Light absorption and scattering by aggregates: Application to black carbon and snow grains

A geometric-optics surface-wave approach has been developed for the computation of light absorption and scattering by nonspherical particles for application to aggregates and snow grains with external and internal mixing structures. Aggregates with closed- (internal mixing) and open-cell configurations are constructed by means of stochastic procedures using homogeneous and core-shell spheres with smooth or rough surfaces as building blocks. The complex aggregate shape and composition can be accounted for by using the hit-and-miss Monte Carlo geometric photon tracing method. We develop an integral expression for diffraction by randomly oriented aggregates based on Babinet's principle and a photon-number weighted geometric cross section. With reference to surface-wave contributions originally developed for spheres, we introduce a nonspherical correction factor using a non-dimensional volume parameter such that it is 1 for spheres and 0 for elongated particles. The extinction efficiency, single-scattering albedo, and asymmetry factor results for randomly oriented columns and plates compare reasonably well with those determined from the finite-difference time domain (FDTD) and the discrete dipole approximation (DDA) computer codes for size parameters up to about 20. The present theoretical approach covers all size ranges and is particularly attractive from the perspective of efficient light absorption and scattering calculations for complex particle shape and inhomogeneous composition.We show that under the condition of equal volume and mass, the closed-cell configuration has larger absorption than its open-cell counterpart for both ballistic and diffusion-limited aggregates. Because of stronger absorption in the closed-cell case, most of the scattered energy is confined to forward directions, leading to a larger asymmetry factor than the open-cell case. Additionally, light absorption for randomly oriented snowflakes is similar to that of their spherical counterparts under the condition of equal geometrical cross section area for both external and internal mixing states; however, nonspherical snowflakes scatter less light in forward directions than spheres, resulting in a substantial reduction of the asymmetry factor. We further demonstrate that small soot particles on the order of 1 μm internally mixed with snow grains could effectively reduce snow albedo by as much as 5-10%. Indeed, the depositions of black carbon would substantially reduce mountain-snow albedo, which would lead to surface warming and snowmelt, critical to regional climatic surface temperature amplification and feedback.     

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.     

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.     

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.     

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.     

Scattering and absorption of light by ice particles: Solution by a new physical-geometric optics hybrid method

A new physical-geometric optics hybrid (PGOH) method is developed to compute the scattering and absorption properties of ice particles. This method is suitable for studying the optical properties of ice particles with arbitrary orientations, complex refractive indices (i.e., particles with significant absorption), and size parameters (proportional to the ratio of particle size to incident wavelength) larger than ∼20, and includes consideration of the edge effects necessary for accurate determination of the extinction and absorption efficiencies. Light beams with polygon-shaped cross sections propagate within a particle and are traced by using a beam-splitting technique. The electric field associated with a beam is calculated using a beam-tracing process in which the amplitude and phase variations over the wavefront of the localized wave associated with the beam are considered analytically. The geometric-optics near field for each ray is obtained, and the single-scattering properties of particles are calculated from electromagnetic integral equations. The present method does not assume additional physical simplifications and approximations, except for geometric optics principles, and may be regarded as a “benchmark” within the framework of the geometric optics approach. The computational time is on the order of seconds for a single-orientation simulation and is essentially independent of the size parameter. The single-scattering properties of oriented hexagonal ice particles (ice plates and hexagons) are presented. The numerical results are compared with those computed from the discrete-dipole-approximation (DDA) method.     

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.     

Inertial deposition of nanoparticle chain aggregates: Theory and comparison with impactor data for ultrafine atmospheric aerosols

Nanoparticle chain aggregates (NCAs) are often sized and collected using instruments that rely on inertial transport mechanisms. The instruments size segregate aggregates according to the diameter of a sphere with the same aerodynamic behavior in a mechanical force field. A new method of interpreting the aerodynamic diameter of NCAs is described. The method can be used to calculate aggregate surface area or volume. This is useful since inertial instruments are normally calibrated for spheres, and the calibrations cannot be directly used to calculate aggregate properties. A linear relationship between aggregate aerodynamic diameter and primary particle diameter based on published Monte-Carlo drag calculations is derived. The relationship shows that the aggregate aerodynamic diameter is independent of the number of primary particles that compose an aggregate, hence the aggregate mass. The analysis applies to aggregates with low fractal dimension and uniform primary particle diameter. This is often a reasonable approximation for the morphology of nanoparticles generated in high temperature gases. An analogy is the use of the sphere as an approximation for compact particles. The analysis is applied to the collection of NCAs by a low-pressure impactor. Our results indicate the low-pressure impactor collects aggregates with a known surface area per unit volume on each stage. Combustion processes often produce particles with aggregate structure. For diesel exhaust aggregates, the surface area per unit volume calculated by our method was about twice that of spheres with diameter equal to the aerodynamic diameter. Measurements of aggregates collected near a major freeway and at Los Angeles International Airport (LAX) were made for two aerodynamic cutoff diameter diameters (d _a,50), 50 and 75 nm. (Aerodynamic cutoff diameter refers to the diameter of particles collected with 50% efficiency on a low-pressure impactor stage.) Near-freeway aggregates were probably primarily a mixture of diesel and internal combustion engine emissions. Aggregates collected at LAX were most likely present as a result of aircraft emissions. In both measurements, the aggregate aerodynamic diameters calculated from the primary particle diameter were fairly close to the stage cutoff diameter. The number of primary particles per aggregate varied one order of magnitude for particles depositing on the same stage. The average aggregate surface area per unit volume was 2.41 × 10⁶ cm⁻¹ and 2.59 × 10⁶ cm⁻¹ (50 nm d _a,50) and 1.81 × 10⁶ cm⁻¹ and 1.68 × 10⁶ cm⁻¹ (75 nm d _a,50) for near-freeway and LAX measurements, respectively. These preliminary measurements are consistent with values calculated from theory.     

Optical properties of ice particles in young contrails

The single-scattering properties of four types of ice crystals (pure ice crystals, ice crystals with an internal mixture of ice and black carbon, ice crystals coated with black carbon, and soot coated with ice) in young contrails are investigated at wavelengths 0.65 and 2.13 μm using Mie codes for coated spheres. The four types of ice crystals show differences in their single-scattering properties because of the embedded black carbon whose volume ratio is assumed to be 5%. The bulk-scattering properties of young contrails consisting of the four types of ice crystals are further investigated by averaging their single-scattering properties over a typical ice particle size distribution found in young contrails. The effect of the radiative properties of the four types of ice particles on the Stokes parameters I, Q, U, and V is also investigated for different viewing zenith angles and relative azimuth angles with a solar zenith angle of 30° using a vector radiative transfer model based on the adding-doubling technique. The Stokes parameters at a wavelength of 0.65 μm show pronounced differences for the four types of ice crystals, whereas the counterparts at a wavelength of 2.13 μm show similar variations with the viewing zenith angle and relative azimuth angle. However, the values of the results for the two wavelengths are noticeably different.     

Microwave scattering properties of sand particles: Application to the simulation of microwave radiances over sandstorms

The single-scattering properties of sand/dust particles assumed to be ellipsoids are computed from the discrete dipole approximation (DDA) method at microwave frequencies 6.9-89.0 GHz in comparison with the corresponding Lorenz-Mie solutions. It is found that the single-scattering properties of sand particles are strongly sensitive to the shapes of the particles. The bulk scattering properties of sandstorms composed of spherical or nonspherical particles are investigated by averaging the single-scattering properties of these particles over log-normal particle size distributions. Furthermore, a vector radiative transfer model is used to simulate microwave radiances. The microwave brightness temperatures in the vertical polarization model are essentially not sensitive to sand particle habit, whereas microwave brightness temperature polarization differences are influenced by particle habit. It is shown that microwave brightness temperatures and brightness temperature polarization differences may be useful for estimating the effective particle sizes and mass loading of sandstorms.     

随机分布烟尘团簇粒子辐射特性研究

基于分形理论,采用蒙特卡罗方法对随机分布的烟尘团簇粒子结构进行了仿真模拟,利用离散偶极子近似(discrete dipole approximation, DDA)方法研究了随机分布的烟尘团簇粒子的辐射特性,分析讨论了分形维数、原始微粒粒径和数量以及复折射率对随机分布烟尘团簇粒子辐射特性的影响.研究表明,在给定分形维数的情况下,烟尘团簇粒子的辐射特性取决于原始微粒粒径、数量及复折射率;原始微粒较小的团簇粒子,当分形维数较小时,吸收截面变化不明显,但当分形维数大于2时,吸收截面骤然增大,然而,对于具有比较大的原始微粒粒径、数量及复折射率的烟尘团簇粒子,吸收截面随着分形维数的增大而单调递减;随着分形维数的增大,团簇粒子的散射截面、消光截面及单次散射反照率均单调递增;从整体上来讲,团簇粒子的辐射特性与等效球形粒子的辐射特性存在着比较大的差别,并且这种差别随着分形维数的增大而减小.该工作对研究气溶胶粒子的辐射及气候效应具有重要的科学价值. 关键词： 烟尘团簇粒子 辐射特性 离散偶极子近似方法     

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     

Application of the pseudo-spectral time domain method to compute particle single-scattering properties for size parameters up to 200

The applicability, efficiency, and accuracy of the pseudo-spectral time domain (PSTD) method are investigated with specific emphasis on the computation of the single-scattering properties of homogeneous dielectric particles. By truncating the high spectral terms, the Gibbs phenomenon is eliminated, and, consequently, the applicability of the PSTD is enhanced. The PSTD simulations for ice spheres, with moderate refractive indices and size parameters up to 200, are compared with the exact Lorenz–Mie solutions at three wavelengths. In addition, the comparison is extended to a case with an extremely large refractive index (7.150+i2.914) and size parameters up to 40. Furthermore, the single-scattering properties of randomly oriented spheroids and circular cylinders for size parameters up to 150 and 75, respectively, are calculated with the PSTD in comparison with those computed from the T-matrix method. The aspect ratio of the spheroid and the diameter-to-length ratio of the circular cylinder are 0.5 and 1, respectively. The relative errors, given by the PSTD for these randomly oriented non-spherical particles, are smaller than 2% for the extinction efficiencies and asymmetry factors and less than 30% for the phase function. The PSTD is also employed to compute the phase matrices of randomly oriented hexagonal columns with size parameters of 50 and 100. The simulations show the PSTD to be a robust method for simulating the single-scattering properties of particles with small-to-medium size parameters and for a wide range of refractive indices.     

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.     

Effect of aggregation on the absorption cross-section of fractal soot aggregates and its impact on LII modelling

This study concerns the effect of particle aggregation on laser heating rate of soot aggregates in laser-induced incandescence. Three aggregate absorption models were investigated: the Rayleigh-Debye-Gans approximation, the electrostatics approximation, and the numerically exact generalized multi-sphere Mie-solution method. Fractal aggregates containing 5-893 primary particles of 30 nm in diameter were generated numerically using a combined particle-cluster and cluster-cluster aggregation algorithm with specific fractal parameters typical of soot. The primary particle size parameters considered are 0.089, 0.177, and 0.354. The Rayleigh-Debye-Gans approximation neglects the effect of particle aggregation on absorption; so it underestimates the aggregate absorption cross-section area by approximately 10%, depending on the aggregate size and primary particle size parameter. The electrostatics approximation is somewhat better than the Rayleigh-Debye-Gans approximation, but cannot account for the effect of primary particle size parameter. The aggregate absorption submodel affects the calculated soot temperature in laser-induced incandescence mainly in the low laser fluence regime. At high laser fluences, the effect diminishes due to the enhanced importance of soot sublimation cooling and neglect of aggregation effect in the sublimation in the present numerical model of laser-induced incandescence.     

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.     

A joint volume-surface model of soot aggregation with the method of moments

In this work, a bivariate model of soot aggregation is formulated within the framework of the Method of Moments with Interpolative Closure (MOMIC). In the bivariate model, soot particles are represented by two independent variables: their volume and surface area. This joint formulation also allows for the blending of aggregation and coalescence with the two as limits. The new formulation is compared to the old formulation with the univariate model as well as both the Direct Quadrature Method of Moments (DQMOM) and Direct Simulation Monte Carlo (DSMC) for a laminar premixed ethylene flame. With the bivariate model, MOMIC is shown to predict volume fraction and number density very accurately and gives some insight into the properties of the aggregates.     

Modelling soot formation in a premixed flame using an aromatic-site soot model and an improved oxidation rate

An updated rate of O₂ oxidation of one to four ring polyaromatic hydrocarbons in premixed flames is presented based on density function theory simulations of oxygen attack at different radical sites on various PAHs. The rate is in agreement with other rates found in the literature; however, it is several orders of magnitude lower than the currently accepted oxidation rate of multi-ring aromatic species, including soot. Simulations are presented of a premixed flame using this improved rate and a new advanced soot particle model, which is developed in this paper. This model includes unprecedented detail of the particles in the ensemble, including the aromatic content, C/H composition and primary-particle aggregate structure. The O₂ oxidation rate calculated in this paper is shown to give a better prediction of particle number density and soot volume fraction for a premixed flame. The predicted particle size distributions are shown also to describe better the experimental data. Predicted C/H ratio and PAH size distributions are shown for the flame. Computed TEM-style images are compared to experimental TEM images, which show that the aggregate structure of the particles is well predicted.     

Examination of wavelength dependent soot optical properties of diesel and diesel/rapeseed methyl ester mixture by extinction spectra analysis and LII measurements

The refractive index of soot is an essential parameter for its optical diagnostics. It is necessary for quantitative interpretation of LII (Laser Induced Incandescence) signals, light scattering or extinction measurements as well as for emissivity calculations. The most cited values have been determined by intrusive methods or without taking into account the soot size distribution and its specific morphology. In the present study, soot generated by the combustion of diesel and diesel/rapeseed methyl ester (RME) mixture (70% diesel and 30% RME) are extensively characterized by taking into account the morphology, the aggregate size distribution, the mass fraction and the spectral dispersion of light. The refractive index m for wavelengths λ between 300 and 1000 nm is determined for diesel and diester fuels by both in-situ and ex-situ methods. The ex-situ method is based on the interpretation of extinction spectra by taking into account soot sizes and fractal morphology with the RDG-FA (Rayleigh–Debye–Gans for Fractal Aggregate) theory. The in-situ approach is based on the comparison of the LII signals obtained with two different excitation wavelengths. The absorption function E(m) and the scattering function F(m) are examined. This study reveals similar optical properties of soot particles generated by both studied fuels even at ambient and flame temperatures. The function E(m) is shown to reach a maximum for λ=250 nm and to tend toward a plateau-like behavior close to E(m)=0.3 for higher wavelength (600<λ (nm)<1000). The function F(m) is found to be quite constant for 400<λ (nm)<1000 and equal to 0.31.     

Simulations of sooting turbulent jet flames using a hybrid flamelet/stochastic Eulerian field method

The stochastic Eulerian field method is applied to simulate 12 turbulent C₁?C₃ hydrocarbon jet diffusion flames covering a wide range of Reynolds numbers and fuel sooting propensities. The joint scalar probability density function (PDF) is a function of the mixture fraction, enthalpy defect, scalar dissipation rate and representative soot properties. Soot production is modelled by a semi-empirical acetylene/benzene-based soot model. Spectral gas and soot radiation is modelled using a wide-band correlated-k model. Emission turbulent radiation interactions (TRIs) are taken into account by means of the PDF method, whereas absorption TRIs are modelled using the optically thin fluctuation approximation. Model predictions are found to be in reasonable agreement with experimental data in terms of flame structure, soot quantities and radiative loss. Mean soot volume fractions are predicted within a factor of two of the experiments whereas radiant fractions and peaks of wall radiative fluxes are within 20%. The study also aims to assess approximate radiative models, namely the optically thin approximation (OTA) and grey medium approximation. These approximations affect significantly the radiative loss and should be avoided if accurate predictions of the radiative flux are desired. At atmospheric pressure, the relative errors that they produced on the peaks of temperature and soot volume fraction are within both experimental and model uncertainties. However, these discrepancies are found to increase with pressure, suggesting that spectral models describing properly the self-absorption should be considered at over-atmospheric pressure.