An aerosol model to predict size and structure of soot particles

An aerosol model to simulate soot formation and growth was developed using moving- and fixed-sectional methods. The new model is composed of a set of subroutines that can be easily combined with the Chemkin package. Using the model, we have simulated soot formation and growth in plug flow reactors.

Our model was compared with a previously published method of moments model for a simulation of the plasma pyrolysis of methane in a plug flow reactor. Inclusion of the transition correction factor for the condensation coefficient led to the prediction of a smaller condensation rate compared with the method of moments model. The average coagulation rate calculated by the sectional model was much higher than that by the method of moments model for a broad particle size distribution. The two models predicted significantly different soot precursor concentration and rates of aerosol processes, but substantially similar particle mass and number for the pyrolysis process.

We have also simulated soot formation and growth in a jet-stirred/plug flow reactor (JSR/PFR) system for which soot size distribution measurements are available in the literature. It is shown that the adjusted-point fixed-sectional method can provide comparable accuracy to the moving-sectional model in a simulation of soot formation and growth. It is also shown that the measured surface growth rate could be much higher than the value used in this study. Soot mass concentrations and size distributions for particles larger than 10 nm were well predicted with a surface reaction enhancement. The primary particle size was underpredicted by only about 30% compared with the measurements, without any model adjustments. As the new model can predict both the particle size distribution and structure, and is suitable for application in complex flows, its application to diverse soot formation conditions will enhance our knowledge on the evolution of soot structures.     

Evaluation and optimisation of phenomenological multi-step soot model for spray combustion under diesel engine-like operating conditions

In this work, a two-dimensional computational fluid dynamics study is reported of an n-heptane combustion event and the associated soot formation process in a constant volume combustion chamber. The key interest here is to evaluate the sensitivity of the chemical kinetics and submodels of a semi-empirical soot model in predicting the associated events. Numerical computation is performed using an open-source code and a chemistry coordinate mapping approach is used to expedite the calculation. A library consisting of various phenomenological multi-step soot models is constructed and integrated with the spray combustion solver. Prior to the soot modelling, combustion simulations are carried out. Numerical results show that the ignition delay times and lift-off lengths exhibit good agreement with the experimental measurements across a wide range of operating conditions, apart from those in the cases with ambient temperature lower than 850 K. The variation of the soot precursor production with respect to the change of ambient oxygen levels qualitatively agrees with that of the conceptual models when the skeletal n-heptane mechanism is integrated with a reduced pyrene chemistry. Subsequently, a comprehensive sensitivity analysis is carried out to appraise the existing soot formation and oxidation submodels. It is revealed that the soot formation is captured when the surface growth rate is calculated using a square root function of the soot specific surface area and when a pressure-dependent model constant is considered. An optimised soot model is then proposed based on the knowledge gained through this exercise. With the implementation of optimised model, the simulated soot onset and transport phenomena before reaching quasi-steady state agree reasonably well with the experimental observation. Also, variation of spatial soot distribution and soot mass produced at oxygen molar fractions ranging from 10.0 to 21.0% for both low and high density conditions are reproduced.     

Transient soot dynamics in turbulent nonpremixed ethylene-air counterflow flames

The dynamics of soot formation in turbulent ethylene-air nonpremixed counterflow flames is studied using direct numerical simulation (DNS) with a semi-empirical soot model and the discrete ordinate method (DOM) as a radiation solver. Transient characteristics of soot behavior are studies by a model problem of flame interaction with turbulence inflow at various intensities. The interaction between soot and turbulence reveals that the soot volume fraction depends on the combined effects of the local conditions of flow, temperature, and fuel concentration, while the soot number density depends predominantly on the high temperature regions. Depending on the relative strength between mixing and reaction, the effects of turbulence on the soot formation lead to three distinct paths in deviating the data points away from the laminar flame conditions. It is found that turbulence has twofold effects of increasing the overall soot yield by generating additional flame volume and of reducing soot by dissipating soot pockets out of high-temperature regions. The relative importance between the two effects depends on the relative length scales of turbulence and flame, suggesting that a nonmonotonic response of soot yield to turbulence level may be expected in turbulent combustion.     

Numerical study of the effects of gravity on soot formation in laminar coflow methane/air diffusion flames under different air stream velocities

Numerical simulations of laminar coflow methane/air diffusion flames at atmospheric pressure and different gravity levels were conducted to gain a better understanding of the effects of gravity on soot formation by using relatively detailed gas-phase chemistry and complex thermal and transport properties coupled with a semi-empirical two-equation soot model. Thermal radiation was calculated using the discrete-ordinates method coupled with a non-grey model for the radiative properties of CO, CO₂, H₂O, and soot. Calculations were conducted for three coflow air velocities of 77.6, 30, and 5 cm/s to investigate how the coflowing air velocity affects the flame structure and soot formation at different levels of gravity. The coflow air velocity has a rather significant effect on the streamwise velocity and the fluid parcel residence time, especially at reduced gravity levels. The flame height and the visible flame height in general increase with decreasing the gravity level. The peak flame temperature decreases with decreasing either the coflow air stream velocity or the gravity level. The peak soot volume fraction of the flame at microgravity can either be greater or less than that of its normal gravity counterpart, depending on the coflow air velocity. At sufficiently high coflow air velocity, the peak soot volume fraction increases with decreasing the gravity level. When the coflow air velocity is low enough, soot formation is greatly suppressed at microgravity and extinguishment occurs in the upper portion of the flame with soot emission from the tip of the flame owing to incomplete oxidation. The numerical results provide further insights into the intimate coupling between flame size, residence time, thermal radiation, and soot formation at reduced gravity level. The importance of thermal radiation heat transfer and coflow air velocity to the flame structure and soot formation at microgravity is demonstrated for the first time.     

Two-dimensional soot distributions in buoyant turbulent fires

Spatially resolved two-dimensional soot volume fractions were measured using laser-induced incandescence in 7.1 cm methane and ethylene turbulent buoyant flames to study the distributions of soot in vertical and horizontal planes, and to provide data for soot model validation. Factors affecting the LII signals were considered including the laser energy profile and the laser attenuation effects. The absolute soot volume fractions were obtained by comparison to existing extinction measurements. The instantaneous soot images were collected to cover the entire flame height. Statistical quantities of soot volume fractions including mean, root mean square, probability density function, and spatial correlation coefficient were calculated at five downstream locations. The results show that instantaneous distributions of soot volume fractions exhibit significant differences compared to the ensemble averages, strong fluctuation around the mean, relatively homogeneous probability density function, and highly anisotropic spatial correlation.     

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.     

随机取向烟尘团簇粒子的光学截面的数值计算

采用蒙特卡罗方法根据团簇—团簇凝聚（CCA）模型对由球形原始微粒凝聚而成的烟尘团簇粒子进行了模拟,利用离散偶极子近似（DDA）方法数值计算了不同原始微粒粒径和数目组成的随机取向的烟尘团簇粒子的总消光截面、吸收截面及散射截面等光学特性参数,研究了原始微粒粒径及数目对随机取向烟尘团簇粒子光学特性的影响。结果表明：当入射波长一定时,随机取向烟尘団簇粒子的光学特性主要取决于原始微粒的粒径和数目;烟尘团簇粒子对不同波段激光的吸收和散射存在差别,这种差别随原始微粒粒径及数目变化而变化。这一工作为研究电磁波在烟尘中的传输特性提供重要参考数据。     

Effect of soot shape on soot radiation

It is increasingly recognized that soot particles play an important role in the radiative heat transfer from flames and smoke. After their formation, these minute particles usually conglomerate into different forms, with the limiting shapes being the spheres and long chains which can be modeled as infinite cylinders. The present work analyzes the effect of soot shape on soot radiation. The spectral extinction coefficient of spheres, being lower than that of the cylindrical particles, falls off rapidly in the near i.r. The shape effect on soot radiation is found to be more pronounced at low temperatures than at high temperatures. In flame radiation calculations the radiative contribution of the various conglomerated soot shapes can be properly accounted for by assuming spherical and polydisperse soot particles. Based on the extinction characteristics of the particles, an experimental method for determining the amount of spherical and cylindrical particles in a soot cloud is suggested.     

随机分布烟尘簇团粒子缪勒矩阵的数值计算

利用蒙特卡罗方法根据团簇-团簇凝聚（CCA）模型对由球形原始粒子凝聚而成的烟尘簇团粒子进行了模拟,用离散偶极子近似（DDA）方法对随机分布的烟尘簇团粒子的缪勒矩阵元素进行了数值计算,给出了不同入射波长情况下随机分布烟尘簇团粒子的缪勒矩阵元素与组成簇团粒子的基本粒子的粒径和数目的数值关系,为进一步研究随机分布簇团粒子的形成机理、形态特性、散射特性提供了一种理论方法. 关键词： 烟尘簇团粒子 缪勒矩阵 离散偶极子近似方法     

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.     

Modification to Nagle/Strickland-Constable model with consideration of soot nanostructure effects

The oxidation rates of diesel soot from the combustion chamber of a running diesel engine were calculated based on the particle size distributions at different crank angles. The primary particle diameter and nanostructure of soot were obtained by means of high-resolution transmission electron microscopy (HRTEM). The soot characteristics were also investigated by oxidative thermogravimetry and Raman scattering spectrometry.

The results showed the soot nanostructures were dependent on engine operation conditions and combustion phases. The oxidation rates were found to differ by nearly fourfold from that calculated by the Nagle/Strickland-Constable (NSC) model for the soots studied here. The varied oxidation rates were interpreted in terms of differences in nanostructure between the soots. The experimental results were used to modify the NSC model and the fringe length of in-cylinder diesel soot was chosen to describe the influence of graphitisation on the oxidation of soot. The modified NSC model lessened the deviation between measurements and predictions.     

Prediction of soot formation characteristics in a pulverized-coal combustion field by large eddy simulations with the TDP model

In this study, the soot formation characteristics in a pulverized-coal combustion field formed by a 4 kW Central Research Institute of Electric Power Industry (CRIEPI) jet burner were predicted by large eddy simulation (LES) employing a tabulated-devolatilization-process model (TDP model) [N. Hashimoto et al., Combust. Flame 159 (2012) 353–366]. This model enables to take into account the effect of coal particle heating rate on coal pyrolysis. The coal-derived soot formation model proposed by Brown and Fletcher [A. L. Brown and T. H. Fletcher, Energy Fuels 12 (1998) 745–757] was employed in the LES. A comparison between the data predicted by LES and the soot volume fraction distribution data measured by laser induced incandescence confirmed that the soot formation characteristics in the coal combustion field of the CRIEPI burner can be accurately predicted by LES. A detailed analysis of the data predicted by LES showed that the soot particle distribution in this burner is narrow because the net soot formation rate is negative on both sides of the base of the soot volume fraction. At these positions, soot particles diffused from the peak position of soot volume fraction are oxidized due to a relatively high oxygen concentration. Finally, the effect of soot radiation on the predicted gas temperature distribution was examined by comparing the simulation results obtained with and without soot radiation. This comparison showed that the maximum gas temperature predicted by the simulation performed with soot radiation was over 100 K lower than that predicted by the simulation performed without soot radiation. From result strongly suggests the importance of considering a soot formation model for performing numerical simulations of a pulverized-coal combustion filed.     

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.     

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.     

Transported JPDF modelling and measurements of soot at elevated pressures

Accurate measurements and modelling of soot formation in turbulent flames at elevated pressures form a crucial step towards design methods that can support the development of practical combustion devices. A mass and number density preserving sectional model is here combined with a transported joint-scalar probability density function (JDPF) method that enables a fully coupled scalar space of soot, gas-phase species and enthalpy. The approach is extended to the KAUST turbulent non-premixed ethylene-nitrogen flames at pressures from 1 to 5 bar via an updated global bimolecular (second order) nucleation step from acetylene to pyrene. The latter accounts for pressure-induced density effects with the rate fitted using comparisons with full detailed chemistry up to 20 bar pressure and with experimental data from a WSR/PFR configuration and laminar premixed flames. Soot surface growth is treated via a PAH analogy and soot oxidation is considered via O, OH and O₂ using a Hertz-Knudsen approach. The impact of differential diffusion between soot and gas-phase particles is included by a gradual decline of diffusivity among soot sections. Comparisons with normalised experimental OH-PLIF and PAH-PLIF signals suggest good predictions of the evolution of the flame structure. Good agreement was also found for predicted soot volume statistics at all pressures. The importance of differential diffusion between soot and gas-phase species intensifies with pressure with the impact on PSDs more evident for larger particles which tend to be transported towards the fuel rich centreline leading to reduced soot oxidation.     

Investigation of soot sensitivity to strain rate in ethylene counterflow soot formation oxidation flames

Soot sensitivity to strain rate is mainly responsible for soot formation intermittence in practical combustion devices. This work provides a fundamental study on soot formation in Soot Formation Oxidation (SFO) counterflow flames at varying strain rates. While the problem has been extensively studied in Soot Formation (SF) configurations, where the dominant process is nucleation, investigations remain scarce in the corresponding SFO cases. In the latter, the high temperatures and strong oxidative environments make the surface reactions prevail over nucleation. The work provides a new dataset for ethylene SFO flames in a wide range of strain rates and sheds light on the main processes concurring in determining soot strain rate sensitivity in such conditions. In particular, the peak of soot volume fraction (SVF) is primarily controlled by surface growth and oxidation. The latter becomes progressively more dominant on the side of the SVF distribution toward the oxidizer nozzle, where the presence of oxidizing agents is significant. The soot mechanism adopted predicts a SVF distribution and sensitivity to strain rate in agreement with experimental data. The latter is found similar to corresponding SF cases, although soot loads in the two configurations differ by almost an order magnitude, and the SVF sensitivity is known to be more accentuated for lower soot loads. A deeper investigation revealed that the nucleation process through dimerizations primarily controls the SVF sensitivity, providing the onset of soot necessary for further growth. Then, the latter tends to reduce SVF sensitivity depending on its impact. PAH sensitivities mostly agree with theoretical observation even though further validations on the kinetic mechanism are needed to improve its predictions in lean conditions. The simplistic yet effective model based on the hybrid method of moments and the employment of a reduced kinetic mechanism makes the approach amenable for turbulent computational fluid dynamic (CFD) simulations.     

Optical properties of soot nanoparticles

In this paper, the dipole-dipole approximation is used to characterize the dynamical electromagnetic properties of two types of carbonaceous nanoparticles modelling the basic constituents of aircraft soot particles. The corresponding polarizability per unit volume is then compared with the one calculated for equivalent defect-free structures and with the one resulting from a continuum model. It is found that the polarizability per unit volume strongly depends on the details of the structure of the nanoparticle, and that this dependence could be used to discriminate between different carbonaceous particles using optical scattering experiments in the visible or near-UV domain.     

3-D simulation of soot formation in a direct-injection diesel engine based on a comprehensive chemical mechanism and method of moments

Here, we propose both a comprehensive chemical mechanism and a reduced mechanism for a three-dimensional combustion simulation, describing the formation of polycyclic aromatic hydrocarbons (PAHs), in a direct-injection diesel engine. A soot model based on the reduced mechanism and a method of moments is also presented. The turbulent diffusion flame and PAH formation in the diesel engine were modelled using the reduced mechanism based on the detailed mechanism using a fixed wall temperature as a boundary condition. The spatial distribution of PAH concentrations and the characteristic parameters for soot formation in the engine cylinder were obtained by coupling a detailed chemical kinetic model with the three-dimensional computational fluid dynamic (CFD) model. Comparison of the simulated results with limited experimental data shows that the chemical mechanisms and soot model are realistic and correctly describe the basic physics of diesel combustion but require further development to improve their accuracy.     

Understanding soot particle size evolution in laminar ethylene/air diffusion flames using novel soot coalescence models

Two coalescence models based on different merging mechanisms are introduced. The effects of the soot coalescence process on soot particle diameter predictions are studied using a detailed sectional aerosol dynamic model. The models are applied to a laminar ethylene/air diffusion flame, and comparisons are made with experimental data to validate the models. The implementation of coalescence models significantly improves the agreement of prediction of particle diameters with the experimental data. Sensitivity of the soot prediction to the coalescence parameters is analysed. Finally, an update to the coalescence model based on experimental observations of soot particles in the flame oxidation regions has been introduced to improve its predicting capabilities.     

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.