Joint-scalar transported PDF modeling of soot formation and oxidation

The ability of the transported probability density function (PDF) approach to reproduce the evolution of mean, rms fluctuations, and conditional PDFs of soot is explored in the context of two turbulent ethylene diffusion flames at Reynolds numbers of 11,800 and 15,600. The chemical similarity between surface reactions and PAH formation is explored on the basis of a second ring PAH analogy, and soot oxidation is accounted for through reactions with O, OH, and O₂. The method of moments is used to account for coagulation and agglomeration in the coalescent and fractal aggregate limits. The soot model is coupled with a transported PDF approach closed at the joint-scalar level to directly account for interactions between turbulence, and the solid and gas phase chemistry. The latter is represented by a systematically reduced reaction mechanism for ethylene featuring 144 reactions, 15 solved and 14 steady-state species. Radiation from soot and gas phase species is accounted for through the RADCAL method and the inclusion of enthalpy into the joint-scalar PDF. Predicted temperature and soot statistics compare well with experimental data indicating the practical potential of the approach and the importance of turbulence-chemistry interactions in the context of soot formation and burnout.     

Modelling of aromatics and soot formation from large fuel molecules

There is a need for prediction models of soot particles and polycyclic aromatic hydrocarbons (PAHs) formation in parametric conditions prevailing in automotive engines: large fuel molecules and high pressure. A detailed kinetic mechanism able to predict the formation of benzene and PAHs up to four rings from C₂ fuels, recently complemented by consumption reactions of decane, was extended in this work to heptane and iso-octane oxidation. Species concentrations measured in rich, premixed flat flames and in a jet stirred reactor (JSR) were used to check the ability of the mechanism to accurately predict the formation of C₂ and C₃ intermediates and benzene at pressures ranging from 0.1 to 2.0 MPa. Pathways analyses show that propargyl recombination is the only significant route to benzene in rich heptane and iso-octane flames. When included as the first step of a soot particle formation model, the gas-phase kinetic mechanism predicts very accurately the final soot volume fraction measured in a rich decane flame at 0.1 MPa and in rich ethylene flames at 1.0 and 2.0 MPa.     

Effects of benzene,cyclo-hexane and n-hexane addition to methane on soot yields in high-pressure laminar diffusion flames

Effects of doping high pressure methane diffusion flames with benzene, cyclo-hexane and n-hexane were investigated to assess the sooting propensity of three hydrocarbons with six carbons at elevated pressures. Amount of liquid hydrocarbons added to methane constituted 7.5% of the total carbon content of the fuel stream. The pressure range investigated extended up to 10 bar and the experiments were carried out in a high pressure combustion chamber capable of establishing stable laminar diffusion flames with various fuels at elevated pressures and was used in similar experiments previously. Temperatures and soot volume fractions were measured using the spectral soot emission technique capturing spectrally-resolved line-of-sight intensities which were subsequently inverted using an Abel type algorithm to obtain radial distributions assuming that the flames are axisymmetric. The total mass carbon flow of the fuel stream was kept constant at 0.524 mg/s in neat methane, benzene-doped methane, cyclo-hexane-doped methane, and n-hexane-doped methane flames to have tractable measurements at all pressures. Measured maximum soot volume fractions and evaluated maximum soot yields showed that benzene-doped methane flame had the higher values than cyclo-hexane doped methane flames which in turn had higher values than n-hexane doped methane flames at all pressures. Sooting propensity dependence of the three hydrocarbons on pressure can be ranked as, in descending order, n-hexane, cyclo-hexane, and benzene; however, the difference between pressure dependencies of n-hexane and cyclo-hexane was within the measurement error margins. Ratio of soot yields of benzene to n-hexane doped flames changed from about 2 at 2 bar to 1.2 at 10 bar; the ratio of benzene to cyclo-hexane doped flames showed similar trends.     

Analysis of the impact of agglomeration and surface chemistry models on soot formation and oxidation

Models for soot aggregation that account for the influence of soot surface chemistry on mass growth and oxidation are still at the formative stage. Past studies have considered techniques ranging from the method of moments to stochastic approaches and significantly different sensitivities to chemical processes such as mass growth and oxidation have been reported. The method of moments is computationally efficient and can yield encouraging results for laminar flames as well as for turbulent flames when combined with transported probability density function (PDF) methods. However, an assessment of the sensitivity to constituent model assumptions is not trivial and information regarding the soot size distribution is incomplete. In the current work, the ability of a sectional method to reproduce population dynamics data has been evaluated along with the sensitivity of predictions to closure elements associated with soot nucleation, agglomeration, surface growth and oxidation. A detailed chemistry model with 285 chemical species and 1520 reactions was used for the gas phase. It is shown that the approach to the fuel lean sooting limit can be reproduced with reasonable accuracy and that the inclusion of fractal aggregates and surface chemistry effects improve agreement with experimental data.     

Soot formation and temperature field structure in co-flow laminar methane-air diffusion flames at pressures from 10 to 60 atm

The effects of pressure on soot formation and the structure of the temperature field were studied in co-flow methane-air laminar diffusion flames over a wide pressure range, from 10 to 60 atm in a high-pressure combustion chamber. The selected fuel mass flow rate provided diffusion flames in which the soot was completely oxidized within the visible flame envelope and the flame was stable at all pressures considered. The spatially resolved soot volume fraction and soot temperature were measured by spectral soot emission as a function of pressure. The visible (luminous) flame height remained almost unchanged from 10 to 100 atm. Peak soot concentrations showed a strong dependence on pressure at relatively lower pressures; but this dependence got weaker as the pressure is increased. The maximum conversion of the fuel’s carbon to soot, 12.6%, was observed at 60 atm at approximately the mid-height of the flame. Radial temperature gradients within the flame increased with pressure and decreased with flame height above the burner rim. Higher radial temperature gradients near the burner exit at higher pressures mean that the thermal diffusion from the hot regions of the flame towards the flame centerline is enhanced. This leads to higher fuel pyrolysis rates causing accelerated soot nucleation and growth as the pressure increases.     

An evaluation of gas-phase micro-mixing models with differential mixing timescales in transported PDF simulations of sooting flame DNS

The use of transported probability density function (TPDF) models to predict soot has the strong advantage that the effects of turbulent fluctuations on soot source terms can be rigorously accounted for. However, soot processes are closely coupled to gas-phase composition. Among the open issues for gas-phase micro-mixing is the species-dependence of mixing timescales. The objective is to carry out an evaluation on the effect of incorporating differential mixing timescales among gas-phase species in a TPDF simulation for soot prediction. A DNS having the configuration of a temporally evolving, non-premixed ethylene flame with a four-step, three-moment soot model is considered as the target for evaluation. The DNS dataset is applied to provide key inputs for TPDF simulations to limit the sources of error to micro-mixing. TPDF simulations with the interaction by exchange with the mean (IEM) and modified Curl (MC) models, which impose the same mixing timescale to all species, underpredict soot mass fraction and overpredict extinction levels regardless of the prescribed mixing frequency. By incorporating differential mixing timescales among gas-phase species, IEM-DD and MC-DD models yield notable improvement in predictions of the overall extinction and soot levels, highlighting the benefit of accounting for differential mixing timescales. A TPDF simulation with the Euclidean minimum spanning tree (EMST) model yields even better predictions, illustrating that the localness in composition space remains a critical issue. The indicated species mixing frequencies by the EMST model are shown to follow the DNS results qualitatively, illustrating that the micro-mixing process based on the Euclidean distance in composition space reproduces to a certain extent the differential mixing timescales due to reaction. Finally, it is shown that incorporating differential mixing timescales of soot moments is expected to have limited value as the mixing timescales of soot moments are sufficiently large to safely neglect soot mixing.     

Modelling nongrey gas-phase and soot radiation in luminous turbulent nonpremixed jet flames

Much progress has been made in radiative heat transfer modelling with respect to the treatment of nongrey radiation from both gas-phase species and soot particles, while radiation modelling in turbulent flame simulations is still in its infancy. Aiming at reducing this gap, this paper introduces state-of-the-art models of gas-phase and soot radiation to turbulent flame simulations. The full-spectrum k-distribution method (M.F. Modest, 2003, Journal of Quantitative Spectroscopy & Radiative Transfer, 76, 69–83) is implemented into a three-dimensional unstructured computational fluid dynamics (CFD) code for nongrey radiation modelling. The mixture full-spectrum k-distributions including nongrey absorbing soot particles are constructed from a narrow-band k-distribution database created for individual gas-phase species, and an efficient scheme is employed for their construction in CFD simulations. A detailed reaction mechanism including NO _x and soot kinetics is used to predict flame structure, and a detailed soot model using a method of moments is employed to determine soot particle size distributions. A spherical harmonic P₁ approximation is invoked to solve the radiative transfer equation. An oxygen-enriched, turbulent, nonpremixed jet flame is simulated, which features large concentrations of gas-phase radiating species and soot particles. Nongrey soot modelling is shown to be of greater importance than nongrey gas modelling in sooty flame simulations, with grey soot models producing large errors. The nongrey treatment of soot strongly influences flame temperatures in the upstream and the flame-tip region and is essential for accurate predictions of NO. The nongrey treatment of gases, however, weakly influences upstream flame temperatures and, therefore, has only a small effect on NO predictions. The effect of nongrey soot radiation on flame temperature is also substantial in downstream regions where the soot concentration is small. Limitations of the P₁ approximation are discussed for the jet flame configuration; the P₁ approximation yields large errors in the spatial distribution of the computed radiative heat flux for highly anisotropic radiation fields such as those in flames with localized, near-opaque soot regions.     

Modeling nongray gas-phase and soot radiation in luminous turbulent nonpremixed jet flames

Much progress has been made in radiative heat transfer modeling with respect to treatment of nongray radiation from both gas-phase species and soot particles, while radiation modeling in turbulent flame simulations is still in its infancy. Aiming at reducing this gap, this paper introduces state-of-the-art models of gas-phase and soot radiation to turbulent flame simulations. The full-spectrum k-distribution method (Modest, M.F., 2003, Journal of Quantitative Spectroscopy & Radiative Transfer, 76, 69–83) is implemented into a three-dimensional unstructured CFD code for nongray radiation modeling. The mixture full-spectrum k-distributions including nongray absorbing soot particles are constructed from a narrow-band k-distribution database created for individual gas-phase species, and an efficient scheme is employed for their construction in CFD simulations. A detailed reaction mechanism including NO _x and soot kinetics is used to predict flame structure, and a detailed soot model using a method of moments is employed to determine soot particle size distributions. A spherical-harmonic P₁ approximation is invoked to solve the radiative transfer equation. An oxygen-enriched, turbulent, nonpremixed jet flame is simulated, which features large concentrations of gas-phase radiating species and soot particles. Nongray soot modeling is shown to be of greater importance than nongray gas modeling in sooty flame simulations, with gray soot models producing large errors. The nongray treatment of soot strongly influences flame temperatures in the upstream and the flame-tip region and is essential for accurate predictions of NO. The nongray treatment of gases, however, weakly influences upstream flame temperatures and, therefore, has only a small effect on NO predictions. The effect of nongray soot radiation on flame temperature is also substantial in downstream regions where the soot concentration is small. Limitations of the P₁ approximation are discussed for the jet flame configuration; the P₁ approximation yields large errors in the spatial distribution of the computed radiative heat flux for highly anisotropic radiation fields such as those in flames with localized, near-opaque soot regions.     

Implementation of an advanced fixed sectional aerosol dynamics model with soot aggregate formation in a laminar methane/air coflow diffusion flame

An advanced fixed sectional aerosol dynamics model describing the evolution of soot particles under simultaneous nucleation, coagulation, surface growth and oxidation processes is successfully implemented to model soot formation in a two-dimensional laminar axisymmetric coflow methane/air diffusion flame. This fixed sectional model takes into account soot aggregate formation and is able to provide soot aggregate and primary particle size distributions. Soot nucleation, surface growth and oxidation steps are based on the model of Fairweather et al. Soot equations are solved simultaneously to ensure convergence. The numerically calculated flame temperature, species concentrations and soot volume fraction are in good agreement with the experimental data in the literature. The structures of soot aggregates are determined by the nucleation, coagulation, surface growth and oxidation processes. The result of the soot aggregate size distribution function shows that the aggregate number density is dominated by small aggregates while the aggregate mass density is generally dominated by aggregates of intermediate size. Parallel computation with the domain decomposition method is employed to speed up the calculation. Three different domain decomposition schemes are discussed and compared. Using 12 processors, a speed-up of almost 10 is achieved which makes it feasible to model soot formation in laminar coflow diffusion flames with detailed chemistry and detailed aerosol dynamics.     

A computational framework for predicting laminar reactive flows with soot formation

Numerical modeling is an attractive option for cost-effective development of new high-efficiency, soot-free combustion devices. However, the inherent complexities of hydrocarbon combustion require that combustion models rely heavily on engineering approximations to remain computationally tractable. More efficient numerical algorithms for reacting flows are needed so that more realistic physics models can be used to provide quantitative soot predictions. A new, highly-scalable combustion modeling tool has been developed specifically for use on large multiprocessor computer architectures. The tool is capable of capturing complex processes such as detailed chemistry, molecular transport, radiation, and soot formation/destruction in laminar diffusion flames. The proposed algorithm represents the current state of the art in combustion modeling, making use of a second-order accurate finite-volume scheme and a parallel adaptive mesh refinement (AMR) algorithm on body-fitted, multiblock meshes. Radiation is modeled using the discrete ordinates method (DOM) to solve the radiative transfer equation and the statistical narrow-band correlated-k (SNBCK) method to quantify gas band absorption. At present, a semi-empirical model is used to predict the nucleation, growth, and oxidation of soot particles. The framework is applied to two laminar coflow diffusion flames which were previously studied numerically and experimentally. Both a weakly-sooting methane–air flame and a heavily-sooting ethylene–air flame are considered for validation purposes. Numerical predictions for these flames are verified with published experimental results and the parallel performance of the algorithm analyzed. The effects of grid resolution and gas-phase reaction mechanism on the overall flame solutions were also assessed. Reasonable agreement with experimental measurements was obtained for both flames for predictions of flame height, temperature and soot volume fraction. Overall, the algorithm displayed excellent strong scaling performance by achieving a parallel efficiency of 70% on 384 processors. The proposed algorithm proved to be a robust, highly-scalable solution method for sooting laminar flames.     

Modeling soot formation in flames and reactors: Recent progress and current challenges

The study of soot has long been motivated by its adverse impacts on health and the environment. However, this combustion knowledge is also relevant to the production of carbon black and hydrogen via methane pyrolysis which are important commodities. Over the last decade, steady progress has been made in the development of detailed continuum models of soot formation in flames and reactors. Developing more comprehensive models has often been motivated by the need for predicting soot formation over a wider range of conditions (e.g., temperature, pressure, fuels). Measurements with novel experimental techniques have given us new insights into the chemistry, particle dynamics and optical properties of soot particles and even molecules and radicals forming them. Also, multi-scale modeling has enabled us to translate the detailed mechanisms of soot processes based on first principles into computationally efficient but accurate continuum models of soot formation in flames and reactors. However, important questions remain including (1) what is the mechanism of soot inception and surface growth, (2) which gas-phase species are involved in soot inception and surface growth (3) how surface growth and oxidation are affected by soot surface properties. Proposed models need to be evaluated against experimental data over a wide range of conditions to determine their predictive strength. These questions are critical for the accurate prediction of soot formation in flames and its emissions from engines. However, this knowledge can also be used to develop predictive process design and optimization tools for carbon black and other nanocarbon formation in reactors.     

Effect of hydrogen enrichment of laminar ethylene diffusion flames on thermal structure and soot yields at pressures up to 10 bar

A series of high-pressure experiments were conducted to assess the influence of hydrogen enrichment of laminar diffusion flames of nitrogen-diluted ethylene on the thermal flame structure and soot yields at pressures above atmospheric. In parallel experiments, added hydrogen is replaced by helium, either in equal mole fractions or in mass fractions, to evaluate the thermal, dilution, and direct chemical interaction effects of hydrogen in soot formation. Experiments covered pressures from atmospheric to 10 bar. In the first set of experiments, conducted at 3, 6, and 10 bar pressure, base fuel was an ethylene-nitrogen mixture with 33.3% ethylene and 66.7% nitrogen (by mole as well as by mass). This base fuel was doped with either hydrogen or helium such that hydrogen and helium mass fractions and mole fractions in the fuel stream are matched in two cases. In the second set of experiments, which were conducted at 1.2 bar pressure with ethylene as the base fuel, hydrogen or helium is added such that additive mole fraction in the fuel stream was 44%. Temperature measurements in the first set of experiments indicate that, when hydrogen is added to nitrogen-diluted ethylene, the changes in the temperature field of the co-flow diffusion flames are negligible, except at lower in the flame where hydrogen added flames display slightly higher temperatures. When helium is added instead of hydrogen, however, the temperatures were measurably lower than those of the base fuel. Results show that, once the dilution effects are accounted for, the hydrogen addition to ethylene does not suppress soot formation by direct chemical interaction at elevated pressures. These findings, which are not in agreement with the previous experimental results obtained at atmospheric pressure, are discussed in terms of the higher molecular diffusivity of hydrogen and shorter residence times of high-pressure flames.     

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.     

Investigation of mass and energy coupling between soot particles and gas species in modelling ethylene counterflow diffusion flames

A numerical model is developed aiming at investigating soot formation in ethylene counterflow diffusion flames. The mass and energy coupling between soot solid particles and gas-phase species is investigated in detail. A semi-empirical two-equation model is chosen for predicting soot mass fraction and number density. The model describes particle nucleation, surface growth, and oxidation. A detailed kinetic mechanism is considered for the gas phase and the effect of considering radiation heat losses is also evaluated. Simulations were done for a range of conditions that produce low-to-significant amounts of soot using three strategies: first by changing the strain rate imposed on the flow field, second, by changing the oxygen content in the oxidant stream, and third, by changing the pressure. Additionally, the effect of the transport model chosen was analysed. The results showed that, for the flames studied and within the limits of the present work, the soot and gas radiation terms are of primary importance for numerical simulations. Additionally, it was shown that the soot mass and thermodynamic properties coupling terms are, in general, a second-order effect, with an importance that increases as soot amount increases. As a general recommendation, the radiation terms have always to be considered, whereas full coupling has to be employed only when the soot mass fraction, Y_S, is equal to or larger than 0.008. If a higher precision is required, with errors less than 1%, full coupling should be taken into account for Y_S ≥ 0.002. For lower soot amounts, the coupling through soot mass and thermodynamic properties may be neglected as a first approximation, but an error on the total mass conservation will be present. Additionally, discrepancies from considering different transport models (detailed or simplified) are larger than those found from not fully coupling the phases.     

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     

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.     

The effect of preferential diffusion on soot formation in a laminar ethylene/air diffusion flame

The influence of preferential diffusion on soot formation in a laminar ethylene/air diffusion flame was investigated by numerical simulation using three different transport property calculation methods. One simulation included preferential diffusion and the other two neglected preferential diffusion. The results show that the neglect of preferential diffusion or the use of unity Lewis number for all species results in a significant underprediction of soot volume fraction. The peak soot volume fraction is reduced from 8.0 to 2.0 ppm for the studied flame when preferential diffusion is neglected in the simulation. Detailed examination of numerical results reveals that the underprediction of soot volume fraction in the simulation neglecting preferential diffusion is due to the slower diffusion of some species from main reaction zone to PAH and soot formation layer. The slower diffusion of these species causes lower PAH formation rate and thus results in lower soot inception rate and smaller particle surface area. The smaller surface area further leads to smaller surface growth rate. In addition, the neglect of preferential diffusion also leads to higher OH concentration in the flame, which causes the higher specific soot oxidation rate. The lower inception rate, smaller surface growth rate and higher specific oxidation rate results in the lower soot volume fraction when preferential diffusion is neglected. The finding of the paper implies the importance of preferential diffusion for the modeling of not only laminar but maybe also some turbulent flames.     

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.     

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.