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     

Combination of LII and extinction measurements for determination of soot volume fraction and estimation of soot maturity in non-premixed laminar flames

The measurement of soot and soot precursors is important for understanding the formation of soot particles in flames. In this paper, we use the difference between laser-induced incandescence (LII) and two-dimensional extinction measurements to assess the contribution of soot precursors to the extinction measurement. LII measurements are performed with a high spatial resolution of 100 µm to determine the soot volume fraction (f _V) in a laminar ethylene/air non-premixed flame at the standard Gülder conditions. While LII is specific to mature soot only, the extinction data represent attenuation due to mature and young soot (absorption and elastic scattering) and also absorption by soot precursors. The difference between the two measurements indicates the contribution of soot precursors and allows a determination of the maturity of soot. This is important knowledge for those using extinction techniques to measure soot concentration, as the contribution from soot precursors may lead to an overestimation of the mature soot concentration. Further, regions with high soot-precursor concentrations, which lead to soot formation, can be identified.     

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     

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.     

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     

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.     

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.     

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     

火焰烟黑三维温度场和浓度场同时重建实验研究

利用电荷耦合器件摄像机采用烟黑温度场和浓度场同时重建模型对自由火焰烟黑的三维温度场和浓度场进行了同时重建实验研究,所利用的重建模型是基于区域重建的方法.将重建的烟黑温度场和浓度场与文献结果进行了对比,而且还将重建温度场与热电偶所测量的温度场进行了对比.结果表明,重建的烟黑温度场和浓度场与文献结果趋势相一致,重建温度值与热电偶测量值符合较好.因此,同时重建模型可以较好地重建出火焰烟黑的三维温度场和浓度场. 关键词： 火焰烟黑 温度场 浓度场 三维同时重建     

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.     

Influence of soot aggregate structure on particle sizing using laser-induced incandescence: importance of bridging between primary particles

Soot aggregates formed in combustion processes are often described as clusters of carbonaceous particles in random fractal structures. For theoretical studies of the physical properties of such aggregates, they have often been modelled as spherical primary particles in point contact. However, transmission electron microscopy (TEM) images show that the primary particles are more connected than in a single point; there is a certain amount of bridging between the primary particles. Particle sizing using the diagnostic technique laser-induced incandescence (LII) is crucially dependent on the heat conduction rate from the aggregate to the ambient gas, which depends on the amount of bridging. In this work, aggregates with bridging are modelled using overlapping spheres, and it is shown how such aggregates can be built to fulfil specific fractal parameters. Aggregates with and without bridging are constructed numerically, and it is investigated how the bridging influences the heat conduction rate in the free-molecular regime. The calculated heat conduction rates are then used in an LII model to show how LII particle sizing is influenced by different amounts of bridging. For realistic amounts of bridging ( $C_{\rm{ov}}\leq0.25$ ), the primary particle diameters were overestimated by up to 9 % if bridging was not taken into account.     

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     

Determination of soot temperature, volume fraction and refractive index from flame emission spectrometry

An inversion scheme based on tomographic reconstruction of flame emission spectra has been developed for nonintrusive characterization of soot temperature and volume fraction fields within an optically thin axisymmetric flame by extracting characteristic information on soot refractive index from spectral gradients of emission spectra. Its performance is assessed by providing input data obtained from intensities simulated by a direct code based on experimental data for a flame available in the literature. Proposed method was found to be especially powerful in the near-infrared range for accurate prediction of flame properties where spectral variation of optical constants is significant.     

Experimental determination of distributions of soot particle diameter and number density by emission and scattering techniques

A diagnostics method was presented that uses emission and scattering techniques to simultaneously determine the distributions of soot particle diameter and number density in hydrocarbon flames. Two manta G-504 C cameras were utilized for the scattering measurement, with consideration of the attenuation effect in the flames according to corresponding absorption coefficients. Distributions of soot particle diameter and number density were simultaneously determined using the measured scattering coefficients and absorption coefficients under multiple wavelengths already measured with a SOC701 V hyper-spectral imaging device, according to the Mie scattering theory. A flame was produced using an axisymmetric laminar diffusion flame burner with 194 mL/min ethylene and 284 L/min air, and distributions of particle diameter and number density for the flame were presented. Consequently, the distributions of soot volume fraction were calculated using these two parameters as well, which were in good agreement with the results calculated according to the Rayleigh approximation,demonstrating that the proposed diagnostic method is capable of simultaneous determination of the distributions of soot particle diameter and number density.     

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.     

Simulation on simultaneous estimation of non-uniform temperature and soot volume fraction distributions in axisymmetric sooting flames

For visualizing non-uniform absorbing, emitting, non-scattering, axisymmetric sooting flames, because conventional two-color emission methods are no longer suitable, a three-color emission method for the simultaneous estimation of temperature and soot volume fraction distributions in these flames is studied in this paper. The spectral radiation intensities at wavelengths of red, green, and blue, which may be derived from color flame images, are simulated for the inverse analysis. Then the simultaneous estimation is carried out from the spectral radiation intensities by using a Newton-type iteration algorithm and the least-squares method. In this method, a factor is used to balance the wide variation of spectral radiation intensities due to both the wide ranges of temperature and wavelength of the flame radiation. The results indicate that the three-color method is suited for the reconstruction of flame structures with single or double peaks with small difference between the peak and valley. For a double-peaked flame structure with larger peak and valley difference, reasonable result can be obtained just when the mean square deviations of measurement data are small, for example, not more than 0.01.     

Dependence of particle volume fraction on sound velocity and attenuation of EPDM composites

The sound velocity and the attenuation coefficient of EPDM (Ethylene-propylene Diene Monomer) composites incorporated with Silicon Carbide particles (SiCp’s) of various volume fractions (0-40%) were experimentally and theoretically investigated. For the experiment a through-transmission technique was used. For the theoretical prediction, some mechanical property models such as Reuss model and Coherent Potential Approximation (CPA) model etc. were employed. The experimental results showed that the sound velocity decreased with the increase of the SiCp volume fraction up to 30% and then increased with the 40 vol% specimen. The attenuation coefficient was increased with the increasing SiCp volume fractions. The modified Reuss model with a longitudinal elastic modulus predicted most well the experimental sound velocity and elastic modulus results.