Detailed Modelling of CO 2 Addition Effects on the Evolution of Particle Size Distribution Functions in Premixed Ethylene Flames.

Transcription

1 Detailed Modelling of CO 2 Addition Effects on the Evolution of Particle Size Distribution Functions in Premixed Ethylene Flames by Ali Naseri A thesis submitted in conformity with the requirements for the degree of Master of Applied Science Graduate Department of Mechanical and Industrial Engineering University of Toronto c Copyright 2016 by Ali Naseri

2 Abstract Detailed Modelling of CO 2 Addition Effects on the Evolution of Particle Size Distribution Functions in Premixed Ethylene Flames Ali Naseri Master of Applied Science Graduate Department of Mechanical and Industrial Engineering University of Toronto 2016 This study investigates computationally the influence of CO 2 addition on the sooting behavior in premixed ethylene/ oxygen/ argon burner stabilized stagnation flames at the atmospheric pressure. The discrete sectional approach combined with a reversible nucleation model and a novel model of reversible polycyclic aromatic hydrocarbon (PAH) condensation were employed to solve the size evolution of the particle size distribution function (PSDF). The predicted temperature profiles and PSDFs are in reasonably good agreement with the experimental data for nascent soot measured in the burner stabilized stagnation configuration. The evolution of the PSDFs shows that CO 2 addition reduces the soot nucleation and mass growth rates, consequently lowering the soot yield. The addition of CO 2 reduces the concentrations of H, C 2 H 2, and C 6 H 6, which all suppress the soot formation process through a chemical effect, while its thermal effect is negligible. ii

3 Dedication To my family and my friends, for their love, support, and encouragement. iii

4 Acknowledgements Firstly, I am so grateful to almighty God, who led me in this path. When I was leaving my country to start this journey he was the one whom I have been trusting and pacified me in the tough situations. I hope that he will not forget me and forgive me for my mistakes, so that I can receive his guidance to continue my path and succeed. I Would like to thank my lovely supervisor Professor Murray J. Thomson from the bottom my heart for his constant support and guidance during my master s study. Not only has he been a wise advisor and a passionate leader, but also he has been a real friend to me. When I visited Professor Thomson on the U of T campus for the first time, I discussed my concerns with him, and after a short talk I found myself relaxed and hopeful for the future. Beside the knowledge, I have learned many valuable things such as ethics and patience from him. Moreover, I want to express my deepest gratitude to my dear family for their incessant love, support, and passion even from thousands of miles away from me. Much appreciation to my lovely parent who have spent their whole life for my progress and success, and sacrificed, so that I can make my dreams. I thank my darling sister who has always been helpful and considerate to me. My family is my main motivation to continue graduate studies. Finally, I would like to thank Combustion Research Laboratory members and staff, specifically, Dr. Armin Veshkini for sharing his knowledge and expertise with me, Dr. Mohammad Reza Kholghy for his support and friendship, Dr. Yashar Afarin, Dr. Nick Eaves, Anton Sediako, Sina Zadmajid, Tongfeng Zhang, and Tirthankar Mitra. iv

5 Contents 1 Introduction Motivation Literature Review Soot Characteristics Soot Formation Pathways CO 2 Addition Effect Soot Modelling Objectives Methodology Overview Burner Description Gas-Phase Governing Equations Conservation of Mass and Momentum The 2D Cylindrical Coordinates and Similarity Solution Conservation of Energy Radiation Heat Transfer Optically Thin Approximation (OTA) Conservation of Species Chemical Kinetics Mechanism KAUST Mechanism CRECK Mechanism Soot Aerosol Dynamics Model The Sectional Aerosol Dynamics Model Nucleation Model Condensation Model Chemical Surface Growth and Oxidation Models Coagulation Model Fragmentation Model Numerical Method Premixed Stagnation Flame Boundary Condition v

6 3 Results and Discussion Model Verification Temperature Profiles Soot Volume Fraction Particle Size Distribution (PSD) Stagnation Wall Temperature Sensitivity Analysis HACA Effect CO 2 Addition Effects Soot Volume Fraction Particle Size Distribution PAH Condensation Reversibility Effect Wall Temperature Effect Thermal Effect of CO Chemical Effect Species Sensitivity Analysis Nucleation - Condensation Effects Chemical Kinetic File Sensitivity Analysis Concluding Remarks and Future Work Summary Conclusions Future Work Appendices 70 A 71 B 73 Bibliography 79 vi

7 List of Tables 2.1 summary of flame conditions[1] HACA based soot surface growth and oxidation reactions[2], k = AT b e Ea/RT vii

8 List of Figures 1.1 TEM images of soot for 5-decene, 1-decene, n-decane, and biofuel surrogate as a function of height above burner (Source: Reprinted from ref.[3]) Example of the obtained HR-TEM images. Laboratory soot sample formed in the pyrolysis of acetylene-ethanol mixture containing 40% of ethanol in volume at 1375 K and 10% of ethanol in volume at 1475 K (Source: Reprinted from ref.[4]) Schematic of soot morphology(source: Reprinted from ref.[5]) Conceptual mechanisms of soot particle nucleatoin (Source: Reprinted from ref.[6]) Schematic representation of a burner stabilized stagnation flame, including coordinate orientation D visualization of a BSS flame including the 1D grid for the numerical solution. The variable j represents the nodes index, and JJ is the total number of nodes Schematic representation of the major reaction pathways for the formation of large PAHs considered by the KAUST chemical kinetic mechanism (source: picture taken from ref.[2]) Schematic representation of the major reaction pathways for the formation of BIN1B considered by the CRECK chemical kinetic mechanism (source: picture taken from ref.[7]) 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: picture taken from ref.[8]) Soot morphology in a burner stabilized stagnation flame Nucleating species chemical structure Illustration of armchair sites on the surface of a soot particle Schematic of different burner-to-stagnation surface separations Comparison between modelled (solid lines) and measured (symbols) axial temperature profiles of the BSS ethylene flame for a series of H P values Comparison of the measured soot volume fraction (triangles) and model predictions (circles) as a function of burner-to-stagnation surface separation Comparison of the computed (solid lines) and measured (symbols) PSDs. The experimental data is adopted from [9] Wall Temperature Sensitivity Analysis Comparison of the different surface reactivity parameters Comparison of the H radical concentration and f v for the spacings 0.6 and 0.8 cm viii

9 3.8 Comparison of the flames C3 (φ = 2.07) and A1 (φ = 2.00) for the burner to stagnation surfaces of 0.55 and 0.80 cm Comparison of the computed (circles) and measured (triangles) soot volume fraction for the addition of 0.0%, 12%, and 18% of CO 2, respectively (see Tab. 2.1) Comparison of the computed (solid lines) and measured (symbols) PSDs. The experimental data is adopted from [1] Comparison of the constant (column a) and reversible (column b) condensation model Stagnation wall temperature sensitivity analysis for the measured boundary condition, 470 K; the flame C3 boundary condition, 497 K; and the flame C3 boundary condition plus the measurement uncertainty, 530 K. The comparisons has been made for the spacing 0.6 cm Comparison of the effect of CO 2 (frame (a)) and chemically inert specie FCO 2 (frame (b)) on the PSDs Comparison of the effect of CO 2 and chemically inert specie FCO 2 on the temperature profiles Comparison of the effect of CO 2 (frame (a)) and chemically inert specie FCO 2 (frame (b)) on the concentration of C 2 H Comparison of the specific heat capacity of CO 2 and Ar. The value C P /R u is dimensionless Effect of CO 2 addition on the major species including hydrogen radical, hydroxyl, acetylene, and benzene for the spacing 0.6 cm Effect of CO 2 addition on the nucleating species concentrations for the spacing 0.6 cm. Frame (b) represents the normalized PAH summation at the stagnation plane over a range of burner-to-stagnation surface separations Normalized sensitivity analysis of anthanthrene, compared at x = 0.2 cm for flames A1, A2, and A3 on the spacing of 0.6 cm. Reactions include CO 2 and CH 2 are marked by green and red, respectively Normalized sensitivity analysis of benzene, compared at x = 0.04 cm for flames A1, A2, and A3 on the spacing of 0.6 cm. Reactions include CO 2 and CH 2 are marked by green and red, respectively Absolute rate of production for acetylene, compared at x = 0.04 cm for flames A1, A2, and A3 on the spacing of 0.6 cm Normalized sensitivity analysis of acetylene, compared at x = 0.04 cm for flames A1, A2, and A3 on the spacing of 0.6 cm Comparison of soot mass generated by HACA, nucleation, and condensation for the spacing 0.6 cm Soot total mass fraction for the flames A1, A2, and A3 over a range of burner-to-stagnation surface separations including 0.5, 0.6, and 0.8 cm Soot condensation mass fraction for the flames A1, A2, and A3 over a range of burnerto-stagnation surface separations including 0.5, 0.6, and 0.8 cm Soot nucleation mass fraction for the flames A1, A2, and A3 over a range of burner-tostagnation surface separations including 0.5, 0.6, and 0.8 cm Normalized soot nucleation and condensation mass fraction for the flames A1, A2, and A3 over a range of burner-to-stagnation surface separations including 0.5, 0.6, and 0.8 cm. 60 ix

10 3.28 Comparison of the nucleation mass, condensation mass, and total mass of soot for the spacing 0.6 cm Particle size distribution function for (a) KAUST mechanism and (b) CRECK mechanism PSD comparison for the constant condensation, frame (a); reversible condensation model with the original temperature boundary condition, frame (b); and reversible condensation model with another reported temperature, frame (c) Condensation efficiency comparison for the original wall temperature, frame (a), and another reported temperature, frame (b) Boundary temperature effects on the f v prediction. frame (a) shows the computed f v compared with measurements for the original temperature boundary condition; frame (b) represents a similar concept to frame (a) but the computed values for the spacing 0.8 cm has been replaced with new ones calculated at new temperature Condensation efficiency comparison for the original wall temperature and four condensable species including: (a)anthantherene, (b) benzo(ghi)fluoranthene, (c)benzo[ghi]perylene, and (d)pyrene A.1 Carbon monoxide and propargyl concentrations compared for flames A1, A2, and A A.2 Hydrogen radical and Hydroxyl concentrations compared for flames A1, A2, and A A.3 Oxygen radical and CH2* concentrations compared for flames A1, A2, and A B.1 Comparison of the different chemical kinetic mechanisms for the CO 2 addition effects on the concentration of acetylene B.2 Comparison of the different chemical kinetic mechanisms for the CO 2 addition effects on the concentration of hydrogen radical B.3 Comparison of the different chemical kinetic mechanisms for the CO 2 addition effects on the concentration of hydroxyl B.4 Comparison of the different chemical kinetic mechanisms for the CO 2 addition effects on the concentration of benzene B.5 Comparison of the different chemical kinetic mechanisms for the CO 2 addition effects on the concentration of pyrene x

11 Nomenclature Roman Symbols V k Diffusion velocities, cm/s Q C c P D f f f s f v G g z H Heat loss Particles velocity vector Specific Heat of mixture under the constant pressure condition Fractal dimension Net body force Section spacing factor Soot volume fraction Gibbs energy Axial gravitational force Enthalpy h Species specific enthalpy k Reaction rate n v P r R u S T u u i V v W x Y Particle number density, cm 3 Pressure, pa Radial coordinate, cm Universal gas constant Entropy Temperature, K Axial velocity, m/s Velocity tensor Diffusion velocity Radial velocity, m/s Molecular weight,g/mol Height above burner, cm Mass fraction xi

12 z Axial coordinate, cm Acronyms BSS Burner Stabilized Stagnation EGR Exhaust Gas Recirculation GC/MS Gas Chromatography/Mass Spectrometry GDE General Dynamics Equation GHG Green House Gas HACA Hydrogen Abstraction Carbon Addition HRTEM High Resolution Transmission Electron Microscope KAUST King Abdullah University of Science and Technology LMMS Laser Microprobe Mass Spectrometry LTE Local Thermodynamics Equilibrium MD Molecular Dynamics NOC Nano-particles of Organic Carbon OTA Optically Thin Approximation PAH Polycyclic Aromatic Hydrocarbon PM Particulate Matter PNP Precursor Nano-Particle PSD Particle Size Distribution RTE Radiative Transfer Equation TEM Transmission Electron Microscope Greek Symbols χ Species mole fraction ω Chemical reaction rate κ P Plank mean absorption coefficient. λ Second viscosity coefficient, Eq. 2.2 λ Thermal conductivity of the mixture, Eq µ Dynamic viscosity, pa s ψ Stream function ρ density, g/cm 3 σ Stephen Boltzman constant θ Angular coordinate Subscripts i Reaction index j Grid index xii

13 k r s Species index Radiation Soot xiii

14 Chapter 1 Introduction 1.1 Motivation Energy is one of the necessary requirements for the humans life, and a reliable and accessible supply of energy is crucial for the sustainability of modern societies. Currently, fossil fuels supply about 80% of the global energy consumption [10]. It is estimated that the entire demand for energy will grow constantly all through the world with especially large rises in the demands from emerging economies. The overall liquid fuels consumption of the world, as an example of the world s hydrocarbon consumption, is predicted to expand by 33 million barrels per day for the duration of thirty years, starting from 2010, which is equivalent to 30% of the current consumption [11]. Energy use has adverse environmental and health consequences that have led to considerable restrictive regulations. The generation of energy from fossil fuels is mostly produced by combustion which is a source of atmospheric emissions such as NO X, green house gases (GHGs), and particulate matter (PM). PM is a known pollutant and its health and environmental consequences are linked directly to its size [6]. Combustion derived nano-particles known as soot are a significant part of the ambient fine particulate matter (PM 2.5 ) [12]. The adverse influences of PM 2.5 on public health have been well recorded by epidemiological researches. Time-series studies of the short-term effects of air pollutants, conducted around the world, have steadily described noticeable connection between daily mortality and daily exposure to PM 2.5. Two large-scale group studies organized in the United States reported increased mortality associated with an increase in annual average PM 2.5 levels. According to some other studies, trafficgenerated fine particulate air pollution, indicated by soot, may constitute greater risk on the human health than PM 2.5 from other sources [12]. The World Health Organization Regional Office for Europe performed a recent systematic review on the health effects of black carbon and found that threatening effects from both short and long-term studies are much higher for soot compared to PM 10 and PM 2.5 when the particulate measures are expressed per µg/m 3. Soot particle aerosols have significant impacts on climate change through several mechanisms: absorption of solar radiation; influence on cloud formation; and deposition on the snow and ice [12, 13]. Black carbon in soot is the dominant absorber of visible solar radiation in the atmosphere. Black carbon is often transported over long distances, mixing with other aerosols along the way. The aerosol mix can form transcontinental plumes of atmospheric brown clouds, with vertical extents of 3 to 5 km. Because of the combination of high absorption; a regional distribution roughly aligned with solar irradiance; and 1

15 Chapter 1. Introduction 2 the capacity to form widespread atmospheric brown clouds in a mixture with other aerosols, emissions of black carbon are the second strongest contribution to current global warming, after carbon dioxide emissions. In the Himalayan region, solar heating from black carbon at high elevations may be just as important as carbon dioxide in the melting of snowpacks and glaciers. The interception of solar radiation by atmospheric brown clouds leads to dimming at the Earth s surface with important implications for the hydrological cycle, and the deposition of black carbon darkens snow and ice surfaces, which can contribute to melting, in particular of Arctic sea ice [14]. For these reasons, governments are setting stricter particulate emission regulations like EURO 6 and ICAO in both automotive and aviation engines, respectively. Most of these regulations limits the total particulate mass emissions over different periods of time. However, there are increasing considerations that possible effects of other particulate characteristics, such as particle number, particle morphology, molecular structure, and detailed chemical speciation on the environment and health should be taken into account [6]. In this way, a comprehensive understanding of the risks associate with PMs may be achieved. Thus, understanding the soot mass growth pathways as well as evolution of particle size distributions has received considerable attention [15]. Formation of condensed-phase materials is present in many flames. These materials form generally as nanoparticles suspended in combustion products [6]. Soot particles are emitted from various combustion processes, mostly the incomplete rich combustion of fossil fuels, biofuels, and biomass[12]. Improvement of effective technologies to reduce soot emissions from combustion applications has been an attractive research area over the past years [16]. The dilution of the fuel and/or oxidizer mixture stream is an established method (e.g., exhaust gas recirculation (EGR)) to develop low temperature combustion in order to prevent both soot and NO X formation. CO 2 is one of the major components of combustion products; understanding how addition of CO 2 affects the flame properties and soot formation requires attention. The big picture of the soot modelling research is to come up with a detailed generic soot model which can be applicable for different flame conditions. After such a reliable model is developed the main features can be extracted and implemented into CFD softwares for design purposes. Predictive models would enable engine, furnace, and other practical device designers to tune various design and operating parameters without the necessity for highly priced experimentation and prototype building. Although this idea is worthy, it is very challenging. The detailed modelling of soot formation for laboratory scale burners has been started recently. Therefore, based on the viewpoint that has been forecast for the environmental and industrial researches, the present work seeks the further validation and improvement of a recently developed soot model which is capable of predicting soot volume fraction, particle nanostructure and size distribution. Addition of CO 2 could be a perturbing factor for the flame simulations to see how robustly the code performs in capturing the effects of different disturbing elements. Soot formation process is highly reversible [6]; the concept of reversibility in terms of modelling has been introduced by Eaves et al. [17, 18] and Veshkini et al. [15]. Although the existence of reversibility in soot models is necessary based on the physical characteristics of the process, this feature needs to be studied with details in order to find the probable defects that the reversible model may possess.

16 Chapter 1. Introduction 1.2 Literature Review Soot Characteristics 3 Soot particles are the product of fuel rich combustion and mostly form in high temperature zones. Particles generated in different conditions including laminar premixed and diffusion flames show universal structures [19]. However, the nanostructure and aggregation features of the soot nuclei depend on the flame type, locations within a flame, and other factors like residence time. Fig. 1.1 depicts the structure evolution of soot samples as observed by transmission electronic microscope (TEM) for four different fuels of a coflow burner along the flame axis and wing. Figure 1.1: TEM images of soot for 5-decene, 1-decene, n-decane, and biofuel surrogate as a function of height above burner (Source: Reprinted from ref.[3]). At low heights above the burner, the number of particles is high but the size of them is small. It is also observed that there are many liquid like particles available along the center line close to the fuel tube tip as shown in lower frames of Fig As the height above burner increases, the aggregates solidify and become more apparent due to the growth and carbonization process which results in dehydrogenation and higher C/H ratio. The nascent soot particles, also referred to as precursor nanoparticles (PNP) and nanoparticles of organic carbon (NOC), are assumed spherical particles which their size ranges from 1 to 5 nm in diameter. Their spherical appearence and absence of aggregation are indications of liquid-like behaviour and supposition of coalesce upon collision [20]. Laser microprobe mass spectrometry (LMMS) [21], gas chromatography/mass spectrometry (GC/MS) [22] and high-resolution transmission electron microscopy (HRTEM) [23] measurements indicated that the nascent particles can be thought of as polymer-like

17 Chapter 1. Introduction 4 structures containing polycyclic aromatic hydrocarbon (PAH) molecules ranging in molecular masses from 152 to 302 amu. Elemental analysis of nascent soot particles shows that these particles have a relatively low atomic C/H ratio of which can also be associated with their high chemical reactivity [23]. 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 [24, 25]. The nascent particles may also be absorbed onto the surface of the aggregates upon collision [25]. Mature soot particles, as illustrated in Fig. 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% [26]. 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 thousands [26]. The long chain soot aggregates and a comprehensive assortment of particles set the probable complexity in the characterization, and more importantly in soot formation modelling. This complication is addressed by experimental evidence that soot aggregates show a fractal-like structure [27]; these aggregates have a universal fractal dimension around D f = 1.8, even when an aggregate is composed of two or three primary particles[28]. Fractal dimension is used to calculate the surface area and rate of size change of the aggregates. The fact that aggregates resemble fractals enables us to implement the theory of fractal aerosol in both laser measurements and simulations [25]. Figure 1.2: Example of the obtained HR-TEM images. Laboratory soot sample formed in the pyrolysis of acetylene-ethanol mixture containing 40% of ethanol in volume at 1375 K and 10% of ethanol in volume at 1475 K (Source: Reprinted from ref.[4]). GC/MS measurements [22] and liquid chromatography [29] substantiate the availability of 2 to 10 ring PAHs as the components of mature soot particles. The transition from nascent soot particles to mature soot aggregates is accompanied by an increase of carbon to hydrogen ratio (C/H) which results in higher density for aggregates (ρ s = g/cm 3 [30]) compared to the nascent soot particles (ρ s = g/cm 3 [31]). The coexistence of the singlet spheroids and the carbonaceous aggregates also has been observed in particle size distribution (PSD) measurements in laminar premixed flames [1, 9, 32]. In the later flames the bimodal PSD evolves from a unimodal PSD as a function of time and height. The bimodal particle

18 Chapter 1. Introduction 5 size distribution is an indication of coexistence of nascent and mature soot particles. Comparison of the measured PSD with the TEM results [3] and electrical mobility measurements [33] 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 Soot Formation Pathways According to the aerosol dynamics, the transition of gas-phase molecular structures to the condensedphase is known as nucleation. The freshly formed fine particles grow in size and mass by means of joining to together, surface reactions, and condensation of large gas-phase species. Grown single particles stick to each other and form fractal-shape structures (soot) through aggregation. It is worth to mention that all these steps are highly reversible due to the thermodynamics properties that soot particles have [6]. At the end, oxidation leads soot particles to lose mass. These processes take place mainly concurrently in short periods of time as shown in Fig Most of these fundamental processes that govern soot formation are not well understood; in order to include them in simulations, a mathematical model that can capture the underlying physics of each step must be developed.

19 Chapter 1. Introduction 6 Figure 1.3: Schematic of soot morphology(source: Reprinted from ref.[5]). Fuel pyrolysis and oxidation is the first stage of the soot formation from pure hydrocarbon flames. Generally, the simple fuel combustion chemistry is relatively well known, and fairly precise chemical kinetic mechanisms exist for the desired fuels [34, 35]. The next step includes the formation of light cyclic aromatic hydrocarbons from the gas-phase species of the fuel decomposition. Propargyl (C 3 H 3 ) recombination or chemically activated isomerization is the main rout toward the formation of the first aromatic ring [36]. There are different routes after the first aromatic ring to form larger multicyclic aromatic compounds (i.e. PAHs); among them, the the hydrogen-abstraction-carbon-addition (HACA) reaction sequence [37] is one of the most effective pathways. The combination of fuel pyrolysis/oxidation and PAH formation and growth routes have been used to produce chemical kinetic mechanisms to describe the formation of PAH species [38, 39]. Emergence of condenced-phase materials in combustion products comes after the appearance of large PAH species in the gas phase. Three conceptual pathways may be hypothesized for soot nucleation from large PAHs, e.g. anthanthrene. As shown in Fig. 1.4, path A shows the growth of planar PAHs into curved, fullerene-like structures; paths B and C involve the physical coalescence and chemical coalescence of PAHs into crosslinked three-dimensional structures, respectively [6]. Indirect experimental evidence supports PAH dimerization (paths B and C) as the initial nucleation step [6]. Further growth of these structures in this manner leads to emergence of nascent soot particles. Additional mass growth as well

20 Chapter 1. Introduction 7 as dehydrogenation of the nascent particles is marked as the beginging of the solid state [40]. Figure 1.4: Conceptual mechanisms of soot particle nucleatoin (Source: Reprinted from ref.[6]). Addition of small hydrocarbon species can contribute to the soot particles growth. Acetylene is the dominant mass growth species which plays its role in the HACA process [41]. 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 mechanism. There is conclusive evidence that young soot particles formed in premixed flames have a coreshell structure, with the core being aromatic in nature and the shell being aliphatic. Again, the nature of binding between aromatic and aliphatic constituents remains unclear. The mass growth of soot can proceed without the presence of gas-phase H atom, indicating that the HACA mechanism may be incomplete to describe the entire process of soot formation [6]. The condensation of the gas-phase PAHs on the surface of the soot particles is also a feasible soot growth pathway, which is referred to as PAH-soot surface condensation [42]. Although the experiments posit that PAH clusters are the building block of soot[43], molecular dynamics (MD) studies show that the adsorbed PAH species are not stable[44]; thus, a better comprehension of such processes is required. The last step in the soot formation and growth process is aggregation. Aggregation involves two types of soot structural growth: coagulation and coalescence. The formation of fractal-like aggregates as a result of particle collisions is called coagulation which affects the evolution of PSD, number density, and morphology. After the collision, soot particles may undergo structural evolution which is a function of particle state, surface reactivity, temperature, residence time, etc. [8]. Coalescence leads the collision of liquid-like nascent soot particles to complete merging of the colliding particles [45]. 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 the coalescence process, neck formation, and aggregation. The amount of soot emissions depends on the oxidation of the soot. There are three possible oxidation pathways: reactions with O, OH and O 2. Oxidation by OH radical prevails in near stoichiometric and fuel-rich flame conditions [46]. Eventhough under the mentioned conditions some oxidation can occur through collisions with O, contribution from OH outruns the O radical s involvement [47]. The OH oxidation efficiency is a function of OH collisions with soot particles that result in the removal of a carbon atom; this efficiency is reported to be 0.13 [46, 47]. In fuel lean conditions, oxygen plays a crucial role in soot oxidation due to abundance of O 2. Research has indicated that changes of both initial structure of soot [23] and structure of soot during oxidation [47] complicates defining a universal oxidation rate.

21 Chapter 1. Introduction CO 2 Addition Effect In this section there will be a discussion on the CO 2 addition influences on the soot formation process. Several experimental studies, specially for coflow diffusion flames, have been performed to investigate the effect. According to the literature [1, 16], CO 2 addition suppresses soot formation in most of the flame conditions; however, there are unanswered questions regarding the role of CO 2 in the process. There is evidence which suggests the suppression of soot is due to the thermal effects [48, 49], while the majority of the literature posits that the observed phenomenon is mostly due to chemical effects. Schug et al. [48] and Abhinavam et al. [49] concluded that the soot formation suppression is due to thermal effects. Abhinavam et al. [49] measured the concentrations of soot precursor species including C 2 H 2 and C 6 H 6 for different diluents such as argon, helium, and carbon dioxide. The different levels of soot precursors produced in the diluted flames are attributed to the differences in the transport properties of the diluents, where the thermal diffusivities cause the temperature difference between the helium flame (hottest flame) and the carbon dioxide-diluted flame (coolest flame). This feature makes carbon dioxide a better suppressant among the diluents tested. Du et al. and Zhang et al. [50, 51] found that CO 2 hinders the soot formation chemically; they measured concentrations of species to investigate the dilution effect. Liu et al. [52] took advantage of a numerical model, and determined that CO 2 addition suppresses the soot nucleation by lowering the acetylene and enhancing the concentration of OH radicals; reactions CO 2 +H CO+OH and CO 2 +CH HCO+CO were found to be responsible for the chemical effects of CO 2 addition. In a more recent paper, Liu et al. [16] studied the effects of fuel dilution by CO2 and N2 on soot formation and the flame structure in laminar coflow C2H4/air diffusion flames both experimentally and numerically including soot simulation; according to their study, CO 2 s role in the soot suppression process is mainly due to its chemical effects. According to Guo et al. [53], CO 2 addition reduces the H radical formation which consequently results in lower pyrene concentrations. Less PAH reduces the inception rate. The chemical effects of CO 2 on soot formation are more complex in premixed flames[16], and technically the soot formation process totally differs between premixed and diffusion combustion. In the premixed flames soot starts to form after passing the flame front and in the post flame region, while in the diffusion flames soot forms in a fuel rich heated zone before reaching the flame front. Zhang et al. [54], in a numerical simulation of soot precursors in a plug flow reactor, insisted on the chemical effect of CO 2 addition. They determined that the reaction CO 2 +H CO+OH is pretty fast at intermediate temperature; the mentioned reaction competes with the reaction O 2 +H O+OH in depleting the H radicals. Tang et al. [1] did a thorough experimental investigation and a chemistry simulation of species to understand how CO 2 addition affects the PSD function evolution. They concluded that that CO 2 addition hinders particle inception, and thermal effect plays a minor role. Tang et al. took advantage of a burner stabilized stagnation (BSS), which minimizes the problem of probe perturbation in experiments. This burner was used earlier by Abid et al. and Camacho et al. [9, 32] to follow the evolution of PSD function of nascent soot. Up to here, there is a consensus among different researches about chemical effects of CO 2 addition on soot formation; however, disagreement still exists on how the added CO 2 affects the soot formation chemically, even via inception or surface growth. In addition,some studies suggest CO 2 addition does not always suppress soot formation[55, 56]; however, inclusion of CO 2 in the combustion reactants seems a pragmatic solution to prevent soot formation in the contemporary devices. Utilizing this capability

22 Chapter 1. Introduction 9 requires a better understanding of the morphology in different conditions. A numerical study for a premixed case accompanied with a soot model could be helpful to find out the reasons which accounts for the phenomenon Soot Modelling Soot modelling is a multiscale problem because it includes a variety of time and length scales such as angstroms for atomic level scales (10 10 m), nanometers for dimers and soot particles (10 9 m), milimeters for flow scales (10 3 m), and centimeters for burner geometry (10 2 m). In order to address the multiscale problems the smallest/shortest length/time scales should be taken into account to model the processes based on the understanding. One of obstacles in these sort of problems is to set up a balance between the accuracy and simplicity of the model. Kennedy [57] has reported the early achievements of developments of soot models. According to the time/length scales and the model complication, soot models can be classified into three categories: empirical soot models; semi-empirical soot models; detailed soot models. Empirical soot models have their origins in correlations that have been derived experimentally. The correlations usually reflect the influence of variation of different flame parameters, e.g., pressure, temperature, and equivalence ratio on the sooting behaviour. These correlations are coupled with flame models to relate the amount of soot produced with the operating conditions. The empirical models are fairly fast, compared to other types, which make them suitable for industrial purposes. The purpose of semi-empirical models is to increase the accuracy and keep the simplicity by including the elementary soot formation/oxidation routes in the model. Fairweather et al. [58] have developed one of the most widely used semi-empirical models. The model solves two transport equations, one for the soot mass fraction and one for the soot primary particles. The Fairweather model includes soot particle inception, surface growth, oxidation, and coagulation which are estimated empirically. The major disadvantage of the empirical correlation implementation is the limited validity of the model, i.e., the model functions properly for the calibration cases. The final classification is made up of the detailed soot models. These are complicated and computationally intensive models. The detailed soot models take advantage of the cutting edge aerosol dynamics prediction tools which make them reliable of finding a proper solution for a wide range of aggregate structures. The most recent chemical and physical kinetic mechanisms describing PAH and soot formation/oxidation are embodied into the detailed models. These models can yield comprehensive information about the factors influencing particles for a broad range of conditions. This characteristic enables them to investigate the fundamentals of soot formation. The simulation of the combustion and soot particles in flames comprises the following steps: modelling the flow field (solving the Navier-Stokes equations); predicting the temperature (solving the energy equation); calculating the gas-phase composition (solving the gas-phase chemistry);

23 Chapter 1. Introduction 10 and finally, calculating the soot variables (solving the aerosol dynamics equations); which all of these steps are intimately coupled. Detailed models require a detailed chemical kinetic mechanism which simultaneously describes the pyrolysis and oxidation of fuels as well as the formation and growth of PAH species. PAH formation and growth involve broad range of species and pathways which makes the chemical mechanisms to include hundreds of species and thousands of reaction, even for simple fuels [38, 39, 59, 60]; this adds a noticeable computational burden to the simulations. The proper aerosol dynamics models for studying soot comprises sectional methods [7, 15, 61 64], Galerkin methods [65, 66], stochastic methods [67], and moment methods [68, 69]. These capable algorithms can capture the majority of the particle properties with moderate computational resources; however, modifications to these models to extract additional information, dramatically increase their complexity and computational cost. An advanced sectional aerosol dynamics model [15, 70] 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 [70], shock tubes [71], and coflow diffusion flames [18, 72, 73]. The sectional soot aerosol dynamic model is described in detail in Chapter Objectives In the current work, a comprehensive soot model will be used to calculate the PSD functions for BSS flames. The base ethylene/oxygen flame along with three different composition of argon and CO 2 will be studied to investigate the effect of CO 2 inclusion. The simulation results will be validated against experimental measurements performed by Tang et al. [1]; the plots of PSD functions for different burnerto-stagnation-surface separations and soot volume fractions (f v ) will be compared to experimental data to find a better insight into the effect of CO 2 on the soot inception and growth. When the model is proved to capture the trends and values fairly good, it will be used to answer the following questions regarding the influence of CO 2 addition qualitatively: Is the suppression effect of CO 2 due to thermal or chemical factors; What are the chemical reactions involved in this soot reduction process; Between the nucleation and condensation, which step is affected more. Moreover, there will be a discussion on the temperature effect on the condensation model. The influence of the chemical kinetic file on the evolution of PSDs will be studied as well. This study is the first work which takes advantage of a BSS flame soot model to investigate the CO 2 addition effect; thus, we are able to see the influence of dilution on the HACA surface and other factors in the soot morphology.

24 Chapter 2 Methodology 2.1 Overview The scope of this chapter is the demonstration of the governing equations and variables that are fundamental for the chemically-reacting flow simulations in this work. Firstly, there will be a discussion about the experimental setup that has been used to compare the modelling results with. The similarity solution of the generalized governing equation are employed in modelling different flames considered in the current work. This method forms the governing equations as one-dimensional boundary value problem valid along the center line of a stagnation flow. The aforementioned approach has been used to model the premixed burner stabilized flames. It also includes an explanation on a sectional approach for modelling combustion-derived particulate matter (soot) formation. In the upcoming sections, the burner description, gas-phase governing equations, soot aerosol dynamics model, and finally the numerical method used to solve the governing equations will be discussed. 2.2 Burner Description Fig. 2.1 shows the schematic of a burner stabilized stagnation (BSS) flame. Laminar premixed flat ethylene flames with an unburned composition of 16%(mol) ethylene, 24% (mol) oxygen and 60% (mol) argon were generated by a commercial McKenna burner with a stainless outer layer and a 6 cm-diameterbronze water-cooled porous sintered plug. The unburned fuel and oxidizer mixture leaves the plug with an equivalence ratio, ϕ, of 2 and a cold gas velocity of 8 cm/s (298 K and 1 atm). The McKenna burner has a water cooling system, embedded within the porous plug, which prevents the burner damage. A shroud of nitrogen, at cm/s, isolates the flame from the surrounding air to keep the flame stabilized. An S-type Pt-Pt-10%Rh thermocouple coated with a Y/Be/O mixture to hinder surface catalytic reaction was used to measure the flame temperature[1]. A flat plate, which is called stagnation plate, is located at a distance to the burner and parallel to it to form the stagnation flame. A tubular probe made up of stainless steel with a bore size of 6.1 mm and wall thickness of mm was embedded in the stagnation plate to take samples. A sample orifice with a diameter of 0.16 mm was drilled in the middle of the tubular probe by laser. A type-k thermocouple embedded in the stagnation plate to measure the orifice temperature. The orifice temperature was about 465 ± 30 K during sampling. The burner to stagnation plate distance H p was determined by 11

25 Chapter 2. Methodology 12 a Vernier height gauge with an accuracy of ±0.02 cm. The particle size distribution was measured by Scan Mobility Particle Sizer (SMPS, Model 3936)[1]. Table 2.1: summary of flame conditions[1] Flame 0.0% CO 2 : A1 12.0% CO 2 : A2 18.0% CO 2 :A3 C 2 H O Ar CO Three flames with different fuel composition were examined thoroughly (see, Table 2.1). Flame A1 has no CO 2 content in the unburned fuel mixture and has been studied by Abid et al.[32] and Camacho et al.[9]; this flame can be noticed as a reference sooting flame for comparison. In flames A2 and A3, 20% and 30% of argon were replaced by CO 2, respectively[1]. Orifice z Flame Front r Premixed Fuel and Oxidizer Figure 2.1: Schematic representation of a burner stabilized stagnation flame, including coordinate orientation. The work by Tang et al. [1] has been selected for this study because it contains rich measurements of the soot properties of interest. Soot volume fraction (f v ), particle number density, and particle diameters are the important properties in soot research. Most of the experimental data in the literate

26 Chapter 2. Methodology 13 provide only soot volume fraction. Models can be easily tweaked to predict soot volume fraction with a good agreement. However, a model can be accounted reliable if it functions properly in terms of capturing all three mentioned properties. The modelling tool that will be explained in the coming sections will be validated against f v, soot number density, and particle diameters measured by Tang et al. [1]. 2.3 Gas-Phase Governing Equations Conservation of mass and momentum (Navier-Stokes), conservation of energy, and conservation of species compose the gas-phase governing equations. The solution of these equations describes the flow field, pressure, temperature, and gas mixture compounds. In order to to solve all the equations, species production rate, transport properties, and thermodynamics properties have to be evaluated to calculate the source terms. In the following sections all the conservation equations and evaluation method of thermo-chemical properties will be explained Conservation of Mass and Momentum The mass conservation equation (continuity) in tensor form is depicted in Eq ρ t = (ρu k ) (2.1) x k In Eq. 2.1 the ρ is the density of the mixture, t refers to the time, and u k is the velocity component in the x k direction. Eq. 2.2 presents the general form of the Navier-Stokes equations in tensor form. ρ u j t + ρu u j k = p + x k x j x j ( λ u ) k + [ ( ui µ + u )] j + ρf i (2.2) x k x i x j x i where λ is the second viscosity coefficient, µ is the dynamic viscosity and f i is the net body force. The 2D Cylindrical Coordinates and Similarity Solution The flame configuration used in this study is the BSS premixed flame which consists of a cylindrical tube with an axisymmetric flow field (Fig. 2.1). The tube carries the fuel and oxidizer mixture toward the plate, and the flow velocity reaches zero close to the plate. Since the flow is axisymmetric, the governing equations become 2D when they are expressed in cylindrical coordinates. Assuming θ = 0 for axisymmetric flow, the cylindrical form of Eqs. 2.1 and 2.2 is as follows: 1 r r (rρv) + ρu z = 0 (2.3) ρv u r + ρu u z = p z + 1 r r 2 3 z ( rµ u r ) ( µ u z ) ) + 2 z + 1 r r ( µ u z ( rµ v z ) 2 [ ] u 3 z r r (rv) ) (2.4) + ρg z

27 Chapter 2. Methodology 14 ρv v r + ρu v z = p r + ( z µ v ) + 2 z r ( µ u r z ( rµ v ) r r ) 2uv r r r u 3 r 2 [ µ r r (rv) r (rv) u u r z ] r r ( rµ u ) + z (2.5) In Eqs. 2.4 and 2.5, r and z are the radial and axial coordinates; v and u are the radial and axial velocities; p is the pressure, and g z is the axial gravitational acceleration. The Eqs. 2.2 and 2.3 can be simplified to a 1D boundary value problem by inserting a stream function in the form ψ(z, r) = r 2 U(z) into the mentioned equations. When such a stream function is introduced v/r and other variables become free of r [74]. Kee et al. [75] have suggested the following variables: G(z) = ρv r F (z) = ρu 2 (2.6) (2.7) Implementing Eqs. 2.6 and 2.7 in the continuity, Eq. 2.3, yields G(z) = df (z) dz (2.8) Likewise, the radial momentum equation satisfies when H = 1 r p = constant (2.9) r Consequently, the axial momentum equation becomes H 2 d dz ( F G ρ ) + 3 G2 ρ + d [ µ d dz dz ( )] G = 0 (2.10) ρ The approach used above to simplify 2D Navier-Stokes equation into a 1D momentum equation, Eq. 2.10, is called similarity solution. The 1D grid that used for the solution of Eq is depicted in Fig In this figure j represents the index of grid nodes, and JJ is the total number of grid points. Although Eq have been formulated with respect to z, the simulation code uses the variable X for the height above burner.

28 X direction Chapter 2. Methodology 15 j = JJ j = JJ - 1 j = JJ - 2 j = JJ - 3 Flame j = 4 j = 3 j = 2 j = 1 Premixed Fuel-Air Mixture Figure 2.2: 2D visualization of a BSS flame including the 1D grid for the numerical solution. variable j represents the nodes index, and JJ is the total number of nodes. The Conservation of Energy The conservation energy equation is depicted in Eq as a function of temperature [76]. ρc p T t + ρc p v. T =.(λ T ) ρ c p,k Y k v k. T h 0 k ω k W k + Q r (2.11) where, from left to right, the first term is temporal rate of change of temperature, the second term stands for the convective heat transfer, and c p represents the specific heat of mixture under constant pressure. On the other side of Eq. 2.11, the first term shows the conductive heat transfer and λ is the thermal conductivity of the mixture; the second term represents the heat flux rate due to species diffusion, and v k is the diffusion velocity of the k th species. h 0 k in the third term is the kth species specific enthalpy, and the whole term is total rate of enthalpy generation by chemical reactions. finally, Q r represents the heat loss due to radiation of soot and other gaseous species. In Eq the effect of soot and gas-phase species can be separated in the right hand side. As a result, the energy equation for a 1D axisymmetric

29 Chapter 2. Methodology 16 burner (BSS configuration) is as follows: ρc p u T z ( λ T ) z z KK + ρ k=1 T KK c p,k Y k v k,z z + h 0 s ω s W s k=1 Q r = 0 h 0 k ω k W k + ρc p,s Y s v s,z T z + (2.12) Here, subscript k refers to parameters pertaining to species k and subscript s denotes soot related parameters; KK is the total number of species in the gas phase. Radiation Heat Transfer In laminar flame simulations, radiation heat transfer has been identified as one of the major heat loss sources. Radiation heat transfer plays a role in temperature prediction, as well as soot and flame structure. Although many processes involved in soot formation process are endothermic, since soot is the prominent source of radiation, it affects the temperature noticeably. The heat loss due to radiation decreases the soot formation rate which, consequently, reduces heat loss. Thus, there is a feedback loop between soot and temperature and vice versa which combines the soot formation and radiation heat transfer. Eq expresses the radiative transfer equation (RTE) for an axisymmetric cylindrical system, assuming the medium stays in local thermodynamic equilibrium (LTE)[77]. µ I v r η I v r φ + ξ I v z = κ vi v + κ v I bv (2.13) where, parameters I v, I bv and κ v represent spectral intensity, spectral black-body intensity, and the spectral absorption coefficient, respectively; µ, η, and ξ are directional cosines. The left hand side calculates the rate of change of spectral intensity. On the other side of Eq. 2.13, the first term is responsible for the reduction of radiant energy leaving an element of volume of the medium. The second one represents the emission rate of the matter. Integrating the RTE along all solid angles and over the entire spectrum yields the overall radiation heat transfer rate. There is no explicit solution for the radiation heat transfer equation because it is an integro-differential equation. Thus, the solution to such equations requires a few simplifying assumptions. The method that has been adopted for the current work is called optically thin approximation (OTA) which helps to calculate the term Q r in Eq Optically Thin Approximation (OTA) Optical thickness is a measure of the ability of a path length of a medium to attenuate the radiation of a given wavelength. This dimension-less parameter, τ 0v, for a matter with homogeneous composition, temperature, and pressure is defined as: τ 0v = κ v L (2.14) where L is a characteristic length. In the condition of optically thin limit (τ 0v 1), the radiation by a fluid element will go directly to the bounding surfaces and any absorption by the fluid will be negligible. As a result, the radiation transfer equation turns to [78]: Q r = 4σκ P (T 4 T 4 ) (2.15)

30 Chapter 2. Methodology 17 Here, σ is the Stefan-Boltzman constant; κ p is the Plank mean absorption coefficient of the mixture; T and T are the local and the ambient temperatures, respectively. Liu et al. [79] compared different radiation models and concluded that OTA can predict the temperature of low sooting laminar premixed flames fairly well. Therefore, in this study the OTA method has been used to consider the radiation heat transfer from three species including CO, CO 2, and H 2 O, as well as soot particles. κ P = P H2Oκ H2O + P CO2 κ CO2 + P CO κ CO (2.16) In Eq. 2.16, P i and κ i denote the partial pressure and the Plank mean absorption coefficient of species i, respectively. The plank mean absorption coefficient for each species is calculated using Eq κ i = A ij T j, i = H 2 O, CO 2, and CO (2.17) j=0 Here, A ij is the polynomial coefficient of a species expressed in terms of temperature [80]. Soot particles are supposed to act as Rayleigh absorber-emitters [81]. The Plank mean absorption coefficient can be calculated using the following equation [82]: κ P s = 3.83Cf v T (2.18) where f v represents soot volume fraction, and C is a constant [82] as follows: nk C = 36π (n 2 k 2 + 2) 2 (2.19) + 4(nk) 2 in which, 1n + ik which denotes the complex refractive index of soot, is set to be i [83] Conservation of Species Determination of the gas chemical composition in a reacting flow, where there are several chemical species available, requires a conservation equation for each of the available chemical species. This mass transfer equation in axisymmetric cylindrical coordinates comes as follows: ρv Y k r + ρu Y k z = 1 r r (rρy kv k,r ) z (ρy kv k,z ) + W k ω k k = 1, 2,..., KK (2.20) where Y k is the mass fraction of the k th species; V k,r and V k,z are the species radial and axial diffusion velocities for the k th species, respectively; W k denotes the molecular weight of the k th species; KK is the total number of gaseous species. The k th species molar production rate, ω k, per unit volume and for non-third body reactions can expressed by Eq Here, ( N R KK KK ω k = v ki k fi [X k ] v ki k ri i=1 k=1 k=1 [X k ] v ki ) (2.21) v ki = v ki v ki (2.22)

31 Chapter 2. Methodology 18 N R represents the total number of reactions; The forward and reverse reaction rates of the i th reaction are shown by k fi and k ri, respectively; v ki and v ki are the stoichiometric coefficients of the reactants and products, respectively; X k denotes the molar concentration of the k th species. Chemical reaction source term, ω k, contains the link between soot formation/oxidation and gas-phase chemistry. The Eq expresses the conservation of species for a 2D cylindrical domain. Considering the assumptions for the premixed 1D flame, the conservation equation takes the following form: ρu Y k z + z (ρy kv k ) W k ω k = 0 k = 1, 2,..., KK (2.23) Chemical Kinetics Mechanism Two chemical kinetics mechanisms, which both take advantage of recently advanced PAH formation pathways, have been utilized in this work to describe the gas-phase reaction kinetics. The first chemical mechanism have developed by the Clean Combustion Research Centre at King Abdullah University of Science and Technology (KAUST) and this mechanism will be referred to as the KAUST mechanism hereafter. The other chemical kinetic mechanism used in this work has been developed by CRECK Modelling Group at Polytechnic University of Milan, and it will be referred as CRECK mechanism hereafter. In the following sections, there will be a brief explanation for each mechanism with an emphasis on the PAH formation pathways. KAUST Mechanism The KAUST mechanism includes the pyrolysis and oxidation of fairly light fuels, C 1 C 4 [39]. This mechanism comprises of 202 species and 1351 reactions. The KAUST mechanism is capable of describing the PAH growth up to the formation of coronene (A 7 ). According to this mechanism, A 1 can form via

32 Chapter 2. Methodology 19 Figure 2.3: Schematic representation of the major reaction pathways for the formation of large PAHs considered by the KAUST chemical kinetic mechanism (source: picture taken from ref.[2]). three pathways including propargyl (C 3 H 3 ) recombination, addition of C 2 H x on C 4 H y molecules, and addition of CH 3 on cyclopentadienyl (C 5 H 5 ) radicals. PAHs larger than A 1 can also grow through three routes involving HACA; reactions containing species with odd-carbon number such as indenyl (C 9 H 7 ), C 5 H 5, and C 3 H 3 ; and the addition of C 4 H 4 to large PAH radicals. The reactions included in this chemical mechanism are fundamental reactions which contain detailed species. In fundamental reactions the stoichiometric coefficients of the reactants and products, v ki and v ki in Eq. 2.21, are integer numbers which require less memory from the computational point of view. The open source CHEMKIN 2.0 library which is a package to calculate chemical generation rates and thermodynamics properties can easily handle these sort of chemical kinetic files. In order to calculate the reaction rates of unavailable reactions in the literature, quantum calculations were utilized. Since PAH molecules are large in size and their reactions are relatively independent of pressure, the rate constants for PAH reactions were estimated in the high pressure limits. A reasonable agreement between measured and simulated PAH concentrations were obtained in several laminar premixed and counterflow flames which verifies the model reliability to predict PAH concentrations [39]. CRECK Mechanism The CRECK mechanism is a detailed chemical kinetic model for the pyrolysis and combustion of a large variety of fuels at high temperature conditions. The review and assessment of the mechanism were hierarchically conducted, in the sequence of the foundational C 0 C 4 species; the reference fuels of alkanes (n heptane, iso octane, n decane, n dodecane), cyclo alkanes (cyclohexane and methyl cyclo hexane) and the aromatics (benzene, toluene, xylene and ethylbenzene); and the oxygenated fuels of alcohols,

33 Chapter 2. Methodology 20 C 3 H 6 O isomers, ethers (dimethyl ether and ethyl tertiary butyl ether), and methyl esters up to methyl decanoate [38]. This mechanism contains 249 species and 8153 reactions. There are also PAH formation and growth reactions from the single aromatic ring, A 1, to two artificial PAH species known as BIN1A and BIN1B which their chemical formulas are C 20 H 16 and C 20 H 10, respectively. In rich conditions, benzyl radicals are important precursors of PAH components, via the radical recombination reactions as well as C 2 H 2 addition (HACA) [38]. Figure 2.4: Schematic representation of the major reaction pathways for the formation of BIN1B considered by the CRECK chemical kinetic mechanism (source: picture taken from ref.[7]). Contrary to KAUST mechanism, CRECK involves lumped species which results in reactions with real stoichiometric coefficients. Although this is not an issue in terms of the combustion theory, in practice, the codes should be able to handle this type of reactions. The open source CHEMKIN package that has been used in this study seems to be capable of dealing with such reactions; however, the code could not calculate the ω k using Eq for the reactions which include real stoichiometric coefficients. After further development and modification the problem was fixed and the CRECK mechanism was used in this work. 2.4 Soot Aerosol Dynamics Model In the soot study, the interesting properties are usually soot particle size, concentration, and interaction with gas phase. Fig. 2.5 summarizes the physical and chemical processes that evolve the soot particle size distribution for a soot particle trapped in a microscopic volume of gas. All these processes can be classified into two groups: internal interactions which includes gas-to-particle conversion and coagulation; and external processes involving diffusion and thermophoresis which transports the particles across the boundary of the volume. The Smoluchowski equation [84] provides detailed information to derive a general dynamic equation (GDE) for the particle number density, n(v, r, t), along with all the mentioned processes. Sufficiently small surface-to-volume ratio has been assumed in order to prevent deposition

34 Chapter 2. Methodology 21 on the walls and sedimentation. The GDE for the tracking of the particle number density, n v, in the volume range between v and v + dv is as follows [8]: n v t +.n vv =.D n v + [ ] nv + t growth [ ] nv + t coag. [ ] nv.cn v (2.24) t frag. where the diffusion coefficient, D, is a function of particle size, and c is the particle velocity vector resulting from the external force field; the second term on the right hand side, is the summation of the growth rates; the third term refers to the collisions of the particles; the fourth term represents the influence of fragmentation on the number density changes. 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: picture taken from ref.[8]). The explicit solution to the GDE is very complicated, i.e., impossible for a couple of reasons. Firstly, the GDE is a nonlinear, partial integro-differential equation; moreover, a boundless number of discrete particle sizes exists in an aerosol-containing environment. As a result, the solution to the GDE requires numerical modelling. One of the proposed numerical schemes to handle this equation is finite sectional approximation [85]. The suggested method is utilized to quantify the continuous size/mass spectrum using a set of sections, or bins, in which all the particles are supposed to have the same size, or they have a defined size distribution within the section. The discretization of the entire size domain into the size classes reduces the number of conservation equations required from infinity to the number of sections. This possibility permits the tracking of the multiple integral quantities per section. As an example, beside the particles number density, surface area of the particles, aggregate structure, and composition of the particles can be followed. In the coming section, the sectional approach that has been used in this thesis will be explained, and there will be a discussion on the mathematical models representing different soot formation stages.

35 Chapter 2. Methodology The Sectional Aerosol Dynamics Model The sectional aerosol model that has been incorporated in this work is derived from the fixed pivot approach in the classical sectional description of the particle population balance equation [86]. fractal-like solid soot aggregates mass spectrum is distributed into a number of quantified classes, i.e., particle mass bins. A fixed defined mass is assigned for each section which contains a collection of aggregates. The typical mass of each section follows a geometric progression with a common ratio f s, known as spacing factor, and a scale factor equal to the mass of a dimer, U DIM. The correlation among the mass of section i, U i, the common ratio, and the scalar is expressed in the following equation. The U i = U DIM f i 1 s (2.25) All soot aggregates in a section are assumed to be of similar enough characters that they can be modelled using mean characteristics. The criteria for distributing soot aggregates into sections is their mass. A transport equation is considered for the number density of soot aggregates and solved for each section. In the nucleation step the dimers form from gas-phase incipient species. The soot dimers are assumed to be spherical, and they occupy the first section. Soot particles move from lower sections to the higher ones via processes which increase their mass, e.g., coagulation and surface growth. conversely, oxidation or fragmentation pushes the higher section particles to lower sections. Beside the aggregate number density equation, another transport equation is required to track the primary particle number density per section. The introduced transport equation lets the model to estimate the soot nano-structure by conserving the primary particles for the aggregates [87 89]. A few assumptions have been made to simplify the primary particle number density equation. Firstly, primary particles are treated as solid spheres. Secondly, the primary particles inside the aggregates of the same section share similar enough features, so that they can be modelled using mean characteristics, and they connect together by point contact, i.e., particle necking is neglected. Particle coalescence is also neglected. Finally, a universal fractal dimension, D f, of 1.8 is assumed for the agglomorates larger than the primary nuclei; while smaller particles are supposed to behave like dense spheres (D f = 3.0) [26, 27, 89]. Fixed fractal dimension supposition is usual in aerosol dynamic models when simultaneous particle nucleation, coagulation, and surface growth processes are taking place. Using the fractal dimension, the mass of a single aggregate, the primary particle number density, and the aggregate number density, the aggregates nano-structure can be completely specified. The following soot properties can be derived from an aerosol dynamic model: particle size distribution (PSD), soot volume fraction (f v ), primary particle diameter, aggregate surface area, and number of primary particles per aggregate. According to the above-mentioned explanations, the transport equations for aggregate and primary particle number densities in an axisymmetric cylindrical coordinate for each section are expressed in the following relations. ρv N a i r ρv N p i r + ρu N a i z + ρu N p i z = 1 r ( rρn a r i Vi,r a ) ( ρn a z i Vi,z) a + ρ Ṡi a (2.26) = 1 ( rρn p i r r V p ) ( i,r ρn p i z V i,z) p + ρ Ṡ p i (i = 1, 2,..., MS) (2.27)

36 Chapter 2. Methodology 23 The 1D assumptions convert the Eqs and 2.27 to: ρu N a i z = z (rρn a i V a i ) + ρṡa i (2.28) ρu N p i z = z (rρn p i V p i ) + ρṡp i (i = 1, 2,..., MS) (2.29) In Eqs and 2.29, superscripts a and p represent the parameters related to aggregates and primary particles, respectively; N i denotes the number of the i th sectional soot aggregates per unit mass of the gaseous mixture; V i is diffusive velocity of soot particles; MS expresses the total number of soot sections, and Ṡi is the total summation of the source and sink terms correlated with the mass change within each section. following equation: Ṡ i = ( ) Ni + t nu The mentioned term can be described in terms of the soot processes using the ( ) Ni + t cond ( ) Ni + t sg ( ) Ni + t ox ( ) Ni + t coag ( ) Ni t fr (2.30) where, the processes considered are inception (nu), surface condensation (cond), chemical surface growth (sg), oxidation (ox), coagulation (coag) and fragmentation (f r). The soot nucleation is only considered for the first section. Fig. 2.6 depicts all above mentioned processes along the axis of the flame. OH O2 OH O2 OH O2 Oxidation O2 OH O2 OH z Growth r Nucleation PAH Formation Premixed Fuel and Oxidizer Fuel Pyrolysis Figure 2.6: Soot morphology in a burner stabilized stagnation flame.

37 Chapter 2. Methodology 24 Nucleation Model In the PAH-based soot formation models, the generation and growth of aromatic species connects the combustion gas-phase chemistry and soot formation zone. Evidence shows the formation of small soot particles depends on the existence of PAH species [90]. Thus, the dimerization of a pair of PAH molecules is considered as the nucleation model. The dimer formation rate is proportional to the rate of collision of PAH species [59]. According to Sabbah et al. [44], Wang [6], Eaves et al. [17, 18], and Veshkini et al. [15], the pair of PAH molecules constructing a dimer can separate due to the thermodynamics condition which is very routine in the flame temperature; thus, the presence of efficiencies in the nucleation models is necessary to account for the dimer dismantling. In order to avoid dealing with arbitrary or tuned efficiencies and to improve the nucleation model based on a fundamental understanding of the dimerization process, the nucleation process has been allowed to be reversible. PAH + PAH Dimer (2.31) The forward rate of dimerization is determined by the rate of physical collision of the nucleating PAH molecules in the free-molecular regime, similar to the non-reversible nucleation model. The forward rate of dimerization and the forward rate coefficient (k F W D ) for a dimer composed of PAH j and PAH k are calculated according to Eqs and 2.33, respectively: ( NDIM t ) F W D = k F W D [P AH j ] [P AH k ] (2.32) k F W D = 2.2 8π ( ) N C,P AHj + N C,P AHk kb T ( ) 2 dp AHj + d P AHk A 2 ρ C mass N C,P AHj N v (2.33) C,P AHk where k B is the Boltzmann constant; C mass is the mass of a carbon atom; N C,P AH is the number of carbon atoms in the incipient PAH species; d P AH is the diameter of the incipient PAH species; A v is Avogadro s number; and [P AH i ]denotes the molar concentration of the incipient PAH species. Following the work by Eaves et al. [17, 18], the reverse rate coefficient (k REV ) is calculated from the relationship between the dimerization equilibrium constant and rate coefficients, Eq k F W D k REV = K p,d (RT ) n [17, 18] (2.34) The assumption of gaseous species for the dimers leads n to be equal to 1. In order to calculate the equilibrium constant of dimerization, Eq. 2.35, the Gibbs free energy of dimerization has to be evaluated, which is related to enthalpy and entropy through the following relation: G D = H D T S D. The following equations can be derived using statistical mechanics [91] considering the assumptions described in [17, 18] to estimate the change in enthalpy and entropy of the nucleation processes for any arbitrary PAH PAH collision: ( ) K p,d = exp G D R T (2.35) 6 ( ) H D 1 = E0 4k B T hcv e hcvi/k i BT 1 (2.36) i=1

38 Chapter 2. Methodology 25 S D R u [ (m3 hc B ) 3/2 ] 1 B2 h 3 P σ 1 σ 2 = ln 2m 1 m 2 B3 π 2 (e 1 k B T ) 4 + σ 3 6 { hvi /k B T ( )} (2.37) exp hvi/k BT 1 ln 1 e hvi/k BT i=1 Here, H D is the enthalpy change due to dimerization, S D is the entropy change due to dimerization, R u is the universal gas constant, k B is the Boltzman constant, T is the gas temperature, h is Plank s constant, c is the speed of light, m 1 and m 2 are the masses of the two colliding entities, m 3 is the combined mass of the two entities, σ i are the symmetry numbers, with dimers assumed to have no symmetry (σ i = 1), and B i are the rotational constants. Two remaining parameters, E 0 and v i, influence both enthalpy and entropy change. E 0 is the binding energy, and v i is the i th (out of 6 in total) vibration mode frequency created when nucleation process takes place. It is assumed that the frequencies of the colliding objects remain constant during the nucleation processes, which indicates PAHs stick to each other via physical coalescence [6]. According to the literature review performed by Veshkini et al. [15] and Eaves et al. [17, 18] on the importance of reversibility in soot formation and its associated parameters, the binding energy of coronene dimer, 69.2 KJ/mol, has been picked to be incorporated into the Eq The study of Eaves et al. [17, 18] also provides information about the vibrational frequencies; based on the equilibrium constant proposed for pyrene dimerization, an effective vibration frequency of 18 cm 1 can be inferred. Due to the limited computational resources, the nucleation model cannot consider all the possible PAHs as nucleating species. According to Veshkini et al. [15], the species anthanthrene, benzo[ghi]perylene, and benzo(ghi)fluoranthene have the features of the PAH molecules. These three species are available in KAUST II mechanism. For the CRECK mechanism, the largest PAHs available in the species are pyrene, BIN1A, and BIN1B, which the last two have 20 carbon atoms. The molecular structure of the mentioned species is shown in Fig Figure 2.7: Nucleating species chemical structure.

39 Chapter 2. Methodology 26 Condensation Model The absorption of large gas-phase species to the particle s surface is one of the heterogeneous gas-toparticle conversions known as condensation. Similar to nucleation, the collision of condensing species and the surface of the particles builds the base of the condensation model [92]. The PAHs that are allowed to condensate are the same as those were introduced to the nucleation process. The code has the ability to consider other PAHs as well. In previously developed soot models, a 100 % sticking probability upon collision is a common assumption [15]; however, based on the flame thermodynamics condition the freshly attached PAHs can easily evaporate from the surface of the soot particles due to high reversibility [6] which requires the condensation model to be reversible. Neither a single condensation efficiency nor a functional form can satisfactorily reproduce all soot morphological parameters [15]. Therefore, a condensation model is required to calculate the reverse rate of condensation process based on the flame conditions. Eaves et al. [17, 18] developed an efficiency based reversible model to study soot formation in the Santoro coflow diffusion flame. According to the work by Eaves [17, 18] the combination of fully reversible nucleation model and an efficiency based reversible condensation model can reasonably predict all the soot morphological properties. However, The condensation model that has been used in the current work has been adopted from Veshkini et al. work [15]. This novel model is based on an equilibrium stand point of view. In their study soot particles in each section are assumed to be a unique species with properties of a large PAH molecule with the same mass. The mass growth via PAH addition will transform a soot particle to a particle with higher mass which is described by the reaction as follows: Soot i + np AH Soot i+1 (2.38) Here, n in the Eq denotes the total number of PAHs needed to push a particle from section i to i + 1, and can be calculated with: n = W T P AH U i (f s 1)A v (2.39) Here, W T P AH is the molecular weight of the PAH; U i is the mass of section i; f s is the sectional factor, and A v is the Avogadro s number. The equilibrium constant of the mentioned reaction can be calculated with Eq ( ) ( K p,c = exp G C = exp H C T ) S C = RT RT N i+1 N i χ n eq,p AH (2.40) where N i is the number density of soot particles in the i th section. In order to calculate the equilibrium constant and Gibbs free energy, very similar to nucleation model, the following equations can be derived using statistical mechanic principles to determine the enthalpy and entropy change for the addition of n PAH molecules to a soot particle: H D = ne0 4nk B T + 6n i=1 ( ) hcv e hcvi/k i [15] (2.41) BT 1

40 Chapter 2. Methodology 27 S D R u [ (m3 (hc B 1 ) n ) 3/2 ( B2 = ln 2 n m n 1 m B 2 3 6n i=1 h 3 P π 2 (e 1 k B T ) 4 ) n σ n 1 σ 2 { hvi /k B T exp hvi/k BT 1 ln ( 1 e hvi/k BT )} (2.42) σ 3 ] + where n is the number of PAH molecules, H D is the enthalpy change due to dimerization, S D is the entropy change due to dimerization, R u is the universal gas constant, k B is the Boltzman constant, T is the gas temperature, h is Plank s constant, c is the speed of light, m 1 and m 2 are the masses of the two colliding entities, m 3 is the combined mass of the two entities, σ i are the symmetry numbers, and B i are the rotational constants. The estimated equilibrium constant is substituted into Eq to calculate the mole fraction of the PAH. The equilibrium concentration of condensing PAH species is incorporated in a Heaviside function to form a condensation efficiency function which is shown in Eq γ ik = [ [ ( ) 1 ]] (2.43) Kp,Ck N 1 + exp 2 4χ i n P AHk N i+1 2 Here, n is the PAH coefficient in reaction 2.38 and determined by Eq. 2.39; χ P AHk is the mole fraction of the k th condensing PAH species and K p,ck is the corresponding species equilibrium constant for condensation. Similar to the nucleation process, the binding energy of coronene dimer, 69.2KJ/mol, has been picked to be incorporated into the Eq It has also been found that the collision vibration frequency of 17 cm 1 can satisfactorily reproduce all morphological soot properties. The condensation efficiency, γ Cond., is the sticking probability which takes into account the probability of the molecules bouncing off the surface after collision. condensation rate can be calculated using the following equation: I cond,i = K PAH k=1 Using the condensation efficiency and other parameters the γ ik β ik N C,k C mass [P AH] k N a i (2.44) where I cond,i is the mass growth rate of the i th section soot agglomerate due to condensation in the unit of g s /g mix /sec, and is non-negative value; β ik is the collision kernel of the k th condensing species and the i th section soot aggregate. According to the sectional scheme the mass growth must be distributed among all mass sections. The mass of aggregates in each section is fixed; therefore, the mass growth of an aggregate in section i is reflected by transferring the equivalent amount of mass in terms of number of aggregates from section i to section i + 1. In the primary particle transport equation, Eq. 2.29, the growth term is multiplied by the number of primary particles per aggregate in order to conserve the primary particle numbers. The above stated descriptions are presented mathematically in following relations: ( N a i t ) cond = I cond,l m 2 m 1 if i = 1 I cond,i 1 m i m i 1 I cond,i I cond,ms 1 m MS m MS 1, m i+1 m i if i = 2,..., MS 1 if i = MS (2.45)

41 Chapter 2. Methodology 28 ( N p ) i = t cond I cond,l m 2 m 1 if i = 1 I cond,i 1 m i m i 1 n p,i 1 I cond,ms 1 m MS m MS 1 n p,i 1 I cond,i m i+1 m i n p,i if i = 2,..., MS 1 if i = MS (2.46) Here, m i is the aggregate mass of the section i; n p,i is the number of primary particles per aggregate of the section i which is equal to N p i N. It should be emphasized that for the first and last section the sum i a of all growth terms must equal zero to make sure that no new particles are numerically formed due to growth processes. MS ( N a i t i=1 ) cond MS ( N p ) i = = 0 (2.47) t cond i=1 Chemical Surface Growth and Oxidation Models The soot surface heterogeneous reactions with the gas-phase species used in this work are expressed in Tab The renowned hydrogen-abstraction-carbon-addition (HACA) is responsible for the mass growth and oxidation by oxygen [59, 92]. The kinetics of the surface reactions in HACA scheme is a function of surface sites, the arm chair sites depicted in Fig. 2.8 which contains four carbon atoms. These carbon atoms could be saturated, C soot H, or dehydrogenated, C soot, on the particle surface. Figure 2.8: Illustration of armchair sites on the surface of a soot particle. Table 2.2: HACA based soot surface growth and oxidation reactions[2], k = AT b e Ea/RT ( ) ( cm No. Reaction A 3 mol.s b E kcal ) a 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 The following equation is useful to calculate the concentration of the saturated sites on the particle s surface.

42 Chapter 2. Methodology 29 [C soot (H)] = A s A v χ Csoot (H) (2.48) Here, A s (cm 2 /cc) is soot surface density; A v is the Avogadro s number; and χ Csoot (H) is the number of the sites per unit surface area of the soot particles and estimated to be 0.23 [59]. The concentration of dehydrogenated sites, [(C) soot ], is calculated with χ Csoot in similar way. The following equation calculates χ Csoot using as steady state assumption. 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 ] (2.49) As a result, the mass increase rate due to HACA (S 4 ), and the mass reduction rate caused by O 2 oxidation (S 5 ) are: I C2H 2,i = 2αC mass A s,i A v (k 1 [H] + k 2 [OH])χ Csoot Hk 4 [C 2 H 2 ] N p i k 1 [H 2 ] + k 2 [H 2 O] + k 3 [H] + k 4 [C 2 H 2 ] + k 5 [O 2 ] (2.50) I O2H 2,i = 2αC mass A s,i A v (k 1 [H] + k 2 [OH])χ Csoot Hk 5 [O 2 ] N p i k 1 [H 2 ] + k 2 [H 2 O] + k 3 [H] + k 4 [C 2 H 2 ] + k 5 [O 2 ] (2.51) In Eqs and 2.51, A s,i is the primary particle surface area in the section i, and α is the surface reactivity parameter. According to Tab. 2.2, the reaction S 6 is another source for soot oxidation. This oxidation rate can be estimated based on kinetic theory with a probability γ OH as follows: I OH,i = γ OH β OH,i C mass [OH] N a i (2.52) The surface growth source term, ( N i ) t, is evaluated by substituting I sg cond,i with I C2H 2,i using Eqs and The surface oxidation source terms are calculated using the following relations: ( N a i t ) ( N p ) i = t ox ox = I ox,2 I ox,2 m 2 m 1 I ox,i+1 m i+1 m i Iox,i I ox,ms m MS 1 m MS Iox,1 m1 if i = 1 m i m i 1 if i = 2,..., MS 1 if i = MS m 2 m 1 n p,2 Iox,1 m 1 if i = 1 I ox,i+1 m i+1 m i n p,i+1 I cond,ms if i = MS m MS 1 m MS n p,ms Iox,i m i m i 1 n p,i if i = 2,..., MS 1 (2.53) (2.54) The reason that different relations are used for the growth and oxidation stems from the fact that oxidation moves particles from high sections to low sections while the growth processes do the opposite. Coagulation Model Coagulation is the sticking of the two soot particles when they collide. The role of this process is to increase the soot aggregate size. Coagulation adds to the number density of aggregates in higher mass sections, while decreases soot aggregate concentration in lower mass sections. Thus, coagulation keeps the number of primary particles constant, while reduces the number of aggregates. The coagulation rate is calculated using binary collision rate of soot particles estimated in the entire Knudsen numer

43 Chapter 2. Methodology 30 regime [70, 93] using a sticking probablity [63]. The coagulation rate in the i th section for aggregates and primary particles are calculated as ( N a i t ) coag = j ( N p ) i = t coag j k k ( 1 δ ) jk η ijk β jk ξ jk Nj a Nk a Ni a 2 ( 1 δ ) jk η p,ijk β jk ξ jk N p j 2 N p k N p i MS m=1 MS m=1 β im ξ im N a m (2.55) β im ξ im N a m (2.56) { k [1, i] j [k, i] m i 1 < m j + m k < m i+1 } In equations 2.55 and 2.56, δ jk is the Kronecker delta; β jk is the Boltzman collision kernel of two aggregates from the sections j and k; and ξ jk represents the coagulation collision coefficient. The mass and number of aggregates have to be kept constant during the coagulation step; therefore, the freshly formed aggregates are transferred to two consecutive sections. This division has been accomplished using parameter η ijk which is defined as follows: m i+1 (m j+m k ) m i+1 m i ifm i m j + m k m i+1 m η ijk = i 1 (mj +m k ) m i 1 m i ifm i 1 m j + m k m i 0 else Moreover, the parameter η p,ijk in Eq is defined according to the following expression: (2.57) η p,ijk = m i m j + m k (n p,j + n p,k ) (2.58) Fragmentation Model The cracking of the fractal-shape aggregate chain into smaller aggregates is known as fragmentation. In the current work, only the oxidation-driven fragmentation has been incorporated into the model. The model considers the aggregates breakage into two children aggregates with identical mass; moreover, no fragmentation takes place for an aggregate containing fewer than two primary particles. According to the assumptions, the fragmentation rate of the aggregates in the section i is expressed by ( N a i t ) fr Γ + S 2 N2 a if i = 1 = (Γ 1)S i Ni a + Γ +S i+1 Ni+1 a if i = 2,..., MS 1 (Γ 1)S MS NMS a if i = MS (2.59) Γ +S 2N a 2 ( N p ) np,2 f s if i = 1 i = (Γ 1)S t i Ni an p,i + Γ+Si+1N a i+1 np,i f s if i = 2,..., MS 1 fr (Γ 1)S MS NMS a n p,ms if i = MS (2.60) where Γ and Γ + denote breackage distribution functions which moves the newly formed children aggregates int two neighbor sections in order to conserve the mass and number of aggregates. The breakage distribution functions are estimated as [94]:

44 Chapter 2. Methodology 31 Γ = f s 2 f s 1 Γ + = f s f s 1 The term S i in Eq is the fragmentation rate per aggregate and is adopted from [94]: (2.61) (2.62) S i = r ox,i (n p,i ) 1/D f (2.63) where r ox,i represents the oxidation rate on a mass basis of soot aggregates in the i th section per unit surface area; D f is the aggregate fractal dimension Numerical Method The main differential equations described in previous sections do not have explicit solutions; therefore, a numerical approach is required to find a very close estimation to the real solution with an error tolerance of The premixed boundary value problem is solved numerically based on the finite difference framework. In the following sections, the details for the numerical method that was utilized for the premixed stagnation flame will be presented. Premixed Stagnation Flame The OPPDIF code has been designed to simulate a premixed/diffusion counter-flow flame in a 1D domain [95]. This code can be modified to a burner stabilized stagnation using the non-slip boundary condition at the oxidizer boundary. The described soot aerosol dynamics model has been coupled with OPPDIF code to predict the soot desired properties in premixed stagnation flames. The differential equations in OPPDIF code are discretized using the finite difference approximation. The discretization of the sectional aggregate number density and primary particle number density has been carried out similar to the species conservation equation discretization. The code has the capability to switch between second order central difference and first order windward difference methods for the convective terms. The terms that are not differentiated, such as the chemical production rate terms, are calculated at the mesh points j. Other parameters that do not come within the derivatives are also evaluated at the mesh points. Discretization of the governing equations forms a nonlinear system of equations. The Newton s method has been implemented to find the solution to this system of equations which is cast in residual form as follows: F (v) = 0 (2.64) where v is the vector of all unknowns and F (v) is the vector of all equations. If v, an approximated solution vector, is guessed for the unknowns, the equations F likely will not tend to zero; rather, evaluating the functions F by the v as an input will form the residual vectors: F (v ) = RES (2.65) The final goal is to find values for the unknowns vector, v, with zero residuals, F (v ) = 0. OPPDIF

45 Chapter 2. Methodology 32 takes advantage of the modular solver subroutine TWOPNT to address the boundary value problem. TWOPNT uses a hybrid method to find the solution. This subroutine utilizes the modified damped Newton s method to attempt solution of the steady state, and when the newton iteration is diverging it turns to time integration [96]. After the time evolution performed on the solution, TWOPNT restarts the Newton s method to converge the solution to the steady state. The Newton s method produces a series of intermediate unknown vectors, { v (n)}, that converges to the solution of nonlinear equations: ( ) 1 F v (n+1) = v n + F (v (n) ) (2.66) v v (n) The Newton s method is not computationally efficient and is afflicted by lack of robustness. The calculation of F v, Jacobian matrices, is highly time consuming, and the convergence to the solution depends on a very good initial guess v 0. The modified Newton s method imposes the following modifications to the primary method. Firstly, since the linear system changes minimally from one iteration to the next, the Jacobian matrix updates after a few number of iterations. Second, a damping factor λ (n) has been defined for the evaluation of v (n+1) from v (n) in order to adjust the solution in each iteration and reduce the chance of divergence. As a result, the Eq changes to: v (n+1) = v n + λ (n) ( J (n)) 1 F (v (n) ) (2.67) Here, the damping factor reduces according to a geometric progression. λ (n) = 2 0.5, 2 1.0,..., (2.68) In order to form the elements of the Jacobian matrix, a finite difference perturbation method is suggested by [97]. References [73, 95, 96, 98] provide detailed information regarding the OPPDIF code, numerical method, and modified Newton s method. Boundary Condition The boundary conditions at the inlet nozzle are express below: F = ρ Iu I 2 (2.69) G = ρv = 0 (2.70) r ( ) dh = 0 (2.71) dz I T = T I (2.72) ρuy k + ρv k Y k = (ρuy K ) I (2.73) ρun i + ρv i N i = (ρun i ) I (2.74) where, the index I refers to the input value of parameters which can be derived from the experimental setup information; V k and V i represent the diffusion velocity of the k th specie and soot aggregate of the section i, respectively. The inflow boundary condition specifies the total mass flux, including diffusion and convection. If there would be a gradient at the boundary, the conditions would allow diffusion to

46 Chapter 2. Methodology 33 the upstream. The boundary condition at the stagnation plane is listed below: F = 0 (2.75) G = ρv = 0 (2.76) r ( ) dh = 0 (2.77) dz W T = T W (2.78) ( ) dvk Y z ρ = W k ω k (2.79) dz W ( ) DNi = 0 (2.80) dz Since the nonslip boundary condition assumption has been made, u, v, and V k are all zero at the stagnation wall. The wall temperature, T W, equals the measured temperature. The axial convective velocity reduces to zero in the proximity of the wall which produces a diffusive flux equal to the chemical source term of each specie at the stagnation wall. W

47 Chapter 3 Results and Discussion The results on the contribution of CO2 addition to the soot formation in burner stabilized stagnation (BSS) premixed flames are presented in the following order. The first section will discuss the model validation against benchmark ethylene flames. Within the mentioned section, computed temperature profiles, soot volume fraction (f v ), and particle size distributions (PSDs) are compared with measurements from [9], respectively. Then a wall temperature sensitivity analysis will reveal how dependent the code is on the boundary temperature. After validation, the model was used to see to effect of CO 2 addition on the PSDs. In the second section, the computed f v and PSDs for the CO 2 -diluted flames will be compared with experimental results from [1]. Then, the reversibility of the soot model and boundary temperature effect on the morphology will be expressed. At the end of this section, the role of CO 2 in the soot formation process will be explained. Finally, the influence of the chemical kinetic file on the evolution of PSDs and capturing the CO 2 addition effect will be presented. 3.1 Model Verification The model that has been utilized in this thesis was adopted from the work by Veshkini et. al. [15]. This model couples the OPPDIF code, which calculates the flame temperature and gas-phase species composition, with a sectional aerosol dynamics model, which is a bridge between gas-phase chemistry and solid-phase particulates. Soot volume fraction, particle nanostructure, and size distribution are soot properties of interest. The simulation tool used in the current work can predict the mentioned properties considering flame temperature, mixing effects, and residence time. A radiation heat transfer model was also incorporated into the model to account for the radiation heat loss emitted from CO 2, H 2 O, and soot particles. The soot nucleation and condensation models incorporated in this work use different parameters than what is suggested by Veshkini et al. [15]. This fact necessitates the revalidation of the model using a similar test case before moving toward the main problem. 34

48 Chapter 3. Results and Discussion 35 z r HP = 0.5 cm z r HP = 0.6 cm z r HP = 0.7 cm Premixed Fuel and Oxidizer Premixed Fuel and Oxidizer Premixed Fuel and Oxidizer Figure 3.1: Schematic of different burner-to-stagnation surface separations. Properties of soot measured in flame C3 [9] were chosen as the validation test for the model discussed above. This flame was also used by Veshkini et al. [15] and Saggese et al. [7] for a similar purpose. Camacho et al. [9] generated soot in a 16.3% ethylene 23.7% oxygen 60%argon BSS flame at atmospheric pressure. The cold gas velocity was 8 cm/s (298 K and 1 atm). The soot was sampled along the centerline of the flame through an orifice which is drilled into the stagnation surface. A scanning mobility particle sizer was used to analyze the gas sample over a range of burner-to-stagnation surface separations, Fig. 3.1, to measure the PSDs. The volume fractions of the particles, f v, were calculated via the detailed PSDs. In the BSS flame setup, each burner-to-stagnation surface represents a distinct flame although the inlet conditions are the same. This difference stems from the temperature and velocity profile changes due to the different burner-to-stagnation surface separations. Since each spacing forms a unique boundary condition, all the probe sampling techniques should consider each spacing as a unique flame [7]. The experimental measurements over the separation range of 0.55 to 0.8 cm have been used for the model verification Temperature Profiles Soot formation process is a strong function of temperature; as a result, accurate prediction of the flame temperature is a necessary requirement for predicting the properties related to soot. Soot mostly forms in the post flame region, i.e., the region after the peak temperature. The inclusion of radiation heat transfer model prevents temperature overprediction in the post flame region. Fig. 3.2 compares the computed and measured temperature profiles for a series of burner-tostagnation surface separations, H P. The peak temperature is all around 1830 K; however, the burnt gas cools off at different rates depending on the H P. In general, the computed temperature profiles capture the experimental results within their uncertainties. This means the model solves the energy equation correctly and provides a reliable temperature profile to calculate other thermodynamics properties for the next steps.

49 T(K) T(K) T(K) T(K) T(K) Chapter 3. Results and Discussion H P = 0.55 cm H P = 0.7 cm X(cm) H P = 0.6 cm X(cm) H P = 0.8 cm Simulation Experiment X(cm) X(cm) Figure 3.2: Comparison between modelled (solid lines) and measured (symbols) axial temperature profiles of the BSS ethylene flame for a series of H P values Soot Volume Fraction Soot volume fraction, f v, is a global measure of a flame s sooting behaviour. The numerical prediction of f v values satisfies many industrial purposes. In the experiment, soot volume fraction is derived using the integration of the PSD with respect to the particle diameter, while in the modelling, f v is calculated using the mass fraction and density of soot particles. Comparison of the calculated and experimental soot volume fraction as a function of burner-to-stagnation surface separation is presented in Fig The agreement between the measurements and the simulations is reasonably good.

50 f v (ppm) Chapter 3. Results and Discussion Experiment Simulation Height Above Burner, H P Figure 3.3: Comparison of the measured soot volume fraction (triangles) and model predictions (circles) as a function of burner-to-stagnation surface separation. Although soot volume fraction is an important parameter of interest and can provide enough information about the total soot formed in a flame, it does not present other useful information about the soot aggregate structures. Current emission regulations, e.g. PM 2.5, are based solely on the mass of particles emitted. However, according to Wang [6], soot models have to be able to predict the chemical composition of nascent soot and its size distribution since the environmental and human health effects of soot emission are more directly related to the PSD and chemical composition than particle mass Particle Size Distribution (PSD) At a detailed level, the model generates the evolution of the PSDs reasonably well from nucleation level to later stages of mass/size growth, as shown in Fig PSDs show detailed information about the size of the particles and their population; more importantly, they can depict different stages of the soot morphology. The PSDs are computed at the stagnation surface. The model predicts the overall progression of the PSDs; all the computed lines are in a qualitative agreement with the measurements.

51 fdsafaf Particle Size Particle Distribution, Diameter, D P DN/Dlog (nm) D P (cm -3 ) Chapter 3. Results and Discussion E+12 H P = 0.55 cm 1.0E E E+09 H P = 0.7 cm E E E+06 Particle Diameter, D P (nm) E H P = 0.60 cm 1.0E H P = 0.8 cm E E E E E Particle Diameter, D P (nm) Experiment Simulation Figure 3.4: Comparison of the computed (solid lines) and measured (symbols) PSDs. The experimental data is adopted from [9]. Studying the PSD functions can help identifying the roles of different processes in forming aggregates. In lower spacings such as 0.55 cm the size distribution is unimodal. By moving from H P 0.6 cm to H P 0.7 cm, the unimodal distribution becomes bimodal due to the growth, e.g. condensation, and coagulation processes as the height increases. Meanwhile, the curve widens, indicating large aggregates are formed Stagnation Wall Temperature Sensitivity Analysis As mentioned in the section 3.1.3, the PSD function is computed at the stagnation surface location. Moreover, the wall temperature is used as the temperature boundary condition. Soot formation is a strong function of temperature. In this work, the temperature that has been assigned to the wall boundary was derived from the experimental measurements [9]. According to Camacho et al. [9], Tang

52 PSD, DN/Dlog D P (cm -3 ) Chapter 3. Results and Discussion 39 et al. [1], and Abid et al. [32], the embedded thermocouple into the stagnation surface measures the temperature within the uncertainty range of ±30 K. This fact necessitates a wall temperature sensitivity analysis to see how temperature changes affect the PSDs H P = 0.55 cm H P = 0.8 cm Experiment Tw = 460 Tw = 497 Experiment Tw = 510 Tw = 470 Tw = 520 Tw = 485 Tw = 550 Tw = Particle Diameter, D P (nm) Figure 3.5: Wall Temperature Sensitivity Analysis The comparison between measurements (symbols) and modelled (solid lines) PSDs over a range of wall temperatures is depicted in Fig. 3.5 for the spacings 0.55 and 0.8 cm. The left frame shows even 10 K difference in wall temperature represents a noticeable effect on the PSDs. The right frame investigates the similar influence in a larger spacing. The analysis shown in Fig. 3.5 expresses how sensitive the model is to the stagnation wall boundary temperature. As a result, the ±30 K temperature uncertainty should be considered in determining the proper temperature boundary condition HACA Effect The very popular hydrogen abstraction carbon addition (HACA) process is one of the pathways for the formation of polycyclic aromatic hydrocarbons (PAHs). There are evidences in coflow diffusion flames which show that HACA mechanism is important in soot mass/surface growth [16, 17, 79]. Moreover, in premixed BSS flames, Tang et al. [1] suggests that HACA plays a role in the soot growth; Saggese et al. [7] also incorporated this pathway into their BSS flame soot model, and based on their sensitivity analyses, this process is important. Wang [6] provides evidence that most of the soot growth in BSS flames occur in a region which the temperature drops to 1450 K and the concentration of the H atoms is too small to account for the radical formation on the soot surface; thus, the observed growth is unexpected in terms of the HACA mechanism. Veshkini et al. [15] showed that HACA plays a minor role in the growth process using a thorough sensitivity analysis. The model that was used in this work includes the HACA surface growth, in which alpha is the efficiency of the process. The comparison of the two extreme cases is depicted in Fig Solid black line shows fully-disabled surface reactivity, and dashed blue line represents 100% surface reactivity. The soot model generates very similar PSDs for the abovementioned extreme cases which means the HACA mechanism in BSS flames might not be

53 Mole Fraction Soot Volume Fraction (ppm) PSD, dn / dlog D P (cm -3 ) Chapter 3. Results and Discussion 40 as active as it is in the coflow diffusion flames H P = 0.60 cm Experiment Alpha = 0.0 Alpha = Particle Diameter, D P (nm) Figure 3.6: Comparison of the different surface reactivity parameters. 6.0E E E E E E-04 H P 1.2E-02 = 0.6 cm 4.8E E E E E E E+00 H radical E-04 fv 5.0E-03 H P = 0.8 cm 4.0E E E E E-04 H P = 0.8 cm H radical fv 2.0E E E E E E E E E E E E E E X(cm) 0.0E+00 H radical fv Figure 3.7: Comparison of the H radical concentration and f v for the spacings 0.6 and 0.8 cm. The reactions that are taken into account for the HACA surface growth model are listed in table 2.2. H radical exists in the majority of the reactions introduced in table 2.2. According to Wang [6], successful HACA surface growth requires H radicals to activate a position on the surface of the soot for addition of an acetylene molecule. The H radical concentration along with f v has been depicted with respect to the height above burner in Fig f v is a soot global parameter which shows the mass growth trend. Based on Fig. 3.2, the flame front is located at 0.1 cm above the burner tip. Fig. 3.7 shows that most of the soot growth occurs in the post flame region and very close to the stagnation wall. Moreover, the concentration of H radical is almost zero in the region that most of the soot mass growth occurs. As a result, the species generation term of the reactions involved in the HACA soot surface growth would be negligible, which means ineffective HACA growth. This conclusion is consistent with

54 Chapter 3. Results and Discussion 41 the study by Saggese et al. [7]. In their work, they have shown that by decreasing the HACA reactions rates by a factor of ten, the change that happens to the PSD is insignificant. This means weakening the HACA process does not affect the evolution of PSDs and growth process. Up to here, the model was validated against the experimental measurements for different parameters of interest. The modelling tool is now ready to study other BSS flames. The dilution of the fuel and/or oxidizer mixture stream is an established method to develop low temperature combustion in order to prevent both soot and NO x formation. CO 2 is one of the major components of combustion products, and there is experimental evidence that diluting the unburnt fuel mixture with CO 2 would suppress the soot formation [1, 12]; however, there are unanswered questions in this field. Here after, the scope of the work is about the CO 2 addition effects on premixed BSS ethylene flame sooting behaviour.

55 PSD, dn/dlog D P (cm -3 ) Chapter 3. Results and Discussion CO 2 Addition Effects The soot properties that are studied in this section were chosen from the work by Tang et al. [1]. They measured the PSD functions for three different ethylene BSS flames over a range of burner-to-stagnation surface separations. Tang et al. [1] generated soot in a 16% ethylene 24% oxygen 60% argon BSS flame at atmospheric pressure for the first flame, A1. For the second and third flames, 20% and 30% of Ar has been replaced with CO 2, respectively. The summary of the flame compositions is available in table 2.1. The cold gas velocity was 8 cm/s (298 K and 1 atm) for all cases. The soot was sampled along the centerline of the flame through an orifice which is drilled into the stagnation surface. A scanning mobility particle sizer was used to analyze the gas sample to produce the PSDs. The flame C3 discussed in section 3.1 on the page 35 is very similar to flame A1 in terms of the measurement technique and boundary condition; however, there is a minor difference among their equivalence ratios, φ. The equivalence ratios for the flames C3 and A1 are 2.07 and 2.00, respectively. As a result, it is worth to compare both experimental and computed PSDs for a few spacings to see what is the effect of equivalence ratio and how the model captures the effect. Fig. 3.8 shows the comparison between computed and measured PSDs for the flames C3 and A1. According Fig. 3.8, the model captures the trend of experimental data; however, it does not show the noticeable diameter reduction observed in measured PSDs. This discrepancy could be attributable to the chemical kinetic file, imprecise stagnation wall temperature, or measurement data scatter. The experimental PSDs for flames C3 and A1 have been measured at different locations, and the particle sizer apparatus is highly sensitive to the ambient pressure and temperature H P = 0.55 cm (a) H P = 0.80 cm (b) Particle Diameter, D P (nm) C3 Exp. A1 Exp C3 Num. A1 Num. Figure 3.8: Comparison of the flames C3 (φ = 2.07) and A1 (φ = 2.00) for the burner to stagnation surfaces of 0.55 and 0.80 cm. The measurements in [1] show addition of CO 2 drastically reduces both soot particle sizes and volume fraction. There are hypotheses on the role of CO 2 in the soot formation suppression; however, a detailed

56 Chapter 3. Results and Discussion 43 soot model is required to check all the suppositions to become more certain about the phenomenon. According to the literature review performed in the section 1.2.3, the introduced model was used to answer the following questions in the upcoming sections: Is the suppression effect of CO 2 due to thermal or chemical factors; What are the chemical reactions involved in this process; Between the nucleation and condensation, which one is affected more Soot Volume Fraction In this section the influence of the CO 2 addition on the soot volume fraction, f v, is studied. The comparison between computed (circle-solid line) and measured (triangle-dashed line) is shown in Fig For the flame A1, 0.0% CO 2, the agreement between the modelling and experimental result is good. Addition of CO 2 reduces the soot volume fraction. The frames (b) and (c) of Fig. 3.9 show the model can capture the reduction, but it does not predict the correct value for all the burner-to-stagnation surface separations % CO % CO Soot Volume Fraction, F V (a) Exp. Num % CO (b) Exp. Num (c) Exp. Num X(cm) (d) Height Above Burner, H P (cm) 0.00 % Exp % Num % Exp % Num % Exp % Num Figure 3.9: Comparison of the computed (circles) and measured (triangles) soot volume fraction for the addition of 0.0%, 12%, and 18% of CO 2, respectively (see Tab. 2.1).

57 Chapter 3. Results and Discussion 44 The frame (d) summarizes the calculated and measured f v for all three flames; the simulation results are in a qualitative agreement with the experimental data in capturing the CO 2 suppression effect. Although the model may not work properly for the 18% CO 2 dilution, capturing the reduction trend could be adequate for the purpose of this study Particle Size Distribution The PSDs which depict information about the particle sizes and population are discussed in this section. The measured PSDs over 5 burner-to-stagnation surface separations derived from the work by Tang et al. [1] show the addition of CO 2 reduces both the particle sizes and numbers (Fig. 3.10). The reduction of the numbers could be attributable to the lower nucleation rates due to the CO 2 inhibition effects. The smaller diameter size might stem from the lower agglomeration rates due to less availability of particles or less active PAH condensation. The introduced soot model was used to reproduce the PSDs. For each of the 5 spacings of interest, three flames had to be simulated which resulted in 15 simulations. 60 sections have been selected to capture the evolution of PSDs. The spacing factor, f s, discussed in section 2.4.1, has been chosen to be 1.2 for the spacings 0.5 and 0.55 cm; 1.3 was used for other larger spacings. The computed and measured PSDs are compared in Fig. 3.10, and they show a qualitative agreement. The numerical results also support that having CO 2 as a diluent in the fuel and oxidizer mixture reduces the soot formation and growth. For the flame A1, 0.0% CO 2, the agreement of the particle sizes seems fairly good; however, for the flames A2 and A3 as the burner-to-stagnation surface separation increases the simulation is not able to capture the spread between the points which representing the increasing amounts of CO 2. The modelling tool used in this work consists of different modules including flame simulator (the OPPDIF code), chemical reactions and thermodynamics libraries, and the soot model. Any defect or lack of accuracy in each segment could account for this discrepancy. In the following sections there will be a discussion about the possible sources of error.

58 Particle Size Distribution, dn P /dlog D P (cm -3 ) Chapter 3. Results and Discussion H P = 0.50 cm H P = 0.55 cm 0.00 % Exp % Num % Exp % Num % Exp % Num H P = 0.70 cm H P = 0.60 cm 1 7 H P = 0.80 cm Particle Diameter, D P (nm) Figure 3.10: Comparison of the computed (solid lines) and measured (symbols) PSDs. The experimental data is adopted from [1].

59 Particle Size Distribution, DN/Dlog D P (cm -3 ) Chapter 3. Results and Discussion PAH Condensation Reversibility Effect The reversible PAH condensation model used in this work has been adopted from the work by Veshkini et al. [15]. Many soot models take advantage of constant condensation models. The model in this work can also be switched to constant condensation. The advantage of reversible condensation is to calculate the rate of PAH desorption from the surface of the soot based on the flame condition rather than a tuned constant value. Fig shows the importance of reversibility in capturing the CO 2 addition influence on the particle sizes. Similar tests for higher spacings have been performed by Veshkini et al. [15] show the constant condensation model cannot capture even the bimodality of the PSD function H P = 0.50 cm (a) H P = 0.50 cm (b) H P = 0.60 cm H P = 0.60 cm Particle Diameter, D P (nm) % Exp % Num % Exp % Num % Exp % Num. Figure 3.11: Comparison of the constant (column a) and reversible (column b) condensation model.

60 Particle Size Distribution, dn/dlog D P (cm -3 ) Chapter 3. Results and Discussion Wall Temperature Effect In section a stagnation wall temperature sensitivity analysis have been performed, and the modelling result showed that the PSD functions are highly sensitive to the boundary temperature. The PSDs for different stagnation wall temperature have been compared for the spacing 0.6 cm in Fig The purpose of this section is to investigate the effect of wall temperature on the capturing the CO 2 addition effect. Three possible boundary temperatures including the measured temperature and uncertainty limits are studied here for the spacing 0.6 cm. The model overpredicts the diameter at 470 K; at 530 K, the diameters of particles are underpredicted; the middle temperature, 497 K, shows the best agreement among the possible boundary conditions. The stagnation wall temperature has been determined using an embeded thermocouple. The mentioned thermocouple reports the average temperature of the gas and the water cooled wall. however, the code only considers the domain inside the gas. These facts suggest that the reported measured temperature could be slightly lower than the real gas temperature, i.e., a wall temperature of 510 K can capture the exact diameter T Wall = 470 K 00.0 % Exp % Num % Exp % Num % Exp % Num T Wall = 497 K T Wall = 530 K Particle Diameter, D P (nm) Figure 3.12: Stagnation wall temperature sensitivity analysis for the measured boundary condition, 470 K; the flame C3 boundary condition, 497 K; and the flame C3 boundary condition plus the measurement uncertainty, 530 K. The comparisons has been made for the spacing 0.6 cm.

61 PSD, dn/dlog D P (cm -3 ) Chapter 3. Results and Discussion Thermal Effect of CO 2 Preliminary results have been presented in previous sections. This part seeks the answer to the first question of interest regarding the thermal or chemical influence of CO 2 addition. The answer to this question cannot be found from experimental investigation since it is not possible to conduct experiments in which the thermal and dilution effects of CO 2 could be separated from its chemical effects. The thermal influence can be isolated by defining a fictitious CO 2 specie, named FCO 2. FCO 2 is a chemically inert specie that does not react, but possesses the identical thermal properties, transport characteristics, and the third body collision efficiencies as CO 2. This method have been successfully used in [1, 16] to study the CO 2 addition effects on the soot precursors and volume fraction. Liu et al. [16] took advantage of the mentioned approach to calculate soot volume fraction for a coflow diffusion flame. Tang et al. [1] used the fictitious specie approach to study the soot precursors for a few BSS flames; they only simulated the flame chemistry without a soot model H P = 0.60 cm CO 2 (a) H P = 0.60 cm FCO 2 (b) Particle Diameter, D P (nm) 00.0 % Exp % Num % Exp % Num % Exp % Num. Figure 3.13: Comparison of the effect of CO 2 (frame (a)) and chemically inert specie FCO 2 (frame (b)) on the PSDs. In the current work the specie FCO 2 was used to imitate CO 2 thermal effects on the evolution of PSD function. For the addition of 0.0% CO 2 or FCO 2, the model generates similar PSDs, solid navy blue lines in Fig Replacing 12.0% and 18.0% of argon with CO 2 shows a significant diameter reduction in frame (a) of Fig. 3.13; frame (b), which only reflects the thermal effect, shows a slight size reduction compared to frame (a). Since the axes are in log-scale, the figure may not reflect the extent of reduction. The size reduction observed in frame (b) is attributable to higher specific heat of CO 2 compared to argon. In order to elaborate the thermal effects of CO2, similar comparisons for temperature and acetylene have been performed and are presented next.

62 C 2 H 2 Mole Fraction T(K) Chapter 3. Results and Discussion (a) 1900 CO2 (b) FCO % % 12.0 % 12.0 % 18.0 % 18.0 % X(cm) 00.0 % 12.0 % 18.0 % Figure 3.14: Comparison of the effect of CO 2 and chemically inert specie FCO 2 on the temperature profiles. Comparison of the computed temperature profiles of the flames diluted with CO 2 and FCO 2 is depicted in Fig In both frames, the peak temperature are almost the same; however, the higher heat capacity of CO 2 and FCO 2 accounts for the slight difference in peak temperatures. It is interesting that the temperature profiles of both diluents are identical which means the thermal properties of the CO 2 are more important in terms of the temperature prediction, and its chemical role does not seem to have an effect (a) 0.04 CO2 (b) FCO X(cm) 00.0 % 12.0 % 18.0 % Figure 3.15: Comparison of the effect of CO 2 (frame (a)) and chemically inert specie FCO 2 (frame (b)) on the concentration of C 2 H 2.

63 Chapter 3. Results and Discussion 50 Acetylene is one of the most important species in terms of PAH formation and growth. Any changes in acetylene concentration affects the PAH formation and result in noticeable variations in soot. As expected, the frame (b) of Fig shows that addition of FCO 2 does not change the equilibrium concentration of acetylene in the post flame region. The flame front is located at 0.1 cm, and the slight difference in acetylene concentration seen in preflame zone is due to the tiny temperature differences; however, the frame (a) clearly illustrates the chemical role of CO 2 in acetylene suppression. C P /R u CO2 Ar T(K) Figure 3.16: Comparison of the specific heat capacity of CO 2 and Ar. The value C P /R u is dimensionless. In order to compare the thermal properties of CO 2 and Ar, specific heat capacities are plotted in Fig The dimensionless value C P /R u has been calculated using the following relation: C P R u = a 1 + a 2 T + a 3 T 2 + a 4 T 3 + a 5 T 4 (3.1) where C P is the specific heat capacity, R u is the universal gas constant, T is the temperature, and a i are the polynomial coefficients of the curve fitting process. The values for a i have been derived from the thermochemical data accompanied by KAUST chemical mechanism files [39]. Fig clearly shows that CO 2 has larger C P which means it can take away more heat from the flame through the exhaust gas. That is why a slight temperature decrease is observed in Fig after addition of CO 2. In terms of the Ar chemical role, if the reactions in the KAUST mechanism are investigated, it can be seen that Ar do not play any role in none of the reactions while there are 18 reactions which contain CO 2 in their reactants. In sum, the first question out of three discussed in section 3.2 on page 43 could be answered in the following way: CO 2 dilution suppresses the soot formation both chemically and thermally, but the chemical effect is more evident, and the thermal effect seems weaker compared to chemical influence. This result shows that the thermal effect is not negligible. The modelling tool can be used to go deep into the chemistry side to track the reactions that are behind the phenomenon.

64 Mole Fraction Chapter 3. Results and Discussion Chemical Effect Based on the discussion in section 2.4, it can be inferred that CO 2 addition might not have a direct effect in soot formation process. Section explains that soot is suppressed due to CO 2 chemical role in the reactions. Moreover, the nucleating species are of great importance since they are the bridge between the gas-phase chemistry and condensed-phase particles. As a result, the current section tries to investigate the chemical reactions in order to find the exact role of CO 2 in the observed phenomenon. 8.E-04 H 1.E-04 OH 6.E-04 8.E-05 4.E-04 2.E E-4 6.0E-4 4.0E-4 2.0E-4 0.0E E-05 4.E-05 2.E-05 0.E E C2H2 2.0E-2 0.E+00 5.E Benzene C6H6 4.E E-2 3.E E-2 2.E E-3 1.E E E X(cm) A1 0.0 % CO2 A2 12.0% CO2 A3 18.0% CO2 Figure 3.17: Effect of CO 2 addition on the major species including hydrogen radical, hydroxyl, acetylene, and benzene for the spacing 0.6 cm. The computed mole fractions of H radical, hydroxyl, acetylene and benzene, four major species, have been depicted for the spacing 0.6 cm in Fig These concentrations have been computed using CHEMKIN Pro software without considering soot formation. Acetylene is the precursor to formation of the first aromatic ring, benzene, and the building block of the growth of larger PAHs. Benzene is the base molecule that larger PAHs form from this species through different pathways; thus, differences in the mole fraction of benzene due to addition of CO 2 will result in a difference in nucleating species, PAHs with 6 or 7 rings, and soot yield. Fig shows that replacing 12% and 18% of Ar with CO 2 causes the concentration of acetylene to reduce 15.6% and 21.5%, respectively; the reduction for benzene is 20.1% and 29.2%, respectively.

65 Mole Fraction Chapter 3. Results and Discussion E-07 Benzo[ghi]perylene E E E E E E E (a) 0.0E E-06 A4R5 benzo(ghi)fluoranthene 8.0E Normalized PAH Level H P (cm) Anthanthrene (b) 6.0E E E E E E-06 (c) (d) 0.0E E X(cm) 00.0 % 12.0 % 18.0 % Figure 3.18: Effect of CO 2 addition on the nucleating species concentrations for the spacing 0.6 cm. Frame (b) represents the normalized PAH summation at the stagnation plane over a range of burnerto-stagnation surface separations. In this study, dimers are assumed to form via physical coalescence of large PAHs including anthanthrene, benzo[ghi]perylene, and benzo(ghi)fluoranthene. These species, known as nucleating species, are the feed stock to the soot model; moreover, the same species are allowed to condensate on the surface of soot particles in the condensation growth model. Fig compares the nucleating species concentrations for different CO 2 contents for the spacing 0.6 cm. The summation of 3 PAHs at the stagnation surface location have been normalized for the flames A1, A2, and A3 over a range of burner-to-stagnation surface separations in frame (b) of Fig This figure shows, addition of 12% and 18% CO 2 results in 38.2% and 51.2 % PAH suppression for the flames A2 and A3, respectively. This reduction caused by addition of CO 2 in the concentration of PAHs will result in a reduction in both soot nucleation and condensation as shown in Fig The effect of CO 2 addition on other important species including O, CO, etc. is presented in Appendix A. In order to understand the role of CO 2 in this process and answer the second question, a thorough species sensitivity analysis is required.

66 Chapter 3. Results and Discussion 53 Species Sensitivity Analysis In the previous section the concentration plots of PAH species showed that addition of CO 2 would reduce the concentration of acetylene and nucleating PAH species. According to the literature [16], the reaction CO 2 +H CO+OH, which is called water shift reactoin, plays an important role in soot suppression by depleting H radical [1, 16]. H radical is an important specie to HACA mechanism which is one of the major PAH growth pathways. The comparison of H radical concentration for the flames A1, A2, and A3 has been depicted in Fig This figure shows addition of CO 2 affects the content of H radical at its peak value. Although the observed difference seems insignificant, it seems to have a noticable effect on species like benzene which are in their formation zone. Appendix A contains the comparison of numerous species regarding the effect of CO 2 addition. This section tries to dig out other reactions which are involved in this process in order to answer the second question of the section 3.2. The reaction pathway analysis tool of CHEMKIN pro software has been used to perform a sensitivity analysis on the species of interest including anthanthrene, acetylene, benzene, carbon monoxide, carbon dioxide, hydroxyl radical, and hydrogen radical without considering soot. The mentioned tool is capable of drawing reaction pathways and calculating the reaction sensitivity to track the most influential reactions for a specific specie. Figure 3.19: Normalized sensitivity analysis of anthanthrene, compared at x = 0.2 cm for flames A1, A2, and A3 on the spacing of 0.6 cm. Reactions include CO 2 and CH 2 are marked by green and red, respectively. Since nucleating species are the bridge between gas-phase chemistry and solid particles, at the first step, the sensitivity analysis was performed on them. Fig shows the sensitivity analysis of anthanthrene. The analysis has been performed at 0.2 cm which looks to have the fastest growth of this specie. The first three important reactions affect the formation and consumption of anthanthrene contain

67 Chapter 3. Results and Discussion 54 H radical; this fact can show how difference in H radical content can cause anthanthrene suppression. CO 2 addition changes the hierarchy of the reactions involved in the flame chemistry, which consequently causes the concentration change in important species. As mentioned earlier, sensitivity analysis is tool which finds the most influential reactions for the formation of a specific specie. Contrarily to what is claimed about the water shift reaction, the sensitivity analysis results shown in Fig do not include water shift reaction which means it is not important. Moreover, regarding the role of CO 2 +H CO+OH effects on soot suppression [1, 16], there is no experimental evidence to support this hypothesis. Instead, a reaction appears after addition of CO 2 which does not exist in the base flame, A1. The sensitivity analysis reveals the mentioned reaction as follows: CH 2 + CO 2 CH 2 O + CO (3.2) where CH 2 is called activated methylene and CH 2 O is formaldehyde. Interestingly, reaction 3.2 contains CO 2 and CO. It was tried to find a direct relation between the participant species of the mentioned reaction and anthanthrene to account for the suppression effect. However, the effort was unsuccessful which means the role of reaction 3.2 should be investigated in the precursors species. Figure 3.20: Normalized sensitivity analysis of benzene, compared at x = 0.04 cm for flames A1, A2, and A3 on the spacing of 0.6 cm. Reactions include CO 2 and CH 2 are marked by green and red, respectively. All the large PAHs form from benzene which necessitates to perform sensitivity analysis for benzene as well. Fig shows the normalized benzene sensitivity for the flames A1 (0.0% CO 2 ), A2 (12.0% CO 2 ), and A3 (18.0% CO 2 ), receptively. The positive sensitivity means that the reaction promotes the production rate of the specie of study. According to Fig. 3.20, the reaction 3.2 does not exist in flame A1, and it appears in flame A2; Finally, in flame A3 reaction 3.2 goes to higher priority. The negative sensitivity value of the reaction 3.2 also shows that this reaction reduces the formation of A1. The

68 Chapter 3. Results and Discussion 55 sensitivity analysis reveals another important reaction, which is marked by red in Fig. 3.20, as follows: C 2 H 2 + CH 2 C 3 H 3 + H (3.3) As mentioned in section 2.3.3, the propargyl, C 3 H 3, recombination is one the major pathways to form the first aromatic ring, Benzene, via the following reaction: 2C 3 H 3 C 6 H 6 (3.4) Reaction 3.4 is marked by blue in Fig Considering reactions 3.2,3.3, and 3.4, it can be inferred that addition of CO 2 depletes the CH 2 radical; less acetylene and CH 2 form less propargyl, C 3 H 3 ; and finally, less propargyl suppresses the formation of benzene. The reduction in the formation of benzene propagates throughout larger PAHs, and decreases the soot formation. Figure 3.21: Absolute rate of production for acetylene, compared at x = 0.04 cm for flames A1, A2, and A3 on the spacing of 0.6 cm. In the next step, the acetylene which is the building block of PAHs will be studied using the reaction pathway analysis tool. The absolute rate of production and sensitivity analysis of acetylene are depicted in Figs and 3.22, respectively. According to Fig. 3.22, the reaction 3.2 does not exist in flame A1; however, flames A2 and A3 include this reaction, and it has a higher priority in flame A3 which is consistent with the initial CO 2 concentration. In order to find out the relation between CO 2 and acetylene, reactants and products of reaction 3.2 has been tracked which disclosed the following sequence of reactions: CH 2 + CO 2 CH 2 O + CO CH 2 + C 2 H 4 H 2 CC + CH 4 (3.5) H 2 CC(+M) C 2 H 2 (+M) (3.6) Based on Fig. 3.21, the reaction 3.6 represents one of the reactions responsible for the production of acetylene, and addition of CO 2 makes this reaction less effective. As a result, CO 2 addition depletes CH 2 radical via reaction 3.2; consequently, less CH 2 produces less H 2 CC in reaction 3.5. Finally, the reaction 3.6 becomes less effective due to smaller concentration of H 2 CC.

69 Chapter 3. Results and Discussion 56 Figure 3.22: Normalized sensitivity analysis of acetylene, compared at x = 0.04 cm for flames A1, A2, and A3 on the spacing of 0.6 cm. In summary, the second question discussed in section 3.2 can be answered as follows: the chemical effect of CO 2 addition on the soot formation process is partly attributable to the reaction CH 2 + CO 2 CH 2 O + COİt seems that this reaction is not the only one which reflects the CO 2 addition effect. Since many of reactions are interrelated, recognizing a single reaction as the cause of this observation is complicated; thus, more effort is required to clarify this issue.

70 Chapter 3. Results and Discussion Nucleation - Condensation Effects This section seeks the answer to the third question discussed in section on page 43. In addition to condensation, there is another surface growth mechanism included in the model which is called HACA surface growth and it has been explained in section Before comparing the influence of CO 2 on the condensation and nucleation, it is worthwhile to discuss the effect of CO 2 on HACA process. 1.E-03 1.E-05 Mass of Soot (g soot / cm 3 gas) 00.0% CO2 12.0% CO2 18.0% CO2 1.E-07 1.E-09 1.E-11 1.E-13-80% -52% HACA Nucleation Condensation Total Figure 3.23: Comparison of soot mass generated by HACA, nucleation, and condensation for the spacing 0.6 cm. According to Tang et al.[1], CO 2 reduces soot growth through HACA. In order to investigate this hypothesis, Fig compares the mass of soot generated by HACA, Nucleation, and Condensation separately for each percentage of CO 2. The vertical axis of the figure is in log scale. This figure shows addition of 12% and 18% co2 reduces the HACA surface growth by 80% and 52% respectively. However, HACA mass is significantly smaller than nucleation and condensation which means the HACA is negligible. Most of the mass forms during soot formation comes from the nucleation and condensation processes according to the assumptions made in section 2.4. The comparison of the soot total mass for flames A1, A2, and A3 over a range of burner-to-stagnation surface separations is depicted in Fig By increasing the spacing, mass grows more, and the difference between the mass of A1, A2, and A3 becomes less. This result is consistent with the computed PSDs presented in Fig. 3.10; however, the experimental measurement shows a drastic suppression trend at higher spacings similar to lower spacings.

71 Soot Condensation Mass Fraction Soot Total Mass Fraction Chapter 3. Results and Discussion E E-07 H P = 0.5 cm 2.5E E-06 H P = 0.6 cm 2.5E E-05 H P = 0.8 cm 4.0E E E E E E E E E E E+00 A1 A2 A3 A1 A2 A3 A1 A2 A3 Flame type: 0.0% CO2 (A1), 12.0% CO2 (A2), 18.0% CO2 (A3) Figure 3.24: Soot total mass fraction for the flames A1, A2, and A3 over a range of burner-to-stagnation surface separations including 0.5, 0.6, and 0.8 cm. Since the code tracks the number of primary particles all through the flame, the number of particles formed by nucleation can be easily calculated by the summation of primary particle numbers. The assumption of having no coalescence makes the tracking of primary particle numbers possible. The mass produced via nucleation can be derived by multiplying the total number of primary particles by the average mass of dimers, g. Subtracting the nucleation mass from the total mass yields the produced mass due to PAH condensation, i.e., HACA and other growth processes are ineffective. The soot condensation and nucleation mass fraction graphs over a range of burner-to-stagnation surface separations are presented in Figs and 3.26, respectively. 8.0E-07 H P = 0.5 cm 2.5E-06 H P = 0.6 cm 2.5E-05 H P = 0.8 cm 6.0E E E E E E E E E E E E E E+00 A1 A2 A3 A1 A2 A3 A1 A2 A3 Flame type: 0.0% CO2 (A1), 12.0% CO2 (A2), 18.0% CO2 (A3) Figure 3.25: Soot condensation mass fraction for the flames A1, A2, and A3 over a range of burner-tostagnation surface separations including 0.5, 0.6, and 0.8 cm. Comparison of Figs and 3.25 shows that these graphs are very similar to each other which means most of the mass forms during soot formation process comes from the condensation as well as other growth processes. The nucleation mass fractions, Fig. 3.26, are comparable for all three spacings due to the similar vertical axis bounds. The nucleation rate is increasing with respect to the spacing which makes sense because by increasing the spacing the residence time increases and more primary

72 Soot Nucleation Mass Fraction Chapter 3. Results and Discussion 59 particles form. But the faster increase rate of nucleation for flames A2 and A3 is strange. Considering only nucleation with the condensation model turned off, the produced mass should be proportional to the nucleating PAH mass ratios. Since all the cases studied in this work were run with reversible condensation model, the PAH trend is not evident in the nucleation mass graph, Fig This means that nucleation cannot work independent of the condensation model and the reversible condensation model affects the nucleation rates as well. 1.0E E E-07 H P = 0.5 cm 8.0E E-07 H P = 0.6 cm 8.0E-08 H P = 0.8 cm 6.0E E E E E E E E E E E E+00 A1 A2 A3 A1 A2 A3 A1 A2 A3 Flame type: 0.0% CO2 (A1), 12.0% CO2 (A2), 18.0% CO2 (A3) Figure 3.26: Soot nucleation mass fraction for the flames A1, A2, and A3 over a range of burner-tostagnation surface separations including 0.5, 0.6, and 0.8 cm. The normalized nucleation and condensation mass fractions over a range of spacings are depicted in Fig This figure shows by increasing the separation distance both nucleation and condensation become stronger for the flames A2 and A3 relative to A1. The stronger condensation is a feature of larger spacing as experimental measurements verifies that by showing a bimodal behaviour in PSDs (Fig. 3.10). This question might come into mind how stronger condensation causes more nucleation. The reversible nucleation establishes a bridge between the gas-phase molecules and dimers. If dimers stay in the first bin and do not grow they have the possibility to decompose to nucleating gas-phase PAHs which reduces the nucleation rate. However, if they grow through condensation or other growth mechanisms, they move to upper sections. What the code recognizes as nucleation is the number of primary particles. If a particle wants to decompose to its constituent PAHs, the particle should be in the first section. The growth process through condensation pushes the particles to upper sections which consequently reduces the chance of reverse nucleation. In order to capture the CO 2 suppression reasonably good for all spacings, the normalized masses in Fig should have a similar trend among spacings, while the results show lack of it.

73 Normalized Mass Fraction Chapter 3. Results and Discussion Nucleation Condensation Burner-to-stagnation surface distance (cm) A1 A2 A3 Figure 3.27: Normalized soot nucleation and condensation mass fraction for the flames A1, A2, and A3 over a range of burner-to-stagnation surface separations including 0.5, 0.6, and 0.8 cm. 1.E-04 Soot Mass Comparison for HP = 0.6 cm -95% 1.E-05 1.E-06-55% -37% -84% 1.E-07 Nucleation Condenstaion Total Figure 3.28: Comparison of the nucleation mass, condensation mass, and total mass of soot for the spacing 0.6 cm. In conclusion, in order to compare the effect of CO 2 on nucleation and condensation the spacing 0.6 cm has been selected because the model captures the reduction in diameter fairly good and both nucleation and condensation are present in this spacing. Fig compares the mass of soot derived from nucleation and condensation for each percentage of CO 2 separately. The vertical axis is in log scale. If we calculate the reduction of nucleation mass for 12% and 18% CO 2 we get 55% and 37% reduction, respectively. Similar calculations for condensation show 95% and 84% reduction, respectively.