Time-resolved laser-induced incandescence and ... - OSA Publishing

Time-resolved laser-induced incandescence and laser elastic-scattering measurements in a propane diffusion flame Peter O. Witze, Simone Hochgreb, David Kayes, Hope A. Michelsen, and Christopher R. Shaddix

Laser-induced incandescence 共LII兲 and laser elastic-scattering measurements have been obtained with subnanosecond time resolution from a propane diffusion flame. Results show that the peak and timeintegrated values of the LII signal increase with increasing laser fluence to maxima at the time of the onset of significant vaporization, beyond which they both decrease rapidly with further increases in fluence. This latter behavior for the time-integrated value is known to be characteristic for a laser beam with a rectangular spatial profile and is attributed to soot mass loss from vaporization. However, there is no apparent explanation for the corresponding large decrease in the peak value. Analysis shows that the peak value occurs at the time in the laser pulse when the time-integrated fluence reaches approximately 0.2 J兾cm2 and that the magnitude of the peak value is strongly dependent on the rate of energy deposition. One possible explanation for this behavior is that, at high laser fluences, a cascade ionization phenomenon leads to the formation of an absorptive plasma that strongly perturbs the LII process. © 2001 Optical Society of America OCIS codes: 120.0120, 120.1740, 290.5850, 350.4990.

1. Introduction

Laser-induced incandescence 共LII兲 has become a widely used diagnostic for the investigation of soot in combustion systems ranging from fundamental burners1–3 to practical devices such as Diesel engines.4 – 6 Unique features of the technique are its apparent simplicity and excellent sensitivity, estimated to be better than one part per trillion 共⬃2 ␮g兾m3兲.7 Previous research has shown good agreement between the LII signal and soot volume fraction in flames1–3 or combustion exhaust,8,9 as determined independently by laser light extinction or gravimetric sampling. These studies have been performed with a wide range of laser excitation wavelengths and pulse energies and for a variety of wavelength bands and temporal gates for detection. One might expect that the following conditions would need to be satisfied for the detected LII signal to be proportional to soot volume fraction: 共1兲 the probed soot consists of

The authors are with the Sandia National Laboratories, P.O. Box 969, Livermore, California 94551-0969. The email address for P. O. Witze is [email protected]. Received 4 October 2000; revised manuscript received 5 February 2001. 0003-6935兾01兾152443-10$15.00兾0 © 2001 Optical Society of America

single or loosely aggregated primary particles that are small compared to the wavelengths of the laser excitation and the collected LII signal 共such that Rayleigh-limit light absorption and emission occur兲; 共2兲 the peak particle temperatures reached during the laser pulse are relatively insensitive to the particle diameter; 共3兲 the soot particle mass vaporization is either negligible or largely independent of particle diameter; and 共4兲 the detected LII signal is dominated by thermal emission occurring during laser excitation or shortly thereafter, such that sizedependent conductance cooling does not influence the signal. Some information supporting the validity of 共1兲 has been obtained by transmission electron microscopy grid sampling and analysis of soot in various environments,10 –12 and some data demonstrating the necessity of 共4兲 have been reported,3,13 but little information has been gathered relative to 共2兲 and 共3兲. One of the advantageous characteristics of LII observed in a number of early experiments3,14 is the rapid rise in LII signal with increasing laser fluence until a nearly constant plateau signal strength is reached. This aspect of LII is useful to make measurements in strongly absorbing environments because it eliminates the need for corrections to the measured LII signal that are due to laser beam absorption, as long as the initial laser fluence level is suitably far into the plateau regime 共a correction for 20 May 2001 兾 Vol. 40, No. 15 兾 APPLIED OPTICS

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LII signal attenuation is still needed under these circumstances兲. In fact, further experimental and modeling research has revealed that the apparent LII signal plateau is an artifact of the offsetting effects of laser ablation of soot particles 共decreasing the total radiating soot mass per unit volume兲 and expansion of the excitation probe volume with increasing laser fluence when a laser beam is used with a Gaussian spatial profile and unconstrained imaging optics. When using a spatially uniform, rectangular beam, or a Gaussian beam with imaging of a fixed volume, Ni et al.3 have shown that the LII signal reaches a peak and then decreases significantly with increasing laser fluence. Virtually all the LII measurements of particle volume fraction reported in the literature were obtained by some form of time averaging of the LII signal, with either analog integrators or video cameras. Typically, averaging times ranging from 20 to 1000 ns are used, with the phasing usually set to start with the laser pulse 共prompt detection兲, although some have waited until after the laser pulse before beginning the average 共delayed detection兲. The latter approach has been used3,6 to eliminate unwanted elasticscattered light or laser-induced fluorescence signals from polycyclic aromatic hydrocarbons or C2 fragments15 produced from the LII excitation, but at the expense of some bias in the LII signal toward slowercooling large particles. Most,2,8,13,16 however, have favored prompt detection because of its strong signals and minimal sensitivity to particle size. Use of prompt detection also reduces any effects resulting from size-dependent vaporization of the soot particles 共because a portion of the measurement is obtained prior to significant vaporization兲. In this paper we report subnanosecond, timeresolved measurements of LII signals and elastic soot scattering obtained with a rectangular-profile laser beam in a diffusion flame for a wide range of laser fluences. This combination of LII and laser elasticscattering 共LES兲 measurements provides important information concerning the dynamics of the LII excitation and emission processes. We use the timeresolved LII data to analyze the effects of various choices of time averaging as commonly used in LII applications and previously investigated by Vander Wal.13 We also analyze the LII and LES measurements at the time of peak LII value and perform a time-resolved analysis. Furthermore, by assuming that the LES is in the Rayleigh regime, we also obtain a second, independent measure of particle volume fraction for both the time-averaged and the instantaneous analyses. 2. Experimental Setup

A schematic diagram of the experimental setup is shown in Fig. 1. The second harmonic of an injection-seeded Nd:YAG laser was used for excitation. The pulse repetition rate was 10 Hz, and the maximum energy per pulse was approximately 1 J. The spatial beam profile 共supplied by the laser manufacturer兲 was approximately rectangular, with a di2444

APPLIED OPTICS 兾 Vol. 40, No. 15 兾 20 May 2001

Fig. 1. Experimental setup: HWP, half-wave plate; TFP, thinfilm polarizer; NDF, neutral-density filter; PD, photodiode; LPF, long-wave-pass filter; BPF, bandpass filter.

ameter of 7 mm; no beam focusing optics were used. The laser fluence was controlled with a half-wave plate and thin-film polarizer. The laser energy was measured with a calorimeter-type powermeter. The coflow burner, with diameters of 50 and 75 mm for the fuel and oxidizer flows, respectively, was operated on propane and air. The flow rates were adjusted to maximize stability of the diffusion flame, which included use of a small amount of premixed air with the inner propane flow. The burner and laser beam are shown approximately to scale in Fig. 1. The measurement volume consisted of the entire intersection region between the laser beam and the flame. The measurements thus represent an average of an inhomogeneous soot distribution. Three measurements were obtained simultaneously with fast photodiode 共PD兲 detectors: 共1兲 incident temporal profile of the laser pulse, detected through a neutral-density filter; 共2兲 LII signal, detected through a long-wave-pass filter with a 570-nm cutoff; and 共3兲 LES signal, detected through a neutral-density filter and an interference bandpass filter centered at 532 nm, with a 10-nm full width at half-maximum 共FWHM兲. Because the electronic signal from the PD’s was high-pass filtered at 75 kHz, steady-state emissions from the flame were not a problem. Similar PD’s were used to detect the LII and LES signals and the laser temporal profile, one unamplified with a response time of 0.3 ns 共for the incident laser pulse兲 and the other amplified with a response time of 0.5 ns 共for the LII and LES兲. All three signals were recorded simultaneously with a digital oscilloscope with a bandwidth of 500 MHz and a maximum digitization rate of 5 gigasamples兾s. To evaluate the frequency response of the PD’s and oscilloscope acquisition system, LES was recorded simultaneously with both types of PD for a single laser pulse with the injection seed turned off, which maximizes the high-frequency structure in the laser pulse. Although there were small differences in the

Fig. 2. Time-resolved LII signals 共average of 400 events兲 for laser fluences of 0.02, 0.04, 0.06, 0.10, 0.12, 0.20, 0.32, 0.45, 0.72, 1.26, and 2.48 J兾cm2. The bold dotted curve is the LES signal 共arbitrary units兲 from the LII probe volume.

response to the fine details of the higher modes of the laser pulse, the response of the PD’s and oscilloscope was sufficient to measure the temporal profiles accurately. 3. Time-Resolved Measurements

Figure 2 presents an ensemble of time-resolved LII measurements for laser fluences varying from 0.02 to 2.48 J兾cm2. 共There is no physical significance to the time t ⫽ 0. Data acquisition was triggered by the laser Q switch, and an arbitrary delay time was used to minimize the null period at the beginning of the data record.兲 A typical LES profile for low laser fluence is also shown as a reference for the temporal nature of the laser pulse. These data are averages of 400 laser pulses and are similar to the results of Ni et al.,3 except that we include a wider range of fluences. In general, as laser fluence increases, the timeresolved maximum of the LII signal increases until 0.20 J兾cm2, after which it monotonically decreases whereas the time of the maximum occurs progressively earlier. At the highest fluences, a second peak appears in the LII signals which is unexpected. There is no obvious evidence of non-LII contributions to these signals. For example, when the blocking efficiency of elastically scattered light is increased by more than 2 orders of magnitude, it has no effect on the waveform. We measured the LII signal through a long-wave-pass filter with a cutoff wavelength at 610 nm instead of 570 nm and an interference bandpass filter centered at 688 nm, and again we observed no change in the waveform, which rules out the possibility that this second peak is attributable to laserinduced fluorescence from C2 共there is a Swan band at 564 nm兲 or polycyclic aromatic hydrocarbons 共which is broadband兲. Eckbreth17 observed a somewhat similar behavior at high fluences, which he attributed to the changing optical behavior of the dye-laser medium with time during the pulse; this caused the flux and beam size to change. There is no analogous problem with our laser.

Another unexpected behavior in the data of Fig. 2 is the relatively rapid decay from the maximum of the LII signal for the lowest fluence of 0.02 J兾cm2. In general, one would expect the particle cooling rate to increase monotonically with increased particle temperature. The fact that the minimum cooling rate is observed for the third curve, with fluence of 0.06 J兾cm2, suggests that, for the two lower fluences, an unidentified physical process is taking place. Finally, the time of the maximum LII signal increases over the first three data points, after which it occurs progressively earlier. Although this change would be consistent with the onset of significant vaporization of the soot, LES measurements presented in Section 4 show that there is no measurable particle volume change below a fluence of 0.2 J兾cm2. There are two processes that conceivably could account for these seemingly anomalous trends in the timeresolved LII profiles at low fluence: Stephan flow and thermal annealing. Stephan flow18 refers to the bulk transport of mass or heat away from a particle in response to a concentration or temperature gradient established during the vaporization process. The existence of Stephan flow reduces the magnitude of all diffusive transport processes between particles and bulk gas, including the heat conduction process that determines the particle cooling rate once the particle temperature falls below the equilibrium vaporization temperature. Although it is possible that increasing particle vaporization rates, and therefore increased Stephan flow, reduces conductive cooling of the laser-heated particles at the lowest fluences shown in Fig. 2 共before the effects of increasing peak temperature and decreasing particle size overcome the influence of Stephan flow at higher fluences兲, the data analysis presented in Section 4 suggests that significant vaporization rates are not initiated until higher fluences. At these higher fluences, Stephan flow undoubtedly reduces the conduction loss rates during particle vaporization and shortly thereafter, consistent with the slow particle temperature decay recently measured by Schraml et al.19 Thermal annealing refers to the high-temperature microstructural reorganization of the carbon material within the soot particles that makes them more graphitic. Soot particles, particularly within diffusion flames, are composed of relatively small aromatic units, typically arranged concentrically around an amorphous core.20 –23 For sufficiently strong heat treatments 共defined by a combination of temperature and hold time兲, the length of the ordered areas increases and adjacent ordered planes become more tightly packed, densifying the particle. This increased turbostratic ordering of the carbon results in increased electron delocalization and modified optical properties, increasing the optical absorptivity in particular.24 Laser beam extinction measurements presented in Section 4 共in Fig. 5兲 in this paper suggest that an increase in the soot particle optical extinction coefficient occurs at low fluences. Indeed, Vander Wal and Choi12 collected transmission electron mi20 May 2001 兾 Vol. 40, No. 15 兾 APPLIED OPTICS

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Fig. 3. Time-resolved LES signals 共average of 400 events兲 for laser fluences of 0.02, 0.04, 0.06, 0.10, 0.12, 0.20, 0.32, 0.45, 0.72, 1.26, and 2.48 J兾cm2.

Fig. 4. Time-averaged LII signals for various averaging periods as a function of laser fluence.

croscopy micrographs that directly demonstrated significant ordering of soot particles excited with a laser beam at relatively low fluences for LII. With respect to the increasing cooling rates seen at the lowest fluences in Fig. 2, increases in thermal annealing of the laser-heated soot 共as expected with increasing laser fluences and increasing peak laser temperatures兲 would result in optical emissivity of the soot that increases with time during and after the laser pulse, decreasing the observed LII decay with time after its peak intensity. At yet higher fluences, the predominant thermal annealing effects likely occur early during the laser pulse itself, with a subsequent reduction of influence on the observed LII decay rate. The time-resolved LES measurements corresponding to the fluences used in Fig. 2 are presented in Fig. 3. The curves for the five lowest fluence levels are essentially identical and mimic the waveform of the incident laser pulse. For higher fluences, it is clear that significant vaporization has occurred. A fluence of 0.20 J兾cm2 produced the maximum instantaneous LII signal 共Fig. 2兲, and these LES data suggest that the scattering cross section has been slightly reduced by laser heating at this level. It is not known whether this reduction is due to mass loss or material property changes. In the remainder of this paper we focus on various approaches to the analysis of the data presented in Figs. 2 and 3. In Section 4 we analyze these data using time-averaging procedures, followed by two sections on time-resolved approaches that include use of LES to estimate the time-resolved volume reduction from laser-induced vaporization.

when gated cameras are used to record LII signals, it is often not possible to achieve such short exposure times,2,4 and longer exposures are often desired to increase the overall signal-to-noise ratio.15 We therefore included longer times in this sensitivity analysis in a manner similar to that of Vander Wal.13 In general, the LII data in Fig. 4 show a rapid rise to a maximum, followed by a more gradual decay to an essentially constant value for fluences greater than 1.0 J兾cm2. The location of the LII maximum occurs at lower fluences as the prompt interval is increased until it reaches the maximum at the same fluence as the delayed data, at 0.2 J兾cm2. This maximum in the LII signal is interpreted typically as the onset of significant vaporization, denoted as F*. For a Gaussian profile laser beam, it is at this point that the LII signal becomes approximately constant, independent of further increases in the laser fluence 共see, e.g., Ni et al.3兲. For our nearly rectangular profile beam, there is no plateau at F*. The curve in Fig. 4 for delayed LII detection, with an integration interval from 30 to 50 ns, shows similar behavior to the prompt data, except that the maximum for the former is nearly five times the asymptotic value beyond 1.0 J兾cm2, whereas this ratio for the 0 –25-ns integration period is approximately only two. This delayed LII signal is governed by conductive heat transfer, whereas the prompt LII measurements are controlled by the vaporization process. Ni et al.3 have shown that delayed LII signals are sensitive to the particle-cooling-rate dependence on primary particle size. Prompt measurements are thus generally preferred. Delayed LII measurements, however, are often performed because of the ease of rejection of background signals from LES and laser-induced fluorescence. For a spatially uniform laser beam profile, we believe that a region of constant LII signal for fluences greater than 1.0 J兾cm2 has not been previously reported. The data of Ni et al.3 are limited to fluences at ⬍1.0 J兾cm2, but at that point they show a trend of approaching a constant value. Snelling et al.25 com-

4. Time-Averaged Analysis

Figure 4 shows prompt 共during the laser pulse兲 LII measurements obtained when we averaged the timeresolved signals of Fig. 2 for intervals ranging from 25 to 50 ns and delayed 共after the laser pulse兲 measurements for the interval from 30 to 50 ns. As shown by the LES curve in Fig. 2, a 25-ns interval best captures the laser heating period. However, 2446


Fig. 5. Particle volume fraction change inferred from laser beam extinction measurements, LII, and LES measurements by use of Rayleigh and RDG PFA theory.

pare theoretical predictions with the Ni et al.3 data that clearly show that current LII theory does not predict this constant region. 共The LII behavior in this region cannot be explained by a change in the laser beam spatial profile at high energies, because we ran the laser at full power and controlled the fluence using a polarization splitter and half-wave plate.兲 Wainner and Seitzman26 have reported LII measurements for fluences as high as 50 J兾cm2. For a 532-nm Gaussian laser beam formed into a sheet, they observed a plateau region between 0.1 and 1.0 J兾cm2, beyond which the broadband LII signal increased rapidly with increasing fluence, even though the particle size steadily decreased. They suggest that this increased signal is non-LII 共i.e., nonblackbody兲. We suspect that this unknown mechanism is responsible for the flatness of the LII measurements in Fig. 4 for fluences greater than 1.0 J兾cm2; that is, the decrease in the true LII signal with increased fluence is compensated by a non-LII signal. Laser beam extinction measurements were also made as a function of fluence with a calorimeter powermeter, which is analogous to time-averaged prompt analysis. The flame was moved in and out of the laser beam to measure the attenuation ratio I兾I0, which is presented in Fig. 5 as the normalized volume fraction, calculated from ln共I兾I 0兲 V ⫽ , V max ln共I兾I 0兲 max

(1)

where Vmax is assumed to be the initial particle volume fraction prior to laser-induced vaporization. Unexpectedly, these measurements show an increase in extinction 共by approximately 20%兲 with increased fluence for values less than 0.2 J兾cm2. As discussed above, we believe that this effect results from an increase in the optical absorptivity from thermal annealing of the laser-heated soot. It is also possible that there may be a contribution from increased optical absorptivity as a function of soot temperature.27–29 Because the point of maximum extinction coincides with the threshold fluence F* for

the LII measurements in Fig. 4, we chose this for the normalizing volume fraction Vmax. For fluences larger than F*, the extinction monotonically decreases with increased fluence, indicative of mass loss from laser-induced vaporization. If it is assumed for fluences greater than F* that the soot temperature quickly 共i.e., early in the laser pulse兲 reaches a constant vaporization temperature 共which is only approximately true兲, prompt LII signals can be interpreted as a direct measure of particle volume fraction. In Fig. 5, curves 共a兲, we compare the prompt 共25-ns兲 LII data, normalized at F*, with the extinction measurements. For fluences up to 0.9 J兾cm2, there is excellent agreement between the LII and the extinction measurements. For larger fluences, the LII results are constant whereas the extinction measurements continue to decrease. As discussed above, the former behavior is unexpected, and the latter behavior is expected for particle size reduction from vaporization. In Fig. 5, curves 共b兲, we compare the extinction measurements with an estimate of particle volume fraction that assumes the LES is predominantly in the Rayleigh regime, where the particle diameter d is much smaller than the laser wavelength ␭, i.e., d ⬍⬍ ␭兾␲. This condition is satisfied by primary soot particles, where diameters are in the range of tens of nanometers. On the other hand, aggregates may exceed 100 nm in size, which encroaches on the Rayleigh assumption for the 532-nm wavelength of our laser. Rigorous requirements for an aggregate to scatter according to Rayleigh theory are that the primary particles are spherical, monodisperse, have identical refractive indices, and act independently. Because typical soot does not satisfy these conditions, it is common to assume that small aggregates will scatter as volume-equivalent spheres according to Rayleigh theory 共Santoro et al.30兲. The elasticscattering intensity ILES in the Rayleigh regime is proportional to I៮ Nd6, where N is the number of aggregate particles and I៮ is the average laser intensity in the probe volume, which can be estimated from the extinction measurements to be I៮ ⫽

I ⫺ I0 . ln共I兾I 0兲

(2)

Therefore the particle volume fraction V can be estimated to be proportional to 共ILES兾I៮ 兲1兾2 if it is assumed that N is a constant that cancels with normalization by Vmax, the volume fraction at F*. The Rayleighderived volume fraction results presented in Fig. 5 were calculated for a 25-ns integration interval of the data presented in Fig. 3; consequently these are a measurement of the average soot volume fraction integrated over the laser pulse. Compared with the extinction results, Rayleigh theory is seen to predict a slower rate of volume loss with increased fluence. The combined application of extinction and LES measurements permits use of the Rayleigh–Debye– Gans 共RDG兲 theory for polydisperse fractal aggregates31 共PFA’s兲. This theory has been shown by 20 May 2001 兾 Vol. 40, No. 15 兾 APPLIED OPTICS

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Farias et al.32 to provide good estimates of primary particle size for agglomerates that do not rigorously satisfy the Rayleigh-limit criteria. Koÿlu¨33 has shown that the primary particle size dp can be inferred from the ratio of the differential scattering coefficient for a scattering angle perpendicular to the direction of propagation and the plane of polarization of the incident beam Cscat共90°兲 relative to the absorption coefficient Cabs according to dp ⬀

冋

C scat共90°兲 C abs

册

1兾3⫺Df

,

(3)

where Df is the mass fractal dimension of ⬃1.8 for flame-generated soot.34,35 Approximate values of the scattering and absorption cross sections can be derived from the measured extinction and scattering signal Sscat共90°兲, i.e., C abs ⫽

⫺ln共I兾I 0兲 , Nnl

(4)

C scat共90°兲 ⫽

S scat共90°兲 , NnlI៮

(5)

where l is the length of the absorption path and the scattering volume, n is the number of primary particles per aggregate, and N is the number concentration of aggregate particles. The combination of Eqs. 共2兲, 共4兲, and 共5兲 and relation 共3兲 results in the following RDG PFA expression for normalized particle volume fraction: V⬀

冋

S scat共90°兲 I0 ⫺ I

册

1.36

.

(6)

Measurements analyzed with relation 共6兲 are compared with the extinction results in Fig. 5, curves 共c兲. Normalization was again performed at F*, and results for smaller values of fluence are not shown. In general, the agreement between F* and 0.9 J兾cm2 is similar to the Rayleigh theory results. There is more scatter in the RDG PFA results, caused by the inverse proportionality to the extinction measurements, which were not as well behaved as the LII and LES measurements. For fluences ⬎0.9 J兾cm2, RDG PFA predicts a nearly constant volume fraction, similar to the LII results, and shows the largest disparity from the extinction measurements of any of the techniques presented. Finally, in Fig. 5, curves 共d兲, we compare the results for the Rayleigh and RDG PFA theories. For fluences ⬍1.0 J兾cm2, the agreement is good, although there is considerably more scatter in the latter data because the analysis involves the ratio of individual measurements, which accentuates the scatter in the data. For fluences greater than 1.0 J兾cm2, the RDG PFA predicts larger sizes, which is due mainly to the presence of the extinction term in the denominator of relation 共6兲. However, because 2448


Fig. 6. Instantaneous maximum LII signal LIImax 共normalized at F*兲, particle volume fraction change inferred from the instantaneous LES at LIImax, and the partial fluence at the time of LIImax.

we believe there are non-LII emissions and the possible existence of plasmas 共discussed in Section 5兲 in this fluence region, there is reason to suspect that the LES is influenced by other effects than the characteristics of the soot itself. Considering the very close agreement between the Rayleigh and the RDG PFA theories outside of this region, and the greater scatter in the data by the latter analysis, we chose to report just the Rayleigh theory analysis of the LES measurements in the remainder of this paper. 5. Instantaneous-Value Analysis

The measurements presented thus far confirm that laser heating significantly alters the physical nature of the particulate matter in the probe volume, thus affecting the elastic scattering and incandescence emission behavior. Although we do not fully understand all the phenomena associated with the rapid heating of extremely small carbon particles, mass loss should contribute significantly to reduced LII signals for increased laser fluence. This effect can be minimized if the LII measurement is taken to be the maximum instantaneous value LIImax. Although it is likely that the maximum occurs somewhat later than the onset of measurable laserinduced vaporization 共because of superheating of the particles兲, it is a well-defined point on temporal LII curves for different fluences, as shown in Fig. 2. However, the data in Fig. 2 also show that LIImax decreases significantly with increased laser fluence, contrary to expectations. Presented in Fig. 6 are the measurements of LIImax as a function of laser fluence. These results exhibit behavior similar to the prompt LII results presented in Fig. 4, with a maximum occurring at approximately 0.2 J兾cm2. Perhaps the most notable difference from the integrated LII data is the continual decay in LIImax for fluences above 1.0 J兾cm2—the integrated results were constant in this region. Also shown in Fig. 6 are the relative particle volume fraction estimates from the instantaneous LES at the

time of LIImax when Rayleigh scattering is assumed. That is, V⬀

冉冊 I LES I

0.5

,

(7)

LIImax

where I is the instantaneous laser intensity measured with a PD 共see Fig. 1兲. These results show that significant mass loss has occurred by the time of maximum LII signal and that there is measurable mass loss for fluences less than what we previously identified as F* 共0.2 J兾cm2兲. Finally, at large fluences the LII signal has dropped from its peak value almost 40% more than the particle volume fraction inferred from the Rayleigh-scattering interpretation of the LES. This difference could be attributable to errors if the soot particle scattering is assumed to be Rayleigh-like, or another possibility is that decay in LIImax is stronger than would be given by actual soot volume loss that is due to a decrease in the extent of thermal annealing of the soot at LIImax as the fluence level is increased 共decreasing the available time for thermal annealing before LIImax is reached兲. To emphasize further how unexpected the LIImax measurements are, in Fig. 6 we show the partial incident laser fluence into the probe volume at the time of LIImax 共note that the abscissa is the laser fluence for the entire pulse兲. The nearly constant values of partial fluence for laser fluences greater than F* confirm that essentially the same amount of incident laser energy produced LII signals that were reduced dramatically with increased laser fluence. In other words, for a constant amount of incident energy the instantaneous maximum in the LII signal decreased as laser power increased. Furthermore, the LES signals suggest that this characteristic partial fluence results in increased soot vaporization with stronger total fluence, perhaps because of a reduction in conductance losses during faster particle heat up. One possible explanation for the decrease in LII signal with increased laser power is the formation of a plasma around the soot particles. Lushnikov and Negin36 describe an optical breakdown phenomenon that results in a dense plasma cloud that is an effective absorber and scatterer of light. The existence of such a plasma would limit the laser heating of a particle or attenuate incandescence from it; however, one would also expect an increase in extinction and LES from the increased effective size, which is not the case with our experimental results. Smith37 has noted that laser intensities as low as 1 MW兾cm2 are sufficient to create a plasma from an aerosol, but for carbon particles ⬍5 ␮m he predicts a breakdown threshold of 300 GW兾cm2. For our laser, F* of 0.2 J兾cm2 corresponds to approximately only 30 MW兾 cm2, which suggests that breakdown is not likely. However, the validity of this analysis for primary soot particles of the order of 50 nm is also highly questionable. The measurements of partial laser fluence in Fig. 6 suggest an alternative to use of LIImax as a measure

Fig. 7. Instantaneous LII signal at various levels of partial laser fluence. The dashed curve is the result from Fig. 6 for LIImax.

of particle volume fraction with minimal bias from mass loss by laser-induced vaporization. Use of the instantaneous LII signal at the time of a specified amount of partial laser fluence offers a more general approach. The results from this analysis are presented in Fig. 7 as a function of laser fluence for four different partial laser fluences. The results from Fig. 6 for LIImax are also shown for reference. These data indicate that a very low partial fluence of 0.03 J兾cm2 is necessary to achieve a plateau in the LII behavior. This is far below the fluence required to reach the vaporization temperature of carbon and thus is further evidence that the desirable regime where LII is independent of laser beam attenuation through the probe volume does not exist for the laser beam profile of this experiment. Shown in Fig. 8 are the corresponding particle volume fraction measurements estimated for Rayleigh scattering. The data were normalized by the values at 0.03 J兾cm2. For even the lowest partial fluence of 0.03 J兾cm2, these results indicate that there either has been some mass loss or that laser heating has reduced the scattering cross section of the soot.

Fig. 8. Instantanous relative particle volume fraction inferred from LES for various levels of partial laser fluence. 20 May 2001 兾 Vol. 40, No. 15 兾 APPLIED OPTICS

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Fig. 9. Time-resolved measurements of laser intensity, LES, and LII, and values of V兾V0 inferred from the LES signal for a laser fluence of 0.72 J兾cm2.

Fig. 10. Particle volume fraction reduction V兾V0 as a function of the partial laser fluence 共log10 scale兲 for different values of laser fluence 共total pulse兲.

6. Time-Resolved Analysis

is comfortably above the discretization resolution of the transient recorder. The abscissa used for the results presented in Fig. 9 is time. However, it is more useful to plot the data as a function of the partial fluence, as shown in Fig. 10 for a range of total laser fluences. These results show that mass loss from laser-induced vaporization is strongly dependent on the laser irradiance 共W兾 cm2兲 and not simply the partial fluence.

The ratio of instantaneous elastic scattering ILES共t兲 to instantaneous laser intensity I共t兲 defines a scattering efficiency ␩共t兲 that depends on the coupling of the incident laser fluence with the soot in the probe volume and the geometry of the collection optics. At low fluences, it can be assumed that laser heating has a negligible effect on particle size and number, so that the scattering efficiency can be taken to be a constant ␩0. It then follows that the instantaneous volume fraction V共t兲 can be expressed as

冋册冋

V共t兲 ␩共t兲 ⫽ V0 ␩0

0.5

1 I LES共t兲 ⫽ ␩ 0 I共t兲

册

0.5

,

(8)

where V0 is the initial, prevaporization volume fraction, if it is assumed that the particle field is frozen during the laser pulse, that the scattering is in the Rayleigh regime, and that laser heating affects only the particle size and not the number. To implement this procedure, it is extremely important to have the proper phasing between the laser and the LES signals, such that the transit time of light becomes an issue. At a low laser fluence, we determined that a phase shift of 2.6 ns was needed for the measured laser profile to coincide with the LES signal from the probe volume. We then used this phase-shift value for all other fluence levels. Figure 9 shows an example of this analysis for a total fluence of 0.72 J兾cm2. The LII data are shown just for reference, but note that the inflection in the LII curve corresponds to the end of a linear rate-ofmass-loss period, which occurs considerably before the end of the laser pulse; this behavior was found to occur at all high laser fluences. The case selected for this example was for a relatively high fluence level, which minimizes the interval duration available to compute ␩0 prior to the onset of vaporization. As indicated by the noisy results at the beginning of the laser pulse, the normalization process must include a finite period in which the absolute value of the signals 2450


7. Conclusions

LII and LES measurements have been obtained with subnanosecond time resolution from a propane diffusion flame. We analyzed the measurements using both the conventional time-averaged methodology and the two instantaneous procedures. Because the preferred prompt method is biased by laser-induced vaporization, our intent with the instantaneous procedures was to obtain measurements at the time of maximum LII signal, prior to significant mass loss. We found that LIImax is sensitive to the rate of energy deposition. For the same partial laser fluence, mass loss increased with increased total laser fluence, implying that quantitative measurements will require calibration at a specific fluence, preferably the minimum to initiate vaporization. 共This was also the conclusion of Vander Wal and Jensen,38 who recommended a fluence of 0.3– 0.5 J兾cm2.兲 Because it is difficult to determine laser fluence accurately and because volume loss from laser-induced vaporization depends on the instantaneous laser intensity, we believe it is best to use in situ measurements to set the fluence level. For a laser beam with a rectangular spatial profile, we recommend setting the fluence to achieve the maximum instantaneous LII signal, which was shown to correspond to a volume loss of approximately 10%. For a laser that produces a monotonically increasing value for LIImax with increasing fluence, such as for a Gaussian beam profile, we recommend setting the fluence to achieve a specified level of volume loss determined by LES. An unexpected result of this study is that, for a

constant amount of incident energy, the instantaneous maximum in the LII signal decreased as laser power increased. This behavior cannot be easily explained by mass loss from vaporization, aggregate breakup, or morphology changes. One possible explanation is the occurrence of a cascade breakdown phenomenon that leads to the formation of a plasma cloud around the soot particles that attenuates the LII signal. This research was performed at the Combustion Research Facility of the Sandia National Laboratories and was funded by the U.S. Department of Energy, Office of Transportation Technologies. David Kayes was partially supported by the Ford Motor Co., as well as by the U.S. Environmental Protection Agency through the MIT Center on Airborne Organics. The authors thank Bob Green for numerous discussions and helpful comments and Greg Smallwood and David Snelling of the National Research Council of Canada for their insightful suggestions during preparation of this paper. References 1. R. L. Vander Wal and K. J. Weiland, “Laser-induced incandescence: development and characterization towards a measurement of soot volume fraction,” Appl. Phys. B 59, 445– 452 共1994兲. 2. C. R. Shaddix, J. E. Harrington, and K. C. Smyth, “Quantitative measurements of enhanced soot production in steady and flickering methane兾air diffusion flames,” Combust. Flame 99, 723–732 共1994兲. 3. T. Ni, J. A. Pinson, S. Gupta, and R. J. Santoro, “Twodimensional imaging of soot volume fraction by the use of laserinduced incandescence,” Appl. Opt. 34, 7083–7091 共1995兲. 4. J. E. Dec, A. O. zur Loye, and D. L. Siebers, “Soot distribution in a D. I. Diesel engine using 2-D laser-induced incandescence imaging,” SAE paper 910224 共Society of Automotive Engineers, Warrendale, Pa., 1991兲. 5. Y-H. Won, T. Kamimoto, H. Kobayashi, and H. Kosaka, “2-D soot visualization in unsteady spray flame by means of laser sheet scattering technique,” SAE paper 910223 共Society of Automotive Engineers, Warrendale, Pa., 1991兲. 6. J. A. Pinson, D. L. Mitchell, R. J. Santoro, and T. A. Litzinger, “Quantitative, planar soot measurements in a D. I. Diesel engine using laser-induced incandescence and light scattering,” in SAE paper 932650 共Society of Automotive Engineers, Warrendale, Pa., 1993兲. 7. R. T. Wainner, J. M. Seitzman, and S. R. Martin, “Soot measurements in a simulated engine exhaust using laser-induced incandescence,” AIAA J. 37, 738 –743 共1999兲. 8. D. R. Snelling, G. J. Smallwood, R. A. Sawchuk, W. S. Neill, D. Gareau, W. L. Chippior, F. Liu, and Ö. L. Gu¨lder, “Particulate matter measurements in a Diesel engine exhaust by laserinduced incandescence and the standard gravimetric procedure,” in SAE paper 1999-01-3653 共Society of Automotive Engineers, Warrendale, Pa., 1999兲. 9. M. E. Case and D. L. Hofeldt, “Soot mass concentration measurements in Diesel engine exhaust using laser-induced incandescence,” Aerosol Sci. Technol. 25, 46 – 60 共1996兲. 10. I. Colbeck, B. Atkinson, and Y. Johar, “The morphology and optical properties of soot produced by different fuels,” J. Aerosol Sci. 28, 715–723 共1997兲. ¨.O ¨ . Koÿlu¨, C. S. McEnally, D. E. Rosner, and L. D. Pfefferle, 11. U “Simultaneous measurements of soot volume fraction and par-

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