The effect of particle aggregation on the absorption and emission properties of mono- and polydisperse soot aggregates

This study concerns the effect of soot-particle aggregation on the soot temperature derived from the signal ratio in two-color laser-induced incandescence measurements. The emissivity of aggregated fractal soot particles was calculated using both the commonly used Rayleigh–Debye–Gans fractal-aggregate theory and the generalized Mie-solution method in conjunction with numerically generated fractal aggregates of specified fractal parameters typical of flame-generated soot. The effect of aggregation on soot temperature was first evaluated for monodisperse aggregates of different sizes and for a lognormally distributed aggregate ensemble at given signal ratios between the two wavelengths. Numerical calculations were also conducted to account for the effect of aggregation on both laser heating and thermal emission at the two wavelengths for determining the effective soot temperature of polydisperse soot aggregates. The results show that the effect of aggregation on laser energy absorption is important at low fluences. The effect of aggregation on soot emissivity is relatively unimportant in LII applications to typical laminar diffusion flames at atmospheric pressure, but it can become more important in flames at high pressures due to larger primary particles and wider aggregate distributions associated with enhanced soot loading.     

Influence of complex component and particle polydispersity on radiative properties of soot aggregate in atmosphere

The effects of morphological structure, water coating, dust mixing and primary particle size distribution on the radiative properties of soot fractal aggregates in atmosphere are investigated using T-matrix method. These fractal aggregates are numerically generated using a combination of the particle-cluster and cluster-cluster aggregation algorithms with fractal parameters representing soot aggregate in atmosphere. The radiative properties of compact aggregate notably deviate from that of the branched one, and the effect of morphology changes on the radiative properties in wet air cannot be neglected. However it is reasonable to use realization-averaged radiative properties to represent that of the aggregates with certain morphology. In wet air, the scattering, absorption and extinction cross-section and symmetry parameter of soot aggregates coated with water notably increase with water shell thickness. The mixing structures of dust have little effect on radiative properties of aggregates, but the volume fraction of dust has an obvious effect on extinction, scattering and absorption cross-section of aggregates when the size parameters are above the Rayleigh limit. Although the primary particle size distribution of soot aggregate has mild effect on the scattering albedo and asymmetry parameter, the deviations of the extinction, scattering, absorption cross-section among the three size distributions are significant in this study. The size distribution has a significant effect on forward scattering of phase function, while the effect can be neglected as the size parameter approaches to the Rayleigh limit.     

Instantaneous in-flame measurement of soot volume fraction, primary particle diameter, and aggregate radius of gyration via auto-compensating laser-induced incandescence and two-angle elastic light scattering

A new combination of soot diagnostics employing two-angle elastic light scattering and laser-induced incandescence is described that is capable of producing non-intrusive, instantaneous, and simultaneous, in situ measurements of soot volume fraction, primary particle size, and aggregate radius of gyration within flames. Controlled tests of the new apparatus on a well-characterized laminar flame show good agreement with existing measurements in the literature. From a detailed and comprehensive Monte Carlo uncertainty analysis of the results, it was found that the uncertainty in all three measured parameters is dominated by knowledge of soot properties and aggregation behavior. The soot volume fraction uncertainty is dominated by uncertainty in the soot refractive index light absorption function; the primary particle diameter uncertainty is dominated by uncertainty in the fractal prefactor; while the uncertainty in the aggregate radius of gyration is dominated by the uncertainty in the width of the distribution of aggregate sizes.     

Effects of soot absorption and scattering on LII intensities in laminar coflow diffusion flames

Absorption and scattering of laser-induced incandescence (LII) intensities by soot particles present between the measurement volume and the detector were numerically investigated 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 effects of absorption and scattering on LII intensities are found to be significant under the conditions of this study, especially at the shorter detection wavelength and when the soot volume fraction is higher. Such a wavelength-dependent signal-trapping effect leads to a lower soot particle temperature estimated from the ratio of uncorrected LII intensities at the two detection wavelengths. The corresponding soot volume fraction derived from the absolute LII intensity technique is overestimated. The Beer-Lambert relationship can be used to describe radiation attenuation in absorbing and scattering media with good accuracy provided the effective extinction coefficient is adequately.     

Influence of polydisperse distributions of both primary particle and aggregate size on soot temperature in low-fluence LII

An improved aggregate-based low-fluence laser-induced incandescence (LII) model has been developed. The shielding effect in heat conduction between aggregated soot particles and the surrounding gas was modeled using the concept of the equivalent heat transfer sphere. The diameter of such an equivalent sphere was determined from direct simulation Monte Carlo calculations in the free molecular regime as functions of the aggregate size and the thermal accommodation coefficient of soot. Both the primary soot particle diameter and the aggregate size distributions are assumed to be lognormal. The effective temperature of a soot particle ensemble containing different primary particle diameters and aggregate sizes in the laser probe volume was calculated based on the ratio of the total thermal radiation intensities of soot particles at 400 and 780 nm to simulate the experimentally measured soot particle temperature using two-color optical pyrometry. The effect of primary particle diameter polydispersity is in general important and should be considered. The effect of aggregate size polydispersity is relatively unimportant when the heat conduction between the primary particles and the surrounding gas takes place in the free-molecular regime; however, it starts to become important when the heat conduction process occurs in the near transition regime. The model developed in this study was also applied to the re-determination of the thermal accommodation coefficient of soot in an atmospheric pressure laminar ethylene diffusion flame. PACS 44.05.+e; 61.46.Df; 65.80.+n     

Some theoretical considerations in modeling laser-induced incandescence at low-pressures

Laser-induced incandescence (LII) of nanoparticles at low pressures has received some attention in recent years as a particle sizing technique or a technique for inferring the mean value of the absorption function of the particle material. In this paper, we are concerned with some fundamental issues in the theory of LII with particular attention paid to those encountered at very low pressures. The commonly adopted Rayleigh approximation for particle laser energy absorption and subsequent thermal emission is critically evaluated against the Mie solution in the range of size parameter relevant to LII. The Rayleigh approximation can cause significant error in particle laser energy absorption rate, especially when shorter wavelengths are used, and potentially in the particle temperature inferred from the two-color LII. We also demonstrate that claims that low-pressure LII can be used for particle sizing are flawed, due to the use of an incorrect expression for radiation heat loss rate from the particles in this regime, and unjustified neglect of particle sublimation heat loss. Using the currently best available carbon sublimation rate expression and physical parameters, the relative importance of heat conduction, thermal radiation, and sublimation heat loss from an isolated carbon particle was investigated for different ambient pressures, particle temperatures and particle diameters. To ensure particle radiation heat loss is dominant over conduction and sublimation the ambient pressure and the particle temperature should be kept respectively lower than 10^-4 atm and below about 2800 K. Under these conditions the effective temperature of a particle ensemble containing non-aggregated polydisperse primary particles to the power of -4 is proportional to the mean value of the particle absorption function, provided the particles are in the Rayleigh regime in the near infrared. The effect of aggregation on particle absorption and emission is briefly discussed. PACS 44.10.+i; 44.40.+a; 61.46Df     

Numerical investigation of the effect of soot aggregation on the radiative properties in the infrared region and radiative heat transfer

The effect of aggregation on soot radiative properties in the infrared region of the spectrum is numerically investigated using Rayleigh-Debye-Gans theory for fractal aggregates (RDG-FA). In order to use the RDG-FA theory for a wide range of aggregate sizes and wavelengths, the predicted phase functions, scattering and absorption coefficients are compared with a more accurate theory, the integral equation formulation for scattering—IEFS. The importance of scattering when compared with absorption is investigated, as well as the effect of aggregation on the phase function shape and on the scattering cross section. It is concluded that in the case of small aggregates formed with small primary particles the scattering coefficient is negligible compared with the absorption coefficient, and scattering and aggregation of primary particles can be ignored. Thus, the Rayleigh approximation can be used leading to isotropic scattering. In the case of large aggregates constituted by large primary particles, aggregation becomes important and the scattering cross section is of the same order of magnitude of the absorption cross section. Moreover, the phase function becomes highly peaked in the forward direction. Therefore, the Rayleigh and the equivalent volume Mie sphere approximations are not valid, and the RDG-FA method emerges as a good compromise between accuracy and simplicity of application. However, radiative transfer calculations between two infinite, parallel, black walls show that scattering may always be neglected in the calculation of total radiative heat source and heat fluxes to the walls. The minor influence of scattering on the accuracy of the predictions is explained by the shift between the spectral region where scattering is important and the region where the spectral radiative heat source is large.     

Relationship between soot volume fraction and LII signal in AC-LII: effect of primary soot particle diameter polydispersity

Theoretical analysis and numerical calculations were conducted to investigate the relationship between soot volume fraction and laser-induced incandescence (LII) signal within the context of the auto-compensating LII technique. The emphasis of this study lies in the effect of primary soot particle diameter polydispersity. The LII model was solved for a wide range of primary soot particle diameters from 2 to 80 nm. For a log-normally distributed soot particle ensemble encountered in a typical laminar diffusion flame at atmospheric pressure, the LII signals at 400 and 780 nm were calculated. To quantify the effects of sublimation and differential conduction cooling on the determined soot volume fraction in auto-compensating LII, two new quantities were introduced and demonstrated to be useful in LII study: an emission intensity distribution function and a scaled soot volume fraction. When the laser fluence is sufficiently low to avoid soot mass loss due to sublimation, accurate soot volume fraction can be obtained as long as the LII signals are detected within the first 200 ns after the onset of the laser pulse. When the laser fluence is in the high fluence regime to induce significant sublimation, however, the LII signals should be detected as early as possible even before the laser pulse reaches its peak when the laser fluence is sufficiently high. The analysis method is shown to be useful to provide guidance for soot volume fraction measurements using the auto-compensating LII technique.     

Measurement of soot morphology by integrated LII and elastic light scattering

A compact experimental setup that integrates laser-induced incandescence (LII) and one-angle elastic light scattering (1A-ELS) to measure the size of polydisperse soot aggregates is described. A 532 nm laser and a detection angle of 35 degrees were employed, which provided sensitivity for aggregate radius of gyrations (R _g) of R _g≤200 nm. Both lognormal and self-preserving distribution functions are compared with width parameters derived from both aggregation theory and transmission electron microscopy (TEM) measurements. Using these distributions, mean aggregate sizes derived from the scattering measurements are compared. The LII+1A-ELS technique is validated with a two-angle elastic light scattering (2A-ELS) approach with an additional detection angle at 145 deg. Unlike LII+1A-ELS, the 2A-ELS technique has the advantage of not requiring knowledge of soot optical properties. Good agreement is found between the two techniques for a given distribution. A fundamental discrepancy exists between distributions derived from TEM and those according to aggregation theory, limiting the accuracy of both 2A-ELS and LII+1A-ELS. The dependence of both techniques on laser fluence and hence soot temperature is examined and discussed.     

Investigation on thermal accommodation coefficient and soot absorption function with two-color Tire-LII technique in rich premixed flames

Although the two-color laser-induced incandescence technique (2C-LII) has proved to be a significant tool for soot diagnostics, many efforts are still required to gain a whole understanding of the chemical and physical processes involved. Time-resolved two-color LII measurements are carried out in a rich ethylene/air premixed flame at different heights above the burner and by changing the laser fluence. The prompt LII at two wavelengths and the corresponding soot incandescence temperature are obtained at different stages of the soot growth and under different laser irradiations. The decay rate of the LII signals, as a method for soot sizing, is investigated at different laser fluence. The time-resolved LII curves, obtained in the low laser fluence regime, are analyzed by a numerical simulation, available on the web. By considering the gas/particle initial temperature obtained with thermocouple measurements and by knowing soot particle diameter with previous TEM and extinction/scattering measurements, information about soot parameters, such as absorption function and thermal accommodation coefficient are obtained. The presence of the so-called young or mature soot along the flame height is strictly related to different optical and heat-exchange properties necessary to fit all the experimental data available.     

Influence of the cumulative effects of multiple laser pulses on laser-induced incandescence signals from soot

The effect of multiple laser pulses reaching soot particles before an actual laser-induced incandescence (LII) measurement is investigated in order to gain some insights on soot morphological and fine structure changes due to rapid laser heating. Soot, extracted from a premixed and a quenched diffusion flames, is flowing through a tubular cell and undergoes a variable number of pulses at different fluence. The response of soot is studied by the two-color LII technique. Transmission electron microscopy (TEM) analysis of laser-modified soot aggregates from the diffusion flame is also presented. The results indicate that even at low laser fluences a permanent soot transformation is induced causing an increase in the absorption function E(m). This is interpreted as an induced graphitization of soot particles by the laser pulse heating. At high fluences the vaporization process and a profound restructuring of soot particles affect the morphology of the aggregates. Soot from diffusion and premixed flames behaves in a similar way although this similarity occurs at different fluence levels indicating a different initial fine structure of soot particles.     

Influence of soot particle aggregation on time-resolved laser-induced incandescence signals

Laser-induced incandescence (LII) is a versatile technique for quantitative soot measurements in flames and exhausts. When used for particle sizing, the time-resolved signals are analysed as these will show a decay rate dependent on the soot particle size. Such an analysis has traditionally been based on the assumption of isolated primary particles. However, soot particles in flames and exhausts are usually aggregated, which implies loss of surface area, less heat conduction and hence errors in estimated particle sizes. In this work we present an experimental investigation aiming to quantify this effect. A soot generator, based on a propane diffusion flame, was used to produce a stable soot stream and the soot was characterised by transmission electron microscopy (TEM), a scanning mobility particle sizer (SMPS) and an aerosol particle mass analyzer coupled in series after a differential mobility analyzer (DMA-APM). Despite nearly identical primary particle size distributions for three selected operating conditions, LII measurements resulted in signal decays with significant differences in decay rate. However, the three cases were found to have quite different levels of aggregation as shown both in TEM images and mobility size distributions, and the results agree qualitatively with the expected effect of diminished heat conduction from aggregated particles resulting in longer LII signal decays. In an attempt to explain the differences quantitatively, the LII signal dependence on aggregation was modelled using a heat and mass transfer model for LII given the primary particle and aggregate size distribution data as input. Quantitative agreement was not reached and reasons for this discrepancy are discussed.     

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.     

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.     

Laser induced incandescence measurements of soot volume fraction and effective particle size in a laminar co-annular non-premixed methane/air flame at pressures between 0.5–4.0 MPa

An auto-compensating laser-induced incandescence (AC-LII) technique was applied for the first time to measure soot volume fraction (SVF) and effective primary particle diameter (dp_eff) in a high pressure methane/air non-premixed flame. The measured dp_eff profiles had annular structures and radial symmetry, and the particle size increased with increasing pressure. LII-determined SVFs were lower than those measured by a line of sight attenuation (LOSA) technique. The LOSA measured soot volume fractions were corrected for light scattering using the Rayleigh–Debye–Gans polydisperse fractal aggregate (RDG-PFA) theory, the dp_eff data, and assumptions regarding the soot aggregate size distribution. The correction dramatically improved agreement between data obtained using these two measurement techniques. Qualitatively, soot volume distributions obtained using LII had more annular shapes than those obtained using LOSA. Nonetheless, it has been demonstrated that the AC-LII technique is very well suited for application in media where attenuation of the excitation laser pulse energy can exceed 45%. This paper also underlines the importance of correcting LOSA SVF measurements for light scattering in high pressure flames. PACS 07-60.-j; 47.70.Pq; 65.80.+n; 78.67.-n     

Modeling of soot aggregate formation and size distribution in a laminar ethylene/air coflow diffusion flame with detailed PAH chemistry and an advanced sectional aerosol dynamics model

Soot aggregate formation and size distribution in a laminar ethylene/air coflow diffusion flame is modeled with a PAH-based soot model and an advanced sectional aerosol dynamics model. The mass range of solid soot phase is divided into 35 discrete sections and two variables are solved for in each section. The coagulation kernel of soot aggregates is calculated for the entire Knudsen number regime. Radiation from gaseous species and soot are calculated by a discrete-ordinate method with a statistical narrow-band correlated-k based band model. The discretized sectional soot equations are solved simultaneously to ensure convergence. Parallel computation with the domain decomposition method is used to save computational time. The flame temperature, soot volume fraction, primary particle size and number density are well reproduced. The number of primary particles per aggregate is overpredicted. This discrepancy is presumably associated with the unitary coagulation efficiency assumption in the current sectional model. Along the maximum soot volume fraction pathline, the number-based and mass-based aggregate size distribution functions are found to evolve from unimodal to bimodal and finally to unimodal again. The different shapes of these two aggregate size distribution functions indicate that the total number and mass of aggregates are dominated by aggregates of different sizes. The PAH-soot condensation efficiency γ is found to have a small effect on soot formation when γ is larger than 0.5. However, the soot level and primary particle number density are significantly overpredicted if the PAH-soot condensation process is neglected. Generally, larger γ predicts lower soot level and primary particle number density. Further study on soot aggregate coagulation efficiency should be pursued and more experimental data on soot aggregate structure and size distribution are needed for improving the current sectional soot model and for better understanding the complex soot aggregation phenomenon.     

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     

2D aggregate sizing by combining laser-induced incandescence (LII) and elastic light scattering (ELS)

The combination of laser-induced incandescence and elastic light scattering has been further developed to allow for a quantitative two-dimensional determination of characteristic properties of soot aggregates, namely radius of gyration R _g and number N _p of primary particles per aggregate. In demonstrating the principle of the method, we have in a first approach approximated the particle ensemble as monodisperse and used a structure factor with an exponential cut-off function. Nonetheless, experiments performed on a laminar premixed ethene flame demonstrate basically good agreement with observations from literature and data from electron microscopy on thermophoretically obtained samples.     

Understanding in-cylinder soot reduction in the use of high pressure fuel injection in a small-bore diesel engine

This study shows how soot particles inside the cylinder of the engine are reduced due to high pressure fuel injection used in a light-duty single-cylinder optical diesel engine fuelled with methyl decanoate, a selected surrogate fuel for the diagnostics. For various injection pressures, planar laser induced incandescence (PLII) imaging and planar laser-induced fluorescence of hydroxyl (OH-PLIF) imaging were performed to understand the temporal and spatial development of soot and high-temperature flames. In addition, a thermophoresis-based particle sampling technique was used to obtain transmission electron microscope (TEM) images of soot aggregates and primary particles for detailed morphology analysis. The OH-PLIF images suggest that an increase in the injection pressure leads to wider distribution of high-temperature flames likely due to better mixing. The enhanced high-temperature reaction can promote soot formation evidenced by both a faster increase of LII signals and larger soot aggregates on the TEM images. However, the increased OH radicals at higher injection pressure accelerates the soot oxidation as shown in a higher decreasing rate of LII signals as well as dramatic reduction of the sampled soot aggregates at later crank angles. The analysis of nanoscale carbon layer fringe structures also shows a consistent trend that, at higher injection pressure, the soot particles are more oxidized to form more graphitic carbon layer structures. Therefore, it is concluded that the in-cylinder soot reduction at higher injection pressure conditions is due to enhanced soot oxidation despite increased soot formation.