laser-induced incandescence: excitation intensity

10
Laser-induced incandescence: excitation intensity Randall L. Vander Wal and Kirk A. Jensen Assumptions of theoretical laser-induced incandescence ~LII! models along with possible effects of high- intensity laser light on soot aggregates and the constituent primary particles are discussed in relation to selection of excitation laser fluence. Ex situ visualization of laser-heated soot by use of transmission electron microscopy reveals significant morphological changes ~graphitization! induced by pulsed laser heating. Pulsed laser transmission measurements within a premixed laminar sooting flame suggest that soot vaporization occurs for laser fluences greater than 0.5 Jycm 2 at 1064 nm. Radial LII intensity profiles at different axial heights in a laminar ethylene gas jet diffusion flame reveal a wide range of signal levels depending on the laser fluence that is varied over an eight fold range. Results of double- pulse excitation experiments in which a second laser pulse heats in situ the same soot that was heated by a prior laser pulse are detailed. These two-pulse measurements suggest varying degrees of soot structural change for fluences below and above a vaporization threshold of 0.5 Jycm 2 at 1064 nm. Normalization of the radial-resolved LII signals based on integrated intensities, however, yields self- similar profiles. The self-similarity suggests robustness of LII for accurate relative measurement of soot volume fraction despite the morphological changes induced in the soot, variations in soot aggregate and primary particle size, and local gas temperature. Comparison of LII intensity profiles with soot volume fractions ~ f v ! derived by light extinction validates LII for quantitative determination of f v upon calibration for laser fluences ranging from 0.09 to 0.73 Jycm 2 . © 1998 Optical Society of America OCIS codes: 120.0120, 120.1740, 140.0140. 1. Introduction Successful application of laser-induced incandes- cence ~LII! to diverse combustion processes requires proper choice of excitation and detection conditions. Previous research has addressed detection of the soot incandescence. 1 Here we discuss excitation of the incandescence. Central to excitation of the incan- descence is the laser fluence that greatly affects the absolute LII intensity, temporal decay rate, and sig- nal shot-to-shot reproducibility. Yet these observ- ables also depend on soot physical parameters such as final particle temperature, 2–7 potential morpholog- ical changes, andyor mass loss. 8 If the dependence of the LII signal on each of these factors was known as a function of laser fluence, then theoretical LII models potentially could be used to select the appro- priate laser fluence. Theoretical LII models based on energy conserva- tion equations possess several assumptions, however. First, these models treat only a single isolated spher- ical particle of uniform composition. Actual soot particles consist of primary particles partially con- nected or fused and assembled within open branched- chain aggregates. 9 As a result, particle–particle shielding effects can occur during both absorption and emission, leading to slower or uneven heating and slower cooling, respectively. Second, the phys- ical properties ~density, heat capacity, and optical properties! used in theoretical models are taken to be identical to those of graphite at 300 K. 2–7 It is rather unlikely that the physical properties of soot at 4000 K are similar to those of graphite at 300 K. Conse- quently, application of an energy balance equation to determine radiative emission ~LII intensity! based on energy gained through laser heating is likely to be inaccurate. Third, none of these theories consider morphological alteration or variation of either soot aggregates or the constituent primary particles by pulsed laser heating except for surface vaporization at high laser fluences. Albeit on a vastly longer time scale, heat treatment studies of carbon black, a type of soot, have demonstrated that vast structural When this research was performed R. L. Vander Wal was with Nyma, Incorporated, Brook Park, Ohio 44142. He is now with the National Center for Microgravity Research, NASA Lewis Research Center, M. S. 110-3, 21000 Brookpark Road, Cleveland, Ohio 44135. K. A. Jensen is with the Department of Engineering, Uni- versity of Chicago at Illinois, 842 West Taylor Street, Chicago, Illinois 60607. Received 3 December 1996; revised manuscript received 26 No- vember 1997. 0003-6935y98y091607-10$15.00y0 © 1998 Optical Society of America 20 March 1998 y Vol. 37, No. 9 y APPLIED OPTICS 1607

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Page 1: Laser-Induced Incandescence: Excitation Intensity

Laser-induced incandescence: excitation intensity

Randall L. Vander Wal and Kirk A. Jensen

Assumptions of theoretical laser-induced incandescence ~LII! models along with possible effects of high-intensity laser light on soot aggregates and the constituent primary particles are discussed in relation toselection of excitation laser fluence. Ex situ visualization of laser-heated soot by use of transmissionelectron microscopy reveals significant morphological changes ~graphitization! induced by pulsed laserheating. Pulsed laser transmission measurements within a premixed laminar sooting flame suggestthat soot vaporization occurs for laser fluences greater than 0.5 Jycm2 at 1064 nm. Radial LII intensityprofiles at different axial heights in a laminar ethylene gas jet diffusion flame reveal a wide range ofsignal levels depending on the laser fluence that is varied over an eight fold range. Results of double-pulse excitation experiments in which a second laser pulse heats in situ the same soot that was heatedby a prior laser pulse are detailed. These two-pulse measurements suggest varying degrees of sootstructural change for fluences below and above a vaporization threshold of 0.5 Jycm2 at 1064 nm.Normalization of the radial-resolved LII signals based on integrated intensities, however, yields self-similar profiles. The self-similarity suggests robustness of LII for accurate relative measurement of sootvolume fraction despite the morphological changes induced in the soot, variations in soot aggregate andprimary particle size, and local gas temperature. Comparison of LII intensity profiles with soot volumefractions ~ fv! derived by light extinction validates LII for quantitative determination of fv upon calibrationfor laser fluences ranging from 0.09 to 0.73 Jycm2. © 1998 Optical Society of America

OCIS codes: 120.0120, 120.1740, 140.0140.

1. Introduction

Successful application of laser-induced incandes-cence ~LII! to diverse combustion processes requiresproper choice of excitation and detection conditions.Previous research has addressed detection of the sootincandescence.1 Here we discuss excitation of theincandescence. Central to excitation of the incan-descence is the laser fluence that greatly affects theabsolute LII intensity, temporal decay rate, and sig-nal shot-to-shot reproducibility. Yet these observ-ables also depend on soot physical parameters suchas final particle temperature,2–7 potential morpholog-ical changes, andyor mass loss.8 If the dependenceof the LII signal on each of these factors was knownas a function of laser fluence, then theoretical LII

When this research was performed R. L. Vander Wal was withNyma, Incorporated, Brook Park, Ohio 44142. He is now with theNational Center for Microgravity Research, NASA Lewis ResearchCenter, M. S. 110-3, 21000 Brookpark Road, Cleveland, Ohio44135. K. A. Jensen is with the Department of Engineering, Uni-versity of Chicago at Illinois, 842 West Taylor Street, Chicago,Illinois 60607.

Received 3 December 1996; revised manuscript received 26 No-vember 1997.

0003-6935y98y091607-10$15.00y0© 1998 Optical Society of America

models potentially could be used to select the appro-priate laser fluence.

Theoretical LII models based on energy conserva-tion equations possess several assumptions, however.First, these models treat only a single isolated spher-ical particle of uniform composition. Actual sootparticles consist of primary particles partially con-nected or fused and assembled within open branched-chain aggregates.9 As a result, particle–particleshielding effects can occur during both absorptionand emission, leading to slower or uneven heatingand slower cooling, respectively. Second, the phys-ical properties ~density, heat capacity, and opticalproperties! used in theoretical models are taken to beidentical to those of graphite at 300 K.2–7 It is ratherunlikely that the physical properties of soot at 4000 Kare similar to those of graphite at 300 K. Conse-quently, application of an energy balance equation todetermine radiative emission ~LII intensity! based onenergy gained through laser heating is likely to beinaccurate. Third, none of these theories considermorphological alteration or variation of either sootaggregates or the constituent primary particles bypulsed laser heating except for surface vaporizationat high laser fluences. Albeit on a vastly longer timescale, heat treatment studies of carbon black, a typeof soot, have demonstrated that vast structural

20 March 1998 y Vol. 37, No. 9 y APPLIED OPTICS 1607

Page 2: Laser-Induced Incandescence: Excitation Intensity

changes occur in carbon black particles upon expo-sure to high temperatures. Often the formation ofhollow particles is observed.10 Recent transmissionelectron microscopy ~TEM! investigations of pulsedlaser-heated soot have confirmed that the high tran-sient temperature in the LII process results in simi-lar structural changes in the laser-heated soot.8Thus calculations of optical properties ~radiativeemission characteristics! of an unaltered soot particlewill not be physically representative. Fourth, for la-ser intensities beyond those required to heat the sootparticle to roughly 4000 K, LII models predict aclamping of the particle temperature at 4000 K be-cause of mass loss by surface vaporization.3,5 Earlyexperimental evidence, however, indicated that thesoot particles could be superheated to 5500 K.2 Inconjunction with this, LII models consider C3 to bethe major product evolved in surface vaporizationbased on thermodynamic equilibrium.2–7 Whereasstudies have detected9 and even purposefully pro-duced C2 with laser vaporization of soot,11 no inves-tigation has reported C3 detection. The heats ofvaporization of these species are significantly differ-ent. Thus final particle temperatures, calculatedthrough an energy balance equation, are subject togreat uncertainty at the onset of vaporization.These assumptions and associated uncertainties im-pair the ability of theory to guide selection of theappropriate excitation laser fluence.

Typically the dependence of the LII signal on theexcitation laser fluence is measured empirically. Acommon observation is that the LII signal increasesrapidly, becomes rather constant, and then decreaseswith increasing excitation laser fluence.12,13 The re-gion of roughly constant signal level has been re-ferred to as a plateau region. For fluences producingthis plateau, LII signal variations that are due tolaser energy fluctuations andyor beam attenuationare minimized. As a matter of practical utility, alaser fluence within this region is then chosen forsubsequent measurements. In this approach, thepotential dependence of the LII signal on primaryparticle size, aggregate morphology, and initial par-ticle temperature and the possible variation of thesedependencies with laser fluence remains unad-dressed. Furthermore, details of the dependence ofLII on the excitation wavelength and geometry ~beamor sheet! are convolved with the detection conditions.Most significantly, the underlying physical processesresponsible for the observed fluence dependence areignored. Thus the accuracy of LII for relative fv de-termination at different laser fluences12–16 remainsunaddressed.

Several changes can occur in the soot upon laserheating whose effect on the incandescent intensityand variation with laser fluence are uncertain. Forexample, the aggregate could fuse together to form asingle large particle. If this occurred, the particlemay not fulfill the Rayleigh size criteria. Then theradiative emission would not reflect the volume of theincandescing material, an essential premise for sootvolume fraction determination by incandescence.

1608 APPLIED OPTICS y Vol. 37, No. 9 y 20 March 1998

Another possibility is that the aggregate could frag-ment into its constituent primary particles. Thechanges in surface area and mass that would accom-pany these scenarios is unclear and thus the magni-tude of their effect on the LII signal is too. Asurprising observation is the formation of hollowshells in laser-heated soot.8 The effects of thistransformation remain to be quantified. Giventhese possibilities and their unquantified effects onthe LII signal, concern about laser-induced alterationof the soot is warranted. Thus accurate fv determi-nation by LII will require a better understanding ofthe physical process of the induced incandescenceand experimental tests of its accuracy at differentfluence levels.

To experimentally assess potential changes in-duced in the soot by pulsed laser heating, results arepresented here in which the laser-heated soot is di-rectly visualized and optically characterized. Directvisualization of soot morphology changes is providedby TEM images of the laser-heated soot. We provideoptical characterization by measuring the LII signalproduced by a second laser pulse heating the samesoot in situ as a prior laser pulse. The observedchanges in soot morphology observed from TEM im-ages and decreased optical LII signal levels gener-ated by a second laser pulse are considered relevantto measurements made with one laser pulse. Laser-induced changes are most likely to occur while thesoot particle is at the highest temperatures, i.e., dur-ing and shortly after the excitation laser pulse. It isthese times that coincide with the optimal LII signalcollection period based on theoretical estimates2–7

and experimental observations.12–16 To determinethe fluence at which mass loss occurs, the transmis-sion of the LII excitation laser pulse through a richpremixed sooting acetyleneyair flame is monitored asa function of excitation laser fluence.

To test the accuracy of LII for relative fv determi-nation at different laser fluences, radial LII intensityprofiles from a laminar ethyleneyair diffusion flameare examined over a range of laser fluences. Theseprofiles are corrected for LII signal attenuation aris-ing from intervening soot between the measurementplane and camera16,17 to facilitate comparisons.These LII radial profiles illustrate the range of signallevels achieved through variation of the excitationlaser fluence. Normalization of these profiles bytheir integrated intensity removes the absolute in-tensity differences and provides indications of thechanges accompanying the pulsed laser heating andsensitivity to primary particle size and local temper-ature. Comparison between the LII profiles and fvprofiles determined through a full-field light extinc-tion method18 is made to test the relative accuracy ofLII for fv for fluences ranging from 0.09 to 0.73 Jycm2.Consequences for valid fv determination from thefirst laser pulse given observed changes in the sootand dependence on primary particle and aggregatesize are also discussed.

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2. Experiment

Figure 1 is an experimental schematic. For thepulsed laser transmission and fluence dependencemeasurements in the premixed flame, a 0.065-in.~0.165-cm!-thick galvanized steel disk with a centralaperture of 0.187-in. ~0.475-cm! diameter selected thecentral portion of the laser beam.

For the dual-pulse experiments, light at 1064 nmfrom two identical pulsed Nd:YAG lasers was com-bined by a half-wave plate and polarizing beam split-ter as shown in the experimental schematic in Fig. 1.A beam expansion telescope formed by a 250-mmand 1300-mm focal length lenses followed by a spher-ical cylindrical lens of 1500-mm focal length formedthe laser beams into a sheet. The beam foci weresheets placed at the center of the burner having awidth of 450 mm as determined through knife-edgeprofiling.19 We controlled the energies of the twolaser pulses independently by varying the flash-lampenergy of each laser. Digital delay generators con-trolled the firing of both lasers and served to synchro-nize the laser pulses. To facilitate nomenclature,the first laser pulse is designated as P1 with thesecond designated as P2; the corresponding LII sig-nals are referred to as LII~1! and LII~2!, respectively.A typical laser pulse separation was 10 ms, whereasthe duration of each pulse was nominally 10 ns.

Pulsed laser transmission and fluence dependencemeasurements were performed in a rich premixedacetyleneyair flame supported on a McKenna burnershown in Fig. 1 with only one laser pulse. For thisflame, the fuel and airflow rates were 1.9 and 9.7 slm,respectively, whereas a N2 flow of 5 slm was used forthe shroud. A flat steel disk of 50-mm diameter sup-ported 21 mm above the burner stabilized the flame.A commercial volume absorber power meter mea-sured the laser energy after transmission throughthe flame. Radial LII intensity profiles were ob-tained at different axial heights in a laminar ethylenediffusion flame with fuel flow rate of 0.231 slm and

Fig. 1. Experimental diagram. PMT, photomultiplier tube; H. V.,high voltage.

surrounding air coflow rate of 42.8 slm. The burnerconsisted of a 10.5-mm inner diameter fuel tube sur-rounded by a 101-mm-diameter ceramic honeycomb.

For the pulsed laser transmission and fluence de-pendence measurements, the LII signal was collectedwith a 1:2 magnification telescope of 100-mm and200-mm focal length, 50-mm-diameter, fused-silicalenses. This telescope coupled the LII signal into afused-silica optical fiber that terminated at the en-trance of a 0.25-m monochromator fitted with a pho-tomultiplier tube ~PMT!. The optical fiber image atthe burner center line was 1 mm in diameter. Thearea of that image and the laser sheet thickness de-fine the spatial resolution. The spectral bandwidthover which the LII signal was collected was 10 nm.A boxcar integrator under computer control collectedthe PMT signal using a 50-ns sampling gate widthcoincident with the LII signal. Neutral density fil-ters maintained the signal within the dynamic rangeof the PMT.

Radial LII intensity profiles were generated fromLII images that were captured with a gated intensi-fied array camera and frame grabber. A bandpassinterference filter transmitting from 400 to 450 nmpreceded the fy4.5, 105-mm focal length ultraviolettransmitting camera lens. Digital delay generatorssynchronized the camera video signal, laser, and in-tensifier gate to capture either LII~1! or LII~2!. Im-age processing and analysis were performed withcustom and commercial software. Extinction-derived profiles were obtained with full-field lightextinction followed by deconvolution. Further de-tails of this technique are contained in Ref. 18.

Thermophoretic sampling measurements wereperformed with a double-action air-driven piston.The dwell time of the probe within the flame wascontrolled by custom electronics that actuated a dual-valve solenoid to govern the pressurized airflow.TEM grids were attached to the probe by a sandwichgrid holder consisting of a 0.003-in.-thick brass shimwith a 2-mm-diameter hole exposing both sides of theTEM grid. This grid holder was attached to the in-sertion rod of the probe by a small set screw. Light-scattering measurements off the probe tip were usedto characterize the insertion, dwell, and retractionprocess of the probe. Results were well representedby a trapezoid function with 10-ms insertion and re-traction times. The dwell time was variable bymeans of the control electronics and was typically10–30 ms. To synchronize the probe insertion rela-tive to the excitation laser pulse, a preceding laserpulse triggered a digital delay generator, which inturn triggered the probe insertion after an empiri-cally determined time delay. In these experiments,the laser beam was apertured with a galvanized steeldisk and left unfocused to produce a beam with a6-mm diameter and with a uniform beam intensityprofile. The laser beam was directed through theethylene flame at 50-mm height above burner ~HAB!while the probe sampled the soot at a downstreamposition of 60-mm HAB. Published flow velocities20

confirmed that a 30-ms residence time within the

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Page 4: Laser-Induced Incandescence: Excitation Intensity

flame is sufficient to capture soot that had beenheated by the laser pulse with use of our apparatusand timing scheme.

3. Results and Discussion

A. Soot Morphological Changes

Figure 2 shows an image of a soot aggregate thermo-phoretically captured in situ without ~top! and with~bottom! the laser passing through the flame. Incontrast to the nonlaser-heated aggregate, consider-able structure is observed within the primary parti-cles composing the laser-heated aggregate. Theuniform appearing primary particles in the lower ag-gregate likely were part of another ~nonirradiated!aggregate that became attached subsequent to thelaser irradiation through aggregate clustering.Banded ribbons composed of groups of parallel linesappear both within the primary particles and alongthe perimeter. These bands are comprised of stacksof carbon–atom layer planes. This is seen moreclearly in the high-resolution TEM image shown inFig. 3. Each of the dark lines represents a graphiticlayer plane viewed on edge ~oriented parallel to theviewing direction! thereby blocking the electron-beam transmission and thus appearing opaque.The spacing between the graphitic layer planes isapproximately 3.5 A, typical of turbostratic graphiticcarbon.21 The relative transparency of the centralregion of the primary particles seen in Fig. 2 relative

Fig. 2. TEM images of soot heated in situ by the laser and sub-sequently thermophoretically sampled.

1610 APPLIED OPTICS y Vol. 37, No. 9 y 20 March 1998

to the nonlaser-heated soot is due to a central voidwithin the primary particle structure. Angle-tiltingexperiments confirmed the three-dimensional struc-ture of the particles and hollow shell-like structure ofthe particles. In addition, some of the primary par-ticles appear more fused than in nonlaser-heatedsoot.

The similarity between the structures in Figs. 2and 3 and those observed in heat treatment studies ofcarbon black21 suggests similar physical processesleading to their formation. By analogy with thesestudies, it appears that the soot particle structureacquires considerable fluidity at the elevated temper-atures, allowing thermal annealing to occur.10 Thisannealing process is energetically favored becausereactive radical sites and layer plane defects are elim-inated. Thus a thermodynamically more stable gra-phitic structure is obtained.10 The formation ofgraphitic shells can naturally arise during the coolingprocess of the laser-heated soot. As the particlecools, crystallites and extended carbon–atom layerplanes running parallel to the surface become frozenin place.22 These then serve as a template againstwhich interior crystallites and atomic layer planescan align and form. Because graphite possesses ahigher density than amorphous carbon,23 the gra-phitic shells have a higher density than the originalcarbonaceous soot. Consequently, formation of gra-phitic shells without a change in particle outer di-mensions will consume interior matter. Thus massrearrangement rather than loss can account for themajority of the central void.22,24

In this graphitization process, however, the aggre-gate appears in general not to fragment or coalesceinto a fused ball. As the heat treatment studiesfound, the aggregate structure generally remains in-tact. Although little mass loss appears to have oc-

Fig. 3. High-resolution image of laser-heated soot ~in situ! by thelaser and subsequently thermophoretically sampled.

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curred as shown in Fig. 2, at higher laser fluences~..0.5 Jycm2!, preliminary TEM observations haverevealed smaller primary particles ~by approximately50% in diameter! because of expected mass lossthrough surface vaporization.17 These observationsare similar to those found by pulsed laser heating ofsoot in controlled environments.8 As discussed,given these observations of laser-altered soot struc-tural changes, the validity of predictions by use ofexisting theoretical LII models that do not account forsuch changes is doubtful.

B. Pulsed Laser Transmission

Figure 4~a! shows the relation between the transmit-ted laser energy through the premixed sooting flameas a function of the incident fluence. The initial lin-ear portion of the transmitted energy through theflame indicates that the soot is absorbing a constantfraction of the incident laser energy. With increas-ing laser intensity, this relation changes. An inci-dent laser fluence near 0.5 Jycm2 marks the onset ofthe rapid increase in transmitted excitation laser en-ergy. This sharp increase is consistent with thehigher transmission of the later portion of the laserpulse because of soot vaporization by the preceding

Fig. 4. ~a! Pulsed laser transmission through the premixed soot-ing flame. ~b! LII signal variation with incident laser energy.

portion of the laser pulse. Using a knife-edge beamprofile measurement,19 we found the laser beam 1yeradius to be 1 mm. The resulting laser fluence ofnearly 0.5 Jycm2 is significantly higher than thevalue of 0.23 Jycm2 reported in Ref. 4 at which in situabsorption and scattering changes first became ob-servable. This difference is readily explained by thedifferent excitation wavelengths for the incandes-cence used in Ref. 4 and in this study. The excita-tion wavelength used here is 1064 nm, whereas inRef. 4 it is 532 nm. The absorption constant for sootat 1064 nm is less than half that at 532 nm, scalingroughly as 1yl.25 Thus a factor of at least 2 higherfluence would be expected in the present study, as isobserved.

C. Laser-Induced Incandescent Intensity Dependence

Figure 4~b! shows the LII signal variation with inci-dent laser fluence. Similar curves have been re-ported previously12,13 but without the benefit of theTEM observations as shown in Fig. 2 or data such aspresented in Fig. 4~a!. Common to such curves is asteeply rising portion followed by a plateau where theLII signal is rather independent of the excitation la-ser intensity. Beyond a certain laser intensity, thesignal decreases.

Several physical processes are hidden by such aplot. The relative independence of the signal on la-ser energy ~intensity! near 0.25 Jycm2 suppresses thefact that at such laser intensities, dramatic morpho-logical changes are occurring in the laser-heated sootas shown in Figs. 2 and 3. With continued increasein laser fluence past 0.25 Jycm2, the LII signal con-tinues to change despite the apparent constancy in-dicated by Fig. 4~b!. The peak LII intensityincreases while the temporal decay rate of the signalalso increases. Increased peak intensity leads to in-creased LII signal whereas an increased decay rateleads to a lowered signal integrated over the detectorgate width. Over a small range of laser fluences, thetrade-off between these changes is almost even. Theincreasing temporal decay rate reflects the fastercooling of the laser-heated particle because the sur-face areaysolid volume ratio is far greater for hollowshells ~see Fig. 2! than for solid particles. For laserfluences greater than 0.5 Jycm2, the temporal decayrate of the LII continues to increase while the peakintensity begins to decrease as well. This is consis-tent with vaporization leaving less-incandescent ma-terial leading to a decrease in the absolute LIIintensity. Less mass with a likely larger surface-to-solid volume ratio would also cool faster given thereduced heat content and larger relative surface area.This hypothesis is supported by the observed rapidenergy transmission increase occurring near 0.5Jycm2 as shown in Fig. 4~a!. Less absorbing mass inthe laser path due to vaporization by the leadingportion of the laser pulse would lead to an overallincreased transmission of the excitation pulse en-ergy.

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Page 6: Laser-Induced Incandescence: Excitation Intensity

D. Correction of Radial Laser-Induced IncandescentProfiles for Signal Attenuation

In any incoherent laser-induced emission process, at-tenuation of the laser-induced emission by absorptionbetween the measurement plane and imaging systemcan occur. As applied to soot incandescence, high sootconcentrations can produce significant attenuation ofthe LII signal. For example, an fv of 10 parts permillion ~ppm! over a path length of 1 mm results in 9%attenuation at 425 nm and 6% attenuation at 633 nmwhen the refractive-index values reported for acety-lene soot26 at these wavelengths are used. Moreover,the attenuation from an intervening cylindrical sootshell between the LII signal and detector will result ina radially varying degree of signal attenuation becauseof the different chord lengths through the sootshell.16,17 This attenuation alters both the shape andthe intensity of the LII profiles.16,17 To compare theLII-derived fv distributions with those obtained fromdeconvoluted extinction data,18 the attenuated signalmust be corrected. Soot levels and path lengths typ-ical of this diffusion flame result in approximately 10–20% corrections to peak LII intensities. In theabsence of prior known extinction data, other proce-dures that use multiple line-of-sight extinction data16

or a single line-of-sight absorption measurement canbe used.17 With measured radially resolved extinc-tion data, the radial LII intensity profiles presented inFigs. 5–7 are corrected for this self-absorption of theLII signal for this flame and burner configuration.

E. Comparison between Laser-Induced Incandescence~1!and Laser-Induced Incandescence~2! Radial IntensityProfiles

Figures 5~a!–5~c! illustrate the variation in LII inten-sities with changing laser intensity produced by P1whereas Figs. 5~d!–5~f ! show the corresponding LIIprofiles resulting from P2. The signal intensityvariation with P1 laser intensity shown in Figs. 5~a!–5~c! reflects the fluence dependence curve illustratedin Fig. 4~b!. With increasing laser intensity, the sig-nal at 60-mm HAB initially increases in both theaxial and the annular regions, reaching near con-stant levels for fluences between 0.36 and 0.55 Jycm2

and thereafter decreases. Similar trends are ob-served for the profiles produced by P1 at 40-mm and20-mm HAB.

In contrast to the absolute intensities produced byP1, the LII intensities produced by P2 are signifi-cantly lower than those produced by P1 except for thetwo lowest laser fluences as is shown in Figs. 5~d!–5~f !. These profiles produced by P2 reflect a trade-off between laser fluence and laser-induced changesin the soot. With increasing fluence of P2, the LIIsignal increases. Yet with increasing excitation flu-ences, both pulses contribute to morphologicalchanges andyor mass loss. These morphologicalchanges alter the optical and heat transfer propertiesand may leave less material remaining after the laserpulse to incandesce, thus leading to lower LII signals.If increasing fluence leads to increasing change, then

1612 APPLIED OPTICS y Vol. 37, No. 9 y 20 March 1998

the least amount of change would be expected at thelowest laser fluence. As a result, the LII intensitiesproduced by P1 and P2 ~at a very low fluence level!would then be equal because P2 heats soot that isnearly unaltered in structure. This is in fact ob-served in Figs. 5~a!–5~f ! at each axial height in theradial profiles produced by the laser fluence of 0.09Jycm2.

Interestingly, although generally lower in absoluteintensity, the profiles in Figs. 5~d!–5~f ! also show aninitial increase with laser intensity and then a sub-sequent decrease. However, the dependence on la-ser fluence is shifted relative to that observed for P1.In the profiles produced by P1 at fluences of 0.36 and0.55 Jycm2, the relative intensities in the annularregion are nearly constant. In the profiles producedby P2, lower fluence levels of 0.18 and 0.36 Jycm2 nowresult in similar intensities in the annular region ateach axial height. For fluences of 0.55 Jycm2 andgreater, dramatic decreases in LII intensity producedby P2 are observed. This different variation withlaser fluence reflects the changes in the optical andthermal properties resulting from the graphitizationandyor mass loss of the soot caused by P1 or increasedsusceptibility to these processes. In contrast, theaxial intensities at 40-mm HAB exhibit a differenttrend with laser fluence. Despite the similar inten-sities in the annular region for the profiles obtainedat 0.18 and 0.36 Jycm2, the axial intensities differmarkedly. These variations between the axial andannular regions may reflect the radial variation inprimary particle size between these positions andthis effect on the relative LII signal. To more clearly

Fig. 5. Radial LII intensity profiles obtained at the indicatedheights above the burner.

Page 7: Laser-Induced Incandescence: Excitation Intensity

discern such differences, the radial intensity profilesmust be scaled to account for the intensity differ-ences.

To account for the changes in signal levels at thedifferent laser intensities, normalization of each ra-dial LII intensity profile by its integrated intensityremoves the absolute intensity variations producedby different laser fluences. This allows a clearercomparison of relative intensity variations. The re-sults, shown in Fig. 6, reveal that the profiles for60-mm and 20-mm HAB exhibit self-similarity. De-spite the differences in the absolute intensities, thenormalized profiles produced by P1 and P2 exhibitsimilar radial intensities at 60-mm and 20-mm HABfor all laser fluences. This illustrates the robustnessof LII for yielding accurate relative fv profiles. At60-mm HAB, the profiles produced by P1 agreewithin 1y25% at all radial positions. The similar-ity in the soot particle size, structure, and local tem-perature at all radial positions at 60-mm HAB, as

Fig. 6. Normalized radial LII intensity profiles from Fig. 5. Seetext for details.

Table 1. Similarity in Soot Particle Size, Structure, andLocal Temperature

HAB~mm! dp ~nm!a D63 ~nm!b

Temperature~K!

Annular Axial Annular Axial Annular Axial60 27 29 116 98 1800 160040 32 26 121 76 1800 160020 27 — 95 — 1700 1400

aRef. 28 ~annular values only!.bRef. 29.

listed in Table 1, implies that any alteration of thesoot morphology andyor mass loss that occurs wouldhappen uniformly at all radial positions. Thus if notequal absolute intensities, similar relative LII inten-sities result. The similarity of the profiles shown inFig. 6~d! produced by P2 to each other and to thoseproduced by P1 further support this explanation.Similar agreement is also observed at 20-mm HABfor profiles produced by P1 and P2. Radial varia-tions in soot particle structure are not readily resolv-able at this axial height. Steep spatial gradients inconcentration, velocity, and temperature facilitatespatial averaging of soot particles within the narrowannular soot shell. The slightly higher normalizedintensity produced by the lowest fluence level of P1 islikely attributable to the associated low signal level,thus increasing measurement uncertainty. Al-though some differences are observed at 20-mm HABin the profiles produced by P2, they still agree within1y210%. Thus even though different absolute in-tensities are produced by P1 and P2 at 60- and 20-mmHAB ~as expected for laser-altered soot!, normaliza-tion reveals self-similarity in the relative radial LIIintensities.

In contrast to the other axial positions, the profilesproduced by P1 and P2 at 40-mm HAB @Figs. 6~b! and6~e!# exhibit significant radial dissimilarities. Theprofiles produced by P1 decrease in the annular re-gion while increasing in the axial region with increas-ing laser fluence. A similar but more accentuatedtrend is observed in the profiles produced by P2.Possibilities that could account for this observed ra-dial variation include size-dependent heating andcooling effects related to primary particle and aggre-gate size, local gas temperature, and altered sootmorphology or vaporization. As indicated in Table1, the largest variation in these parameters occurs atthis height. The likelihood of each is considerednext.

Based on fluence dependence measurements pre-sented in Fig. 4, with the exception of the highestlaser fluence, we obtained the profiles produced by P1and P2 using fluences below the vaporization thresh-old. Thus vaporization cannot account for the ob-served trend. As mentioned above, at 40-mm HAB,there is a significant radial variation in primary par-ticle size with the smallest particles being found inthe axial region. In the absence of vaporization, allparticle sizes are predicted by theory3 to heat at thesame rate given that for particles in the Rayleigh sizeregime; absorption scales volumetrically. This thenpredicts no variation in the peak LII signal level withprimary particle size. After the excitation laserpulse, conduction, dependent on the particle surfacearea, controls the cooling rate whereas the particlevolume determines the amount of heat to be removed.Given the ratio of surface to volume for a spherescales as 1yr, where r is the particle radius, smallerprimary particles will cool faster than larger parti-cles. Thus the axial intensity would decrease rela-tive to the annular intensity with increasing laserfluence or remain in similar proportion to it, depend-

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Page 8: Laser-Induced Incandescence: Excitation Intensity

ing on detection conditions. This is contrary to theobserved trend seen in Fig. 6.

A second alternative is the local temperature. Itis higher in the annular region compared with theaxial region ~see Table 1!. Given this variation, pri-mary particles in the annular region will heat tohigher temperatures by starting at a higher temper-ature and also cool at a slower rate. With increasinglaser fluence, these effects should become proportion-ally smaller. As the soot is heated to ever highertemperatures, the initial temperature becomes asmaller fractional contribution to the final particletemperature. Yet the near equality of the radial in-tensity profiles at the two lowest laser fluences asshown in Fig. 6~b! is inconsistent with this explana-tion because the higher laser fluence should lessenthe effect of initial particle temperature causing theaxial intensity to increase consistently relative tothat of the annular region.

A third possibility is due to the graphitization ofthe soot by the pulsed laser heating. Recent resultsto be published elsewhere have shown these changesto vary in degree with excitation laser fluence.These results show that soot particles become in-creasingly graphitized with increasing laser fluence.In this process, the primary particle develops a shellstructure with a hollow interior.8 Primary particleswithin an aggregate become more highly connectedand at sufficient laser fluences ~yet below the vapor-ization threshold! can become merged to produce asingle hollow particle. Evidence of this can be seenin the TEM images presented in Figs. 2 and 3. Sucha process increases the effective surface area of theparticle relative to the solid volume. This increasein surface area and void volume is proportionallylarger for larger primary particles and the larger ag-gregates containing more linked primary particles.Thus as the primary particles and aggregates in-crease in surface area while decreasing in solid vol-ume, the cooling rates increase. Given the radialvariation in primary particle and aggregate size, theLII signals would be expected to decrease in the an-nular region while increasing in the axial region withincreasing laser fluence as observed for fluences be-low the vaporization threshold. This explanationrests upon three assumptions: ~a! that thesechanges do not involve significant mass loss thatwould alter the amount of material remaining to in-candesce after the laser pulse, ~b! that changes in thesurfaceyvolume ratio affect the cooling rate of theparticle more than differences in local temperature atshort detection times ~which if higher in the annularregion compared with the axial region would offsetsuch changes in the cooling rates!, and ~c! that theabsorption and emission properties of soot aggregatesscale linearly with the number of primary particleswithin the aggregate as predicted by detailed numer-ical calculations.27

In summary, for laser fluences of less than 0.5Jycm2, the overall self-similarity of the normalizedintensity profiles underscores the fact that LII yieldsan accurate relative measure of fv. Having assessed

1614 APPLIED OPTICS y Vol. 37, No. 9 y 20 March 1998

the self-consistency of the LII radial profiles at dif-ferent excitation laser intensities, we next examinethe absolute accuracy of LII.

F. Comparison between Laser-Induced Incandescence~1!Profiles with Extinction-Derived Results

To illustrate the agreement of the fv profiles deter-mined by LII and extinction, Fig. 7 shows a compar-ison between the corrected LII profiles and profilesobtained with full-field light extinction.18 To matchthe LII profiles at the different axial heights with thelight extinction data, a single scale factor was appliedto each radial profile. This constant was the samefor all axial heights. This scaling factor was deter-mined by ratioing the fv values derived by light ex-tinction to the LII intensities. This ratio was formedby first summing the radial fv values at each axialheight, adding these path-integrated values fromeach axial height together, and then dividing by thesum of the three radially summed LII intensitiesfrom each axial height. General good agreement be-tween the radial LII intensity profiles and radial fvprofiles is observed at each axial height.

At each axial height, the peak LII annular valuesfor all fluences of P1 between 0.09 and 0.73 Jycm2

match the fv values to within 15% at 60-mm HAB, towithin 10% at 40-mm HAB, and 5% at 20-mm HAB.Agreement in the axial region is somewhat less de-finitive because of the undulations in the fv profiles.These are artifacts introduced by the deconvolution ofthe extinction data. The magnitude of these varia-tions is strongly dependent on the symmetry of the

Fig. 7. Comparison between radial LII intensity profiles from Fig.5 with those determined from previous extinction measurements.See text for details.

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extinction data. Based on Fig. 7~b!, it appears thatfluences between 0.18 and 0.36 Jycm2 produce thebest overall agreement for the range of primary par-ticle sizes and local temperatures at this axial height.At other axial heights, fluences below and above thevaporization threshold produce similar agreementwithin experimental uncertainty. Thus, despite thecompletely different physical processes by which fv isdetermined in LII and extinction, the overall agree-ment observed between LII and fv profiles for laserfluences below and above the vaporization thresholdis highly encouraging for LII measurements.

What is more remarkable is that this agreement isdemonstrated over nearly an eight fold range in ex-citation fluence despite different types and degrees ofstructural change induced in the soot. Evidence ofthese changes is demonstrated in the profiles pro-duced by P2. In general, the best agreement ~within10%! between the LII and fv profiles is observed at thelowest shown fluence level of 0.18 Jycm2. This isconsistent with this lowest fluence level producingthe least change in the soot. This is most clearlyseen in Fig. 7~e! showing the profiles for 40-mm HAB.Increasing fluence produces increasing differencesbetween the LII and fv profiles as both Figs. 7~d! and7~e! show. As Figs. 7~a!–7~c! show, however, thesechanges produced by P1 and probed by P2 do notimpair the ability of LII to yield accurate quantitativefv values when calibrated. This accuracy was fore-shadowed by the self-similarity of the normalizedLII~1! profiles seen in Figs. 6~a!–6~c!.

The agreement observed here is highly encourag-ing given the wide range of soot particle size, mor-phology, and growth or oxidation state. Thisindicates the robustness of LII for accurate relativesoot volume fraction measurements over a widerange of laser fluences, soot particle sizes, and localtemperatures.

4. Conclusions

LII signal levels depend strongly on excitation laserfluence. In addition to changes in signal levels, dif-ferent laser fluences can cause different physicalchanges in both soot primary particles and aggre-gates. Both in situ optical measurements and TEMimages of thermophoretically sampled soot confirmlaser-induced morphological changes in the soot par-ticles. At lower values of laser fluence, TEM imagesreveal a thermal annealing process occurring withinthe primary particles without noticeable fragmenta-tion or coalescence of the aggregate structure. Athigher laser intensities, in situ optical measurementsindicate vaporization of the irradiated soot. Using asecond laser pulse to heat the same soot heated by aprior laser pulse confirms optically the varying typeand degree of change in the soot with varying exci-tation laser fluence. Despite these changes, normal-ized LII radial intensity profiles at different axialpositions within the laminar diffusion flame revealself-similarity. Laser fluences .0.3 Jycm2 are re-quired to achieve self-similarity of LII signals as ob-served from unnormalized LII intensity profiles.

Laser fluences ,0.5 Jycm2 appear to avoid severemass loss and other soot morphological changes asdemonstrated by pulsed laser transmission measure-ments. An added advantage is that, between theselaser fluences, the LII signal is relatively indepen-dent of laser intensity fluctuations for specific spec-tral and temporal detection conditions. The similarrelative LII intensity profiles in this range of laserfluences indicates insensitivity of LII to soot primaryparticle size, aggregate structure, and local temper-ature. The agreement of the LII profiles correctedfor attenuation because of soot absorption with fvvalues derived through light extinction suggests ro-bustness of LII for absolute determination of sootvolume fraction for excitation fluences ranging from0.09 to 0.73 Jycm2.

R. L. Vander Wal acknowledges support underNASA contract NAS3-27186 with Nyma, Inc., andK. A. Jensen acknowledges the support of a visitinggraduate student stipend sponsored through theOhio Aerospace Institute. The authors thank PaulS. Greenberg for collecting the full-field extinctiondata for the ethylene diffusion flame and the helpfulconversations about the technique.

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