Primary Particle Number Density Research Articles

H2/NH3 Addition Effects on Flame Characteristics and Soot Formation in Ethylene Inverse Diffusion Flame

Zero-carbon alternative fuels such as hydrogen and ammonia are gaining popularity. Blending these fuels with hydrocarbons is an intermediate approach to mitigate soot and carbon dioxide production. Recent studies have concentrated their attention to the effects of ammonia and hydrogen on the soot production of hydrocarbon fuels. It is still necessary to completely comprehend how this influence is dependent on the type of fuel and flame configuration. In this work, the effect of hydrogen and ammonia addition on soot production in ethylene laminar inverse diffusion flames (IDF) was numerically examined for the first time. The thermal, chemical, and combined effects of hydrogen and ammonia were assessed by fictitious species. The experimental results from the literature were used to validate the temperature and soot volume fraction profiles. Results indicated that the flame temperature and the production of radicals are promoted chemically by hydrogen addition but inhibited under the thermal effect of ammonia. The principal source of the reduction in OH-represented flame height, soot volume fraction, average diameter, and primary particle number density in the IDF is the thermal effect of additives, and hydrogen addition performs better than ammonia. The major and intermediate species, the aromatic hydrocarbons, and the soot formation or oxidation reaction rates are decreased mainly by the hydrogen and ammonia thermal effect while increased moderately by the chemical effect. Therein, the reduction in soot generation is mainly due to the polycyclic aromatic hydrocarbon condensation rate being slowed down by additives. The inhibition is attributed to the thermal effect of additions, and hydrogen behaves better than ammonia.

Simulating yield and morphology of carbonaceous nanoparticles during fuel pyrolysis in laminar flow reactors enabled by reactive inception and aromatic adsorption

Carbon black and soot are synthesized by gas-phase pyrolysis of hydrocarbons. Inception, surface growth, and coagulation control process yield and agglomerate morphology. Here, we present a sectional population balance model (SPBM) coupled with chemistry to simulate carbon black formation by ethylene pyrolysis in laminar flow reactors. The SPBM tracks agglomerate size distribution and morphology. New particles are formed by the dimerization of polycyclic aromatic hydrocarbons (PAHs) and grow with hydrogen abstraction acetylene addition as well as the addition of PAHs on their surface. Three different dimerization models for inception and PAH adsorption are compared: irreversible, reversible, and reactive. With irreversible PAH dimerization and surface growth, more than 90% of PAH mole fraction converts to particles even at low-temperatures (T<1200 K) causing an overestimation of the primary particle number density due to non-stop new particle formation. With reversible dimerization, the mass yield is underestimated by more than a factor of 3. With reversible dimerization and surface growth followed by a chemical bond formation step (chemical dimerization/reactive model), particles form and grow mostly at high temperatures (T>1200 K); the particle size distribution, as well as the average primary particle and mobility diameters are predicted within 30% of measurements. The reactive model enhances the agglomerate morphology prediction in the low-temperature regions of the reactor and appears to be more consistent with the latest understanding of inception and surface growth.

Numerical and experimental investigation of soot precursor and primary particle size of aviation fuel (RP-3) and n-dodecane in laminar flame

RP-3 is the most popular aviation fuel in China and its soot emission raises serious concern. The current study analyzed the soot precursors of RP-3 and n-dodecane in laminar flame, and integrated the corresponding poly-aromatic hydrocarbons (PAHs) growth mechanisms with popular RP-3 and n-dodecane oxidation mechanisms to improve the soot formation prediction for both fuels. The sizes of soot precursors were determined by the fringe lengths of soot particles. At dimensionless height DH = 0.25 of RP-3 and DH = 0.50 of n-dodecane, the geometric mean fringe lengths of RP-3 and n-dodecane are measured to be 0.67 nm and 0.64 nm respectively, which approximate to the size of the five-ringed (A5) poly-aromatic hydrocarbon. An A5 growth mechanism was then added on both popular RP-3 and n-dodecane oxidation mechanisms respectively. The base oxidation mechanisms for both fuels only contain the mono-aromatic hydrocarbons formation and benzene was treated as soot precursors in simulation. After validation by the ignition delay time and flame speed in literature, the combined mechanisms were then used to simulate the soot property and validated by the measured primary particle diameter. The simulation results suggested that the computed soot precursor concentrations of the combined mechanisms are smaller than that of the base mechanism. The combined mechanisms enhance the soot nucleation process which increases the primary particle number density prediction, and weaken the soot growth process which decreases the soot volume fraction prediction for both fuels. Eventually, the proposed combined mechanisms including the large PAHs growth provide a better agreement with the measured primary particle diameter.

Prediction of aggregate shape using bubble size in suspension during microwave irradiation in the process of aggregation

To efficiently operate microwave assisted nanoparticle synthesis, thermal behavior around aggregate during irradiation must be well-understood to ensure stable operation. The key information in this regard are aggregate size and shape. In this study, aggregate size before the irradiation and maximum bubble size during the irradiation were measured at the different induction time and varying number density of primary particle. It was found that maximum bubble size is more closely related to the number density of aggregate than the number density of primary particles. Further analysis on the results indicates that aggregate size and shape can be estimated using known data of bubble size. These findings provide useful information on how microwave assisted nanoparticle formation can be better operated.

Experimental and Numerical Investigation into the Effects of Unsaturated Carbon Bonds of Hydrocarbon Fuels on Soot Formation in Laminar Diffusion Flames

ABSTRACT Fuel structure is the main factor controlling soot behavior. Compared to the carbon number, the unsaturated carbon bonds have a greater effect on soot formation. This work analyzed the mechanism of C = C and C ≡ C on soot by adding ethylene and acetylene to the fuel stream of methane laminar diffusion flame experimentally and numerically. The results showed that the blending of C2H4 results in an increase of flame height without causing smoking, while the C2H2 addition up to 40% results in soot wings. The effect of C ≡ C bond on the flame structure and natural luminosity is much higher than that of C = C bond. The peak soot volume fraction (SVF) increases with the increasing blending ratio of C2H4 and C2H2, but the latter is one order of magnitude higher. The promotion effect of C ≡ C on soot growth attributes to the synergistic increase of HACA rate and PAHs condensation rate, while that of C = C is mainly due to the increased HACA rate. With the increase of unsaturated carbon bond concentration, the primary particle number density increases, the soot inception process is advanced. This trend is further enhanced with the increase of carbon bond unsaturation due to the shortening of the precursor formation pathway and the acceleration of reaction rate. With the increase of C2H4 blending ratio, the peak O2 oxidation rate increases linearly, while with the increase of C2H2 ratio, peak O2 oxidation rate increase first and then decrease, peaks at 40% ratio. Compared with O2 oxidation, the OH oxidation rate is not sensitive to carbon bond unsaturation and unsaturated carbon bond concentration.

A post processing technique to predict primary particle size of sooting flames based on a chemical discrete sectional model: Application to diluted coflow flames

A numerical post-processing strategy to reconstruct the size of soot primary particles is presented in this work in the context of the chemical sectional models. The proposed technique is based on solving the transport equation of the primary particle number density for each considered aggregate size. The chemical source terms are derived from the corresponding chemical reactions.The validity of the proposed approach is tested on target flames of the International Sooting Flame (ISF) Workshop. In particular, first, a laminar premixed ethylene flame is considered. Profiles of soot volume fraction and mean primary particle size are compared between simulation and measurements and a satisfactory agreement is observed, validating the proposed post-processing strategy. Second, a laminar coflow ethylene flame is put under the scope. Numerical results are compared to experimental data once again in terms of soot volume fraction and primary particle size. The sensitivity to model parameters, such as accounting for surface rounding and the choice of the smallest aggregating particle size, is explored.Once validated, the effect of dilution on the mean primary particle diameter in laminar diffusion flames is examined. The general trends observed experimentally are recovered. The correlation between temperature, precursor concentrations, soot volume fraction and primary particle diameter is explored. Finally, formation rates and residence time along the particle trajectories are investigated to explain the effect of dilution on the spatial localization of the biggest particles along the flame. The relation between the soot volume fraction and the mean primary particle diameter is examined.

The role of reactive PAH dimerization in reducing soot nucleation reversibility

Abstract Nucleation of incipient soot or carbon black nanoparticles has significant scientific and industrial importance because it influences the particle size distribution, morphology and composition, hence its health and environmental impact as well as functional properties. R eversible P olycyclic Aromatic Hydrocarbon (PAH) C lustering (RPC) with van der Waals forces (vdW) was proposed recently as opposed to I rreversible P AH C lustering (IPC) for soot nucleation (Eaves et al., Proc. Combust. Inst, 35 (2015) 1787) to relax the assumption of stable dimer formation with physical bonds at flame temperatures. Here, the necessity of considering chemical bond formation between PAHs in a dimer for reducing soot nucleation reversibility in ethylene coflow diffusion flames with a wide range of nitrogen dilution ratios is demonstrated. An RPC model with C hemical B ond F ormation (RPC CBF) is developed and its performance is compared to those of RPC and IPC models. Only the RPC CBF model with low reversibility for PAH addition on the surface of soot primary particles can predict soot volume fraction, average primary particle diameter, primary particle number density and the bimodal size distribution of soot agglomerates on the flame centerline within experimental uncertainty. While the IPC model overpredicts soot concentrations by a factor of five with increased dilution, the RPC model underpredicts it by more than two orders of magnitude for the flame with 68% nitrogen dilution. The RPC model fails to predict the observed bimodality of agglomerate particle size distribution in flames with low dilution because its predicted nucleation rate is much weaker compared to that of growth. Accounting for chemical bond formation for dimers is essential to form enough nuclei with increasing dilution and temperature. Also, low reversibility for PAH addition is required to predict the balance between nucleation and surface growth, hence the average size of soot primary particles.

Simultaneous measurements of gas temperature, soot volume fraction and primary particle diameter in a sooting lifted turbulent ethylene/air non-premixed flame

Simultaneous, planar measurements of flame temperature (T), soot volume fraction (fv), primary particle diameter (dp) and the derived number density of primary particles (Np) are reported in a well characterized, lifted ethylene jet diffusion flame, both to increase confidence in measurement accuracy and to provide new joint statistics. Planar measurements of temperature were performed using non-linear excitation regime two-line atomic fluorescence (nTLAF) of indium with an improved optical arrangement over those reported previously, and were found to yield good agreement with previous measurements obtained with coherent anti-Stokes Raman spectroscopy (CARS). Planar measurements of soot volume fraction and primary particle diameter were performed using time-resolved laser-induced incandescence (TiRe-LII). On the flame centreline, both the measured values of dp and fv grow with axial distance to peak near to the mid height of the flame. The joint probability density functions (PDF) of the measured T, fv, dp and derived Np were obtained from the two-dimensional images and assessed at 15 locations in the flame (5radial×3axial locations). Strong correlations were found between fv, dp and Np, while they exhibit a moderate correlation with flame temperature. The changes in PDFs with radial and axial locations and the most probable values are also reported.

Structural effects of biodiesel on soot formation in a laminar coflow diffusion flame

Structural effects of biodiesel in terms of unsaturation, i.e. C=C double bonds, its position and the presence of the ester moiety on soot formation are studied in this paper. Laminar coflow diffusion flames of 5-decene, 1-decene, n-decane, and a biodiesel surrogate consisting of a 50%/50% molar blend of n-decane and methyl-octanoate are selected for the investigation. It is observed that the presence of unsaturation promotes soot formation in the flames by increasing soot chemical surface growth species and soot inception species (aromatics) as it is evident from the larger primary particle size and number density of soot particles in the 1-decene, and 5-decene flames compared to the n-decane flame, respectively. More centrally located C=C double bond further speeds up soot inception as it promotes the formation of aromatic species. This is also evident from earlier detection of soot on the centerline and higher soot primary particle number density of the 5-decene flame compared to 1-decene and n-decane flames measured by the laser extinction and thermophoretic sampling methods, respectively. Effects of the ester moiety on soot formation are more on the concentrations of soot chemical surface growth species because the biodiesel surrogate flame has similar number density of primary particles compared to the n-decane flame but soot primary particles have smaller diameters.

CoFlame: A refined and validated numerical algorithm for modeling sooting laminar coflow diffusion flames

Mitigation of soot emissions from combustion devices is a global concern. For example, recent EURO 6 regulations for vehicles have placed stringent limits on soot emissions. In order to allow design engineers to achieve the goal of reduced soot emissions, they must have the tools to so. Due to the complex nature of soot formation, which includes growth and oxidation, detailed numerical models are required to gain fundamental insights into the mechanisms of soot formation. A detailed description of the CoFlame FORTRAN code which models sooting laminar coflow diffusion flames is given. The code solves axial and radial velocity, temperature, species conservation, and soot aggregate and primary particle number density equations. The sectional particle dynamics model includes nucleation, PAH condensation and HACA surface growth, surface oxidation, coagulation, fragmentation, particle diffusion, and thermophoresis. The code utilizes a distributed memory parallelization scheme with strip-domain decomposition. The public release of the CoFlame code, which has been refined in terms of coding structure, to the research community accompanies this paper. CoFlame is validated against experimental data for reattachment length in an axi-symmetric pipe with a sudden expansion, and ethylene–air and methane–air diffusion flames for multiple soot morphological parameters and gas-phase species. Finally, the parallel performance and computational costs of the code is investigated. Program summaryProgram title: CoFlameCatalogue identifier: AFAU_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AFAU_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public License, version 3No. of lines in distributed program, including test data, etc.: 94964No. of bytes in distributed program, including test data, etc.: 6242986Distribution format: tar.gzProgramming language: Fortran 90, MPI. (Requires an Intel compiler).Computer: Workstations.Operating system: Linux.RAM: From 16 GB to over 1000 GB depending on size of system being simulatedClassification: 22.Nature of problem:Soot formation in laminar diffusion flames with detailed description of thermodynamics, kinetic, and transport dataSolution method:Finite volume method utilizing the pseudo-transient SIMPLE algorithm and locally coupled chemistry solverAdditional comments:The code was specifically developed for modeling soot formation in laminar diffusion flamesRunning time:From hours to a month depending on the complexity of the chemical mechanism and the disparity between the initial guess and the final solution.

Soot measurements by two angle scattering and extinction in an N2-diluted ethylene/air counterflow diffusion flame from 2 to 5 atm

The soot formed in an N2-diluted ethylene/air counterflow diffusion flame at elevated pressure was investigated using two angle light scattering/extinction technique. To provide a well-controlled pressurized environment for the flame, a novel pressure vessel was built with the required optical access. The soot parameters were measured along the centerline of the counterflow flame. These properties included soot volume fraction (fv), primary particle diameter (dp), population averaged radius of gyration (Rg) and number density of primary particles (np). The Rayleigh–Debye–Gans theory for Fractal Aggregates (RDG-FA) was used to retrieve these properties from scattering and extinction measurements. Soot volume fraction was measured via light extinction from 2 to 5atm while maintaining the same global strain rate at all pressures. Scattered light from soot particles was measured at 45° and 135° and primary particle diameter was calculated using scattering/extinction ratio and the radius of gyration was determined from the dissymmetry ratio. Soot volume fraction, primary particle diameter and radius of gyration all increased with pressure while the number density of primary particles decreased with increasing pressure.

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 exhaust gas recirculation on diesel particulate matter morphology and NOx emissions

Diesel particulate morphology and nitrogen oxides (NO x) emissions were investigated in detail to reveal the effects of exhaust gas recirculation (EGR). The different rates of EGR were precisely controlled by using a customized engine control unit in a 1.7 l turbocharged common-rail direct-injection diesel engine. The tests, which combined two different EGR modes (i.e. constant boost pressure (CBP) and constant oxygen-to-fuel ratio (COFR)), were designed to decouple the effects of EGR thermal and dilution processes. Particulate samples were collected directly from the raw engine exhaust by using a novel thermophoretic soot-sampling system. The samples were examined and imaged with a high-resolution transmission electron microscope and quantitatively analysed by using a customized image-processing/data-acquisition system. Results showed that the particulate dimensions, number density of primary particles, and soot yield all changed significantly under various EGR rates. The NO x emissions also varied significantly as the EGR rate changed, showing a typical trade-off with respect to the data measured for particulate emissions. At low EGR rates, the thermal effect was the dominant phenomenon that affected the changes of the measured morphological characters, while at higher EGR rates the dilution effect became more important. However, the fractal geometry of diesel particulates did not change significantly between the two EGR modes, suggesting that the influence of EGR dilution was less than that of the thermal process. EGR operation providing a COFR at the same EGR rate yielded a significant benefit in particulate emissions and engine power output, while still maintaining the reduction of NO x emissions at a satisfactory level.

Determination of soot scattering coefficient from extinction and three-angle scattering in a laminar diffusion flame

The total scattering coefficient is determined from three multiangle scattering measurements at different heights above the burner in a nonsooting laminar ethylene diffusion flame. The local extinction coefficient is determined from multichord extinction measurements. The above analysis quantifies the contribution from scattering to extinction without knowledge of the soot primary particle diameter or the morphology of the aggregates, and the absorption coefficient can now be determined. The primary particle diameter, the number density of primary particles, the average number of primary particles in an aggregate, and the width of the lognormal distribution function for the number of primary particles in an aggregate are calculated using the absorption coefficient and assumed constant values for the fractal dimension, the fractal prefactor, and the complex refractive index for soot. The values for the primary particle diameter obtained from the in situ measurements in this study compare well with those obtained from transmission electron microscopic measurements of thermophoretically sampled soot aggregates in a previous study at all heights in the diffusion flame, while the calculated soot structure parameters compare well with previous studies only at heights between 30 and 50 mm above the burner.

Characterization of Nano‐Particles Using Laser‐Induced Incandescence

AbstractLaser‐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.

Effects of polydispersity of chainlike aggregates on light-scattering properties and data inversion.

A systematic evaluation of the effects of polydispersity of chainlike aggregates in terms of primary particle number density and size on the scattering quantities and data inversion is presented. For aggregates with refractive index in the range absolute value(m-1) = 0.8-1.2, average size parameter x < 0.40, and primary particle number Np < 20, it is shown that the effects of polydispersity of primary particle size on the light-scattering quantities are much stronger than the polydispersity of the number of primary particles per aggregate. For aggregates with polydisperse primary particle size, the assumption of monodispersity tends to underestimate the real and imaginary parts of the refractive index and the number of primary particles. Specifically, for values of the distribution width sigma greater than 0.10, the effect of polydispersity of the size of primary particles must be considered in the data inversion schemes. Furthermore, in the same range of values for the refractive index, particle size parameter, and primary particle number, the assumption of monodispersity for aggregates with polydisperse particle number tends to underestimate the value of the real part of the refractive index and overestimate the value of the imaginary part of the refractive index and primary particle size. However, for values of the distribution width sigma less than 0.60, the effects of polydispersity of primary particle number can be neglected. In addition, the suitable pairing sets of the measured scattering quantities for data inversion are presented and discussed.

Agglomerate parameters and fractal dimension of soot using light scattering—effects on surface growth

Measured scattering, extinction coefficients, and dissymmetry ratios at 0.488 μm from a premixed propane-oxygen flame with a fuel equivalence ratio of φ 0 = 1.8 are combined with the scattering and extinction model for agglomerates to determine each of the following: primary particle diameter, number density of primary particles, and the total number of agglomerates as a function of position in the flame. The inferred primary particle diameters vary in the range from 0.009 to 0.029 μm whereas the fractal dimension of the agglomerate was estimated to be 1.7. In addition, both the Mie and agglomerate analysis of scattering and extinction data yield effective diameters that differ only by 1.8% or less for this type of flame system. However, the growth rates determined from the Mie scattering and extinction analysis are found to be higher by 106% or more when compared with the growth rates inferred from the agglomerate analysis.

Effects of soot agglomeration on radiative transfer

A detailed analysis is presented of soot-particle agglomeration for a premixed flame with a fuel equivalence ratio of φ 0 = 1.8. Measured scattering and extinction coefficients and dissymmetry ratios at 0.488 μm are combined with a scattering and extinction model for agglomerates to estimate each of the following: primary particle diameter, number density of primary particles and the total number of agglomerates as a function of position in the flame. The inferred primary particle diameters vary in the range from 0.009 to 0.029 μm, whereas the number of primary particles per agglomerate varies from 11 to 24. The inferred agglomerate parameters, along with the measured spectral emissivities in the wavelength range 0.4–6.7 μm and the known refractive indices of soot, are combined to yield the spectral and total emissivities of soot. Comparisons are carried out with the results of previous investigations. It is shown that for the type of flame studied, for which the degree of agglomeration is low, the governing parameter in soot radiation is the refractive index.

Soot aerosol dynamics in a laminar ethylene diffusion flame

A thermophoretic sampling technique is used to examine the soot morphological characteristics inside a coannular ethylene/air diffusion flame at atmospheric pressure. The data acquired with this sampling technique are combined with information obtained by others using optical diagnostics on an identical flame. The spatial variation of primary particle diameter, combined with particle velocity measurements performed by Santoro, allow the calculation of specific soot surface growth rate, primary particle number density, soot surface area and molecular flux of the growth species throughout the growth region. Specific soot burnout rates are also obtained throughout the oxidation region. A discussion about the spatial distribution of the soot aerosol processes is given. The particles are formed low in the flame (z≅5mm) on the fuel rich side of the flame sheet, close to the main reaction zone. They subsequently follow paths to the upper regions of the flame, growing through both agglomeration and surface growth reactions and finally they disappear entirely under the oxidative attack of various species. A bimodal integral solution of the aerosol dynamic equation that accounts for particle inception, free molecular coagulation and surface growth reactions is used to model the soot dynamics in the flame. This model is used to study the soot formation and growth processes throughout the lower and intermediate portions of the flame along a path line that coincides with the annular region. An estimate of the particle inception rate is obtained as a result of these calculations.