Understanding Soot Particle Growth Chemistry and Particle Sizing Using a Novel Soot Growth and Formation Model

Transcription

1 Understanding Soot Particle Growth Chemistry and Particle Sizing Using a Novel Soot Growth and Formation Model by Armin Veshkini A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Department of Mechanical and Industrial Engineering University of Toronto Copyright by Armin Veshkini, 2015

2 Understanding Soot Particle Growth Chemistry and Particle Sizing Using a Novel Soot Growth and Formation Model Abstract Armin Veshkini Doctor of Philosophy Department of Mechanical and Industrial Engineering University of Toronto 2015 Research efforts are focused on advancing the understanding of soot modeling by computing soot formation in laminar flames using a detailed sectional aerosol dynamic model. Toward an end goal of developing a robust model of soot formation applicable to a wide range of conditions, soot coalescence models are introduced, a correlation for the surface reactivity is proposed, PAH contributions to soot formation in premixed and nonpremixed flames are investigated, and a condensation efficiency model is developed and validated. The effects of the soot coalescence process on soot particle diameter predictions are studied. Two coalescence models based on different merging mechanisms are implemented into the soot model. The models are applied to a laminar ethylene/air diffusion flame, and comparisons are made with experimental data to validate the models. The implementation of coalescence models significantly improves the agreement of prediction of particle diameters with the experimental data. A comprehensive study follows in which a function for surface reactivity of soot particles is developed to eliminate tunable constants, and have a single model able to predict soot in many ii

3 coflow ethylene/air flames. This study investigates how the surface reactivity of soot particles varies with particle thermal age. The surface reactivity function is applied to coflow diffusion flames with varying fuel/air ratios and fuel dilution, and to partially premixed coflow flames for a range of equivalence ratios. Comparisons are made with experimental data to validate the model. Very good agreement is seen between numerical predictions and experimental measurements for soot volume fraction on the annular regions of the flames. The final part of this thesis explores the role of PAH-soot modeling on burner stabilized stagnation premixed flames and a coflow diffusion flame. Two chemical mechanisms are employed to model both flames. It is found that one of the mechanisms gives more accurate description of the PAH chemistry in premixed flames while the other improves the agreement of soot predictions in diffusion flames and the results and conclusion are drastically effected by the choice of PAH mechanism. An equilibrium based condensation efficiency model is developed and combined with a reversible nucleation model to predict soot formation in both premixed and nonpremixed flames. Compared to the measured data, soot PSDs are reasonably well predicted. Effects of different soot formation processes on PSD predictions are characterized. In the diffusion flame, soot predictions with the developed soot model are comparable with the previous soot model predictions. However, employing a reversible nucleation model leads to a delay in onset of soot formation in the diffusion flame. iii

4 Acknowledgments I would like to express my deepest gratitude to my supervisors, Professor Murray J. Thomson and Professor Seth B. Dworkin for their constant guidance and support through my studies at the University of Toronto. Thank you both for being a wise guide, a passionate leader, and a good friend. Much appreciation to Professor Ömer L. Gülder and Professor Markus Bussmann for being members on my PhD supervisory committee. I also thank Professor James S. Wallace for serving on my examination committee. It was an honour to have Professor Andrea D Anna from the University of Naples Federico II serving as my external examiner. His insights into my work were invaluable. I would also like to thank Dr. Nadezhda Slavinskaya and Professor Uwe Riedel of the German Aerospace Center (DLR) for providing the chemical reaction mechanism, thermodynamic data, and transport data for ethylene combustion and PAH formation. Gratefulness to all my colleagues in the Combustion Research Group, specifically, Mohammadreza Kholghy, Babak Borshanpour, Amir Alikhanzadeh, Kaveh Khalilian, Milad Zarghami, Sina Moloodi, Dr. Tommy Tzanetakis, and Dr. Victor Chernov. I also owe a debt of gratitude to Dr. Meghdad Saffaripour for his friendship through many years of collaboration. My contemporary, Nick Eaves, deserves a special recognition for sharing his knowledge and fruitful discussions. Lastly, I owe my gratitude to my parents who are unwavering sources of encouragement and support. I also want to express my gratitude to Leila whose love and support have made this thesis possible. Computations were performed on the Ryerson University Sandy Bridge computing cluster and the GPC supercomputer at the SciNet HPC Consortium. SciNet is funded by: the Canada Foundation for Innovation under the auspices of Compute Canada; the Government of Ontario; Ontario Research Fund Research Excellence; and the University of Toronto. iv

5 Table of Contents Acknowledgments... iv Table of Contents... v List of Tables... ix List of Figures... x List of Appendices... xix Chapter 1 Introduction Motivation Literature Review Soot Characteristics Soot Formation Pathways Soot Modeling Objectives and Outline of Subsequent Chapters Chapter 2 Mathematical Model Overview Gas-Phase Governing Equations Conservations of Mass and Momentum The Two-Dimensional Cylindrical Coordinates The One-Dimensional Similarity Solution Conservation of Energy Radiation Heat Transfer Optically thin approximation (OTA) Discrete-ordinate method (DOM) Conservation of Species Mass Chemical mechanism DLR mechanism KAUST mechanism Soot Aerosol Dynamics Model The sectional aerosol dynamics model Nucleation model v

6 Condensation model Chemical surface growth and oxidation models Coagulation model Fragmentation model Transport Properties Diffusion coefficients Numerical Methods D coflow diffusion flame Boundary conditions Premixed stagnation flame Boundary conditions Chapter 3 Soot Particle Coalescence Overview Introduction The Collision-Coalescence Mechanism Rate of Coalescence Viscous Flow Transport Transport by Diffusion Coalescence Model Cut-off Model (Model I) Sintering Model (Model II) Methodology Numerical Model Results and Discussion Annular Pathline Comparison Centerline Comparison Sensitivity analysis Cut-off Diameter Coalescence Characteristic Time Coalescence and Oxidation Conclusions vi

7 Chapter 4 Soot Particle Surface Reactivity Overview Introduction Numerical Model Methodology Soot Surface Reactivity Thermal Age Results and Discussion Surface Reactivity Analysis Parameter Study Gas phase chemistry parameters Soot model parameters Conclusions Chapter 5 Reversibility of Nucleation and Condensation Introduction Methodology Burner and Flame Description Model Description Sectional aerosol dynamic model Reversible nucleation Condensation Efficiency Soot models Results and Discussion PAH Chemistry Reversible Nucleation Model Condensation Efficiency Sensitivity analysis Diffusion Flames Conclusions Chapter 6 Conclusions and Future Work Summary and Conclusions vii

8 6.2 Original contributions Recommendations for future work Appendices Bibliography viii

9 List of Tables Table 2.1 Table 4.1 HACA based soot surface growth and oxidation reactions [86], k = ATbe EaRT HACA based soot surface growth and oxidation reactions [86], k = ATbe EaRT Table 4.2 Proposed functional forms of α for models based on the HACA mechanism Table 4.3 Proposed functional forms of α for models based on the HACA mechanism Table 4.4 Table 5.1 Flames used to derive a function for surface reactivity and the optimized α for each flame that reproduces the most accurate soot concentration on the wings Difference between nucleation and condensation models used to simulate flames ix

10 List of Figures Figure 1.1 Figure 1.2 TEM images of soot particle samples along the centerline of a coflow diffusion flame of a surrogate for Jet A-1 at different heights above the fuel tube exit (Source: Reprinted from ref. [35]) TEM image of soot sample formed from ethylene pyrolysis in a flow reactor at 1475 K in the presence of nitrogen oxides (specifically N 2 O); (Source: Reprinted from ref. [72]) Figure 1.3 Schematic diagram of soot formation (Source: Reprinted from ref. [89]) Figure 2.1 Figure 2.2 Figure 2.3 Figure 2.4 Figure 2.5 Schematic representation of a coflow flame, including coordinate orientation and computational domain (not drawn to scale) Schematic representation of a burner stabilized stagnation flame, including coordinate orientation Schematic representation of the major reaction pathways for the formation of large PAHs considered by the DLR chemical kinetic mechanism Schematic representation of the major reaction pathways for the formation of large PAHs considered by the KAUST chemical kinetic mechanism Processes shaping the particle size distribution function in a small volume element of gas. Diffusion and sedimentation involve transport across the walls of the element. Coagulation, nucleation, and growth take place within the element. (Source: Reprinted from ref. [106]) Figure 2.6 Illustration of armchair sites on the surface of a soot particle Figure 2.7 Coflow code solver program structure Figure 2.8 Schematic of the coflow diffusion flame boundary conditions and the non-uniform structured mesh Figure 3.1 Schematic of coalescence process of two colliding particles Figure 3.2 TEM images of soot particle samples along the centerline of a coflow diffusion flame of a surrogate for Jet A-1 at different heights above the fuel tube exit (Source: Reprinted from ref. [35]) x

11 Figure 3.3 Schematic representation of aggregate formation with cut-off coalescence Figure 3.4 Schematic representation of the sintering model for soot particle coalescence Figure 3.5 Figure 3.6 Figure 3.7 Figure 3.8 Figure 3.9 Schematic representation of burner configuration of Santoro flame [58]. [Courtesy of Dr. Meghdad Saffaripour, University of Toronto.] Comparison of the predicted soot volume fraction along the annular pathline exhibiting the maximum soot volume fraction using a sintering coalescence model (solid line), the cut-off coalescence model (dashed line) and no coalescence (dotdashed line) with the experimental measurements by [58] Comparison of the predicted soot volume fraction along the annular pathline exhibiting the maximum soot volume fraction using a sintering coalescence model (solid line), cut-off coalescence model (dashed line) and no-coalescence (dotdashed line) with the experimental measurements by [192] Comparison of the predicted average primary particle diameter along the annular pathline exhibiting the maximum soot volume fraction, using a sintering coalescence model (solid line), cut-off coalescence model (dashed line) and no coalescence (dot-dashed line) with the experimental measurements by [56] Comparison of the predicted primary particle number density along the annular pathline exhibiting the maximum soot volume fraction using a sintering coalescence model (solid line), cut-off coalescence model (dashed line) and no coalescence (dot-dashed line) with the experimental measurements by [39,57] Figure 3.10 Comparison of the predicted aggregate number density along the annular pathline exhibiting the maximum soot volume fraction using a sintering coalescence model (solid line), cut-off coalescence model (dashed line) and no coalescence (dotdashed line) with the experimental measurements by [57,192] Figure 3.11 Figure 3.12 Comparison of the predicted average number of primary particles per aggregate along the annular pathline exhibiting the maximum soot volume fraction using a sintering coalescence model (solid line), cut-off coalescence model (dashed line) and no coalescence (dot-dashed line) with the experimental measurements by [57,192] Comparison of the predicted average primary particle diameter along the centerline using a sintering coalescence model (solid line), cut-off coalescence model (dashed line) and no coalescence (dot-dashed line) with the experimental measurements by [37] xi

12 Figure 3.13 Figure 3.14 Figure 3.15 Figure 3.16 Figure 3.17 Figure 3.18 Figure 3.19 Figure 3.20 Comparison of the predicted soot volume fraction along the centerline using a sintering coalescence model (solid line), cut-off coalescence model (dashed line) and no coalescence (dot-dashed line) with the experimental measurements by [37,38,58] (a log scale is used so that comparisons can be made at heights less than 4 cm) Variation of surface to volume ratio along the centerline using a sintering coalescence model (solid line), cut-off coalescence model (dashed line) and no coalescence (dot-dashed line) Comparison of the predicted average primary particle diameter using different cutoff diameter coalescence models a) along the annular pathline exhibiting the maximum soot volume fraction with the experimental measurements by [56] and b) along the centerline with the experimental measurements by [37] Variation of the characteristic coalescence time of a 10 nm soot particle with temperature with four different activation energies Comparison of the predicted average primary particle diameter along the annular pathline exhibiting the maximum soot volume fraction using a) different activation energy and b) different pre-exponential factor for the sintering coalescence model with the experimental measurements by [56] Effect of reduction of characteristic time on the predicted maximum primary particle diameter along the annular pathline exhibiting the maximum soot volume fraction Computational isotherms (left panel) and isopleths of O 2 mole fraction (right panel) in the Santoro coflow diffusion flame Comparison of the predicted average primary particle diameter along the annular pathline exhibiting the maximum soot volume fraction using different sintering coalescence models with an oxidation cut-off, and the experimental measurements by [56] Figure 4.1 Illustration of armchair sites on the surface of a soot particle Figure 4.2 Total mass yield (gsoot/gmix) by all soot growth processes, HACA surface growth, and inception plus PAH condensation for a soot particle travelling a) along the centerline and b) along the pathline of maximum soot on the wings, for the Santoro flame [58] (SA) xii

13 Figure 4.3 Comparison of computed peak soot volume fractions on the wings using α = 0.45 for all SM and SA flames with experimental data from [192] and [41] for coflow diffusion ethylene-air flames Figure 4.4 Figure 4.5 Figure 4.6 Figure 4.7 Figure 4.8 Figure 4.9 Figure 4.10 Comparison of computed peak soot volume fractions on the wings using an optimized average α for each flame (The value of α for each flame is shown below the computed result) with experimental data from [192], [41] and [212] for coflow diffusion ethylene-air flames Average soot particle surface reactivity, α, as a function of a) peak flame temperature and b) instantaneous temperature at the peak soot concentration on the wings a) Average soot particle surface reactivity, α, as a function of thermal age at the location of peak soot concentration on the wings (the line is the correlation for α, Eq. 4.5). b) The integral of α, as a function of thermal age at the location of peak soot concentration on the wings (the line is the integral of the correlation for α, Eq. 4.6) Comparison of computed peak soot volume fractions on the wings using the α function based on thermal age (Eq. 4.6), with experiments from [29,41,192,212].88 Isopleths of soot volume fraction (ppm) of the SM40 (left panel), SM80 (middle panel) and SA (right panel) flames. The left side of each panel is the model computed with the new α function. The right side is the experimental data ([41] and [212]) Variation of surface reactivity and soot volume fraction as a function of soot particle residence time along the wings for SA and SM60 flames Variation of surface reactivity and soot volume fraction as a function of soot particle thermal age along the wings for SA, SM80 and SM40 flames Figure 4.11 Comparison of computed (left panel) and experimental (right panel, from [192]) isotherms of the SA flame Figure 4.12 Figure 4.13 Comparison of numerical and experimental (from [215] and [37].) temperature profiles along the centerline of the flames, as a function of axial height Comparison of the computed (lines) and experimental (symbols) a) concentrations of acetylene at the z = 7 mm and z = 20 mm axial heights as a function of radial distance from the centreline for the SA flame (measurements from [34]) b) xiii

14 concentrations of acetylene on the centreline for the SM40 and SM80 flames (measurements from [215]) c) concentrations of benzene on the centreline for the SM40, and SM80 flames (measurements from [215]) Figure 5.1 Schematic representation of a burner stabilized stagnation flame, including coordinate orientation Figure 5.2 Condensation efficiency (Eq. 5.1) variation with temperature Figure 5.3 Figure 5.4 Figure 5.5 Comparison of experimental data (symbols) from [19] and calculated (lines) centerline temperature profiles at several separation distances between the burner and stagnation surface. Temperature measurement uncertainties and the positional uncertainty are shown with bars Main species profiles computed with the KAUST mechanism (solid lines), and with the DLR mechanism (dashed lines) for a burner stagnation surface separation of Hp = 1.0 cm Main radicals and small aromatic molecules profiles computed with the KAUST mechanism (solid lines), and with the DLR mechanism (dashed lines) for a burner stagnation surface separation of Hp = 1.0 cm Figure 5.6 Comparison of computed soot volume fraction (of which the particle diameter, D > 2.5 nm) of the KAUST and DLR mechanisms with Model 1 as a function of separation distance with experimental data [21] Figure 5.7 Figure 5.8 Computed benzo(a)pyrene (A5) mass fraction profiles with the DLR mechanism as a function of height above the burner for six different burner stabilized stagnation flames Computed anthanthrene (A6) mass fraction profiles with the KAUST mechanism as a function of height above the burner for six different burner stabilized stagnation flames Figure 5.9 Comparison of soot particle number density (of which the particle diameter, D > 2.5 nm) computed with constant efficiency nucleation (Model 1), reversible nucleation and constant efficiency condensation (Model 2), and reversible nucleation and temperature dependent condensation efficiency (Model 3) as a function of separation distance, with experimental data [21] Figure 5.10 xiv Comparison of soot volume fraction (of which the particle diameter, D > 2.5 nm) computed with constant efficiency nucleation (Model 1), reversible nucleation and constant efficiency condensation (Model 2), and reversible nucleation and

15 temperature dependent condensation efficiency (Model 3) as a function of separation distance, with experimental data [21] Figure 5.11 Figure 5.12 Figure 5.13 Figure 5.14 Figure 5.15 Figure 5.16 Figure 5.17 Figure 5.18 xv Comparison of computed soot particle size distributions using reversible nucleation and constant efficiency condensation (Model 2), and reversible nucleation and temperature dependent condensation efficiency (Model 3) at several separation distances between the burner and stagnation surface, with experimental data [21] Equilibrium constant for dimerization of PAHs employed in the reversible nucleation model with different average vibration frequencies as a function of temperature Comparison of computed soot particle size distribution using different intermolecular vibrational frequencies for the reversible nucleation model and a constant efficiency condensation (γcond = 5%) at several separation distances between the burner and stagnation surface with experimental data [21] (effect of vibrational frequencies on Model 2 predictions) Computed anthanthrene (A6) mass fraction profiles as a function of height above the burner for the Hp = 1.2 cm burner stabilized stagnation flame using three models: without soot, with dimerization frequency of 26 cm -1, and with dimerization frequency of 14 cm Comparison of computed soot particle size distribution with reversible nucleation model and different constant efficiencies for condensation (γcond) at several separation distances between the burner and stagnation surface with experimental data [21] (effect of condensation on Model 2 predictions) Comparison of computed soot particle size distribution using different coagulation efficiencies for the reversible nucleation model and constant efficiency condensation (γcond = 5%) at several separation distances between the burner and stagnation surface, with experimental data [21] (effect of coagulation on Model 2 predictions) Comparison of (a) soot particle number density and (b) soot volume fraction (of which the particle diameter, D > 2.5 nm) computed with reversible nucleation and equilibrium based condensation efficiency (Model 4), and reversible nucleation and a constant efficiency condensation (Model 2), as function of separation distance, with experimental data [21] Comparison of computed soot particle size distribution using reversible nucleation and equilibrium based condensation efficiency (Model 4), and reversible

16 nucleation and a constant efficiency condensation (Model 2), at several separation distances between the burner and stagnation surface, with experimental data [21] Figure 5.19 Figure 5.20 Figure 5.21 Figure 5.22 Figure 5.23 Figure 5.24 Figure 5.25 Comparison of effects of (a) dimerization binding energy, (b) dimerization vibrational frequency, (c) surface reactivity, and (d) condensation vibrational frequency on computed soot particle size distribution using reversible nucleation and equilibrium based condensation efficiency (Model 4) for the 0.8 cm separation distances between the burner and stagnation surface flame with experimental data [21] Isopleths of soot volume fraction (ppm) of the Santoro ethylene/air coflow diffusion flame [58] computed using Models 1, 2, and 4 and experimental data from [212] Computed contours of particle number density (cm -3 ) with Model 1, Model 2, and Model 4 of the Santoro ethylene/air coflow diffusion flame [58] Computed contours of anthanthrene, A6, mole fraction with Model 1, Model 2, and Model 4 of the Santoro ethylene/air coflow diffusion flame [58] Comparison of the predicted a) soot volume fraction, b) average primary particle diameter, c) primary particle number density, and d) aggregate number density along the annular pathline exhibiting the maximum soot volume fraction of the Santoro ethylene/air coflow diffusion flame [58] using Model 1 (dot dashed line), Model 2 (dashed line), and Model 4 (solid line), with the experimental measurements by [39,57,58,192] Comparison of the predicted a) soot volume fraction, b) average primary particle diameter, c) primary particle number density, and d) aggregate number density along the centerline of the Santoro ethylene/air coflow diffusion flame [58] using Model 1 (dot dashed line), Model 2 (dashed line), and Model 4 (solid line), with the experimental measurements by [37 39,58,192] Isopleths of soot volume fraction (ppm) of the Santoro ethylene/air coflow diffusion flame [58] computed using the KAUST and DLR mechanisms and soot Model 4, with experimental data from [212] Figure a. 1 xvi Predicted particle size distribution functions at different axial heights above the burner along the annular pathline of the maximum soot volume fraction, and along the centerline

17 Figure b. 1 Figure b. 2 Figure b. 3 Figure b. 4 Figure b. 5 Figure b. 6 Figure b. 7 Figure b. 8 Figure b. 9 Comparison of the predicted soot volume fraction along the wings using alpha function (solid line) and constant alpha (dashed line) with the experimental measurements by [58] Comparison of the variation of predicted soot volume fraction with residence time along the wings using alpha function (solid line) and constant alpha (dashed line) with the experimental measurements by [192] Comparison of the predicted average primary particle diameter along the wings using alpha function (solid line) and constant alpha (dashed line) with the experimental measurements by [56] Comparison of the predicted primary particle number density along the wings using alpha function (solid line) and constant alpha (dashed line) with the experimental measurements by [39,57] Comparison of the predicted aggregates number density along the wings using alpha function (solid line) and constant alpha (dashed line) with the experimental measurements by [57,192] Comparison of the predicted number of primary particles per aggregate along the wings using alpha function (solid line) and constant alpha (dashed line) with the experimental measurements by [33,57] Comparison of the predicted soot volume fraction along the centerline using alpha function (solid line) and constant alpha (dashed line) with the experimental measurements by [37,38,58] Comparison of the predicted average primary particle diameter along the centerline using alpha function (solid line) and constant alpha (dashed line) with the experimental measurements by [37] Comparison of the predicted aggregates number density along the centerline using alpha function (solid line) and constant alpha (dashed line) with the experimental measurements by [192] Figure b. 10 Comparison of the predicted number of primary particles per aggregate along the wings using alpha function (solid line) and constant alpha (dashed line) with the experimental measurements by [37] xvii

18 Figure c. 1 Figure c. 2 Comparison between experimental data from [233] and calculated mole fraction of major gaseous products Comparison between experimental data from [233] and calculated mole fraction of benzene and various PAHs xviii

19 List of Appendices Appendix A Appendix B Appendix C xix

20 1 Chapter 1 Introduction 1.1 Motivation More than 80% of the world s energy supply comes from hydrocarbon sources including natural gas, petroleum, and coal [1]. It is expected that the total demand for energy will increase steadily throughout the world with particularly large increases in the demands from emerging economies. Total world consumption of liquid fuels, as a sample of the world s hydrocarbon consumption, is estimated to increase by 33 MMbbl/d throughout the course of thirty years, starting from 2010, which is equivalent to 30% of the current consumption [2]. Energy use has adverse environmental and health consequences that have led to considerable restrictive regulations. Particulate matter (PM) is a known pollutant and its health and environmental consequences are linked directly to their size. Combustion-derived nano-particles, such as soot, are a significant source of particles smaller than 2.5 µm (PM 2.5 ) in urban areas. The role of the chemical composition of the particles or the source of the particles on their adverse effects are yet to be examined, however, health outcomes have a stronger correlation with exposure to combustionderived particulates than with particulates from other sources [3]. U.S., Canadian and Europe-based epidemiological studies have measured relationships between exposure to PM 2.5 and health outcomes including: cardiovascular morbidity, respiratory symptoms, increases in hospitalization; mortality from cardiovascular and respiratory diseases

21 2 and from lung cancer, along with various other health complications [4]. The International Agency for Research on Cancer recently listed the exhaust from diesel engines, and exposures to some PAHs as carcinogenic [3]. Polycyclic aromatic hydrocarbons (PAH), as well as metals and inorganic salts are among the constituent elements of soot particles. These components are currently seen as responsible for the hazardous nature of combustion-driven particulate matter. The environmental effects of particulate matter are mainly related to PM s optical properties. These effects of PM include impairment of visibility in rural and urban areas, effect on climate by scattering incoming solar radiation and influencing cloud properties, and ecological effects [4]. For these reasons, stricter regulations are now targeting particulate emissions in both automotive (e.g., EURO 6) and aviation (e.g., ICAO) engines. Most of these regulations set limitations for the cumulative particulate mass emissions over different periods of time. However, there are growing concerns that potential effects of other particulate characteristics, such as particle number, particle morphology, and detailed chemical speciation on the environment and health should be considered [5 8]. In this way, a comprehensive understanding of the risks associate with PMs may be achieved [9]. Thus, understanding the soot mass growth mechanisms as well as formation of particle size distributions has received significant attention. Controlling particulate emissions to abide with regulations while maintaining high efficiency has been one of the challenges of combustion research and development. Novel combustion strategies include low-temperature combustion (LTC) strategies as in homogeneous charge compression ignition (HCCI), stratified-charge, compression-ignition (SCCI), and gasoline direct injection (GDI) in internal combustion engines, and staged combustion in advanced gas turbines, such as twin annular premixing swirler (TAPS) mixer technology [10]. These strategies offered a significant fuel efficiency improvement and pollutant emissions reduction potential. To address the challenges facing developing significantly more fuel efficient engines, it is crucial to advance the science underpinning novel combustion strategies. Advancements needed relevant to soot emission include: a fundamental understanding of soot formation in lean (diluted) fuel-air mixtures at high pressure and temperature conditions representative of internal combustion engine and gas turbine enviroments; robust soot models based on the fundamental chemical and

22 3 physical processes and their coupling in novel combustion regimes; a framework for developing a multiscale model by combining the computational tools and methodologies [10]. Therefore, based on the perspective that has been projected for the environmental and industrial research, the present work seeks to extend the development and use of soot formation models in combustion simulation that are capable of predicting soot volume fraction, particle nanostructure and size distribution and to advance computer modeling robustness toward capturing the changes of flame temperature, mixing and residence time. Predictive models would allow engine designers to tune various design and operating parameters without the need for costly experimentation. However, there is an urgent need for a more fundamental understanding as many soot formation and oxidation processes are poorly understood. 1.2 Literature Review The remarkable advances on the kinetics of carbon nanoparticle formation and their final properties, depending on the precursor, temperature, pressure, and concentration have been comprehensively reviewed by Haynes and Wagner [11], Glassman [12], Kennedy [13], Richter and Howard [14], Frenklach [15], D Anna [16], Wang [17], and Eremin [18]. Build upon these valuable studies, a brief review of soot particle characteristics, formation pathways, and modeling will be presented in the following sections Soot Characteristics Soot particles are generated in high temperature fuel rich regions of a combustion chamber when burning a variety of fuels. Reported flame generated soot particles observed in a variety of conditions including laminar premixed [19 28] and diffusion flames [29 45] as well as turbulent flames [46 50] exhibited universal structures. Nonetheless, the nanostructure and aggregation properties of soot particles present in a flame evolve in accordance to the type of the flame, and the locations within a given flame. Figure 1.1 presents the structure evolution of a soot sample as observed by transmission electronic spectroscopy (TEM) along the centerline of a coflow diffusion flame of a surrogate for Jet A-1 at different heights above the fuel tube exit. The diversity in nanostructure has been attributed to the evolutionary process which transforms nascent soot particles into mature particles.

23 4 Figure 1.1 TEM images of soot particle samples along the centerline of a coflow diffusion flame of a surrogate for Jet A-1 at different heights above the fuel tube exit (Source: Reprinted from ref. [35]). Dobbins and coworkers [30,39,51 58], D'Anna and coworkers [16,46,59 61], and Wang and coworkers [17,62 64] have investigated the evolution and characteristics of nascent soot particles in premixed and diffusion flames. The nascent soot particles, also referred to as precursor nanoparticles (PNP) and nanoparticles of organic carbon (NOC), are nearly spherical particles with sizes in the range 1-5 nm in diameter. Their spherical shape and lack of aggregation are evidence of liquid-like behaviour and presumption of coalesce upon collision [52]. The low contrast TEM images observed in [35,65] suggests that nascent soot particles are semi-transparent to an electron beam and have low visible absorption. Chemical and spectroscopic analysis through identification of the chemical bonds and C and H elements give an indication of the chemical nature of the particles. Laser microprobe mass spectrometry (LMMS) [53], gas chromatography/mass spectrometry (GC/MS) [66] and high-resolution transmission electron microscopy (HRTEM) [22] measurements indicated that the nascent particles can be thought of as polymer-like structures containing PAH molecules ranging in molecular masses from 152 to 302 amu. Evidence of aliphatic and aromatic bonds and occasionally oxygen have been detected by UV-visible absorption and fluorescence spectroscopy and Fourier-Transformed Infrared (FTIR) spectroscopy [16,27,60]. Elemental analysis of nascent soot particles shows that these particles have a relatively low atomic C/H ratio of ~ [22,26,27,67] which can also be associated with their high chemical reactivity [22]. Nanoparticles have low coagulation rates at flame temperatures due to the weak Van der Waalsinteractions between particles relative to their thermal energy. The presence of functional groups containing oxygen within the nanoparticles may also be related to the low coagulation efficiency of the particles [16].

24 5 Simultaneous coagulation of the 1 5 nm particles, addition of compounds from the gas-phase, and loss of H atoms direct particles towards gaining a graphitic structure, and eventually transforms nascent soot particles to aggregate carbonaceous and hardened primary particles [16,52]. The nascent particles may also be absorbed onto the surface of the aggregates upon collision [52]. Mature soot particles, as illustrated in Figure 1.2, consist of small spherical units that are referred to as primary particles. Primary particle diameters generally range from 20 to 60 nm, with standard deviations of 15% 25% [68]. The primary particles within an aggregate have nearly identical diameters, and form chain-like aggregated structures that have broad distributions of the number of primary particles per aggregate ranging from a few up to several thousand [39,68]. The elongated chain aggregate structure and the broad aggregation range of soot particles impose the potential complexity in the characterization, and to a greater extent in simulating soot particles. The complexity associated with aggregate structures is alleviated by the experimental observations that soot aggregates exhibit a fractal-like structure. Aggregates produced in a wide variety of flames exhibit a near universal fractal dimension of D f = 1.82 ± 0.06 [69] for turbulent flames and around 1.8 for laminar flames [57,70], even when an aggregate consists of only few primary particles [68,71]. The low fractal dimension of the soot particles indicates that they have open structures as opposed to more compact near spherical structures. The fractal dimension is also a measure of rate of change of aggregate size with the number of primary particles per aggregate. In addition, the fact that soot aggregates have fractal-like structures, allows the implementation of fractal aerosol theory in the modeling and laser diagnostics of soot aggregates. Mature particles have a more opaque, black material optical properties [52]. Figure 1.2 TEM image of soot sample formed from ethylene pyrolysis in a flow reactor at 1475 K in the presence of nitrogen oxides (specifically N 2 O); (Source: Reprinted from ref. [72]).

25 6 Aggregated particles have high elemental carbon content. GC/MS measurements [66] verified the existence of 2 to 4 ring PAHs, and liquid chromatography [73] measurements identified existence of 5 to 10 ring polycyclic aromatic species as the constituents of mature soot particles. The conversion of nascent soot particles to mature soot aggregates in flames is accompanied by an increase of the carbon to hydrogen ratio (C/H), ranging from 6 to 20 [22,23,26,27,66]. The mass density of mature soot material (ρ s = g/cm 3 ) [11] is also expected to be substantially higher than that of nascent soot (ρ s = g/cm 3 ) [63,67]. Nascent soot particles are often observed at low heights in laminar diffusion flames. The chained aggregates form in the higher flame region and a transition stage consisting of ill-defined, composite particles separates the two particle regimes [35,53,62]. Hu and Köylü [69] reported that if the flame is transformed to near turbulent or fully turbulent, all particle morphologies can coexist in a diffusion flame. The coexistence of the singlet spheroids and the carbonaceous aggregates also has been observed in particle size distribution (PSD) measurements in laminar premixed flames [62,63]. In the later flames the bimodal PSD evolve from a unimodal PSD as a function of time and height. The bimodal particle size distribution is an indication of coexistence of nascent and mature soot particles. Comparison of the measured PSD with the TEM results [62] and electrical mobility measurements [74] indicates that the particles < 5 nm in diameter are associated with the nascent soot particles (nucleation mode) which exhibit a distinctive behavior from the nm particles (the accumulation mode). Particles belonging to the accumulation mode, display the expected soot properties that are characterized by light scattering and TEM: they gain mass and increase their size due to surface growth and reduce in number due to coagulation as a function of residence time. Meanwhile, the mean size and number density of the nucleation mode remains nearly constant everywhere in the flame. Since the nascent particles grow and coagulate with other particles, the consistent presence of the nucleation mode implies a continuous nucleation. These observations link the shape of the particle size distribution to the morphology and mode of particles.

26 Soot Formation Pathways Emergence of the condensed-phase from the gas phase is known as nucleation. The newly formed particles gain mass and grow in size through coalescence, surface reactions and condensation of vapor species. The growth process continues by transforming the monomer particles into fractal structures through aggregation. Finally, the soot particles lose mass and size during oxidation and fragmentation processes. These processes mostly occur simultaneously in a flame and over very short periods of time, as schematically illustrated in Figure 1.3. Many of the underlying processes that control soot formation are not well understood. For each of these processes, a model must be developed that captures the fundamental physics that is occurring and interacts with other models too. The initial step in soot formation from pure hydrocarbon flames is the pyrolysis and oxidation of the fuel. In general, simple fuel pyrolysis and oxidation is relatively well known. Reasonably accurate reaction mechanisms exist for the fuels of interest [75 78]. The next step involves the formation of light aromatic hydrocarbon species in the gas phase from hydrocarbons generated during fuel pyrolysis. Propargyl (C 3 H 3 ) recombination and chemically activated isomerization is the main route toward formation of the first aromatic ring [79,80]. Alternative routes for formation of light aromatics are described by: cyclohexane dehydrogenation [81], formation of naphthalene from cyclopentadienyl (cy-c 5 H 5 ), allyl recombination, i-c 4 H 3 +C 2 H 2, and i- C 4 H 5 +C 2 H 2 [82]. The identified growth pathways beyond the first aromatic ring to form larger multi-ringed aromatic species (i.e., PAHs) are the hydrogen abstraction carbon addition (HACA) reaction sequence [83], free radical addition schemes, methyl substitution/acetylene addition pathways [14], cyclopentadienyl moiety in aromatic ring formation [15,84], and reactions between aromatic radicals and aromatic molecules [85]. Both fuel pyrolysis/oxidation and PAH formation and growth pathways have been combined to generate reaction mechanisms describing the formation of PAH species [84,86 88].

27 8 Figure 1.3 Schematic diagram of soot formation (Source: Reprinted from ref. [89]). Onset of condensed phase materials follows the appearance of large PAH species in the gas phase. Two well-received approaches to postulate a soot nucleation mechanism among others are collision coagulation [90,91] and chemical coalescence [92,93]. The collision coagulation hypothesis is that the Van der Waals interaction force becomes sufficiently large after PAH growth to a certain size so that it can hold together a pair of PAHs during physical collision, thus forming PAH dimers. The sequence of collisions among PAH dimers and PAH molecules leads to the formation of PAH trimers, PAH tetramers and so on. Meanwhile, PAH species constituting the PAH stacks keeps growing via molecular chemical reactions. Subsequently, the PAH clusters evolve into solid particles. Most of the PAH-based soot models consider PAH dimerization as the bridge from the gas phase to the solid phase [15]. The alternative hypothesis is that aliphatic linking of 2-, 3-aromatic rings form 3-dimensional structures. Further growth of these structures in this manner leads to emergence of nascent soot particles. Additional mass growth as well as dehydrogenation of the nascent particles is marked as the emergence of the solid state [92]. The latter mechanism is referred to as chemical coalescence.

28 9 Currently, experimental data characterizing the transition zone from the gas phase to the condensed-phase are very limited due to the nature of the processes. Indirect experimental evidence such as the observation of the bimodality in the size distribution functions of nascent soot particles in premixed flames [19,63], supports both pathways as the initial nucleation step [17]. Theoretical aspects of particle nucleation were discussed by Herdman and Miller [94] for collision coagulation and by Violi and Venkatnathan [95] for chemical coalescence using largescale, statistical mechanics simulations and molecular dynamics. Both of these studies verified the possibility of formation of condensed phase in a flame environment through the proposed mechanisms. More recently studies which include a broader range of flames in terms of mixing and temperature such as Chung and Violi [96] and D Anna [16] showed that particle inception can be considered as the result of both a chemical growth and a physical coagulation and contribution of these two pathways to the particle inception rate varies according to the combustion conditions. Wang [17], however, showed that neither of the current nucleation theories are comprehensive enough to comply with the new findings with regards to the PAH and nascent soot thermo/chemical characteristics, and proposed that more comprehensive theories such as PAH coalescence through π-electron interactions, are required. The growth of the soot particle can occur by the addition of small hydrocarbon species. This process is currently described by the hydrogen abstraction carbon addition (HACA) mechanism [15,86,90]. The soot surface is assumed to consist of hydrogenated sites with a predefined density. Mass growth on soot surface requires H-abstraction to form an aryl radical site, followed by acetylene attack in a manner similar to the gas-phase PAH growth mechanism. Observations have been made that cannot be explained in the context of the HACA mechanism: the surface reactivity changes with time and temperature [97,98], the existence of aliphatic compounds in nascent soot [45,62,99] and soot mass growth without the presence of gas-phase H atoms [63,100]. These observations are indication of incompleteness of the HACA mechanism to describe the entire process of soot surface growth. Deposition of PAH species on the surface of the soot particles is also considered a viable growth route for soot particles, which is referred to as PAH-soot surface condensation [90,101]. Molecular dynamics studies suggest that these adsorbed PAH species are not stable [102,103]. Yet the experiments suggest that PAH stacks are indeed the building block of soot [104,105]. A better understanding is needed of the processes that stabilize these absorbed PAH species.

29 10 The final stage in the soot particle formation and growth mechanism is aggregation. The process of formation of fractal-like aggregate structures as a result of particle collisions is termed coagulation. Coagulation determinatively influences shaping of soot particle size distribution, soot number density, and soot morphology. After collision, soot particles may experience structural evolution. The restructuring processes is a function of particle state, surface property, primary particle diameter, temperature, residence time, etc. [106]. The collision of liquid-like nascent soot particles leads to complete merging of the colliding particles which is known as the coalescence process [54]. The slow restructuring rate of the mature particles leads to the formation of the fractal-like aggregate structure. Observation of neck formation at the contact points of primary particles within an aggregate can be interpreted as partial coalescence or surface growth obliteration [39]. The soot particles restructuring mechanisms are not well understood. New models are needed to estimate the maturity of the particles as well as comprehensive coagulation models that describe coalescence process, neck formation, and aggregation. The oxidation of the soot determines the amount of soot emissions. The soot is consumed primarily by reactions with O, OH and O 2. In near stoichiometric and fuel-rich conditions oxidation by OH radical is the predominant mechanism for soot oxidation [107]. Under these conditions some oxidation occurs via collisions with O. However, contribution from O is much less in comparison to OH [108]. The rate of OH oxidation can be described by the fraction of collisions of OH with soot particles that result in the removal of a carbon atom. The collision efficiency of OH radicals with the soot particles reported to be 0.13 [107,108]. Although OH oxidation is faster compared with O 2, under fuel lean conditions oxygen plays a crucial role in soot oxidation due to abundance of O 2. Molecular oxygen oxidation has been represented by power-law kinetics [108]; however, research has indicated that changes of both initial structure of soot [22,109] and structure of soot during oxidation [108] complicates defining a universal oxidation rate. The structure of soot particles can also be affected by soot oxidation. An increase in particle number has been reported by Neoh et al. [110] in lean premixed flames and by Xu et al. [111] and Puri et al [57] in the oxidation region of diffusion flames. The increase in the numbers of aggregates as well as the decrease in number of primary particles per aggregate was attributed to fragmentation. Since the change in aggregate morphology is not seen for fuel-rich conditions, it

30 11 is linked to O 2 oxidation. Although this phenomenon has been observed, the mechanism is debated. One of the proposed mechanisms for fragmentation assumes that the aggregate chain breaks at the bridges between particles which were weakened by oxidation. The other proposed mechanism postulates that internal burning of soot particles by oxygen cause the break-up of individual primary particles within an aggregate, dividing the aggregate into smaller aggregates with fewer particles [108] Soot Modeling A broad range of length and time scales are involved in soot simulations. The relevant length scales include: - Angstroms for atomic and molecular level scales (10-10 m) - Nanometers for dimers and soot particles (10-9 m) - Millimeters for flow scales (10-3 m) - Centimeters for burner geometry (10-2 m) which make soot modeling a multiscale problem. The approach towards dealing with multiscale problems is to model the processes at the smallest/shortest length/time scales based on fundamental understanding and to resolve the larger/longer length/time scales. One of the challenges of these systems is to keep a balance between simplicity of the model and loss of accuracy and predictability. The advancements made in early stages of developing soot models was reviewed by Kennedy [13]. Based on the level of length/time scale to be resolved and the complexity of the models, soot models were divided into three categories: empirical soot models, semi-empirical soot models, and detailed soot models. Experimentally derived correlations are the essence of the empirical soot models. The correlations include variation of different combustion parameters such as pressure, equivalence ratio, and temperature, on soot formation/oxidation. These correlations are embedded into empirical soot models to relate the amount of soot produced with the operating conditions. The empirical models are mostly suitable for industrial applications. Semi-empirical soot models attempts to add a level of sophistication to the soot modeling by including rudimentary soot formation and oxidation mechanisms in the model. The two-equation

31 12 model by Fairweather et al. [112] is one of the most popular semi-empirical soot models. It solves one transport equation for the soot mass fraction, and a second equation for the primary particle number density. Inception, surface growth, oxidation and coagulation are the soot processes that are considered in the Fairweather model which are empirically estimated. The drawback of relying on empirical correlations is confinement of the model validity to the model calibration cases. The final category includes the detailed soot models. These are the most complex and computationally expensive soot models. The detailed soot models are equipped with the most advanced aerosol dynamics prediction tools which are capable of resolving a wide distribution of polydispersed aggregate structures. State of the art chemical and physical mechanisms describing PAH and soot formation/oxidation are incorporated into the detailed models to achieve a rigorous description of processes involved with soot particles. These models can be employed to provide detailed information regarding parameters influencing particles for a broad range of conditions, which makes them a suitable tool for studying the fundamentals of particle formation/oxidation. In order to simulate combustion and soot particles in a flame, a detailed soot model needs to model the flow field (solving the Navier-Stokes equations), predict temperature (solving the energy equation), calculate gas phase composition (solving the gas-phase chemistry), and soot (solving the aerosol dynamics equations) all of which are closely coupled. Prerequisite of a detailed soot model is a detailed chemical kinetic mechanism that not only is capable of describing the pyrolysis and oxidation of hydrocarbon fuels but also can model the formation and growth of PAH species. Due to vast variation of species and pathways involved in PAH formation and growth, the detailed chemical mechanisms designated for the simplest hydrocarbon fuels include hundreds of species and thousands of reactions [86 88], which add a substantial computational load to detailed soot simulations. The aerosol dynamics models that are suitable for detailed soot models are moment methods [90,113], stochastic methods [114], Galerkin methods [115,116] and sectional methods [41,117,118]. These are efficient algorithms that with moderate computational costs can resolve the majority of particle properties. However, modifications to these models to extract additional chemical/physical resolutions exponentially increase their complexity and computational

32 13 expense. An example is the Monte Carlo (MC)/molecular dynamics (MD) calculations that have been developed to bridge the time/length scales between molecular and particle levels in soot formation [94,119,120]. The ability of these models to simultaneously resolve particle size distribution, and morphology as well as chemical composition of the particles attracted a lot of attentions in soot particle studies. The MC/MD models are viewed as a potential candidate for development of the next generation of soot models. However, improving computational capabilities and developing high efficiency algorithms for Monte Carlo methods are necessary before application of these methods becomes feasible for flame simulations and soot particle studies. An advanced sectional aerosol dynamics model [121] is used in this thesis that can provide soot morphology in addition to mean soot properties and the size distribution of particles. Two equations, number densities of aggregates and primary particles, are solved per section which allows resolving the formation and coagulation of the fractal-like soot aggregates as well as soot polydispersity. Abilities of the sectional soot model to successfully simulate soot formation has been demonstrated in plug flow reactors [121], shock tubes [122], and coflow diffusion flames [123,124]. The sectional soot aerosol dynamic model is described in detail in Chapter Objectives and Outline of Subsequent Chapters The objective of the subsequent chapters of this work will be to advance the field of computational soot modeling by focusing on detailed laminar flame simulation using a sectional soot method. The goal will be to move toward developing a robust model of soot formation that can predict the mass, size distribution and aggregate structure of soot in laminar flames for a wide range of conditions. This effort will include developing numerical models to simulate processes which were not considered in the previous soot models, improving known weaknesses in a commonly used soot model, increasing the soot modeling knowledge base by studying the sensitivity of soot predictions to the involved processes and parameters, and extending the applicability of the soot model to laminar diffusion, partially premixed as well as premixed flames. Chapter 2 will describe the governing equations that are necessary in combustion modeling and the numerical methods to solve those equations. These equations will include the equations governing the fluid dynamics, which are conservation of mass and conservation of momentum.

33 14 Conservation equations of species mass and energy will then be introduced to complete the set of equations necessary to fully resolve the gas phase. The two configurations that will be considered in the present work are the coflow diffusion flame and the burner stabilized stagnation (BSS) premixed flame. The appropriate form of the governing equations that complies with each of the flame configuration will be presented. The chapter will then proceed by introducing the soot model to be used, including the equation of conservation of soot sectional aggregate number density as well as primary particle number density. Next, the thermodynamic, chemical kinetic and transport models that will be used in the present work will be stated, and the chapter will conclude by describing the numerical solution procedures along with the boundary conditions which will be incorporated in simulations of laminar ethylene/air flames. The soot model development chapters are arranged in chronological order. The objectives of Chapter 3 will be to introduce two particle coalescence models applicable to soot particle simulations. The introduced coalescence models will be applied to a laminar coflow ethylene/air diffusion flame, and comparisons will be made with experimental data to validate the models. The effects of these coalescence models on predictions of soot particle morphology will be quantified. Chapter 4 will proceed as a comparative study of soot chemical growth for a variety of ethylene/air flames, and it will specifically investigate how surface chemical reactivity can be affected by temperature and residence time. Based upon this comparison, a function for surface reactivity of soot particles based on temperature-time histories of particles will be proposed. The sectional soot model with the new soot surface reactivity function is used to simulate multiple coflow ethylene air flame. The coflow flames include several coflow diffusion ethylene/air flames with varying fuel flow rate, and fuel dilution, and multiple partially premixed coflow ethylene/air flames with varying equivalence ratios. Predictions of soot concentration will be compared to experimental data for validation. In Chapter 5 a more ambitious study is undertaken to present a model that is capable of predicting soot in both premixed and diffusion flames. The role of PAH chemistry will be investigated in PAH growth dominant flames which are the burner stabilized stagnation (BSS) premixed ethylene flames. Prediction of soot particle size distribution with a reversible nucleation model will be compared to efficiency based nucleation models in the BSS premixed

34 15 flames. The effects of dimerization equilibrium parameters as well as other soot formation processes on predictions of PSDs are quantified. The chapter will then proceed by introducing a novel model for PAH condensation that considers the possibility of PAH evaporation through equilibrium conditions. Equilibrium parameter effects of the soot particle size distribution predictions will be characterized. The chapter will conclude by evaluating the described model s performance in modeling soot formation in a diffusion coflow ethylene/air flame. Finally, Chapter 6 presents a summary of the conclusions of the present work, as well as recommendations for future investigations.

35 16 Chapter 2 Mathematical Model 2.1 Overview This chapter will present the governing equations and state variable relationships that are necessary for the chemically-reacting flow simulations in the present work. This will include details on a sectional representation for modeling particulate (soot) formation. Two forms of governing equations are employed in modeling different flames modeled in this work. The first set of governing equations describes the two-dimensional reacting flow in cylindrical coordinates which are utilized for modeling axisymmetric coflow diffusion flames. The second set of governing equations is a similarity solution of the generalized governing equations, which casts the governing equations as a one-dimensional boundary value problem valid along the centerline of a stagnation flow. The burner stabilized premixed flames has been simulated using the latter set of governing equations. The gas phase governing equations are presented in the next section. In the subsequent section, the soot aerosol dynamic model is described. Finally, the numerical methods used to solve the governing equations are described in Section Gas-Phase Governing Equations The gas-phase governing equations include conservation of mass and momentum (Navier- Stokes), conservation of energy and conservation of species. The solution to these equations

36 17 provides the flow field velocity, pressure, temperature and gas mixture composition. In addition, species chemical kinetics, transport properties and thermodynamic properties have to be evaluated. In the subsequent subsections all the conservation equations are presented followed by the evaluation method of thermo-chemical properties Conservations of Mass and Momentum The continuity equation in tensor form is presented in Eq. 2. ρ t + x k (ρu k )=0 ( 2.1) Here, ρ is the density of the mixture, is time, u k is the velocity component in the x k direction. The general representations of the Navier-Stokes equations in tensor form are depicted in Eq ρ u j t + ρu u j k = p + x k x j x j ( λ u k x k ) + x i [ μ u i + u j ( x j x i )] +ρf j ( 2.2) where λ is the second viscosity coefficient, μ is the dynamic viscosity and f j is the net body force The Two-Dimensional Cylindrical Coordinates One of the flow configurations to be studied is that of a coflow laminar diffusion flame. Figure 2.1 shows a schematic representation of the burner and flame geometry, with the computational domain superimposed on the image. Since the flow is axisymmetric, the governing equations become two-dimensional when they are expressed in cylindrical coordinates. For axisymmetric flow ( θ =0 ), the governing equations 2.1 and 2.2 are written in cylindrical coordinates as: ρv u r +ρu u z = p z + 1 r 2 3 z 1 r r u r (rμ (μ u z ) + 1 r (rρv) + ρu z r ) +2 z v r (rμ z ) +ρg z =0 ( 2.3) (μ u z ) 2 3 μ z [ r r (rv) ] ( 2.4)

37 18 ρv v r +ρu v z = p r + v z (μ z ) + 2 r r r v r (rμ r ) 2 3 u (rμ z ) + u z (μ r ) 2μv 1 μ r r [ r r (rv) ] r μ 3 r 2 r (rv) μ u r z ( 2.5) Here, r and z are the radial and axial coordinates; v and u are the radial and axial velocities; p is the pressure; g z is the axial gravitational acceleration. z Symmetry r Figure 2.1 Schematic representation of a coflow flame, including coordinate orientation and computational domain (not drawn to scale) The One-Dimensional Similarity Solution The second set of flame configurations are for the burner stabilized stagnation (BSS) premixed flame which is shown schematically in Figure 2.2. The burner consists of a circular nozzle carrying the premixed fuel and oxidizer toward a plate. This configuration produces an axisymmetric flow field with a stagnation plane. The three dimensional partial differential equations can be reduced to a one-dimensional boundary value problem by introducing a stream

38 19 function in the form ψ(z,r) = r 2 U(z) into the governing equations in the cylindrical coordinate (Eq. 2.3 to 2.5). v/r and other variables become independent of r when such a stream function is assumed [125]. Following Kee et al.[126] the following variables have been defined: for which continuity, Eq. 2.3, reduces to G(z) = ρv r F(z) = ρu 2 G(z) = df (z) dz ( 2.6) ( 2.7) ( 2.8) Similarly, the radial momentum equation will be satisfied if H= 1 p = constant ( 2.9) r r and the axial momentum equation become H 2 d FG dz ( ρ ) + 3G2 ρ + d dz [ μ d G dz ( ρ )] =0 ( 2.10) Figure 2.2 orientation. Schematic representation of a burner stabilized stagnation flame, including coordinate

39 Conservation of Energy The conservation of energy equation is presented in terms of temperature [127] in Eq T ρc p t + ρc p v. T =.(λ T) ρ c p,k Y k v k. T h 0 kω k W k +Q r ( 2.11) Here, the first term on the left hand side represents the temporal rate of change of temperature; the second term represents convection heat transfer, and c p is the specific heat of the mixture under constant pressure. On the right hand side of Eq. 2.11, the first term is the contribution from conduction and λ is the thermal conductivity of the mixture; the second term is the heat flux rate due to species diffusion, and v k is the diffusion velocity of the kth species; the third term is the rate of enthalpy production by chemical reaction; h 0 k is the k th species specific enthalpy; and Q r is the change in energy density due to radiation from soot and gaseous species. All the terms on the right hand side can be expressed as the sum of the effects of gas-phase species and soot particles. Thus, the energy equation for a steady state axisymmetric condition in the cylindrical coordinate is: T ρc p ( v r +u T z ) = 1 r T r (rλ r ) + T z (λ KK h 0 k ω k W k k=1 ρc p,s Y s ( v s,r KK z ) ρ c p,k Y k ( v k,r k=1 T T r +v s,z T T r +v k,z z ) z ) h s 0 ω s W s +Q r ( 2.12) where subscript k denotes those parameters related to gas species k and subscript s is used for soot particles. KK represents the total number of species in the gas phase. Eq is solved for predicting temperature for the coflow diffusion flames. For the BSS configuration, the axisymmetric cylindrical energy equation, Eq. 2.12, is transformed similar to the momentum equation into Eq ρc p u T z T z (λ z ) +ρ c p,k Y k v k,z Q r =0 KK k=1 T z KK + h 0 k ω k W k k=1 +ρc p,s Y s v s,z T z +h s 0 ω s W s ( 2.13)

40 Radiation Heat Transfer Radiation heat transfer has been recognized as an important flame heat-loss mechanism in modeling laminar flames. Radiation heat transfer is not only necessary for prediction of temperature but it is also coupled with soot and flame structure. Soot is the dominant source of radiation in sooting flames which can noticeably influence flame temperature. However, most of the processes involved in soot formation are endothermic. Radiation heat transfer lowers the rate of soot formation therefore reduces heat-loss by radiation. The feedback loops from soot on radiation and temperature and vice versa couple the soot formation with radiation heat transfer. The radiative transfer equation (RTE) for an axisymmetric cylindrical system, considering the medium to be in local thermodynamic equilibrium (LTE), is given in Eq [128]. μ I υ r η I υ r φ +ξ I υ z = κ υ I υ +κ υ I bυ ( 2.14) Here, μ, η and ξ are directional cosines. Parameters I υ, I bυ and κ υ denote spectral intensity, spectral blackbody intensity and the spectral absorption coefficient, respectively. The left hand side refers to the rate of change of spectral intensity ((. s )I υ ). The first term on the right hand side represents the reduction of radiant energy leaving an element of volume of matter due to absorption. The last term on the right hand side of the RTE equation is the rate of emission by the matter. The radiation heat transfer rate is calculated by integrating the RTE over all solid angles and over the entire spectrum. Since the radiation heat transfer equation is an integrodifferential equation, its solution is quite difficult. Therefore, it is necessary to introduce some simplifying assumptions to solve the RTE. In this work two methods has been adopted for estimation of the radiation heat transfer rate. The optically thin approximation (OTA) is used to calculate the Q r term in Eq for the BSS premixed flames. The more sophisticated discrete ordinate method (DOM) is incorporated to evaluate the radiation heat transfer rate for the coflow diffusion flame configuration. Optically thin approximation (OTA) Optical thickness is a dimension-less parameter which is a measure of the ability of a path length of matter to attenuate radiation of a given wavelength. For a medium with uniform composition, temperature and pressure optical thickness, τ 0υ, is defined as

41 22 τ 0υ =κ υ L ( 2.15) where L is a characteristic dimension. In the condition of τ 0υ 1, which refers to the optically thin limit, the radiation emitted by a given fluid element will travel directly to the bounding surfaces and any absorption by the fluid will be negligible. Therefore the radiation transfer equation will become [129]: Q r = 4σκ P (T 4 4 T ) ( 2.16) where σ is the Stefan-Boltzmann constant; T and T are the local and the ambient temperatures, respectively; κ P is the Plank mean absorption coefficient of the mixture. Liu et al. [130] by comparing different radiation models concluded that the optically thin approximation could predict the temperature field for a low sooting laminar flame reasonably well. Therefore radiation heat transfer for the premixed flames has been estimated using the OTA method. In the present work radiation from three species, CO, CO 2, and H 2 O, and soot has been considered. For the gaseous species the Plank mean absorption coefficient of the mixture, κ P, is calculated from Eq κ P =P H2 O κ H 2 O +P CO 2 κ CO2 +P CO κ CO ( 2.17) Here, P i and κ i are the partial pressure and the Plank mean absorption coefficient of species i, respectively. The Plank mean absorption coefficient is obtained as follows: 5 κ i = A ij T j j=0, i = H 2 O, CO 2 and CO ( 2.18) where A ij is the polynomial coefficient of a species expressed as a function of temperature [131]. Soot particles are assumed to be Rayleigh range absorber-emitters [132]. The Plank mean absorption coefficient for soot was estimated according to [133] as κ Ps = 3.83Cf v T ( 2.19) Here, f v is the soot volume fraction and C is constant taken to be [133] nk C = 36π (n 2 k 2 +2) 2 + 4(nk) 2 ( 2.20) where, 1n + ik is the complex refractive index of soot, assumed to be i [134].

42 23 Discrete-ordinate method (DOM) The radiation intensity is a function of the location, the direction of propagation of radiation and of wavelength. One simplifying strategy to find radiation intensity is to divide the entire solid angle (φ =4π) into a finite number of ordinate directions and assume an average intensity within given intervals of the solid angle. This assumption would discretize the radiation transfer equation directionally into series of coupled linear differential equations. This procedure yields the discrete-ordinates method [128]. DOM is developed without any presumption about the opacity of the medium which makes it suitable for strong luminous and heavily sooting flames. In addition, the DOM algorithm is highly compatible with the finite volume method and can be readily incorporated into multi-dimensional finite volume codes. In terms of accuracy, DOM has shown robustness comparable to the ones from more detailed and computationally intensive Monte-Carlo methods [135]. Originally proposed by Liu et al. [130], the directional discretization has been obtained using a T 3 quadrature set [136] for the DOM radiation model. The RTE is written for each ordinate and the integral terms are replaced by a Gaussian quadrature summed over each ordinate. The directional cosines and weight functions of the T 3 quadrature for the axisymmetric cylindrical coordinate are taken from [130]. Radiation from CO, CO 2, H 2 O and soot has been considered. Mixture radiative properties have been evaluated using the statistical narrow-band-based correlated-k (SNBCK) method [137]. The employed SNBCK divides the spectral band into nine optimized nonuniform wide bands covering the spectral range from 150 to 9300 cm 1. The radiative absorption characteristics for each band are approximated using an exponentially decaying function [130,137,138]. The average radiation intensity at each narrow band is determined by integrating the exponential function over the bandwidth which is numerically estimated using the 4-point Gauss-Legendre quadrature scheme [139]. The spectral absorption coefficient of soot is assumed to be 5.5f v ν with f v being the soot volume fraction and ν the wavenumber of each spectral band. The DOM equations are discretized using the finite volume method. A total of 36 ordinate intensity equations are calculated to find the monochromatic radiation passing through a volume element.

43 Conservation of Species Mass In order to determine the chemical composition of a gas mixture in a reacting flow, where there are numerous chemical species present, a conservation equation can be written for each of the chemical species present. This mass transfer equation in axisymmetric cylindrical coordinates is as follow ρv Y k r +ρu Y k z = 1 r r ( rρy k V k,r) z ( ρy k V k,z) + W k ω k ( 2.21) k = 1, 2,, KK where Y k is the k th species mass fraction; V k,r and V k,z are the k th species radial and axial diffusion velocities, respectively; W k is the k th species molecular weight; KK is the total number of gaseous species; ω k is the kth species molar production rate per unit volume and for non-three-body reactions can be calculated by N R KK ω k = ν ki ( k fi [ X j] ν ji i=1 j=1 KK k ri [ X j] ν" ji j=1 ) ( 2.22) where ν ji = ν" ji ν ji ( 2.23) N R is the total number of reactions; k fi and k ri are the forward and reverse rate of reaction i, respectively. The interactions between soot formation/oxidation and gas-phase chemistry is included in the chemical reaction source term, ω k. The species conservation equation 2.21 in the stagnation flow takes the following form Chemical mechanism ρu Y k z + z (ρy k V k ) W k ω k = 0 k = 1, 2,, KK ( 2.24) The gas-phase chemical kinetics has been described using two chemical kinetics mechanisms both utilizing recently advanced PAH formation pathways. The first chemical mechanism has been developed by the German Aerospace Center (DLR) chemical kinetics department and it will be referred to as DLR mechanism hereafter. The other chemical kinetic mechanism used in this work has been developed by the Clean Combustion Research Center at King Abdullah

44 25 University of Science and Technology (KAUST) and this mechanism will be referred to as the KAUST mechanism hereafter. A brief description of each of these mechanisms with an emphasis on PAH formation pathways is given in the following sections. DLR mechanism Details of the DLR mechanism can be found in [87,140,141]. This chemical kinetic model, developed for methane and ethane-fueled flames, contains 93 species and 719 reactions. The mechanism provides growth and oxidation of PAH species up to five-ring aromatic species. The C 0 C 2 chemistry in the DLR mechanism is based on the Leeds model [142] with updates from [75]. The dominant routes for formation of the first aromatic ring in the DLR mechanism based on [87] are the following reactions: i C 4 H 5 +C 2 H 2 A1+H ( 2.25) C 3 H 3 +C 3 H 3 A1 ( 2.26) H 2 CCCCH + C 2 H 3 A1 ( 2.27) The growth mechanism considered for aromatic species beyond benzene as it is shown in Figure 2.3 are: HACA, hydrogen atom migration yielding the five- and six-member rings, interconversion of five- and six-member rings and zigzag aromatic edges; free radical addition schemes, methyl substitution/acetylene addition pathways, cyclopentadienyl moiety in aromatic ring formation and reactions between aromatic radicals and molecules. Several small radicals and small molecules containing one to six carbon molecules were employed in the mentioned PAH molecule growth and for the H atom abstraction from hydrocarbons. The hydrogen atom migration was considered as part of the HACA reaction set. Most of the PAH reactions are multi-step elementary reaction sequences including a lot of intermediate species and are studied in most cases only qualitatively. These sequences have been included in this model as lumped reactions (e.g., aromatic + aromatic/cyclic). Reaction rates of heavy PAH molecules have been estimated based on the reaction rates of analogy reactions of one- and two ring-molecules. The estimation of the reaction rates of aromatic + aromatic/cyclic reactions has been done by increasing the frequency factors in the Arrhenius expression. For the reactions of heavy PAHs with small radicals and molecules corresponding reaction rates for small PAH molecules were adopted.

45 H, O, OH, C 2 H, 26 The reaction mechanism has been validated for flame speeds of methane and ethylene; concentrations profiles of small molecules and radicals, medium size and high molecular mass rings and of soot volume fractions in laminar premixed flames as well as at shock tube conditions [140], counterflow non-premixed flames [87], and a laminar coflow diffusion flame [141]. C2H 2, C 4 H, C 4 H 2 +C 2 H (-H) O(-CO) +C 4 H 5 (-H, -H 2 ) CH H, O, OH H 2, OH, H 2 O CH 2 H, OH H2, H 2O H, OH,C 2 H H 2, H 2 O,C 2 H 2 CH 3 (-H 2 ) CH H 2 +C 2 H 2 (-H) HACA HACA CH 3 (-H) +C 4 H 4 C 4 H 2 +H (-H 2 ) C3 H 3 CH HACA HACA CH HACA, CH 2 +C 4 H 4, C 4 H 3, C 4 H 2 HACA +, +H (-H 2 ) HACA HACA C 4 H 2 CH CH Figure 2.3 Schematic representation of the major reaction pathways for the formation of large PAHs considered by the DLR chemical kinetic mechanism. KAUST mechanism The KAUST mechanism is developed for modeling C 1 C 4 fuel oxidation [88]. The mechanism contains 202 species and 1351 reactions. The PAH growth up to the formation of coronene (A 7 ) is included in this mechanism. The fuel pyrolysis/oxidation and molecular growth up to benzene were based on USC Mech [143]. The A 1 growth pathways considered in this mechanism involve propargyl (C 3 H 3 ) recombination, addition of C 2 H x on C 4 H y molecules, and addition of CH 3 on

46 2C 2 H 2, H 27 cyclopentadienyl (C 5 H 5 ) radicals. The reactions for the growth of PAHs larger than benzene are HACA, reactions involving species with odd-carbon number species such as indenyl (C 9 H 7 ), benzyl (C 6 H 5 CH 2 ), C 5 H 5 and C 3 H 3 and the addition of C 4 H 4 to large PAH radicals. C3 H 3 H, CH 3, C 4 H 4 C 3 H 3 C 2 H 4 CH C 3 H 3 CH 2C 2 H 2, H C3 H 3 H, CH 3, 2C 2 H 2, H C 4 H 4 H, CH 3, C 3 H 3 C2 H 2 CH C 2 H 2 C4 H 4 C 2 H 2 C 2 H 2 C 2 H 2 H, CH 3, C 3 H 3 CH C 4 H 4 H, C 2 H 2 H, C 2 H 2 CH 3, C 2 H 2 CH 3, C 2 H 2 CH C 3 H 3, C 2 H 2 C 3 H 3, C 2 H 2 Figure 2.4 Schematic representation of the major reaction pathways for the formation of large PAHs considered by the KAUST chemical kinetic mechanism. The reaction rates for PAH molecule reactions that were not present in the literature were determined through quantum calculations using the density functional theory along with the transition state theory. The rate constants for PAH reactions were obtained in the high pressure limit, as PAH molecules are large in size and their reactions do not exhibit substantial pressure dependence. The KAUST mechanism has been validated in several laminar premixed and counterflow flames, where a reasonable agreement between the observed and simulated PAH concentrations were obtained [88].

47 Soot Aerosol Dynamics Model Soot particle size, concentration, and interaction with the gas phase are usually the soot properties of most interest. For a soot particle confined in an infinitesimal volume of gas, the physical and chemical processes shaping the size distribution are summarized in Figure 2.5. These processes could be divided into two groups. The first group is the collection of those processes occurring inside the element including gas-to-particle conversion and coagulation. The second group are external processes that transport particles across the boundaries of the element such as diffusion and thermophoresis. A general dynamic equation (GDE) for the particle number density, n(v, r, t), that includes all of these processes can be derived from the Smoluchowski equation [144]. This equation is also referred to as a population balance equation. For the number density of the particles in a volume range between v and v+dv, n v, the general dynamic equation for the particles contained in a large chamber with a sufficiently small surfaceto-volume ratio to neglect deposition on the walls and sedimentation, is expressed by [106]. n v t +.n v v =. D n v + n v n + v n + v.cn [ t ] growth [ t ] coag [ t ] v ( 2.28) frag In this expression, the diffusion coefficient D is a function of particle size and c is the particle velocity resulting from the external force field; the second term on the right-hand side is the summation of the growth terms; the third term on the right-hand side represents collisions between particles; the fourth term on the right-hand side represents the change in number density due to the fragmentation process. Figure 2.5 Processes shaping the particle size distribution function in a small volume element of gas. Diffusion and sedimentation involve transport across the walls of the element. Coagulation, nucleation, and growth take place within the element. (Source: Reprinted from ref. [106])

48 29 In general, an infinite number of discrete particle sizes are present in an aerosol-containing environment. In addition, the GDE is a nonlinear, partial integrodifferential equation. Thus, numerical modeling is required. One of the numerical solution procedures for the dynamic aerosol balance equation is finite sectional approximation [145]. This method is used to approximate the virtually continuous size spectrum by a set of size classes, or sections, within which all particles are assumed to be of the same size or the functional form of the size distribution within the section is specified. By dividing the entire particle size domain into sections and dealing only with one integral quantity in each section, the number of conservation equations required is simply equal to the number of sections. There is also the possibility to track multiple integral quantities per section. For example in addition to particle number density, particle surface area, number of particles per aggregate, and composition of the particles can be tracked within each section. For each independent quantity a GDE should be solved per section. In the sections that follow, the sectional method used in this thesis is described and the mathematical methods for characterizing aerosol size and chemical properties are discussed The sectional aerosol dynamics model The sectional soot aerosol dynamics model used in this thesis is based on the fixed pivot approach in the classical sectional description of the particle population balance equation [146]. The mass range of the fractal-like solid soot aggregates is divided into a number of discrete sections (i.e., particle mass bins). Each section represents a collection of aggregates with a fixed prescribed mass. The representative mass of sections is a geometric progression with common ratio f s, also called the sectional spacing factor, and the scale factor equal to the mass of a dimer, U DIM. Eq shows the relationship between the mass of each aggregate in section i, U i (g #), the common ratio and scale factor. i 1 U i =U DIM f s ( 2.29) All soot aggregates in a section are assumed to be of similar enough character that they can be modelled using mean characteristics. Soot aggregates fall into individual sections according to their mass. A transport equation for the number density of soot aggregates is constructed and solved in each section. The nucleation step is the process of formation of dimers from the gasphase incipient species. The soot dimers are assumed to be spherical and are added to the first section. Processes which increase the mass of aggregates (i.e., coagulation and surface growth)

49 30 move particles from lower sections to the higher sections. On the other hand, higher section particles move to lower sections by oxidation or fragmentation. In addition to the aggregate number density equation, a transport equation for primary particle number density is considered for each section. By conserving the primary particles within the aggregates, the additional transport equation enables the model to predict the experimentally observed fractal-like aggregate structures of soot particles [39,56,57]. Some simplifying assumptions have been made to derive the primary particle number density equation. Primary particles are considered to be spherical. Similar to the aggregates, it is assumed that the primary particles within aggregates of the same section are similar enough that they can be modelled using mean characteristics and they are connected together by point contact (i.e., particle necking has been neglected). Another simplifying assumption is having a universal fractal dimension, D f, of 1.8 for aggregates larger than the primary spherule mass; whereas smaller particles are assumed to be dense spheres (D f = 3.0) [57,68,70]. A constant fractal dimension is a common assumption in aerosol dynamics modeling under concurrent particle nucleation, coagulation, and surface growth processes [113,124,147]. The structure of an aggregate could now be completely determined by knowing the fractal dimension, the mass of a single aggregate in the section, the primary particle number density, and the aggregate number density. The soot properties that can be extracted are as follow: particle size distribution (PSD), soot volume fraction, primary particle diameter, aggregate surface area, and number of primary particles per aggregate. Based on the above descriptions, the conservation equations for aggregate number density and primary particle number density in an axisymmetric cylindrical coordinate in each section are as follows: ρv N i a a r +ρu N i z = 1 r r ( rρn a a i V i,r) z ( ρn a a i V i,z) +ρs i a ( 2.30) p p ρv N i r +ρu N i z = 1 r r ( p p rρn i Vi,r) z ( p p p ρn i Vi,z) +ρs ( 2.31) i (i=1,2,,ms) Here, superscripts a and p refers to those parameters associated with aggregates and primary particles, respectively; N i is the number of i th sectional soot particles per unit mass of the gaseous mixture; MS is the total number of soot sections; V i is the diffusive velocity of soot particles in section i, and S i contains the source and sink terms associated with the rate of change of sectional mass and can be expressed in terms of soot process:

50 31 S i = N i N + i N + i N + i N + i N + i ( t ) nu ( t ) cond ( t ) sg ( t ) ox ( t ) coag ( t ) ( 2.32) fr where, the processes considered are inception ( ), surface condensation ( ), chemical surface growth ( ), oxidation ( ), coagulation ( ) and fragmentation ( ). Inception is considered only for the first section. For the 1-D stagnation flow, Eqs and 2.31 transform to: Nucleation model ρu N i a z + z ( ρn i a V i a ) ρs i a =0 ( 2.33) p ρu N i z + z ( p p p ρn i Vi ) ρs i =0 ( 2.34) (i=1,2,,ms) In view of the PAH-based soot formation pathways, the formation and growth of aromatic species bridges the main combustion zone chemistry and soot formation. This assumption is founded based on evidence of dependency of the existence of small soot particles on PAH species [11,148,149]. Therefore, nucleation is modeled based on dimerization of a pair of PAH molecules. The rate of formation of dimers is considered to be proportional to the rate of collision of PAH species [86,91]. A sticking efficiency has been used to calculate nucleation rate from the collision rate. Nucleation is determined by the rate of collision of the nucleating PAH molecules in the free-molecular regime as: N 1 = A v 8πk B T ( t ) nu ρ 2 C mass K PAH K PAH η N C,k + N C,j d PAH,k +d PAH,j kj N C,k N C,j ( 2 ) k=1 j=k 2 [PAH] k [PAH] ( 2.35) N i = 0 (i = 2,3,, MS) ( t ) nu In this expression, k B is the Boltzmann constant; C mass is the mass of a carbon atom; N c is the number of carbon atoms in the incipient PAH species; d PAH is the diameter of the incipient PAH species; A v is Avogadro's number; [PAH] denotes the mole concentration of the incipient PAH species. K PAH is the total number of nucleating species; η kj is the sticking efficiency of the two colliding PAHs. Different PAH nucleating species has been used in this work ranging from pyrene to coronene. Pyrene is the most widely used PAH nucleating species in soot modeling [86,91,150,151]. Recent experimental studies determined the PAH molecules that participate in

51 32 soot production have a mean fringe length of 0.65 nm [104] and a mass range of 202 amu to 374 amu [53]. These findings suggest that dimerization of PAH molecules from 20 carbon atoms to 30 carbon atoms is plausible. More details about the nucleation model and the PAH species is provided in the following chapters Condensation model One of the heterogeneous gas-to-particle conversions is the growth of the particle due to adsorption of gas phase species to the surface of particle which is referred to as condensation. Similar to nucleation, condensation is modeled based on collision of condensing species and the surface of particles [91]. The PAH molecules allowed to condense are assumed to be identical to the PAH molecules that form dimers. The rate of change of mass in section is calculated by K PAH a I cond,i = γ ik β ik N C,k C mass [PAH] k N i k=1 ( 2.36) where I cond,i is the rate of mass growth of the i th section soot aggregates due to condensation in the unit of g s /g mix /sec, and is always non-negative; β ik is the collision kernel of the k th condensing species and the i th section soot aggregate; γ ik is the sticking probability which takes into account the probability of the molecules bouncing off the surface after collision. The evaluated mass growths have to be interpreted in the terms of the sectional model. Since the mass of aggregates are fixed, the growth of mass of an aggregate in section i is reflected in the sectional model by transferring the equivalent amount of added mass in terms of number of aggregates from section i to section i+1. In order to conserve the primary particle numbers the growth term for the primary particle is multiplied by the number of primary particles per aggregate in the transport equations for primary particles (e.g., Eq. 2.31). The above descriptions have been shown in Eqs and I cond,1 a m 2 m 1 N i I cond,i 1 = ( t ) I cond,i cond m i m i 1 m i+1 m i I cond,ms 1 m MS m MS 1 if i =1 if i=2,,ms 1 if i =MS ( 2.37)

52 33 I cond,1 if i =1 p m 2 m 1 N i I cond,i 1 = ( t n ) cond m i m p,i 1 I cond,i n i 1 m i+1 m p,i if i=2,,ms 1 ( 2.38) i I cond,ms 1 n m MS m p,i 1 if i =MS MS 1 Here, is the representative mass of the section aggregate;, is the number of primary particles per aggregate of the section and it is equal to /. It has to be noted for the first section, condensation would cause particles to leave this section therefore the growth rate is always negative, and since this section only contains soot monomers the rate for primary particles and aggregates are equal. In contrast, the growth term of the last section is always positive. It should be emphasized that the sum of all the growth terms are equal to zero to ensure that no new particles are numerically formed due to growth processes. MS ( i=1 MS p N = i =0 ( 2.39) t ) cond ( t i=1 ) cond N i a Chemical surface growth and oxidation models The heterogeneous reactions of soot particle surfaces with the gas phase considered in this thesis are detailed in Table 2.1. The soot mass growth and oxidation by oxygen, O 2, is based on the well-known hydrogen abstraction carbon addition (HACA) scheme [86,91]. In the HACA scheme, the kinetics of the surface reactions are described using the concept of surface sites (an armchair site, which is a site with four carbon atoms as illustrated in Figure 2.6), which are carbon atoms either saturated (C soot H) or dehydrogenated (C soot ) on the surface of soot particles. The concentration of saturated sites, [C soot H] (mole/cc), is calculated by Eq [C soot H] = A s A v χ Csoot H ( 2.40) Armchairsite Figure 2.6 Illustration of armchair sites on the surface of a soot particle.

53 34 Table 2.1 HACA based soot surface growth and oxidation reactions [86], k =AT b e E a RT. No. Reaction A ( cm 3 mol.s) b E a ( kcal mol ) S1 C soot H+ H C soot + H S2 C soot H+ OH C soot + H 2 O S3 C soot + H C soot H S4 C soot + C 2 H 2 C soot H+ H S5 C soot + O 2 2CO + product S6 C soot H+ OH CO + product γ OH =0.13 where is the number of sites per unit soot surface area and estimated to be 0.23 site/å2 [86]; A s (cm 2 /cc) is the surface density of soot particles and A v is Avogadro s number. The concentration of dehydrogenated sites [C soot ] is similarly calculated with χ Csoot as the number of dehydrogenated sites (C soot ) per unit surface area. Finally by assuming a steady state for C soot, χ Csoot can be calculated from Eq and substituted to find the S4 and S5 rates χ Csoot = (k 1 [H] +k 2 [OH])χ Csoot H k 1[H 2] +k 2[H 2 O] +k 3 [H] +k 4[C 2 H 2] +k 5[O 2] Thus, the mass growth rate due to HACA and mass reduction rate due to O 2 oxidation are I C2 H 2,i =2αC A s,i (k 1 [H] +k 2 [OH])χ Csoot Hk p 4[C 2 H 2]N i mass A v k 1[H 2] +k 2[H 2 O] +k 3 [H] +k 4[C 2 H 2] +k 5[O 2] I O2,i =2αC mass A s,i A v (k 1 [H] +k 2 [OH])χ Csoot Hk p 5[O 2]N i k 1[H 2] +k 2[H 2 O] +k 3 [H] +k 4[C 2 H 2] +k 5[O 2] ( 2.41) ( 2.42) ( 2.43) where A s,i is the primary particle surface area in the i th section; α is the surface reactivity parameter. As it is a focus on this thesis, a complete description of α is provided in Chapter 4. Soot oxidation by the OH radical is modeled based on kinetic theory with a probability, γ OH, the portion of collisions that result in reaction, of 0.13 [86,107,108]. I OH,i =γ OH β OH,i C mass [OH]N i a ( 2.44) ( N i t ) is evaluated using Eqs and 2.38 by substituting I cond,i with I C2 H sg 2,i. The source terms due to surface oxidation are calculated as follows:

54 35 a N i = ( t ) ox I ox,2 I ox,1 m 2 m 1 m 1 I ox,i+1 I ox,i m i+1 m i m i m i 1 I ox,ms m MS 1 m MS if i =1 if i=2,,ms 1 if i =MS ( 2.45) I ox,2 n p m 2 m p,2 I ox,1 if i =1 1 m 1 N i I ox,i+1 = ( t n ) ox m i+1 m p,i+1 I ox,i n i m i m p,i if i=2,,ms 1 ( 2.46) i 1 I ox,ms n m MS 1 m p,ms if i =MS MS The difference between the way the growth source terms are evaluated and the way oxidation terms are evaluated lies in the fact that oxidation moves particles from high sections to low sections while the growth terms do the opposite Coagulation model Coagulation, which is the joining together of two soot particles when they collide, increases soot aggregate size, effectively increasing soot aggregates number in a higher-mass section while decreasing soot aggregate concentration in lower-mass sections. In total, coagulation decreases the total number of aggregates while having no effect on the total number of primary particles. The coagulation rates is estimated to be equal to the binary collision rate between soot aggregates calculated in the entire Knudsen number regime [121,122] with a sticking probability [118]. The coagulation terms for aggregates and primary particles in section are calculated as: ( a N i = 1 δ jk ( t ) coag ( 2 ) η ijk β jk ξ jk N j a a N j k k N i p MS a a N i β im ξ im N m = 1 δ jk t ) ( 2 ) η p,ijk η ijk β jk ξ jk N j a a p N j k k N i β im ξ im N m a coag m=1 MS m=1 ( 2.47) ( 2.48) { k [1, i] j [k, i] m i 1 <m j +m k <m i+1} In this expression, δ jk is the Kronecker delta; β jk is the collision kernel of two aggregates from the j th and the k th sections [121,122,152] and ξ jk is the coagulation efficiency of this collision [118]. In order to conserve the mass and number of aggregates during the coagulation modeling

55 36 the newly formed aggregates are transferred into two consecutive sections. This division has been accomplished using parameter η ijk which defined as follows [121,122]: m i+1 (m j +m k) if m i m j +m k <m i+1 m i+1 m i η ijk = m i 1 (m j +m ( 2.49) k) if m i 1 <m j +m k <m i m i 1 m i 0 else η p,ijk in Eq assigns primary particles to two adjacent sections based on the mass average of the number of primary particles per aggregates. η p,ijk and η ijk together in Eq ensure that the primary particle size is conserved [121,122]. m η p,ijk = i m j +m (n p,j +n p,k) ( 2.50) k Fragmentation model Fragmentation is the process of breakage of the aggregate chain connecting primary particles. In this work, only oxidation-driven fragmentation has been considered. The model assumes that aggregates break into two daughter aggregates with equal mass and no fragmentation occurs for an aggregate containing fewer than two primary particles. Based on these assumptions the fragmentation rate of the aggregates in the section is expressed as [123,153] a N i Γ + S 2 N a 2 = ( t ) (Γ 1)S i N a a i + Γ + S i+1 N i+1 fr a (Γ 1)S MS N MS if i =1 if i=2,,ms 1 if i =MS ( 2.51) Γ + S 2 N a 2 n p,2 if i =1 p N f i s = ( t ) fr (Γ 1)S i N a i n p,i + Γ + S i+1 N a i+1n p,i+1 ( 2.52) if i=2,,ms 1 f s a (Γ 1)S MS N MS n p,ms if i =MS Here, Γ and Γ + are breakage distribution functions that distribute the newly formed aggregates into two adjacent sections such that the number and mass of aggregates are conserved. The breakage distribution functions are calculated as [153]: Γ = f s 2 ( 2.53) f s 1 Γ + = f s f s 1 ( 2.54)

56 37 In Eq S i is the fragmentation rate per aggregate and is taken from [153] S i = r ox,i(n p,i) 1D f ( 2.55) where, r ox,i is the rate of oxidation on a mass basis of soot aggregates in section i per unit surface area; D f denotes the aggregate fractal dimension. 2.4 Transport Properties In order to solve the governing equations outlined in previous sections, transport properties of the gas and soot particles need to be evaluated. The diffusion velocities of the k th gaseous species (V k in Eq. 2.21) and soot particles (V i in population balance equation, Eqs ) are calculated using a mixture-average formulation. This approximation for the diffusion velocities implements only a Fickian description of diffusion for each component of the mixture. In this matter the interactive diffusive effects caused by concentration gradients of different mixture component on each other are neglected. In order to ensure the diffusion velocities do not violate conservation of mass, a correction velocity, as detailed in [154], is added to the expression for the diffusion velocity. Thus, the diffusion velocity is calculated as: V k,xi =V D,xi +V T,xi +V c,xi ( 2.56) where V D,xi and V T,xi are the ordinary diffusion and thermal diffusion velocities, respectively and V c,xi is the correction diffusion velocity. The ordinary diffusion velocity and thermal diffusion velocity of the k th species are obtained by: V D,xi = D k χ k χ k x i ( 2.57) V T,xi = D T k 1 T ( 2.58) ρy k T x i where χ k is the k th species mole fraction; D T k is the k th species thermal diffusion coefficient; D k is the mixture diffusion coefficient for the k th species. The ordinary diffusion velocity and thermal diffusion velocity (also known as thermophoretic velocity) of the i th aggregates are obtained by a V Ds,x i = D i a a N i a N i section soot x i ( 2.59) a 1 T V Ts,x i = D T,i ( 2.60) T x i

57 38 a where D T,i is the i th section thermal diffusion coefficient; D i a is the diffusion coefficient of the i th section aggregate. The thermophoretic velocity for the primary particles and aggregates are the same. The ordinary diffusion velocity is calculated as follows: p V Ds,x i = D i a N i p N i p x i ( 2.61) Note that the same D i a appears in both primary particle and aggregate diffusion velocities. This is because the aggregates are composed of the primary particles. The diffusion velocity represents the velocity with which each species moves relative to the bulk fluid velocity. The diffusion velocities must thus satisfy the conservation expression: KK+MS j=1 Y j V j =0 ( 2.62) By substituting diffusion velocities for species and soot into the above equation, the following expression for the correction velocity is obtained: KK MS Y V c,xi = D k k + D T a k 1 T + D a N x i ρ T x k=1 i i m i i +D a a 1 T x T,i m i N i ( 2.63) i T x i=1 i In all simulations, the thermal diffusion is retained only for H 2 and H and is neglected for the other species Diffusion coefficients For the gaseous species the mixture diffusion coefficient, D k, for the k th species is calculated as [155]: 1 Y D k = k KK χ j j=1,j k D j,k ( 2.64) where D j,k is the binary diffusion coefficient. The k th species thermal diffusion coefficient D T k is evaluated from D T k =D k Θ k ( 2.65) where Θ k is the thermal diffusion ratio [156]. Two different approximations have been used to evaluate the diffusion coefficients for the soot particles. For modeling the coflow diffusion flame the binary diffusion coefficient of soot aggregates, D a i, is given as:

58 39 D a i = k B T C c (Kn) ( 2.66) 3πμd m where k B is the Boltzmann constant; μ is the gas viscosity; d m is the mobility diameter; C c (Kn) is the Cunningham slip correction factor as a function of the Knudsen number Kn and is calculated as [157] The Knudsen number Kn is defined as: C c (Kn) = Kn ( 2.67) Kn = 2λ mfp ( 2.68) d m with λ mfp being the mean free path of the gas. The mobility diameter and the absorbing cluster radius have been studied by many researchers. In the current sectional aerosol dynamics model, the calculation of mobility diameter is as follows: 2r p n p 0.43 free-molecular regime d m = D f ( 2.69) 2R f ( 2 ) continuum regime where r p is the primary particle radius; n p is the number of primary particles per aggregate; and the outer radius of an aggregate R f is defined as: R f =r p(fn p) 1D f ( 2.70) with f being the volume filling factor which accounts for the fact that even in a closely packed structure, the spherical monomers cannot occupy the whole available volume [158]. a The thermal diffusion coefficient of soot aggregates D T,i are calculated according to Talbot et al. [159] as follows: a D T,i = 0.55μ ρ ( 2.71) In modeling the stagnation flame, as discussed by Abid et al. [19], the diffusion velocities are the main drivers of particles and species as they approach the stagnation plate. Therefore, the particle diffusion coefficients are determined through a more sophisticated expression proposed by Li and Wang [160]. The binary diffusion coefficient has the form similar to Einstein s diffusion coefficient expression: D a i = 3 k B T (1+α ) ( 2.72) 2 2πm r Nd 2 (1,1) m Ω avg

59 40 Here, m r is the reduced mass of the gas molecule and particle, m r =m g m p (m g +m p) and m p is the (1,1) mass of the particle; N is the number density of the gas; Ω avg and α are the average reduced collision integral and the correction factor taken from [160]. The thermal diffusion coefficient for soot aggregates are taken from [161]. a D T,i = (1,2) Ω avg λ (1,1) ( 2.73) Nk B (1,2) where λ is the thermal conductivity of gas; Ω avg is the average reduce collision integral determined based on expression given in [161]. 2.5 Numerical Methods Two numerical approaches are used to find the solutions to the governing equations described in the previous sections for various reacting flows studied in this work. Discretization of the governing equations for the coflow diffusion flames is done using a control volume scheme. Parallel computing has been utilized to speed up the calculation for these flames. The premixed boundary value problem is solved numerically based on the finite difference framework. The details of the modeling methodology for the coflow diffusion flames and the premixed stagnation flame are presented in the following sections D coflow diffusion flame The gas-phase governing equations and the sectional soot equations are discretized based on the finite volume method on a staggered grid for the coflow diffusion flames. The Semi-Implicit Method for Pressure Linked Equations (SIMPLE algorithm) is used to handle the pressure and velocity coupling [162]. The coupling between pressure and velocity in the SIMPLE algorithm is achieved by transforming the continuity equation into the pressure correction equation. The diffusive terms are discretized using the second order central difference scheme while the convective terms are discretized by the power law scheme [162]. Pseudo-time marching is used to arrive at the converged steady state solution from the initial guess. The equations of mass, momentum, species, energy, and sectional soot are highly coupled within themselves and through detailed thermodynamic and transport relations and chemical kinetics. However, to alleviate the strong interaction between the flow and combustion, and to avoid Ω avg

60 41 saturating memory capacity by simultaneously solving this system of partial differential equations, the governing equations are solved in a semi-coupled way. In this method, the conservative quantities are divided into three categories: the fluid flow, the gas phase and the aerosol dynamic. Quantities in each category are solved separately and will be updated in the next iteration. Since the flow field acts as the carrier of the gas phase and the solid phase, it can be anticipated that a fast established flow field will provide a stable base for the reactions and therefore make the species equations easy to converge. The gas phase and the aerosol dynamic that involve multi-species, multi-step, chemical reactions are sensitive and stiff systems, and account for most of the CPU time in the computations. The most effective approach to minimize the computational costs is to reduce the iteration number by implementing efficient CFD methods which are compatible with parallel computing. Therefore, the efficient Tri-Diagonal Matrix Algorithm (TDMA) has been used to solve radial momentum, axial momentum, pressure correction and energy equations. In order to overcome the stiffness of the soot and species equations the source term is treated implicitly. In this method the source term,, is estimated using the Taylor series expansions [163]: R n+1 α = R n R α + α 2 Y Y m + O( Y m m m) m ( 2.74) Neglecting the second and higher order terms, the source terms are linearized using Eq The resulting Jacobian matrices are obtained by the perturbation method [164]. The Gaussian elimination method is used to solve the resulting linear system at each control volume. The species equations are solved control-volume-by-control-volume until the whole computational domain is covered. Then the sectional soot aggregates and number densities are solved in the same fashion as the species equation. Offering a potential solution to the computationally intensive combustion simulations, the Coflame code takes advantage of parallel computing by dividing most of the computational load between several computational processing units. Since most of the computational load is from species and sectional soot equations, these parts are parallelized. The parallelization has been done using the domain decomposition method (DDM) [165]. The computational domain is decomposed into NUMP sub-domains. Each sub-domain is consisted of a fixed set of

61 42 computational nodes with boundaries extending in the radial direction. Each sub-domain is then assigned to a processor for calculation and the calculations in all sub-domains are carried out simultaneously which makes NUMP the number of computing processors used. The parallel programming has been performed using message passing interface (MPI) [166]. The structure of the code to solve the system of equations is depicted in Figure 2.7. The numerical procedures solve for axial velocity u, radial velocity v, pressure correction p, gaseous species mass fractions Y k (k = 1, 2,, KK), sectional soot aggregate number densities N a p i (i = 1, 2,, MS), sectional soot primary particle number densities N i (i = 1, 2,, MS) and finally temperature T. Convergence is deemed to be achieved when the maximum relative error of flame temperature, species concentration, and soot volume fraction are all less than Sandia's CHEMKIN [167] and TRANSPORT [168] libraries are incorporated to calculate the gaseous species thermal properties, transport properties and chemical reaction rates from the database associated with the selected reaction mechanism. Initial Guess Solve Axial Momentum Solve Radial Momentum Solve Pressure Correction Correct Velocities and Pressure CHEMKIN Librery CHEMKIN Link File CHEMKIN Interpreter Chemical Mechanism Thermodynamic Data Solve Species Mass Solve Sectional Soot TRANSPORT Library TRANSPORT Link File TRANSPORT Fitting Solve Energy Transport Data Update Mixture Density No Check Convergence Criteria Yes Solution file Figure 2.7 Coflow code solver program structure.

62 Boundary conditions Inlet conditions are specified for the fuel and air streams at the z =0 boundary. Symmetry conditions are enforced at the centerline, i.e., at r = 0. Free-slip conditions are assumed at the outer radial boundary (e.g., at = cm). Zero-gradient conditions are enforced at the exit boundary. The mesh and boundary conditions are illustrated schematically in Figure 2.8. Figure 2.8 Schematic of the coflow diffusion flame boundary conditions and the non-uniform structured mesh Premixed stagnation flame The described soot sectional aerosol dynamic model has been added to the OPPDIF code [169] in order to simulate soot formation in the premixed stagnation flame. Discretization of the differential equations in the OPPDIF code uses finite differencing techniques for nonuniform mesh spacing. The discretization of the sectional aggregate number density and primary particle number density has been carried out similar to the species conservation equation discretization. Convective terms are discretized using the second order central difference approximation with the option to switch to the first order windward differences for better convergence.

63 44 The diffusive term in the species conservation equation and the sectional soot number density equations are approximated using an average-central difference approximation. The ordinary and thermal diffusion velocities for soot and species are approximated at the j ± 1/2 positions. The correction velocity V c is computed using Eq at the midpoints by summation of the diffusion velocities for all the species and soot particles. Upon calculation of the correction velocity the full diffusion velocities at midpoint is determined by adding the correction velocity to the diffusion velocity. Then the diffusion term is evaluated with the following difference approximation: d dz (ρy k V k ) j (ρy k V k ) j+1 2 (ρy k V k ) j 1 2 z j+1 2 z j 1 2 ( 2.75) All the non-differentiated terms, such as the chemical production rate terms, are evaluated at the mesh points j. Coefficients not appearing within derivatives are also evaluated at the mesh points. For the implementation of the Newton s method solution of the governing equations, once the coupled, nonlinear system of equations has been discretized, the system of equations is cast in residual form as follows: F(v) = 0 ( 2.76) in which v is the vector of all unknowns and F(v) is the vector of all equations. If v, a collection of approximate solution vectors, are chosen for the unknowns, the equations F likely will not vanish. Instead, the vector of residuals F(v ) is formed by evaluating the functions F : F(v ) = RES ( 2.77) The objective is to seek values, v, with zero residuals, F(v )=0. OPPDIF uses the modular solver routine TWOPNT to solve the boundary value problem. TWOPNT uses modified damped Newton s method to attempt solution of the steady-state equations, and resorts to time integration when the Newton iteration is not converging [164]. After time integration evolves the solution toward the steady state, TWOPNT returns to Newton s method to rapidly converge on the steady solution. From the initial estimate, v 0, Newton s method produces a sequence {v (n) } that converges to the solution of the nonlinear equations:

64 45 v (n+1) =v (n) F 1 + ( v ) F (v (n) ) ( 2.78) v (n) This algorithm is computationally intensive and suffers from lake of robustness. Evaluation of the Jacobian matrices F / v is time consuming, and convergence to the solution usually requires a very good initial guess v 0. The modified Newton method necessitates the following refinements to the original method. First, the Jacobian matrix is only updated after a finite number of iterations as Jacobian evolution is the most costly component of the algorithm, and the changes in the linear system is minimal from one iteration to the next. Second, so as to conservatively adjust the solution in each iteration, and reduce the likelihood of divergence, a damping parameter λ (n) has been introduced for the evaluation of v (n+1) from v (n). In this way the iteration becomes: where the damping factor decreases geometrically. v (n+1) =v (n) +λ (n) (J (n) ) 1 F (v (n) ) ( 2.79) λ (n) =2 0.5, 2 1.0,, ( 2.80) The elements of the Jacobian are formed by finite difference perturbations in the manner suggested by [170]. For more details of OPPDIF code, numerical method and modified Newton method please refer to [124,164,169,171] Boundary conditions The boundary conditions at the nozzles are: F= ρ I u I 2 ( 2.81) G=0 ( 2.82) ( dh dz ) =0 ( 2.83) I T=T I ( 2.84) ρuy k +ρv k Y k =(ρuy K ) I ( 2.85) ρun i +ρv i N i =(ρun i ) I ( 2.86)

65 46 The inflow boundary condition specifies the total mass flux, including diffusion and convection, rather than the species fraction ( Y k =Y k,i). If gradients exist at the boundary, these conditions allow diffusion into the nozzle. The boundary conditions at the stagnation wall are: F=0 ( 2.87) G=0 ( 2.88) ( dh dz ) W =0 ( 2.89) T=T W ( 2.90) ρ ( dv k Y k dz ) W = W k ω k ( 2.91) dn i =0 ( 2.92) ( dz ) W u, v, and V k are all zero at the stagnation wall as a no slip condition is assumed. The stagnation wall has a temperature T W equal to the measured temperature. The axial convective velocity was assumed to vanish, leading to an diffusive flux equal to that of the chemical source term for each species at the stagnation surface an assumption expected to be valid so long as the free radical concentrations are negligible immediately below the stagnation surface, as suggest by [19].

66 47 Chapter 3 Soot Particle Coalescence 3.1 Overview Soot comprises fractal-like chains of order of 100 small spherical particles. Soot aerosol morphology properties of interest include primary particle size (and/or size distribution) and number of primary particles per aggregates. Agglomerates are not rigid structures. Evidence of internal restructuring of aerosol agglomerates and the flexibility of nanoparticle chains is discussed in this chapter. Methods have been developed for relating particle properties to process conditions and the properties of the material composing the particles, namely the solid or liquidstate diffusion coefficient, surface energy, and particle density. The collision-coalescence mechanism of particle growth discussed in this chapter is thought to control primary particle size in the flames. Two coalescence models are proposed for predicting soot particle morphology in laminar coflow diffusion flames in this chapter. Finally, effect of different coalescence model parameters on prediction of primary particle diameter is investigated. 3.2 Introduction The final stage in the soot particle formation and growth mechanism is aggregation. The process of formation of fractal-like aggregate structures as a result of particle collisions is termed coagulation. Coagulation has a determining effect on the shaping of soot particle size distributions, soot number density, and soot morphology. After collision, soot particles may

67 48 experience structural evolution. The aggregate form may change due to (a) condensation and evaporation from its surface, (b) heating, and (c) mechanical stresses. The ability of aggregates to change their shape has important implications for aggregate transport and light scattering, as well as specific surface area, which plays a critical role in particle growth mechanisms. Thermal restructuring of soot aggregates is the focus of this chapter. The restructuring processes is depends on particle state, surface property, primary particle diameter, temperature, residence time, etc. [106]. The collision of liquid-like nascent soot particles leads to complete merging of the colliding particles which is known as the coalescence process [54]. The slow restructuring rate of the mature particles leads to the formation of the fractal-like aggregate structure. Observation of neck formation at the contact points of primary particles within an aggregate can be interpreted as partial coalescence or surface growth obliteration [39]. Figure 3.1 schematically presents the three stages in coalescence of particles. Although coalescence itself does not change the total mass of soot particles, it changes soot morphology, soot number density, and the soot particle size distribution. Therefore, it plays an important role in the structural evolution of soot particles. Figure 3.1 Schematic of coalescence process of two colliding particles The Collision-Coalescence Mechanism Aggregate formation is based on a series of steps assumed to proceed as follows: - Formation of particle precursor and condensable species - Nucleation - Collision-coalescence of nascent particles (the particles may behave in a liquid-like or solid-like manner during the coalescence period) - Termination or significant deceleration of coalescence due to increased particle size and/or reduction of temperature - Agglomeration of fractal-like structures as coalescence ceases from subsequent collision

68 49 - Continuous coalescence and neck formation of particles within the agglomerate structures Some of these processes may go on simultaneously. In addition, particles continuously gain mass through different physical and chemical growth processes. Therefore, the primary particles composing the agglomerates become considerably larger than the nascent particles. Particle diameter is a function of the temperature, growth and oxidation history that influence particle s thermo/chemical as well as geometrical properties. In general, the rate of particle coalescence is directly proportional to temperature, producing large singlet particles at high temperatures with a low specific surface area [106]. Based on experimental observations, three structures for soot particles produced in flames, as illustrated in Figure 3.2, can be identified: A cloud of individual spherical particles (Left panel of Figure 3.2), Fractal-like agglomerates (Right panel of Figure 3.2), and a continuum of states between these two limiting cases. From the mechanistic point of view, the difference between the rate of collision and coalescence shape the final structure of particles. The presence of a spectrum of particle structures at different stages in the flame is the evidence of variation of the rate of coalescence versus collision. In order to parametrize the collision and coalescence processes, two characteristic times are defined. The characteristic time of coagulation or collision is the average time between binary particle collisions, τ c, and the characteristic time of coalescence is the time for two particles to coalesce into a single sphere after making contact, τ f. The formation of spherical particles is the outcome of having the coalescence time τ f much smaller than τ c. When colliding particles cease to coalesce and τ f τ c, particles with agglomerate structures will be produced. Allowing for a finite rate of coalescence once two particles have collided will provide the basis for analyzing the structural evolution of particles. Figure 3.2 TEM images of soot particle samples along the centerline of a coflow diffusion flame of a surrogate for Jet A-1 at different heights above the fuel tube exit (Source: Reprinted from ref. [35]).

69 50 Dworkin et al. [141] have shown that the sectional soot model described in Chapter 2 combined with the developed mechanism (the DLR mechanism) is capable of accurately predicting soot volume fraction in an ethylene/air coflow diffusion flame. However, the model performance to predict the primary particle properties was unsatisfactory. Major underprediction of the primary particle diameter followed by overprediction of number density of primary particles was obtained using the sectional soot model. These results are an indication of a deficiency in modeling soot primary particles. One of the processes involving primary particles that was not considered in the Dworkin et al. [141] study is particle coalescence. The coalescence process increases the diameter of the primary particle by merging the primary particles in contact, which also reduces the total number of primary particles. Therefore, in this chapter coalescence models that are suitable for sectional soot modeling have been developed. A limited number of soot coalescence models can be found in the literature. Most soot models that consider the coalescence process rely on the assumption of instantaneous particle merging for small particles [41,172,173]. Ulrich and Subramanian [174] represents one of the first modeling approaches that highlighted the importance of a finite coalescence rate on prediction of soot particle structures. A coalescence model has been proposed in the work by Ulrich and Subramanian [174] and was employed for prediction of flame generated silica particles. Sander et al. [175] also proposed a coalescence model and characteristic time for SiO 2 particles which were further used by Sander et al. [176] and D Anna et al. [177] to predict soot particle formation and their size distribution in premixed flames. In the sections that follow, the coalescence processes are incorporated in a model applicable to the sectional primary particle number density equation. Expressions are derived for τ f in terms of material properties and process conditions from the collision-coalescence theory. The resulting models have been used to predict particle morphology in a coflow diffusion ethylene/air flame. 3.3 Rate of Coalescence The coalescence mechanism for liquid particles and solid particles are different. For liquids, the mechanism of coalescence usually considered is viscous flow. For solids, diffusion and evaporation-condensation are the most common mechanisms for nanoparticle coalescence. These

70 51 mechanisms can be incorporated in the primary particle number density conservation equation through suitable expressions for the loss of primary particles due to coalescence considering its characteristic time. The coalescence rate can be derived from the linear rate law for decrease in the surface area [178]. Considering an agglomerate particle composed of primary particles, the coalescence rate can be expressed as follows [179]: dn P dt Viscous Flow Transport 2 = 3 τ f ( n p n 3 ( 3.1) p ) For liquid particles, coalescence takes place by viscous flow. After two droplets are in contact, the surface tension forces the doublet shape to change and reach its equilibrium state. The deformation continues to minimize surface free energy. The shear forces, however, resist against fluid layer motions to approach a spherical shape. Thus, for these particles, the characteristic coalescence time of two equal-sized spheres of diameter, d p, is given by [180]: τ f = πμd p σ ( 3.2) where μ is the viscosity and σ is the surface energy Transport by Diffusion Unlike liquid particle, the equilibrium form for solid particles in contact is not predetermined. The exact shape corresponding to the minimum surface Gibbs free energy should be estimated by a Wulff construction [181] involving complex calculations of crystal plane rearrangements. One common assumption to avoid the cumbersome calculations is that the particles are spherical and their properties are isotropic. Thereafter, the characteristic time,, can be obtained as [182] τ f = 3 64π k B TV Dσv m ( 3.3) where is the Boltzmann constant; is the temperature; is the particle volume; is the surface tension; is the molecular volume, and is the solid-state diffusion coefficient. The value of D corresponds to the dominant transport route for example, lattice, grain boundary, or surface diffusion [106]. Nanosized particles like soot have high ratios of surface area to volume, and it is expected that surface diffusion is the dominant diffusion route for these particles. The

71 52 driving force for surface diffusion is the gradient of the chemical potential along the surface. Therefore, the diffusion coefficient is a function of surface free energy and the width of the surface layer which makes it depend strongly on the temperature. An Arrhenius form with an activation energy can be used to describe the temperature dependency of the diffusion coefficient [106]. 3.4 Coalescence Model The coalescence mechanisms proposed for solid and liquid particles suggest that as the temperature increases, the rate of coalescence increases exponentially [179,180,182,183]. Most coalescence mechanisms are based on the assumption that at high temperatures the particles are liquid and coalesce instantaneously. As the temperature decreases, the particles become solid and the rate of coalescence dramatically reduces. There is also a transition state between the liquid phase and solid phase [183]. For soot particles however, a different pattern has been observed [30,53,184,185]. These studies on the evolution of soot particles suggest that nascent soot particles have liquid-like behaviour. The soot particles at early stages will present as one spherical droplet in the flames and show no sign of aggregation [35,184,185]. This behaviour can be interpreted as being of high coalescence rate for young soot particles. As these particles traverse the flame, and experience higher temperatures, they transform to solid particles and form fractal-like aggregates. The solidification of soot particles has been attributed to the carbonisation process [35, ]. Carbonisation is a collection of chemical activities of the inter-particle elements and rearrangements of the internal structures near the surface of soot particles, which results in solidification of the particles and alteration of the surface chemical reactivity. The phase change part of the carbonisation process is the focus of this chapter. The effect of the carbonisation on the surface reactivity will be discussed in the next chapter. Kholghy et al. [35] observed an abrupt change of soot particles from liquid-like droplets to fractal-like aggregates around 1500 K in a diffusion flame, suggesting a chemical reaction with an activation energy that is overcome at that temperature. Reilly et al. [185] and Dobbins et al. [53], by measuring soot particle carbon and hydrogen content observed an increase in carbon to hydrogen ratio (C/H) as the particles went through the carbonization process. Therefore, these

72 53 studies imply that the carbonization reaction involves hydrogen release and carbon-carbon bond formation. In spite of all efforts put into studying the carbonization process, the chemical mechanism of carbonization is not well understood and further investigation needs to be conducted to assess the reaction rates and other thermo/chemical properties of the process. Nonetheless, two approaches to model coalescence of soot particles are proposed here. The first approach is the simpler model to implement. This model only takes into account the dependency of coalescence rate on the primary particle diameter and this model will be called the cut-off model hereafter. The second model, which will be called the sintering model hereafter, is based on the neck growth model, Eq. 3.1, with a characteristic time as a function of primary particle diameter and temperature Cut-off Model (Model I) The cut-off model is based on the idea of immediate merging of colliding particles having particle diameters less than a finite value, as it is displayed schematically on the left side of Figure 3.3. The assumption of instantaneous fusion has been applied by Fenimore and Jones [187], Howard et al. [188], and Smooke et al. [41] to describe soot particle disappearance rates in flames. Such an assumption is valid if particles rapidly coalesce between collisions. The assumption is consistent with the observations of single, discrete, spherical particles in the electron micrographs of small soot samples by Bonne et al. [24] and Homann [25]. The cut-off diameter model in the sectional soot aerosol dynamic model has been implemented by modifying parameter η p,ijk, Eq. 2.50, in the primary particle coagulation model: η p,ijk = { 1 mi m j +m k (n p,j +n p,k) if d p,i <d Cut if d p,i >d Cut ( 3.4) where d Cut is the cut-off diameter. The cut-off diameter represents the diameter at which the particles experience phase change and transfer from a liquid-like state into a solid state. Smooke et al. [41] choose 25 nm as the cut-off diameter for modeling soot formation in laminar diffusion flames. Woods and Haynes [97] suggest that all colliding particles must coalesce until their sizes exceed 20 nm. The cut-off diameter represents the size of which the particles experience a phase change from liquid-like to solid. Therefore in this study cut-off diameter has been chosen to be d Cut =20 nm.

73 54 Figure 3.3 Schematic representation of aggregate formation with cut-off coalescence Sintering Model (Model II) The sintering model allows merging of the colliding soot particles with a finite residence time. The residence time is a function of local temperature and particle diameter. Figure 3.4 depicts the coalescence mechanism considered in the sintering model. The neck growth model described by Eq. 3.1 determines the rate of coalescence of primary particles within a single aggregate. In order to find the total rate of coalescence for particles present in the section, the rate by the neck growth model is ( = 3 2 t ) τ f ( n p n 3 a p N ) i Sint N i p ( 3.5) In order to have an accurate expression for characteristic coalescence time,, it is necessary to identify the different regimes of soot coalescence, verify the transition conditions from liquidlike to solid-state, and know particle thermo/chemical properties such as its structure and chemical composition. Unfortunately, such information is unavailable due to the lack of fundamental understanding of part of the kinetics of soot particles. Therefore, assumptions have to be made for the form of the characteristic time. The model does not distinguish solid and liquid particles and a single coalescence mechanism has been used for all the particles. The characteristic time has been assumed to be proportional to the forth power of primary particle diameter, [179]. The dependency on the forth power diameter is typical for solid particles

74 55 [179], and it was enforced here to ensure formation of fractal-like aggregates when the primary particle diameters are large enough (e.g., 20 nm). An Arrhenius function has been used to account for the temperature dependency of the diffusion coefficient in Eq. 3.3 [106]. The activation energy and pre-exponential terms are adjusted to allow small particles to merge. τ f = d p Texp 4 ( 3.6) ( T ) Figure 3.4 Schematic representation of the sintering model for soot particle coalescence. 3.5 Methodology The coalesce models are implemented in the sectional soot model to predict soot particle formation in the atmospheric pressure, non-smoking, coflow laminar ethylene/air diffusion flame, first studied by Santoro et al. [58] (referred to as the Santoro flame hereafter). The Santoro burner configuration is schematically depicted in Figure 3.5. The coflow burner consists of an 11.1 mm inner diameter fuel tube at the center of the burner surrounded by the cylindrical air passage with an inner diameter of mm. Gaseous C2H4 fuel flows at a mean velocity of 3.98 cm/s (flow rate 3.85 cm 3 /s) and the air flows at a mean velocity of 8.9 cm/s (flow rate cm 3 /s) at room temperature conditions. A ceramic honeycomb structure is installed into the air annulus straightening the air flow. Although the fuel and air flows are at atmospheric temperature and pressure, due to the anchoring of the flame around the fuel tube, some heating of the fuel tube and fuel flow does occur. In order to reconcile the fuel tube preheating, the inlet

75 56 fuel flow temperature boundary has been increased to 650 K as recommended by [ ]. The flow configuration generates a stable, sooting, nonsmoking flame, with a visible flame height of approximately 88 mm. This particular flame has been chosen because extensive experimental measurements of soot particles have been obtained during over 30 years of studies of this flame. These measurements include soot volume fraction, average primary particle diameter, aggregate number densities, primary particle number densities, fractal dimension, and average number of primary particles per aggregate [33,37,38,56 58,192]. Most relevant to coalesce are those experimental data on soot particle morphology, i.e., average primary particle diameter, primary particle number densities, and average number of primary particles per aggregate. Air Air Fuel Figure 3.5 Schematic representation of burner configuration of Santoro flame [58]. [Courtesy of Dr. Meghdad Saffaripour, University of Toronto.] Numerical Model For the gas phase, the fully coupled elliptical conservation equations for mass, momentum, energy, and species mass fraction are solved. The model utilizes the axi-symmetrical nature of the flame, and equations are solved in the two-dimensional (z and r) cylindrical co-ordinate system. A detailed description of the governing equations, boundary conditions, and solution methodology can be found in Chapter 2. The DLR chemical mechanism (see chemical

76 57 mechanisms in Chapter 2) with 93 species and 719 reactions was applied to describe the oxidation of the fuel and the formation of PAHs. Soot is modeled using the detailed fully coupled sectional aerosol dynamics model discussed in Chapter 2. In this approach the continual soot particle mass distribution is divided into a discrete number of soot clusters, each with an assigned mass. For this study, the soot particle mass range is divided into 35 discrete sections that describe the soot particle diameter ranging between 0.86 nm and 3.3 μm. Conservation equations of soot aggregate number densities, and primary particle number densities are solved for each soot section. Nucleation is modeled based on the collision of PAH molecules with 5 aromatic rings, i.e., benzopyrene and benzo[ghi]flouranthene, in the free-molecular regime [40,193], which serves as a connection between the gas phase reaction mechanism and the first soot section, with collision efficiency of 100%. The HACA mechanism [86] is used to describe soot particle surface growth with a constant surface reactivity, α, of 0.45 for the soot models with coalescence. While this parameter is the subject of detailed investigation later in this thesis, here it is held constant to isolate the effect of coalescence modelling. PAH condensation is modelled based on collision theory between 5 member ring PAH molecules and aggregates, with a collision efficiency of 0.5 [147]. A constant coagulation efficiency, ξ, of 0.2 is chosen based on the recommendation of Zhang et al. [118]. 3.6 Results and Discussion In order to test the coalescence models, the Santoro flame [58] has been simulated using two models. Included in the first model is the cut-off coalescence model with the 20 nm diameter chosen as the limiting factor for coalescence. The second set of computations employed the sintering model with a characteristic time described by Eq The predicted soot properties using these models are compared to measured soot properties. The soot properties of interest are soot volume fraction, soot aggregate number density, primary particle number density, average number of primary particles per aggregate, and average primary particle diameters. The predictions of soot formation in the Santoro flame [58] using the model without any coalescence (Model 0) are also included for comparison. For Model 0, the surface reactivity parameter, α, of has been used based on the results of Dworkin et al. [141]. The predicted soot results will

77 58 be presented over two regions in the flame. The soot concentration peaks at the annular region in the Santoro flame [58], therefore, the soot properties along the streamline passing through the maximum soot concentration location, also known as flame wing will be presented. The soot predictions along the centerline of the flame are also included. The importance of these two regions in the flame, as will be discussed in the next chapter, is in the difference between soot growth mechanisms. Soot formation on the wings is dominated by chemical surface growth whereas along the centerline, soot growth via PAH addition is the main soot growth route. Finally, the effect of different parameters in the coalescence models has been investigated Annular Pathline Comparison The predicted soot volume fraction along the annular pathline exhibiting the maximum soot concentration as a function of height above the fuel tube, and residence time, are depicted in Figure 3.6 and Figure 3.7, respectively. The soot predictions verify that all three soot models are able to predict the soot concentration within the uncertainty range of experimental measurements from the literature [58,192]. The agreement of predicted soot volume fractions with experimental data was expected since the parameter α for each model was deliberately chosen to correctly reproduce the maximum soot volume fraction in the flame. The reason being, now that all the models have the same amount of mass of soot in their system, a more sensible assessment of their abilities to predict particle morphology could be made.

78 59 [58] Figure 3.6 Comparison of the predicted soot volume fraction along the annular pathline exhibiting the maximum soot volume fraction using a sintering coalescence model (solid line), the cut-off coalescence model (dashed line) and no coalescence (dot-dashed line) with the experimental measurements by [58]. [192] Figure 3.7 Comparison of the predicted soot volume fraction along the annular pathline exhibiting the maximum soot volume fraction using a sintering coalescence model (solid line), cut-off coalescence model (dashed line) and no-coalescence (dot-dashed line) with the experimental measurements by [192]. Improving predictability of the soot aerosol dynamics model for average particle diameter is the pivotal milestone of adding the coalescence process. As presented in Figure 3.8, the model without coalescence underpredicts the primary particle diameter everywhere along the pathline exhibiting maximum soot concentration. The no-coalescence model predicts the maximum

79 60 average primary particle diameter to be 3.79 nm whereas the experimental data from the literature [56] shows the maximum primary particle diameter to be in the range of nm. Addition of a coalescence model with either a cut-off diameter or sintering profoundly improved the particle diameter predictions. The maximum particle diameter predicted by the cut-off model and the sintering model are 22 and 30 nm, respectively. [56] Figure 3.8 Comparison of the predicted average primary particle diameter along the annular pathline exhibiting the maximum soot volume fraction, using a sintering coalescence model (solid line), cut-off coalescence model (dashed line) and no coalescence (dot-dashed line) with the experimental measurements by [56]. Although both of these coalescence models improved the predictions of average diameter, they present distinctive behaviour which can be explored to gain a better understanding of the nature of soot particle growth. The cut-off model shows a rapid growth in particle diameter in the regions closer to the fuel tube before the diameter of primary particles hits the 20 nm cut-off limit, which arrest the coalescence process. In this region, z <3 cm, predicted particle diameter by the cut-off model shows better agreement with the experiments. The underprediction of particle diameter by the sintering model and the reasonable predictions of the cut-off model in the lower heights of the flame suggest that the apparent sintering rate is much faster than the rate used in the model in this region. The results are reminiscent of the liquid-like behaviour observed by Kholghy et al. [35] in this region in the diffusion flame. An increase in temperature (see Eq. 3.6) and number of primary particles per aggregate (see Eq. 3.5, and will be discussed later with regard to Figure 3.11) at heights above z =3 cm accelerates the sintering rate in this region

80 61 which results in primary particle diameters as large as 30 nm. Finally, above the z =4 cm height, the soot particles enter the oxidation zone and particle diameter decreases due to lose of mass. An important observation which is similar between the cut-off model and the model without coalescence is the negligible increase of particle diameter in the regions where coalescence is not present. This observation becomes more intriguing when the diameter profile, Figure 3.8, is compared with the soot volume fraction profile, Figure 3.6. While the diameter is modestly increased, significant mass has been added to the soot particles from the gas phase. The soot volume fraction for the cut-off model increased from 4.4 ppm, at z =2 cm where the average particle diameter is 20 nm, to 12 ppm at z =4 cm where the particle diameter reaches only 22 nm. In other words, the average diameter only increased by 10%, while soot mass has been almost tripled. The primary particle number density profile, depicted in Figure 3.9, can be used to further elucidate the situation. When entering the region where coalescence has ceased, the primary particle number density vastly increases. Since the growth mechanisms are surface dependent, most of the additional mass will be absorbed by the small particles, which have a higher surface to volume ratio. Therefore, the mass addition, instead of growing the existent particles, will be distributed among the newly incipient soot particles. Thus, the increase in the soot mass will barely result in an increase in the average particle diameter. [39] [57] Figure 3.9 Comparison of the predicted primary particle number density along the annular pathline exhibiting the maximum soot volume fraction using a sintering coalescence model (solid line), cut-off coalescence model (dashed line) and no coalescence (dot-dashed line) with the experimental measurements by [39,57].

81 62 The number of primary particles is controlled by the nucleation process and there are assumptions in the soot model which make nucleation more favourable. Nucleation and condensation are the two processes that compete to absorb PAHs into the condensed phase. Nucleation is modeled as being 100% efficient where condensation efficiency is considered to be 20% [147]. Also the shape of the condensed phase matter present in the first few sections is considered to be a complete sphere, where in reality these are stacks of PAHs. Since the surface of area of mass equivalent sphere is appreciably less than the PAH stacks, the spherical shape assumption under-represents the area of the small particles. Condensation is a surface dependent process, therefore the dimer shape assumption further supresses condensation. The final outcome of these assumptions is that most of the PAH growth will be contribute to an increase in the number of particles (Figure 3.9) as opposed to an increase of the existing particle volume (Figure 3.8). These observations are consistent with the results of Saffaripour et al. [40] and Eaves et al. [193]. For more discussion on nucleation and condensation please refer to Chapter 5. Similar to the particle diameter predictions, the cut-off coalescence model in the lower flame heights shows good agreement with the experimental data from [39,57] while the sintering model overpredicts the number density of primary particles. Upstream in the flame, the sintering model predicted particle number density to drop within the uncertainty range of experimental data, whereas the cut-off model now overpredicts the particle number density. Both particle diameter and number density results imply that a combination of these two models may be necessary in order to predict soot morphology along the wings. Predicted aggregate number density and number of primary particles per aggregate along the wings are plotted in Figure 3.10 and Figure 3.11, respectively. Both of these properties are directly dependent on the coagulation and fragmentation processes. Both coalescence models were able to predict aggregate number density along the pathline of maximum soot within the uncertainty of the experimental data. It should be noted that in the presented modeling results, only aggregates larger than 5 nm in diameter, which is the threshold for the experimental measurements have been considered in calculating total number of aggregates. While not changing the coalescence models results substantially, neglecting the particles smaller than 5 nm is the primary reason for the undeprediction of aggregate number density of the model without coalescence.

82 63 [57] [192] Figure 3.10 Comparison of the predicted aggregate number density along the annular pathline exhibiting the maximum soot volume fraction using a sintering coalescence model (solid line), cut-off coalescence model (dashed line) and no coalescence (dot-dashed line) with the experimental measurements by [57,192]. [57] [33] Figure 3.11 Comparison of the predicted average number of primary particles per aggregate along the annular pathline exhibiting the maximum soot volume fraction using a sintering coalescence model (solid line), cut-off coalescence model (dashed line) and no coalescence (dot-dashed line) with the experimental measurements by [57,192]. The number of primary particles per aggregate ( ) results that are depicted in Figure 3.10 further emphasize the observations made earlier from the particle diameter and number density results. The cut-off model underpredicts downstream of the flame while the sintering model overpredicts compared to the experimental data in these areas. This result suggests that the

83 64 soot particle coalescence characteristic time should be somewhere between the instantaneous cut-off model and the sintering model lower in the flame. However, overprediction of the number of primary particles by all three models on the higher heights above the fuel tube suggests that too many particles are forming. The coalescence process being dependent on the rate of collision as well as thermophysical properties of particles is not solely accountable for dissipation of primary particles. An alternative mechanism for controlling particle formation would be to limit the nucleation process. In the models employed in this section it is assumed that all the collisions between PAH molecules are 100% efficient in nucleating particles. However, recent studies by Sabbah et al. [102] and Wang [17] on PAH dimerization suggest that the dimerization process is not thermodynamically favored and is highly reversible. The studies by Saffaripour et al. [40] and Eaves et al. [193] also confirm that if a very low nucleation efficiency is employed, or the nucleation process is modeled as fully reversible, the relevant average soot morphological parameters along the wings and centerline can be predicted reasonably. Indeed, a combination of both of these pathways would be more representative of the nature of soot particle formation Centerline Comparison For further validation and comparison of the coalescence models, the soot particle predictions along the centerline of the Santoro flame [58] are presented here. Only the primary particle diameter and soot volume fraction results are presented here due to similarities of the prediction trends observed on the wings. The average primary particle diameter predictions along the centerline for the cut-off model, sintering model, and the no-coalescence model with the experimental data from Koylue et al. [37] are shown in Figure Both coalescence models improved the diameter predictions substantially compared to the model without coalescence, which similar to the wings results, underpredicts the primary particle diameter. The most distinctive difference between the predictions of primary particle diameter along the centerline with those along the wings is that the cut-off model predicts larger particles all along the centerline. However, on the wings the maximum diameter predicted by the sintering model was larger compared to the cut-off model, and it was closer to the measured diameter. The high temperature dependency of the sintering model underlies its underperformance. The soot formation on the centerline starts in the inner regions of the flame, where the temperature that the soot particle experiences is lower than the flame temperature. The temperature does not exceed

84 K on the centerline until after z = 8.5 cm where soot formation has ceased and the particles have entered the oxidation zone (see Figure 3.13). The temperature profile experienced by the particles on the wings is completely contrary. The soot formation starts near the flame front where the temperature is above 1700 K and the temperature never drops below 1500 K. The high sensitivity of the sintering rate to the temperature and the difference between the temperature profiles along the wings and centerline caused the sintering model to underperforme along the centerline. [37] Figure 3.12 Comparison of the predicted average primary particle diameter along the centerline using a sintering coalescence model (solid line), cut-off coalescence model (dashed line) and no coalescence (dot-dashed line) with the experimental measurements by [37]. The soot volume fraction profiles along the centerline are depicted in Figure The cut-off model and the no-coalescence model predict the soot volume fraction reasonably well compared to the experimental data by [37,38,58]. The predicted soot volume fraction by the sintering model is lower than the predictions of the two other models and it is lower than the experimental data. The soot formation along the centerline is dominated by PAH growth processes, i.e., nucleation and condensation as discussed by Thomson and coworkers [141,194,195]. The PAH condensation rate as described in Chapter 2 is modeled based on the collision of PAH molecules in the gas with the soot particles, and the collision rate is a function of soot surface area. For a given mass of soot, if the set of particles consists of smaller particles, there will be a higher chance for PAH molecules to collide and adsorb onto the soot particles. In other words, PAH adsorption will be supressed when the surface to volume ratio is lower. The surface to volume ratio profiles along the centerline are illustrated in Figure The sintering model has the

85 66 lowest surface to volume ratio, therefore, predicts a lower soot volume fraction and it is not as efficient as the two other models in adsorption of the gas phase PAHs. It should be noted that the surface to volume ratio is calculated based on the weighted average of the particles surface to volume ratio at each location. For the cut-off model this value is substantially higher than the mean surface to volume ratio. The difference between the two values is an indication of the presence of a great number of small particles in the particle size distribution which has low contribution to the overall mass. [58] [38] [37] Figure 3.13 Comparison of the predicted soot volume fraction along the centerline using a sintering coalescence model (solid line), cut-off coalescence model (dashed line) and no coalescence (dot-dashed line) with the experimental measurements by [37,38,58] (a log scale is used so that comparisons can be made at heights less than 4 cm).

86 67 Figure 3.14 Variation of surface to volume ratio along the centerline using a sintering coalescence model (solid line), cut-off coalescence model (dashed line) and no coalescence (dot-dashed line). Studying the particle size distribution (PSD) function can help identifying the roles of different processes in forming aggregates. The predicted PSDs along the wings and centerline on the Santoro flame are provided in Appendix A for various heights above the burner. Both on the wings and centerline, unimodal distributions are found at lower heights, where the aggregate number density is dominated by small aggregates, suggesting that nucleation is the dominant process. The unimodal distribution becomes bimodal due to the growth and coagulation processes as the height increases. Meanwhile, the curve widens, indicating large aggregates are formed. As particles enter the oxidation region, the distribution becomes unimodal again and the area under the curve reduces Sensitivity analysis In this section the effect of different coalescence model parameters on the soot particle diameter predictions will be examined. Three different coalescence parameters will be analysed. First to be studied is the effect of the choice of cut-off diameter. The effect of activation energy in the sintering characteristic time function, Eq. 3.6, on the predicted particle diameter will be discussed next. Finally, a discussion on the effect of coalescence on particle diameter in the soot oxidation zone will be provided.

87 Cut-off Diameter The only assigned parameter in the cut-off coalescence model is the cut-off diameter for which the boundary between instantaneous merging of the colliding particle and agglomeration is defined. In order to investigate the effect of the choice of the cut-off diameter, soot formation in the Santoro flame [58] is simulated using three different cut-off diameters, namely 15, 20, and 25 nm. The predicted primary particle diameter along the wings and centerline are presented in Figure 3.15a, and Figure 3.15b, respectively. The particle diameter profiles in Figure 3.15 show a strong dependence of predicted maximum diameter with the choice of cut-off diameter. In all three cases the predicted maximum diameter both on the wings and the centerline are very close to the cut-off diameter. The observed dependency of the predicted diameter on the cut-off diameter, as was discussed in Section 3.6.1, is mostly due to the highly efficient nucleation model which forms a vast number of small particles. Since the smaller particles have a high surface to volume ratio, they have a higher tendency to absorb the available mass from the gas phase in competition with the larger particles. Thus, the mass addition, instead of growing the existent particles, will be distributed among the newly incipient soot particles and will barely result in an increase in the particle average diameter. [56] [37] (a) Figure 3.15 Comparison of the predicted average primary particle diameter using different cut-off diameter coalescence models a) along the annular pathline exhibiting the maximum soot volume fraction with the experimental measurements by [56] and b) along the centerline with the experimental measurements by [37]. (b)

88 Coalescence Characteristic Time The next parameter that is the subject of study is the coalescence characteristic time, τ f, present in the sintering model. The Arrhenius function for the characteristic time, Eq. 3.6, has a preexponential factor and an activation energy that needs to be estimated, ideally based on the comprehensive study of the surface characteristics of soot particles under a flame environment. However, such knowledge of the soot particle surface is not available. Instead, by analysing the effect of pre-exponential and activation energy parameters on the prediction of soot particles, an estimated range for these parameters can be identified. Decreasing any of these parameters will decrease the characteristic time, meaning that the time needed for particles to merge reduces. Therefore, the coalescence process becomes more efficient and the existence of larger particles is expected to be predicted. In order to quantitatively evaluate the influence of τ f on the predicted particle size, the sintering model with four different activation energies has been employed to model soot particles in the Santoro flame [58]. The τ f profiles for a 10 nm soot particle as a function of temperature with the four activation energies are shown in Figure The highest activation energy for the characteristic time is EA 1 = (1/K) and the following characteristic coalescence times, each has an 8% lower activation energy than the preceding characteristic coalescence time. The predicted particle diameter profiles along the wings using these four activation energies are shown in Figure 3.17a. The characteristic time reduces by an average factor of 3.5 when the activation energy reduces from EA 1 = to EA 2 = This reduction of the characteristic time leads to an increase of the maximum primary particle diameter predicted from 30 nm to 43 nm (43% increase) on the wings. Similar trends are obtained when the preexponential factor in the characteristic time has been altered. Shown in Figure 3.17b is the predicted particle diameter using different pre-exponential factors. When the pre-exponential factor is reduced from A 1 = (s/nm 4 ) by a factor of two, the predicted maximum particle diameter is increased by 20%.

89 70 Figure 3.16 Variation of the characteristic coalescence time of a 10 nm soot particle with temperature with four different activation energies. [56] [56] (a) Figure 3.17 Comparison of the predicted average primary particle diameter along the annular pathline exhibiting the maximum soot volume fraction using a) different activation energy and b) different pre-exponential factor for the sintering coalescence model with the experimental measurements by [56]. The effect of reducing the characteristic time on the predicted maximum particle diameter is graphically depicted in Figure The coalescence process is dependent on particle collision. This graph is showing that if the coalescence residence time is further decreased, the particle diameter will not increase linearly and the particle diameter reaches its maximum limit, which is the diameter of the aggregate; meaning that all the primary particles within the aggregate are (b)

90 71 completely merged, and the particle is now a singlet sphere. This result further emphasizes the dependency of the coalescence process on particle collision. If there were insufficient particle coagulations, the rate of coalescence would become irrelevant. Figure 3.18 Effect of reduction of characteristic time on the predicted maximum primary particle diameter along the annular pathline exhibiting the maximum soot volume fraction Coalescence and Oxidation The treatment of coalescence processes in the oxidation region is the focus of the final section of this chapter. A vast number of studies have been carried on in the literature focused on soot particle evolution and examination of their internal structure. Based on extensive studies of soot formation in different flames, a number of scenarios have been proposed for soot particles evolution. Some of these scenarios related to soot formation in diffusion flames have been reviewed by Kholghy et al. [35]. Although there is an ongoing debate about the early stages of soot formation, the soot evolution studies unanimously conclude that soot particles eventually reach a rigid state [30,35,185,196]. The rigidifying process of soot particles is attributed to carbonization. Carbonization is described as a complex process involving formation of activated complexes, molecular rearrangement, polymerization, and dehydrogenation [55,197]. However, the current coalescence models are not sensitive to the carbonization of particles. Moreover, both coalescence models overpredict the particle diameters in the oxidation regions (higher heights of the flame) while the models predict the soot volume fraction in agreement with the experiments (see Figure 3.6). This overprediction of diameter is caused by the fact that

91 72 the coalescence models continue to merge particles during their oxidation with the same rate as the nascent soot particles. To address this deficiency, a coalescence termination criterion has been added to the sintering model. Those studies of soot particle evolution in diffusion flames suggest that the soot particles are carbonized by the time they enter the oxidation region [35,51,53,58,185]. Therefore, the coalescence process has been set to cease when entering the oxidation zone. Since molecular oxygen is the main oxidizer of the soot particles in the diffusion flames, the concentration of oxygen in the mixture has been used to identify the oxidation region and the sensitivity of the results to the oxidation concentration is investigated. Three different cases have been modeled with a different O 2 concentration considered to define the oxidation region in each case. The O 2 mole fraction isopelths are depicted on the right panel of Figure 3.19, where the boundaries of the oxidation zone for each case are identified with the black solid line. The corresponding O 2 mole fractions for each of these boundaries are 0.02, 0.002, and , respectively. Computed isotherms of the Santoro flame [58] are also included on the left panel of Figure 3.19 to clarify the locations of each of the boundaries with respect to the flame front. Figure 3.19 Computational isotherms (left panel) and isopleths of O 2 mole fraction (right panel) in the Santoro coflow diffusion flame.

92 73 The predicted particle diameter for the three cases with a coalescence termination in the oxidation region and the original sintering model along with the experimental data is presented in Figure The predicted diameter profiles confirm the effectiveness of the additional termination criteria in the oxidation region. While the predicted soot diameter in the growth region remains unchanged compared to the original sintering model, the predicted diameters are reduced in the oxidation region and show more consistency with the measured particle diameters in both magnitude and the slope of diameter reduction. The third case with the O 2 mole fraction of as the oxidation boundary is underpredicting particle diameters, suggesting that the reduction of the coalescence region has been too intense. However, the first two cases predict particle diameters that are within the uncertainties of the experimental data in the oxidation region. Therefore, an O 2 mole fraction in the range of 0.02 and can be considered as a reasonable estimation for identifying the soot oxidation region in this flame and termination of the coalescence process. [56] Figure 3.20 Comparison of the predicted average primary particle diameter along the annular pathline exhibiting the maximum soot volume fraction using different sintering coalescence models with an oxidation cut-off, and the experimental measurements by [56]. 3.7 Conclusions In this chapter, two different soot particle coalescence models have been implemented into a two dimensional flame code to explore soot formation and oxidation in the non-smoking laminar coflow ethylene/air diffusion flame of Santoro [58], in combination with a PAH-based soot model and a detailed sectional aerosol dynamics model. The first coalescence model considered

93 74 instantaneous merging of particles upon collision if the diameters of the colliding particles are less than a cut-off diameter. The second coalescence model was based on gradual sintering of particles through surface diffusion. The rate of coalescence in the second model is a function of temperature, particle size, as well as number of particles per aggregate. The predicted soot results have been compared with the results of the model without coalescence and the experimental data from literature. The reported soot morphology properties included primary particle diameter, particle number density, aggregate number density, and number of primary particles per aggregate along the annular pathline exhibiting maximum soot concentration and centerline of the flame. Both coalescence models exhibited significant improvement in predicting soot particle morphology. The cut-off model in the lower heights of the flame predicted soot particle properties that are in closer agreement with the experiment data, while the sintering model predicted profiles that are more consistent with the measured properties in terms of overall shape and magnitude. Sensitivity of the soot prediction to the coalescence parameters has been analysed. The coalescence parameters studied were the cut-off diameter in the first model, and the characteristic time of coalescence in the sintering model. Finally, an update to the coalescence model based on experimental observations of soot particles on the flame oxidation regions has been introduced to improve its predicting capabilities. The updated model terminates the coalescence during the soot oxidation which leads to improvement of particle size predictions in this region. Soot particle coalescence is shown to be a complicated phenomenon. However, because it may significantly affect soot structure that in turn affects soot properties such as its health effect and environmental effect, this phenomenon is worth detailed investigation. In the future, more detailed theoretical and experimental studies should be conducted to gain a fundamental understanding of soot particles surface properties and chemical characteristic evolution.

94 75 Chapter 4 Soot Particle Surface Reactivity 4.1 Overview The effect of soot surface reactivity, in terms of the evolution of sites on the soot particles surface available for reaction with gas phase species, is investigated via modeling numerous ethylene/air flames, using a detailed combustion and sectional soot particle dynamics model. A new measure of soot particles age is introduced. A methodology has been developed to study soot particle surface reactivity. Subsequently, it is investigated if the surface reactivity can be correlated with the particle age. An exponential function giving a smooth transition of surface activity with particle age is employed to model a variety of ethylene/air flames, which differ in fuel stream dilution levels, fuel stream premixing, and burner configurations. Excellent agreement with measured soot volume fractions of a variety of flames, burners, and datasets could be obtained with this approach. The newly developed function based on particle age eliminates the need to fit soot surface growth parameters to each experimental condition. Finally, the applicability and limitation of the new surface reactivity function for use in detailed soot formation models is discussed. 4.2 Introduction Several stages have been identified during soot formation and oxidation. Soot formation starts with inception, which is the appearance of the first nano-scale soot particles. The newly incipient

95 76 soot particles can grow through surface growth via surface chemical reaction and polycyclic aromatic hydrocarbons (PAH) condensation, and through particle coagulation. Finally, soot particles lose mass and size during oxidation and fragmentation processes. Among all the different processes, surface growth is known to be responsible for most of the soot mass yield in many systems [198]. As a soot particle traverses hot fuel rich regions, the surface of the particle reacts with the gas phase. The chemical kinetics of the soot surface has been the subject of several studies. These studies concluded that acetylene is the primary growth species independent of the fuel type [11,198]. Based on this observation and the fact that the formation of soot proceeds via PAHs, it has been proposed that the reaction sequence for the build-up of PAHs and soot should be analogous. The most widely used theoretical model to describe the formation and growth of aromatics is the hydrogen abstraction carbon addition (HACA) mechanism [11,199]. The HACA mechanism consists of a repetitive sequence of radical site formation by hydrogen abstraction, followed by carbon addition, most often by acetylene bonding, forming an additional aromatic ring. It is proposed that soot growth in flames also occurs at active sites. The reaction scheme used to account for surface growth and oxidation is detailed in Table 4.1. The kinetics of the surface reactions are described using the concept of surface sites (an armchair site is a site with four carbon atoms as illustrated in Figure 4.1), which are carbon atoms either saturated (C soot H) or dehydrogenated (C soot ) on the surface of soot particles. The concentration of saturated sites, [C soot H] (mole/cc), is calculated by Eq. 4.1: [C soot H] = A s A v χ Csoot H ( 4.1) Armchairsite Figure 4.1 Illustration of armchair sites on the surface of a soot particle.

96 77 where χ Csoot H is the number of sites per unit soot surface area; A s (cm 2 /cc) is the surface density of soot particles and A v is Avogadro s number. The concentration of dehydrogenated sites [C soot ] is similarly calculated with χ Csoot as the number of dehydrogenated sites (C soot ) per unit surface area. Finally by assuming a steady state for C soot, χ Csoot can be calculated from Eq. 4.2 and be used to find the individual rate of each of the soot reactions listed in Table 4.1. χ Csoot = (k 1 [H] +k 2 [OH])χ Csoot H k 1[H 2] +k 2[H 2 O] +k 4[C 2 H 2] +k 5[O 2] ( 4.2) Table 4.1 HACA based soot surface growth and oxidation reactions [86], k =AT b e E a RT. No. Reaction A ( cm 3 mol.s) b E a ( kcal mol ) S1 C soot H+ H C soot + H S2 C soot H+ OH C soot + H 2 O S3 C soot + H C soot H S4 C soot + C 2 H 2 C soot H+ H S5 C soot + O 2 2CO + product S6 C soot H+ OH CO + product γ OH = 0.13 It was experimentally observed that the reactivity of surface sites changes with increasing particle growth or age [11,198,200,201]. Hence, this process is often called surface ageing. It was attributed to a decrease of active surface sites, i.e., sites that are accessible for reaction. Other experimental studies [97,98,148,198] showed the dependency of soot ageing on temperature. More recently, by analyzing surface growth pathways, Kronholm and Howard [202] cast doubt on the monotonically decreasing behaviour of soot reactivity with residence time if C 2 H 2 is assumed to be the dominant soot surface growth reactant. The notion of active sites on the soot particle surface was introduced into kinetic soot modeling by Frenklach and Wang [199]. In conjunction with a decrease in concentration of C H sites [198,199], it was used as an explanation for the experimental observation of surface ageing. On a mechanistic basis, Frenklach and co-workers [90,203,204] attributed surface ageing to the formation of defects on the particles surface generated during surface growth. Surface ageing was also attributed to the reversibility of the HACA surface growth scheme [ ]. The surface ageing effect was embedded into the HACA surface reaction scheme by introducing a

97 78 steric parameter, α, which is positive and less than unity. Therefore the reaction rate for an individual reaction, for example S4 from the Table 4.1 above, becomes: R 4 = α k 4 [C 2 H 2][C soot ] ( 4.3) A review of the assumptions made in the soot surface growth scheme clarifies the necessity of the α parameter. The number density of the C soot H sites, χ Csoot H, was estimated based on the assumption that the surface is covered with stacks of benzene rings [86]. The distance between the stacks is 3.51 Å and it was assumed that 2 C H bonds are available per benzene ring length (2.46 Å). Thus χ Csoot H was calculated to be 2/( ) = 0.23 site/å2. Considering that all of these sites are accounted for as armchair sites, this value is the theoretical maximum value of soot surface site density. The nanostructure of soot particles has been experimentally studied in [23,53,104]. All of these studies concluded that soot particles are composed of stacks of 4 to 8- ring PAHs. If for estimation of χ Csoot H it was assumed that the surface of the soot particles is covered with a 5-ring PAH such as benzopyrene (A5) in accordance with the recent findings, the number of C H bounds available per unit length on average would be 0.5 site/å which results in χ Csoot H = 0.5/3.51 = 0.14 site/å2. Similarly, if it were assumed that the surface is covered with layers of coronene (A7) as opposed to the classical benzene-surface assumption, the number of C H bounds available per unit length on average would be 0.4 site/å and subsequently the number density of the C soot H sites, χ Csoot H = site/å2. Thus, the estimated value of χ Csoot H would be 25% to 50% less than the originally proposed value if the surface of the soot particles is assumed to be covered by the layers of 4 to 8-ring PAHs. The rate coefficients of the heterogeneous reactions, presented in Table 4.1, were estimated based on analogous gas phase reactions of one-ring aromatics. The rate coefficient steric factor (A) of each of the C soot H sites is assumed to be one sixth of the benzene molecule. Also the activation energy is chosen to be constant for all the soot particles and 3 (kcal/mol) less than the corresponding gas phase analogous reaction of one-ring aromatics. However, it has been shown by [11,23,109,208] that the C/H ratio of soot particles which represents the carbonization or graphitization of soot, increases with residence time of the soot particles, and results in less chemical reactivity. In conclusion, the empirical ageing parameter, α, reconciles the inaccuracies of treating sites on the soot surface as corresponding sites on gaseous PAH molecules.

98 79 While initially a constant fraction of active sites was used with the kinetic soot model [198,199], it was later expressed as a function of flame temperature [209], and subsequently as a function of flame temperature and mean particle size [86]. Several studies measured the ageing parameter, α, based on the HACA surface growth scheme in laminar premixed and diffusion flames with different fuels, pressures, and flame temperatures, and proposed a temperature dependent function for the ageing parameter [28,31,32,36,44,150,208]. However, the predicted value of α yielded by those forms is 1.0 for most of the sooting region of laminar diffusion flames, which is quite close to the theoretical maximum value of available soot surface sites, and unrealistically high. Dworkin et al. [141] shows that if particle inception is enhanced by more accurate prediction of PAH molecules in the gas phase, α could be kept within a more realistic range to achieve physically accurate values of soot volume fraction. By calculation of particle age distributions in simulated premixed flames, Singh et al. [114] proposed two correlations for the fraction of active sites. However, their attempt to relate particle ageing with flame temperature in order to find a general expression for α was unsuccessful. The various forms of α proposed in the literature are summarised in Table 4.2. The value for α that is predicted for each of these functions at 1700 K, which is close to the local temperature in most of the sooting region in the diffusion flames, is included in this table. These values show a great discrepancy among different proposed functions for α. In some of these studies, such as [150] and [141], despite the similarities in the flames studied and soot surface growth models implemented, different values for α have been employed to achieve the same soot volume fraction predictions. This discrepancy is a consequence of using different reaction mechanisms and obtaining different predictions for the soot precursors. A role of the chemical mechanism in soot growth is to derive the concentration of the four species, H, OH, C 2 H 2 and the nucleating PAH, which are directly used by the soot growth model. Most of the mechanisms are validated and perform well in prediction of small species (i.e., H, OH and C 2 H 2 ). However, as is comprehensively discussed in [141], due to the complexity and uncertainties involved in growth pathways of heavy PAH molecules, the performance of different chemical mechanisms in the prediction of heavy PAH molecule concentrations can be vastly different. The role of the chemical mechanism and its interaction with the soot model has been discussed in more depth in Chapter 5.

99 80 Table 4.2 Proposed functional forms of α for models based on the HACA mechanism. Proposed by Function α at 1700K Frenklach and Wang [199] Appel et al. [86] tanh(a log μ 1 +b) 0.93 El-Leathy et al. [36] exp(12100/t ) 1.0 Guo et al. [150] exp(900/t ) 0.9 Dworkin et al. [141] Singh et al. [114] 1 for A p for A p >0.012 Singh et al. [114] exp ( CA p ) 0.71 where μ 1 is the first size moment of the soot particle distribution, and a and b are fitted parameters and found to be T, and T, respectively. where A p is particle residence time. different values for C have been used for each of the flames studied. The aim of the present study is to propose a systematic method to define a function that relates the reactivity of soot surface sites with flame properties. Employing a detailed sectional soot model, several ethylene diffusion flames are studied. Thomson and coworkers [141,195,210] have shown that for each diffusion flame, a constant value for α could be implemented to predict soot concentration with reasonable accuracy for different fuels, pressures, and burners. From the knowledge gained through studying these flames, a novel approach to describe soot surface reactivity is introduced. First, a definition of the ageing parameter is proposed. It is investigated if the surface reactivity of the soot particles could be correlated with particle age. Using a detailed sectional model and comparisons to experimental data in the literature, abilities and limitations of these approaches are investigated. 4.3 Numerical Model A detailed description of the governing equations, boundary conditions, and solution methodology can be found in Chapter 2. For the gaseous phase, the fully coupled elliptical conservation equations for mass, momentum, energy, and species mass fraction are solved. The model utilizes the axi-symmetrical nature of the flame, and equations are solved in the twodimensional (z and r) cylindrical co-ordinate system. The DLR chemical mechanism (see the chemical mechanisms section in Chapter 2) with 93 species and 719 reactions was applied to describe the oxidation of the fuel and the formation of PAHs.

100 81 Soot is modeled using the detailed fully coupled sectional aerosol dynamics model discussed in Chapter 2. In this approach the continuum soot particle mass distribution is divided into a discrete number of soot clusters, each with an assigned mass. For this study, the soot particle mass range is divided into 35 discrete sections that cover the soot particle diameter ranging between 0.86 nm and 3.3 μm. Conservation equations of soot aggregate number densities, and primary particle number densities are solved for each soot section. Nucleation is modeled based on the collision of two pyrene molecules in the free molecular regime [86,90], which serves as a connection between the gaseous phase reaction mechanism and the first soot section with collision efficiency of 1. The HACA mechanism [86] is used to describe soot particle surface growth. PAH condensation is modelled based on collision theory between pyrene molecules and aggregates, with a collision efficiency of 0.5 [147]. A constant coagulation efficiency, ξ, of 0.2 is chosen based on the recommendation of Zhang et al. [118]. Soot particle coalescence has been modeled using the cut-off model described in Chapter 3 with a cut off diameter of 20 nm. 4.4 Methodology Twelve different laminar diffusion and partially premixed ethylene flames differing in fuel inlet dilution level, inlet velocities, and burner configuration were simulated. These flames were chosen since they were the subjects of previous studies ([141] and [211]). The experimental datasets of Santoro et al. [192] (SA), Smooke et al. [41] (SM) Shaddix and Smyth [212] (SY) and Arana et al. [29] (PM) were used for comparison (see Table 4.3). Three flames, i.e., SM40, SM80 and SA, were investigated in more detail as they differ markedly in their sooting behaviour Soot Surface Reactivity Similar to observations by Dworkin et al. [141], soot forming on the centerline region of the flame is less sensitive to α than the soot forming on the annulus region (wings) near the edge of the flame. Probing the contribution of different processes to the soot mass yield confirms that inception and PAH condensation is the dominant mechanism for soot generation along the centerline. It also shows that soot volume fraction on the wings is more representative of surface growth and the role of α in simulations of soot particles. As an example, contributions of different soot growth processes on the centerline and wings for the Santoro flame [58] (SA) are

101 82 presented in Figure 4.2. This graph shows that 80% of the peak soot mass on the centerline comes from PAH growth processes, which is based on physical collisions, and do not rely on particle surface chemistry. On the contrary, the relative contribution of PAHs to peak soot mass on the wings is less than 8%, and nearly 92% of the peak soot mass is from HACA surface growth. Thus, the main focus of this study is on soot growth along the wings in order to investigate and analyze soot particle surface reactivity. Table 4.3 Proposed functional forms of α for models based on the HACA mechanism. Flame Designation Fuel Volumetric Conc. (%) Fuel Stream Equivalence Ratio ( ) Inlet Velocity(cm/s) Fuel Cold gas SA SAM SM SM SM SM SM SY SY SY PM PM PM Fuel tube diameter (cm) Reference 1.11 [192] 0.4 [41] 1.11 [212] 1.11 [29] (a) 0.09 (b) Mass Yield Total Mass Yield Mass From HACA Mass From PAH Mass Yield Total Mass Yield Mass From HACA Mass From PAH z(cm) z(cm) Figure 4.2 Total mass yield (g soot /g mix ) by all soot growth processes, HACA surface growth, and inception plus PAH condensation for a soot particle travelling a) along the centerline and b) along the pathline of maximum soot on the wings, for the Santoro flame [58] (SA).

102 83 Dworkin et al. [141] showed that with a constant value for α the model is able to predict soot concentration on the wings of the SA flame. Therefore, the same value for α that could predict soot concentration on the wings of the SA flame has been employed here to simulate all the flames as a base case for comparison. The maximum soot concentrations on the wings predicted with this α with experimental data from [192] and [41] with experimental uncertainty estimated based on the experimental technique are shown in Figure 4.3. As the dilution level of inlet fuel increases, the difference between computed and measured soot concentration become more significant. This result emphasizes the necessity of a variable form for α. Although for each flame, a constant α can be found which leads to a precise prediction of maximum soot concentration, this would merely be a curve fit and would not leverage the knowledge base of surface ageing. Such a procedure however, is a precursor to our analysis. By examining several α values for each flame, a different value for α for each flame that reproduces the most accurate soot concentration on the wings is found. These values, representing average surface reactivity of each flame, are then used to derive functions that are then tested in the numerical algorithm in the context of the current knowledge base of ageing. The comparison of the computed soot concentration with an optimum α and the experimented data from [41,192,212] are shown in Figure 4.4. The constant α for each flame is tabulated in Table 4.4. In the following sections, scenarios and procedures used to obtain α functions will be described. Soot Volume Fraction (ppm) SM60 SM80.2 SM80 SA 10 SM40 SM32 1 Computed with α = Experimental by [192] [40] 0.01 Experimental by [41] Flames Figure 4.3 Comparison of computed peak soot volume fractions on the wings using α = 0.45 for all SM and SA flames with experimental data from [192] and [41] for coflow diffusion ethylene-air flames.

103 84 Table 4.4 Flames used to derive a function for surface reactivity and the optimized α for each flame that reproduces the most accurate soot concentration on the wings. Flame Designation Optimized Average α SA 0.45 SY SY SY SM SM SM SM SM Soot Volume Fraction (ppm) SM32 SM40 Figure 4.4 Comparison of computed peak soot volume fractions on the wings using an optimized average α for each flame (The value of α for each flame is shown below the computed result) with experimental data from [192], [41] and [212] for coflow diffusion ethylene-air flames Thermal Age SM60 SM80.2 SM80 Flames Experimental studies have indicated that soot surface reactivity is a function of temperature [28,32,44,53,97,98,104,148,199,201, ]. Thus, as the first attempt to define a function for α, a comparison was made between the reference α for each flame to the corresponding peak flame temperature, and to the instantaneous temperature at the location of peak soot concentration on the wings. This comparison is shown in Figure 4.5 for a variety of diffusion ethylene-air flames. Consistent with Singh et al. [114], it is impossible to identify a unique SA SY41 SY46 SY48 Computed with ref. α Experimental by [192] [40] Experimental by [41] Experimental by [212] [42]

104 85 function of either peak flame temperature or local temperature at the location of peak soot concentration that can cover reference α values for all flames. Figure 4.5 Average soot particle surface reactivity, α, as a function of a) peak flame temperature and b) instantaneous temperature at the peak soot concentration on the wings. In addition to temperature, experimental studies signify age of a particle as the inducer of surface reactivity variation [22,98]. Based on these observations, a new ageing parameter is introduced, namely thermal age (T a ). The thermal age is defined as the integral of temperature to which a particle has been exposed with respect to time (a temperature-time history, Eq. 4.4) along the particle pathway. The thermal age accommodates effects of both temperature and residence time. This new definition of soot particle age inherently considers that the more time a particle spends in a hotter region, the more its surface reactivity is subject to change. T a = Tdt ( 4.4) s To investigate correlations between α and the thermal age of individual particles, the age distribution of soot particles was obtained. The values of reference α implemented for each flame were plotted as functions of thermal age of a particle at the peak soot concentration of the respective flames (shown in Figure 4.6a). Despite the differences in their measurement techniques, and flame configurations, the nine flames align monotonically when surface activity of these flames are compared with their corresponding thermal age. It was suggested that the fraction of active surface sites varies exponentially with its age [3,8]. This idea was adopted and

105 86 an exponential function was used to correlate thermal age and fraction of active sites. The correlated exponential function is presented in Eq. 4.5 and its variation with thermal age is depicted in left side of Figure 4.6 with a solid line. α = 0.6 exp ( 25.4 T a ) ( 4.5) Although, Eq. 4.5 is fitted to the data points with minimal deviation (R 2 = 0.94), it is not representative of the local available active sites on a soot surface. Since the average surface reactivity has been used to develop Eq. 4.5, this function is only suitable to predict an average α to model a flame. The surface growth rate (ω s) is defined as the rate of increase of the soot mass via heterogeneous reaction of the soot surface with the gas phase; as shown in Eq. 4.3, this mass growth rate is proportional to the instantaneous surface reactivity of the soot particles (ω s α). Soot formation on the wings, being dominated by surface chemistry [141], is a metric to examine the surface growth model s predictive capability. Since surface growth is the rate of mass increase, the computed peak soot concentration on the wings could be interpreted as the cumulative effect of all the chemical reactions having occurred on the surface of the soot particle from nucleation to this point (fv ω sdt). Based on the proportionality of ω s and α and the assumption that α is a function of thermal age, the proper strategy to assign a function for α is through comparison of the integral of α with respect to thermal age. αdt can be thought of as the representative surface character of a soot particle spanning from its inception to any moment in time. Such an integral takes into account the temporal variation in surface character of a particle at its corresponding thermal age for each flame. The α values presented in Table 4.4 are integrated along the pathline of maximum soot on the wings in the growth region for each flame with respect to thermal age and the results of this integral is demonstrated on the right side of Figure 4.6. In order to find the instantaneous α, the exponential function fitted to the integrated α has been differentiated. The function coefficients have been optimized for the most accurate prediction of peak soot concentration on the wings. The final function is shown in Eq. 4.6 and variation of the integral of this function with thermal age is depicted on the right side of Figure 4.6 with a solid line. α= exp 2 T ( a T a ) ( 4.6)

106 87 Figure 4.6 a) Average soot particle surface reactivity, α, as a function of thermal age at the location of peak soot concentration on the wings (the line is the correlation for α, Eq. 4.5). b) The integral of α, as a function of thermal age at the location of peak soot concentration on the wings (the line is the integral of the correlation for α, Eq. 4.6). 4.5 Results and Discussion The newly developed function, Eq. 4.6, has been implemented in the sectional model. First, conservation equations of momentum, energy and soot number density are solved. Then, at each location in the flame, the trajectory of the soot particle is calculated based on the flow velocity, and the corresponding path of a fluid parcel, and then corrected for soot transport. All necessary properties are interpolated along the trajectory of the soot particle. Starting from the nucleation point, the thermal age is calculated and integrated along the trajectory. A unique α is calculated at each streamwise location of a fluid parcel containing soot. At a given height above the fuel tube, α is likely to vary radially as each radius represents a different pathline on which velocities, temperature, and thus T a may all vary. Simulations have been repeated for all the flames with this function. In Figure 4.7, the peak experimental and computed wing soot volume fractions are compared with experimental error bars estimated based on the techniques used. Results reported in Figure 4.7 show excellent overall comparisons of peak soot concentrations for multiple flames considering different experimental datasets, ranging three orders of magnitude of soot concentration. It should be noted that the partially premixed flames (PY flames) and the SAM flame were not used during the development of the function for α, and yet the surface reactivity

107 88 model is able to accurately predict the soot volume fraction for these flames without any further model adjustment. [192] [41] [212] [29] Figure 4.7 Comparison of computed peak soot volume fractions on the wings using the α function based on thermal age (Eq. 4.6), with experiments from [29,41,192,212]. Computed and experimental soot volume fraction contours are presented side by side for the SM40, SM80 and SA flames on Figure 4.8. The experiments depict a dramatic shift in the location of maximum soot away from the centreline to the wings as ethylene concentration in the fuel stream is increased. For instance, the peak soot concentrations occur on the wings near z = 4 cm for the SM80 flame, contrarily, in the SM40 flame, peak soot concentration is on the centerline near z = 2.2 cm. Comparison of the model with experiments reveals that the model prediction of the initial formation of the soot on the wings is in good agreement with the experiments. The model captures the general shape and magnitude of the soot isopleths for all the flames. Moreover, the model captures the extent of the soot along the wings and the peak soot concentration both in magnitude and location on the wings. However, the model failed to predict the transition of peak soot concentration from the wings toward centerline as fuel dilution is increased. Similar behaviour of this model has been reported by Dworkin et al. [141] and Eaves et al. [195]. Both of these studies suggest that the discrepancy is due to PAH chemistry. As discussed earlier, centerline soot growth is driven highly by PAH based growth mechanisms and any miss-representation of the PAH concentration in the gas phase directly affects the soot concentration on the centerline. These results suggest that future studies to investigate new

108 89 pathways to form PAH molecules in the gas phase chemistry are needed, which is beyond the scope of this work. SM40 SM80 SA z(cm) r(cm) r(cm) Figure 4.8 Isopleths of soot volume fraction (ppm) of the SM40 (left panel), SM80 (middle panel) and SA (right panel) flames. The left side of each panel is the model computed with the new α function. The right side is the experimental data ([41] and [212]) Surface Reactivity Analysis r(cm) The variation of surface reactivity calculated using Eq. 4.6 with soot particle residence time along with predicted soot volume fraction for the SA and SM60 flames are shown on Figure 4.9. The form of the new function suggests that the soot particle surface reactivity increases in the early stages of soot formation in the SA flame, then it reaches its maximum (which does not coincide with the maximum rate of soot formation) and then gradually decreases as the particles traverse the flame. There are processes that increase surface reactivity and processes that 0.0 0

109 90 suppress surface reactivity. The shape of the α curve represents the balance between these competing processes. The increase in the surface reactivity is partly due to the increase of the number density of the C soot H sites. Recent studies of detailed Monte-Carlo simulations on graphene layer surface reactions [213,214] concluded that during the HACA growth process, χ Csoot H increases. In addition, deposition of PAH molecules on the surface adds new sites. It is shown in [113] that PAH deposition is the main contributor to the increase of hydrogenated site density. A comparison of the soot mass gained by PAH-based processes (Figure 4.2) on the wings with the increase in α in Figure 4.9 also confirms the observed relationship between PAH deposition and an increase in the surface reactivity by [113]. Simultaneously, there are processes causing deceleration of the surface growth. One of these processes is carbonization, which involves polymerization, dehydrogenation, and bond formation/rearrangements between PAH layers forming the soot particles. The carbonization process which has received much attention in both experimental and theoretical studies [22,86,109,113,198,208], could be characterized by the carbon to hydrogen ratio (C/H) within a soot particle. It is suggested [22,113,208] that C/H for nascent soot particles is close to 2.0, which is the typical value for a five member ring PAH, and it is between 5 and 10 for the mature soot particles. Analogous to PAH molecules, as the C/H ratio increases, it is expected that the soot particles would tend to be more stable, and thus less chemically reactive. Another factor which could affect solid particle reactivity is the size of the particles. When a small solid particle with negligible vapour pressure is in chemical equilibrium with the gas phase, the equilibrium constant is proportional to the particle internal pressure [106]. The internal pressure of the particle is related to the particle size by the Laplace formula p = 2σ/r. Substituting pressure in the equilibrium constant equation, the equation could be expressed as a function of particle size. RT ln K P = G 0 T + 2ν sv sσ r where ν is the stoichiometric coefficient and v is the volume per mole of solid particles. From Eq. 4.7, the effect of finer particles is to increase the equilibrium constant. The increase in internal pressure caused by reducing particle size, which is evident in the Laplace formula, leads to an increase in thermodynamic activity of the particle substance. Since the average primary ( 4.7)

110 91 particle size increases in the growth region, the particle size will have a reducing effect on the surface reactivity. Figure 4.9 Variation of surface reactivity and soot volume fraction as a function of soot particle residence time along the wings for SA and SM60 flames. Figure 4.10 Variation of surface reactivity and soot volume fraction as a function of soot particle thermal age along the wings for SA, SM80 and SM40 flames. The initial value of α still remains to be estimated. The incipient soot particle is a 0.86 nm diameter sphere that consists of two pyrene molecules. Each pyrene molecule has 10 C H sites. Assuming that all of these sites are on the surface of soot particles, the calculated χ Csoot H is an order of magnitude lower than the estimated value of 0.23 (#/Å 2 ). Since the average value of α is on the order of 0.1, based solely on the above calculation, the initial value for α should be in

111 92 the order of There is a need for further investigation to reach a better estimation of the surface reactivity of incipient soot particles. However, the results are not sensitive to the initial value of α as long as it is in the order of The variation of α for two different flames as a function of residence time is presented in Figure 4.9. A comparison of these curves shows that at the same residence times in these two flames different values of α would be obtained with the proposed function. However, if the α variation is plotted as a function of thermal age, as shown in Figure 4.10, the α for all of the flames converge to a single curve. The soot concentration variation predicted for different flames along the wings shows that for some of the flames, the surface reactivity is dominated by the processes that induces higher α as the soot grows, such as in the SM40 flame, but this is not always the case. For instance most of the soot mass in the SA flame is formed in the region of decreasing α. Therefore one has to be cautious when it comes to studying surface reactivity of soot particles. These results suggest that it is essential that every theory proposed for surface reactivity should be tested in several different temperature and residence time conditions before reaching any conclusions. In section 4.4, it was stated that the focus has been on the regions where the soot growth is dominated by acetylene. Therefore, this function represents the effect acetylene addition has on surface growth. Based on the assumption that HACA growth via C 2 H 2 is the only chemical growth pathway for soot particles that is independent of the fuel, it is expected that the proposed α function will perform equally well for predicting soot formation in other hydrocarbon-fuelled flames as well. One barrier to test this hypothesis is the availability of a reliable chemical mechanism Parameter Study It was shown in Figure 4.7 and Figure 4.8 how well the soot model is able to predict soot concentration on the wings; however there are several prerequisites for a flame model to exploit the proposed function. These requirements could be divided into two main groups; the parameters that are derived from the gas phase chemistry and the soot parameters that are predicted by the soot model.

112 Gas phase chemistry parameters The most important parameters from the gas phase that affect surface reactivity are temperature, acetylene concentration, hydrogen radical concentration, and to some extend PAH concentration. Temperature plays two important roles in modeling surface growth. First, the reactions in the HACA surface scheme (Table 4.1) are temperature dependent; especially the hydrogen abstraction reaction, S1, which has the highest activation energy. The second role of the temperature is in the α function. The proposed α is a function of thermal age which is derived from temperature. In order to examine the performance of the model in predicting temperature, computed and measured temperature contours for the SA flame are depicted in Figure 4.11 and for a more quantitative comparison, temperature profiles on the centerline for the SM40, SM80 and SA flames are demonstrated in Figure The model reproduces temperature very well, particularly on the wings. The slight overprediction in the vicinity of the centerline which is also evident in Figure 4.12, are in the regions where soot is underpredicted. The associated underestimation of soot radiation caused the temperature to be overpredicted. As it was stated in the previous sections, it would have been more relevant if all the analysis and discussion were made on the flame wings; the reason comparisons were made on the centerline in Figure 4.12 and Figure 4.13 is because of unavailability of experimental data on the wings. Figure 4.11 Comparison of computed (left panel) and experimental (right panel, from [192]) isotherms of the SA flame.