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.     

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 and measurements of size distributions in premixed ethylene and benzene flames

This study demonstrates the major differences in the evolution of the particle size distributions (PSDs), both measured and modeled, of soot in premixed benzene and ethylene flat flames. In the experiments, soot concentration and PSDs were measured by using a scanning mobility particle sizer (SMPS, over the size range of 3-80 nm). The model employed calculations of gas phase species coupled with a discrete sectional approach for the gas-to-particle conversion. The model includes reaction pathways leading to the formation of nano-sized particles and their coagulation to larger soot particles. The particle size distribution, both experimental and modeled, evolved from a single particle mode (the nucleation mode) to a bimodal size distribution. An important distinction between the results for the ethylene and benzene flames is the behavior of the nucleation mode which persists at all heights above the burner (HAB) for ethylene whereas it was greatly suppressed at greater HAB for the benzene flames. The explanation for the decreased nucleation mode at higher elevations in the benzene flame is that the aromatics are consumed in the oxidation zone of the flame. Fair predictions of particle-phase concentrations and particle sizes in the two flames were obtained with no adjustments to the kinetic scheme. In agreement with experimental data, the model predicts a higher formation of particulate in the benzene flame as compared with the ethylene flame.     

Nano organic carbon and soot in turbulent non-premixed ethylene flames

Spectral optical techniques are combined to characterise the distribution of large-molecule soot precursors, nanoparticles of organic carbon, and soot in two turbulent non-premixed ethylene flames with differing residence times. Laser-induced fluorescence, laser-induced incandescence and light scattering are used to define distributions across the particle size distribution. From the scattering and laser-induced emission measurements it appears that two classes of particles are formed. The first ones are preferentially formed in the fuel-rich region of the flame closer to the nozzle, have sizes of the order of few nanometers but are not fully solid particles, because the constituent molecules still maintain their individual identity exhibiting strong broadband fluorescence in the UV. The second class of particles constituted by solid particles, with sizes of the order of tens of nanometers are able to absorb a sufficient number of photons to be heated to incandescent temperatures. These larger particles are formed at larger residence times in the flame since they are the result of slow growth processes such as coagulation or carbonization. The flames are also modeled in order to produce mixture fraction maps. A new discovery is that nanoparticles of organic carbon concentration, unlike soot, does correlate well with mixture fraction, independent of position in the flame. This is likely to be a significant benefit to future modelling of soot inception processes in turbulent non-premixed flames.     

Surface deposition and coagulation efficiency of combustion generated nanoparticles in the size range from 1 to 10 nm

The size distribution of the nanoparticles formed in premixed ethylene–air flames and collected thermophoretically on mica cleaved substrates is obtained by atomic force microscopy (AFM). The distribution function extends from 1 to about 5 nm in non-sooting flames and in the soot pre-inception region of the richer flames, while it becomes bimodal and larger particles are formed in the soot inception region of the slightly sooting flames. The distribution is compared with the size distribution of nano-sized organic carbon (NOC) and soot particles, obtained by “in situ” multi-wavelength extinction and light scattering methods. The deposition efficiency is estimated from the differences between these two size distribution functions as a function of the equivalent diameter of the nanoparticles. Furthermore, the coagulation coefficient of particles in flame is obtained from the temporal evolution of the number concentration of the nanoparticles inside the flames. NOC particles, which are rapidly produced in locally rich combustion regions, have peculiar properties since their sticking coefficient both for coagulation and adhesion result to be orders of magnitudes lower than that expected by larger aerosols, like soot particles. The experimental results are interpreted by modelling the van der Waals interactions of the nanoparticles in terms of Lennard-Jones potentials and in the framework of the gas kinetic theory. The estimated adhesion and coagulation efficiencies are in good agreement with those calculated from AFM and optical data. The very low efficiency values observed for the smaller particles could be ascribed to the high energy of these particles due to their Brownian motion, which causes thermal rebound effects prevailing over adhesion mechanisms due to van der Waals forces.     

Effect of fuel/air ratio and aromaticity on the molecular weight distribution of soot in premixed n-heptane flames

Soot growth from inception to mass-loading is studied in a wide range of molecular weights (MW) from 10⁵ to 10¹⁰u by means of size exclusion chromatography (SEC) coupled with on-line UV-visible spectroscopy. The evolution of MW distributions of soot is also numerically predicted by using a detailed kinetic model coupled with a discrete-sectional approach for the modeling of the gas-to-particle process. Two premixed flames burning n-heptane in slightly sooting and heavily sooting conditions are studied. The effect of aromatic addition to the fuel is studied by adding n-propylbenzene (10% by volume) to n-heptane in the heavily sooting condition. A progressive reduction of the MW distribution from multimodal to unimodal is observed along the flames testifying the occurrence of particle growth and agglomeration. These processes occur earlier in the aromatic-doped n-heptane flame due to the overriding role of benzene on soot formation which results in bigger young soot particles. Modeled MW distributions are in reasonable agreement with experimental data although the model predicts a slower coagulation process particularly in the slightly sooting n-heptane flame. Given the good agreement between model predictions and experiments, the model is used to explore the role of fuel chemistry on MW distributions. Two flames of n-heptane and n-heptane/n-propylbenzene in heavily sooting conditions with the same temperature profile and inert dilution are modeled. The formation of larger soot particles is still evident in the n-heptane/n-propylbenzene flame with respect to the n-heptane flame in the same operating conditions of temperature and dilution. In addition the model predicts a larger formation of molecular particles in the flame containing n-propylbenzene and shows that soot inception occurs in correspondence of their maximum formation thus indicating the importance of molecular growth in soot inception.     

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.     

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.     

Particle formation in opposed-flow diffusion flames of ethylene: An experimental and numerical study

An experimental and numerical study on particles inception and growth is performed in opposed-flow diffusion flames of ethylene and air characterized by different sooting tendencies. Spectrally resolved UV-visible laser induced fluorescence, laser induced incandescence and laser light scattering measurements are used to characterize different classes of combustion-generated compounds. A detailed kinetic model accounting for both gas-phase and particle formation is used. Comparison between experimental results and numerical predictions gives a qualitative view of the mechanism of particle formation in opposed-flow flames.Particle inception is the result of both chemical growth and coagulation of aromatic compounds. In the region close to the flame front where the temperature is relatively high and radicals are abundant, the particle inception is due to a chemical growth mechanism by which aromatic molecules add aromatic radicals leading to the formation of biphenyl-like structures. The growth process continues as high-molecular mass aromatics are moved away from the flame zone towards the stagnation plane by the addition of acetylene and other aromatics forming particles of increasing sizes. Graphitization of these particles and thermal annealing lead to the formation of soot particles. At relatively lower temperatures, found across the stagnation plane, particles growth still occurs and it is mainly due to a process of physical coagulation of PAHs.The experimental and numerical results obtained in this work demonstrate and explain the sensibility of inception and growth of particles to radical concentration and temperature in opposed-flow flame configurations.     

Characterization of nanoparticles of organic carbon (NOC) produced in rich premixed flames by differential mobility analysis

Differential mobility analysis (DMA) is used to measure on-line the size distributions of inception particles in atmospheric pressure premixed ethylene air flames ranging from C/O = 0.61 to 0.69, just at the onset of soot formation. DMA is also used, in combination with electrospray, to measure the size distributions of suspended flame products captured in water samples. The DMA systems used for this work employ detectors sensitive to the full range of molecular clusters/nanoparticles in gas-to-particle conversion processes (as small as about 1 nm) and they have much larger sheath gas flow rates than is typically used to reduce losses and peak broadening by diffusion. The measured size distributions show that the first particles observed in flames have a size of 2 nm, consistent with previous in situ measurements by light scattering and extinction (LSE) and the off-line measurements of material captured in water samples from the same flames. For richer flames, the quantity of the 2 nm particles measured increases, and the width of its size distribution shifts asymmetrically toward larger sizes. A numerical coagulation model assuming size-dependent coagulation efficiency predicts well the experimentally measured size distributions in the flames examined. Similarly, the slightly larger size distributions measured by atomic force microscopy of inception particles deposited on surfaces can also be attributed to the size-dependent coagulation/adhesion efficiency. The results imply that the smaller nanoparticles formed in combustion processes have a longer lifetime than those larger than 6-7 nm and may play an important role in the formation of fine organic carbon particulate in the atmosphere.     

Experimental and numerical study of the evolution of soot primary particles in a diffusion flame

The evolution of primary soot particles is studied experimentally and numerically along the centreline of a co-flow laminar diffusion flame. Soot samples from a flame fueled with C₂H₄ are taken thermophoretically at different heights above the burner (HAB), their size and nano-structure are analysed through TEM. The experimental results suggest that after inception, the nascent soot particles coagulate and coalesce to form larger primary particles (?～?5 to 15 nm). As these primary particles travel along the centreline, they grow mainly due coagulation and condensation and a layer of amorphous hydrocarbons (revealed by HRTEM) forms on their surface. This amorphous layer appears to promote the aggregation of primary particles to form fractal structures. Fast carbonisation of the amorphous layer leads to a graphitic-like shell around the particles. Further graphitization compacts the primary particles, resulting in a decrease of their size. Towards the flame tip the primary particles decrease in size due to rapid oxidation. A detailed population balance model is used to investigate the mechanisms that are important for prediction of primary particle size distributions. Suggestions are made regarding future model development efforts. Simulation results indicate that the primary particle size distributions are very sensitive to the parameterization of the coalescence and particle rounding processes. In contrast, the average primary particle size is less sensitive to these parameters. This demonstrates that achieving good predictions for the average primary particle size does not necessarily mean that the distribution has been accurately predicted.     

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.     

The role of DME addition on the evolution of soot and soot precursors in laminar ethylene jet flames

Dimethyl ether (DME) has received considerable attention as a fuel additive to reduce the emission of particulate matter (PM) due to its low-temperature chemistry, molecularly bound oxygen atom and the absence of CC bonds. However, the effect of DME addition on the evolution of soot and particularly soot precursors is not entirely understood. This study aims to shed light on this issue by blending different proportions of DME with diffusion, E60, and partially premixed, PP12, base cases of laminar ethylene flames using the Yale benchmark burner. Laser-induced fluorescence (LIF) intensity and decay time are used to characterize the structure and evolution of soot precursors, while laser-induced incandescence (LII) is utilized to determine the soot volume fraction (SVF) and the effective primary particle diameter (D_p). For the diffusion flames, the addition of 10% DME increases the concentrations of both soot and soot precursors. With the further addition of DME to 20%, the SVF decreases to levels similar to those of E60 and then decreases further with 30% DME addition. All diffusion flames with DME addition exhibit higher concentrations of soot precursors than those of the reference E60 case. For PP12, the addition of 10% DME shows similar concentrations of soot precursors and a slight reduction in the SVF which continues to decrease with further increases in DME additions to the PP12 flame. The addition of DME seems to have little effect on the soot particle diameters for all the studied flames. Overall, the PP flames result in smaller mean particle diameters than the diffusion flame counterparts.     

Investigation of the transition from lightly sooting towards heavily sooting co-flow ethylene diffusion flames

Laminar, sooting, ethylene-fuelled, co-flow diffusion flames at atmospheric pressure have been studied experimentally and theoretically as a function of fuel dilution by inert nitrogen. The flames have been investigated experimentally using a combination of laser diagnostics and thermocouple-gas sampling probe measurements. Numerical simulations have been based on a fully coupled solution of the flow conservation equations, gas-phase species conservation equations with complex chemistry and the dynamical equations for soot spheroid growth. Predicted flame heights, temperatures and the important soot growth species, acetylene, are in good agreement with experiment. Benzene simulations are less satisfactory and are significantly under-predicted at low dilution levels of ethylene. As ethylene dilution is decreased and soot levels increase, the experimental maximum in soot moves from the flame centreline toward the wings of the flame. Simulations of the soot field show similar trends with decreasing dilution of the fuel and predicted peak soot levels are in reasonable agreement with the data. Computations are also presented for modifications to the model that include: (i) use of a more comprehensive chemical kinetics model; (ii) a revised inception model; (iii) a maximum size limit to the primary particle size; and (iv) estimates of radiative optical thickness corrections to computed flame temperatures.     

Modeling and simulation of titanium dioxide nanoparticle synthesis with finite-rate sintering in planar jets

Numerical simulations of titanium dioxide nanoparticle synthesis in planar, non-premixed diffusion flames are performed. Titania is produced by the oxidation of titanium tetrachloride using a methane–air flame. The flow field is obtained using the two-dimensional Navier–Stokes equations. The methane–air flame and oxidation of titanium tetrachloride are modeled via one-step reactions. Evolution of the particle field is obtained via a nodal method which accounts for nucleation, condensation, coagulation, and coalescence with finite-rate sintering. The modeling of finite-rate sintering is accomplished via the use of uniform primary-particle size distribution. Simulations are performed at two different jet-to-co-flow velocity ratios as well as with finite-rate and instantaneous sintering models. In doing so we elucidate the effect of fluid mixing and finite-rate sintering on the particle field. Results show that highly agglomerated particles are found on the periphery of the eddies, where the collisions leading to nanoparticle coagulation occur faster than nanoparticle coalescence.     

Laser-induced incandescence technique to identify soot nucleation and very small particles in low-pressure methane flames

This paper presents the study we carried out on the formation of soot particles in low-pressure premixed CH₄/O₂/N₂ flames by using Laser-Induced Incandescence (LII). Flames were stabilised at 26.6 kPa (200 torr). Four different equivalence ratios were tested (Φ = 1.95, 205, 2.15 and 2.32), Φ = 1.95 corresponding to the equivalence ratio for which LII signals begin to be measurable along the flame. The evolution of the LII signals with laser fluence (fluence curve), time (temporal decay) and emission wavelength is reported at different heights above the burner. We specifically took advantage of the low-pressure conditions to probe with a good spatial resolution the soot inception zone of the flames. Significant different behaviours of the fluence curves are observed according to the probed region of the flames and Φ. In addition, while the surface growth process is accompanied by an increase in the LII decay-times (indicator of the primary particle diameter) at higher Φ, decay-times become increasingly short at lower Φ reaching a constant value along the flame at Φ = 1.95. These behaviours are consistent with the detection of the smallest incandescent particles in the investigated flames, these particles having experienced very weak surface growth. Flame modelling including soot formation has been implemented in flames Φ = 2.05 and 2.32. Experimental quantitative soot volume fraction profiles were satisfactorily reproduced by adjusting the fraction of reactive soot surface available for reactions. The qualitative variation of the computed soot particle diameter and the relative weight of surface growth versus nucleation were consistent with the experimental observations.     

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.     

Similarities and dissimilarities in n-hexane and benzene sooting premixed flames

The flame structure of atmospheric-pressure sooting premixed flames of aliphatic and aromatic hydrocarbons with the same carbon atom number (hexane and benzene) were studied at similar temperatures and C/O ratios by sampling and chemical and spectroscopic analysis. The differences in the oxidation mechanism of hexane and benzene in fuel-rich conditions were found to produce a different chemical environment in the yield of light hydrocarbons and their relative compositions where soot inception occurs. The predominance of acetylene and simple aromatic reactants in the oxidation region of the benzene flame favoured the early appearance and steep rise of soot particles. Large formations of saturated and unsaturated hydrocarbons were observed in the main oxidation region of the hexane flame whereas a delayed formation of aromatics (mainly PAH) was observed at soot inception only after complete oxygen consumption. There are differences in soot inception mechanisms reflected by the soot structure from UV-vis spectral shapes and mass specific absorption coefficients. In the benzene flame, they appeared to be more ordered and aromatic with a narrower size of aromatic systems and/or more curved aromatic structures. By contrast, less ordering with a more complex aliphatic/aromatic structure and a larger variety of aromatic systems were found to characterize soot formed in the hexane flame.     

Numerical simulations of soot aggregation in premixed laminar flames

In this paper we make use of a detailed particle model and stochastic numerical methods to simulate the particle size distributions of soot particles formed in laminar premixed flames. The model is able to capture the evolution of mass and surface area along with the full structural detail of the particles. The model is validated against previous models for consistency and then used to simulate flames with bimodal and unimodal soot particle distributions. The change in morphology between the particles from these two types of flames provides further evidence of the interplay among nucleation, coagulation, and surface rates. The results confirm the previously proposed role of the strength of the particle nucleation source in defining the instant of transition from coalescent to fractal growth of soot particles.     

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.