Discrete-sectional Model Research Articles

Prediction of Soot in an RQL Burner Using a Semi-Detailed Jeta-1 Chemistry

Abstract The present work proposes a methodology to include accurate kinetics for soot modeling taking into account real fuel complexity in Large Eddy Simulation of aeronautical engines at a reasonable computational cost. The methodology is based on the construction of an analytically reduced kinetic mechanism describing both combustion and gaseous soot precursors growth with sufficient accuracy on selected target properties. This is achieved in several steps, starting from the selection of the detailed kinetic model for combustion and soot precursors growth, followed by the determination of a fuel surrogate model describing the complex real fuel blend. Finally the selected kinetic model is analytically reduced with the code ARCANE while controlling the error on flame properties and soot prediction for the considered fuel surrogate. To perform all evaluation and reduction tests on canonical sooting flames, a Discrete Sectional Model for soot has been implemented in Cantera. The resulting code (Cantera-soot) is now available for the fast calculation of soot production in laminar flames for any fuel. The obtained reduced kinetic scheme is finally validated in a Rich-Quench-Lean burner of the literature in terms of soot prediction capabilities by comparison of LES coupled to the Lagrangian Soot Tracking model with measurements. Results show a significant improvement of the soot level prediction when using the reduced more realistic kinetics, which also allows a more detailed analysis of the soot emission mechanisms. This demonstrates the gain in accuracy obtained with improved reduced kinetics, and validates the methodology to build such schemes.

Comprehensive simulations of new particle formation events in Beijing with a cluster dynamics–multicomponent sectional model

Abstract. New particle formation (NPF) and growth are a major source of atmospheric fine particles. In polluted urban environments, NPF events are frequently observed with characteristics distinct from those in clean environments. Here we simulate NPF events in urban Beijing with a discrete-sectional model that couples cluster dynamics and multicomponent particle growth. In the model, new particles are formed by sulfuric acid–dimethylamine nucleation, while particle growth is driven by particle coagulation and the condensation of sulfuric acid, its clusters, and oxygenated organic molecules (OOMs). A variable simulation domain in the particle size space is applied to isolate newly formed particles from preexisting ones, which allows us to focus on new particle formation and growth rather than the evolution of particles of non-NPF origin. The simulation yields a rich set of information including the time-dependent NPF rates, the cluster concentrations, the particle size distributions, and the time- and size-specific particle chemical compositions. These can be compared with the field observations to comprehensively assess the simulation–observation agreement. Sensitivity analysis with the model further quantifies how metrics of NPF events (e.g., particle survival probability) respond to model input variations and serves as a diagnostic tool to pinpoint the key parameter that leads to simulation–observation discrepancies. Seven typical NPF events in urban Beijing were analyzed. We found that with the observed gaseous precursor concentrations and coagulation sink as model inputs, the simulations roughly captured the evolution of the observed particle size distributions; however, the simulated particle growth rate was insufficient to yield the observed particle number concentrations, survival probability, and mode diameter. With the aid of sensitivity analysis, we identified under-detected OOMs as a likely cause for the discrepancy, and the agreement between the simulation and the observation was improved after we modulated particle growth rates in the simulation by adjusting the abundance of OOMs.

Oxygen effects on soot formation in H2/n-heptane counterflow flames

Blending of hydrocarbon fuels with hydrogen is a practically feasible way to rapidly integrate a carbon neutral energy vector in the transport sector and to effectively reduce harmful particulate matter emissions. This work investigates the effects of hydrogen (H2) addition on soot formation in n-heptane in low strain rate counterflow diffusion flames with different oxygen mole fractions (XO2=0.3 ∼ 0.45). Flame temperature, soot volume fraction (fv), monocyclic (MAHs), and polycyclic aromatic hydrocarbons (PAHs) are measured by using OH-2C-PLIF/thermocouple, LII/LE, and PAH-LIF methods, respectively. Measurements of n-heptane flames with addition of helium (He), as an inert gas with a specific heat capacity similar to that of H2, are also carried out and compared. Numerical simulations are then performed using a soot discrete sectional model coupled with detailed gas-phase kinetics to interpret the data obtained. Temperature and soot volume fraction profiles are better predicted by 2D simulations, which account for the non-negligible impact of radial diffusion and buoyancy under low strain rate conditions. Then, it is shown that both the fv and PAH yields almost linearly decrease by increasing H2 or helium (He) addition. The reduction of PAHs and soot is larger in n-heptane/H2 flames due to H2 chemical effects, absent in the n-heptane/He flames, hampering the formation of peri‑condensed structures. The effect of O2 concentration in the oxidizer stream is also studied. Experimental and simulation results show that PAHs and soot increase with XO2 for all flames. Finally, the effects of H2/He addition varying XO2 on soot formation are investigated. With the increase of XO2, the difference in the peak flame temperatures of n-heptane/H2 and n-heptane/He flames decreases. Consequently, compared to the neat n-heptane flame, the reduction of peak fv becomes more and more pronounced in the case of hydrogen addition rather than the helium addition since the H2 soot inhibiting chemical effect prevails over the H2 temperature effect which instead promotes soot formation.

Tutorial: The discrete-sectional method to simulate an evolving aerosol

The discrete-sectional method to solve the general dynamic equations is a useful tool for the simulation of an evolving aerosol population. This tutorial is intended to equip the reader with the necessary knowledge to implement this method for a single component system. To this end, we provide step-by-step instructions on the construction of a discrete-sectional model, including details on simulation bin configurations and all the necessary equations to describe relevant physical processes in an aerosol, i.e. condensation/evaporation, coagulation, and external particle losses. Supplementary to the text is a functional, open source MATLAB code that implements the framework introduced in this tutorial. The interested readers can use the code either for learning purposes or to meet research demands. Lastly, we designed six test cases not only to verify the validity of our discrete-sectional model, but also to help the reader gain insight into the evolution of aerosol systems.

Effects of radiation modeling on non-premixed sooting flames simulations under oxyfuel conditions

Radiative heat modeling has a central role for the simulation of soot formation in flames. Radiation heat transfer, gas-phase chemistry and soot formation are strongly coupled and highly dependent on temperature. Thus, it is of primary importance that simplified radiative models are able to reproduce detailed simulations at conditions found in flames of interest. In this work, the capabilities of the superposition WSGG radiation model is compared to the LBL spectral integration for a set of laminar non-premixed counterflow flames of ethylene burning with oxygen-rich oxidizer. The numerical solutions for both thermal radiation approaches are fully coupled with detailed chemistry and a discrete sectional model for soot formation. The role of thermal radiation and the importance of radiation absorption on soot formation were explored through systematic replacement of N2 by CO2 on either the fuel or on the oxidizer. In addition, the validity of the simplified optically thin approximation for modeling such flames was also discussed. The spectral superposition WSGG model is able to accurately describe general flame structure and soot predictions respective to the LBL integration for both the reference flame and for the cases of CO2 addition in the fuel and in the oxidizer mixtures. For the CO2 addition flames, the WSGG model tends to overestimate the radiation emission on high temperature regions and to overestimate the radiation absorption on low temperatures towards the reactant with CO2 addition. However, these discrepancies were not sufficient to significantly influence the flame structure. Some non-negligible discrepancies are observed only at very small strain rates. Finally, the evaluation of the soot spectral radiation coefficient (Cκ,s) reveled an important influence on the soot volume volume fraction for low levels of CO2 addition.

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.

Effects of CO2 addition on soot formation of ethylene non-premixed flames under oxygen enriched atmospheres

Regulations related to soot emissions are becoming more stringent due to the negative impact of soot on the environment and human health. Thus, not only the total mass of soot released from hydrocarbon combustion have to be controlled but also its particle size distribution. Combustion technologies such as oxygen-enriched and oxy-fuel allied with flue gas recirculation have demonstrated their potential for reducing pollutants while improving combustion efficiency. In this context, this work explores the effect of CO2 addition on the soot formation process under an oxygen enriched atmosphere. A set of laminar counterflow ethylene flames are numerically studied for CO2 addition on either the fuel or the oxidizer mixtures for the same CO2 amount in the reaction layer. The numerical approach accounts for detailed chemistry and transport properties, together with an advanced model for thermal radiation and the discrete sectional model for soot formation. It was observed that CO2 suppresses the formation of species such as hydrocarbon radicals (C2H, C3H3), C2H2 and A1, which are important PAHs building block species directly involved in the soot formation process. For the same amount of CO2 in the reaction layer, it was found a more expressive suppression of the aforementioned species concentrations when CO2 was added to the fuel mixture. Moreover, for the same amount of CO2 in the reaction layer, it was also found that while chemical effects played a major role on the formation of C2H2, C3H3 and PAHs for the CO2 addition on the oxidizer side, both chemical and thermophysical effects are important for CO2 addition on the fuel side. In both cases, the temperature profile was mainly influenced by thermophysical effects while the soot volume fraction was mainly influenced by chemical effects. Finally, the particle-size distribution reveled to be strongly bimodal and slightly sensitive on the CO2 addition for the current flames.

Soot Modeling of Ethylene Counterflow Diffusion Flames

ABSTRACTCombustion-generated nanoparticles cause detrimental effects to not only health and environment but also combustion efficiency. A detailed kinetic mechanism employing a discrete sectional model is validated using experimental data obtained in laminar counterflow diffusion flames of ethylene/oxygen/nitrogen. Two configurations, named Soot formation (SF) and soot formation/oxidation (SFO) flames, are modeled using one-dimensional simulations. Radiative heat losses reduce the maximum flame temperature in the range of 20–60 K and therefore reduce soot volume fraction by ~ 10%. The model predictions accounting for the radiation effects are quite satisfactory. The model can reproduce the qualitative trends of soot volume fraction peaks that are slightly shifted toward the oxidizer zone with the increased oxygen content. In SF flames, the model predicts the maximum soot volume fraction quite well with the largest discrepancy of two folds. The particle stagnation locations can be reproduced by the model, although they are slightly shifted toward the oxidizer nozzle by ~ 0.4 mm. In SFO flames, the most considerable discrepancy is observed at the least sooting flame (xF,o = 0.23) in which the model over-predicts the maximum soot volume fraction by a factor of two. The effect of soot oxidation is important. The model shows that neglecting oxidation of soot significantly increases soot volume fraction in SFO flames by two folds while SF flames are only marginally affected. Also, ignoring soot oxidation leads to the presence of soot particles in the oxidizer zone where they are not observed experimentally. OH is the most effective oxidizer because the sooting zone is located inside the flame region. The effect of thermophoresis is also investigated. It strongly influences SFO flames due to the high temperature gradient. The model accounting particle diffusivities from Stokes–Cunningham correlation can better characterize the distinct particle stagnation plane of SF flames due to their low diffusion coefficients.

Nucleation and growth of Y2O3 nanoparticles in a RF-ICTP reactor: a discrete sectional study based on CFD simulation supported with experiments

Synthesis of yttria (Y2O3) nanoparticles in an atmospheric pressure radiofrequency inductively coupled thermal plasma (RF-ICTP) reactor has been investigated using the discrete-sectional (DS) model of particle nucleation and growth with argon as the plasma gas. Thermal and fluid dynamic information necessary for the investigation have been extracted through rigorous computational fluid dynamic (CFD) study of the system with coupled electromagnetic equations under the extended field approach. The theoretical framework has been benchmarked against published data first, and then applied to investigate the nucleation and growth process of yttrium oxide nanoparticles in the plasma reactor using the discrete-sectional (DS) model. While a variety of nucleation and growth mechanisms are suggested in literature, the study finds that the theory of homogeneous nucleation fits well with the features observed experimentally. Significant influences of the feed rate and quench rate on the distribution of particles sizes are observed. Theoretically obtained size distribution of the particles agrees well with that observed in the experiment. Different thermo-fluid dynamic environments with varied quench rates, encountered by the propagating vapor front inside the reactor under different operating conditions are found to be primarily responsible for variations in the width of the size distribution.

Modeling of particle generation in laser ablation plasma

In this study, we used the general dynamic equation (GDE) for aerosols, combined with particle charging by positive ions and electrons, to simulate particle generation in laser ablation plasmas. The population balance equations based on Brownian coagulation and diffusion charging theory were represented by using a discrete-sectional model. The temporal evolution of the particle size distribution was simulated at three different initial number concentrations of neutral monomers, positive ions and electrons, as well as at two different gas pressures.The simulated average particle size increased with time and with increasing initial concentration of neutral monomer and gas pressure. The particle growth was affected by the particle charging when both number ratios of positive ion to neutral monomer and of electron to neutral monomer are higher than 0.1. Simulated particle size distributions were compared with SEM images of particles collected at different sampling points and gas pressures in actual plasmas operating at conditions similar to those simulated. Changes of particle size with increasing distance between the target and the sampling point and with increasing the pressure were well reproduced by simulations. However, particle diameters calculated were much smaller than SEM images because physical values, such as, initial concentrations of monomer, positive ions and electrons and the recombination probability of electron and positive ions, used in calculations were invalid.

Analysis of iron particle growth in aerosol reactor by a discrete-sectional model

The growth of iron particles by thermal decomposition of Fe(CO)5 in a tubular reactor was analyzed by using a one dimensional discrete-sectional model with the coalescence by sintering of neighboring particles incorporated in. A thermal decomposition of Fe(CO)5 vapor to produce iron particles was carried out at reactor temperatures varying from 300 to 1,000°C, and the effect of reactor temperature on particle size was compared with model prediction. The prediction exhibited good agreement with experimental observation that the primary particle size of iron was the largest at an intermediate temperature of 800°C. Model prediction was also compared with Giesen et al.’s [1] experimental data on iron particle production from Fe(CO)5. Good agreement was shown in primary particle size, but a considerable deviation was observed in primary particle size distribution. The deviation may be due to an inadequate understanding of the sintering mechanism for the particles within an agglomerate and to the assumption of an ideal plug flow in model reactor in contrast to the non-ideal dispersive flow in actual reactor.

A discrete-sectional model for particle growth in aerosol reactor: Application to titania particles

A one-dimensional discrete-sectional model has been developed to simulate particle growth in aerosol reactors. Two sets of differential equations for volume and surface area, respectively, were solved simultaneously to determine the size distributions of agglomerates and primary particles. The surface area equations were derived in such a way that the coagulation integrals calculated for the volume equations could be used for the surface area equations as well, which is new in this model. The model was applied to a production of TiO2 particles by oxidation of titanium tetrachloride. Model predictions were compared with experimental data and those of a two-dimensional sectional model. Good agreement was shown in calculated particle size distributions between the present model and the two-dimensional model, which is more rigorous but demands a large amount of computer time and memory. Compared to experimental data, the primary particle size calculated by the model was more sensitive to the variation of reactor temperature.

A One-Dimensional Model for Coagulation, Sintering, and Surface Growth of Aerosol Agglomerates

The size of the primary particles in aerosol agglomerates is determined in part by the interplay of surface growth, coagulation, and sintering. These processes are modelled by a one-dimensional (1-D) discrete-sectional model, DISGLOM2, which predicts the evolution of agglomerate and primary particle size distributions. DISGLOM2 is an extended version of DISGLOM (Rogak 1997), in which particles smaller than the "melting diameter" were assumed to sinter instantly while bigger particles did not sinter at all. Gradual sintering, "condensational obliteration" (whereby primary particles are lost during heavy surface growth), and diffusional wall deposition have been incorporated into DISGLOM2. Results from DISGLOM2 were comparable with those from 2-D sectional models, but DISGLOM2 was much faster. In addition, DISGLOM2 includes the effects of "condensation" of small spherical particles on large agglomerates, which were not modelled previously. The effect of condensation was shown to be significant at low temperature. DISGLOM2 was used to predict the primary particle diameter of titania particles generated by precursor reaction. By adding gradual sintering, the growth rate of agglomerate particles by coagulation was slightly decreased and the primary particle size considerably increased compared with the results given by DISGLOM. Although DISGLOM2 is an efficient model of the relevant physical processes, the predictions are sensitive to the kinetics of precursor reactions and particle sintering, which can be difficult to characterize in real experimental systems.

Interpretation of structure formation during the sol-gel transition of a resorcinol-formaldehyde solution by population balance

Growth of colloidal particles formed during the sol-gel transition of a resorcinol-formaldehyde (RF) solution was simulated based on the population balance equation by using the discrete-sectional model (DSM). During the early stage of the sol-gel transition, the transient change of sizes of colloidal particles estimated by this method agreed well with the previous experimental observation by dynamic light scattering (DLS), which confirmed the influence of the catalyst concentration of a starting RF solution on the growth rate of the particles. From the size distribution of colloidal particles predicted at the gelation time, the surface area of a RF hydrogel after the completion of the sol-gel transition was estimated, which coincided with the BET surface area of a RF aerogel because the porous structure of a hydrogel was maintained and few micropores were formed during supercritical drying.

Aerosol behavior in chromium waste incineration

Cr 2O 3 is considered as the dominant incineration product during the combustion disposal of chromium waste. A hydrogen/air diffusion flame was employed to simulate the industrial process of incineration. Cr 2O 3 aerosols were generated inside the flame by the gas phase reaction of chromium and oxygen. Chromium came from the rapid decomposition of chromium hexacarbonyl (Cr(CO) 6) at room temperature and was carried into the combustion chamber by hydrogen. Aerosol and clusters can then be easily formed in the flame by nucleation and coagulation. A two dimensional Discrete-Sectional Model (DSM) was adopted to calculate the Cr 2O 3 aerosol behavior. The experimental measurement method was Dynamic Light Scattering. The numerically predicted results agreed well with those of the experimental measurement. Both results show that the Cr 2O 3 aerosol size reached about 70 nanometers at the flame top.

Analysis on plasma chemistry and particle growth corona discharge process for NO/sub ξ removal using discrete-sectional method

The particle formation and growth combined with plasma chemistry in the pulsed corona discharge process (PCDP) to remove NO/sub x/ were analyzed by the discrete-sectional model. In the PCDP, most of the NO is converted into NO/sub 2/ and, later, into HNO/sub 3/ which reacts with NH/sub 3/ to form the NH/sub 4/NO/sub 3/ particle. In the beginning of the reactor, we have the high concentration of small size particles and, later, the particle size distribution in the reactor becomes bimodal with the large size and small size particles and, finally, becomes monodisperse with the large size particles. As the average electron concentration increases, it takes a shorter reactor length to remove the NO/sub x/. As the initial NO and H/sub 2/O concentrations decrease, the NH/sub 3/ is consumed more slowly to form the ammonium nitrates particles. As the averaged electron concentration and initial H/sub 2/O concentration increase, the large size particles grow more quickly and the particle size distribution becomes bimodal earlier. As the initial NO and NH/sub 3/ concentrations increase, the diameter of large size particles becomes larger by the faster coagulation between particles. The predicted NO/sub x/ conversion and particle size distribution were in close agreements with the published experimental results at the averaged electron concentration of 2/spl times/10/sup 5/ cm/sup -3/ in this study.

Production of Monodisperse Nanoparticles and Application of Discrete-Monodisperse Model in Plasma Reactors

The particle growth in plasma reactor were investigated by using the discrete-monodisperse (D-M) model for various process conditions. The monodisperse large sized particle distribution predicted by the D-M model are in good agreement with the large sized particles by the discrete-sectional model and also in the experiments by Shiratani et al. (1996). Some fractions of the small size particles are in a neutral state or even charged positively, but most of the large sized monodisperse particles are charged negatively. As the mass generation rate of monomers increases, the large sized particles grow more quickly and the production rate of nanoparticles of 100nm by plasma reactor increases. As the initial electron concentration or the monomer diameter increases, it takes longer time for the large sized particles to grow up to 100nm, but the large sized particle concentration of 100nm increases and the resulting production rate of large sized particles of 100nm increases. As the residence time increases, the time for the large sized particles to grow up to 100nm decreases and the large sized particle concentration of 100nm increases and, as a result, the production rate of large sized particles of 100nm increases. We propose that the plasma reactor can be a good candidate to produce monodisperse nanoparticles.

The changes in particle charge distribution during rapid growth of particles in the plasma reactor

The changes in particle charging were investigated during the rapid growth of particles in the plasma reactor by the discrete-sectional model and the Gaussian charge distribution function. The particle size distribution becomes bimodal in the plasma reactor and most of the large particles are charged negatively, but some fractions of small particles are in a neutral state or even charged positively. As the particles accumulate in the plasma reactor, the amount of electrons absorbed onto the particles increases, while the electron concentration in the plasma decreases. As the mass generation rate of small particles (monomers) decreases or as the initial electron concentration increases, the electron concentration in the plasmas increases and the particle charge distribution is shifted in the negative direction and the fraction of particles charged negatively and the average number of electrons per particle increase. With the decrease in monomer diameter, the electron concentration decreases in the beginning of plasma discharge, but, later, increases. For high mass generation rate of monomers or for low initial electron concentration or for small monomer diameter, the fraction of particles in a neutral state increases and the particle size distribution becomes broader.

Rapid growth of particles by coagulation between particles in silane plasma reactor

The changes of particle size distribution were investigated during the rapid growth of particles in the silane plasma reactor by the discrete-sectional model. The particle size distribution becomes bimodal in the plasma reactor and most of the large sized particles are charged negatively, but some fractions of small sized particles are in a neutral state or even charged positively. As the mass generation rate of monomers increases or as the monomer diameter decreases, the large sized particles grow more quickly and the particle size distribution becomes bimodal earlier. As the mass generation rate of monomers decreases, the electron concentration in the plasmas increases and the fraction of particles charged negatively increases. With the decrease in monomer diameter, the electron concentration decreases in the beginning of plasma discharge but later increases.

Modeling particle growth and deposition in a tubular CVD reactor

A computational model is developed to simulate the particle formation, growth, and deposition in a tubular CVD reactor. The model takes into account the momentum, heat, and mass transfers, chemical reaction, Brownian coagulation, Brownian diffusion, thermal diffusion, and thermophoresis that occur within the reactor. The chemical system is illustrated by the formation of TiO 2 particles through oxidation of TiCl 4. A set of coupled partial differential equations is solved with the finite volume method to give spatial distributions of velocities, pressure, temperature, TiCl 4 concentration, and sizes of TiO 2 particles, from which the deposition mass fluxes and size distributions of exit TiO 2 particles can be readily evaluated. In the model, the growth of particles is simulated by the discrete-sectional model, which can cover particle growth from monomers up to the submicron size. Among other things, the simulation predicts a maximum deposition flux near the reactor entrance and a rebound in deposition flux near the reactor exit, which have been observed in several experimental studies. The model also reveals a delay in evolution of size distribution near the reactor wall as compared to that of the bulk. This delay signifies that the size distribution of depositing particles at the wall is in general different from that of the bulk, which normally is the measured one. The effects of important operating parameters such as temperature, pressure, inlet TiCl 4 concentration, and inlet stream velocity on various system performance indicators are also investigated.