser injection current to wavelengthcalibrations.Even though the WMS signal is normalized to the

incident laser intensity, the conversion of photocur-rent to WMS signal voltage varies from channel tochannel. These variations may arise from differ-ences in the frequency and the wavelength responseof each detector, amplifier gains, and the signalresponse of other electronic components. The rela-tive response of each detection channel is character-ized in two ways. First the laser is modulated with asinewave at a frequency a few kilohertz below the1-MHz reference to the detection electronics. As aresult the WMS output signal is a sinusoidal wave-form at the beat frequency of a few kilohertz. Therelative amplitude of this signal in each channelreflects all the individual variations in the systemresponse. The second approach is simply to measurethe water vapor signal across the fiber frame in roomair with the 1393- or the 1345-nm laser. Because theoptical path lengths are the same for each channel,and the humidity is constant 1and measurable2, therelative channel responses are found. Both methodsprovide similar results, with uncertainties within anygiven channel being 65%, and with channel-to-channel differences of up to 620%. These lattervariations can be easily removed by adjustments ofthe variable gain stages in the detection circuitry.The former variations appear to be due to day-to-daydrifts in the electronics that result from the systemtemperature, nonlinear response of the divider 1inten-sity normalization2 circuitry, or other unidentifiedsystematic errors. The overall electronic constant Cis determined by measurement of water vapor absor-bances in room air at known humidity and tempera-ture.Second-harmonic 12f 2 signals produced by WMS

are directly proportional to absorbance, but the scal-ing is best determined by direct experimental calibra-

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tion. As shown in Eq. 152, the WMS signal is propor-tional to the product of the absorbance, an electroniccalibration factor C, and a WMS factor f 1m, f2.Although f 1m, f2 is readily calculated, we must cali-brate the modulation injection current to m. We dothis for each laser by recording WMS line shapes ofknown water or methane concentrations 1296 K, 590Torr2 as a function of the modulation current and byfitting the peak–trough heights to computed values off 1m, f2. From this calibration m and f 1m, f2 at anytemperature, mole fraction, and pressure are deter-mined.The wavelength tuning response of an InGaAsP

diode laser to injection current is not linear and is alsoa function of the current tuning rate.12 To evaluateline shapes, we must know the wavelength tuningrate across the absorption feature as the laser injec-tion current is ramped. We measure this by passingthe laser beam through an etalon with a free spectralrange of 300 MHz. The fringe spacing versus theinjection current is fit to a third-order polynomial toattain the nonlinear response function for each laser.The higher-order terms are minor, and nonlineardistortion is of the order of 10%.The surprisingly large signals observed at larger

radii led us to question the HITRAN specific linedesignation and the spectral parameters attributed tothe line at 7435.6 cm21. Any error in rotationalenergy, reference 1296 K2 line strength, or broadeningcoefficients would cause erroneous results. We per-formed three experiments to test the HITRAN spectralparameters. First wemademeasurements in aMatt-son Fourier transform infrared spectrometer with theinstrument resolution set at 0.125 cm21 FWHM.The cell was filled to either a total pressure of 10.0Torr of pure water vapor, which provides a Doppler-limited line shape or to a total pressure of 590 Torr ofroom air at known absolute humidity. The inte-grated area under the absorbance line shape is re-lated to the line strength, S 5 e 5ln3I0@I1n24@Nl6dn,which we measure as 17.8 6 2.92 3 10223 cm2 mol-ecules21 cm21. For comparison, the HITRAN6 value forthis line is listed as 8.79 3 10223 cm2 molecules21

cm21. The uncertainty in thismeasurement ismostlythe resolution limitation of the Fourier transforminfrared spectrometer.The second set of experiments verified the rota-

tional ground-state energy of this line. Line strengthsvary exponentially with Erot. To measure the rela-tive cross sections at differing temperatures, the1345-nm laser beam traversed a path through aLindberg high-temperature furnace, which is capableof operation to 1100 °C. The central 8-cm-long por-tion of the oven retains a constant temperature1610°2. A cell that allowed for the cooler portion ofthe oven 1i.e., the region between the constant-temperature zone and the laser or the detector2 to bepurged with dry air was used so that the temperatureof each measurement was well defined. Room air isused in the cell so that the water vapor concentrationis accurately known when the absolute humidity is

2796 APPLIED OPTICS @ Vol. 34, No. 15 @ 20 May 1995

measured. Corrections for the thermal emission ofthe furnace into the detector are made when thesignal is normalized to laser 1dc2 intensity. The experi-mental results are best represented by a curve approxi-mating the 1557 6 100 cm21 rotational energy, inagreement with the HITRAN line designation.Finally, we examined the Lorentz broadening pa-

rameters for water that are listed in HITRAN. Recentexperimental studies suggest that the HITRAN values1which are based on older calculations2 are inaccu-rate.12,18 Delaye et al.19 compute temperature-depen-dent broadening coefficients for collisions of watervapor with N2, O2, water, and CO2. Individual val-ues are provided for all water rotational energy levelsup to 2900 cm21, and formulas are provided to permitcalculations of the coefficients for any rotational tran-sition. In addition, this paper shows that, at hightemperatures, all transitions approach a limitingvalue for each collision pair.The differences between the HITRAN and the Delaye

et al. coefficients can be dramatic. For the line at7435.6 cm21, Delaye et al. predict a room temperatureN2 broadening coefficient of 0.0168 cm21 atm21, andHITRAN lists this value as 0.0504 cm21 atm21. Thetemperature coefficients are also quite different.Examination of a room-temperature humidity spec-trum shows aWMS line-shape trough–trough separa-tion of 0.095 cm21. The HITRAN listings predict aseparation of 0.21 cm21 for this line, and Delaye et al.predict a separation of 0.093 cm21. Based on previ-ous experimental data12,18 and our current measure-ments, we choose to use Delaye et al.’s numbers for allbroadening coefficients of water. Table 2 lists theparameters used in these calculations for the 7435.6-cm21 line of water vapor. The formula19 used tocompute the broadening coefficients from these val-ues is

b1T2 5 53b11300

T 2r1

4s

1 3b21300T 2r2

4s

261@s

. 192

In the analyses of our microgravity data, we as-sume that all collisions of water vapor with speciesother than water can be represented by the N2broadening parameters. This is reasonable becausepressure broadening is a minor contribution to thelinewidth at higher temperatures and because theother major broadening species 1O2, CO22 have broad-ening effects similar to that of N2.The observed sensitivity for detection of water

vapor with the 1345-nm laser in units of fractional

Table 2. Water Broadening Coefficients A300 KB for the7435.6-cm21 Line

Collision Partner b1 r1 b2 r2 s

N2 0.0186 20.12 0.0146 20.21 3H2O 0.1939 0.38 0.1724 0.35 2O2 0.0111 20.07 0.0096 20.12 12CO2 0.0401 0.47 0.0362 0.50 3

Table 3. Summary of Experimental Conditions for Microgravity Drops

Run No. Fuel Flow 1scc@s2 Gas Detected m 1mA2 Height 1mm2 Ignition Gravity

a C3H8 1.5 H2O 10.0 32.2 Post 0b C3H8 1.5 H2O 10.0 24.2 Post 0c C3H8 1.5 H2O 10.0 16.2 Post 0d C3H8 1.5 H2O 9.9 9.0 Post 0e C3H8 1.5 H2O 10.0 3.8 Post 0f C3H8 1.5 H2O 10.0 3.8 Pre 1—No Dropg CH4 3.0 H2O 10.0 32.2 Post 0h CH4 2.0 H2O 9.8 16.2 Post 0i CH4 3.0 H2O 10.0 16.2 Post 0j CH4 3.0 CH4 29.4 16.2 Pre 0k CH4 3.0 H2O 10.0 9.0 Post 0l CH4 3.0 CH4 29.4 6.1 Post 0m CH4 3.0 H2O 10.1 3.8 Post 0n CH4 3.0 H2O 10.0 3.8 Post 0o CH4 3.0 H2O 10.0 3.8 Pre 0p CH4 3.0 H2O 10.1 3.8 Pre 1—No Drop

absorbance is 1.5 3 1024 1signal to noise 5 1, band-width 122Hz2. The bandwidth is the result of coaver-aging of eight scans. Sensitivity is limited only bythe formation of interference fringes 1etalons2 in theoptical path that are caused by the 1 3 8 fiber-opticsplitter. If we subtract the residual etalons from ourdata, the random noise is at the bit resolution of ourA@D converter and corresponds to a sensitivity in thelow 1026 absorbance range. For an ideal system, thecomputed detection limit3 varies as the gas tempera-ture and the mole fraction change but has a value ofapproximately 3 3 1026. Although the factors limit-ing the observed value could also include fiber noise,electronics noise, and laser-generated terms, only theetalons appear to have any significant role.

5. Results

Twenty-three drops of the test rig were made, withdiffering combinations of fuel, gas flow, and heightabove the nozzle tip. The data used in the finalanalyses are shown in Table 3. All these experi-ments used the 0.0825-cm-radius nozzle. The flowsfor the methane and the propane flames correspond tosource Reynolds numbers of 155 and 290, respectively.These conditions mirror those in previous micrograv-ity experiments by other researchers, in which flamesizes and temperatures 1by the use of color film2 weremeasured.15–17The temperature profiles for the experimental mi-

crogravity flames are obtained from detailed calcula-tions,11 with pressure, nozzle radius, and gas flow setto match the experiments. Because the computedtemperature profiles are steady-state values, wemustassume some functional form for the transition fromroom temperature to steady state. Before the dropand during the first drop scan 1,100-ms drop time2,the temperature is set at 300 K. The temperatureprofiles in each channel are then assumed to increaselinearly to the steady-state value over a 300-msperiod.

As part of the initial testing, a black and whitevideo of one drop was taped to provide a visual imageof the flame before and during microgravity. Anillustration of the predrop 11-g2 and dropping 1micro-gravity2 flames is shown in Fig. 10. Also illustratedare the positions of the eight lines of sight of the laserduring these experiments. Notice how themicrograv-ity flame is wider, with a shorter flame front 1stoichio-metric surface2. The upper portion of the flame is notimaged by the camera. The methane flow rate wasapproximately 5.7 scc@s. For the measurements dis-cussed below, the flame heights are somewhat smallerbecause of lower flow rates.Water vapor profiles are taken at heights ranging

from 3.8 to 32.2 mm. Figure 11 shows the measuredspatial distribution of the steady-state water vapormole-fraction in a normal-gravity methane flamecompared with a flame in microgravity at approxi-mately the same height 13.9 mm2. The normal-gravity flame exhibits the expected narrow watervapor mole-fraction profile, with the peak near r 5 6mm. In microgravity the flame expands signifi-cantly in size and appears to stabilize rapidly, consis-tent with the videos. However, the measured watervapor profiles appear bimodal, with a broad inner

Fig. 10. Videotaped flame profiles before and during 1at t 5 2.0 s2microgravity drop.

20 May 1995 @ Vol. 34, No. 15 @ APPLIED OPTICS 2797

peak 1as might be expected in a zero-gravity flame2and a larger peak at distances near 20mm. Althoughthe maximum observed value of the mole fraction isconsistent with expectations 1with a theoretical maxi-mum equilibrium value expected to be near 0.22, itsposition at r . 12 mm is not expected. This signal atlarger radii is observed at all heights in both propaneand methane and cannot be explained as an experi-mental artifact that is due to even gross errors in theassumed temperature field.Figure 12 shows a contour plot of water vapor in

the propane flame at a height of 16.2 mm. Theabscissa denotes the measurement time relative tothe release of the package, and the ordinate shows theradial distance from the center of the flame. Molefractions are noted by density contours. At 0.1 s theignition can be observed. The values of the molefractions between 0.1 and 0.4 s depend on the as-sumed temperature rise and should be taken only assuggestive values. A contour map of the experimen-tal data in the propane flame at a release time of 2.0 sfor heights between 3.8 and 32.2 mm is shown in Fig.13. The inner signal peaks match up well to theexpected position of the flame front, and the outerwater peaks extend into a region that should be 1atleast from steady-state calculations2 at room tempera-ture. It is possible that these signals arise from theignition process or from the transition of the flamefrom normal to zero gravity. The extent of watervapor at larger distances is enhanced in flames thatare ignited after transition to microgravity, but thiseffect is still observed to a lesser extent in preignited

Fig. 11. Comparison of water vapor mole fractions in normal- andzero-gravity methane–air flames at the 3.9-mm height.

Fig. 12. Contour plot of microgravity water vapor mole fractionsin the propane–air flame versus drop time and radial position atthe 16.2-mm height.

2798 APPLIED OPTICS @ Vol. 34, No. 15 @ 20 May 1995

flames. Diffusion rates in zero gravity are very slow1,1 cm2@s2, which can be seen in the edges of thecontour plots, where the signal slowly spreads tolarger radii after the initial transition tomicrogravity.Because buoyancy is negligible in microgravity, diffu-sion and the jet momentum are the primary mass-transportmechanisms. Water vapor formed or trans-ported to large radii on initiation of the drop would beexpected to remain there for the duration of theexperiment and to disappear very slowly. This couldbe examined in future experiments with the NASALewis 5.18-s drop facility or by longer-duration air-borne parabolic trajectory microgravity studies.Finally, methane profiles near the nozzle tip were

also measured. Methane is observed only at thelowest measured height 13.8 mm2 and only at radialdistances of 0 and 3 mm, as expected. The signal-to-noise ratio in these measurements is poor 1,2:12because of the low absorption cross section of the linewe monitored and a relatively strong interference byetalons arising in the fiber splitter. Methane wassuccessfully observed in normal-gravity flames with asingle detection channel. Future measurements willuse the R132 line at 6046.95 cm21, which is reachedwhen the laser is operated at a lower temperature.The absorption cross section for this line at flametemperatures is 6 times larger than for the R112 lineused here.The major sources of error in these experiments are

the detection electronics, the system calibration, theAbel inversion process, the conversion of radial signalto mole fraction, and the assumed temperature field.Table 4 lists the overall errors 11s2 for each of thesesources. The standard error of the reported molefraction computed from these numbers is approxi-mately 14% for all flame regions inwhich the tempera-ture exceeds ,700 K, except near the flame center,

Fig. 13. Contour map of water vapor mole fractions at 2.0-s droptime as a function of height above and radial distance from thecenter of the propane flame. The intersections of the grid linesdenote the positions of the measured points. The thick dashedcontours encompass the region of maximum water vapor predictedby the model.11

where the estimated error rises to approximately28%. These values are based on the assumption thatthe estimated temperatures are accurate to 650°,except at the flame center, where we assume anuncertainty of 6150°. The other factors limitingaccuracy are the small number of Abel transformchannels 182 and the fact that these are independentchannels 1requiring separate electronic circuitry2.

6. Discussion

Numerical simulations of the Abel inversion demon-strate that our analytical approach is valid but alsopoint out the weaknesses in this method. The lim-ited spatial resolution cannot resolve sharply varyingstructures, such as those near the flame center atnormal gravity. Also, the temperature profile usedto represent the spatial region around each radialpoint is critical. In regions of large temperaturegradients 1again like those near the flame center2, anerror in the estimated temperature could lead to asignificant error in the computed mole fraction.The mole-fraction contours are dependent on the

selection or measurement of local gas temperatures.We are forced to rely on computed temperature fields,and the results of this choice are reflected in the data.At temperatures below 500 K, i.e., on the outskirts ofthe flame, the apparent mole fractions are muchlarger than anticipated. Because the cross section isapproximately a factor of 10 smaller at 300 K than inthe hottest flame regions, smaller raw signals areconverted to relatively larger mole fractions. Thusany underestimation of the temperatures 1when be-low 500K2 can lead to erroneously highmole fractions.If the highest temperatures are overestimated, simi-lar errors will occur, but these will be much smallerbecause the cross-section terms are less volatile, andthe result of errors at high temperature is at most asmall shift in the peak of the mole-fraction map.There are no previous experimental microgravity

data with which to compare our results. Previousvideo and film measurements of flame shapes are theonly hints of temperature profiles.15 As a result, wecannot tell whether our observed mole fractions atlarge radii arise from 112 errors in our estimatedtemperature fields 1a broad, warm, say 400–500 K,region might exist2, 122 ignition artifacts, 132 error inthe water vapor line broadening coefficients, or 142some unknown cause. We have already discussedthe effect of temperature uncertainties. The processof ignition in zero gravity is poorly understood. At

Table 4. Sources of Experimental Uncertainties

Source Error 161s2

Electronics 7.2%System calibration 3.7%Abel transform 19.5% 1channel 12 to 14.2%

1channel 82Calculation of mole fraction 10.7%Temperatures 150° in flame center

50° elsewhere

ignition, the initial flame is effectively premixed, sothat water vapor might be more broadly distributed.This ignition may leave a wide spatial region warmerthan we estimate, which would lead to an overestima-tion of the water mole fraction at large radii.Alternatively, the preheating of the igniter wire maydrive off large amounts of adsorbed water vapor. Inthe absence of buoyancy, any excess water vaporwould persist for a few seconds. Our data indicatethat this outer shell of water vapor is formed in theinitial ignition and peaks at somewhat later periodsat greater heights above the nozzle. It also can beseen to spread by diffusion at later drop times.Despite these uncertainties, we firmly believe thatthe data at large radii are real. Clearly furtherstudy is warranted, andmeasurements at larger radii1to avoid artificial Abel extension procedures2 andlonger drop times 1to approach steady state better2 aredesirable.For the methane mole-fraction profiles, methane

peaks near the center as expected, but the data arenot very quantitative because of poor signal to noise.The line strengths for methane vary steeply withtemperature, and an accurate knowledge of the tem-peratures near the flame center is critical. In retro-spect, a rotational line of larger quantum numbershould have been used, which would have a weakertemperature dependence as well as a larger crosssection. With sufficient cooling, the present laser formethane is capable of reaching the R132 line.

7. Conclusions

A multichannel diode-laser–fiber-optic system wasused tomeasurewater vapor concentrations in nonpre-mixed, laminar, microgravity flames. This system1in normal gravity2 was also shown to be capable ofmonitoring methane and gas temperature. The fun-damental spectroscopic parameters and calibrationconstants required for quantitative measurements bythe use of this system were measured in laboratorystudies. An extensive set of experiments in pre-mixed and nonpremixed flames were performed innormal gravity to evaluate the accuracy of tempera-ture and concentration measurements based on thediode-laser absorption technique. These experi-ments permitted evaluation of the effects of usingAbel inversion methods to determine radial profilesfrom the measured line-of-sight projections across theflames. The prototype systemwas successfully testedon the 2.2-s microgravity drop facility at the NASALewis Research Center. These experiments yieldeda great deal of useful data relevant to microgravitycombustion research.These measurements represent the first quantita-

tivemeasurements of species concentrations inmicro-gravity flames. Although more data are clearlyneeded, these results suggest that large amounts ofwater vapor occur at distances removed from theouter surface of the flame, where theoretical predic-tions do not expect any water vapor. Even when theexperimental uncertainties in this region are ac-counted for, the observed water signal is real and

20 May 1995 @ Vol. 34, No. 15 @ APPLIED OPTICS 2799

large. These concentrations are not seen in normal-gravity flames. When pre- and postignited flamesare compared, this shell has differing appearances.It is closer to the flame center in the preignited caseand does not extend to outer radii as rapidly. Clearlya chemical steady state is not achieved in any of theseexperiments, as we observe diffusion occurring overthe nearly 2 s during which the flame 1according to thevideos2 appears stable. Inner shells of water vaporcan be seen at locations that do agree reasonably wellwith predictions and at mole-fraction levels that alsoshow good agreement.Our overall assessment of the use of diode-laser

high-frequency wavelength modulation detection forstudies of microgravity flames is that this method isfundamentally sound and should provide accuratedata that no other approach can achieve at present.The lasers have proven very reliable, and the systemfunctioned nearly perfectly during the drop experi-ments. The fiber-optic cable did not interfere withthe drops and transmitted the data as expected. Thefiber collimator and the detection frame proved rug-ged and maintained alignment despite the severity ofthe environment.Analysis of the strengths and weaknesses of this

system has revealed several areas in which designimprovements might improve the sensitivity andreliability of the system. These areas include lasers,multichannel capability, and signal processing.

A. Laser Availability and Performance

Important advances are continually being made inthe fabrication of near-infrared and visible diodelasers. These advances are likely eventually to leadto the availability of high-power single-frequencylasers at any desired wavelength. These lasers willalso have characteristics 1tuning, mode structure,power profiles2 more suited to spectroscopic applica-tions.

B. Multichannel System

The fiber-optic-based multichannel system developedin this program was the source of much trial anderror in design. Most of these difficulties arosebecause of the propensity of the fiber system toinduce unwanted etalons that limit measurementsensitivity. The need for careful angling of opticalsurfaces relative to the optical axis has been described.However, the present limitation is etalon formationin the splitter. A second problem in the multichan-nel approach as used in this system is the require-ment for multiple detection electronics circuits. Toachieve better and more accurate data, we need tohave as many spatial measurements as possible and,in fact, 16 channels or more would be preferred. Theproblem with this approach is that each independentdetection channel raises the cost and complexity ofthe system. More important, multiple detectionchannels increase the error and the experimentaldifficulty by creating a need to calibrate individualchannel responses. One solution to this problem

2800 APPLIED OPTICS @ Vol. 34, No. 15 @ 20 May 1995

that is under study is to use a variation of opticalscanning of the laser beam across the flame, withdetection of the beam with a single detection circuit.The trade-off is a decrease in the ultimate detectionlimit because the effective bandwidth of the systemwill be reduced. However, inmany cases, such as thecase of water vapor described here, the observedsignals are far above the detection noise limit.

C. Signal-Processing Approaches

Current methods use extensive analog signal process-ing 1amplification, mixers, and filters2 before digitiza-tion of the WMS waveform. Recently, a great deal ofinterest has arisen over the use of digital signal-processing techniques to process the measured photo-currents.20,21 We are currently investigating the useof high-speed, high-bit-accuracy A@D converters toperform front-end digital signal processing of the rawphotocurrents. The photocurrent is first digitizedand then digitally mixed, filtered, normalized, etc.Performing these operations on the digitized signalsnumerically can potentially improve the results signifi-cantly. Digital filters and mixers are much betterthan their analog counterparts, having near idealresponses and no induced noise or nonlinearities.A second area of investigation is the use of digitallyprogrammed modulation waveforms and ramps.InGaAsP near-infrared lasers have nonlinear fre-quency and nonuniform intensity responses that giverise to unwanted harmonic signals and residual ampli-tudemodulation that interferewith the ideal analyses.We have shown that customized modulation wave-forms can be used to minimize these problems and toprovide more ideal WMS line shapes for subsequentanalysis.Our final conclusion is that accurate temperature

maps of microgravity flames are essential for under-standing the chemistry and dynamics, in both qualita-tive and quantitative senses. Laser absorption dataare quite sensitive in many cases to the local tempera-ture. Although we are now capable of obtainingthese temperatures for water vapor with the 1393-nmlasers, even simple thermocouple array measure-ments would be very useful.We believe that the methodology of WMS will be

successful in elucidating the chemical and the dynami-cal mechanisms of combustion under microgravityand hope that this publication motivates more re-search into the use of diode-laser-based diagnosticsfor combustion studies.

The authors thank David Bomse of SouthwestSciences for his assistance in developing the data-acquisition software and DeVon Griffin and RandallVander Wal of Sverdrup Technology for their helpduring the drop experiments. We also appreciatethe computational data provided by Jerry Ku ofWayne State University. This work was supportedby NASAunder contract NAS3-25981.

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diagnostics in microgravity,’’ in Second International Micro-

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2. J. Lekan, E. S. Neumann, and R. G. Sotos, ‘‘Capabilities andconstraints of NASA’s ground-based reduced gravity facilities,’’in Second International Microgravity Combustion DiagnosticsWorkshop, NASA Conf. Publ. 10113 1NASA Lewis ResearchCenter, Cleveland, Oh., 19922, pp. 45–60.

3. J. A. Silver, ‘‘Frequency-modulation spectroscopy for tracespecies detection: theory and comparison among experimen-tal methods,’’Appl. Opt. 31, 707–717 119922.

4. D. S. Bomse, J. A. Silver, and A. C. Stanton, ‘‘Frequency-modulation spectroscopy for trace species detection: experi-mental comparison of methods using a lead-salt diode laser,’’Appl. Opt. 31, 718–731 119922.

5. J. Reid and D. Labrie, ‘‘Second-harmonic detection with tun-able diode lasers—comparison of experiment and theory,’’Appl. Phys.B 26, 203–210 119812.

6. L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland,M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C.Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R.Brown, and R. A. Toth, ‘‘The HITRAN molecular database:editions of 1991 and 1992,’’ J. Quant. Spectrosc. Radiat.Transfer 48, 469–507 119922.

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20 May 1995 @ Vol. 34, No. 15 @ APPLIED OPTICS 2801