Modeling of time-resolved laser-induced incandescence transients for particle sizing in high-pressure spray combustion environments: a comparative study

In this study experimental single-pulse, time-resolved laser-induced incandescence (TIRE-LII) signal intensity profiles acquired during transient Diesel combustion events at high pressure were processed. Experiments were performed between 0.6 and 7 MPa using a high-temperature high-pressure constant volume cell and a heavy-duty Diesel engine, respectively. Three currently available LII sub-model functions were investigated in their performance for extracting ensemble mean soot particle diameters using a least-squares fitting routine, and a “quick-fit” interpolation approach, respectively. In the calculations a particle size distribution as well as the temporal and spatial intensity profile of the heating laser was taken into account. For the poorly characterized sample environments of this work, some deficiencies in these state-of-the-art data evaluation procedures were revealed. Depending on the implemented model function, significant differences in the extracted particle size parameters are apparent. We also observe that the obtained “best-fit” size parameters in the fitting procedure are biased by the choice of their respective “first-guess” initial values. This behavior may be caused by the smooth temporal profile of the LII cooling curve, giving rise to shallow local minima on the multi-parameter least squares residuals, surface sampled during the regression analysis procedure. Knowledge of the gas phase temperature of the probed medium is considered important for obtaining unbiased size parameter information from TIRE-LII measurements. PACS 42.62.-b; 51.30.+i; 82.20.Wt     

Modeling laser-induced incandescence of soot: enthalpy changes during sublimation, conduction, and oxidation

This paper presents an analysis of several equations used to model laser-induced incandescence (LII) of soot. The analysis focuses on sub-models of the change in particle enthalpy during sublimation, conduction, and oxidation. Assuming that pressure is constant, expressing the conductive cooling rate in terms of enthalpy instead of energy, thereby accounting for expansion work, increases the signal decay rate and has an effect comparable to increasing the thermal accommodation coefficient from 0.30 to 0.38. Accounting for oxidative heating decreases the signal decay rate and has an effect comparable to decreasing the accommodation coefficient from 0.30 to 0.25. As an estimate of magnitude of these effects, primary particle sizes inferred from signal decay rates measured at low fluences may be over-predicted by as much as 17% if oxidation is neglected in the model at O₂ partial pressures of ～0.2 bar, under-predicted by 24% if expansion work is neglected, and under-predicted by only 9% if both are neglected. This paper also provides updated parameterizations for average enthalpies of formation, molecular weights, and total pressures of sublimed carbon clusters for use in LII models.     

Influence of spatial laser energy distribution on evaluated soot particle sizes using two-colour laser-induced incandescence in a flat premixed ethylene/air flame

Time-resolved laser-induced incandescence (LII) has been developed rapidly during the last decade as a useful non-intrusive technique for particle size determination. Still several parameters should be investigated in order to improve the accuracy of LII for particle sizing and the spatial distribution of the laser energy is one of these. Generally a top-hat profile is recommended, as this ensures a uniform heating of all particles in the measurement volume. As it is generally not straightforward to create a uniform beam profile, it is of interest to establish the influence of various profiles on the evaluated particle sizes. In this work we present both an experimental and a theoretical investigation of the influence of the spatial profile on evaluated sizes. All experiments were carried out using a newly developed setup for two-colour LII (2C-LII) which provides online monitoring of both the spatial and temporal profile as well as the laser pulse energy. The LII measurements were performed in a one-dimensional premixed sooting ethylene/air flame, and evaluated particle sizes from LII were compared with thermophoretically sampled soot particles analysed using transmission electron microscopy (TEM). The results show that although there is some influence of the spatial laser energy distribution on the evaluated particle sizes both in modelling and experiments, this effect is substantially smaller than the influence of the uncertainties in gas temperature and the thermal accommodation coefficient.     

Effects of volatile coatings on the laser-induced incandescence of soot

We have measured time-resolved laser-induced incandescence (LII) from combustion-generated mature soot extracted from a burner and (1) coated with oleic acid or (2) coated with oleic acid and then thermally denuded using a thermodenuder. The soot samples were size selected using a differential mobility analyzer and characterized with a scanning mobility particle sizer, centrifugal particle mass analyzer, and transmission electron microscope. The results demonstrate a strong influence of coatings on the magnitude and temporal evolution of the LII signal. For coated particles, higher laser fluences are required to reach signal levels comparable to those of uncoated particles. The peak LII curve is shifted to increasingly higher fluences with increasing coating thickness until this effect saturates at a coating thickness of ~75 % by mass. These effects are predominantly attributable to the additional energy needed to vaporize the coating while heating the particle. LII signals are higher and signal decay rates are significantly slower for thermally denuded particles relative to coated or uncoated particles, particularly at low and intermediate laser fluences. Our results suggest negligible coating enhancement in absorption cross-section for combustion-generated soot at the laser fluences used. Apparent enhancement in absorption with restructuring may be caused by less conductive cooling.     

Determining aerosol particle size distributions using time-resolved laser-induced incandescence

The particle size distribution within an aerosol containing refractory nanoparticles can be inferred using time-resolved laser-induced incandescence (TR-LII). In this procedure, a small volume of aerosol is heated to incandescent temperatures by a short laser pulse, and the incandescence of the aerosol particles is then measured as they return to the ambient gas temperature by conduction heat transfer. Although the cooling rate of an individual particle depends on its volume-to-area ratio, recovering the particle size distribution from the observed temporal decay of the LII signal is complicated by the fact that the LII signal is due to the incandescence of all particle size classes within the sample volume, and because of this, the particle size distribution is related to the time-resolved LII signal through a mathematically ill-posed equation. This paper reviews techniques proposed in the literature for recovering particle size distributions from TR-LII data. The characteristics of this problem are then discussed in detail, with a focus on the effect of ill-posedness on the stability and uniqueness of the recovered particle size distributions. Finally, the performance of each method is evaluated and compared based on the results of a perturbation analysis. PACS  44.05.+e; 47.70.Pq; 78.70.-g; 65.80.+n; 78.20.Ci     

High-vacuum time-resolved laser-induced incandescence of flame-generated soot

We have measured time-resolved laser-induced incandescence of flame-generated soot under high-vacuum conditions (4.1×10⁻⁶ mbar) at an excitation wavelength of 532 nm with laser fluences spanning 0.06–0.5 J/cm². We generated soot in an ethylene/air diffusion flame, introduced it into the vacuum system with an aerodynamic lens, heated it using a pulsed laser with a spatially homogeneous and temporally smooth laser profile, and recorded LII temporal profiles at 685 nm. At low laser fluences LII signal decay rates are slow, and LII signals persist beyond the residence time of the soot particles in the detection region. At these fluences, the temporal maximum of the LII signal increases nearly linearly with increasing laser fluence until reaching a plateau at ∼0.18 J/cm². At higher fluences, the LII signal maximum is independent of laser fluence within experimental uncertainty. At these fluences, the LII signal decays rapidly during the laser pulse. The fluence dependence of the vacuum LII signal is qualitatively similar to that observed under similar laser conditions in an atmospheric flame but requires higher fluences (by ∼0.03 J/cm²) for initiation. These data demonstrate the feasibility of recording vacuum LII temporal profiles of flame-generated soot under well-characterized conditions for model validation.     

Laser-induced incandescence for soot-particle sizing at elevated pressure

This paper describes the applicability of laser-induced incandescence (LII) as a measurement technique for primary soot particle sizes at elevated pressure. A high-pressure burner was constructed that provides stable, laminar, sooting, premixed ethylene/air flames at 1–10 bar. An LII model was set up that includes different heat-conduction sub-models and used an accommodation coefficient of 0.25 for all pressures studied. Based on this model experimental time-resolved LII signals recorded at different positions in the flame were evaluated with respect to the mean particle diameter of a log-normal particle-size distribution. The resulting primary particle sizes were compared to results from TEM images of soot samples that were collected thermophoretically from the high-pressure flame. The LII results are in good agreement with the mean primary particle sizes of a log-normal particle-size distribution obtained from the TEM-data for all pressures, if the LII signals are evaluated with the heat-conduction model of Fuchs combined with an aggregate sub-model that describes the reduced heat conduction of aggregated primary soot particles. The model, called LIISim, is available online via a web interface. PACS 65.80.+n; 78.20.Nv; 42.62.-b; 47.70.Pq     

Soot volume fractions and primary particle size estimate by means of the simultaneous two-color-time-resolved and 2D laser-induced incandescence

An original approach of laser-induced incandescence consisting in the simultaneous recording of the two-color-time-resolved and 2D LII signal is described in this paper. The application of this approach in an atmospheric pressure diffusion flame fueled with isooctane as well as inside the combustion chamber of a diesel engine is presented. Soot volume fraction and primary particle diameters are calculated, and the results are discussed. The mean diameter estimated by fitting the LII modeled curve on the experimental one is compared with the results obtained through soot sampling and microscope analyzing. The influence of the thermal accommodation coefficient and soot refractive index function is also discussed. PACS 47.80.-v; 42.40.Pa; 42.62.Eh; 47.54.De     

Time-resolved two-color LII: size distributions of nano-particles from gas-to-particle synthesis

A two-color LII technique for in situ measurements of particle size distributions is described. The technique is based on the simultaneous detection of time-resolved LII signals at two different wavelengths with one-dimensional spatial resolution using a newly developed experimental setup. The ratio of both LII signals yields particle temperatures as a function of time and location. Measured particle temperature decays are numerically simulated based on a detailed cooling model for particle ensembles. Particle size distributions are obtained by fitting simulated particle temperature decays to measured ones using multi-dimensional non-linear regression. The two-color LII technique for particle sizing can be applied to a wide range of materials because it is independent of the optical properties of the particle material. Exemplarily, the measuring technique is applied to investigate the synthesis of nanoscaled metal oxide particle in a laser vaporization reactor.     

Influence of long pulse duration on time-resolved laser-induced incandescence

Time-resolved laser-induced incandescence (LII) signal of soot in an ethylene laminar diffusion flame was measured with varying laser pulse durations in the range 50–600 ns. This study presents original results since the majority of LII studies reported are based on 7–10-ns pulse duration. The LII signal from soot is a combination of heating and cooling processes of different time scales, and the influence of the pulse duration is therefore particularly relevant. The most striking finding is that when the pulse durations is longer than approximately 100 ns, the time-resolved LII signal reveals a rebound of the LII signal during its slow decaying part. This feature occurs preferably at high fluence and is unexpected as none of the physical and chemical processes known to control LII signal behaviour, and their models suggest such an effect. The phenomenon occurs with both top hat and near Gaussian temporal laser shapes. Inspection of the time-resolved emission spectra shows no indication of a laser-induced fluorescence effect, although gas-phase PAH generated during the laser heating of soot particles cannot be rejected. Other hypotheses are that the mechanism responsible for that behaviour is linked to a slow rate change of the soot morphological characteristics or to the generation of new particles during the long-duration laser excitation. Finally, experiments show that soot volume fraction measured by integrating the temporal LII signal is not affected by the pulse duration in any regions of the flame, implying that the LII method is applicable with long pulse duration lasers.     

Comparison of LII derived soot temperature measurements with LII model predictions for soot in a laminar diffusion flame

Laser-induced incandescence (LII) was used to derive temperatures of pulsed laser heated soot particles from their thermal emission intensities detected at two wavelengths in a laminar ethylene/air co-annular diffusion flame. The results are compared to those of a numerical nanoscale heat and mass transfer model. Both aggregate and primary particle soot size distributions were measured using transmission electron microscopy (TEM). The model predictions were numerically averaged over these experimentally derived size distributions. The excitation laser wavelength was 532 nm, and the LII signal was detected at 445 nm and 780 nm. A wide range of laser fluence from very low to moderate (0.13 to 1.56 mJ/mm²) was used in the experiments. A large part of the temporal decay curve, beginning 12–15 nsec after the peak of the laser excitation pulse, is successfully described by the model, resulting in the determination of accommodation coefficients, which varies somewhat with soot temperature and is in the range of 0.36 to 0.46. However, in the soot evaporative regime, the model greatly overpredicts the cooling rate shortly after the laser pulse. At lower fluences, where evaporation is negligible, the initial experimental cooling rates, immediately following the laser pulse, are anomalously high. Potential physical processes that could account for these effects are discussed. From the present data the soot absorption function, E(m), of 0.4 at 532 nm is obtained. A procedure for correcting the measured signals for the flame radiation is presented. It is further shown that accounting for the local gas temperature increase due to heat transfer from soot particles to the gas significantly improves the agreement in the temperature dependence of soot cooling rates between model and experiments over a large range of laser fluences.     

Modeling laser-induced incandescence of soot: a summary and comparison of LII models

We have performed a comparison of ten models that predict the temporal behavior of laser-induced incandescence (LII) of soot. In this paper we present a summary of the models and comparisons of calculated temperatures, diameters, signals, and energy-balance terms. The models were run assuming laser heating at 532 nm at fluences of 0.05 and 0.70 J/cm² with a laser temporal profile provided. Calculations were performed for a single primary particle with a diameter of 30 nm at an ambient temperature of 1800 K and a pressure of 1 bar. Preliminary calculations were performed with a fully constrained model. The comparison of unconstrained models demonstrates a wide spread in calculated LII signals. Many of the differences can be attributed to the values of a few important parameters, such as the refractive-index function E(m) and thermal and mass accommodation coefficients. Constraining these parameters brings most of the models into much better agreement with each other, particularly for the low-fluence case. Agreement among models is not as good for the high-fluence case, even when selected parameters are constrained. The reason for greater variability in model results at high fluence appears to be related to solution approaches to mass and heat loss by sublimation. PACS 65.80.+n; 78.20.Nv; 42.62.-b; 44.05.+e     

Derivation of a temperature-dependent accommodation coefficient for use in modeling laser-induced incandescence of soot

This paper presents a derivation of an expression to estimate the accommodation coefficient for gas collisions with a graphite surface, which is meant for use in models of laser-induced incandescence (LII) of soot. Energy transfer between gas molecules and solid surfaces has been studied extensively, and a considerable amount is known about the physical mechanisms important in thermal accommodation. Values of accommodation coefficients currently used in LII models are temperature independent and are based on a small subset of information available in the literature. The expression derived in this study is based on published data from state-to-state gas-surface scattering experiments. The present study compiles data on the temperature dependence of translational, rotational, and vibrational energy transfer for diatomic molecules (predominantly NO) colliding with graphite surfaces. The data were used to infer partial accommodation coefficients for translational, rotational, and vibrational degrees of freedom, which were consolidated to derive an overall accommodation coefficient that accounts for accommodation of all degrees of freedom of the scattered gas distributions. This accommodation coefficient can be used to calculate conductive cooling rates following laser heating of soot particles.     

On the dependence of the laser-induced incandescence (LII) signal on soot volume fraction for variations in particle size

“The laser-induced incandescence (LII) signal is proportional to soot volume fraction” is an often used statement in scientific papers, and it has – within experimental uncertainties – been validated in comparisons with other diagnostic techniques in several investigations. In 1984 it was shown theoretically in a paper by Melton that there is a deviation from this statement in that the presence of larger particles leads to some overestimation of soot volume fractions. In the present paper we present a detailed theoretical investigation of how the soot particle size influences the relationship between LII signal and soot volume fraction for different experimental conditions. Several parameters have been varied; detection wavelength, time and delay of detection gate, ambient gas temperature and pressure, laser fluence, level of aggregation and spatial profile. Based on these results we are able, firstly, to understand how experimental conditions should be chosen in order to minimize the errors introduced when assuming a linear dependence between the signal and volume fraction and secondly, to obtain knowledge on how to use this information to obtain more accurate soot volume fraction data if the particle size is known. PACS 42.62.-b; 44.40.+a; 61.46.Df; 78.70.-g; 65.80.+n     

Characterization of Nano‐Particles Using Laser‐Induced Incandescence

Laser‐induced incandescence (LII) is introduced as a valuable tool for the characterization of nanoparticles. This optical measurement technique is based on the heating of the particles by a short laser pulse and the subsequent detection of the thermal radiation. It has been applied successfully for the investigation of soot in different fields of application, which is described here in the form of an overview with a focus on work done at the LTT‐Erlangen during the last 10 years. In laboratory flames the soot primary particle size, volume concentration, and relative aggregate size have been determined in combination with the number density of primary particles. Furthermore, the primary particle sizes of carbon blacks have been measured in situ and online under laboratory conditions and also in production reactors. Measurements with different types of commercially available carbon black powders, which were dispersed in a measurement chamber yielded a good correlation between LII results and the specified product properties. Particle diameters determined by LII in a furnace black reactor correlate very well with the CTAB‐absorption number, which is a measure for the specific surface area. It turned out that the LII method is not affected by variations of the aggregate structure of the investigated carbon blacks. The LII signal also contains information on the primary particle size distribution, which can be reconstructed by the evaluation of the signal decay time at, at least, two different time intervals. Additionally, soot mass concentrations have been determined inside diesel engines and online measurements were performed in the exhaust gas of such engines for various engine conditions simultaneously providing information about primary particle size, soot volume, and number concentration. The LII results exhibit good correlation with traditional measurement techniques, e.g., filter smoke number measurements. In addition to the soot measurements, primarily tests with other nanoparticles like TiO₂ or metal particles are encouraging regarding the applicability of the technique for the characterization of such different types of nanoparticles.     

The interpretation of the LII signal in optically dense combusting sprays

A numerical investigation was made of the generation and behaviour of the LII signal in optically dense combusting sprays at conditions similar to those in the combustion chamber of compression ignition engines and gas turbines. The influence of particle size, particle morphology and size distribution on the behaviour of the LII signal, and the scattering and absorption of light, and the consequences that different calibration procedures have on the accuracy of the results were studied. Results show that, as the particle size or aggregation increases, light extinction is not caused only by absorption but also by scattering, which contributes more than 10% to the total extinction of light. Particle shape effects are important, irrespective of particle size. The form, soot concentration gradients and optical thickness of the flame cause an uneven laser fluence across the measuring volume that affects the generation of the LII signal. In addition, the quotient between the transmitted and incoming laser pulses across the flame borders can be as small as a percentage of unity. The interpretation of the induced signal is further challenged by the loss of signal between the measuring volume and the detection arrangement, thus causing the detection of spectrally distorted and weaker signals with an erroneous profile of the local amount of carbonaceous particles. An appropriate calibration procedure must be followed to obtain results that are quantitatively representative. External calibration was found to be inappropriate for these systems since it can lead one to underestimate the local volume fraction for almost two orders of magnitude. Implementing an in situ calibration along a line can lead to underestimate or overestimate the local mean volume fraction by a factor of two. However, the use of an in situ calibration procedure using a laser sheet that propagates through the complete measuring volume can reduce the error in estimating the mean soot volume fraction to a 30%. The latter was found to be the most adequate among the studied calibration routines.     

Numerical investigation of the effect of signal trapping on soot measurements using LII in laminar coflow diffusion flames

Laser-induced incandescence has been rapidly developed into a powerful diagnostic technique for measurements of soot in many applications. The incandescence intensity generated by laser-heated soot particles at the measurement location suffers the signal trapping effect caused by absorption and scattering by soot particles present between the measurement location and the detector. The signal trapping effect was numerically investigated in soot measurements using both a 2D LII setup and the corresponding point LII setup at detection wavelengths of 400 and 780 nm in a laminar coflow ethylene/air flame. The radiative properties of aggregated soot particles were calculated using the Rayleigh–Debye–Gans polydisperse fractal aggregate theory. The radiative transfer equation in emitting, absorbing, and scattering media was solved using the discrete-ordinates method. The radiation intensity along an arbitrary direction was obtained using the infinitely small weight technique. The contribution of scattering to signal trapping was found to be negligible in atmospheric laminar diffusion flames. When uncorrected LII intensities are used to determine soot particle temperature and the soot volume fraction, the errors are smaller in 2D LII setup where soot particles are excited by a laser sheet. The simple Beer–Lambert exponential attenuation relationship holds in LII applications to axisymmetric flames as long as the effective extinction coefficient is adequately defined.     

LII–lidar: range-resolved backward picosecond laser-induced incandescence

A novel concept for remote in situ detection of soot emissions by a combination of laser-induced incandescence (LII) and light detection and ranging (lidar) is presented. A lidar setup based on a picosecond Nd:YAG laser and time-resolved signal detection in the backward direction was used for LII measurements in sooty premixed ethylene–air flames. Measurements of LII–lidar signal versus laser fluence and flame equivalence ratio showed good qualitative agreement with data reported in literature. The LII–lidar signal showed a decay consisting of two components, with lifetimes of typically 20 and 70 ns, attributed to soot sublimation and conductive cooling, respectively. Theoretical considerations and analysis of the LII–lidar signal showed that the derivative was proportional to the maximum value, which is an established measure of soot volume fraction. Utilizing this, differentiation of LII–lidar data gave profiles representing soot volume fraction with a range resolution of ~16 cm along the laser beam propagation axis. The accuracy of the evaluated LII-profiles was confirmed by comparison with LII-data measured simultaneously employing conventional right-angle detection. Thus, LII–lidar provides range-resolved single-ended detection, resourceful when optical access is restricted, extending the LII technique and opening up new possibilities for laser-based diagnostics of soot and other carbonaceous particles.     

Laser-induced incandescence for soot particle size and volume fraction measurements using on-line extinction calibration

A novel technique for two-dimensional measurements of soot volume fraction and particle size has been developed. It is based on a combined measurement of extinction and laser-induced incandescence using Nd:YAG laser wavelengths of 532 nm and 1064 nm. A low-energy laser pulse at 532 nm was used for extinction measurements and was followed by a more intense pulse at 1064 nm, delayed by 15 ns, for LII measurements. The 532-nm beam was split into a signal beam passing the flame and a reference beam, both of which were directed to a dye cell. The resulting fluorescence signals, from which the extinction was deduced, together with the LII signal, were registered on a single CCD detector. Thus the two-dimensional LII image could be converted to a soot volume fraction map through a calibration procedure during the same laser shot. The soot particle sizes were evaluated from the ratio of the temporal LII signals at two gate time positions. The uncertainty in the particle sizing arose mainly from the low signal for small particles at long gate times and the uncertainty in the flame temperature. The technique was applied to a well-characterized premixed flat flame, the soot properties of which had been previously thoroughly investigated. Received: 21 June 2000 / Revised version: 11 September 2000 / Published online: 7 February 2001