Article pubs.acs.org/EF
Modeling Formation and Oxidation of Soot in Nonpremixed Flames Mariano Sirignano,† John Kent,‡ and Andrea D’Anna*,† †
Dipartimento di Ingegneria Chimica, dei Materiali e della Produzione Industriale, Università degli Studi di Napoli Federico II, Italy School of Aerospace, Mechanical & Mechatronic Engineering, University of Sydney, Australia
‡
S Supporting Information *
ABSTRACT: A detailed kinetic mechanism of aromatic growth, particulate formation, and oxidation is presented and is tested in nonpremixed laminar flames of methane and ethylene at atmospheric pressure. Model development is refined in strict connection with new experimental data on the formation and oxidation of high molecular mass compounds and incipient particles. Reaction pathways leading to the formation of incipient particles, their transformation to soot, their oxidation, and the oxidation-induced fragmentation of particles and aggregates have been included by using a multisectional approach for the particle process. Predictions within a factor of 2−3 are obtained for major oxidation and pyrolysis products as well as trace aromatic species and particulate concentrations. The newly developed model predicts the concentration of the particles, their sizes, morphology, and chemical properties in nonpremixed flames of methane and ethylene with a wide range of particle formation without any condition-dependent adjustments to the kinetic scheme. A wide range of particle sizes is covered from nanoparticles formed on the fuel side of the flames to larger soot particles and particle aggregates formed in the flame wings. The trend of the H/C ratio of the particles along the flame axis is also predicted well. It decreases to very low values typical of mature soot particles when large aggregates are produced. The new mechanism for particle oxidation, which includes the oxidation-induced fragmentation of particles and aggregates, has shown the importance of accurate modeling of particle oxidation to correctly predict particle burnout and particle size in nonpremixed flames.
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INTRODUCTION The understanding of the formation and burnout mechanism of combustion-generated particles is still a challenge. In recent years, the combustion community has faced this issue by implementing new experimental techniques and has obtained much data on details of particle formation in combustion. The remarkable advances in the mechanism of soot formation and oxidation have been reviewed periodically over the last 30 years,1−4 and many key issues have been discussed in the proceedings of a recent workshop.5 These data have yielded information on steps which limit particle formation and have helped in the development of detailed kinetic mechanisms of particle formation in flames.6−31 Most of the kinetic models developed in the last years have focused their attention to the transition from gas-phase to particles. PAH stacking is considered the controlling step in particle formation. Models which combine stacking of PAHs with the molecular growth of aromatic compounds have recently been proposed.17,22 Surface reactions with gas-phase species, mainly acetylene and PAHs, and coagulation of the particles determine their final concentration and size distribution. Surface growth is based on a chemical analogy of gas-phase aromatic chemistry. Two different approaches have been used to couple gas-phase chemistry with aromatic growth mechanisms: the method of moments9,18−20 and the discrete sectional method.10,17,21−23 In the method of moments, the detailed description of particle dynamics is modeled in terms of moments of the particle size distribution function. In the discrete-sectional method the ensemble of aromatic compounds with molecular mass higher than the largest aromatic compounds in the gas-phase is divided into classes of different molecular mass, and all reactions are © 2013 American Chemical Society
treated in the form of gas-phase chemistry using compound properties such as mass, numbers of carbon and hydrogen atoms averaged within each section. A different approach has been developed by Violi and coworkers11,28−31 and Kraft and co-workers.12−15,24−27 A detailed population balance model is introduced to bridge the gap between particle population dynamics and gas-phase reactions; the population balance is solved using the direct simulation Monte Carlo method. Today there is a need to have detailed kinetic mechanisms able to reproduce the concentration of particles, their sizes, morphology, and chemical properties in premixed as well as diffusion-controlled combustion. Particle characteristics as well as particle concentration have a role in human health32,33 and the environment.34 We have previously presented21,22 a kinetic mechanism with a sectional approach for the modeling of the particle-phase overtaking the issue of the increasing number of C atoms in the high molecular mass species. The model includes fuel oxidation and growth of species by fuel pyrolysis and by particulate formation, i.e. the growth of aromatics into particle nuclei, particle growth by surface reactions, coagulation, and finally particle oxidation and agglomeration. In this first version of our sectional method, lumped species were defined just by number of carbon atoms. The sectional approach, also in its first version,10 provides mass and size distribution of total particulates. Premixed flames of methane, Received: January 11, 2013 Revised: March 13, 2013 Published: March 18, 2013 2303
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which is mostly the same as presented previously.17 The detailed gas-phase kinetic mechanism is built onto the GRI-Mech 3.0 for C1 and C2 species41 and the Miller and Melius mechanism for C3 and C4 species.42 It considers the sequential addition of acetylene molecules6 and the self-combination of resonantly stabilized radicals to account for the molecular growth of aromatic cycles up to pyrene.43−45 With respect to the previous kinetic mechanism used to model premixed flames,17 the main changes are the kinetic rate of ethylene pyrolysis and minor changes in the production of small radicals. Due to these changes the prediction of some species is slightly improved also in premixed flame conditions. The complete kinetic scheme is reported in the Supporting Information. The Lumped Molecular Growth and Particle Inception Mechanism. Starting from pyrene, all of the compounds with larger molecular masses are considered as lumped species. The reactions accounting for molecular weight growth and oxidation are treated on the basis of similarity with gas-phase reactions involving PAHs. Starting from pyrene, the molecular growth of aromatics is initiated by an H atom loss (Rx1, Rx2, and Rx3) as schematized in Table 1 which reports the reactions involving lumped molecular species in their stable (ARM1) and radical form (ARM1*). The collision frequency is evaluated by kinetic theory; although the reactions for the lumped species cannot be considered as elementary reactions, this approximation is the main foundation of the sectional approach, and it is applied to all the particle-phase reactions. Details on the collision frequency calculations and estimate of the activation energy are reported in a previous publication.36 Termination reactions of aromatic radicals with other aromatic radicals (Rx4) end the growth sequence. Aromatic molecules with a fixed number of C atoms exist in a large number of isomers having different H atoms. Figure 1 shows a schematic representation of the possible aromatic molecules having approximately the same number of C-atoms and different H/C. Peri-condensed aromatic compounds (PCAH) with a fixed number of C atoms are sketched in panels a and b of Figure 1. The PCAHs having the lowest amount of H atoms are maximally condensed six-member ring structures (Figure 1a,b). Their H/C ratio decreases to very low values as the molecular size increases; the largest of these compounds is a graphene sheet. Consequently, the discretization in the number of C and H atoms furnishes a rough estimation of the molecular structure of the aromatic compounds.35 Formation of peri-condensed aromatic compounds (PCAH) is modeled by addition of acetylene (Rx5)6 (the H-AbstractionAcetylene Addition mechanism). Formation of incompletely condensed aromatics, also named oligomers of aromatic compounds (panels c and d in Figure 1), is modeled both by H atom substitutions by a pericondensed structure, e.g. the formation of phenyl-pyrene or naphthylpyrene, and by aromatic radical addition to nonaromatic double bounds, such as those of pentagons condensed peripherally with hexagons (acenaphthylene type) and those of compounds like phenanthrene (Rx6). The H/C ratio of the oligomers remains comparable to those of the aromatic molecules involved in the reactions, and it remains quite unchanged as the molecular weight of the oligomers increases. Aromatic oligomers usually assume a nonplanar structure due to the less rigid structure of the σ-bond connecting the aromatic molecules. The molecular mass of both pericondensed and incompletely condensed aromatics can grow indefinitely forming extremely large molecules. PCAH are formed adding only acetylene
ethylene, n-heptane, benzene, and larger hydrocarbons have been studied at varying operating conditions.22 The same kinetic scheme was used with a few changes to the gas-phase reactions, particularly the ethylene pyrolysis reactions and surface addition of acetylene and benzene to incipient particles, to simulate nonpremixed flames of methane, ethylene, and butane.21 Good predictions of gas- and particle-phase concentrations and particle sizes were obtained in nonpremixed flames for a kinetic mechanism with better acetylene prediction, which resulted in increased surface reaction rates relative to the mechanism previously used to simulate premixed flames. The model reproduced the low concentration of particulates (about 0.5 ppm) in a coflowing methane/air flame and the high concentration (near 10 ppm) of soot in ethylene and butene diffusion flames.21 Some shortcomings of the model were evident: i) modeled oxidation rates were not high enough to correctly predict particle burnout in heavily sooting diffusion flames despite matching modeled temperature to the data and ii) predicted particle sizes were much higher, by a factor of 3−5, than those measured.21 To address these points we have improved the treatment of the inception and growth pathways of particles in nonpremixed flames. Based on the recently proposed multisectional mechanism, the kinetics has been coupled to features such as H/C ratio and to morphology. This mechanism has been tested for the simulation of premixed flames.35 In the new multisectional mechanism besides the discretization of the particlephase in terms of C and H atom numbers,36 the particles are described by three different morphologies based on their state of aggregation: single high molecular mass molecules, clusters of molecules (particles), and agglomerates of particles. The C atom number (i.e., the particle mass), the H/C (i.e., the degree of aromatic extension), and the morphology is specified for each particle. This approach enabled the chemical evolution and internal structure of particles formed in flames to be followed in atmospheric premixed flat flames of methane, ethylene, and benzene, at different equivalence ratios for which a large set of experimental data exists.35,37 The detailed particle structure model now allows inclusion of dehydrogenation pathways leading to soot particle graphitization38 and O2 induced fragmentation.39,40 The inclusion of the dehydrogenation mechanism for soot and precursor nanoparticles is important to predict the concentration of particles in the wings of diffusion flames because dehydrogenation controls the relative abundance of stable and radical species on the particles and hence the mechanism of surface growth by acetylene. Also the inclusion of the fragmentation model is considered important to correctly simulate the soot burnout at the end of the flame. The latest version of the multisectional mechanism is presented in this paper. The model is tested on nonpremixed flames of methane and ethylene at atmospheric pressure. Predictions are compared with experimental data on gas-phase species concentrations, particle volume fractions, H/C, and size. Sensitivity of the predictions to particulate-phase reaction rates, particularly oxidation, is reported in the paper.
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KINETIC MECHANISM The kinetic mechanism of molecular growth and oxidation is based on the lumping of the high-molecular mass species by their number of C and H atoms. It is coupled with the detailed mechanism of oxidation and pyrolysis of the hydrocarbon fuels 2304
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Table 1. Lumped Species Mechanism molecules: ARM1 Rx1 Rx2 Rx3 Rx4 Rx5 Rx6 Rx7 Rx8 Rx9 Rx10
ARM1i + H ↔ ARM1*i + H2 ARM1i + OH ↔ ARM1*i + H2O ARM1i → ARM1*i + H ARM1*i + ARM1*i → ARM1i ARM1*i + C2H2 → ARM1i ARM1*i + ARM1i → ARM1i + H ARM1i + H → ARM1i + H + H2 ARM1i + OH → ARM1i + HCO ARM1*i + O2 → ARM1*i + CO + CO ARM1i + ARM1i → ARM2i clusters of molecules (particles): ARM2
Rx11 Rx12 Rx13 Rx14 Rx14 Rx15 Rx16 Rx16 Rx16 Rx17 Rx18 Rx19 Rx20 Rx20 Rx20 Rx21 Rx22 Rx22 Rx22
ARM2i + H ↔ ARM2*i + H2 ARM2i + OH ↔ ARM2*i + H2O ARM2i → ARM2*i + H ARM2*i + ARM1*i → ARM2i ARM2*i + ARM2*i → ARM2i ARM2*i + C2H2 → ARM2i ARM2*i + ARM2i → ARM2i + H ARM2*i + ARM1i → ARM2i + H ARM1*i + ARM2i → ARM2i + H ARM2i + H → ARM2i + H + H2 ARM2i + OH → ARM2i + HCO ARM2*i + O2 → ARM2*i + CO + CO ARM1i + ARM1i → ARM2i ARM1i + ARM2i → ARM2i ARM2i + ARM2i → ARM2i ARM2i + ARM2i → ARM3i ARM2i + O2 → ARM2i + ARM2i ARM2i + O2 → ARM2i + ARM1i ARM2i + O2 → ARM1i + ARM1i agglomerates of particles: ARM3
Rx22 Rx23 Rx24 Rx25 Rx25 Rx25 Rx26 Rx27 Rx27 Rx27 Rx27 Rx27 Rx28 Rx29 Rx30 Rx31 Rx32 Rx32 Rx32 Rx33 Rx33
ARM3i + H ↔ ARM3*i + H2 ARM3i + OH ↔ ARM3*i + H2O ARM3i → ARM3*i + H ARM3*i + ARM1*i → ARM3i ARM3*i + ARM2*i → ARM3i ARM3*i + ARM3*i → ARM3i ARM3*i + C2H2 → ARM3i ARM3*i + ARM1i → ARM3i + H ARM3*i + ARM2i → ARM3i + H ARM3*i + ARM3i → ARM3i + H ARM3i + ARM1*i → ARM3i + H ARM3i + ARM2*i → ARM3i + H ARM3i + H → ARM3i + H + H2 ARM3i + OH → ARM3i + HCO ARM3*i + O2 → ARM3*i + CO + CO ARM2i + ARM2i → ARM3i ARM3i + ARM3i → ARM3i ARM1i + ARM3i → ARM3i ARM2i + ARM3i → ARM3i ARM3i + O2 → ARM3i + ARM3i ARM3i + O2 → ARM3i + ARM2i
Figure 1. Schematic representation of aromatic molecules (ARM1 species) having approximately the same number of C-atoms and different H/C. Pericondensed aromatic hydrocarbons (panels a and b) and incompletely condensed aromatics (panels c and d).
(Rx7). Dehydrogenation has been already examined in a previous work on premixed flames,36 evaluating both its impact of the final prediction of particles amount and H/C ratio. The dehydrogenation is mandatory to predict the H/C ratio of the particles and thus their capability to give radicals and to chemically grow. It is not possible to predict reasonably the H/C of the high molecular mass species without taking into account a specific dehydrogenation channel. A single dehydrogenation channel has been considered. In contrast to the previous, published version of the model,35 here dehydrogenation has been considered to occur only on stable species and not on radicals. This affects premixed flames slightly but does change diffusion flame predictions. It is considered that during the dehydrogenation process, because of the complexity of the structures with increasing number of C atoms, the radicals formed through the attack of an H atom cyclize to form a closed aromatic ring. The limiting stage is the rearrangement of the structure to expel an H atom and to form a new stable species with a lower H/C ratio and consequently a higher aromaticity. An activation energy of 25,000 cal/mol has been estimated to better represent the experimental data,35 and dependence of the reaction rate on the number of H atoms in the structure is also considered. The molecular growth process competes with molecule oxidation by a hydroxyl radical and an O2 molecule (Rx8 and Rx9). The OH radical is used to oxidize the stable molecule, whereas the O2 molecule oxidizes the radicals. The activation energy of the oxidation by OH (Rx8) is estimated from similar reactions for benzene and PAHs, and the collision frequency accounts for the size of the particles involved. Oxidation by O2 molecules (Rx9) uses the rate constant of naphthyl + O2 accounting for the increase of collision frequencies of Xu et al.46 although the reactions for the lumped species cannot be considered as elementary reactions. Atomic oxygen, O, is not taken into consideration in the particle-phase reaction, being a species generally present at a concentration level more than one order of magnitude lower than OH overall in the flame. Together with chemical growth, the physical process of PAH coagulation (stacking), i.e. long-range interaction between colliding entities, occurs to form particle nuclei (Rx10).
(Rx5), whereas if an aromatic molecule is added an aromatic oligomer is formed (Rx6). The reaction rates for these reactions are built using the same activation energy as for the gas-phase reactions and taking into account the increasing collision frequency due to increasing size of the particles. An incompletely condensed aromatic can also undergo dehydrogenation reactions migrating to pericondensed molecules 2305
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with other molecules or other clusters (Rx20). If two clusters merge into one to reduce free surface area, so as to minimize free energy, a coalescence event occurs. The formed cluster assumes a spherical shape. As the cluster size increases, the time scale of the molecule coalescence becomes larger than the time scale of the agglomeration process. During the agglomeration process the colliding entities maintain their own structures, and they form agglomerates of particles (Rx21). The current model introduces a discretization which accounts for the formation of chainlike agglomerates of particles, defined as ARM3 in the tables. Particle agglomerates (ARM3) can undergo the same reactions as the clusters of molecules (ARM2) and the single molecules (ARM1) as reported in Table 1 (agglomerates of particles). The same kinetic parameters used to account for molecular growth and particle inception are also used for the reactions involving the primary particles (clusters of molecules - ARM2) and the particle agglomerates (ARM3). In this case Ci and Cj reported in the reaction rates represent the number of C atoms inside the reacting entities (molecules, particles, and aggregates of particles). The characteristic coalescence and agglomeration times for the particles are calculated following Sander et al.49 Particle and agglomerate coagulation use the same values of the coagulation efficiency calculated for molecules. Details of the evaluation of the passage from coalescence to agglomeration processes have been reported in a previous work.36 Model results show that particles with an equivalent size of about 10 nm have a rate of coalescence higher than that of agglomeration. This behavior is reversed for structures with equivalent size of about 20 nm. For particles of 10−20 nm, coalescence and agglomeration rates are similar which means that these particles can coalesce or agglomerate with the same probability. The coalescence-agglomeration ratio does not drastically affect the final concentration of the particles, but it does determine the size of the primary particles which constitutes particle agglomerates. The Particle Oxidation Mechanism. Particles can be oxidized in their stable and radical form by OH and O2, respectively. These processes are generally considered as surface processes able to subtract carbon atoms from the particles. Fragmentation of particles can occur if the oxidizing species is able to penetrate the particles and remove C atoms from a weak point causing the break-up of the particles and large aggregates into smaller particles and aggregates. These processes can be referred to as oxidation-induced fragmentation and can be seen as particular events of oxidation. Results by Sarofim and coworkers39,40 have shown the importance of oxidation-induced fragmentation in correctly determining the burnout rate of particles. The reactions of the fragmentation process have been included by Mueller et al.50 to account for particle size distribution in premixed flames. In that model only the fragmentation of aggregates was considered, whereas the break-up of single particles was not taken into account. Fragmentation can involve large aggregates containing a large number of primary particles. Stepwise splitting up of large aggregates because of oxidation-induced fragmentation can lead to smaller aggregates formed by just two primary particles. In this case a subsequent fragmentation forms isolated primary particles. Fragmentation can also involve primary particles where internal burning fragments single particle into smaller clusters. This process can continue producing very small cluster fragments.
The current model introduces a further discretization which accounts for the formation of clusters of molecules (particle nuclei) here defined as ARM2. Clusters of molecules are stacks of PAHs held together by van der Waals interactions. Binding energies which form these clusters depend on the dimensions of the interacting aromatic molecules and on the capability of the aromatic molecules to reach an interaction distance. PCAHs which have an intrinsic planar structure can easily reach an interaction distance and arrange in parallel stacks. Oligomers of aromatics tend to assume a nonplanar structure so that the steric conformation of these molecules hinders π-electrons of the molecules reaching an interaction distance. This conformation is responsible for lower binding energies. Dehydrogenation of molecules leads to a more pericondensed structure, inducing planarity in the molecules and increasing the capability of the molecules to reach an interaction distance. As a consequence, stacking of PAHs depends on molecule sizes and on the extent of the π-orbitals on the molecule. Molecule size is accounted for through the number of C-atoms, whereas the H/C accounts for the extent of the π-orbitals on the molecule: for the same C-atom number, high H/C means a low extent of the π-orbital in the molecule and consequently a nonplanar structure and hence a lower coagulation rate. On the other hand, low H/C means a large extent of the π-orbital on the molecule, resulting in an intrinsic planar structure and hence a higher coagulation rate. Molecule coagulation (Rx10) is considered irreversible at this stage, and its reaction rate is modeled by considering a coagulation efficiency with respect to the collision frequency. Collision frequency increases with the increase of molecular mass of the molecules, whereas the coagulation efficiency, γ, depends on both the temperature and chemistry of the colliding molecules. The Hamaker constant is used to account for molecule chemistry. From benzenic ring to graphite the Hamaker constant ranges from 3 × 10−20 J to 5 × 10−19 J. A value of 5 × 10−20 J has been assigned to a compound with an H/C ratio of 0.5. The values of the Hamaker constant for the other compounds have been linearly scaled on the H/C ratio. The coagulation efficiency is evaluated by following D’Alessio et al.47 γ = 1 − (1 + Φ0 /T) exp[−Φ0 /T]
(1)
evaluated as a function of the interaction potential Φ0 between coagulating entities. The latter is a linear function of the Hamaker constant.48 Values of the interaction potential Φ0 between coagulating entities for fixed temperature and Hamaker constant are reported in the Supporting Information. Computed coagulation efficiency is of the order of 10−4 for small colliding entities and increases to values of about 0.1 when the C number is about 106. These values are in agreement with experimental coagulation rates.47 The modeled results show that high H/C molecules, i.e. mostly comprising incompletely condensed aromatics and hence nonplanar compounds, have a much lower coagulation efficiency than low H/C molecules, i.e. planar pericondensed aromatic compounds, for the same number of C atoms.36 The Lumped Particle Growth Mechanism. Clusters of molecules, i.e. particle nuclei, (ARM2) can continue to react in the same way as the molecules (ARM1). Table 1 (clusters of molecules) reports the reactions involving ARM2 compounds. They can add molecules to increase their sizes (Rx11−Rx16) or remove H-atoms by dehydrogenation (Rx17) or C-atoms by OH and O2 oxidation (Rx18 and Rx19), or they can coagulate 2306
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referred to as Basic Structure Units (BSUs)52 can be schematized as cylindrical units having equal base diameter and length of about 1 nm. These BSUs are randomly organized in the particles and are separated from each other by “pores” having a length of the same order of magnitude of the BSU and a size of about 0.5 nm. Molecular oxygen oxidizes a particle on its surface, but it can also penetrate the pores internally to oxidize the particle. We have evaluated the Knudsen diffusion of molecular oxygen in the pores from the kinetic theory of gases by replacing the path length with the pore diameter and the rate of the surface oxidation by O2 for a range of particles. By comparing the characteristic diffusion time with the characteristic reaction time of surface oxidation with O2 at a flame temperature of 1500 K and with the geometrical characteristics of the pores above-reported, the process is in the reaction limited regime. This leads to the hypothesis that diffusivity of O2 is not the controlling step in the internal oxidation of particles. On the other hand, because of the faster reactivity of OH, it does not penetrate the pores but oxidizes the particle on its surface. When oxidation by O2 occurs in the depth of the pores, the particle can fragment into two parts by again considering the removal of δ C-atoms. The number of C-atoms in the BSU, nCBSU, is obtained from the above-described HR-TEM images; the BSU is estimated to contain 4 aromatic molecules each of 25 C-atoms. The number of BSUs constituting a particle, nBSU, is obtained by dividing the number of C-atoms in the particle by the number of C-atoms constituting the BSU
Fragmentation of aggregates (Rx33) and single particle fragmentation (Rx22) are conceptually different. The fragmentation of aggregates into smaller aggregates of primary particles is mainly linked with the presence of material condensed from the gas-phase or added to the particle by surface reactions which fill the space between the particle contact points. The fragmentation of particles into smaller particles deals with the internal structure of the single particles. The aggregates are fragmented when oxidation occurs at the contact points of the primary particles. Since particle aggregates break apart as a result of selective burning by molecular oxygen,39,40,50 the fragmentation rate should be related to the O2 oxidation rate. Molecular oxygen oxidizes the aggregate on its surface. If the oxidation occurs close to a weak link between two of the primary particles belonging to the aggregate, then fragmentation may occur. A fragmentation event can be modeled to occur after the removal of a fraction of C-atoms from the particles close to the point of contact between particles. It is considered that there is more than one pair of carbon atoms holding the aggregate together. The weak links are the contact points between the particles and the number of contact points in the aggregates can be estimated by dividing the total mass of the aggregates by the average mass of the primary particles. The probability that the oxidation occurs at a weak link between two particles is equal to the inverse of the number of active sites for O2 oxidation on the particle surface nactive sites = χπdP 2
(2)
n BSU = nC P /nC BSU
where χ is the number of sites per unit area, and πdP is the primary particle surface area. Each oxidation event removes 2 carbon atoms (Rx30). To have an oxidation event which is able to activate fragmentation, a fraction δ of C-atoms has to be removed. The number of C-atoms that must be removed to cause fragmentation can be expressed as 2
δC = α*nC P
The number of pores, npores, can be evaluated from the volume of a single pore relative to the particle volume. For cylindrical pores with a depth L, of the same order of magnitude of the BSU (1 nm) and diameter, w, of about 0.5 nm, the internal surface area of the pores is obtained. However, the point of weakness in the pore is considered to be at the bottom, and so only this fraction of pore area is used. Particle fragmentation rate is related to O2 oxidation rate by evaluating the probability that the oxidation occurs at the bottom of the pores after removal δ of C-atoms. This number of carbon atoms is given here by
(3)
where nCP is the total number of carbon atoms per primary particles, and α is the fraction of the total number of C-atoms constituting the primary particles to be removed. The fragmentation rate of aggregates is then given by k f = k O2*(nP − 1)/((χ *π *dP 2)*δC)
δCpores = β*nC P
(4)
(5)
P
where again nC is the total number of carbon atoms per primary particles, and β represents the fraction of C-atoms in the particle that must be removed to cause fragmentation of the particle. The fragmentation rate for the particles (Rx22) is then
where χ = 1.7 × 1019 m−2 is the number of sites per unit area.51 Here dP is the size of the primary particles, and nP is the number of primary particles in the aggregate which can be calculated as nP = nCA/nCP, where nCA is the number of C-atoms in the aggregate. A similar approach is used to model fragmentation of particles into smaller particles (Rx22). Experimental data obtained by HR-TEM on incipient particles52 show that that particles appear to be composed of clusters of aromatic compounds. Long range interactions between clusters and σ-bond connections between aromatic compounds belonging to different clusters are responsible for the coalescence of the aromatic clusters.53 Generally the average molecular mass of the aromatic compounds included in a cluster is such that its length in the HR-TEM images is of the order of 1 nm which corresponds to compounds having about 20−25 C-atoms. The number of aromatics in well-organized structures is always of the order of 4−5 stacked planes at a distance of about 0.35 nm.52 As a consequence, organized structures in incipient particles often
k f = k O2*(πw 2 /4/(πwL + πw 2 /4))*n pores /(δCpores)
(6)
Two adjustable parameters are present in the oxidationinduced fragmentation model, α and β, where α is the fraction of the total number of C-atoms constituting the primary particles to be removed to cause aggregate fragmentation, and β is the fraction of C-atoms in the particle that must be removed to cause fragmentation of the particle. We have used the experimental data of Echavarria et al.40 to estimate reasonable values of the two unknowns. In the Echavarria et al. experiment, a two-stage burner was used to generate soot in an ethylene-rich premixed flame, which served as the first stage; the soot was then burned in a secondary, ethylenelean premixed burner. Particle size distribution functions (PSDFs) 2307
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Figure 2. PSDFs measured by Echavarria et al.40 at different heights above the secondary flame burner (from the top: 0, 2.5, 3, 4, and 5 mm). Model predictions are compared considering fragmentation with different values of α, i.e. the aggregate fragmentation parameter 0.001 (dashed line), and 0.01 (full line), and without considering fragmentation (dotted line). Full line at HAB = 0 mm is the best fit of the experimental data.
Figure 3. PSDFs measured by Echavarria et al.40 at different height above the secondary flame burner (from the top: 0, 2.5, 3, 4, and 5 mm). Model predictions are compared for different values of α and β: full line (α = 0.01 and β = 0.05); black dashed line (α = 0.001 and β = 0.05); black dotted line (α = 0.1 and β = 0.05); gray dashed line (α = 0.01 and β = 0.005); gray dotted line (α = 0.01 and β = 0.5). 2308
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Figure 4. Number concentration of particles measured by Echavarria et al.40 in size intervals of less than (ultrafine mode - bottom) and greater than 10 nm (fine mode - top) compared with model predictions without fragmentation (dotted lines) and with fragmentation parameters set at α = 0.01 and β = 0.05 (full lines).
were measured with a scanning mobility particle sizer able to measure particles in the range from 3 to 160 nm. High dilution ratios were used to minimize particles losses and coagulation in the sampling system; corrections for diffusion losses and coagulation along the sampling line were carried out. In addition, temperature profiles and the concentrations of stable gases - H2, O2, CO, and CO2 - were measured along the secondary flame axis. This experimental setup allowed to investigate soot oxidation in several conditions of oxidant concentration. In particular, it was possible to tune the equivalence ratio in the flames in order to increase the relative abundance of O2 and OH and hence the relative importance of oxidation and fragmentation mechanisms. Echavarria et al. showed that evidence of particle fragmentation was observed only for the leaner flame in the range of height above the burner (HAB) from 0 to 5 mm. We have used such flame conditions − the leaner flame − to perform a sensitivity analysis of the oxidation parameters to the experimental data. Figure 2 shows the PSDFs measured at different heights above the secondary burner compared with model simulations for different values of α, i.e. the aggregate fragmentation parameter. Experimental PSDF at HAB = 0 mm showed that the initial distribution was mostly in the fine mode (particles diameter >10 nm) with little contribution of particles less than 10 nm. We have used the experimental temperature profile, experimental conditions measured at the surface of the top burner (mass flow rate, H2, CO, CO2, O2 concentration), and the PSDF which fits the experimental data as inputs to the model (line in Figure 2 at HAB = 0 mm). The PSDF at the top burner has been modeled as constituted by only particle aggregates. This hypothesis is confirmed by model simulations of rich premixed flames which show that particles larger than 10 nm
Figure 5. Temperature and species radial profiles in nonpremixed methane flame. From top to bottom: temperature, methane, acetylene, and benzene. Data from ref 56. Locations 10 mm (◇, . . .), 20 mm (□, - - - -), 25 mm (○, ____) above nozzle.
are essentially constituted by aggregates of primary particles.35 Modeled data have been shifted to correctly account for the sampling effects due to the water-cooled probe by matching the measured gas-phase species with the modeled ones. Experimental data showed this PSDF did not change significantly up to 2.5 mm. At 2.5 mm, particles in the ultrafine mode (particles diameter 3 mm, particles in the ultrafine mode are burned, as evidenced by the decrease in number concentration. The model reproduces the decrease of number concentration of the ultrafine particle mode but does not predict the almost complete burnout experimentally found. The decrease of the number of the fine mode particles is due to the fragmentation and oxidation of the larger aggregates.
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MODEL PREDICTIONS IN NONPREMIXED FLAMES The complete model is here used to simulate nonpremixed flames fuelled by methane and ethylene. Computations are carried out in a domain 100 mm axial by 50 mm radial. A typical grid size in the flame region being 0.1 mm radial by 1−2 mm axial has been used. Finer grids do not appreciably change the results. All the species equations are solved simultaneously at each spatial location in turn by 2310
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Figure 7. Predicted and measured temperature and species radial profiles in nonpremixed ethylene coflowing flame. Left 20 mm height, right 30 mm height. Experimental data from ref 57. Temperature (□, ___); ethylene (◆, - - - -); acetylene (■, ___); benzene (●, ___).
into approximate agreement with the measured temperatures. For both methane and ethylene diffusion flames the same values for the soot absorption coefficient are used. It is worth noting that the matching of the temperature is not an adjustment to the scheme but a way to correctly take into account the radiation process.21 The flames have been studied experimentally by several research groups using a variety of techniques to measure particles. They include sampling and chemical analysis of gaseous stable species,56,57 thermophoretic mass transfer and chemical characterization of condensed species,38,56 UV-laser induced emission spectroscopy (laser-induced incandescence and laser induced fluorescence),58,59 and broadband absorption measurements and laser scattering/extinction.60,61 For all the investigated flames the simulations have been performed setting the fragmentation parameters at α = 0.01 and β = 0.05. Figure 5 shows modeled concentration profiles of methane, acetylene, and benzene against experimental data from Smooke et al.56 in a nonpremixed, coflowing methane/air flame. Predicted temperatures are obtained by setting the radiation soot absorption coefficient to match measured temperature at the location of peak temperature. Temperature profiles are also shown in Figure 5. The methane fuel concentration shows that the general shape and structure of the nonpremixed flame is
a modified Newton−Raphson scheme. Velocity and enthalpy employ a tridiagonal matrix form of solution. For a converged solution, the mean absolute residual for a species, normalized by the species maximum value, is typically of order 10−8, and overall carbon element mass balance error is less than 0.1%. Transport and thermodynamic properties for the gas-phase species are from the Chemkin41 database. Binary diffusion coefficients of species in nitrogen are used, and the gas viscosity is approximated as that for nitrogen at every temperature. Diffusivities of the large sectional species are obtained from Stokes friction with Cunningham correction factors based on the Knudsen number.54 Thermophoretic flux is applied to all the sections. The enthalpies of the sectional species are made the same per unit mass as that for pyrene; sectional species reactions do not change mixture temperature. The molecular mass distribution is defined by a range of thirty-one sections; the last section results empty for all the investigated cases, indicating that the scheme is not artificial constricted. The energy equation is fully solved and temperature is calculated. Radiative transfer is modeled by the discrete transfer method.55 Radiation heat loss is strongly influenced by the absorption coefficient of soot whose concentration is a dependent variable here. The soot absorption constant is therefore set to a fixed value to bring the predicted temperatures 2311
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Figure 8. Total particulate volume fraction (left) and mean particle size (right) profiles in nonpremixed ethylene coflowing flame. From bottom to top radial profiles at 20 mm, 30 mm, 60 mm, and 70 mm height. Volume fraction data by laser induced incandescence.59 D63 data by scattering and extinction.60,61 Modeled data: continuous lines represents results of the complete mechanism, dashed lines represents results of the mechanism without particle fragmentation induced by oxidation (divided by 3).
particle sizes dominate the whole field, as shown on the right side of Figure 6. The particle mean size D63 is defined as
represented well. The important pyrolysis species in the processes of soot inception and growth, acetylene and benzene, are also shown. The model somewhat underpredicts their concentrations on the flame axis, whereas off-axis (where most part of the soot is formed) the predictions are better. Radial profiles of predicted and measured particulate volume fraction are reported at three heights on the left side of Figure 6. Total particulates measured by thermophoretic deposition56 and by laser induced fluorescence and incandescence emission58 are shown, and the variation in the data indicates the uncertainty in these measurements. In any case the total particulate volume fraction in the methane flame is low, approximately 1 ppm maximum, and the model is in accordance with the data. Small
D63 = {Σ(NiDi6)/Σ(NiDi 3)}1/3
(7)
and is in the range of 1−7 nm, i.e. mainly nanoparticles. The model predicts this size range. Figure 6 reports as dashed lines the model predictions if the oxidation induced fragmentation model was removed from the kinetic scheme. The effect of the fragmentation model on the total particulate volume fraction is not strong at the three heights. Conversely, fragmentation affects the prediction of the mean particle sizes which are about a factor of 3−5 larger when fragmentation is not taken into account. 2312
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The nonpremixed, coflowing nonsmoking ethylene/air flame of Santoro and co-workers57,60,61 has also been modeled. Figure 7 shows the comparison between predicted and measured temperature and species for this flame. Temperature, ethylene, acetylene, and benzene profiles are shown at 20 mm and 30 mm above the nozzle. The temperature and the fuel concentration are well represented by the model at all heights. Benzene and acetylene predictions are somewhat high in the lower part of the flame and do not show the measured decay of these species at 30 mm height. Radial profiles of particulate volume fractions are shown on the left side of Figure 8 at measurement heights, 20, 30, 60, and 70 mm above the nozzle. Attention is focused onto soot volume fractions measured by LII,59 which are an order of magnitude higher than in the methane flame (Figure 6) with maximum values of 8 ppm. The model gives good predictions of soot volume fractions and in particular reproduces the observed burnout of particles at 70 mm. Particle size D63 is shown on the right side of Figure 8 at the same heights. In contrast to the methane flame large particles are formed in this flame with sizes of the order of 100−200 nm.60 The model responds well to the heavily sooting fuel by generally representing the measured sizes of the particles. The predictions are in excellent agreement in the flame wings whereas the model reproduces the experimental data by a factor of 3 along the flame axis. This discrepancy can be mostly associated with the large uncertainty in measuring on the flame axis. This is true for soot volume fraction and even more for the D63 measurements which derive from a complex procedure involving a chordal inversion.60 Nevertheless, it is without doubt that the model reproduces trends and maximum values of soot and D63 correctly. Figure 8 reports as dashed lines the model predictions without particle fragmentation by oxidation. Oxidation-induced fragmentation, which is in parallel with surface oxidation, reduces particle size thereby increasing the number concentration and also the rate of oxidation. The inclusion of oxidation-induced fragmentation pathways has improved model accuracy relative to our previous work21 to predict particle size and complete particle burnout. The oxidation by OH radical remains a major process also in the examined conditions, but the fragmentation due to molecular oxygen appears to be determinant for the complete burnout of the soot particles. The model correctly reproduces soot concentrations in the wings. Mean particle sizes are also well reproduced. Maximum particle size is of the order of 100−150 nm compared with about 300−400 nm without fragmentation. The H-to-C ratio of the particulate collected along the flame axis was measured by Dobbins et al.38 The discrimination between C and H in the model allows us to calculate the H/C in the diffusion flame. Figure 9 shows the comparison between measured and calculated H/C along the axis of the nonsmoking ethylene flame. Particles were extracted from selected heights of this nonpremixed, coflowing, ethylene flame using thermophoretic sampling followed by chemical analysis by laser microprobe mass spectroscopy.38 The model follows the trend of H/C showing values of about 0.7, typical of PAH, close to the nozzle. Thereafter at about 40 mm, H/C decreases sharply to about 0.2−0.3 where soot formation starts on the flame axis. The model does not correctly predict the height where H/C decreases, whereas the overall prediction of the dehydrogenation process is matched. The discrepancy found in the location, along the flame axis, of the dehydrogenation process is within
Figure 9. Comparison of predicted H/C along the flame axis of nonpremixed ethylene flame with experimental data from ref 38.
the experimental error, which can be reasonably evaluated to be at least ±1 mm, due to the insertion of a probe in a diffusion flame.
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CONCLUSIONS The newly developed scheme for aromatic growth, particulate formation, and oxidation is presented and tested over a range of different operating conditions in rich premixed and nonpremixed flames of methane and ethylene. The kinetic model has been refined by comparing model predictions with experimental data for the formation and oxidation of high molecular mass species and particles. Good predictions are obtained for major oxidation and pyrolysis products, trace species, particle concentrations, and particle size distributions. The predictions in premixed and nonpremixed flames of methane and ethylene at atmospheric pressure are made without any condition-dependent adjustments to the scheme. The model predicts well particle concentrations of less than 1 ppm and 2 nm size in methane flames to 8 ppm and 150 nm in ethylene flames. The model predicts H/C of particles along the flame axis. In the external zones of nonpremixed flames, the particle size distribution functions develop toward a bimodal shape and H/C decreases to very low values typical of mature soot particles. Both effects are well captured by the model. Particle burnout is now well predicted by the inclusion of oxidation-induced fragmentation. This is an important phenomenon needed to obtain correct particle size and to predict complete soot burnout in nonpremixed flames.
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ASSOCIATED CONTENT
S Supporting Information *
The complete list of the reactions involved in the oxidation and pyrolysis of the fuels and the complete list of the lumped mechanism of molecular growth and particle inception used to simulate diffusion flame configurations. The values of the interaction potential between coalescing and agglomerating entities are also reported. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest. 2313
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NOMENCLATURE ARM1 = a lumped molecule in its stable form ARM1* = a lumped molecule in its radical form ARM2 = a cluster of molecules in its stable form ARM2* = a cluster of molecules in its radical form ARM3 = a chainlike aggregate of particles in its stable form ARM3* = a chainlike aggregate of particles in its radical form Clusters = stacks of PAHs held together by van der Waals interactions Aggregates = agglomerates of particles formed when the colliding entities maintain their own structures Stacking = long-range interaction between colliding PAHs Coagulation = long-range interaction between colliding entities Coalescence = merging of two clusters into one to reduce free surface area to minimize free energy. The so formed cluster assumes a spherical shape and can be seen as a larger cluster of molecules than the previous two Agglomeration = coagulation of two clusters maintaining their own structure. The formed entity assumes a chainlike structure Fragmentation = the break-up of particles and large aggregates into smaller particles and aggregates
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