Development and Validation of a Partially Coupled Soot Model for Turbulent Kerosene Combustion in Industrial Applications

Transcription

1 Development and Validation of a Partially Coupled Soot Model for Turbulent Kerosene Combustion in Industrial Applications by Bijan Shahriari A thesis submitted in conformity with the requirements for the degree of Master of Applied Science Graduate Department of Mechanical and Industrial Engineering University of Toronto Copyright 2014 by Bijan Shahriari

2 Development and Validation of a Partially Coupled Soot Model for Turbulent Kerosene Combustion in Industrial Applications Abstract Bijan Shahriari Master of Applied Science Graduate Department of Mechanical and Industrial Engineering University of Toronto 2014 Soot emissions are by-products of combustion that are well documented to have adverse effects on human health and the environment. Consequently, these emissions are becoming a target for stricter regulations. However, obstacles exist in the implementation of soot models in Computational Fluid Dynamics codes with complex geometry, such as ensuring carbon mass conservation as soot forms. This challenge is due to the thermochemistry interactions in turbulent codes being preprocessed (included in look-up tables), not solved for directly. This study considers the development of a soot model for kerosene combustion. Coupling is introduced between the soot and gas phase by including nucleation rates within the flamelet library, and by adjusting the concentrations of key soot precursors through additional transport equations. Validation has been performed for turbulent coflow kerosene flames at pressures of 1 and 4.8 bar. This simplified model reasonably predicts the soot volume fraction without tuning of the inception rate. ii

3 Acknowledgments First, I would like to thank my co-supervisors Professor Murray J. Thomson and Professor Seth B. Dworkin for their guidance, and the knowledge they passed on to me over the course of this thesis. Completing the work presented in this document would have been impossible without their support and patience. I am also grateful to my colleagues at the Combustion Research Lab, who accompanied me on this journey, providing distractions in the lab when work became mundane. In particular, I would like to thank Kaveh Khalilian, Nick Eaves, Armin Veshkini, and Meghdad Saffaripour for helping me understand important concepts related to this body of work. I would also like to thank HPCVL, SciNet, and ANSYS Inc. for their support. Finally, a special thank you goes to my family and friends, who have provided constant love and support over the course of my life, and especially during the last two years. iii

4 Table of Contents Acknowledgments... iii Table of Contents... iv List of Tables... vii List of Figures... viii List of Appendices... xii 1 Introduction Motivation Objectives Literature Review Turbulent Combustion Modelling Modelling of Fluid Dynamics Modelling of Combustion Laminar Flamelet Model PDF Look-up Tables Chemical Mechanisms Soot Formation Process Physical Aspects of Soot Inception Surface Growth Oxidation Coagulation Soot Modelling Relevant Experimental Data...16 iv

5 2.5 Previous Modelling Efforts Validation Case Gas Turbine Combustors Mathematical Formulation Turbulent Reacting Flows Governing Equations Favre Averaged Conservation Equations and k ε Model Choice of RANS Model Chemical Mechanism and Kerosene Surrogate Laminar Flamelet Model Soot Model Transport Equations Soot Source Term Inception Surface Growth Oxdiation Coagulation Coupling Radiation Model Source Term Linearization Model Description Overview Boundary Conditions UDF Implementation Define Source...52 v

6 4.3.2 Define Absorption Define Diffusivity Define Adjust Parallel Computing Results and Discussion Flame A: 1 Bar Flame Structure, Species and Soot Fields Comparison with Experiment Effect of Coupling Effect of HACA Growth Flame E: 4.8 Bar Flame Structure, Species and Soot Fields Comparison with Experiment Effect of HACA Growth Convergence and Computational Cost Conclusions and Future Work...86 References...88 Appendix A Chemical Mechanism Modifications...97 Appendix B Formation Rates of A2 and A Appendix C User Defined Functions vi

7 List of Tables Table 2-1: Categorization of different combustion applications [7]... 6 Table 2-2: Experimental conditions for the Young flames [40] Table 3-1: HACA mechanism for soot surface growth [25], = Table 3-2: Reaction rate constants for soot oxidation in Arrhenius form [52], = Table 3-3: Curve fit parameters for H 2 O and CO 2 Planck-mean absorption coefficients [63] Table 4-1: Boundary conditions for the numerical model of the 1 bar Young flame Table 4-2: Boundary conditions for the numerical model of the 4.8 bar Young flame vii

8 List of Figures Figure 2-1: Turbulence modelling approaches Figure 2-2: Counterflow diffusion geometry for laminar flamelet model [8] Figure 2-3: Trace of a fluid parcel with fluctuating mixture fraction [4] Figure 2-4: TEM pictures of soot aggregates for a premixed flame (left) [18] and a non-premixed flame (right) [19] Figure 2-5: Graphical overview of soot formation process [20] Figure 2-6: HACA scheme for the formation of 2-ringed aromatics [23] Figure 2-7: HACA scheme for the formation of multi-ringed aromatics [23] Figure 2-8: Soot modelling approaches Figure 2-9: Experimental setup for the Young flames [40] Figure 2-10: Comparison of soot inception models by Wen et al. Figure from [41] Figure 3-1: Coupling of inception model Figure 4-1: CFD geometry (not to scale) Figure 4-2: CFD model, computational mesh in metres Figure 4-3: CFD model, circular wedge geometry Figure 4-4: Degree of coupling between the different model subcomponents Figure 5-1: 1 bar soot volume fraction Figure 5-2: 1 bar soot number density (A2 left, A5 right) Figure 5-3: 1 bar flame. Soot particle diameters along the centerline viii

9 Figure 5-4: 1 bar mean mixture fraction Figure 5-5: 1 bar temperature [K] (A2 left, A5 right) Figure 5-6: 1 bar OH mass fraction Figure 5-7: 1 bar O 2 mass fraction (A2 left, A5 right) Figure 5-8: 1 bar C 2 H 2 mass fraction Figure 5-9: 1 bar C 6 H 6 mass fraction (A2 left, A5 right) Figure 5-10: 1 bar flame. Mass fractions of carbon sinks for the A2 and A5 models. From left to right: A2 (naphthalene), A5 (BGHIF), A5 (BAPYR), and A5 (BAPYR*S) Figure 5-11: 1 bar flame. Mean mixture fraction versus axial position along the centerline. Experimental data: [67]. Wen et al.: [41] Figure 5-12: 1 bar flame. Temperature versus axial position along the centerline. Experimental data: [67]. Wen et al.: [41] Figure 5-13: 1 bar flame. Soot volume fraction versus axial position along the centerline. Experimental data: [67]. Wen et al.: [41] Figure 5-14: 1 bar flame. Temperature versus axial position along the centerline for the untuned A2 model. Experimental data: [67] Figure 5-15: 1 bar flame. Soot volume fraction versus axial position along the centerline for the untuned A2 model. Experimental data: [67] Figure 5-16: 1 bar flame. Mean mixture fraction versus radial position at 100 mm (left) and 300 mm (right) above the inlet. Experimental data: [67] Figure 5-17: 1 bar flame. Temperature versus radial position at 100 mm (left) and 300 mm (right) above the inlet. Experimental data: [67] ix

10 Figure 5-18: 1 bar flame. Soot volume fraction versus radial position at 100 mm (left) and 300 mm (right) above the inlet. Experimental data: [67] Figure 5-19: 1 bar flame. The effect of coupling on soot volume fraction along the centerline.. 71 Figure 5-20: 1 bar flame. The effect of HACA growth on soot volume fraction along the centerline for the A2 model Figure 5-21: 1 bar flame. The effect of HACA growth on soot volume fraction along the centerline for the A5 model Figure 5-22: 1 bar flame. The effect of HACA growth on soot volume fraction along the centerline for the uncoupled A2 model Figure 5-23: 1 bar flame. The effect of HACA growth on soot volume fraction radially at a height of 100 mm for the A2 model (left) and the A5 model (right) Figure 5-24: 4.8 bar soot volume fraction Figure 5-25: 4.8 bar soot number density (A2 left, A5 right) Figure 5-26: 4.8 bar flame. Soot particle diameters along the centerline Figure 5-27: 4.8 bar mean mixture fraction Figure 5-28: 4.8 bar temperature [K] (A2 left, A5 right) Figure 5-29: 4.8 bar OH mass fraction Figure 5-30: 4.8 bar O 2 mass fraction (A2 left, A5 right) Figure 5-31: 4.8 bar C 2 H 2 mass fraction Figure 5-32: 4.8 bar C 6 H 6 mass fraction (A2 left, A5 right) Figure 5-33: 4.8 bar flame. Mass fractions of carbon sinks for the A2 and A5 models. From left to right: A2 (naphthalene), A5 (BGHIF), A5 (BAPYR), and A5 (BAPYR*S) x

11 Figure 5-34: 4.8 bar flame. Temperature versus axial position along the centerline. Experimental data: [67] Figure 5-35: 4.8 bar flame. Soot volume fraction versus axial position along the centerline. Experimental data: [67] Figure 5-36: 4.8 bar flame. The effect of HACA growth on soot volume fraction along the centerline for the A2 model Figure 5-37: 4.8 bar flame. The effect of HACA growth on soot volume fraction along the centerline for the A5 model xi

12 List of Appendices Appendix A.Chemical Mechanism Modifications Appendix B..Formation Rates of A2 and A5 Appendix C...User Defined Functions xii

13 1 Introduction This chapter provides a brief summary of the motivations behind and the objectives of this thesis. 1.1 Motivation Particulate emissions, such as soot, are by-products of combustion that are known to have adverse effects on human health, the environment, and jet engine combustors. In terms of health effects, soot particles have been linked to heart and lung disease, along with various other health complications [1]. In terms of environmental effects, soot is considered to be one of the most significant contributors to global warming, behind CO 2, due to its strong radiative properties [2]. Finally, soot formation in jet engines causes increased radiative heat transfer towards the combustor walls, thus compromising the durability of these combustors [3]. For these reasons, it is expected that such emissions will increasingly become a target for stricter regulations in the near future, particularly in the aviation industry where use of fuels and combustion are unavoidable. As regulations come into place, industry will need to develop new engines or modify existing designs in order to meet emission targets. As such, there is a strong desire for accurate predictive soot models to aid the design process, and to avoid the expensive and time consuming procedure of developing prototypes, as much as possible. Predictive models allow engine designers to tune various design and operating parameters without the need for costly experimentation. These models have the potential to be a major boon to the design phase, if simulations can be completed within an acceptable amount of time. 1.2 Objectives The goal of this study is the development of an industry-focused soot formation model for the combustion of kerosene (aviation fuel) in industrial applications (particularly gas turbine engines). At present, in academia, there is a keen focus on research surrounding detailed soot models, focused mainly on fundamental understanding. However, in industry, there is a strong desire for simplified soot models that can reasonably predict soot emissions and trends without the computational cost associated with more detailed models. Further, there is a desire for such a 1

14 model to be implemented within the framework of commercially available computational fluid dynamics (CFD) software, such as the FLUENT package provided by ANSYS [4]. Thus, the model described here aims to keep these requirements in mind. It is important to state that the current goal is for a soot model that can reasonably predict trends, rather than exact values for the soot volume fraction. Currently, state of the art soot models are not able to exactly predict soot volume fraction fields without some level of tuning. Thus, the ability of a model to reasonably predict trends when considering differing geometries and operating conditions trumps the ability to exactly predict soot emissions for a particular geometry and set of operating conditions. In completing this thesis work, three main steps were undertaken. First, previous soot modelling efforts in kerosene flames and gas turbines were analyzed, in order to find areas for improvement. Second, an initial round of modelling and validation was performed for available experimental flames. Finally, modelling limitations found in the first round of modelling were addressed, and improved upon. 2

15 2 Literature Review This chapter provides necessary background information and theory needed to understand the work presented in this document. The first subsection provides background information on turbulent combustion modelling. The second subsection deals with the physical processes surrounding soot formation and oxidation. The third subsection considers soot modelling approaches. The fourth and fifth subsections discuss previous modelling efforts that are relevant to the work of this thesis. 2.1 Turbulent Combustion Modelling This section provides background on the modelling of turbulent fluid dynamics and combustion Modelling of Fluid Dynamics For an in depth discussion regarding the history and current state of turbulence modelling, refer to Turbulence Modeling for CFD by David C. Wilcox [5], which is referenced here extensively. In general, three modelling techniques are used to model turbulent flow, and they are presented in Figure 2-1 in order of computational cost. Figure 2-1: Turbulence modelling approaches. 3

16 The technique with the highest computational cost is Direct Numerical Simulation (DNS), which refers to the direct solution of the Navier-Stokes equations at all length scales of interest. While this technique is very straight-forward to implement, and produces the most accurate results, the required grid resolution and associated computational cost narrows down its applicability greatly. This requirement comes from the fact that the length scales associated with turbulence (from the smallest, so-called Kolmogorov scales to the largest scales) range from the order of micrometers to meters and larger. The same wide range is found when comparing the time scales of turbulence. As the largest control volumes and time-steps required must be fractions of the smallest Kolmogorov scales, such models quickly become computationally limited as the scale (i.e., the Reynolds number) of the flow increases. In general, the computational cost of a DNS model increases with Reynolds number by approximately Re 3 [6]. On the other end of the spectrum, the techniques with the lowest computational cost are the socalled Reynolds Averaged Navier-Stokes (RANS) models. The RANS method decomposes relevant flow properties into averaged and fluctuating terms, and then seeks to model the correlations that arise between the fluctuating terms in the RANS equations. These correlations are manifested in the Reynolds stress tensor, which is modelled in different ways depending on the complexity of the chosen RANS model. The simplest RANS models use algebraic equations to compute the Reynolds stresses directly from flow variables. However, these models are generally considered to be too simple for the desired accuracy in most flow configurations. Oneand two-equation models are the next level of complexity. These models rely on the solution of one or two additional transport equations for turbulent properties (e.g., turbulent kinetic energy and turbulent dissipation for the popular k - ϵ model) in order to compute the Reynolds stress tensor. The algebraic and one- or two-equation models all rely on the Boussinesq approximation, which assumes that the Reynolds stress tensor is directly proportional to the strain rate tensor through an eddy viscosity [5]. This is not a physical property of the fluid, but rather a property of the flow, and an analogy to the molecular viscosity. The eddy viscosity transfers momentum caused via turbulent motion in the same way that the molecular viscosity transfers momentum caused via molecular motion. In general, two-equation Boussinesq-based RANS models provide good predictions for many turbulent flows as the inclusion of two transport equations allow for good accounting of the flow history (unlike the algebraic models). 4

17 However, the Boussinesq assumption that the Reynolds stress is aligned with the strain rate tensor leads to errors for a variety of flows: those with sudden changes in mean strain rate, with high curvature, in ducts and pipes with secondary motions, highly 3D and swirling flows, and flows with large regions of separation [5]. For flows with these characteristics, the most applicable RANS-based models are the Reynolds-Stress Models (RSM), which directly derive and solve transport equations for the Reynolds stress tensor. These models no longer rely on the Boussinesq approximation, and are applicable to a larger range of turbulent flows. However, RSM requires more computational resources than Boussinesq-based RANS models. As an aside, for cases where density fluctuations exist in the flow field (e.g., combustion or supersonic flow), the Reynolds averaging method is replaced with Favre averaging. Favre averaging is a modelling technique, which treats flow properties that are affected by density as a summation of their density-weighted average and density-weighted fluctuation. The RANS equations are then replaced by Favre Averaged Navier-Stokes (FANS) equations [5]. The intermediate technique between RANS and DNS is Large Eddy Simulation (LES). The idea behind LES is to use DNS to solve for turbulent motion in the largest eddies, containing most of the turbulent energy, while modelling the turbulent motion at the smallest scales. Since turbulent motion at the smaller scales is generally more homogeneous, isotropic and universal across different flow geometries, more simplified models can be used for these scales. Finally, there are hybrid LES-RANS approaches, which use LES for regions where RANS performs poorly, and RANS everywhere else, in order to minimize the computational complexity of the model, while still maintaining a desired accuracy. The work presented here primarily utilizes the two-equation RANS approach, for which more detail is provided in section Modelling of Combustion As discussed above, the Navier-Stokes equations must be solved in order to describe the mechanical motion of fluids. However, the introduction of reactions within the flow (e.g., in combustion) necessitates the need to solve species conservation equations for tens or hundreds of species, each governed by highly non-linear, Arrhenius-based reaction rates. Once turbulence is 5

18 introduced, the direct solution of these equations quickly becomes computationally intractable for most practical geometries. With the introduction of chemical interactions to a turbulent field, an important parameter becomes the Damköhler number, Da, defined as the ratio of the turbulence time scale (i.e., the Kolmogorov time scale) to the chemical time scale (i.e., a measure of reaction rate): Da = τ τ (2-1) If the Damköhler number is much greater than one, the chemical time scale is assumed to be insignificant compared to the turbulence time scale, which is referred to as fast chemistry. Conversely, if the Damköhler number is much less than one, the chemical time scale dominates, and this is referred to as slow chemistry. In general, the classification of slow and fast chemistry, as well as the degree of premixing, can help categorize combustion applications as shown in Table 2-1 [7]. Table 2-1: Categorization of different combustion applications [7]. Premixed Combustion Partially and Non-premixed Combustion Diesel engines Fast Chemistry Spark-ignition engines Gas turbine engines Combustion in furnaces Slow Chemistry NO x formation in post-flame regions Low NO x burners The work described here can be classified under non-premixed combustion with fast chemistry. Under the fast chemistry regime, one way to model turbulent combustion is with the laminar flamelet model [4] [7]. This model allows for a computationally efficient prediction of species mass fractions in practical geometries, and will be explained further in the following section. 6

19 Laminar Flamelet Model The laminar flamelet model assumes that a turbulent flame can be described by a collection of laminar flamelets infinitely thin flame sheets within which reactions occur in the laminar regime. This assumption is reasonable, because fast chemistry implies that the chemical reactions occur in a thin layer, which is smaller than the length of the smallest turbulent eddies. Hence, the laminar structure of the flame is not disturbed by the turbulence of the flow [7]. Further, the assumption that chemistry occurs within an infinitely thin sheet is mitigated by introducing a parameter referred to as the scalar dissipation, a measure of the strain rate. The counterflow diffusion flame, shown in Figure 2-2, is typically used to model each laminar flamelet. Opposed, axisymmetric fuel and oxidizer jets create the flame geometry. Increasing the velocity of the jets or decreasing the distance between them strains the flame, and shifts it away from chemical equilibrium, until it is extinguished. Through experimental measurements or computational calculations, the species mass fractions and temperature fields can be determined at each location between the two jets, and for a variety of strain rates. Since the mixture fraction, f, (discussed in more detail in Chapter 3) increases from zero at the oxidizer jet to one at the fuel jet, the species mass fraction and temperature measurements can be mapped from physical space to mixture fraction space. Thus, the local flame chemistry at any point in a turbulent flame can be completely described by the mixture fraction, and strain rate (or equivalently, the scalar dissipation) at that point. Since the chemistry of the flame is no longer bound by the physical geometry of the model, it can be entirely preprocessed for a given fuel and oxidizer as a function of mixture fraction and scalar dissipation. The relevant flame parameters are then taken from look-up tables during each solution step, greatly reducing computational costs [4]. 7

20 Figure 2-2: Counterflow diffusion geometry for laminar flamelet model [8] PDF Look-up Tables The generation of the laminar flamelet library does not account for the turbulent fluctuations that exist in the flame. Referring to Figure 2-3, it can be noted that a parcel of fluid at a particular location in the flame can be associated with a fluctuating mixture fraction, centered about a mean value. These fluctuations can be described by a probability density function (PDF), which is incorporated in the calculation of the look-up tables from the flamelet library. More details are provided in section

21 Figure 2-3: Trace of a fluid parcel with fluctuating mixture fraction [4] Chemical Mechanisms In the simplest type of analysis, combustion of a fuel can be modelled as a single-step global reaction between the fuel and oxidizer. However, this simplification cannot capture the chemistry of intermediate species in the combustion process, and is thus entirely inaccurate for modelling of reacting flows. This is especially true for modelling of pollutant formation (such as soot), which relies heavily on intermediate species concentrations. In actuality, the combustion of a hydrocarbon involves tens to hundreds of different species and hundreds to thousands of elementary reaction steps. To capture this reality, reacting flow simulations generally utilize a library of elementary reactions referred to as a chemical mechanism. These mechanisms are generally accompanied by a thermodynamic database file, which describes the specific heats, enthalpies and entropies of the various species. More details regarding the chemical mechanism used in this study is provided in Chapter Soot Formation Process Soot is a by-product of the combustion of hydrocarbons, and consists of small, carbon rich particles. These particles are emitted in the solid phase, unlike other pollutants such as CO 2 and NO x, which are emitted in the gas phase. Soot particles start off as small spherical shapes (called primary particles), which go on to merge and form complex aggregate structures. Heavily sooting flames are often identified visually by large black plumes of exhaust smoke. However, 9

22 soot can also be recognized by the yellow glow radiated from many flames [9]. The physics of soot formation, growth, and oxidation is highly complex, and not completely understood. These processes have been reviewed by several authors, such as Glassman [10], Haynes and Wagner [11], Kennedy [12], Frenklach [13], and the International Sooting Flame Workshop [14] Physical Aspects of Soot In general, the physical characteristics of soot are not strongly related to the type of fuel, flame or operating condition of a process [10]. Refer to Figure 2-4 for pictures of the aggregate structure of soot particles for premixed and non-premixed flames, taken using transmission electron microscopy (TEM). The small spherical shaped objects, or primary particles, typically have diameters of nm [15]. Soot aggregates exhibit fractal structures with fractal dimensions ranging from 1.9 to 2.5 [16]. Finally, the macroscopic density of soot generally lies between 1800 and 2100 kg/m 3 [17]. Figure 2-4: TEM pictures of soot aggregates for a premixed flame (left) [18] and a non-premixed flame (right) [19] 10

23 2.2.2 Inception Soot inception (or nucleation) refers to the mechanism by which the first soot particles are formed. It is generally agreed that the first solid soot particles are formed through the coalescence of polycyclic aromatic hydrocarbons (PAHs). These PAHs, large carbon-containing molecules with multiple aromatic rings (e.g., pyrene), exist in the gas phase, and gradually merge together to form larger and larger carbon structures until, at a certain point, they can be considered to be solid soot particles [11] [13]. This process is represented in Figure 2-5, where fuel and oxidizer react to first form small carbon containing species, then the first aromatic rings, then the first PAHs, and finally go on to form larger PAHs until the first soot particles are considered to be formed [20]. The species that are considered to be important in the formation of PAHs or soot are generally referred to as precursor species. Figure 2-5: Graphical overview of soot formation process [20]. 11

24 The PAH formation process can differ greatly depending on the type of fuel. For aliphatic fuels, which do not contain any aromatic rings, fuel decomposition leads to the formation of small C 2 and C 3 species (e.g., acetylene), which leads to the formation of the first benzene rings through elementary reactions, and eventually leads to larger PAHs [21] [22]. One such sequence of elementary reactions is referred to as H-abstraction C 2 H 2 -addition (HACA), where hydrogen sites are removed from a hydrocarbon through reactions with radicals, and C 2 H 2 is subsequently able to react and bond with the hydrocarbon, increasing its mass and eventually forming large aromatic rings. Examples of these reaction sequences are visualized in Figure 2-6 and Figure 2-7 [23]. Figure 2-6: HACA scheme for the formation of 2-ringed aromatics [23]. 12

25 Figure 2-7: HACA scheme for the formation of multi-ringed aromatics [23]. For fuels containing aromatic species, the HACA process can still contribute to PAH growth. However, the aromatic content present in the fuel itself can contribute greatly to PAH growth, as aromatic species can directly react with each other to form larger aromatic rings [21]. In general, fuels with large amounts of aromatic content will produce much more soot than fuels with large amounts of aliphatic content [10]. 13

26 2.2.3 Surface Growth Soot surface growth refers to the mechanisms by which gaseous hydrocarbon species attach to soot particles, and influence their growth. One such mechanism, proposed by Frenklach and coworkers [13] [24] [25], uses the HACA scheme introduced above as a means for soot surface growth. Here, a radical first reacts with the surface of a soot particle (i.e., a C-H bond) and removes the H atom. This reaction activates the site, and allows it to react with nearby acetylene, which serves to increase the overall carbon mass of the soot particle. Another surface growth mechanism is taken to be surface growth via the addition of PAHs, which physically collide and stick onto a soot particle [26]. The surface growth rate is influenced by the surface area of soot particles, the local concentration of radicals, acetylene, PAHs, and the active surface site density Oxidation Soot oxidation refers to the mechanism by which soot particles lose mass, through reactions with gaseous species. The most important species linked to soot oxidation are O 2 and OH, with O 2 being more important in fuel lean regions, and OH being more important in fuel rich regions [27] [28]. Like surface growth, oxidation is influenced by the surface area of soot particles. In addition, soot oxidation can change the structure of a soot particle, by fragmenting an aggregate into smaller parts [28] [29] Coagulation Soot coagulation (or agglomeration) refers to the mechanism by which particles collide and stick together. While inception, surface growth, and oxidation are mainly chemical processes which govern the mass of soot, coagulation is a physical process that governs the particle size and number density of soot. Small soot particles can collide and merge into larger spheres in a process referred to as coalescence. Larger particles will generally form fractal-like structures upon collision, as shown in Figure 2-4. In some circumstances, particles that collide may not stick together, and will rebound due to thermal effects. Thus, these collisions are associated with a sticking efficiency [30] [31]. 14

27 2.3 Soot Modelling In a review of soot modelling methods, Kennedy identifies three different approaches in order of computational cost: empirical, semi-empirical and detailed [12]. This spectrum is visualized in Figure 2-8. Figure 2-8: Soot modelling approaches. Empirical models are based entirely on experimental correlations. These models relate the amount of soot produced with the operating conditions such as temperature, pressure, equivalence ratio and fuel. They are easy to implement and computationally simple to solve, but can only be applied to very specific operating conditions. These models generally do not provide any insight into the soot formation mechanism (e.g., inception or oxidation rates), and have constants that must be re-tuned if the operating conditions or computational geometries differ significantly from the calibration case [12]. Semi-empirical models are of the next level of sophistication. These models tend to include soot formation and oxidation mechanisms, but generally do not provide information on the aggregate structure of soot or the size distribution of particles. An example of such a model is the wellknown two-equation model of Fairweather et al. [32], which solves one equation for the soot mass fraction, and a second equation for the primary particle number density. The source terms 15

28 for these two transport equations include contributions from inception, surface growth, oxidation and coagulation. Detailed models are the most sophisticated and computationally expensive models available. These models include more complicated soot formation mechanisms, and are able to describe the polydisperse nature of soot particles. Popular detailed modelling methods include the Monte Carlo method [33], the sectional method [34] [35], and the method of moments [36] [37]. 2.4 Relevant Experimental Data In order to test the effectiveness of any numerical model, validation must be performed against relevant experimental data. Most soot measurement studies for kerosene-air flames have focused on laminar flames, and particularly flames at atmospheric pressure. For example, Saffaripour et al. investigated the formation of soot in laminar coflow diffusion flames burning both kerosene, and the Dagaut kerosene surrogate [38] (described in section 3.1.3) at atmospheric pressure. Their experimental results were also compared to numerical results from a detailed model [39]. Unfortunately, very little soot measurement data exists for the turbulent non-premixed combustion of kerosene, particularly at high pressures. The flames of Young et al. [40] (henceforth referred to as Young flames ), turbulent non-premixed kerosene-air flames burning at pressures of 1 to 6.4 atm, represent the most relevant data in the literature, to the author s knowledge. Temperature, mean mixture fraction, and soot volume fraction are among the data measured for these flames, and provide a good basis for the validation of this soot model. Figure 2-9 shows the experimental apparatus, while Table 2-2 shows the experimental conditions for each Young flame. More details of the experimental setup and data are provided in subsequent Chapters 4 and 5. 16

29 Figure 2-9: Experimental setup for the Young flames [40]. Table 2-2: Experimental conditions for the Young flames [40]. Flame A B C D E F Absolute pressure (bar) Fuel flow rate (g/min) Fuel exit velocity (m/s) Fuel exit temperature (K) Air exit velocity (m/s) Exit Reynolds number

30 2.5 Previous Modelling Efforts This section discusses previous modelling efforts, which are relevant to the work presented in this document Validation Case The 1 bar Young flame has been previously modelled by Wen et al. [41] using an 80% n-decane, 20% toluene (by volume) surrogate to represent the complex composition of kerosene. The chemical mechanism included 141 species and 1014 elementary reactions, and the standard k - ϵ model along with a steady laminar flamelet model was used to predict the fluid turbulence and species chemistry. Wen et al. modelled the flame using two soot models, which only differed in the choice of inception rate. The first model of Wen et al. [41], the PAH inception model, used a soot inception rate originally put forward by Hall et al. [42], which was based on the formation rate of two PAHs C 10 H 7 and C 14 H 10 (henceforth referred to as A2 and A3 denoting 2-ringed and 3-ringed aromatic species). Based on laminar methane flame data, Hall et al. proposed the inception rate to be equal to eight times the PAH formation rate via phenyl radicals, benzene and acetylene. Put mathematically, the inception rate used was: [ ] = 8 [ ] [ ][ ] + 8 [ ] (2-2) where the quantities in square brackets are species concentrations, T is the temperature, and c 2 = 127* and c 3 = 178* are constants determined by Hall et al. [42]. The second model of Wen et al. [41], the acetylene inception model, used a soot inception rate first proposed by Leung et al. [43], and validated for laminar ethylene and propane flames. This model considers acetylene to be the major contributor to soot inception via the following reaction and inception rates: 18

31 2 ( ) + (2-3) = 54 [ ] (2-4) where the mass of a soot nucleus, M P = 144 kg/kmol, is a constant. Both models included a soot surface growth term, which focused on particle growth via the addition of acetylene. In addition, both models included soot oxidation terms via the OH radical and O 2. Referring to Figure 2-10, Wen et al. determined that the PAH inception model was able to provide good agreement with experimental measurements, while the acetylene inception model significantly under-predicted the soot volume fraction by one to two orders of magnitude [41]. This is an expected result. The acetylene inception model assumes that the primary soot inception route is through fuel pyrolysis creating acetylene, which then goes on to form the first aromatic rings. This assumption makes sense for small fuel species that have little to no aromatic content (e.g., ethylene and propane for which the acetylene inception model was first validated). However, as kerosene is a complex fuel with significant aromatic content, it is more logical to consider the primary soot inception route to be through PAHs, rather than acetylene. 19

32 Figure 2-10: Comparison of soot inception models by Wen et al. Figure from [41] Gas Turbine Combustors Following the work of Wen et al., Yang applied the PAH inception model described above to a commercial gas turbine combustor using the same chemical mechanism and kerosene surrogate that was used by Wen et al. [44]. The combustor was operated at four different operating conditions, and as spatial soot measurements for the gas turbine were unavailable, the model was only validated against the smoke density at the engine exhaust. It was found that at 7% engine thrust, the model predicted smoke density, but that it over-predicted smoke density at higher thrust levels by one to three orders or magnitude. This over-prediction could be due to a variety of factors. First, the oxidation rates used may have been inadequate, leading to an over-prediction of smoke density. Second, while good fuel surrogates are typically validated for important combustion properties such as laminar flame speed and ignition delay, they are generally not vigorously validated for important soot 20

33 precursors, especially large PAH species [38]. Third, research into PAH formation rates is ongoing, and some of the rates used in the chemical mechanism of Wen et al. may have been incorrect. Fourth, there exists an inability of most turbulent soot models (such as the one employed by Yang) to account for the depletion of soot precursor species due to the transfer of carbon out of the gas phase, and into the solid phase as soot particles grow (strict mass conservation). As mentioned in section 2.1.2, thermochemistry interactions in turbulent codes are generally preprocessed and included in look-up tables, rather than being solved for directly [4]. Thus, once a soot prediction is established, there is no way to modify the flamelet library and obtain new values for soot precursor concentrations. This limitation results in precursor concentrations being too high, and may cause an over-prediction of the soot concentration. In addition to these points, Wen et al. only validated their model for the 1 bar Young flame, and not at higher pressures closer to conditions in a gas turbine combustor [45]. As a result, potential limitations of the model at higher pressures were not investigated. One of the main aims of this study is to address these issues. For example, a more comprehensive chemical mechanism is used to predict PAH formation rates. In addition, coupling measures are introduced for carbon mass moving from the gas phase to the solid phase. As well, the models introduced here have been validated using a high pressure Young flame, in addition to the atmospheric case. Further details regarding these points are provided in the subsequent sections. 21

34 3 Mathematical Formulation This chapter introduces and explains the mathematical equations needed to model the turbulent combustion and soot fields. The first section discusses the modelling of the turbulent reacting flow, the second section discusses the modelling of soot, the third section discusses the radiation model, and the last section discusses source term linearization (a technique used in this work). 3.1 Turbulent Reacting Flows This section presents the mathematical formulations required to model the turbulent fluid dynamics and combustion processes relevant to this thesis Governing Equations For fluid motion in a medium with variable density, the instantaneous conservation equations are presented here in tensor notation [5]. For conservation of mass: where is the density, and is the velocity. + = 0 (3-1) For conservation of momentum: + = + (3-2) = + (3-3) where p is the pressure, is the viscous stress tensor (stress in the i th direction acting on a surface with outward normal in the j th direction), and is the molecular viscosity. 22

35 For conservation of energy: h = (3-4) where T is the temperature, = is the specific internal energy, h = = + / is the specific enthalpy, and is the heat-flux vector, which includes heat loss due to radiation and other sources. For reacting flows, there is also a conservation equation for each species considered in the simulation [45]: + = + (3-5) = (3-6) where is the mass fraction of species i, is the diffusion coefficient of species i, is the mass molecular flux of species i in the j th direction governed by Fick s law, and is the chemical source term (i.e., the rate of formation or destruction of species i). Note that if the flamelet approach is used (as is done in this work), equation (3-5) does not need to be solved. To properly close these equations, two more relationships are required between density, enthalpy, and species mass fraction [45]. First, consider the ideal gas law: = (3-7) where R is the universal gas constant, and is the molecular weight of species i. Second, consider the calorific equation of state: 23

36 h = h (3-8) h = + (3-9) where h is enthalpy, is specific heat at constant pressure for species i, and is the reference enthalpy. The determination of the source term, which couples the species chemistry with the mechanical flow behaviour [45], can now be considered. For a set of RR reactions in a chemical mechanism, which can include participation from N species, we have:, (3-10) where represents each species i, and represent the stoichiometric coefficients of species i in reaction j, and and represent the backward and forward reaction rates for the j th reaction. The chemical reaction rates are typically given in modified Arrhenius form: = exp E (3-11) RT where is referred to as the pre-exponential constant, n is a constant, and E is the activation energy of the reaction. With these definitions, the chemical source term can be calculated as so: = = 1 ( ) ( ) (3-12) (3-13) where = 0 if species i does not participate in reaction j, and where: 24

37 = =, = (3-14) (3-15) Favre Averaged Conservation Equations and k ε Model As covered in section 2.1.1, a computationally efficient method for modelling the conservation equations for turbulent flow is to decompose them into Reynolds and Favre averaged forms [5]. For Reynolds averaging, an instantaneous quantity is broken up into mean and fluctuating components (symbolized by the use of capital lettering or overbar and the prime symbol respectively):, = +, = ( ) +, (3-16) 1 = lim (, ) (3-17) Here, the averaging is performed over a long time span, to remove the random effect of turbulent fluctuations. By definition, the time average of the fluctuating term is zero. To account for large density fluctuations, as occur in combustion applications, Reynolds averaging can be used to break up the density into average and fluctuating parts. However, as a mathematical simplification, Favre averaging can be used to break up relevant flow parameters into their density-weighted average and fluctuating term (symbolized by the tilde and double prime symbol respectively), and thus eliminate density fluctuations from the FANS equations: 25

38 (, ) = ( ) + (, ) (3-18) ( ) = 1 lim 1 (, ) (, ) (3-19) Unlike Reynolds averaging, the conventional time average of the Favre averaged fluctuating term is not zero: = (3-20) Using these definitions, it is possible to derive the Favre averaged conservation equations, presented below [5]: Continuity: Momentum: + = 0 (3-21) + = + (3-22) Energy: h = h + (3-23) The FANS equations introduce correlations between turbulent fluctuations that require modelling, in order to close the equations. The momentum equation is closed by invoking the Boussinesq approximation, which assumes the Reynolds stress tensor ( ) behaves like the viscous stress tensor, and is related to a so-called eddy (or turbulent) viscosity: 26

39 = (3-24) = 1 2 (3-25) where is the turbulent viscosity, k is the turbulent kinetic energy of the velocity fluctuations, and is the Kronecker delta, required to ensure that the Reynolds stress tensor is traceless (like the viscous stress tensor). Prandtl postulated that the turbulent viscosity is related to a turbulent velocity scale, and a turbulent length scale. In the model used for this thesis (the realizable k ε model), these two scales are represented by the turbulent kinetic energy (k), and the turbulent dissipation rate (ε) respectively [4]. = (3-26) In the equation above, is a closure constant, which will be defined below. The turbulence scale terms (k and ε) are determined through postulated, semi-empirical transport equations defined here: + = (3-27) + = (3-28) where is the kinematic viscosity, several closure constants are defined below, and the turbulent dissipation rate is the dissipation rate of turbulent kinetic energy at the smallest scales of turbulence, and is defined as: 27

40 = (3-29) The various closure constants of this model are now presented [4]. For the determination of in the calculation of turbulent viscosity: = 1 + (3-30) = + Ω Ω (3-31) = 4.04, = 6 cos, = 1 3 cos ( 6 ), = (3-32) = 1 2 +, = (3-33) Ω = Ω 2 (3-34) where is the permutation tensor from tensor analysis (unrelated to ε), and is the angular velocity vector. For the determination of the terms required in the k and ε transport equations: 28

41 = 1.44, = 1.9, = 1.0, = 1.2 (3-35) =, = 2 (3-36) =, Pr Pr = = 0.85, = 1 (3-37) = tanh (3-38) = 2, =, = (3-39) where the constants in (3-35) have been chosen such that the model meets certain experimental results, represents the production of turbulent kinetic energy, represents the production of turbulence due to buoyancy, and is related to the turbulent Prandtl number (taken to be 0.85), is the gravity vector component in the i th direction, v is the velocity vector component parallel to the gravity vector, u is the velocity vector component perpendicular to the gravity vector, is the dilatation dissipation term (important in high Mach number flows), is the turbulent Mach number, and a is the speed of sound. In order to close the energy equation, (3-23), three extra correlations must be modelled [5]. The first is the turbulent heat flux vector: = h = = = h (3-40) Pr Pr The molecular diffusion and turbulent transport correlations are generally accounted for in a manner similar to the treatment of viscous and Reynolds stresses: 29

42 = + (3-41) Choice of RANS Model The standard k-ε model was originally proposed in 1972 [46], and since then, several other twoequation models have been proposed. The k-ε models have remained a popular choice for turbulent flow simulations. They are reasonably accurate for a large range of engineering flows, and are generally tuned to the same experimental results that have been used to validate other two-equation turbulence models [5]. Three k-ε models are available: the standard, RNG, and realizable models. The realizable model was chosen for the modelling in this work, because it has been modified to be more consistent with the physics of some turbulent flows, which the other two models do not satisfy. In particular, the realizable model addresses one of the main weaknesses of the standard and RNG models, the plane-jet/round-jet anomaly. This anomaly refers to the ability of these two models to reasonably predict spreading rates for planar jets, but not for round jets. As the realizable model addresses this anomaly with better modelling for the dissipation equation, it is preferred for axisymmetric flows [4] Chemical Mechanism and Kerosene Surrogate Kerosene is a complex fuel consisting of several different hydrocarbon species. Detecting the full array of these species is extremely difficult, and modelling the exact fuel composition is nearly impossible. Further, the exact composition of kerosene can vary depending on the quality or grade of the fuel [45]. Thus, a surrogate mixture of two to three hydrocarbons is generally used to represent the fuel. The surrogate used in this study was proposed by Dagaut et al.; a kerosene mixture consisting of 69% n-decane, 20% n-propylbenzene, and 11% n-propylcyclohexane (by mole). A chemical kinetic mechanism with 263 species, and 2027 reactions was used to model the oxidation kinetics of the surrogate, validated against experimental studies of kerosene in a Jet Stirred Reactor [38]. This mechanism does not describe the formation of large PAHs such as naphthalene (A2), pyrene (A4) or benzo(a)pyrene (A5). Thus, it is important to supplement the mechanism with an appropriate PAH growth mechanism, in order to properly model the species that are important for soot formation. The PAH growth mechanism of Slavinskaya et al. (later enhanced by Dworkin et al.), developed to predict the growth of up to five-ringed aromatic 30

43 species, and validated for methane and ethylene flames, has been selected to enhance the original Dagaut mechanism [47]. This mechanism supplements the original mechanism to a total of 295 species and 2266 reactions. In detailed numerical and experimental studies of laminar kerosene diffusion flames, Saffaripour et al. found that the Dagaut mechanism, supplemented by the PAH growth mechanism of Slavinskaya et al., was able to reasonably predict soot concentrations, compared to other available PAH growth mechanisms [48]. Thus, the choice of using this PAH growth mechanism is considered to be fair. The chemical mechanism file describing the species and reactions used for both the A2 and A5 models (defined below) were created by modifying the mechanisms introduced above. These modifications are presented in CHEMKIN format in Appendix A, and are discussed further in section Laminar Flamelet Model Considering the large number of species and reactions in a typical chemical kinetic mechanism, solving the species conservation equations (3-5) directly in turbulent combustion problems is extremely time consuming from a computational standpoint. As noted in section 2.1.2, one way to simplify this problem, such that the modelling becomes computationally tractable, is to use the laminar flamelet approach. At the core of the flamelet approach is the idea that the instantaneous thermochemical state of a reacting flow (e.g., species mass fractions and temperature) can be related to a conserved scalar called the mixture fraction, f, defined as [4]: =,,, (3-42) where is the elemental mass fraction for element i,, is the mass fraction of element i at the oxidizer stream inlet, and, is the mass fraction of element i at the fuel stream inlet. If the diffusivities of all species are equal a fair assumption in turbulent flow, where turbulent viscosity dominates the definition of mixture fraction is identical for all elements. Thus, the mixture fraction can be thought of as the elemental mass fraction for mass deriving from the fuel 31

44 stream. For a non-premixed system with two streams (fuel and oxidizer), the mixture fraction is, by definition, one at the fuel inlet, and zero at the oxidizer inlet. As was done for turbulent flow variables, the mixture fraction can be broken up into a mean mixture fraction, and a mixture fraction fluctuation: = + (3-43) Assuming that all species have equal diffusivities, the species conservation equation (3-5) can be reduced to one conservation equation for the mean mixture fraction, implemented in ANSYS Fluent as: + = (3-44) where = 0.85 is the turbulent Schmidt number. From this equation, it can be noted that the chemical source term from (3-5) has been eliminated. This is because the mixture fraction equation tracks the conservation of elements, which, unlike species, are always conserved. In addition to the mean mixture fraction, a conservation equation for the mixture fraction variance is solved, to account for the effect of fluctuations on the mixture fraction. + = + (3-45) where the constants used are = 2.86 and = 2.0. As noted in section , the introduction of a strain on the laminar flamelet structure serves to shift the flame away from chemical equilibrium. While the mixture fraction can describe the local equilibrium state, another variable is needed to describe deviations from equilibrium (i.e., the flow field s effect on the flamelet structure). Instead of strain rate, an equivalent variable chosen in laminar flamelet modelling is the scalar dissipation rate (units of 1/s): 32

45 = 2 (3-46) where D is the diffusion coefficient. For a counterflow geometry, the scalar dissipation at the location of the stoichiometric mixture fraction ( ) is given by: = exp 2 (2 ) (3-47) where is the characteristic strain rate, and is the inverse complementary error function. In addition, the mean scalar dissipation at the flame surface (i.e., at = ) can be modelled by: = (3-48) Using these definitions, the transport equations for species and temperature can be re-written in mixture fraction space (independent of physical space) [4]: = (3-49) = , (3-50) where, is the specific heat of species i, is the specific heat of the mixture, is the specific enthalpy of species i, and other quantities have been defined previously. The process of solving these two equations across mixture fraction space is referred to as flamelet generation. As these equations are independent of physical space, this generic step is only required once (although repeated for each value of ). Once the flamelet library is generated it can then be applied to a wide-range of problems. 33

46 After this, the next step is the generation of the PDF look-up tables. A probability density function describing the effect of turbulent fluctuations, using a presumed -PDF function, is used to help calculate the Favre-averaged species mass fractions, temperature, and density: (,, ) = (, ), = (, ) ) ( (3-51) where and are assumed to be statistically independent, such that the PDF can be simplified into two separate terms. can refer to either the temperature, density or species mass fractions. The -PDF function is given by: = 1 1 (3-52) (1 ) = 1 (3-53) (1 ) = (1 ) 1 (3-54) For non-adiabatic systems (such as the one of this work), the effect of enthalpy,, must be considered in these calculations, along with and. Unfortunately, ANSYS Fluent does not account for the effect of enthalpy changes on species profiles (except for the equilibrium solution), as it is considered to be a cumbersome preprocessing step [4]. Consequently, the nonadiabatic PDF look-up tables generated have the following dimensions: (,,, ) (,, ) for the equilibrium solution ( = 0) (,, ) for the non-equilibrium solution ( 0) (,,, ) 34

47 During an iterative solution step, a solution is obtained for, and. The scalar dissipation,, is then calculated using equation (3-48). Using these parameters, the average temperature, species mass fractions, and density are taken from the PDF look-up table. 3.2 Soot Model This section provides the details of the soot models employed for this work Transport Equations Two transport equations are solved for the semi-empirical two equation soot model. Source terms, diffusivities, and absorption coefficients are defined in ANSYS Fluent using User Defined Functions (UDFs) [4]. The first transport equation is for the soot mass fraction: + = + (3-55) = = (3-56) where is the soot mass fraction (kg-soot/kg-mixture), is the source term for soot mass (kg/m 3 -s), and is the turbulent Schmidt number (ratio of turbulent viscosity to diffusion), taken as The second transport equation is for the primary particle number density: + = + (3-57) where is the soot number fraction (particles/kg-mixture), is the source term for soot number density (particles/m 3 -s), and is the turbulent Schmidt number, again taken as The source terms in the above equations are taken as a summation of source terms for several individual processes: 35

48 = + = (3-58) (3-59) where inc refers to inception, sg refers to surface growth, ox refers to oxidation, and coag refers to coagulation Soot Source Term The individual components of the soot source terms introduced above are defined here Inception Two different inception models are considered. The first, referred to as the A2 model, uses the rate of formation of a two-ringed aromatic (naphthalene/c 10 H 8 ) as the basis for the inception rate. The second, referred to as the A5 model, uses the rate of formation of three five-ringed aromatics (Benzo(a)pyrene / BAPYR / C 20 H 12, BAPYR*S / C 20 H 11, and Benzo(ghi)fluoranthene / BGHIF / C 18 H 10 ) as the basis for the inception rate. The A2 model considers soot inception to be equal to the rate of formation of A2 (i.e., naphthalene) given by the chemical mechanism, multiplied by a factor of 15. The multiplication factor is required for the soot prediction to be on the same order of magnitude as the experimental results, and is explored further in Chapter 5. Put mathematically: = 15 (3-60), = 15, (3-61) where is the rate of formation of A2 (kmol/m 3 -s) as determined by 18 reactions in the chemical mechanism, and presented in full in Appendix B. is the molar mass of carbon (12 kg/kmol), is the number of carbon atoms in an A2 molecule (10), is Avogadro s number (6.022*10 26 atoms/kmol), and is the minimum number of carbon atoms in a soot particle. A 36

49 variety of values have been used for in the literature. For example, Chai [49] used a value of 12 in his study of a turbulent methane/air flame, Young and Moss [50] used a value of 12 for a turbulent ethylene/air flame, Wen [45] used a value of 200 for his simulation of the 1 bar Young flame, and Kennedy [51] used for a laminar ethylene/air flame. For this work, = 60 has been used, as per the value used by Woolley et al. [52]. This value has been chosen as it is close to values used for other turbulent flames, and to preserve consistency with the oxidation model of Woolley et al., which has also been used for this work. Note that the oxidation model is affected by the value of, as this parameter affects the surface area of soot particles by influencing the soot number density. The A5 model considers soot inception to be equal to the rate of formation of three five-ringed aromatics (BAPYR, BAPYR*S and BGHIF). Unlike the A2 model, this model does not require the formation rate to be multiplied by a tuning factor in order for the soot prediction to be on the same order of magnitude as the experimental results (explored further in Chapter 5): =, = (3-62) =, = (3-63) where is the rate of formation of A5 (presented in Appendix B), is set to 20, and the formation rate of BGHIF is multiplied by 0.9 to account for the difference in carbon atoms in BGHIF versus BAPYR and BAPYR*S (18, 20 and 20 respectively). In a study of PAH and soot formation in turbulent non-premixed ethylene flames, D Anna et al. [53] found that the concentrations of PAHs, unlike the concentration of soot, correlate well with mixture fraction (independent of flame position). Thus, the use of the flamelet approach, to 37

50 predict soot precursor concentrations for the inception rates introduced here, is considered reasonable. Note that by using this approach, the inception rate becomes tied to the PAH condensation rate (as the formation of large PAHs influences both the inception and PAH condensation processes) Surface Growth Surface growth via acetylene is considered via the H-abstraction C 2 H 2 -addition (HACA) process described in section and in [25]. The HACA mechanism is outlined in the following table: Table 3-1: HACA mechanism for soot surface growth [25], =. No. Reaction A b E a :,,, ( / ) S S2 + + O S S S The HACA process describes chemical reactions on the surface sites of a soot particle, using sites with carbon atoms that are either dehydrogenated ( ) or saturated ( ). The ratio of reactions contributing to soot growth by creating sites to reactions taking away from soot growth by destroying sites, can be used to determine the surface growth rate via acetylene (i.e., forward rate of S4) in grams/cm 3 -s [25]: 38

51 = [ ] (3-64) where forward reaction rates are denoted by SN (for N=1, 2 5 reactions), and reverse reaction rates are denoted by RevSN. The parameter is the fraction of surface sites available to take part in a given reaction, and is taken to be equal to the maximum value of 1.0 for this study. This is further explained in section The concentration of sites can be determined in mole/cm 3 by: = (3-65) where refers to the number of saturated sites per surface area of soot (set to a constant 2.3*10 15 sites/cm 2 [25]), and is the surface density of soot particles (cm 2 /cm 3 ) determined by [52]: = (3-66) 6 = (3-67) where is the diameter of a single primary particle, is the density of the mixture, and is the density of soot, set to 1800 kg/m 3 [17]. In this work, surface growth via the addition of PAHs to the surface of soot particles is considered to be captured by the inception rate (as it is linked to the overall formation rate of a bottleneck PAH species). Thus, only surface growth via acetylene is explicitly defined here. 39

52 Oxdiation Oxidation of soot particles via O 2 and OH radicals is modelled using semi-empirical formulations developed by Woolley et al., and validated for turbulent methane and propane flames [52]: = + (3-68) where the reaction rate constants are shown in the following table: Table 3-2: Reaction rate constants for soot oxidation in Arrhenius form [52], =. Reaction A b T a :,,, ( ) Coagulation The coagulation and coalescence of soot particles decreases the particle number density, and is modelled using the following expression [52]: = (3-69) where is the Boltzmann constant (1.38*10-23 J/K), and is the agglomeration constant, which ranges from 3-9 [54] [55]. In this work, = 9 has been used Coupling As noted previously, one of the shortcomings of the flamelet approach is the inability to account for the mass transfer of carbon atoms between soot particles and the gas phase. In section 2.5.2, 40

53 it was noted that this may have been a factor in the over-prediction of soot emissions by previous models in gas turbine combustors. The model presented here attempts to account for this by introducing coupling to the inception and surface growth models. With respect to the inception model, coupling is added by turning the PAH tied to inception (either A2 or A5) into a carbon sink in the flamelet library. First, the chemical mechanism is modified such that either A2 or A5 is the largest PAH in the mechanism (i.e., in the case of A2, larger PAHs such as A3, A4 and A5 are removed from the mechanism entirely). Second, all reactions forming this PAH in the mechanism are made unidirectional, and oxidation reactions for this PAH are removed entirely. Figure 3-1: Coupling of inception model. Referring to Figure 3-1, the formation rate of this PAH (using the concentrations of its precursor species) is used as the formation rate of soot. Utilizing unidirectional reactions and removing oxidation reactions for A2 or A5 effectively increases the concentration of A2 or A5 to unrealistically high levels. However, this modification is considered acceptable as these two PAHs are able to act as a carbon sinks for soot in the flamelet library. As a result, the concentration of the soot precursors used to form A2 or A5 is reduced to more realistic levels. Using these more realistic formation rates, the soot inception rate can be calculated in the soot UDF. In other words, the formation rate of the modified A2 or A5 species (calculated using the more realistic precursor concentrations) and the inception rate of soot are considered to be equal, as shown in the figure above. With respect to the surface growth model, coupling is added by tracking the amount of acetylene added to soot via the HACA mechanism using a transported scalar: 41

54 + = + (3-70) where is the mass fraction of acetylene added to soot, and is the surface growth rate via the HACA mechanism. The surface growth rate presented in (3-64) is then modified such that the concentration of acetylene added to soot is subtracted from the flamelet value of acetylene: = 2 ( ) ( ) + [ ] (3-71) where = 0 if < 0. Note that this method does not modify the amount of acetylene predicted by the flamelet model. Rather, only the amount of acetylene considered for potential addition to soot in the surface growth model is adjusted. The idea to adjust the amount of acetylene given by the flamelet model via a transported scalar (to account for soot growth) was originally proposed and implemented for a turbulent ethylene-air flame simulation by Khalilian [56]. 3.3 Radiation Model High temperature molecules and soot particles are capable of emitting electromagnetic radiation in different directions, increasing heat transfer out of the combustion zone, and thus reducing flame temperatures. 42

55 The radiative heat flux vector can be expressed by [41]: = 4 (3-72) =, +, (3-73) where is the local temperature, is the ambient temperature, is the Stefan-Boltzmann constant (5.67*10-8 W/(m 2 -K 4 )), and is the absorption coefficient (broken up into the absorption coefficient of soot, and the absorption coefficient of the N gas phase species). As the largely-broadband radiation from soot dominates in this type of flame, it is generally appropriate to use spectral average values such as the Planck-mean absorption coefficient for [57] [58]. For soot, the Planck mean absorption coefficient is given by [59]:, = 3.83 / (3-74) = (3-75) where is the soot volume fraction, = is the second Planck function constant, and is a spectrum-dependant constant. A spectral-averaged value of = 5.0 has been employed in this work, using plots in [59], which are attributed to three different studies conducted on propane combustion generated soot [60][61][62]. For gas phase species, the two most important radiating species (and the only two considered in this model) are H 2 O and CO 2, for which the Planck-mean absorption coefficients have been determined from the 2003 Sandia Workshop, and are presented here [63]: 43

56 , =, +, (3-76) = (3-77) where and are the partial pressures of H 2 O and CO 2 in atmospheres, T is the temperature in K, and the coefficients to are curve fit parameters generated for temperatures between 300 K to 2500 K, and are shown in the following table: Table 3-3: Curve fit parameters for H 2 O and CO 2 Planck-mean absorption coefficients [63] H 2 O CO E With respect to implementation, the Discrete Ordinance (DO) model has been used to model radiation in ANSYS Fluent, with absorption coefficients for both species and soot being defined via UDFs. The DO model is particularly attractive, as it does not assume anything about the optical thickness (i.e., translucence) of the environment, unlike other available models [4]. A gray DO model has been implemented, which means that average values are used for the spectrum dependant parameters such as the absorption coefficient. For more information about the DO model, refer to [4], and [64]. 44

57 3.4 Source Term Linearization Source term linearization is a technique used by ANSYS Fluent to enhance the stability of its solver, and has been utilized to help convergence for the user defined transported scalars [65]. This technique increases stability by increasing the diagonal terms of the solution matrix, and requires the source term to be represented in the following way: = + (3-78) where S is the source term, is the transported scalar, A is the explicit (or constant) component of the source term, and B is the implicit (or active) component of the source term which varies linearly with the scalar. The actual source term,, is then calculated in the following way, based on the previous value of the transported scalar, : = + (3-79) While the explicit component is constant, the implicit component must be defined at each iteration step. ANSYS Fluent uses the Newton-Raphson method (as proposed by Patankar) to calculate the implicit component (based on the source term s Taylor series expansion) [66]: = + = + (3-80) where is the partial derivative of the source term with respect to the scalar. Then, the actual source term, explicit term, and implicit terms can be defined as: = + (3-81) = (3-82) = (3-83) 45

58 4 Model Description This chapter provides further details regarding the experimental set up of the Young et al. flames[40], and outlines the specific details regarding the implementation of the models used to simulate these flames. 4.1 Overview The experimental apparatus of Young et al.[40] is shown in Figure 2-9. The Young flames are confined within a boroscilicate glass tube with a diameter of 155 mm, which is mounted in a pressure casing designed to withstand an operating pressure of up to 17.5 bar. The burner comprises of a 1.5mm diameter nozzle, surrounded by a 0.25 mm coaxial annular slot. An ethylene-oxygen premixed pilot flame is burned on the annular slot to rim-stabilize the kerosene flame. The kerosene is preheated in a prechamber heated to roughly 800 K, and is then flashevaporated to be discharged from the burner nozzle at around 600 K [40]. The thickness of the fuel nozzle is not reported, and is estimated to be 0 mm (i.e., negligible) for these simulations [67]. It should be noted that the numerical simulation does not include the pilot flame s effect on the kerosene flame. This may cause a slight under-prediction of temperature close to the fuel inlet, affecting soot inception rates in that region, and hence affecting the overall soot prediction [41]. Detailed spatial measurements of mean temperature, mean mixture fraction, and mean soot volume fraction are provided in [40] and [67]. Temperature measurements were made via fine wire thermocouple (50 µm diameter), using a mean radiation correction to account for heat transfer with the chamber walls at an assumed temperature of 600 K. Mixture fraction measurements were made via quartz microprobe sampling and mass spectrometric analysis. Finally, soot volume fraction measurements were made via He-Ne laser absorption. For further information regarding the experimental apparatus and measurement techniques employed by Young et al., refer to [40] and [67]. The geometry of the CFD domain is shown in Figure 4-1. The fuel inlet stream consists of vaporized, preheated kerosene discharging from the 1.5mm diameter nozzle, and the oxidizer inlet stream consists of room temperature air discharging from the remaining 155mm diameter 46

59 combustor area. The total combustor height has been reduced to 600mm, as the experimental flame heights and soot measurements lay well within this region. Figure 4-1: CFD geometry (not to scale). This axisymmetric geometry has been implemented as a 90 degree circular wedge with symmetry conditions on its two sides, as shown by the computational mesh and geometry shown in Figure 4-2 and Figure 4-3. The mesh has been generated by ANSYS Fluent s meshing software, and includes 316,265 nodes and 1,818,294 elements. Increased grid refinement has been implemented in the regions surrounding the fuel nozzle and the inner regions of the combustor. The average orthogonal quality of the mesh (i.e., the degree with which elements are positioned at right angles to each other) is 0.866, with a standard deviation of The modelling of this axisymmetric flow via three dimensional circular wedge geometry was also used by Wen et al. [41]. Such a geometry is used to account for the inherently three dimensional nature of turbulence [5]. However, a smaller circular wedge could have been used to help reduce the time required for computations. For example, Wen et al. [41] used a 15 degree wedge. 47

60 Figure 4-2: CFD model, computational mesh in metres. 48

61 Figure 4-3: CFD model, circular wedge geometry. As indicated in Chapter 3, the following modelling techniques have been used for the major model subcomponents: Fluid Turbulence: Realizable k-ε model. Species Chemistry: Non-adiabatic, steady, laminar flamelet model. Radiation: Discrete ordinance model. Soot: Three transport equations are solved for soot mass fraction, soot particle number density and acetylene consumption. The degree of coupling between these subcomponents is indicated in Figure 4-4. Here, information is transmitted between subcomponents via arrows. Full arrows indicate that information is transmitted fully (i.e., full coupling), and dashed arrows indicate that information is only partially transmitted in the direction of the arrow (i.e., partial coupling). For example, the radiation submodel fully receives all of the information it requires to calculate the absorption coefficient (i.e., species, pressure, temperature and soot volume fraction); hence, a full arrow is used from all other subcomponents. However, as indicated above, the laminar flamelet submodel 49

62 used by ANSYS Fluent only updates species mass fractions based on enthalpy changes, from the energy / radiation submodel, in the case of an equilibrium situation (i.e., = 0); hence, a partial arrow is used, although temperature and density are fully coupled to energy / radiation. Furthermore, while measures have been introduced to couple the soot model to the species chemistry predicted by the laminar flamelet model, this is only a partial coupling. Full coupling of these two submodels would require the direct solution of the species mass fraction conservation equations of (3-5), with modifications to the chemical source terms to account for the formation and oxidation of soot particles. Figure 4-4: Degree of coupling between the different model subcomponents Two Young flames are considered here (see Table 2-2): the first at a pressure of 1 bar (referred to as Flame A), and the second at a pressure of 4.81 bar (referred to as Flame E). While Young et al. s Flame F represents the highest pressure at 6.4 bar, it was indicated that they were unable to measure the peak soot volume fraction at this pressure, due to the heavily sooting nature of the flame [40]. Thus, this flame has not been chosen for modelling in this work. For flames A and E, both the A2 and A5 inception model are implemented, and the results compared. 50

63 4.2 Boundary Conditions The boundary conditions for the 1 bar and 4.8 bar cases are presented in Table 4-1 and Table 4-2 respectively. Some properties such as turbulent intensity and turbulent length scale, which were not measured experimentally, have been estimated here using the experimental geometry of the flame, and values employed in previous modelling studies [41]. The velocity profiles of the fuel and air streams are assumed to be uniform. Table 4-1: Boundary conditions for the numerical model of the 1 bar Young flame. Fuel Air Temperature [K] Velocity [m/s] Inlet Turbulent Intensity 5% 3% Turbulent Length Scale [m] Mixture Fraction 1 0 Outlet Wall Pressure = 1 bar Adiabatic, Log-Law, Smooth 51

64 Table 4-2: Boundary conditions for the numerical model of the 4.8 bar Young flame. Fuel Air Temperature [K] Velocity [m/s] Inlet Turbulent Intensity 5% 3% Turbulent Length Scale [m] Mixture Fraction 1 0 Outlet Wall Pressure = 4.8 bar Adiabatic, Log-Law, Smooth 4.3 UDF Implementation ANSYS Fluent allows for the implementation of user defined functions, written in the C programming language, in order to expand the scope of modelling efforts beyond the standard features available. A variety of UDFs were required to implement the A2 and A5 model, and they are provided in full in Appendix C. A brief description of each type of UDF used is presented here. For an in depth overview of ANSYS Fluent UDFs, refer to the ANSYS Fluent UDF Manual [65]. Note that all UDFs must be coded in SI units Define Source Define source UDFs allow for the specification of custom source terms for any of the transport equations solved by ANSYS Fluent. For example, such a UDF can be used to define custom source terms for the energy equation or the turbulent transport equations. In the case of the work presented here, three define source UDFs have been used to define the source terms for three user defined scalars (UDSs) - mass_soot.c, num_soot.c, mass_c2h2.c in Appendix C. These UDSs describe the soot mass fraction, soot primary particle number density, and acetylene added 52

65 to soot mass fraction. The rates for these source terms have been defined as presented in section 3.2.2, and have been specified in SI units. Source terms linearization has been implemented as per section 3.4, to ensure a well-behaved solution (in particular, to ensure that mass fractions lie between 0 and 1) Define Absorption Several UDFs can be used to define the absorption coefficient for the radiation model. The specific one used here is DEFINE_WSGGM_ABS_COEFF (myabs.c), which defines the absorption coefficient for the weighted-sum-of-gray-gases (WSGGM) model. ANSYS Fluent allows for the specification of both gas and soot absorption coefficients with this UDF. However, this model uses custom functions to define soot formation (not ANSYS Fluent s built-in soot models). For this reason, the soot absorption coefficient formally used by ANSYS Fluent is not defined, and the value of the soot absorption coefficient has been added to the gas phase absorption coefficient Define Diffusivity Define diffusivity UDFs allow for the specification of custom diffusivities for species or UDS transport equations. For the work presented here, one define diffusivity UDF (mydiff.c) has been used to define the mass diffusivity of the three UDSs for soot. These diffusivities have been defined using a Schmidt number of Define Adjust A define adjust UDF has been written to limit the values of the UDSs (i.e., mass fractions and number density) to positive values (limit_uds.c). In originally solving for these scalars, it was found that the numerical solution allowed for the existence of small, negative numbers, which are not physically possible (and could potentially cause convergence problems). Thus, this UDF loops through the solution field, and sets any negative value to zero. 4.4 Parallel Computing In order to hasten the convergence of the numerical simulations required for this work, parallel computing has been employed. For the A2 model, computations have been performed using 53

66 ANSYS Fluent version 14, with up to 36 cores, on the High Performance Computing Virtual Laboratory (HPCVL) computing cluster, a member of the Compute Canada group of HPC consortia. The A5 model requires the use of ANSYS Fluent version 15, to overcome limitations imposed on PDF table generation by version 14. Specifically, version 14 generates the PDF table with a maximum of 100 species from the flamelet library, chosen on the basis of highest mass fractions. Version 15 removes this restriction, by allowing all of the species from the flamelet library to be included in the PDF table. While all of the necessary soot precursor species were included in the top 100 species for the A2 model, some were missing for the A5 model, therefore necessitating the use of version 15. Currently, ANSYS Fluent version 15 is not available on HPCVL, and thus computations for the A5 model have been performed on a desktop computer with 4 cores. As a result of the lack of computational resources currently available for the A5 model, some of the simulations presented in the next chapter have only been performed for the A2 model. 54

67 5 Results and Discussion In this chapter, the results of the A2 and A5 model are discussed, first for the 1 bar flame, and then for the 4.8 bar flame. The final subsection of this chapter includes a discussion on convergence and the computational cost of the model. 5.1 Flame A: 1 Bar In this section, the modelling results for the 1 bar flame simulation are discussed. In the first subsection, important contour plots for the A2 and A5 models are presented, and the differences between the two models are discussed. In the second subsection, the modelling results are compared to experimental data. In the third subsection, the effects of the coupling measures introduced previously are discussed. Finally, in the fourth subsection, the effect of HACA growth on the modelling results is shown Flame Structure, Species and Soot Fields The soot volume fraction and soot number density fields for both models are shown in Figure 5-1 and Figure 5-2. The overall soot volume fraction field for the A5 model is shifted higher up in the flame, consistent with the idea that larger PAHs form higher up in the flame. The amount of soot formed is larger for the A5 model than the A2 model, despite the former model requiring an enhanced inception rate (rate is multiplied by 15 for the A2 model, whereas no multiplicative factor is used for the A5 model). This difference is explored further in the next section. 55

68 Figure 5-1: 1 bar soot volume fraction (A2 left, A5 right) The overall transport of a soot particle through the flame can be described by these figures. Early on, in the lower regions of the flame where soot inception is dominant, there exists a high soot number density. As these incipient soot particles grow and merge together, the overall number density goes down, even though the soot volume fraction increases. Where the peak soot volume fraction is reached, the oxidation rate begins to exceed the formation rate (due to higher levels of O 2 and OH in the higher regions of the flame), and the amount of soot decreases. Interestingly, the soot number density peaks on the flame wings, while the soot volume fraction peaks on the flame centreline. The implication is that either that soot inception is dominant on the wings of the flame, and soot particles tend to diffuse to the flame centreline as they coalesce and move upwards, or that the centreline particles are formed largely as a result of surface growth. As will be shown in section 5.1.4, the former implication is causing this effect, as surface growth through HACA for this flame was found to have a minimal impact. Further, the figures show that the A2 model s soot number density field is shifted more towards the flame wings than that of the A5 model. Figure 5-2: 1 bar soot number density (A2 left, A5 right) 56

69 The soot mass and number density fields can be used to calculate the diameter of the soot particles via equation (3-67). This is shown in Figure 5-3 for both the A2 and A5 models along the centerline. Although particle diameters were not measured experimentally, the peak diameters shown in the figure (~25-35 nm) are consistent with experimental studies on the structure of soot [15]. The location of the peak diameter shifts due to using A5 instead of A2 as the PAH tied to inception. The particle diameter plot for the A5 model shows a cusp at ~50 mm along the centreline. This cusp occurs because three different species are tied to soot inception. Comparing mass fractions, the peak for BGHIF and BAPYR*S occur at ~30 mm above the peak of BAPYR along the centreline. As a result, there are two distinct peaks in the soot number density along the centreline, which causes the cusp behaviour shown below. Contour plots of BAPYR, BAPYR*S and BGHIF are shown further below in Figure 5-10, while a contour plot of the soot number density field is shown above in Figure A5 Model A2 Model Primary Particle Diameter [nm] Distance Along Centreline [mm] Figure 5-3: 1 bar flame. Soot particle diameters along the centerline. 57

70 The mixture fraction and temperature fields are strongly tied to the soot field, and are shown in Figure 5-4 and Figure 5-5. Referring to Figure 5-5, the flame of the A2 model clearly burns hotter than that of the A5 model. This is due to the latter model generating a greater amount of soot, which results in more heat loss due to radiation. This hotter temperature field implies an increase in convective processes, which shifts the mean mixture fraction field higher in the flame for the A2 model relative to the A5 model. As a result, from Figure 5-4, it can be noted that the stoichiometric mixture fraction of 0.06 occurs at a height of approximately 320 mm on the centreline for the A2 model, and 260 mm on the centreline for the A5 model. Figure 5-4: 1 bar mean mixture fraction (A2 left, A5 right) Figure 5-5: 1 bar temperature [K] (A2 left, A5 right) The mass fraction contours of OH and O 2 are shown for both models in Figure 5-6 and Figure 5-7. These species play an important role in the soot oxidation process [27] [28]. Comparing both models, it can be noted that the OH and O 2 contours are similar in terms of peak magnitude 58

71 and overall shape. However, the overall contours are shifted higher for the A2 model, due to the differences that exist in the temperature and mixture fraction fields (ultimately resulting from different radiative heat losses due to the different amounts of soot produced by the two models). Figure 5-6: 1 bar OH mass fraction (A2 left, A5 right) Figure 5-7: 1 bar O 2 mass fraction (A2 left, A5 right) The mass fraction contours of C 2 H 2, and C 6 H 6 are shown in Figure 5-8 and Figure 5-9. These hydrocarbons are generally considered to be important in the growth of soot [10] [52]. From the contours of C 2 H 2 (acetylene), the acetylene mass fractions are an order of magnitude greater with the A5 model than with the A2 model. This difference implies that more acetylene is fed into the A2 carbon sink (mass accumulated from soot inception) in the flamelet library than is fed into the A5 carbon sink. That is to say that reactions forming A2 use up more acetylene mass than reactions forming A5. This is separate from acetylene growth due to HACA, as that process is handled by a separate transport equation. However, comparing the contours of C 6 H 6 (benzene), it 59

72 can be noted that the benzene mass fraction is two orders of magnitude lower for the A5 model than it is for the A2 model. This disparity means that more benzene mass is fed into the A5 carbon sink through reactions forming A5 than is fed into the A2 carbon sink through reactions forming A2. Therefore, relative to each other, the A2 model relies more on acetylene to form soot, while the A5 model relies more on benzene. Figure 5-8: 1 bar C 2 H 2 mass fraction (A2 left, A5 right) Figure 5-9: 1 bar C 6 H 6 mass fraction (A2 left, A5 right) Finally, the mass fractions of the carbon sinks for the two models (i.e., naphthalene for the A2 model, and BGHIF, BAPYR and BAPYR*S for the A5 model) are shown in Figure As would be expected for this highly sooting flame, the peak mass fractions are very high. It can be noted that the mass fraction field of BAPYR*S is relatively small, since only one reaction for this carbon sink is included in the chemical mechanism (see Appendix B). Curiously, the peak mass fraction for the A2 model is particularly high at 0.23, even though the peak soot mass fraction (n.b., not volume fraction) is This disparity can be explained by observing spatial distributions within the flame (i.e., the mean mixture fraction at the location of these peaks 60

73 differs greatly). At the location of peak A2, the mean mixture fraction is , while at the location of peak soot, the mean mixture fraction is Figure 5-10: 1 bar flame. Mass fractions of carbon sinks for the A2 and A5 models. From left to right: A2 (naphthalene), A5 (BGHIF), A5 (BAPYR), and A5 (BAPYR*S) Comparison with Experiment Figure 5-11, Figure 5-12, and Figure 5-13 show the comparison of the experimental and numerical mean mixture fraction, temperature, and soot volume fraction along the centreline for the 1 bar Young flame [67], respectively. For comparative purposes, the results of the PAH model of Wen et al. [41] (described in section 2.5) are also included. Note that the model of Wen et al. used a different kerosene surrogate and smaller chemical kinetic mechanism than the models described here, and slight differences in the mixture fraction field was predicted by these models. Further, while Wen et al. used an adiabatic flamelet library, the models described here use non-adiabatic libraries, which can update species and temperature profiles based on the amount of radiative heat loss generated from soot [41]. Despite these points, some important qualitative observations can be made with this comparison. 61

74 1 0.9 Experimental Wen et al. A2 Model A5 Model Mean Mixture Fraction Axial Distance Along Centreline [mm] Figure 5-11: 1 bar flame. Mean mixture fraction versus axial position along the centerline. Experimental data: [67]. Wen et al.: [41]. Considering the mean mixture fraction along the centreline, the three models appear to show good agreement with the experimental results (considering potential uncertainties), indicating that the transport of species, including important soot precursors, is well modelled. Differences between the numerical and experimental values are due to differing levels of soot (which affects radiative heat loss and consequently mixture fraction), uncertainties in the chemical mechanisms employed, uncertainties in the flamelet approach, uncertainties in the experimental results, and inconsistencies in the inlet boundary conditions used for the fuel and oxidizer stream (e.g., a slightly different mass flow of fuel could have been supplied to the combustor in the experiment than in the numerical model). Note that the model of Wen et al. used an adiabatic flamelet library, and therefore was unable to account for the effect of radiative heat losses on the mean mixture fraction profile [41]. 62

75 Temperature [K] Experimental Wen et al. A2 Model A5 Model Distance Along Centreline [mm] Figure 5-12: 1 bar flame. Temperature versus axial position along the centerline. Experimental data: [67]. Wen et al.: [41]. Considering the temperature along the centreline, the A5 model and the model of Wen et al. provide the best agreement with the experimental results in terms of the temperature magnitude. However, the location of the peak temperature appears to be under-predicted by all models. This under-prediction can be attributed to two factors. First, the location of the peak soot volume fraction is under-predicted for all models (as seen in Figure 5-13), which results in the radiative heat loss due to soot occurring lower in the flame than in the experiment. This factor is also the cause of the over-prediction of temperature by the A2 model; since the soot volume fraction field at the location between 200 mm and 400 mm is negligible, almost no radiative heat loss occurs, as opposed to what occurs in the experiment. Second, as a minor effect, differences in the numerical and experimental temperature fields may occur due to the use of spectral-averaged absorption coefficients for all three models (instead of breaking down the absorption coefficient into different values for different wavelengths) [45]. 63

76 2.00E-05 Experimental Wen et al. (A2/A3) (inception rate x8) A2 Model (inception rate x15) A5 Model (inception rate x1) 1.50E-05 Soot Volume Fraction 1.00E E E Distance Along Centreline [mm] Figure 5-13: 1 bar flame. Soot volume fraction versus axial position along the centerline. Experimental data: [67]. Wen et al.: [41]. Considering the soot volume fraction along the centreline, three important points will be discussed below. As a first point, it is noted that the model of Wen et al. [41] appears to predict smoking behaviour (i.e., soot volume fraction does not go to zero), while the models introduced in this study do not. The experimental evidence does not elaborate on soot volume fractions above 400 mm, although they appear to be decreasing. As the focus of this study is not on oxidation, this has not been investigated further. As a second point, it can be noted that to predict the correct order of magnitude for the soot volume fraction, the model of Wen et al. [41] and the A2 model required the PAH-based inception rate to be multiplied by a tuning factor (8 for the model of Wen et al. [41], 15 for the 64

77 A2 model, no factor for the A5 model). Note that the tuning factor for the A2 model has only been selected to obtain the correct order of magnitude for the soot volume fraction, such that the temperature field is correctly predicted. Neither the A2 model nor the A5 model matches the magnitude of the peak experimental soot volume fraction exactly. With this in mind, Figure 5-14 and Figure 5-15 show the temperature and soot volume fraction predictions respectively for the untuned A2 model, where that the soot field is under-predicted by more than one order of magnitude (note the two scales for the vertical axes). This major disparity necessitates a tuning factor for the A2 model Temperature [K] Experimental Untuned A2 Model Distance Along Centreline [mm] Figure 5-14: 1 bar flame. Temperature versus axial position along the centerline for the untuned A2 model. Experimental data: [67]. 65

78 Untuned A2 Model Experimental Soot Volume Fraction (untuned A2 model) 7.00E E E E E E E E E E E E E E E E E E E Distance Along Centreline [mm] Soot Volume Fraction (experiment) Figure 5-15: 1 bar flame. Soot volume fraction versus axial position along the centerline for the untuned A2 model. Experimental data: [67]. Referring back to Figure 5-13 and comparing the tuned A2 model with the model of Wen et al. [41], it can be observed that the A2 model requires a larger tuning factor than the model in [41] (15 versus 8). One reason for this disparity is the introduction of carbon mass coupling measures for the models described here, which serves to effectively decrease the available mass of soot precursors as they are consumed for the A2 model relative to the model in [41]. Another reason is the choice of PAH tied to soot inception. The inception rate employed by Wen et al. [41] used formation rates of PAHs that are spatially coincident or larger than A2 (C 10 H 7 /A2- and C 14 H 10 /A3). Larger PAHs are generally stronger drivers of soot inception as they contain more carbon mass, since they are formed from smaller PAHs such as A2 through reactions with relatively abundant smaller species such as C 2 H 2. This observation was the impetus for attempting numerical simulations with the A5 model (i.e., with the largest PAHs available in the chemical mechanism employed here). Based on the modelling results, it was found that the A5 model requires no tuning for the inception rate to predict the correct order of magnitude of the soot volume fraction (as shown in Figure 5-13 above). Since the A5 model does not require 66

79 tuning, it can be noted that the modified A5 species contains enough carbon mass to act as a proper carbon sink in the flamelet library. As a third point, all three of the models discussed here predict the location of peak soot to be lower in the flame than experiments show (~200 mm for the A2 model, ~180 mm for the A5 model and ~100 mm for the model in [41]). Conceptually, larger PAHs should be able to indicate the location of peak soot better, as they are formed farther up in the flame than smaller PAHs. However, comparing the A2 and A5 model, the location of peak soot does not appear to change appreciably. This may be due to A5 only being formed marginally higher than A2 in this particular flame. However, one major disadvantage of the flamelet approach is its poor ability to capture the slow chemistry effects [4] [7], which would include the formation of larger PAHs and soot. This shortcoming may cause the larger PAHs in the numerical model to be formed closer to the burner than in reality. One way to address these slow chemistry interactions would be to simulate the formation rates of the larger PAHs in the model via transport equations, in a similar manner to how acetylene added to soot is tracked in this model. This approach has very recently been used by Xuan and Blanquart [68] in simulations of a turbulent non-premixed ethylene/air flame, and was shown to delay the formation of PAHs and consequently soot, effectively shifting the location of peak soot higher up in the simulated flame. Curiously, the model of Wen et al.[41], which tied inception to A2 and A3, predicted peak soot to be higher up in the flame than the A2 and A5 models. This difference may be due to the model in [41] being fundamentally different from the A2 and A5 models in a few ways. First, from Figure 5-11, it can be noted that the model of Wen et al.[41] predicted the mean mixture fraction well in the lower region of the flame, while slightly over-predicting it higher in the flame. By contrast, the A2 model and to a lesser extent the A5 model presented here under-predicted the mean mixture fraction lower in the flame, while predicting it well higher in the flame. This under-prediction would affect soot inception rates, which are important in the fuel rich lower regions of the flame. Second, there are differences with the flamelet generation techniques employed Wen et al. developed a custom flamelet generator for their model [45], while the models here use ANSYS Fluent s blackbox flamelet generator [4]. Third, as noted above, Wen et al. used a different kerosene surrogate, and a smaller chemical kinetic mechanism, which would have an influence on the results (particularly the flamelet library). Related to this point, 67

80 Wen et al. considered the growth of A2 and A3 to be tied to only phenyl radicals, benzene, and acetylene (as described in section 2.5.1). In reality, several other species could contribute to the growth of these PAHs (as shown by the reactions governing A2 and A5 formation in Appendix B). Moreover, as noted before, Wen et al. used an adiabatic flamelet library (unlike the models described here), and was unable to account for the effect of radiative heat losses on the temperature and species profiles. Finally, fundamental modelling studies have shown that OH oxidation rates can have a moderate effect on the location of peak soot [69], as OH radicals are generally more abundant in fuel rich regions. The models described herein use a different oxidation model than the one of Wen et al., which could cause a slight shift of the peak soot location. The radial plots of mean mixture fraction, temperature and soot volume fraction are shown at heights of 100 mm and 300 mm above the inlet below. As mentioned above, differences between the A2 and A5 models and the experimental results are primarily due to differences in the predicted soot volume fraction field, and the associated differences in radiative heat losses. Mean Mixture Fraction 4.00E E E E E E E E-02 Experimental A2 Model A5 Model Mean Mixture Fraction 1.00E E E E E E E E E E-02 Experimental A2 Model A5 Model 0.00E Radial Distance [mm] 0.00E Radial Distance [mm] Figure 5-16: 1 bar flame. Mean mixture fraction versus radial position at 100 mm (left) and 300 mm (right) above the inlet. Experimental data: [67]. 68

81 Experimental A2 Model A5 Model Experimental A2 Model A5 Model Temperature [K] Temperature [K] Radial Distance [mm] Radial Distance [mm] Figure 5-17: 1 bar flame. Temperature versus radial position at 100 mm (left) and 300 mm (right) above the inlet. Experimental data: [67]. 2.00E E E-05 Experimental A2 Model (inception rate x15) A5 Model (inception rate x1) 2.00E E E-05 Experimental A2 Model (inception rate x15) A5 Model (inception rate x1) Soot Volume Fraction 1.40E E E E E-06 Soot Volume Fraction 1.40E E E E E E E E E E Radial Distance [mm] -4.07E Radial Distance [mm] Figure 5-18: 1 bar flame. Soot volume fraction versus radial position at 100 mm (left) and 300 mm (right) above the inlet. Experimental data: [67]. Considering the points made above, the A5 model is considered to be a good candidate for simulations in gas turbine combustors. In particular, the ability to reasonably predict the 69

82 magnitude of the peak soot volume fraction without tuning of the inception rate is a major advantage provided by the A5 model compared to other models. Moreover, fundamental studies using detailed codes have also shown that A5 may be a better indicator of soot inception than other PAHs [48] Effect of Coupling It was mentioned in section that previous numerical soot models over-predicted the amount of soot produced by gas turbine combustors, particularly with increasing thrust levels. It was further noted that the lack of coupling of carbon mass between the solid and gas phase in these previous models would have led to soot precursor concentrations that were unreasonably high, which would contribute to the over-prediction of soot. Thus, it is expected that the coupling measures introduced in section would appreciably reduce the predicted soot volume fraction of the model. To test the effect of coupling, an uncoupled version of the A2 model was created. To create this uncoupled model, a new flamelet library has been generated, which uses unmodified reactions for A2 (i.e., two-way reactions with oxidation reactions included), such that A2 no longer acts as a carbon sink for soot, but as a predictor of naphthalene levels in the flame. In addition, the uncoupled model does not solve a transport equation to track the amount of acetylene added to soot, and calculates HACA growth rates based on the flamelet value for acetylene. Due to the limited computational resources available for this study (see section 4.4), an uncoupled simulation was only done for the A2 model. Figure 5-19 shows the comparison of soot volume fractions along the flame centreline for the coupled and uncoupled versions of the A2 model. As expected, the uncoupled model predicts higher soot volume fractions, as the mass of carbon in the gas phase is not conserved in any way. Introducing these coupling measures to the flamelet approach has reduced the peak soot volume fraction by roughly a factor of three along the flame centreline. 70

83 1.60E E-05 Coupled Model Uncoupled Model 1.20E-05 Soot Volume Fraction 1.00E E E E E E Distance Along Centreline [mm] Figure 5-19: 1 bar flame. The effect of coupling on soot volume fraction along the centerline Effect of HACA Growth As kerosene contains a considerable amount of aromatic species, PAHs are expected to play a bigger role in the inception and growth of soot compared to smaller aliphatic compounds such as acetylene. Recently, DNS simulations for n-heptane/air flames have shown that the soot formation process in turbulent flames is dominated by PAH inception and condensation processes, with surface growth via acetylene (and similar compounds) contributing negligibly to soot mass growth [70]. Both the A2 and A5 models introduced here corroborate these findings. From Figure 5-20 and Figure 5-21 (A2 and A5 models respectively), it can be seen that the contribution to soot mass fraction from HACA growth (i.e., ) is approximately two orders of magnitude less than the total soot mass fraction (i.e., ) along the centreline of the flame. 71

84 1.00E E-01 Soot - Total (A2 model) Soot - HACA Contribution (A2 model) Mass Fraction (LOG SCALE) 1.00E E E E E Distance Along Centreline [mm] Figure 5-20: 1 bar flame. The effect of HACA growth on soot volume fraction along the centerline for the A2 model. 1.00E E-01 Mass Fraction (LOG SCALE) 1.00E E E E E-06 Soot - Total (A5 model) Soot - HACA Contribution (A5 model) Distance Along Centreline [mm] Figure 5-21: 1 bar flame. The effect of HACA growth on soot volume fraction along the centerline for the A5 model. 72

85 However, as noted previously, the acetylene field for these two models could be higher if the A2 or A5 sinks did not consume as much acetylene through reactions which were made unidirectional in the mechanism. To account for the consequence of this coupling, the effect of HACA growth was also investigated for the uncoupled A2 model (see the previous section). For this model, it was also found that the contribution to soot mass fraction from HACA growth was one to two orders of magnitude lower than the total soot mass fraction (see Figure 5-22). Despite this, the increased amount of acetylene available in the uncoupled model has boosted the HACA growth rate, as expected. 1.00E E-01 Soot - Total (uncoupled A2 model) Soot - HACA Contribution (uncoupled A2 model) Mass Fraction (LOG SCALE) 1.00E E E E E Distance Along Centreline [mm] Figure 5-22: 1 bar flame. The effect of HACA growth on soot volume fraction along the centerline for the uncoupled A2 model. Further, the effect of HACA growth was also found to be insignificant along the radial positions in the flame. Consider the following plots of the mass fraction of soot and acetylene added to soot at a height of 100 mm above the inlet. 73

86 1.00E+00 Soot - Total (A2 model) Soot - HACA Contribution (A2 model) 1.00E+00 Soot - Total (A5 model) Soot - HACA Contribution (A5 model) Mass Fraction (LOG SCALE) 1.00E E E E-04 Mass Fraction (LOG SCALE) 1.00E E E E E Radial Distance [mm] 1.00E Radial Distance [mm] Figure 5-23: 1 bar flame. The effect of HACA growth on soot volume fraction radially at a height of 100 mm for the A2 model (left) and the A5 model (right). Since HACA growth has been determined to have a weak effect in both the coupled and uncoupled versions of the model, and since the HACA surface growth model implemented here uses the highest possible value for the fraction of reactive surface (i.e., α = 1), the numerical results suggest that the effect of HACA growth is insignificant for this flame. This is due to low radical levels (i.e., low levels of [H] and [OH] in equation (3-64) relative to the terms in the denominator particularly [H 2 ]). 5.2 Flame E: 4.8 Bar In this section, the modelling results for the 4.8 bar flame simulation are discussed. In the first subsection, important contour plots for the A2 and A5 models are presented, and the differences between the two models are discussed. In the second subsection, the modelling results are compared to experimental data. In the final subsection, the effect of HACA growth on the modelling results is discussed Flame Structure, Species and Soot Fields The soot volume fraction and primary particle number density fields for both models are shown in Figure 5-24 and Figure In general, the same observations made in the atmospheric case 74

87 apply here. For example, the A5 model soot field is shifted higher up in the flame, and the soot number density appears to peak on the flame wings, while the volume fraction peaks on the centreline. Note that the A5 model predicts the soot volume fraction to be one order of magnitude larger than the A2 model, and this difference is explored further in the next section. Figure 5-24: 4.8 bar soot volume fraction (A2 left, A5 right) Figure 5-25: 4.8 bar soot number density (A2 left, A5 right) The soot particle diameters along the centreline are shown in Figure As with the atmospheric flame, the peak diameters are in the expected range for soot particles [15]. 75

88 A2 Model A5 Model Primary Particle Diameter [nm] Distance Along Centreline [mm] Figure 5-26: 4.8 bar flame. Soot particle diameters along the centerline. The mixture fraction and temperature fields are the main inputs to the soot model, and are shown in Figure 5-27 and Figure 5-28 for both the A2 and A5 models. Again, like the atmospheric case, noticeable differences exist in the temperature field, due to differing amounts of radiative heat loss. The hotter temperatures cause a slight shift upward in the A2 model mean mixture fraction relative to that of the A5 model. However, this difference is much less pronounced than that of the atmospheric case. 76

89 Figure 5-27: 4.8 bar mean mixture fraction (A2 left, A5 right) Figure 5-28: 4.8 bar temperature [K] (A2 left, A5 right) The mass fraction contours of OH and O 2 are shown for both models in Figure 5-29 and Figure As discussed before, differences in the temperature and mean mixture fraction fields cause differences in the species mass fraction fields. It can be noted that the increased mass fraction of OH available in the A5 model leads to an increase in its soot oxidation rates. Nevertheless, the A5 model predicts a higher soot volume fraction, as shown in Figure

90 Figure 5-29: 4.8 bar OH mass fraction (A2 left, A5 right) Figure 5-30: 4.8 bar O 2 mass fraction (A2 left, A5 right) The mass fraction contours of C 2 H 2, and C 6 H 6 are shown in Figure 5-31 and Figure As explained for the atmospheric case, these figures indicate that acetylene is more important in the production of soot for the A2 model, while benzene is more important in the production of soot for the A5 model. This inference is due to the disparity in the mass fractions of the species between the two models. For example, a much higher mass fraction of benzene in the A2 model compared to the A5 model indicates that the A5 model s carbon sink is consuming more benzene (and a similar argument can be made for acetylene consumption via the A2 carbon sink). 78

91 Figure 5-31: 4.8 bar C 2 H 2 mass fraction (A2 left, A5 right) Figure 5-32: 4.8 bar C 6 H 6 mass fraction (A2 left, A5 right) Finally, the mass fractions of the carbon sinks for both models are shown in Figure Comparing with the atmospheric case (refer to Figure 5-10), the mass fractions of the carbon sinks for both the A2 and A5 models have increased. Of course, this augmentation is consistent with the increase in soot volume fraction shown in Figure

92 Figure 5-33: 4.8 bar flame. Mass fractions of carbon sinks for the A2 and A5 models. From left to right: A2 (naphthalene), A5 (BGHIF), A5 (BAPYR), and A5 (BAPYR*S) Comparison with Experiment Figure 5-34 and Figure 5-35 show the comparison of the experimental and numerical temperature and soot volume fraction along the centreline for the 4.8 bar Young flame [67]. The plot of mean mixture fraction is not included, because the experimental mean mixture fraction was not measured for this pressure. Under heavily sooting conditions, solid carbon deposition on the exterior of the sampling probe made the measurement of mean mixture fraction very difficult. For this reason, Young et al. chose to restrict the measurement of mean mixture fraction to pressures under 3 bar [40]. 80