The Development and Validation of a Simplified Soot Model for use in Soot Emissions Prediction in Natural Gas Fuelled Engine Simulations

Transcription

1 The Development and Validation of a Simplified Soot Model for use in Soot Emissions Prediction in Natural Gas Fuelled Engine Simulations by Justin Jeekee Shum A thesis submitted in conformity with the requirements for the degree of Masters of Applied Science Graduate Department of Mechanical & Industrial Engineering University of Toronto Copyright 2012 by Justin Jeekee Shum

2 Abstract The Development and Validation of a Simplified Soot Model for use in Soot Emissions Prediction in Natural Gas Fuelled Engine Simulations Justin Jeekee Shum Masters of Applied Science Graduate Department of Mechanical & Industrial Engineering University of Toronto 2012 This study employs a novel approach in order to satisfy the need in industry for a computationally inexpensive means to modelling soot formation in engines fuelled by natural gas. The complex geometries found in practical combustion devices along with the requirement to solve turbulent, chemically reacting, and multi-phase flows necessitates this goal. A two-equation model, which tracks soot mass and soot number density, is employed. The goal is to apply this model in engine simulations at Westport Innovations, an industry partner. Experimental data is used to validate the model in various operating conditions. Numerical data obtained from a detailed sectional soot model is also used to augment available validation data, especially with respect to soot formation/oxidation mechanisms. The developed model shows good agreement compared to experimental data and the detailed sectional soot model among all cases considered and will be further tested and applied in Westport s natural gas engine simulations. ii

3 Acknowledgements First and foremost, the author would like to acknowledge his supervisor Professor M.J. Thomson for his valued guidance, direction, and support as without it, this project would not have been possible. The author would also like to acknowledge the assistance provided by Professor S.B. Dworkin as his expertise in soot modelling was most helpful in many stages of this work. Special thanks are also given to Dr. Q. Zhang who provided his prior work on the two equation soot model. The author also acknowledges the Natural Sciences and Engineering Research Council of Canada, Westport Innovations, and Dr. B. Wasmund for financial support. The author would also like to thank Dr. N. Slavinskaya and Professor U. Riedel of the German Aerospace Centre (DLR) and Dr. J. Huang of Westport Innovations for providing the chemical mechanisms, thermodynamic data, and transport data for methane/air combustion. The author would also like to further recognize Dr. J. Huang's contributions to the development and validation of the simplified soot model. Further acknowledgements are given to Dr. G. McTaggart-Cowan, Professor S. Rogak, and the rest of the APC team for their feedback and advice. The SciNet HPC Consortium is also acknowledged for providing the computational resources necessary to complete this project. SciNet is funded by: the Canada Foundation for Innovation under the auspices of Compute Canada; the Government of Ontario; Ontario Research Fund - Research Excellence; and the University of Toronto. Many thanks are also warranted to the author's peers, colleagues, and friends at the Combustion Research Laboratory who all found the time to provide support in too many ways to list. Finally, the author would like to acknowledge his family, friends, and Varsity fencing teammates/coaches for their endless encouragement, helpfulness, and much needed distractions. iii

4 Contents 1. Introduction Motivation Objectives Background and Literature Review An Introduction to Soot Soot Characteristics and overview Soot nucleation/inception Soot particle surface growth Soot particle oxidation Soot particle agglomeration Current Approaches to Soot Modelling Empirical Models Detailed Models Semi-empirical models Particle size distribution and soot aerosol dynamics Laminar Coflow Diffusion Flame Turbulent Combustion Modelling Model Development Methodology Experimental Datasets for Model Validation Comparison to Sectional Detailed Soot Chemistry Model Experimental Cases Considered Considerations for use in Westport Simulations Coupling of Soot Model to Gas Phase Species Consumption Coupling to Radiation Heat Transfer Mathematical Formulation Computational Domain Governing Equations Conservation of mass Conservation of momentum iv

5 Conservation of species Conservation of energy Diffusivity of Gaseous Species Radiation Heat Transfer Simplified Soot Model Soot transport equations Numerical Method Mesh and boundary conditions Parallel Computation Detailed Sectional Soot Model Development and Validation of Soot Model Chapter Outline Sensitivity Analysis of Parameter Terms in Simplified Model Model Development at 1 atmosphere using the Smooke et al. [61] data set Comparisons to numerical data from detailed sectional soot model Model Development at 1 atmosphere using the Schittkowski et al. [76] dataset Comparisons to numerical data from detailed sectional soot model Results at elevated pressures Comparisons to numerical data from detailed sectional soot model Preliminary Results in Engine Simulations Model Improvements Oxidation Mechanism of Soot Model Updated Model Parameters and Improved Results Effect of Coupling Gas Phase Species Consumption and Radiation Computational Cost Comparison Concluding Remarks Conclusion/Summary Future Work v

6 List of Figures Figure 2.1 Example of soot aggregate structure in diesel exhaust. Taken from [6]....6 Figure 2.2 Representation of soot formation in premixed flames. Adapted from [19]...8 Figure 2.4 Five major components of soot modelling Figure 2.5 Typical setup of a laminar coflow diffusion flame adapted from [61] Figure 2.6 Soot formation zones in a coflow diffusion flame along with soot aggregate structure evolution. Adapted from [10] Figure 3.1 Workflow diagram of project Figure 3.2 Adapted workflow diagram of project Figure 3.3 Schematic of high pressure combustion rig taken from [78] Figure 3.4 (a) Table summarizing burner geometry and operating conditions of experiments (b) Diagram of coflow burner defining and Figure 4.1 Schematic of the computational domain (greyed out area) super-imposed on a diagram of a typical laminar coflow diffusion flame. Also illustrated is the orientation of the coordinate system used. Note that the illustration is not to scale. Taken from [75] Figure 4.2 Diagram of typical non-uniform mesh employed in the simulations presented. Adapted from [75] Figure 5.1 Diagram of the wing and centreline regions of a typical flame Figure 5.2 Sensitivity of sooting behaviour to the pre-exponential value of soot inception,. Solid lines show peak values at the wing of the flame and dashed lines show values in the centreline of the flame. A logarithmic scale is applied to the Y-axis Figure 5.3 Sensitivity of sooting behaviour to the pre-exponential value of soot surface growth,. Solid lines show peak values at the wing of the flame and dashed lines show values in the centreline of the flame. A logarithmic scale is applied to the Y-axis. Legend is in Figure Figure 5.4 Sensitivity of sooting behaviour to the pre-exponential value of soot oxidation via O 2,. Solid lines show peak values at the wing of the flame and dashed lines show values in the centreline of the flame. A logarithmic scale is applied to the Y-axis. Legend is in Figure Figure 5.5 Sensitivity of sooting behaviour to the pre-exponential value of soot oxidation via OH,. Solid lines show peak values at the wing of the flame and dashed lines show values in the centreline of the flame. A logarithmic scale is applied to the Y-axis. Legend is in Figure Figure 5.6 Sensitivity of sooting behaviour to the selected incipient particle diameter, with the default value at 12 nm. Solid lines show peak values at the wing of the flame and dashed lines show values in the centreline of the flame. A logarithmic scale is applied to the Y-axis. Legend is in Figure vi

7 Figure 5.7 Sensitivity of sooting behaviour to the selected agglomeration rate,. Solid lines show peak values at the wing of the flame and dashed lines show values in the centreline of the flame. A logarithmic scale is applied to the Y-axis. Legend is in Figure Figure 5.8 Soot volume fraction profiles at different axial heights above the burner. Z1, Z2, Z3, and Z4 correspond to heights of 2.0, 2.25, 2.5, 2.75 cm for experimental measurements and computations from the simplified model for the Smooke et al. [61] flame. For computations from the sectional model, 0.6 cm was added to each axial height to account for the delay in PAH formation Figure 5.9 Contours of soot volume fraction (ppm) generated using the simplified model (left) and detailed sectional model (right) for the Smooke et al. [61] flame Figure 5.10 Contours of soot number density of aggregates (#/cc) generated using the simplified model (left) and detailed sectional model (right) for the Smooke et al. [61] flame Figure 5.11 Contours of soot aggregate mass averaged diameters (nm) generated using the simplified model (left) and detailed sectional model (right) for the Smooke et al. [61] flame Figure 5.12 Example of a pathline of maximum soot Figure 5.13 Diagram of methodology used to compare inception mechanisms between the simplified code and the detailed code Figure 5.14 Calculated plots of soot inception rate, surface growth rate, and oxidation along the pathline of maximum soot for the Smooke et al. [61] flame. The Y-axis is plotted on a logarithmic scale Figure 5.15 Contours of soot volume fraction side by side with experimental measurements in the Schittwkowski et al. [76] flame. Experimental measurements are on the left side of the flame and computations are on the right side of the flame. Results of the simplified model are shown in (a) and results of the detailed model are shown in (b) Figure 5.16 Contours of soot particle diameter in the Schittkowski et al. [76] flame. (a) shows the experimental measurements of primary particle diameter on the left and the calculated contour of primary particle diameter on the right from the detailed model. (b) shows the calculated contour of mass averaged aggregate particle diameter from the detailed model on the left and the simplified model on the right Figure 5.17 Contours of soot particle number density in the Schittkowski et al. [76] flame. (a) Shows the experimental measurements of primary particle number density on the left and the calculated primary particle number density on the right from the detailed model. Different scales are used for each half of the flame. (b) Shows the calculated contour of aggregate particle number density from the detailed model on the left and the simplified model on the right Figure 5.18 Calculated plots of soot inception rate, surface growth rate, and oxidation along the pathline of maximum soot for the Schittkowski et al. [76] flame. The Y-axis is plotted on a logarithmic scale vii

8 Figure 5.19 Contours of soot volume fraction (ppm) with experimental measurements made by Joo and Gülder [79]. Experimental measurements are on the left and calculated contours from the simplified model are on the right. Operating pressures are at 10 atm (a), 20 atm (b), and 40 atm (c) Figure 5.20 Contours of soot volume fraction (ppm) with experimental measurements made by Joo and Gülder [79]. Experimental measurements are on the leftt and calculated contours from the detailed model are on the right. Operating pressures are at 10 atm (a), 20 atm (b), and 40 atm (c) Figure 5.21 (a) Graph illustrating the correction factors employed. (b) The effect of the correction factors on the rates predicted by the utilized oxidation models Figure 5.22 Integrated soot volume fraction (ppm cm 2 ) profiles of the Santoro et al. [74] flames of the F2 Non-smoking flame in (a) and the F4 smoking flame in (b) Figure 5.23 Peak values of soot volume fraction predicted by the simplified model compared to experimental results in the centreline (a) and the wing (b) of the Smooke et al. [61] and Schittkowski et al. [76] flames Figure 5.24 Peak values of mass averaged aggregate particle diameters predicted by the simplified model compared to the detailed model in the centreline (a) and the wing (b) of the Smooke et al. [61] and Schittkowski et al. [76] flames Figure 5.25 Peak values of aggregate particle number density predicted by the simplified model compared to the detailed model in the centreline (a) and the wing (b) of the Smooke et al. [61] and Schittkowski et al. [76] flames Figure 5.26 Peak values of soot volume fraction predicted by the simplified models and detailed model compared to experimental results from Joo and Gülder [79] in the centreline (a) and wing (b) of the flame Figure 5.27 Peak values of mass averaged aggregate diameter as predicted by the simplified models and detailed model in the centreline (a) and wing (b) of the Joo and Gülder [79] flame. An uncertainty of is assumed for the detailed code calculations Figure 5.28 The effect of coupling on the predicted peak soot volume fractions in the wing and centreline (CL) of the Smooke et al. [61] flame and the Schittkowski et al. [76] flame Figure 5.29 Graph illustrating the factor of increase in calculated peak values of soot volume fraction in the wings and centreline (CL) of the high pressure Joo and Gülder [79] flames. From left to right, the 10, 20, and 40 atm cases are shown plotted with respect to the maximum soot volume fractions measured in the experiment. A logarithmic scale is applied to the Y-axis viii

9 List of Tables Table 2.1 List of reactions in the HACA surface growth sequence. Adapted from [13] Table 4.1 Summary of reaction rate constants in the Arrhenius form, where units are in g, cm, mol, s, K Table 4.2 Summary of geometric properties of meshes used in laminar coflow flame simulations Table 4.3 A summary of the major differences between the employed simplified soot model and a previously developed detailed sectional model Table 5.1 List of major parameters in simplified two equation soot model The Smooke et al. [61] data set was used as a baseline case upon which to investigate the sensitivity of soot volume fraction, soot aggregate averaged diameters, soot number density, soot inception rate, soot surface growth rate, and soot oxidation rate (henceforth collectively referred to as sooting behaviour ) to the parameters listed in Table 5.1. Simulations were run where a single parameter was modified while all other parameters were held constant. Then, the effect on the aforementioned soot details relative to the baseline case with initial parameters listed in Table 4.1 and Section 4.5 was recorded. This process was repeated for each parameter listed in Table 5.1. Peak values of sooting behaviour were recorded in both the wing and the centreline of the flame (illustrated in Figure 5.1) Table 5.2 Calculated peak mass averaged aggregate particle diameters (nm) in the Joo and Gülder [79] flames Table 5.3 Calculated peak aggregate particle number densities (#/cc) in the Joo and Gülder [79] flames. 73 Table 5.4 Summary of parameters in simplified model. See Equation (5.3) for definition of correction factor (identical for both O 2 and OH). Changes are highlighted in red and underlined Table 5.5 Representative comparison of computational costs of running the 2-D laminar flame code with the detailed section soot model and the simplified two equation soot model ix

10 Nomenclature Oxidation correction factor parameter Agglomeration constant Minimum number of carbon atoms found in a soot particle Constant pressure specific heat of the mixture Constant pressure specific heat of the species Constant pressure specific heat of soot Primary particle diameter Mass averaged aggregate diameter of soot Activation energy Oxidation correction factor term Soot volume fraction Integrated soot volume fraction Gravitational acceleration Specific enthalpy of the species Specific enthalpy of soot Total number of gaseous species present in the chemical mechanism Mass flow rate Molar mass of carbon Mass of soot Soot number density Aggregate number density Primary particle number density Avogadro s number Pressure Total radiation heat transfer Radial direction Inner radius of fuel tube Outer radius of fuel tube Temperature Oxidation correction factor parameter Axial velocity x

11 Radial Velocity Diffusive velocities in the Radial direction of the Diffusive velocities in the axial direction of the Radial thermophoretic velocities of soot particles Axial thermophoretic velocities of soot particles Molecular weight of the species Molecular weight of soot Mass fraction of the species Soot mass fraction Axial direction Mixture fraction species species Greek Symbols Portion of available surface sites on soot particle for chemical reaction Scalar dissipation Thermal conductivity of the mixture Boltzmann s constant Dynamic viscosity Molar production rate of the species per unit volume Molar production rate of soot per unit volume Collisional efficiency of OH molecules for soot oxidation in simplified model Mixture density Density of soot xi

12 Acronyms CL CRL DOM HACA ILDM NOx PAH SLFM ULFM Centreline (of flame) Combustion Research Laboratory (at the University of Toronto) Discrete Ordinate Method (Radiation Model) Hydrogen-Abstraction-Carbon-Addition Instrinsic Low-Dimensional Manifold Nitric Oxide Polycyclic Aromatic Hydrocarbon Steady/Stationary Laminar Flamelet Model Unsteady Laminar Flamelet Model xii

13 1. Introduction The work described in this thesis represents one component of a collaborative research project between the Combustion Research Laboratory (CRL) supervised by Professor Thomson at the University of Toronto, Professor Rogak and his research group at the University of British Columbia, and Westport Innovations with the aim to aid in the research and development of natural gas fuelled heavy duty compression ignition engines. The development of combustion systems is a complex and time consuming endeavour while the basic operating principles of the technology used today have not changed significantly over the last few decades, there is the ongoing need to address the growing demands of consumers while satisfying stringent environmental policies. Despite recent advances in research and development made to move away from combustion-based devices in an effort to mitigate the effects of global warming and limit harmful pollutant emissions, alternative technologies are unlikely to become viable for widespread use for many years to come [1]. This is especially true in long-distance transportation applications where the use of conventional fossil fuels is necessitated by their high energy density relative to alternative sources such as battery storage. As a result, combustion systems must be able to meet the ever increasing legislated limits on harmful pollutant emissions such as nitric oxides (NOx), carbon monoxide, volatile organic compounds (VOCs), and particulate matter (PM). The design of a combustion system is often an iterative process from the early stage of conception, its eventual design and manufacture, and finally, testing and validation. As such, projects can quickly become both time consuming and expensive as individual prototypes and test rigs are either manufactured or purchased along with the necessary data extraction and analysis tools. To mitigate this, numerical models and predictive tools are often used to assist in the development of combustion systems. Another advantage of numerical modelling is that it provides insight to combustion 1

14 phenomena, fluid flows, and other behaviour that is normally not directly observable by experimental procedures. This type of insight can help to design more efficient and less polluting systems Motivation The focus of this work lies in the development and validation of a numerical model that can accurately predict the emissions of the combustion-generated particulate matter known as soot. The aim is then to apply this model in compression-ignition natural gas fuelled engine simulations in order to gain a better understanding of how and why soot is emitted from these engines. This knowledge will facilitate the ability for rapid and iterative engine design in the difficult task of balancing performance and pollutant emissions. The formation of soot particulate matter in combustion and its subsequent release into the atmosphere has received attention in research and industry due its adverse environmental and health effects. Individual soot particles can often be formed on the scale of 100 nanometers or less. This poses a significant health risk as inhalation of soot particles to the lungs can cause inflammation and cancer. These fine particles are then able to migrate through the bloodstream and damage other vital organs such as the heart or brain [2]. Soot is also known to play a major role in global warming phenomena and is thought to be a major contributor to global warming effects behind CO 2 [3]. From a design standpoint, the deposition of soot particles on equipment can also pose a problem for issues such as maintenance or thermal loading (due to the high thermal absorptivity of soot particles). Also important to note is that the formation of soot in itself represents a degree of inefficiency in converting the energy contained in a fuel to useful work. Thus, it is easy to see why accurately predicting soot formation and emission in combustion devices is an important endeavour. The mechanisms of soot production in combustion are very complex and not yet fully understood. Modelling soot formation in various combustion applications is an ongoing area of research that has received much attention of late [4],[5],[6],[7],[8],[9]. Due to the highly complex nature of soot 2

15 formation, these models are often computationally expensive as they attempt to recreate our current understanding of fundamental soot formation/oxidation mechanisms. This study employs a simplified approach in order to satisfy the need in industry for a computationally inexpensive approach to modelling soot formation in engines fuelled by natural gas, such as those at Westport. As an engine designer for natural gas fuelled compression ignition engines, Westport is interested in low computational cost soot modelling techniques that can allow them to quickly evaluate new engine concepts. The complex geometries found in practical combustion devices along with the requirement to solve turbulent, chemically reacting, and multi-phase flows drives the goal of reducing the computational cost of soot modelling. The use of natural gas, which is mostly composed of methane, is rapidly becoming an important alternative fuel in transportation applications. There is a growing interest in using natural gas as a fuel due to its wider availability (and subsequently, affordability) and lower carbon footprint per unit of energy. Potential greenhouse gas emissions reductions have been estimated to be over 20% per vehicle in large scale industrial applications simply by switching from conventional fuels to natural gas [10]. Natural gas has also been demonstrated to be a cleaner fuel with less harmful pollutant emissions compared to conventional fuels such as diesel or gasoline [11]. In addition, natural gas can be derived sustainably from biomass and can also be collected from landfills, which is sometimes referred to as synthetic natural gas or renewable natural gas. Thus, a switch to natural gas technology could also allow for the use of sustainable fuels Objectives The objectives of the present work are as follows: 1) Develop a simplified yet robust soot model that can be applied (i.e. is computationally tractable) in more complex engine simulations, such as those being carried out at Westport 3

16 Innovations. Specifically, the aim is to apply this model in natural gas fueled compression ignition engines. 2) Validate the developed model in a variety of operating conditions for key soot characteristics such as soot volume fraction, soot number density, and soot particle diameters. If necessary, improve model performance and document this process. 3) Investigate any key issues for soot model behaviour especially when applied to engine simulations at Westport. For example, can the model predict the observed experimental soot emissions? If not, can qualitative trends in soot emissions with changing engine parameters such as load condition be reproduced? Resolve these issues if possible; otherwise, identify possible alternatives or methods for soot model application in engine simulations. 4

17 2. Background and Literature Review This chapter explores some of the background information necessary to fully understand the present work and its associated goals. Current understanding of soot and its formation/oxidation is explored as well as the different approaches that are generally employed to model and predict soot emissions An Introduction to Soot Soot is best described as a type of airborne pollutant that is commonly created as a by-product of hydrocarbon combustion. Unlike other common pollutants such as NOx or CO, which are emitted in the gaseous phase, soot is unique in that it is emitted as a solid usually consisting of a complex aggregate structure composed of many smaller soot particles. These individual soot particles, which are commonly referred to as primary particles, are roughly spherical, mainly composed of carbon, [12] and are graphitic in nature [13]. Soot emissions from combustion applications such as diesel engines are often recognized as dark-black exhaust plumes. The presence of soot within a flame is usually characterized by the yellow-orange glow given off by the flame due to the luminosity of soot particles within the flame Soot Characteristics and overview Many experimental observations have shown that soot primary particles range in size from nanometers (nm) [13],[14],[15]. Soot aggregate structure is fractal in nature and can consist of anything from a few primary particles to hundreds of primary particles. An example of the soot aggregate structure is shown in Figure 2.1. The macroscopic density of a soot particle is usually considered to be between 1.8 [16] to 2.0 [12] grams/cm 3. Finally, the overall characteristics of soot particles do not seem to be strongly dependent on the type of flame, fuel, application, or other types of operating conditions involved [17]. 5

18 Soot in combustion can be characterized in a variety of ways, the most common being soot volume fraction ( ), soot number density, and diameter of primary particles (. Soot volume fraction, which is a unit-less term, is defined as the volume of soot divided by the volume of gas. Soot number density describes the number of soot particles per unit of volume (ex. ) or sometimes as the number of soot particles per unit of mass (ex. refer to the total number of aggregates, denoted as ). In addition, soot number density can or it can refer to the total number of primary particles, denoted as (per volume/mass of the mixture). As seen in Figure 2.1, the number of primary particles per aggregate can often vary by a large amount, even within the same type of flame/application. This is one of the reasons accurately modelling soot can be very difficult, as one needs to keep track of a population of soot particles that can vary in both diameter and aggregate structure. Figure 2.1 Example of soot aggregate structure in diesel exhaust. Taken from [12]. 6

19 Soot formation and oxidation processes have been reviewed by many authors; some of which include the reviews by Glassman [17], Richter and Howard [13], Haynes and Wagner [18], Stanmore et al. [12], and Appel et al. [19]. While the exact details of soot formation and oxidation is still an area of debate, the overall process of soot formation and oxidation is generally agreed to start with precursor formation, particle nucleation (or inception), followed by the parallel processes of soot particle surface growth, particle agglomeration, and soot particle oxidation Soot nucleation/inception Soot nucleation is one of the least understood mechanisms of soot formation, but there is a general consensus that nucleation occurs due to the combination of polycyclic aromatic hydrocarbons (PAHs) that transition to the solid phase [18],[19],[20]. This important step is actually preceded by the pyrolysis of the fuel itself to give rise to various so-called precursor species that provide the input for PAH species. Several precursor species have been identified, with acetylene (C 2 H 2 ) typically receiving the most attention [13]. The smallest aromatic species, benzene (C 6 H 6 ), has also received much attention as a precursor species due to the fact that PAHs can be considered to be grown from benzene [13] via the addition of acetylene. It is thought that one of the bottlenecks to soot inception is the formation of the first aromatic ring (such as benzene or phenyl) and not surprisingly, early work by Glassman [17] showed that aromatic based fuels had a higher tendency to soot when compared to alkanes, alkenes, and alkynes. Glassman [17] identified acetylene as an important precursor species to soot formation and a later review by Richter and Howard [13] also reiterated the same point. Much attention in recent research has been directed at determining exactly how PAHs form and grow from their parent fuels [19],[20],[21]. In Figure 2.2, which illustrates a representation of soot formation in premixed flames, one can observe an example of PAH growth in the molecular zone of the diagram. There is still some debate over which chemical reaction pathways are the most important in forming the first aromatic ring some of which is outlined in [4],[21],[22],[23]. 7

20 Regardless of the PAH formation route considered, once they are formed, they will continue to grow due to subsequent chemical reactions with gaseous species and also collisions with other PAH molecules to form PAH dimers, trimers, etc. At a certain size, the PAH molecules condense and transition to a solid state this results in a nascent soot particle, or in other words, soot particle nucleation. The details of this process are poorly understood as experimental observations of this phenomenon are difficult since these large PAH molecules still have relatively small diameters on the order of 1 nm [13]. Soot inception/nucleation will ultimately add to both the number of soot particles formed and the total mass of soot formed. Figure 2.2 Representation of soot formation in premixed flames. Adapted from [24]. 8

21 Soot particle surface growth Once the PAH molecules have transitioned into solid soot particles, they can continue to grow in size due to heterogeneous chemical reactions with gaseous species on the surface of the soot particle. It is generally agreed upon that acetylene plays a major role in contributing to soot surface growth, as demonstrated in [19],[21],[25]. The amount of available soot surface area for reactions to occur also plays a vital role in determining the amount of surface growth that occurs. Surface growth via acetylene has been described by Frenklach et al. in [19],[21],[26] as the Hydrogen-Abstraction-Carbon- Addition (HACA) reaction sequence, where the C-H bonds on the surface of soot particles can react with gaseous species. The reactions contained in HACA are based off of analogous PAH gas phase reactions and are shown in Table 2.1. represents a reaction site on the surface of the soot particle where a carbon atom is bonded with a hydrogen atom; i.e. it is hydrogenated and non-reactive. These hydrogenated sites can later become dehydrogenated through hydrogen abstraction via H atoms or OH molecules as seen in S1 and S2 (in Table 2.1). represents a de-hydrogenated (reactive/active) site on the surface of the soot particle that can accept acetylene molecules and subsequently result in the growth of the soot particle (reaction S4). Alternatively, these dehydrogenated sites can be re-hydrogenated (S3) or even oxidized (S5 or S6), in which case the soot particle becomes smaller. Technically speaking, reactions S5 and S6 are examples of a soot oxidation mechanism, which will be explored further in Section A phenomenon known as ageing has also been observed in various experiments in these experiments, the tendency of a soot particle to undergo surface growth was observed to decline with increasing particle growth [21]. This can be explained by the HACA mechanism as a reduction in the availability of active sites on a soot particle, a decrease in H atom concentration, and/or an arrival at an equilibrium state for H atoms in the mixture. 9

22 Table 2.1 List of reactions in the HACA surface growth sequence. Adapted from [19]. PAHs have also been proposed to contribute to surface growth in soot particles, in a mechanism commonly referred to as PAH condensation [19],[27]. Similar to how PAH molecules can collide with one another to form nascent soot particles; PAH molecules could also collide with existing soot particles and condense on the surface of them. Macadam et al. [27] showed that in acetylene-lean conditions, surface growth via PAH condensation was especially important. However, in acetylene-rich conditions, surface growth via acetylene was dominant. Regardless of the avenue of soot growth, it is generally agreed that soot surface growth is the dominant mechanism in forming additional soot mass in a flame Soot particle oxidation Soot particle oxidation is the mechanism by which soot particles can be oxidized and converted back into gaseous species. As with soot surface growth, the amount of soot surface area available for oxidizing agents to attack the soot particles plays a role in determining the rate of oxidation. Competition between soot inception and surface growth mechanisms against soot oxidation mechanisms ultimately determines whether or not a flame emits soot particles; i.e. if a flame is smoking or non-smoking. Of the various species that can contribute to soot particle oxidation, O 2 and OH are generally regarded to be the most important [28],[29],[30],[31],[32]. O 2 is generally a major contributor under fuel-lean conditions, while OH is the dominant specie in fuel-rich conditions [33]. Oxidation by other species, such as the oxygen radical O has been investigated [28] and gasification of soot via other species such as H 2 O and NO 2 has also been shown to be possible [12]. Some studies have 10

23 also demonstrated that soot oxidation can lead to changes in the aggregate structure as well, such as fragmentation of the aggregate into smaller structures [33],[34] Soot particle agglomeration Soot particle agglomeration is a unique mechanism of soot growth in that soot nucleation, surface growth, and oxidation are mainly chemical processes where as agglomeration is mainly a physical process. An exception to this is that PAH condensation is also a physical process. Agglomeration is best described as the increase in soot particle size due to the collision of two or more soot particles. For small (and newly formed particles), collisions may actually lead to a phenomenon referred to as coalescence, where the two particles collide and merge into a larger spherical particle due to their liquid-like behaviour [35]. Larger particles that collide can stick to one another and form complex fractal-like aggregate structures as seen in Figure 2.1. Depending on the circumstances of the collision and the particles involved, some intermediary result can occur, where the particles partially merge and form a bridge or neck [16]. It is also worth noting that not all collisions will necessarily result in merging or sticking of the particles involved as observed by Kellerer et al. [36]. D Alessio et al. [37] noted that under certain flame temperature conditions, particles might not stick due to a thermal rebound effect these observations contrast from an earlier belief that all collisions had a 100% sticking efficiency. Ultimately, soot particle agglomeration will generally only affect the total number of soot particles formed with negligible effect on the total mass of soot formed Current Approaches to Soot Modelling Approaches to soot modelling can generally be categorized into three different types of approaches: (i) empirical approaches, (ii) semi-empirical approaches, and (iii) detailed approaches. Soot modelling was first extensively reviewed by Kennedy [38] and the continued development of new soot modelling techniques remains an active area of research today [5],[6],[8],[20],[39]. Figure 2.3 illustrates five major components of a soot model developed for a combustion system. A flow solver is needed to calculate the solutions to the basic conservation equations to give the correct fluid flow field, while 11

24 combustion chemistry is needed to account for ongoing chemical reactions between species present in the simulation. As soot formation is highly coupled to temperature, radiative effects from the flame and soot particles often need to be considered. Finally, the components of the soot model itself must also be included this can be divided into two major parts: (1) Mechanisms which account for soot formation/oxidation and (2) Mechanisms that consider the interactions between different soot particles and also the population distribution of soot particle sizes. While all five components are required for a full detailed approach, many empirical and semi-empirical approaches neglect one of more of these components in the interest of reducing complexity and computational costs. Figure 2.3 Five major components of soot modelling Empirical Models Empirical models are usually based solely on direct correlations between operating conditions and the amount of soot that is emitted i.e. all five components shown in Figure 2.3 could be neglected. In the case where a flow solver is neglected, the soot model could be solely a function of combustion input parameters, such as engine load or fuel input in the case of an empirical model for an engine. They usually have very little computational cost and are quick to implement and run. As a result, they are typically used in applications where it is not computationally feasible to include a more detailed 12

25 model, such as in a diesel engine or gas turbine. These types of combustion applications already use significant computational resources to compute solutions for chemically reacting turbulent flows, and the addition of a detailed soot model would make the calculations intractable. Due to the nature of correlation, empirical models cannot be applied to applications or operating conditions that are significantly different from the baseline from which the model was developed. They also fail to give any insight on the specifics of soot formation; for example, one would not be able to determine precisely where/when/why soot is formed in a diesel engine. For these reasons, empirical models may not be practical for predictive purposes where engine geometries and operating parameters may change radically from case to case. However, that is not to say that empirical models serve no useful purpose. One application where empirical models are useful are in diagnostics systems where a user can be fed real time information on how heavily their engine is sooting based on parameters such as combustion temperatures. Since the engine operating conditions are not expected to change radically compared to prescribed conditions for which the model is calibrated for, soot emissions can be accurately predicted without the need for a complex measurement setup. An example of an empirical model is the one developed by Khan et al. [40] for diesel engines. In this model, Khan and co-workers assumed that the diameters of soot particles did not vary with respect to operating speeds or loads. They also assumed that the overall formation rate of soot was only dependent on inception, neglecting soot growth and oxidation, giving the equation: (2.1) where is the soot mass density [kg/m 3 ], and are model parameters, is the activation energy of soot formation set to 1.7 x 10 5 [kj/kmol], is the volume of the soot formation zone [m 3 ], is the volume of the cylinder contents at normal temperature and pressure [m 3 ], is the partial pressure of unburned fuel [Pa], is the local unburned equivalence ratio, and is the local temperature. As model parameters were adjusted until results fit the available experimental data, the model performed 13

26 reasonably well for the given conditions. However, one would expect that any significant departure from the base set of calibrated data would result in poor performance, due in part to the neglect of many fundamental soot formation/oxidation mechanisms. Another example of an empirical model is the approach developed by Hiroyasu et al. [41]. Hiroyasu and co-workers assumed that soot mass emissions were solely based on pressure, temperature, fuel concentration, and O 2 concentration neglecting intermediary soot formation/oxidation mechanisms and also ignoring the calculation of the number of soot particles. They defined the formation rate of soot mass as: (2.2) where is the formation coefficient, is the oxidation coefficient, and are the local mass fractions for fuel and oxygen, and is the local mass fraction of soot. and are subsequently defined as: (2.3) (2.4) where and are model parameters, and is the pressure and operating pressure, and are activation energies set to 6313 and 7070 [K -1 ] respectively. As with any empirical model, the model performed relatively well as long as the conditions did not stray far from the conditions used to calibrate the model parameters Detailed Models On the opposite end of the spectrum, detailed soot models attempt to replicate the current fundamental understanding of soot formation/growth/oxidation as described in Section 2.1. Detailed soot models are typically based on fundamental combustion chemistry and make use of aerosol 14

27 dynamics theory. An ideal detailed soot model would work for any fuel, combustion application, and operating condition; but in practice, all detailed soot models are still limited to a range of possible scenarios for which the model was developed albeit a much broader range than that of empirical models. A well developed soot model can be applied to various fuels and applications and has better general applicability. An example of this is the detailed model demonstrated in [42] which included complex combustion chemistry to model the formation of PAHs and has since been applied with success to both ethylene/air and methane/air flames under different operating conditions. Detailed models are also capable of giving insight into the soot formation process and are also able to provide information on the population size distribution of soot particles. The disadvantage of using detailed soot models is that they tend to be very computationally expensive most detailed soot models are limited to simulations with simple geometry (1-D/2-D) and laminar flow conditions. A commonly cited example of a detailed model is the one developed by Frenklach and Wang [21],[26],[43] of which the chemical kinetic mechanism that describes everything from the pyrolysis of fuel to the formation of PAHs is an integral component. Further details such as inception via PAH molecules, growth by the HACA mechanism, oxidation, agglomeration, and aggregate structures were also considered in this model. It is important to note that chemical kinetics play a major role in the formation of soot at nearly every phase of soot production (inception, surface growth, and oxidation) [38] and as such, detailed models almost ubiquitously employ some form of a PAH chemical kinetic mechanism. Recent efforts such as those by Dworkin et al. [20] and Chernov et al. [44] have been made in the application of improved PAH chemical mechanisms in detailed soot models. It should be noted that the divide between a detailed model and a semi-empirical model is not clearly defined and many approaches saddle a grey area between the two. An example is the work by Lindstedt [45] which employs a detailed chemical mechanism and simplified soot chemistry to model soot formation in ethylene and propane counterflow diffusion flames. Soot nucleation was based on 15

28 the precursor species of acetylene and benzene, with some focus in the work spent on developing the chemical kinetic mechanism to accurately predict benzene. Oxidation was modelled considering only O 2 as an oxidative species, using rates developed by Lee et al. [31]. Surface growth via acetylene was considered however, the dependence on the surface area of soot was modelled using four different assumptions. One assumption was to assume that surface growth was linearly dependent on the surface area of soot. A second assumption was that the surface growth was dependent on both the surface area and the number of available reaction sites per unit area on the soot particle. The third assumption was that surface growth was only dependent on the number of particles and the final assumption was that surface growth was dependent only on the concentration of acetylene and temperature. Results from Lindstedt s work [45] showed that the third assumption actually produced the best results, although the author conceded that it was in part due to the difficultly in modelling the HACA sequence such that there was confidence in the number of available reaction sites and may have also been a result of the other model parameters that were selected. Reasonable predictions for both the ethylene and propane flame were obtained in terms of soot volume fractions and particle diameters Semi-empirical models Semi-empirical models represent a middle ground between empirical models and detailed models and provide a compromise between computational costs and the ability to model fundamental soot formation/oxidation behaviour. Semi-empirical models tend to incorporate many soot formation/oxidation mechanisms but reduce computational costs by simplifying the chemistry involved. Where detailed models typically require large chemical kinetic mechanisms detailing hundreds of reactions necessary to account for the formation of PAHs, semi-empirical models typically employ simplified chemistry to minimize computational costs. Fairweather et al. [46] developed a model where nucleation of soot particles was solely based on the precursor species acetylene, allowing for a reduced chemical mechanism without the need to 16

29 model PAH formation. This implementation differs from the Lindstedt [45] approach as a simplified chemical mechanism was used. This model was applied to a turbulent diffusion natural gas/air flame where chemistry was solved by using a flamelet library (i.e. species concentrations and temperatures were linked to mixture fraction instead of being explicitly solved). Surface growth was considered only to occur via C 2 H 2 surface reactions and oxidation was considered to occur only via O 2. Further simplifications were made by neglecting soot aggregate structure and assuming all soot particles were solid spheres without the fractal aggregate structure seen in Figure 2.1. Finally, it was assumed that surface growth and oxidation rates were linearly related to the surface area of soot particles. Despite these simplifications, the model performed satisfactorily and unlike a fully empirical model, it could still provide some insight to soot formation/oxidation rates and also provide more detailed soot data such as soot number density and diameters. The model was later updated by Woolley et al. [47] to include inception via benzene molecules as well and also included additional oxidation via OH. It was applied to a turbulent methane/air flame as well as a propane/air flame demonstrating good agreement with experimental results and thereby showing fuel flexibility. The model developed by Fairweather and coworkers represents a popular two-equation approach to soot modelling where one equation is used to track soot volume fraction and a second equation is used to track soot number density. These two equations typically resemble the following form: (2.5) (2.6) where represents the mass of soot,, and represent the mass of soot formed/destroyed due to inception, growth, and oxidation, respectively, represents soot number density, and and represent soot number density from inception and agglomeration, respectively. represents the model specific constants that are usually calibrated based on the exact mechanisms 17

30 used to represent the aforementioned soot mechanisms and the application for which the model is used. A similar two-equation approach was used by Moss et al. [48] where the major difference was in the rate equations used to represent inception, surface growth, oxidation, and agglomeration. Like Fairweather et al. [46], Moss and co-workers [48] assumed that surface growth and oxidation were linearly dependent on soot surface area. A flamelet library was again used to solve for combustion chemistry. Unlike the Fairweather et al. [46] model, only OH oxidation was considered. The model was able to predict reasonable soot volume fractions and soot number densities along the centre-line of an ethylene laminar diffusion flame, but only after some model parameters were adjusted to match experimental data. The model was later extended by Brookes and Moss [49] to a turbulent methane/air jet diffusion flame and compared favourably to experimental results. However, it is important to note that the parameters of the model were again adjusted to fit the experimental data. A two equation approach utilizing a form of the Brookes and Moss [49] model was also recently applied to predicting soot in an automotive diesel engine simulation in a study by Pang et al. [8]. Pang et al. found that the values for constants in the Brookes and Moss model typically found in literature could not reproduce satisfactory soot behaviour in the engine and henceforth needed to carefully calibrate the constants such that the model reproduced experimental results. Hong et al. [50] used aspects of the Fairweather et al. [46] model (namely the inception and oxidation mechanisms) to model soot formation in a diesel engine. A skeletal form of a detailed mechanism for n-heptane was used to calculate combustion chemistry. However, instead of using a simplified acetylene-only based approach for surface growth, a series of surface growth reactions based on available reaction sites was used. In addition, a method of moments was used in order to allow for the tracking of particle size distributions by assuming a log normal distribution. While 18

31 quantitative results were under-predicted in the test cases and the diesel engine, the authors were satisfied with the qualitative trends reproduced. Besides the above-mentioned applications, a two equation soot model has also been applied in laminar methane co-flow diffusion flames [51],[52], laminar methane opposed flow diffusion flames [53], laminar ethylene diffusion co-flow flames [6],[54],[55], laminar ethylene opposed flow diffusion flames [56], turbulent ethylene diffusion co-flow flames [9], laminar heptane opposed flow diffusion flames [57], and laminar acetylene co-flow diffusion flames [58]. A smaller number of applications were also at high pressure [6],[8],[51],[53],[57] as detailed measurements of soot at high pressure are not readily available in the literature. In terms of handling combustion chemistry, some approaches used a flamelet library [9],[47],[49],[52] approach while others calculated detailed chemistry [6],[51],[53],[55],[56]. Other forms of reduced chemical kinetics were also used in [8],[46],[54],[58]. As evidenced by the wide variety of applications, the two equation model shows promise in terms of widespread applicability and low computational cost. A direct comparison of computational costs between an implementation of the two equation model and a detailed soot model is shown in Section Particle size distribution and soot aerosol dynamics One of the challenges of soot modelling, besides handling the complex soot chemistry, is how to track the size and aggregate structure of every soot particle that is formed. In processes with multiphase flow, additional equations are required to describe changes to the population of particles which can evolve due to interactions with other particles or due to chemical reactions with species in other phases. In the case of soot modelling, the population of soot particles can be affected by the parallel processes of nucleation, surface growth, agglomeration, particle fragmentation, and oxidation. These processes can lead to a complex population of differing particles that vary in size, shape, and structure, 19

32 making it computationally expensive to model accurately. The approach to soot modelling can be said to be split into two parts: the interaction between soot particles and the gas phase species (i.e. soot kinetics detailed in the above sections) and the interaction between soot particles (i.e. soot aerosol dynamics) [59]. There are currently a few major methods that are employed to handle soot particle dynamics [39]. One obvious approach would be to directly model each individual particle in the population of particles, coined as a continuous model approach. While the continuous model is accurate, the computational costs are large [60] and the implementation of such a model is also restricted to simple zero to one dimensional cases [39]. A second approach is to model the population of soot particles into discrete sections or bins. The discretization of the particle size distribution allows for computational tractability in more complicated scenarios compared to a continuous approach. Sectional models still provide good accuracy if an adequate number of sections is used to represent the particle size distribution, but the drawback is that each additional variable used to describe the population (e.g. volume, surface area, etc.) increases the number of needed equations exponentially [39]. As such, a single parameter, such as the particle mass per section bin along with a spherical particle assumption is used in most applications of the sectional model. A third approach is a stochastic approach, where the population of particles is determined by using a stochastic algorithm such as the Monte Carlo method. However, while this approach has shown success in laminar flames, this method is also very computationally expensive and is not generally considered for turbulent cases [61]. Another approach of interest is the Method of Moments (MOM) where evolution equations for moments of the population distribution are solved instead of explicitly solving the population distribution. In the MOM, a compromise is made between accuracy and computational costs. Instead of calculating the exact distribution of a particle population, mean quantities (i.e. moments) are computed [39]. A moment can be thought of as a measure of varying aspects in a distribution depending on the order of the moment. Thus, knowledge of all moments from 0 to in essence fully describes the distribution function itself 20

33 [62]. It has been noted that 3-6 moments are generally sufficient for an accurate soot calculation [59]. A final approach is to neglect tracking the particle distribution altogether, as Fairweather et al. [46] did in his implementation of a two equation soot model. In this model, it was assumed that all soot particles were spheres of identical diameter within a control volume (i.e. a monodisperse spherical particle assumption). While this approach can save computational cost, it introduces errors into the model as the above-mentioned assumption is questionable. This can lead to some inaccuracy in predicting the available soot surface area for soot kinetics such as surface growth and oxidation. To handle this error, simplified models that neglect particle aerosol dynamics typically account for these errors by adjusting model parameters and constants in order to compensate for the calculated soot surface areas Laminar Coflow Diffusion Flame In the development of our soot model, it is important to consider the need for a combustion configuration that is amenable to iterative numerical experimentation, has extensive validation data, and is representative of typical combustion conditions within compression ignition engines. While it would be ideal to develop the model in a compression ignition engine configuration, the complicated geometry, reciprocating motion, and turbulent flow would make numerical experimentation difficult due to the associated high computational costs. In addition, due to the nature of combustion in engines, detailed spatial measurements of soot characteristics are nearly non-existent. For these reasons, a steady axisymmetric laminar coflow diffusion flame was selected. This combustion configuration was chosen in part due to its simple laminar flow field which lends itself well to conducting numerous detailed numerical experiments. In addition, the mixing of fuel and air in a diffusion flame can be comparable to processes that occur in compression ignition engines; although admittedly, the effects of turbulent mixing would not be present in a laminar flame. A schematic of a laminar coflow diffusion flame can be seen in Figure

34 Figure 2.4 Typical setup of a laminar coflow diffusion flame adapted from [63] The laminar coflow flame also provides an additional benefit in that soot formation/oxidation mechanisms in the flame span a relatively wide region, which allow for multi-dimensional detailed measurements of soot characteristics. Figure 2.5 illustrates the typical evolution of a soot particle as it undergoes soot formation/oxidation mechanisms in a diffusion flame. In can be seen that inception occurs in the early part of the flame, near the edge of the luminous envelope (the edge of the flame is usually referred to as the wing of the flame). This is not surprising as in diffusion flames, soot is generally formed in high temperature, fuel rich conditions between K [64]. The soot particles that are formed then continue to grow as they progress upwards in the flame, before being oxidized as the temperature in the flame increases. In cases where there is insufficient oxidation in the flame, some soot particles can escape the wings of the flame, causing a smoking flame. In cases where there is enough oxidation to fully oxidize the soot particles formed, the flame is referred to as a non-smoking flame. 22

35 Figure 2.5 Soot formation zones in a coflow diffusion flame along with soot aggregate structure evolution. Adapted from [16] Turbulent Combustion Modelling While the work presented in this thesis focuses on laminar flame simulations, it is important to consider the complexities and complications turbulent combustion modelling brings, as the eventual goal of the work is to apply the soot model in turbulent engine simulations. Turbulent combustion theory and modelling is a large field of research in its own right and as such, the details of turbulent combustion modelling will only be briefly discussed. Extensive reviews of turbulent combustion theory and modelling have been conducted by several researchers, such as the efforts by Bilger et al. [65], Pitsch [66], and Buckmaster et al. [67]. Turbulent combustion modelling can be very difficult and computationally expensive as one needs to simultaneously calculate the complex, evolving fluid fields as well as the ongoing chemical reactions. 23

36 While solving for the fluid field and chemistry simultaneously is computationally tractable for laminar, steady flames, this is not the case for turbulent flames. Instead, chemistry is often de-coupled and/or simplified in order to reduce computational costs. Some important methods used in non-premixed turbulent combustion modelling are discussed below. The first simplification is the assumption that combustion in the turbulent flame is entirely dominated by mixing related phenomena. A variable referred to as mixture fraction ( ) is often used to quantify the local degree of mixing. Mixture fraction can be defined as the local mass of material that originated in the fuel stream divided by the local total mass of the mixture [68]. Thus in the case of a coflow diffusion flame, will be equal to 1 in the fuel stream and equal to 0 in the oxidizer stream. The mixture fraction will vary between 0 and 1 throughout the flame and is said to be a conserved scalar, i.e. the scalar variable is conserved at every point in the flow and there is no creation/consumption of. The general idea of the mixing dominated assumption is that the instantaneous temperature and species composition could be related to the mixture fraction. In the case of Reynolds/Favre-averaged approaches of modelling turbulent flow, the average reaction rate can be obtained by weighting the instantaneous reaction rates related to the probability density function (PDF) of mixture fraction. Unfortunately, soot (and many other pollutants) does not correlate well with mixture fraction [38]. This is due to the fact that soot chemistry is relatively slow and is not in chemical equilibrium. Furthermore, soot particles do not diffuse in the same manner as gaseous species [38]. Therefore, while the assumption of assuming mixing-dominated combustion is computationally feasible and realistic for many applications, it is problematic when attempting to model soot formation/oxidation accurately. Later studies showed that with the assumption of fast chemistry (i.e. when chemical reaction rates are fast compared to fluid mixing rates and species quickly reach their chemical equilibrium levels) one could relate the reaction rates in flames to the rate of scalar dissipation ( ) of the rate of molecular mixing ( ) [65]. The variable is used to describe the instantaneous local departure from equilibrium observed in the diffusion flame a high indicates a 24

37 high rate of removal of heat and species due to turbulent mixing. At a critical, often denoted the rate of heat removal becomes too high and the flame is quenched. A method that was developed and is closely related to the concept of mixing-dominated turbulent combustion is the laminar flamelet model. The key assumption of this approach is that the flame reaction zones are thinner than the smallest length scales of turbulence if this is true, then the turbulent flame can be said to be made up of a collection of smaller laminar flames (i.e. flamelets) [65]. The implication of this is that the local instantaneous species composition and temperature can be derived from a laminar flame that has the same mixture fraction and scalar dissipation. In the Stationary (or Steady) Laminar Flamelet Model (SLFM), the parameters of mixture fraction and scalar dissipation are used to generate a library of values for temperature, species composition, and even reaction rates [65]. This library is usually pre-calculated for a range of and in order to save time during the simulation and is therefore a favourable approach to reducing computational costs. During the CFD calculation, the mixture fraction and scalar dissipation (along with flow fields) would be solved independently of temperatures and species compositions, which could then later be looked up in the flamelet library. Unfortunately, this indirect nature of solving for species compositions and temperatures presents a problem for soot modelling as it is not possible to include the effects of species consumption due to soot formation/oxidation kinetics. A larger problem is that the SLFM has difficulty accurately predicting slow-forming species like NOx despite a relaxed dependence on the assumption of equilibrium chemistry. This is due to the fact that the flamelet structures cannot respond instantaneously to changes in the scalar dissipation ( ). As a result, the SLFM is not appropriate for applications where chemical time scales are comparable (i.e. on the same order of magnitdue) to the flow time scale [69]. In other words, the SLFM is not appropriate for slow chemistry applications (like soot) due to its fast chemistry assumptions. 25

38 The inability of the SLFM to handle transient, non-equilibrium effects has led to the development of an Instationary (or Unsteady) Laminar Flamelet Model (ILFM/ULFM). In this approach, unsteady flamelets are not pre-processed, but instead solved in conjunction with the CFD simulation. One example of an unsteady flamelet model is the one developed by Pitsch et al. [70],[71] which was successfully applied to both a turbulent ethylene jet diffusion flame and turbulent hydrogen jet diffusion flame. Pitsch and coworkers accounted for the "history" of a flamelet by calculating a "flamelet time" which was related to the distance to the fuel nozzle and the axial velocity of the flow [71]. This calculated flamelet time could then be used to resolve the unsteady terms in the transport equations for species mass fractions and temperature. By using this method, Pitsch and coworkers were able to use the ULFM to account for transient affects such as radiative heat transfer [71]. The SLFM and ULFM are widely used in turbulent combustion modelling studies due to the advantage of reduced computational costs and relatively good ability to predict species composition and temperatures. However, it is important to remember the inherent assumption behind both flamelet models that is, that the reaction zone must be thinner than the smallest length scale of turbulence. If this is not true, an alternative method must be used. One such alternative method is the Intrinsic Low-Dimensional Manifold (ILDM), which was first developed by Maas and Pope [72]. Maas and Pope showed that for a given chemical system with a given number of species and reactions, one could decouple the chemical reactions with the fastest timescales, greatly reducing the number of variables needed to describe the system [73]. This is a reasonable assumption as the range of chemical timescales in a simulation can often extend across many orders of magnitude. If enough time passes, the slower time scales begin to dominate the overall behaviour of the system and the faster reactions can be assumed to be at equilibrium the manifold represents a subspace of the entire reaction system where this behaviour is observed [72]. Maas and Pope demonstrated that all reaction trajectories tended to move towards this manifold regardless of the initial conditions specified. Thus, the number of necessary calculations can be reduced by only solving for the slow chemistry that occurs 26

39 on this manifold and neglecting the relatively short amount of time it takes for the reaction trajectory to reach the manifold [72]. As a result, one could feasibly create a low dimension tabulation of the chemical system as a function of a smaller number of so-called progress variables (arbitrary parameters) [69] instead of trying to account for every coupled species and reaction, which can result in a table that would need over 30 dimensions for just a simple methane-air flame [73]. The dimension of the ILDM is related to how much time must pass before the reaction trajectories reach the manifold the shorter the time, the higher the dimension required [74]. The ILDM approach has been applied with some success in applications such as a turbulent methane diffusion jet under high pressure [75] and also in compression ignition engine simulations at Westport Innovations. Compared to the flamelet approach, the ILDM requires more computational resources to tabulate and to utilise within the simulation (due to a higher number of variables in the table), but is more widely applicable to a variety of flame conditions. 27

40 3. Model Development Methodology This chapter outlines the overall methodology employed in developing a simplified soot model for application in natural gas fuelled compression ignition engines. The goal is to begin model development and validation with simple laboratory flame conditions and move to progressively more engine-like conditions. This idealized workflow is illustrated in Figure 3.1. Figure 3.1 Workflow diagram of project 3.1. Experimental Datasets for Model Validation A review of detailed soot measurements for methane and natural gas flames in the literature was conducted in order to determine the availability of validation data. The full review can be found in Appendix A of this thesis. While validation data is widely available for more heavily sooting simple fuels such as ethylene, such as the study by Santoro et al. [76] and other studies detailed in [77], detailed soot data for methane flames is relatively limited. This is due in large part to the lower tendency of soot formation in methane combustion in atmospheric laboratory flame conditions. Nonetheless, datasets with soot measurements were found for coflow laminar diffusion flames, coflow turbulent diffusion flames, counterflow laminar diffusion flames, shocktubes, and laminar premixed flames. In addition, soot measurement data was also available for natural gas fuelled engines, but limited to exhaust measurements. Unfortunately, exhaust-only measurements are not particularly useful for developing a robust soot model as the solution for a "correct" exhaust soot prediction is not a unique one. For example, a model could have an inception rate that is too high, but is absolved by having an 28

41 oxidation rate that is also too high. For this reason, spatially resolved measurements of soot are more useful particularly in applications where there are clearly defined soot formation/oxidation regions. As discussed in Section 2.4 earlier, turbulent combustion modelling presents many of its own challenges that would exceed the scope of this work and as such, development and validation for the data found was not considered. Furthermore, the combustion behaviour of premixed flames and shocktubes is fundamentally different from the combustion behaviour of the non-premixed combustion found in direct injection compression ignition engines. Hong et al. [50] used a similar approach in developing their soot model by using shock tube data from various experiments to calibrate their model and then later applying it to a diesel engine simulation. However, while the model gave reasonable qualitative results, the soot predictions quantitatively were under-predicted. Thus, it was also determined that model development and validation for these cases would not be particularly useful in serving our target application and were also neglected. Consequently, the focus for model development and validation in the work presented focuses on the coflow laminar diffusion flame setup (discussed in further detail in Section 2.3). Fortunately, the body of literature investigated for coflow laminar diffusion flames provided the most volume of soot measurement data of all the types of experimental investigations on soot in methane and natural gas combustion Comparison to Sectional Detailed Soot Chemistry Model Despite the fact that there are several studies on methane/air coflow flames, the majority of the measurements made in these studies are limited to spatially resolved measurements of soot volume fraction only. Spatially resolved measurements of other important soot characteristics, such as number density (primary/aggregate) or soot particle diameter (primary/aggregate) is limited to a study by Schittkowski et al. [78] and is subject to a high degree of uncertainty due to the measurement techniques used. In addition, there exists no data set where measurements were made on the rate of soot formation/oxidation. In order to avoid creating a "curve-fitted" model that is only applicable in 29

42 one or two applications, it is desired to have some avenue of validation for the rates of soot formation/oxidation as well. One strategy to carry out this validation is to use a detailed sectional soot chemistry model that has been developed in parallel in another study [20]. Since this model has been well-validated in a variety of applications [5],[20],[42],[44] we can use this existing model to generate a rich dataset of numerical "measurements" that can fill in the gaps found in literature. Thus, numerical experiments using the sectional detailed soot chemistry model will be run and data from these numerical experiments can be used to supplement existing measurement data in the development and validation of our simplified soot model. This adapted workflow is outlined in Figure 3.2. However, it is important to note that the employed sectional detailed soot model was developed and validated for ethylene/air flames, not methane/air flames. Nonetheless, the similarity between the two fuels and their combustion behaviour (chemical kinetic mechanisms for the two fuels are often interchangeable) should allow for reasonable results from the model to be obtained. Figure 3.2 Adapted workflow diagram of project 30

43 3.3. Experimental Cases Considered Data from studies by Smooke et al. [63], Thomson et al. [79] and Joo and Gülder [80], and Schittkowski et al. [78] was used to validate the developed model over a variety of operating conditions. In the study by Smooke et al. [63], spatially resolved measurements of soot volume fraction were made in the laminar flame using a technique called thermocouple particle densitometry (TPD). With TPD, soot volume fractions are determined by introducing a clean thermocouple into a sooting area of the flame and subsequently relating the measured temperature history to an expected temperature history using thermophoretic mass transfer formulations. The flame in the Smooke et al. [63] case was placed inside a cylindrical chimney enclosure located at the edge of the coflow air inlet. Thomson et al. [79] and Joo and Gülder [80] collected spatially resolved measurements of soot volume fraction but at higher pressures using two non-intrusive techniques - Spectral Soot Emission diagnostics (SSE) and Line-of-Sight-Attenuation (LOSA) - to make their measurements. The details and theory of SSE and LOSA are discussed elsewhere in [81] and [82] respectively. The flame was surrounded with a chimney composed of three flat windows to facilitate optical access and the burner assembly was placed inside a high-pressure assembly which is illustrated in Figure 3.3. Thomson et al. [79] and Joo and Gülder [80] used the same experimental setup but conducted their measurements in separate facilities; however, Joo and Gülder [80] conducted some tests at higher pressures but also only reported measurements using the SSE diagnostics technique. 31

44 Figure 3.3 Schematic of high pressure combustion rig taken from [79]. Finally, in the study by Schittkowski et al. [78], spatially resolved measurements of soot volume fraction, primary particle radius, and primary particle number density were made using a laser-induced incandescence (LII) system, the details of which can be found within the aforementioned study. Figure 3.4 summarizes the burner geometry and operating conditions of the studies investigated in this work. Data Set Geometry (cm) Flow Rates (g/s) Smooke et al. [63] Methane = 0.16 Air = Argon = Thomson et al. Methane = [79] Air = 0.4 Joo and Gülder Methane = [80] Air = 0.4 Schittkowski et al. Methane = [78] Air = (a) Operating Pressure (atm) (b) Figure 3.4 (a) Table summarizing burner geometry and operating conditions of experiments (b) Diagram of coflow burner defining and Considerations for use in Westport Simulations In addition to ensuring the developed simplified model could well reproduce the sooting behaviour observed in the aforementioned experiments, it was important to consider some implications for future application in turbulent engine simulations such as those at Westport Innovations. 32

45 Coupling of Soot Model to Gas Phase Species Consumption As discussed in Section 2.4, many of the current methods employed to calculate turbulent combustion chemistry reduce computational costs by pre-calculating reaction rates, species compositions, and temperatures in a table as a function of various parameters like mixture fraction ( ) or scalar dissipation (. This approach is evident in the flamelet library approach (steady and unsteady) as well in some aspects of the ILDM approach. While this method is an effective way to include combustion chemistry without drastically reducing the chemical mechanism, it presents a major problem for soot modelling. As the species conservation equations are not explicitly solved in these approaches, it is not possible to couple the consumption of gas phases species to the formation/oxidation of soot in these types of simulations. This can potentially cause some overprediction in soot concentration levels as soot formation/growth can continue indefinitely. To investigate the effect that this can have on the performance of the proposed soot model, simulations with and without gas phase species consumption were run and their results were compared Coupling to Radiation Heat Transfer Another important feedback loop that is difficult to implement with the flamelet library and ILDM approach is the radiation heat loss due to soot particles in the flame. In these tabulated approaches to solving for flame temperatures indirectly, it is difficult to incorporate a feedback mechanism by which the presence of soot particles decreases the local temperature. Since a lowered temperature will usually result in reduced reaction rates, neglecting the coupling of radiation heat transfer can result in overpredicted flame temperatures and hence, overpredicted soot levels. Similar to the approach described in Section 3.4.1, simulations with and without coupled radiation heat transfer were run and their results were compared. 33

46 4. Mathematical Formulation This chapter describes the theory and mathematical models employed within the presented work. In particular, the conservation equations solved for mass, momentum, species, and energy for the laminar coflow flame are described as well as the formulations of the simplified soot model Computational Domain The flames considered in this study were all axi-symmetric co-flow laminar diffusion flames and as such, the 3-dimensional flame is reduced to a 2-dimensional computational domain, which reduces computational costs. A cylindrical coordinate system is constructed in the radial ( ) and axial ( ) directions and a representative diagram of the computational domain is shown in Figure 4.1. Figure 4.1 Schematic of the computational domain (greyed out area) super-imposed on a diagram of a typical laminar coflow diffusion flame. Also illustrated is the orientation of the coordinate system used. Note that the illustration is not to scale. Taken from [77] Governing Equations The 2-D laminar coflow diffusion flame code used in this thesis solves fully-coupled elliptical conservation equations for mass, momentum, species, and energy. The laminar flame code used in this study has been widely applied to other laminar coflow diffusion flame studies such as the recent efforts by Guo et al. [83], Zhang et al. [42], Dworkin et al. [20], and Eaves et al. [5]. 34

47 Conservation of mass The equation for conservation of mass is as follows: (4.1) Where is the mixture density and and are the axial and radial velocities respectively Conservation of momentum The equation for the conservation of axial momentum is as follows: (4.2) Here, represents the local pressure, is the dynamic viscosity of the gaseous component of the mixture, and is the gravitational acceleration, assumed to be solely in the axial direction. Similarly, the equation for the conservation of radial momentum is as follows: (4.3) Conservation of species The conservation equations for gaseous species mass fractions are defined as: (4.4) is defined as the mass fraction of the species, and are the diffusive velocities in the axial and radial directions respectively of the species, is the molecular weight of the species, and is the molar production rate of the species per unit volume. is denoted as the total number of gaseous species present in the chemical mechanism. An important point to note is that also includes contributions/consumption due to soot formation/oxidation chemical processes. When 35

48 gaseous species consumption due to soot formation/oxidation were decoupled, only included contributions from chemical reactions between gaseous species only Conservation of energy The equation for the conservation of energy is formulated as: (4.5) Where is the constant pressure specific heat of the mixture, is the local temperature, is the thermal conductivity of the mixture, is the constant pressure specific heat of the species, is the specific enthalpy of the species, is the constant pressure specific heat of soot, is the mass fraction of soot, and are the radial and axial thermophoretic velocities of soot particles, is the specific enthalpy of soot, is the molecular weight of soot, which is considered to be the same as carbon in this study, is the molar production rate of soot per unit volume, and is the total radiation heat transfer from both gaseous species and soot. In specific simulations where radiation heat transfer was decoupled, the term was neglected. Zhang [42] found that only H 2 O, CO 2, and CO contributed significantly to radiation heat transfer compared to the rest of the other gaseous species. Thus, only these species were accounted for (along with radiation from soot particles) in the term. Thermal properties of soot were assumed to be identical to that of graphite the thermal properties of which can be obtained from JANAF thermochemical tables [84] Diffusivity of Gaseous Species The diffusion velocity of gaseous species as noted in Equation (4.4) is calculated in the present work using the following relation: 36

49 (4.6) In the above equation, is the ordinary diffusion velocity of the species, and similarly, is the thermal diffusion (i.e. thermophoretic) velocity of the species. is a correction diffusion velocity term which becomes necessary due to the use of mixture-averaged diffusion coefficients. With the use of a mixture-averaged diffusion coefficient, the net diffusion flux may not sum to zero, so the correction term is applied [85]. and are in turn calculated by using an approximated mixture-averaged formulation [77]: (4.7) (4.8) Here is the mole fraction of the species, is the thermal diffusion ratio of the species, and is the mixture diffusion coefficient of the species. is defined as: (4.9) Here is defined as the binary diffusion coefficient. In this study, thermal diffusion was neglected for all species except for H 2 and H Radiation Heat Transfer Radiation heat transfer in the laminar coflow flame code is calculated using the Discrete Ordinate Method (DOM) and is only briefly described here. The DOM radiation heat transfer model used in this work was first developed by Liu et al. [86] and further details on the DOM model can be found in the respective study. The DOM method is advantageous in that the accuracy of the model is comparable to more computationally intensive approaches such as a Monte-Carlo approach and that it does not require any a priori assumptions about the optical thickness of the flame being modelled [77]. 37

50 Radiation Transfer Equations (RTEs) are numerically solved in an axisymmetric cylindrical coordinate system and the angular and spatial coordinates are discretized using a T 3 quadrature system [86]. This was coupled with a statistical narrow-band-based correlated-absorptivity ( ) model in order to determine the absorption coefficients of the gas phases species H 2 O, CO 2, and CO. The spectral absorption of soot was determined to be: (4.10) Here, is the spectral absorption of soot and is the wavenumber of the spectral band. This formulation was based on experimental measurements by Buckius and Tien [77],[87] Simplified Soot Model The semi-empirical soot model employed in this study is based on previous work done by Fairweather et al. [46] and later updated by Woolley et al. [47]. It adds two equations that track soot mass and soot number density and reduces computational costs by calculating averaged soot particle diameters per control volume instead of tracking the soot particle size distributions and aggregate structures. As a semi-empirical model, some simplifications have been made based on the current understanding of the fundamentals of soot formation and oxidation (reviewed by Frenklach in [21]). This two-equation approach has been shown to have some success in predicting soot in both laminar and turbulent diffusion flames with the majority of work being done at lower pressures (See Section 2.2.3). Soot inception (or nucleation), is typically understood in the literature to be the combination of molecules known as polycyclic aromatic hydrocarbons (PAH) that condense to the solid phase [20]. However, the incipient species in the simplified model is instead chosen to be acetylene, as it is itself a precursor to the formation of PAHs and removes the necessity to include large chemical kinetic mechanisms, which can add to the computational costs of turbulent engine simulations. The chemical formula for soot inception used in the present model is given as: 38

51 (4.11) Originally, Fairweather et al. [46] based inception solely on acetylene, while an update by Woolley et al. [47] also included inception via benzene. Early efforts were made to use benzene in the present work as well; however, as a relatively slow forming species, it was found to be problematic with the ILDM approach of handling turbulent combustion. In addition, well validated chemical kinetic mechanisms for methane combustion that included the formation of benzene were not available in the literature. As Westport already employs a modified GRI-mechanism by Huang et al. [88] that works well at predicting other pollutants (like CO), it was also not desired to change the chemical kinetic mechanism to accommodate benzene formation. Thus, a soot inception mechanism solely through acetylene was employed in this study. As with inception, acetylene is assumed to be the only species that contributes to the surface growth of existing soot particles and is represented by the following chemical reaction: (4.12) As discussed earlier in Section 2.1.3, this is a simplification of the currently understood and accepted mechanism of soot particle surface growth known as HACA. Oxidation in the simplified soot model is considered via surface reactions with O 2 and OH only and is represented as: (4.13) (4.14) While Fairweather et al. [46] originally neglected soot oxidation via OH, this was later included in the two equation model in an update by Woolley et al. [47]. This better corresponds to the currently accepted understanding that O 2 and OH are dominant contributors to soot oxidation. The rate constants for OH oxidation are taken from the study by Fenimore and Jones [28]. The soot chemical reactions (4.11) through to (4.14) are governed by the following equations: (4.15) 39

52 (4.16) (4.17) (4.18) Where denotes a reaction rate determined by a typical Arrhenius rate expression, is the soot particle surface area per unit volume of the mixture, and,, and represent the concentrations of C 2 H 2, O 2, and OH respectively in units of. represents the collision efficiency of the OH molecules, which is set to 20% in this study. The initial values used for the Arrhenius reaction rates in equations (4.15) to (4.18) are listed in Table 4.1. Rates for to are taken from Fairweather et al. [46] while is derived from the rate determined by Fenimore and Jones [28]. 1.35E E E Table 4.1 Summary of reaction rate constants in the Arrhenius form, where units are in g, cm, mol, s, K. As noted in equations (4.16), (4.17), and (4.18), there is a functional dependence on the soot particle surface area for surface growth and oxidation. In addition, Fairweather et al. [46] suggested that this functional dependence can simply be represented as a linear function such that: (4.19) The linear dependence assumption is reasonable as it follows that as the soot particle surface area increases, the tendency of surface reactions occurring would also increase. On the other hand, Liu et al. [89] suggested that the functional dependence would be better represented as a proportional relation to the square root of the soot particle surface area such that: (4.20) The rationale behind this change is related to the phenomenon of soot surface ageing (see Section 2.1.3), where the rate of surface growth for a soot particle tends to decline as it undergoes further 40

53 surface growth. With Liu and coworkers' implementation, the dependence of surface growth on surface area is reduced as the soot particle grows larger. This in effect, according to Liu et al. [89], reproduces an ageing effect of the soot particle. While both functional dependencies hold merit, Liu et al. [89] noted that similar results for both assumptions could be attained if model constants for surface growth were adjusted. Thus, the model in this work uses the linear dependence defined in equation (4.19). The soot aggregate structure in this simplified approach is neglected, and it is assumed that all soot particles are spherical in shape. Thus, the available surface area of soot per unit volume of the mixture is given by: (4.21) Here, mixture. is the soot aggregate number density defined as the number of soot particles per unit mass of, which is the diameter of the representative sphere of soot calculated by using the relation: (4.22) where is the mass fraction of soot, and is the density of soot, taken to be 1.9 [g/cc]. In order to solve for the soot mass fraction and soot number density, two additional source term equations are solved: (4.23) (4.24) Where is the mass of soot, is the molar mass of carbon taken to be [g/mol] in this study, is Avogadro s number and is Boltzmann s constant. represents the minimum number of carbon atoms found in a soot particle, which in a sense, determines the minimum diameter of a soot particle. In this study, was set to 90,000 which translates into an incipient soot particle size of 41

54 approximately 12 nm. The 12 nm size was kept in part due to the minimum detection size of soot particles in common experimental apparatuses. The rationale is that any soot particles smaller than this would not be detected in experiments and therefore not play a role in model validation. Furthermore, previous studies found that the predictions generated by the two equation model were relatively insensitive to the value of selected [45]. is an agglomeration constant that determines the rate at which smaller soot particles combine. For this study, was initially set to 3, but is known to vary between 3 to 9 [45],[46] Soot transport equations The transport of soot in the work presented is calculated in a similar manner to the methods presented by Zhang et al. [42], Eaves et al. [5], and Chernov et al. [44] in similar sooting laminar coflow flame studies. If one accounts for normal diffusion, thermopohresis, and soot formation and oxidation, the soot transport equations for soot mass and number density is as follows: (4.25) (4.26) Thermophoretic velocity in this work is calculated according to the definition provide by Talbot et al. [90] and is given by the equation: (4.27) 4.6. Numerical Method The numerical method used in this work is similar to the methods used in numerical studies of other laminar flames [5],[20],[42],[44],[77]. As such, the reasoning and subsequent development of these approaches is not part of the scope of this work. Further details can be found in [77]. Finite-volume method discretizations were used in order to solve the above-mentioned conservation equations and soot equations. A staggered mesh was employed in order to avoid 42

55 calculated pressure gradients that are independent of the local control volume s pressure. In order to solve the discretized equations, a semi-implicit scheme was used to solve the coupled pressure and velocity as well as the discretized governing equations [91]. A second order central difference scheme is used to discretize the diffusive terms while a power law scheme was used to discretize the convective terms [91]. Momentum and continuity (which is converted to a pressure correction equation) equations are solved independently using a Tri-Diagonal Matrix Algorithm (TDMA). Next, the gaseous species equations are solved simultaneously in each control volume in order to deal with the overall stiffness of the system. Finally, the soot transport equations and energy equation are solved in a segregated manner with the TDMA approach. An arbitrary initial guess for the system is used (typically a temperature of 1900 K and ambient air) and pseudo-time stepping is used to arrive at a converged steady state solution. Chemical reaction rates for gaseous species as well as thermal properties are calculated using subroutines from the opensource CHEMKIN-II [92],[93] libraries. Transport properties of gaseous species including mixture averaged values for fluid viscosities, thermal conductivities, and diffusion coefficients were calculated using TPLIB [85],[94]. Two different chemical mechanisms were used: a C1/C2 mechanism originally developed by Slavinskaya and Frank [7] and a modified GRI-mechanism by Huang et al. [88] developed for low temperature high pressure methane/air combustion. A modified version of the Slavinskaya and Frank [7] mechanism with enhanced PAH growth was also employed in certain simulations. The modifications to this mechanism are described in the work by Dworkin et al. [20] and Slavinskaya et al. [95] Mesh and boundary conditions The properties of the mesh used for finite-volume discretizations varied depending on the experiment and the geometric properties of each mesh can be found in Table 4.2. A non-uniform mesh in all cases is employed in order to resolve the large gradients of temperature, species, velocity, etc. near the flame while reducing computational cost in areas farther away from the flame. Generally 43

56 speaking, the mesh size was kept at a constant small size until a distance of approximately three times the flame height and flame radius upon which a stretching factor was employed to allow the mesh size to grow. This effect can be observed in Figure 4.2. Data Set Number of Control Volumes Size of domain [cm x cm] Initial (stretch start) {stretch factor} [cm, cm, unitless] Smooke et al. [63] 192 x x (1.00) {1.071} Schittkowski et al. [78] Thomson et al. [79] and Joo and Gülder [80] 224 x x (1.99) {1.075} 240 x x (0.31) {1.075} Initial (stretch start) {stretch factor} [cm, cm, unitless] 0.05 (6.70) {1.0205} 0.05 (7.80) {1.03} (1.30) {1.03} Table 4.2 Summary of geometric properties of meshes used in laminar coflow flame simulations. A diagram of the non-uniform mesh is presented in Figure 4.2. As previously mentioned in Section 4.1, the computational domain considered is a 2-dimensional slice of the axisymmetric coflow flame. As a result, in addition to the normal inlet and outflow boundary conditions employed, there are additional constraints for the boundary conditions at the axis of symmetry and outer radial boundary of the computational domain. The inlet condition in all cases was considered to be uniform in both temperature and velocity. The outflow boundary was defined as a zero gradient condition given as: (4.28) Similarly, zero gradient conditions are also imposed on the axis of symmetry: (4.29) The outer radial boundary condition varied depending on whether or not it was an open air flame (i.e. free-slip) or a flame within a chimney (i.e. no-slip). For a free-slip outer radial boundary the following conditions were used: 44

57 (4.30) On the other hand, for a no-slip outer radial boundary condition, the following conditions were used: (4.31) Figure 4.2 Diagram of typical non-uniform mesh employed in the simulations presented. Adapted from [77] Parallel Computation The laminar coflow flame code employed in this work takes advantage of a distributed-memory parallelization with strip-domain decomposition method in order to make calculations tractable and complete within reasonable time limits. Further details on the development of the parallel flame code can be found in [77]. The computational domain is divided uniformly by assigning each row of control volumes perpendicular to the z-axis to an individual CPU. The Message Passing Interface (MPI) library [96] is used to facilitate the communication and distribution of workload between CPUs. Calculations were performed on the General Purpose Cluster (GPC) at the SciNet supercomputer centre using a 8- core Intel Xeon E5540s with 2.53 GHz chip speeds and InfiniBand network connections. 45

58 4.7. Detailed Sectional Soot Model As outlined in Section 3.2, a detailed sectional soot model will be employed to run numerical experiments in order to complement the existing experimental data found in literature and facilitate the validation of the simplified soot model presented in this study. The detailed sectional soot model is the result of an ongoing parallel research program being conducted at the CRL at the University of Toronto and more details on the model can be found in the work presented by Zhang et al. [42],[77]. The major differences between the detailed sectional model and the simplified model are illustrated in Table 4.3. The biggest simplification in the simplified model is the absence of a soot particle size distribution, followed by the simplified inception pathway through acetylene, and the surface growth rate with a linear dependence on soot surface area. Mechanism Simplified Model Detailed Sectional Model Soot Inception Nucleation of soot particles Nucleation of soot particles based on acetylene based on the PAH molecule Surface Growth Oxidation Soot aerosol dynamics Reaction rate based on acetylene and a linear dependence on soot surface area Reaction rates based on oxidation models from Lee et al. (O 2 ) [31] and Fenimore and Jones (OH) [28] and a linear dependence on soot surface area Soot particle size distribution is neglected and all soot particles are assumed to agglomerate into spheres pyrene (A4) HACA surface reaction scheme with an empirical parameter to correct for deficiencies in model Oxidation via O 2 and OH accounted for as part of the HACA surface reaction scheme. OH oxidation based on collisional frequency and O 2 oxidation based on Frenklach and Wang [26] model based on Nagle and Strickland-Constable [30] rate Soot particle size distribution is modeled using a sectional approach with 35 sections to track primary particles and an additional 35 sections to track aggregate structures. The smallest bin size 0.86 nm and the largest bin size is nm Table 4.3 A summary of the major differences between the employed simplified soot model and a previously developed detailed sectional model. 46

59 The detailed sectional model was run using an identical flame code with almost the same governing equations, the exception being the soot transport equations where each section required its own transport equation. The DOM radiation model was used along with the same mesh, boundary conditions, and solvers. An empirical parameter,, is used in the detailed model as a correction factor to account for the actual number of reactive surface sites relative to the number predicted by the current implementation of the HACA model. A value of is typically selected for a simulation such that reasonable predictions of soot volume fractions are made. More details on can be found in [77] and in recent investigations by Dworkin et al. [20] and Eaves et al. [5]. 47

60 5. Development and Validation of Soot Model The simplified soot model developed in this work was based on the two equation approach demonstrated by Fairweather et al. [46]. The model was initially calibrated for a turbulent natural gas flame and as such, the initial model constants are used as a basis for initial investigations on the model s performance in the previously mentioned experimental studies chosen for model validation (in Section 3.3). However, the original Fairweather et al. [46] model lacked OH oxidation, so the Fenimore and Jones [28] OH oxidation model was also included. The initial model constants have been listed earlier in Section Chapter Outline The work described in this chapter will begin with a sensitivity analysis of the model parameters in the simplified soot model in Section 5.2. Calculations and results from the simplified model and detailed sectional model are subsequently presented in Sections Improvements and modifications to the simplified model are discussed in Section 5.7 and updated simulation findings are presented in Section The effect of uncoupling gas phase species consumption and radiation heat transfer from the rest of the model is then subsequently investigated in Section 5.8. Finally, the computational cost between the simplified model and the detailed sectional model is compared in Section Sensitivity Analysis of Parameter Terms in Simplified Model The parameters used in the simplified two equation soot model consist of the pre-exponential term and activation energy in each Arrhenius rate expression for equations (4.15) to (4.18) in Table 4.1. Activation energies for each rate equation have been investigated in previous studies [45],[46] and are considered to be constants in this study and hence kept at their original values listed in Table 4.1. This appears to be a reasonable approach as Woolley et al. [47] also kept the original activation energies when adapting and updating the two equation model for a different combustion application. Additional parameters in the two equation model also consist of the and terms used in the soot number 48

61 density source term equation (4.24). The major parameters investigated in this study are summarized in Table 5.1. The other parameters in the simplified model that were not investigated in this study were the activation energies,, for the inception, growth, and O 2 oxidation Arrhenius rate expressions in equations (4.15) to (4.17). Parameter Note Pre-exponential term in Arrhenius rate expression for soot inception. Pre-exponential term in Arrhenius rate expression for soot surface growth. Pre-exponential term in Arrhenius rate expression for soot oxidation via O 2. Pre-exponential term in Arrhenius rate expression for soot oxidation via OH. Determines the minimum number of carbon atoms in an incipient soot particle and hence determines the minimum diameter of a soot particle. Determines the rate at which soot particles agglomerate. Table 5.1 List of major parameters in simplified two equation soot model. The Smooke et al. [63] data set was used as a baseline case upon which to investigate the sensitivity of soot volume fraction, soot aggregate averaged diameters, soot number density, soot inception rate, soot surface growth rate, and soot oxidation rate (henceforth collectively referred to as sooting behaviour ) to the parameters listed in Table 5.1. Simulations were run where a single parameter was modified while all other parameters were held constant. Then, the effect on the aforementioned soot details relative to the baseline case with initial parameters listed in Table 4.1 and Section 4.5 was recorded. This process was repeated for each parameter listed in Table 5.2. Peak values of sooting behaviour were recorded in both the wing and the centreline of the flame (illustrated in Figure 5.1). 49

62 Figure 5.1 Diagram of the wing and centreline regions of a typical flame. Figure 5.2 Sensitivity of sooting behaviour to the pre-exponential value of soot inception,. Solid lines show peak values at the wing of the flame and dashed lines show values in the centreline of the flame. A logarithmic scale is applied to the Y-axis. Figure 5.2 shows the sensitivity of sooting behaviour on the pre-exponential value of. The legend shown in Figure 5.2 is used for all subsequent graphs in 5.2. Here, Pre-exponential Factor Increase is defined as: Pre-exponential Factor Increase (5.1) 50

63 A similar definition for subsequent Pre-exponential Factor Increase is used in Figure 5.3 to Figure 5.7. Similarly, Change relative to baseline is defined as: (5.2) Not surprisingly, Figure 5.2 demonstrates that all sooting behaviour terms are nearly linearly dependent on the inception rate (a log scale is applied since underpredictions share the same weight as overpredictions, which is not obvious on a linear scale). An increase in inception rate leads to more soot particles being created and hence a higher soot particle number density and soot volume fraction. In addition, the increased soot particle surface area means that surface growth and oxidation mechanisms become stronger as they are linearly related to the soot particle surface area. On the other hand, the inception rate does not seem to largely affect the soot aggregate averaged diameters as the additional soot mass gained due to a higher surface growth rate (due to a higher surface area from a higher number of particles) that is effectively cancelled out by a higher oxidation rate. 51

64 Figure 5.3 Sensitivity of sooting behaviour to the pre-exponential value of soot surface growth,. Solid lines show peak values at the wing of the flame and dashed lines show values in the centreline of the flame. A logarithmic scale is applied to the Y-axis. Legend is in Figure 5.2. The surface growth rate sensitivity analysis, which is illustrated in Figure 5.3, shows that all sooting behaviour aspects are very sensitive to the pre-exponential. The behaviour is less pronounced in the centreline of the flame, and in fact, the soot inception rate and soot number density actually drops in the centreline relative to the baseline case. This can be explained by the fact that inception and surface growth both compete for acetylene, so the increased surface growth rate will reduce the inception rate, thereby lowering the soot particle number density. 52

65 Figure 5.4 Sensitivity of sooting behaviour to the pre-exponential value of soot oxidation via O 2,. Solid lines show peak values at the wing of the flame and dashed lines show values in the centreline of the flame. A logarithmic scale is applied to the Y-axis. Legend is in Figure 5.2. An analysis of the sooting behaviour sensitivity on soot oxidation via O 2, shown in Figure 5.4, revealed that the O 2 oxidation model by Lee et al. [31] has a limited effect on sooting behaviour in the flame compared to surface growth and inception. Only in the extreme case of removing O 2 oxidation entirely does one start to observe significant changes to sooting behaviour characteristics in the wing of the flame. Removing O 2 oxidation creates the asymptote observed in Figure 5.4 as the logarithmic value of zero is undefined. It is worth noting that the sooting behaviour in nearly all cases is unaffected by changes in the O 2 oxidation rate. One exception to this is the O 2 oxidation rate itself, which actually increases faster in the centreline than it does in the wing with increasing O 2 oxidation rate. 53

66 Figure 5.5 Sensitivity of sooting behaviour to the pre-exponential value of soot oxidation via OH,. Solid lines show peak values at the wing of the flame and dashed lines show values in the centreline of the flame. A logarithmic scale is applied to the Y-axis. Legend is in Figure 5.2. The sooting behaviour as affected by the OH oxidation rate, shown in Figure 5.5, is very similar to effects observed with changes to the O 2 oxidation rate described above. As before, the removal of OH oxidation by setting the pre-exponential value of A OH to zero creates the asymptote observed. For the most part, there are minimal changes to the soot volume fraction, soot number density, and soot diameter predictions in the centreline and wing. This is in contrast to the changes to the O 2 oxidation rate where changes in the sooting behaviour in the wings of the flame were much more noticeable. Thus, it appears that the O 2 oxidation model is the dominant oxidizing mechanism in this particular simplified model and flame setup. The competing behaviour between O 2 oxidation and OH oxidation is once again observed as OH oxidation is increased, the O 2 oxidation rate decreases and vice versa. Interestingly, increasing the OH oxidation pre-exponential did not significantly increase the overall peak OH oxidation rate. As the peak OH concentration in the cases investigated did not vary, this suggests 54

67 that in the particular flame investigated, OH concentration is the limiting factor, and not the preexponential of the oxidation rate. Figure 5.6 Sensitivity of sooting behaviour to the selected incipient particle diameter, with the default value at 12 nm. Solid lines show peak values at the wing of the flame and dashed lines show values in the centreline of the flame. A logarithmic scale is applied to the Y-axis. Legend is in Figure 5.2. The sensitivity of sooting behaviour on the parameter, which affects the incipient particle s diameter, is shown in Figure 5.6. It can be observed that the soot particle number density is most affected by the choice of incipient particle diameter, which is not surprising as the source term for soot number density [Equation (4.24)] is heavily influenced by the choice of the parameter. The smaller is, the less inception reactions [Equation (4.11)] are required to occur before a new soot particle is created (and vice versa). This change in soot number density will in turn affect the available soot surface area, and as such, affects the soot surface growth and oxidation rates in a similar manner. However, the overall change in measureable sooting characteristics other than soot number density (i.e. soot volume fraction and soot aggregate diameters) is minimal. 55

68 Figure 5.7 Sensitivity of sooting behaviour to the selected agglomeration rate,. Solid lines show peak values at the wing of the flame and dashed lines show values in the centreline of the flame. A logarithmic scale is applied to the Y-axis. Legend is in Figure 5.2. Sooting behaviour was found to be largely unaffected by the agglomeration parameter, with the exception of soot aggregate diameters and soot particle number density, as discerned in Figure 5.7. This is not too surprising as the agglomeration parameter, only plays a role in the soot number density source term in Equation (4.24). As increases, the tendency of soot particles to combine and agglomerate increases, effectively decreasing the soot particle number density. As this does not affect the soot mass fraction, it follows that the averaged soot particle diameter will also increase Model Development at 1 atmosphere using the Smooke et al. [63] data set Computations were completed based on the experiments performed by Smooke et al. [63] as described in Section 3.3. A modified GRI mechanism developed by Huang et al. [88] was used for simulations that employed the simplified two equation soot model while a detailed mechanism with PAH formation developed by Slavinskaya and coworkers [7],[20],[95] was used for simulations that utilized the sectional soot model. An value of 1 was selected for the simulations conducted with the 56

69 detailed model for this flame. In the following discussion, the term simplified model refers to the base simplified model with constants as outlined in Table 5.5 in Section 5.7. The radial profiles of soot volume fraction measurements and calculated soot volume fractions were compared at four different axial heights in the flame and are shown in Figure 5.8. The detailed sectional code predicted a peak soot volume fraction of 0.49 ppm in the wing of the flame, which matches the experimental peak measurement of 0.49 ppm in the wing of flame. However, the detailed sectional code predicted the peak at a slightly higher axial position in the flame approximately 0.6 cm higher (of which the peak flame height was approximately 6 cm). This is postulated to be the result of delayed PAH formation due to some deficiencies in the chemical mechanism used. Since the detailed code uses PAHs as a direct precursor to soot inception, this delay in sooting behaviour is likely due to the aforementioned slow PAH formation. The improvement of PAH formation behaviour in chemical mechanisms is currently the focus of other ongoing studies and further investigation is outside the scope of this work and instead, the delay was accounted for in the comparisons by simply making the comparisons at an axial offset of 0.6 cm. On the other hand, the simplified model predicted a peak soot volume fraction of 0.24 ppm, which underpredicts by slightly more than a factor of two, just over the reported measurement uncertainty of. However, unlike the detailed sectional model, the peak soot volume fraction is predicted at the correct axial height in the flame since the soot inception is based on acetylene and does not suffer a delay. In both cases, the overall computed radial soot volume fraction profiles capture the general trends found in the experimental measurements. However, at higher axial heights (namely Z3 and Z4), the soot volume fraction predictions from both models are shifted outward in the radial direction, with noticeable underprediction in the centreline. This behaviour has been observed in other studies [5],[20],[63] and appears to be independent of the soot model used. It is theorized that the centreline underprediction is related to deficiencies in the chemical mechanisms' ability to predict the correct amount of soot precursor growth within the centre of the flame. Nonetheless, the qualitative and quantitative results obtained are promising compared to the 57

70 available experimental data. Recent studies by Eaves and coworkers at CRL have also shown that this behaviour might also be due to the fact that the model neglects pre-heating of the fuel tube caused by the flame sitting near the inlet. At the time of writing, this work has not yet been published. Figure 5.8 Soot volume fraction profiles at different axial heights above the burner. Z1, Z2, Z3, and Z4 correspond to heights of 2.0, 2.25, 2.5, 2.75 cm for experimental measurements and computations from the simplified model for the Smooke et al. [63] flame. For computations from the sectional model, 0.6 cm was added to each axial height to account for the delay in PAH formation Comparisons to numerical data from detailed sectional soot model While soot volume predictions from the simplified soot model are promising, the computed values can be improved by adjusting some of the model parameters. However, as previously stated in Section 3.2, it is not desired to simply adjust the parameters at random since arriving at a reasonable prediction is not a unique solution. Instead, the detailed sectional soot model has been employed to produce a numerical data set upon which further details on sooting behaviour can be validated. In the case of Smooke et al. [63], only a few soot volume fraction measurements were made at four heights in the flame, which were not adequate to reproduce a reasonable looking contour of soot volume 58

71 fraction. Thus, contours of soot volume fraction could only be compared amongst the simplified code and detailed sectional model, illustrated in Figure 5.9. Figure 5.9 Contours of soot volume fraction (ppm) generated using the simplified model (left) and detailed sectional model (right) for the Smooke et al. [63] flame. The contours of soot volume fraction compare favourably between the simplified model and the detailed model, with the major difference being the peak soot volume fractions predicted and the slight axial shift in soot as previously observed in Figure

72 Figure 5.10 Contours of soot number density of aggregates (#/cc) generated using the simplified model (left) and detailed sectional model (right) for the Smooke et al. [63] flame. Computed soot number density contours are shown in Figure 5.10 unlike the contour of soot volume fraction, there are significant differences in the predictions of soot number density between the two models. Firstly, the peak soot number density is about 40% higher in the simplified model than in the detailed model, with the peak in the wing instead of in the centreline of the flame. The axial shift in the location of soot is once again observable in the contours. Based on the current implementation of the simplified model, the higher soot number density can be attributed to either an inception rate that is too high, or an agglomeration rate that is too low. It s worth noting that in order to make the comparison reasonable, particles smaller than 12 nm (the incipient particle size in the simplified model) were neglected for the purposes of calculating soot number density in the detailed model. However, particles smaller than 12 nm were still used in the calculation of mass averaged aggregate diameters in the following comparison. Overall, the discrepancy between the two models can also likely be attributed to the lack of soot aerosol dynamics in the simplified model (such as fragmentation of particles) and is a given limitation of the simplified model as it neglects soot aggregate structure. The soot number density is also sensitive to the incipient particle diameter; however, in order to reduce 60

73 soot number density, the incipient particle diameter would have to be increased, making it unrealistic (as most experimental apparatuses start to detect soot particles over a size of ~10 nm). Figure 5.11 Contours of soot aggregate mass averaged diameters (nm) generated using the simplified model (left) and detailed sectional model (right) for the Smooke et al. [63] flame. The contours of mass averaged diameters of soot aggregates, shown in Figure 5.11, were compared to get a better idea of which soot kinetic mechanisms (i.e. inception, surface growth, oxidation, agglomeration) needed improvement and also to evaluate the ability of the model to predict soot diameters. As the minimum size of a soot particle was prescribed to be 12 nm, it is not surprising to see a relatively flat distribution of particle diameters predicted by the simplified model. This is due to the fact that even a miniscule amount of soot calculated by the model outside the core of the flame will be reported to have a diameter of 12 nm. The peak size of diameters between the two models differ by about a factor of two, which suggests the simplified model needs a higher surface growth rate and/or a higher agglomeration rate to produce particles of a larger size. It is also possible the oxidation rates may be too high in the model, which could also result in smaller than expected particles. 61

74 In order to better understand how the model parameters in the simplified model should be modified in order to better reflect fundamental sooting behaviour as calculated by our detailed model, inception, surface growth, and oxidation rates were plotted along the pathline of maximum soot, which can be seen in Figure This tracks the evolution of a soot particle that passes through the point of peak soot volume fraction as it travels through the flame. An example of a soot pathline, which is calculated considering both the bulk fluid velocity and the soot thermophoretic velocity, is illustrated below in Figure Figure 5.12 Example of a pathline of maximum soot. In order to be comparable to the simplified code, the inception rate for the sectional model was calculated by summing the cumulative contributions to soot mass until it reached the incipient soot particle size of the simplified model, which is highlighted in Figure Essentially, the inception rate in the simplified code has all the particle growth and agglomeration built-in from the gaseous phase to its incipient particle size of 12 nm. As such, the inception rate in the sectional code needs to be combined with the particle growth and agglomeration rates that occur between its incipient size of about 0.9 nm to a size of approximately 12 nm. 62

75 Figure 5.13 Diagram of methodology used to compare inception mechanisms between the simplified code and the detailed code. Figure 5.14 Calculated plots of soot inception rate, surface growth rate, and oxidation along the pathline of maximum soot for the Smooke et al. [63] flame. The Y-axis is plotted on a logarithmic scale. The cumulative inception rate in the detailed model is similar in terms of its peak value compared to the inception rate calculated by the soot model, as seen in Figure While the peak inception rate is higher in the simplified model, the major difference is the fact that significant amounts of soot inception happen earlier in the flame than in the sectional model. This can likely be attributed to earlier 63

76 abundance of acetylene in the simplified model and the aforementioned delay in PAH formation in the detailed model. In fact, the shape of the inception rate curves for the detailed and simplified models closely mirror plots of pyrene (PAH) and acetylene concentration, respectively (not shown here). The rates of surface growth and oxidation were observed to be higher in the detailed model compared to the simplified model. However, the simplified model again showed higher rates of surface growth and oxidation lower in the flame, which is not surprising since inception is calculated to occur lower in the flame as well. Similarly, the integrated sum of the rates (i.e. the area under each rate curve) also shared the same comparisons: the integrated inception rate was higher in the simplified model and the surface and oxidation integrated rates were higher in the detailed model. Overall, initial results from the simplified and detailed model of the Smooke et al. [63] flame show that although the simplified model is nearly within the experimental error of measured peak soot volume fraction, modifications to the surface growth rate and agglomeration rate of the simplified model may be warranted. This conclusion arises from the fact that soot number densities appear to be overpredicted in the simplified model while soot aggregate mass averaged diameters appear to be underpredicted, relative to the detailed soot model. In addition, an analysis of the inception, surface growth, and oxidation rates along the pathline of maximum soot reinforce the idea that the current surface growth rate of the simplified model is insufficient Model Development at 1 atmosphere using the Schittkowski et al. [78] dataset Nearly identical computations and analyses were performed using the experimental configuration and data provided by Schittkowski et al. [78] as those described in Section 5.3. Calculations for the simplified model were completed with a modified version of the GRI mechanism by Huang et al. [88]. The detailed model employed a recently developed improved PAH mechanism that is largely the same as the mechanism by Slavinskaya and Frank [7] with a few modifications to some chemical reaction rates. This new PAH mechanism attempts to address some of the deficiencies in PAH formation observed earlier in Section 5.3 and in other ongoing studies. An value of 0.65 was used in the 64

77 detailed model in order to match the calculated peak soot volume fraction to the experimental peak soot volume fraction in the wing of the flame. As before, simplified model refers to the base simplified model with constants as outlined in Table 5.5 in Section 5.7. (a) (b) Figure 5.15 Contours of soot volume fraction side by side with experimental measurements in the Schittwkowski et al. [78] flame. Experimental measurements are on the left side of the flame and computations are on the right side of the flame. Results of the simplified model are shown in (a) and results of the detailed model are shown in (b). Computed soot volume fraction contours from the simplified and detailed models were compared to the experimental measurements made by Schittwkowski et al. [78]. Unfortunately, the raw data from the Schittwkowski et al. [78] flame is no longer available and only the black and white images of the contours from the paper could be used for comparisons. In addition, the method of using an LII diagnostic technique introduces many uncertainties into the measurements made as the LII 65

78 measurement technique currently requires several assumptions about flame and soot properties as an input further details on this process can be found in a study by Will et al. [97]. Since no measurement uncertainty was reported by Schittwkowski et al. [78] for their techniques, an uncertainty of was assumed for the purposes of comparison with calculated results. As the parameter in the detailed model was adjusted to fit the experimental results, it is not surprising that the calculated peak of 0.50 ppm closely matches the apparent measured peak of 0.55 ppm, both in the wings of the flame. However, the location of the calculated peak soot volume fraction is once again slightly shifted upward in the axial direction. On the other hand, the simplified model underpredicted the peak soot volume fraction by about a factor of 4, giving a calculated maximum soot volume fraction of 0.14 ppm. The predicted tip of the flame (indicated by the location of the soot volume fraction contour) also does not reach the same height in the simplified model as observed in the experimental measurements. This suggests that the soot oxidation rates in the flame may be too high, or that inception and growth rates in the model are too low. 66

79 (a) (b) Figure 5.16 Contours of soot particle diameter in the Schittkowski et al. [78] flame. (a) shows the experimental measurements of primary particle diameter on the left and the calculated contour of primary particle diameter on the right from the detailed model. (b) shows the calculated contour of mass averaged aggregate particle diameter from the detailed model on the left and the simplified model on the right. Due to the limited experimental measurements made, only primary particle size of soot particles were reported by Schittkowski et al. [78]. Since primary particles in the simplified model are not tracked (due to the lack of a soot aerosol dynamics model), only a comparison to the detailed sectional model could be made, which is shown in Figure Experimental measurements show a predicted peak primary particle size of approximately 20 nm in the flame, which compares favourably with the detailed model's prediction of a peak primary particle size of 13 nm. In addition, the spatial distribution of primary particle size predicted by the detailed model is a good match to the experimental results. In order to have some insight on the particle sizes being predicted by the simplified model, the mass averaged aggregate diameters are compared amongst the two models. A peak of about 42 nm was predicted by the detailed model and a peak of 20 nm. This reinforces the earlier findings from Section that 67

80 suggest the growth rate and/or the agglomeration rate predicted by the simplified model is too low and/or the oxidation rates are too high. (a) (b) Figure 5.17 Contours of soot particle number density in the Schittkowski et al. [78] flame. (a) Shows the experimental measurements of primary particle number density on the left and the calculated primary particle number density on the right from the detailed model. Different scales are used for each half of the flame. (b) Shows the calculated contour of aggregate particle number density from the detailed model on the left and the simplified model on the right. Similar comparisons were made with respect to particle number density, as seen in Figure For the same reasons described previously, only the detailed model could be used to compare with the experimental data. Here, we observe the first real problem that the detailed model exhibits as the peak value of soot primary particle density is overpredicted by an order of magnitude. This is likely due in part to the detailed model's handling of coalescence, which describes the process in which small, liquid-like soot particles combine into a new primary particle sphere instead of forming a typical soot aggregate structure. Without proper consideration of coalescence, the predicted primary particle number densities can be expected to be overpredicted, as observed. The improvement of this 68

81 coalescence model in the detailed code is ongoing in a parallel research program and is not part of this study. On the other hand, the predicted aggregate particle number densities appear to compare favourably across the simplified and detailed model. Once again, the simplified model predicts a higher peak value by about a factor of 1.5, suggesting again that either the inception rate is too high, or the agglomeration rate is too low Comparisons to numerical data from detailed sectional soot model Using a similar process outlined earlier in Section 5.3.1, soot inception, surface growth, and oxidation rates were compared along the pathline maximum soot volume fraction between the simplified model and the detailed model. The resulting plots, shown in Figure 5.18, illustrate once again that although the peak inception rates predicted by both models are comparable, the peak growth rate and subsequent oxidation rates are too low in the simplified model. This is not too surprising as the earlier comparisons to experimental and numerical data from the detailed model showed that the simplified model underpredicted soot volume fractions and particle diameters. As before, the integrated sum of the rates (i.e. the area under each rate curve) also shared the same results with the resulting integrated inception rate calculated higher in the simplified model and the resulting surface and oxidation integrated rates calculated higher in the detailed model. 69

82 Figure 5.18 Calculated plots of soot inception rate, surface growth rate, and oxidation along the pathline of maximum soot for the Schittkowski et al. [78] flame. The Y-axis is plotted on a logarithmic scale Results at elevated pressures The flames of Thomson et al. [79] and Joo and Gülder [80] were simulated at pressures of 10 atm to 40 atm in order to investigate the performance of the simplified model at higher pressures. Calculations for the simplified model were completed with a modified version of the GRI mechanism by Huang et al. [88]. The detailed model employed the improved PAH mechanism that is based on the mechanism by Slavinskaya and Frank [7] with a few modifications to some chemical reaction rates. An value of 0.10 was used in the detailed model at all pressures investigated as it gave reasonable predictions of peak soot volume fraction for each case investigated. Even better predictions could have been obtained by specifically adjusting the value for each pressure, but it was deemed an unnecessary use of computational resources due to the limited benefits and scientific merit it would to the study. Finally, simplified model refers to the base simplified model with constants as outlined in Table 5.5 in Section

83 (a) (b) (c) Figure 5.19 Contours of soot volume fraction (ppm) with experimental measurements made by Joo and Gülder [80]. Experimental measurements are on the left and calculated contours from the simplified model are on the right. Operating pressures are at 10 atm (a), 20 atm (b), and 40 atm (c). Calculated contours of soot volume fraction from the simplified model are compared with experimental measurements in Figure For the most part, differences in measurements made between LOSA and SSE in Thomson et al. [79] and by SSE in Joo and Gülder [80] were found to be negligible, with the largest differences occurring between LOSA and SSE measurements in Thomson et al. [79] at higher pressures. Further details on the discussions of the cause of these discrepancies can be found in their respective papers, but in the interest of saving the reader the trouble of looking at three nearly identical measurement data sets, only the most recent results from Joo and Gülder [80] are discussed. At all pressures, the spatial distribution of soot volume fraction is well reproduced in the simplified model; however, there is some overall underprediction in the peak soot volume fraction values. Notably, there is significant underprediction on the centreline of the flame, but the values in the wing of the flame are all within experimental uncertainty. This can be attributed in part to the large degree of uncertainty of SSE measurements in the core of the flame, where accuracy is limited due to uncertainty of the temperature measurements and optical limitations due to the thin flame [79]. In 71

84 addition, the general trends observed in the experiment as pressure increases (thinning of flame, higher soot volume fractions) are also well reproduced by the simplified model. (a) (b) (c) Figure 5.20 Contours of soot volume fraction (ppm) with experimental measurements made by Joo and Gülder [80]. Experimental measurements are on the leftt and calculated contours from the detailed model are on the right. Operating pressures are at 10 atm (a), 20 atm (b), and 40 atm (c). The results of the detailed sectional soot model are compared with experimental results in Figure The delayed upward axial shift in soot volume fraction predictions are once again observed, but the predicted values in the wing are well within experimental uncertainty. The centreline soot volume fraction is within experimental uncertainty at 10 atm, but slightly over-predicted at higher pressures. As mentioned earlier, there is some additional uncertainty of the measurements made in the core of the flame. Another possible source of discrepancy is the performance of the refined PAH mechanism, to which the sooting behaviour in the centreline is highly sensitive. The continued development of the PAH mechanism, including its validation at higher pressures, is unfortunately outside the scope of this work. 72