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.     

Optical properties of pigmented coatings taking into account particle interactions

A T-matrix approach is used to obtain the orientation-averaged scattering and absorption cross sections of randomly oriented particle clusters, and the average angular distribution of the radiation scattered by them. The coefficients involved in the expansion of the phase function are obtained from this T-matrix approach, and used in a multiple scattering formalism to characterize the angular distribution of the diffuse radiation propagating through a particulate coating perpendicularly illuminated with collimated visible radiation. Asymmetry between forward and backward propagating diffuse radiation intensities is taken into account by means of this multiple scattering approach, which is based on solving the radiative transfer equation for successive scattering order contributions. A four-flux model is applied to compute the reflectance in terms of wavelength of the incident radiation and particle concentration. An application of the formalism is carried out to predict the optical properties of titanium dioxide pigmented polymer coatings, in terms of the pigment volume fraction and the degree of aggregation.     

Boson peak, flickering noise, backscattering processes and radiative transfer in random media

The method of matrix Green’s functions in the classical theory of electromagnetic waves is stated. This method allows to obtain a closed equation system in the presence of the random media for the calculation both coherent, and incoherent (fluctuating) components of radiation. The density and heterogeneity of scattering media can be arbitrary. The coherent channel is calculated independently. The fluctuating radiation distribution in the medium is developed initially by an interference pattern generated by the coherent channel. The limitations of the processes speed are absent. The theory embraces such phenomena as the boson peak, flickering noise, memory effect, backscattering processes and also conventional radiative transfer equation and Fresnel’s formulae.     

Scattering and propagation of terahertz pulses in random soot aggregate systems

Scattering and propagation of terahertz pulses in random soot aggregate systems are studied by using the generalized multi-particle Mie-solution(GMM) and the pulse propagation theory. Soot aggregates are obtained by the diffusion-limited aggregation(DLA) model. For a soot aggregate in soot aggregate systems, scattering characteristics are analyzed by using the GMM. Scattering intensities versus scattering angles are given. The effects of different positions of the aggregate on the scattering intensities, scattering cross sections, extinction cross sections, and absorption cross sections are computed and compared. Based on pulse propagation in random media, the transmission of terahertz pulses in random soot aggregate systems is determined by the two-frequency mutual coherence function. Numerical simulations and analysis are given for terahertz pulses(0.7956 THz).     

Determination of the soot aggregate size distribution from elastic light scattering through Bayesian inference

Recovering the size distribution of aerosolized soot aggregates from multiangle elastic light scattering data requires the inversion of an integral equation, which is a mathematically ill-posed problem. This paper demonstrates how maximum a posteriori (MAP) inference can be used to stabilize the inversion by introducing prior information about the size distribution of the soot aggregates. Results show that the size distribution can be recovered using only simple smoothness and non-negativity priors if the aggregate number density is known, but otherwise it is necessary to specify additional information about the presumed distribution shape.     

Multiple size group analysis for transient radiative heating of particle polydispersions

The transient radiative heating of particle polydispersions initially at uniform temperature is numerically analyzed. Due to the different radiative heating characteristics between particles, the temperature evolution of particle changes with particle diameter. To take local thermal nonequilibrium between particles into consideration, the particles are discretized into several size groups. The radiative transfer equation in particle polydispersions and the transient energy equation for each particle group are solved by the discrete ordinates method and an implicit finite difference method, respectively. The effects of the standard deviation of particle diameter and the emissivity of particle surface on the thermal evolution of particle polydispersions are analyzed. The results show that, omitting thermal nonequilibrium of particles will result in significant errors in the calculation of radiative heat transfer, especially when the nonuniformity of particle diameter is large.     

Calculating the soot particle size distribution function in turbulent diffusion flames using a sectional method

Soot formation in a turbulent jet diffusion flame is modeled using an unsteady flamelet approach in post-process. In the present work, we apply a detailed kinetic soot model with a sectional method, and study the evolution of the particle size distribution. Detailed information on the evolution of the soot particle size distribution function is acquired. It is found that the particle size distribution function is bimodal throughout the flame. The transition from the small to large particle size distributions is strongly influenced by surface growth and oxidation reactions. We find that large particles are most likely to be emitted from the flame.     

基于递归T矩阵的离散随机散射体散射特性研究

本文根据电磁场矢量球波函数多极点展开原理及矢量叠加定理提出了递归T矩阵算法的矢量形式,并且基于矢量递归T矩阵算法建立了多散射球模拟离散随机散射体散射的三维电磁散射模型.通过计算不同尺寸、随机分布散射球的散射以及分析散射球间的高阶散射效应,结果表明:矢量递归T矩阵算法具有很高的计算精度,算法中包含多散射体间的高阶散射效应,因此能够精确计算多散射体总的散射效应.本文所建模型可应用于土壤湿度探测工程中评估地表下掩埋离散随机散射体散射对雷达回波信号产生的影响.     

Cross section calculations of randomly oriented bispheres in the small particle regime

The T-matrix is used to calculate the extinction cross section of bispherical particle systems in random orientation for a monospherical size parameter x=0.01. Differences between bispherical and monospherical (Mie) results are shown for a range of values of the refractive index. It is found that the size of the T-matrix that needs to be calculated can be large, thus preventing simple dipole approximations from being used. Once the T-matrix is computed, however, only a small number of terms is needed to obtain cross section values.     

Scattering and propagation of UV pulses in soot aerosols

Scattering and propagation of a UV pulse in soot aerosols are studied using generalized multi-sphere Mie theory (GMM) and a two-frequency mutual coherence function. Soot aerosols are obtained by the diffusion-limited aggregation (DLA) model. Scattering characteristics of aggregate structures in soot aerosols are analyzed by GMM theory in detail. Scattering intensities versus scattering angles are given and discussed. The effects of different-positions of the aggregate on the scattering intensities, scattering cross section, extinction cross section, absorption cross section and asymmetry factor are computed and compared. The two-frequency mutual coherence functions of UV pulses in soot aerosols are simulated, and the effects of optical distance, frequency difference are analyzed.     

Characterization of the light scattering by ensembles of randomly distributed soot aggregates

Soot particles formed in combustion processes commonly exist in the form of ensembles of randomly distributed aggregates of small, nearly spherical monomers. In this paper, these randomly distributed aggregates are numerically generated using a combination of the cluster–cluster aggregation algorithm with the Monte Carlo method. Moreover, an efficient and accurate numerical method is presented for characterizing the light scattering by these complex soot particles illuminated by plane wave and Gaussian beam. This method exploits the unique features of the hybrid finite element-boundary integral method and, more importantly, the unique features of soot aggregates. It is designed in such a manner that it first decomposes the original problem into many sub-regions, where each primary particle is regarded as a sub-region, and then it employs the edge-based finite element method to deal with each sub-region. The sub-regions communicate through the near-field Green’s function. To reduce computational burdens, an iterative domain decomposition method in combination with parallel conjugate gradient method is adopted to solve the coupling system of equations. As an illustration, we present some of our preliminary numerical results. The results are expected to provide useful insights into the optical properties of soot particles formed in combustion processes.     

Analysis of the radiative transfer equation with highly assymetric phase function

This paper considers a scalar radiative transfer problem with high scattering anisotropy. Two computational methods are presented based on decomposition of the diffuse light field into a regular and anisotropic part. The first algorithm (DOMAS) singles out the anisotropic radiance in the forward scattering peak using the Small-Angle Modification of RTE. The second algorithm (DOM2+) separates the single scattering radiance as an anisotropic part, which largely defines the fine detail of the total radiance in the backscattering directions. In both cases, the anisotropic part is represented analytically. With anisotropy subtraction, the regular part of the signal, which requires a numerical solution, is essentially smoothed as a function of angles. Further, the transport equation is obtained for the regular part that contains an additional source function from the anisotropic part of the signal. This equation is solved with the discrete ordinates method. A conducted numerical analysis of this work showed that algorithm DOMAS has a strong advantage as compared to the standard discrete ordinates method for simulation of the radiance transmission, and DOM2+ is the best of the three for the reflection computations. Both algorithms offer at least a factor of three acceleration of convergence of the azimuthal series for highly anisotropic phase functions.     

In-flame soot particle structure on the up- and down-swirl side of a wall-interacting jet in a small-bore diesel engine

This study shows how the structure of soot particles within the flame changes due to the relative direction of the swirl flow in a small-bore diesel engine in which significant flame–wall interactions cause about half of the flame travelling against the swirl flow while the other half penetrating in the same direction. The thermophoresis-based particle sampling method was used to collect soot from three different in-flame locations including the flame–wall impingement point near the jet axis and the two 60° off-axis locations on the up-swirl and down-swirl side of the wall-interacting jet. The sampled soot particle images were obtained using transmission electron microscopes and the image post-processing was conducted for statistical analysis of size distribution of soot primary particles and aggregates, fractal dimension, and sub-nanoscale parameters such as the carbon layer fringe length, tortuosity, and spacing. The results show that the jet-wall impingement region is dominated by many small immature particles with amorphous internal structure, which is very different to large, fractal-like soot aggregates sampled from 60° downstream location on the down-swirl side. This structure variation suggests that the small immature particles underwent surface growth, coagulation and aggregation as they travelled along the piston-bowl wall. During this soot growth, the particle internal structure exhibits the transformation from amorphous carbon segments to a typical core–shell structure. Compared to those on the down-swirl side, the soot particles sampled on the up-swirl side show much lower number counts and more compact aggregates composed of highly concentrated primary particles. This soot aggregate structure, together with much narrower carbon layer gap, indicates higher level of soot oxidation on the up-swirl side of the jet.     

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     

Electromagnetic scattering by a morphologically complex object: Fundamental concepts and common misconceptions

Following Keller (Proc Symp Appl Math 1962;13:227-46), we classify all theoretical treatments of electromagnetic scattering by a morphologically complex object into first-principle (or “honest” in Keller's terminology) and phenomenological (or “dishonest”) categories. This helps us identify, analyze, and dispel several profound misconceptions widespread in the discipline of electromagnetic scattering by solitary particles and discrete random media. Our goal is not to call for a complete renunciation of phenomenological approaches but rather to encourage a critical and careful evaluation of their actual origin, virtues, and limitations. In other words, we do not intend to deter creative thinking in terms of phenomenological short-cuts, but we do want to raise awareness when we stray (often for practical reasons) from the fundamentals. The main results and conclusions are illustrated by numerically-exact data based on direct numerical solutions of the macroscopic Maxwell equations.     

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.     

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     

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.