Evaluation of Liquid Fuel Spray Models for Hybrid RANS/LES and DLES Prediction of Turbulent Reactive Flows

Transcription

1 Evaluation of Liquid Fuel Spray Models for Hybrid RANS/LES and DLES Prediction of Turbulent Reactive Flows by Ali Afshar A thesis submitted in conformity with the requirements for the degree of Masters of Applied Science Graduate Department of Aerospace Engineering University of Toronto Copyright 2014 by Ali Afshar

2 Abstract Evaluation of Liquid Fuel Spray Models for Hybrid RANS/LES and DLES Prediction of Turbulent Reactive Flows Ali Afshar Masters of Applied Science Graduate Department of Aerospace Engineering University of Toronto 2014 An evaluation of Lagrangian-based, discrete-phase models for multi-component liquid sprays encountered in the combustors of gas turbine engines is considered. In particular, the spray modeling capabilities of the commercial software, ANSYS Fluent, was evaluated. Spray modeling was performed for various cold flow validation cases. These validation cases include a liquid jet in a cross-flow, an airblast atomizer, and a high shear fuel nozzle. Droplet properties including velocity and diameter were investigated and compared with previous experimental and numerical results. Different primary and secondary breakup models were evaluated in this thesis. The secondary breakup models investigated include the Taylor analogy breakup (TAB) model, the wave model, the Kelvin-Helmholtz Rayleigh-Taylor model (KHRT), and the Stochastic secondary droplet (SSD) approach. The modeling of fuel sprays requires a proper treatment for the turbulence. Reynolds-averaged Navier-Stokes (RANS), large eddy simulation (LES), hybrid RANS/LES, and dynamic LES (DLES) were also considered for the turbulent flows involving sprays. The spray and turbulence models were evaluated using the available benchmark experimental data. ii

3 Acknowledgements I would like to thank Professor C.P.T Groth for giving me the opportunity to study under his supervision at the Aerospace department of the University of Toronto. I appreciate his guidance, support and supervision through the course of my Masters studies. I would like to thank Professor P.S Sampath for reading my thesis and helping me with all the questions I had on sprays and atomization. I would also like to thank Jonathan West for helping me understand the basics of turbulence modeling and assisting me with all the questions I had. Finally, I would like to thank my family and all my friends for their support and encouragement during various stages of my research. This thesis is dedicated to all of them. The financial support of my studies was provided by Pratt and Whitney Canada (P&WC). Computational resources of my research were provided by the SciNet High Performance Computing Consortium available at the University of Toronto. Toronto, 2014 Ali Afshar iii

4 Contents Abstract ii Acknowledgements iii Contents iii List of Tables ix List of Figures x 1 Introduction Motivation Objectives Review of Combustion Models in ANSYS Fluent Assessment of Various Spray Models for Turbulent Flows Evaluation of Hybrid RANS/LES and DLES Prediction of Turbulent Flows Involving Liquid Sprays Simulation Methodology Thesis Summary Fundamentals of Liquid Sprays 8 iv

5 2.1 Introduction Primary Breakup Secondary Breakup Atomizers and Injectors Turbulence Modeling Introduction Reynolds-averaged Navier-Stokes (RANS) Large Eddy Simulation (LES) Hybrid RANS/LES Spray Models in ANSYS Fluent Introduction Droplet Collision Modeling Secondary Breakup Modeling TAB Model Wave Model KHRT Model SSD Model Spray Injection Modeling for Primary Breakup Single Injection Model Group Injection Model Cone Injection Model Solid Cone Injection Model Surface Injection Model v

6 4.4.6 File Injection Model Plain Orifice Atomizer Model Pressure Swirl Atomizer Model Airblast Atomizer Model Flat Fan Atomizer Model Effervescent Atomizer Model Spray Models Investigated in the Current Thesis Numerical Results for Liquid Jet in a Cross-flow Introduction Experimental Cases and Computational Setup Numerical Results Contours of Velocity Spatial Variation of the Droplets Droplet Diameter Droplet Velocity Sensitivity Analysis for Spray Model Constants Delayed Breakup Primary Breakup Analysis of Mesh Sensitivity Numerical Results for Airblast Atomizer Introduction Experimental and Computational Setup Numerical Results vi

7 6.3.1 Contours of Air Velocity Film Thickness Sensitivity Analysis Comparison of Breakup Models Spray Angle Sensitivity Analysis Radial and Tangential Velocities Comparison of the Turbulence Modeling Results for Optimal Parameter Selection Numerical Results for High Shear Fuel Nozzle Introduction Experimental and Computational Setup Numerical Results Contours of Gas Velocity Spatial Variation of the Droplets Conclusions and Future Research Conclusions I: Liquid Jet in a Cross-flow Conclusions II: Airblast Atomizer Conclusions III: High Shear Fuel Nozzle Recommendations for Future Research References 83 A Chemical Kinetics Models in ANSYS Fluent 94 A.1 Introduction A.2 Species Transport and Finite Rate Chemistry vii

8 A.2.1 Volumetric Reactions A.2.2 Wall Surface Reactions A.2.3 Particle Surface Reactions A.3 Non-Premixed Combustion A.3.1 Equilibrium A.3.2 Steady Flamelet A.3.3 Unteady Flamelet A.3.4 Diesel Unsteady Flamelet A.3.5 Adiabatic versus Non-Adiabatic A.4 Premixed Combustion A.4.1 C Equation A.4.2 G Equation A.4.3 Extended Coherent Flame Model A.4.4 Zimont Flame Speed Model A.4.5 Peters Flame Speed Model A.5 Partially Premixed Combustion A.6 Composition PDF Transport A.6.1 Lagrangian A.6.2 Eulerian B Radiation Models in ANSYS Fluent 111 B.1 Introduction B.2 Rosseland Model B.3 P1 Model viii

9 B.4 Discrete Transfer B.5 Surface to Surface B.6 Discrete Ordinates C Emissions and Soot Formation Models in ANSYS Fluent 118 C.1 Introduction C.2 NO x Formation C.2.1 Thermal NO x C.2.2 Prompt NO x C.2.3 Fuel NO x C.2.4 N 2 O Intermediate C.2.5 NO x Reduction C.3 SO x Formation C.4 Soot Formation C.4.1 One Step Model C.4.2 Two Step Model C.4.3 Moss Brookes Model C.4.4 Moss Brookes Hall Model C.5 Decoupled Detailed Chemistry Model ix

10 List of Tables 5.1 Operating conditions for the three test cases Meshes used for LJIC simulations (dimensions in microns) Mesh analysis (dimensions in microns) Meshes used for the airblast atomizer (dimensions in mm) x

11 List of Figures 2.1 Atomization breakup [10] Schematic of the breakup process [11] Primary breakup regimes [22, 23] Primary breakup regimes as a function of Ohnesorge and Reynolds numbers (Zone A=Rayleigh breakup regime, Zone B=first wind-induced breakup regime, Zone C=second wind-induced breakup regime, Zone D=atomization) [22, 24] Primary breakup regimes as a function of Reynolds number and gas density (Zone A=Rayleigh breakup regime, Zone B=first wind-induced breakup regime, Zone C=second wind-induced breakup regime, Zone D=atomization) [22, 23] Primary breakup regimes as a function of Reynolds number, Ohnesorge number, and gas density (Zone A=Rayleigh breakup regime, Zone B=first wind-induced breakup regime, Zone C=second wind-induced breakup regime, Zone D=atomization) [22, 25] Secondary breakup regimes [22, 26] Rayleigh-Taylor and Kelvin-Helmholtz instabilities [22, 27] Atomizers and injectors [1] Pressure swirl atomizer [2] Liquid jet in a cross-flow [52] xi

12 5.2 Experimental setup used by Leong and Hautman [55] Mesh 1 (67000 nodes) [15] Mesh 2 ( nodes) Mesh 3 ( nodes) Mean axial gas velocity for case 1 using RANS (m/s) Mean axial gas velocity for case 1 using DLES (m/s) Mean axial gas velocity for case 1 using LES (m/s) Mean axial gas velocity for case 1 using DES (m/s) Topview of the droplets for case 1 using wave model Spatial variation of the droplets using TAB model Spatial variation of the droplets using wave model Spatial variation of the droplets using KHRT model Spanwise distribution of the droplets for RANS Spanwise distribution of the droplets for DES Spanwise distribution of the droplets for LES Spanwise distribution of the droplets for DLES Droplet diameter found by Sen et al. [12] Droplet diameter for case 1 using RANS turbulence model Droplet diameter for case 1 using wave breakup model Droplet diameter for case 2 using RANS turbulence model Droplet diameter for case 3 using RANS turbulence model Droplet diameter for case 2 using wave breakup model Droplet diameter for case 3 using wave breakup model Droplet axial velocity for case 1 using RANS turbulence model xii

13 5.26 Droplet axial velocity for case 1 using wave breakup model Droplet axial velocity for case 2 using RANS turbulence model Droplet axial velocity for case 3 using RANS turbulence model Droplet axial velocity for case 2 using wave breakup model Droplet axial velocity for case 3 using wave breakup model Droplet diameter for case 1 using wave and RANS models Droplet axial velocity for case 1 using wave and RANS models Droplet diameter for case 1 using wave and RANS models (delayed breakup) Droplet axial velocity for case 1 using wave and RANS models (delayed breakup) Droplet diameter for case 3 using wave and RANS models Droplet axial velocity for case 3 using wave and RANS models Droplet diameter for case 3 using RANS Droplet diameter for case 3 using DES Droplet diameter for case 3 using LES Droplet diameter for case 3 using DLES Droplet axial velocity for case 3 using RANS Droplet axial velocity for case 3 using DES Droplet axial velocity for case 3 using LES Droplet axial velocity for case 3 using DLES Prefilming airblast atomizer [13] Computational domain Sideview of the airblast mesh Contour of the air velocity magnitude for the fine mesh xiii

14 6.5 Contour of the air axial velocity for the fine mesh Computational results for sideview of the droplet breakup using the fine mesh Computational results for spanwise distribution of the droplets using the fine mesh Experimental droplet axial velocity [13] Axial velocity for the fine mesh (film thickness= m) Axial velocity for the fine mesh (film thickness= m) Axial velocity for the coarse mesh (film Thickness= m) Axial velocity for the coarse mesh (film thickness= m) Axial velocity for the coarse mesh (film thickness= m) Axial velocity for the coarse mesh (film thickness= m) Droplet axial velocity for wave model Droplet axial velocity for KHRT model Droplet radial velocity for wave model Droplet radial velocity for KHRT model Axial velocity (spray angle=45, atomizer dispersion angle=15) Axial velocity (spray angle=0, atomizer dispersion angle=45) Axial velocity (spray angle=30, atomizer dispersion angle=15) Axial velocity (spray angle=0, atomizer dispersion angle=15) Experimental droplet radial velocity [13] Experimental droplet tangential velocity [13] Radial velocity (spray angle=0, atomizer dispersion angle=45) Tangential velocity (spray angle=0, atomizer dispersion angle=45) xiv

15 6.27 Radial velocity using UDF (spray angle=0, atomizer dispersion angle=45) Tangential velocity using UDF (spray angle=0, atomizer dispersion angle=45) Axial velocity using RANS and wave models Axial velocity using DLES and wave models Axial velocity using LES and wave models Axial velocity using DES and wave models Comparison of experimental and numerical results for axial velocity [13] Comparison of experimental and numerical results for radial velocity [13] Comparison of experimental and numerical results for tangential velocity [13] High shear fuel nozzle [14] Computational domain for the high shear fuel nozzle [14] Near injector mesh High shear fuel nozzle mesh Contours of mean velocity magnitude Contours of mean axial velocity Experimental air velocity magnitude [14] Numerical air velocity magnitude [14] Air velocity for RANS model Air velocity for LES model Spatial variation of the droplets [14] Near-injector particles for the wave model Numerical results for droplet breakup [14] xv

16 7.14 Experimental results for droplet breakup [14] Droplet breakup using RANS and wave models Spanwise distribution of the droplets using RANS and wave models Droplet breakup using RANS and KHRT models Spanwise distribution of the droplets using RANS and KHRT models Droplet breakup using LES and wave models Spanwise distribution of the droplets using LES and wave models xvi

17 Chapter 1 Introduction 1.1 Motivation Nowadays, liquid fuel is used as an energy source for various types of combustors including internal combustion engines and gas turbines. In many situations, the liquid fuel is atomized into small droplets, which enhances the rate of vaporization of the fuel by increasing the fuel surface exposed to the surrounding gas. The atomization process therefore has direct influence on the combustion performance and level of emissions [1]. It also involves various complex processes including primary breakup, secondary breakup, droplet collisions, droplet evaporation, and coalescence [2]. Several studies have investigated the spray formation and behavior in combustion devices. Spray and atomization analysis may contribute to combustion efficiency and safety by decreasing emissions and increasing combustion performance [3]. Various previous experimental investigations have been conducted on the atomization and droplet breakup phenomena. The experimental facilities utilize high-level optical methods as diagnostic approaches to determine atomization characteristics. Even though extremely useful, these experimental approaches may be costly and may not be able to fully diagnose the breakup phenomenon especially for the region near the atomizer [4]. Computational fluid dynamics (CFD) models have become popular in spray and combustion modeling due to their potentially lower financial cost. Several CFD models have been proposed for spray modeling. Despite the progress made in CFD development in 1

18 Chapter 1. Introduction 2 recent years, an accurate simulation of the atomization process occurring in a combustor is still a challenging task. The current thesis focuses on an evaluation of liquid fuel spray models for turbulent flows. The commercial CFD package, ANSYS Fluent, was used to evaluate a range of primary and secondary breakup models in a Lagrangian based simulation of the atomization process for a range of problems representative of spray processes found in gas turbine engines. The spray models were also assessed in conjunction with different turbulence models including Reynolds-averaged Navier-Stokes (RANS), large eddy simulation (LES) and Hybrid RANS/LES. 1.2 Objectives Review of Combustion Models in ANSYS Fluent In the first phase of this study, the primary combustion models in ANSYS Fluent were reviewed. The findings of this initial review is now briefly summarized. Appendices A-C provide more details on the available combustion models. Firstly, spray modeling in ANSYS Fluent can be done using a Lagrangian-based discrete phase approach. In this approach, the fluid phase is modeled using Navier Stokes equations while the modeling of the dispersed phase is done by tracking a number of droplets or particles. ANSYS Fluent offers various secondary droplet breakup models including the Taylor analogy breakup (TAB), wave, Kelvin-Helmholtz Rayleigh-Taylor (KHRT), and Stochastic secondary droplet (SSD) models. ANSYS Fluent also provides different injection models as primary breakup methods. ANSYS Fluent enables users to model the emissions and soot formation resulted from combustion or other chemical processes. Pollutant modeling in ANSYS Fluent normally consists of NO x formation and SO x formation modelings. The soot formation is also modeled using different approaches such as the one step, two step [5], and Moss Brookes models [6]. ANSYS Fluent offers various approaches for radiation modeling. The simplest radiation model is the Rosseland model which is valid for optically thick mediums [7]. Other

19 Chapter 1. Introduction 3 radiation models in ANSYS Fluent include the P1 model, the discrete transfer radiation model, the surface to surface technique, and the discrete ordinates method (DOM)[8]. The chemical kinetics models in ANSYS Fluent were also reviewed. The mixing combustion models reviewed in ANSYS Fluent include non-premixed combustion, premixed combustion and partially premixed combustion models. ANSYS Fluent also offers different flamelet models including steady, unsteady and diesel unsteady flamelet methods [9]. The chemical kinetics present in turbulent reactive flows can be also modeled via probability density function (PDF) transport models Assessment of Various Spray Models for Turbulent Flows The main focus of this thesis was on modeling of liquid fuel sprays and their effects on the combustion. It was deemed particularly important that the modeling properly incorporates the key physical processes associated with liquid fuel sprays. The flow arising from a fuel injector normally includes two different regions of multiphase flow. The initial multiphase region consists of a liquid core and a dispersed flow region beyond the liquid surface [10]. The liquid fuel spray experiences primary break as the liquid is injected. The formation of irregular liquid fuel elements along the liquid core contributes to primary breakup. The liquid then enters the dilute spray region. Secondary breakup occurs in the dilute spray region due to further irregularities [11]. Secondary breakup results in further diameter reduction of the droplets. The atomization process may also involve other chemical and physical processes such as coalescence, collisions, and evaporation. As mentioned previously, ANSYS Fluent offers different breakup models. Various breakup models were evaluated using previous experimental and numerical data. The following validation cases were used to evaluate the spray modeling capabilities of ANSYS Fluent: Liquid jet in a cross-flow [12]; Airblast atomizer [13]; and High shear fuel nozzle [14]. The liquid jet in a cross-flow case presented by Sen et al. was used as one of the validation cases [12]. Simulations were performed for three experimental test cases originally

20 Chapter 1. Introduction 4 presented by Madabhushi et al. [15]. Droplet diameter and axial velocity were collected on a plane one inch downstream the orifice. The results were compared for different turbulence and breakup models. An airblast atomizer was also used to validate the primary and secondary spray breakup models in ANSYS Fluent in conjunction with different turbulence models. This airblast atomizer was originally presented by Gurubaran et al. [13]. Finally, simulations were also performed for a high shear fuel nozzle [14]. The air velocity was compared for different spray breakup models. The spatial distribution of the droplets was also compared with previous experimental and numerical data. The following secondary breakup models were evaluated for all of these cases: TAB; Wave; KHRT; and SSD. Several primary breakup models such as single injection model, plain orifice atomizer, and airblast atomizer were also evaluated for turbulent flows Evaluation of Hybrid RANS/LES and DLES Prediction of Turbulent Flows Involving Liquid Sprays A component of this thesis was also concerned with the evaluation of different turbulence models for prediction of the atomization process occurring in the combustor of gas turbine engines. The following turbulence models were investigated in this thesis: RANS; LES; Dynamic LES; and Hybrid RANS/LES.

21 Chapter 1. Introduction 5 LES is one of several computational methods currently available for the prediction and modeling of turbulence. LES methods tend to resolve the large eddies directly, while requiring modeling of only the smaller eddies [16]. Pure RANS-based methods can also be used for the numerical treatment of turbulence. RANS methods solve the time-averaged Navier-Stokes equations for the mean motion of the fluid and the turbulence is unresolved and must be modeled [17]. Because of this, RANS methods generally require considerable less CPU time and memory to solve a particular turbulent flow problem; however, in cases involving complex geometries and complex turbulent flows the RANS model may not accurately predict the turbulence. While RANS-based methods are still typically used in most engineering and practical applications, the potential of LES and hybrid RANS/LES methods is now being recognized. Hybrid approaches, combining both RANS and LES methods in a single computation, so-called hybrid RANS/LES methods are also possible, although there have been very few studies of hybrid RANS/LES methods for reactive flows to date [18]. As noted above, both LES and hybrid RANS/LES methods were considered for the prediction of turbulent flows. The dynamic LES or DLES approach is one LES method that was also investigated in this research. DLES uses two filters including a grid LES filter and a test LES filter for resolving the sub-grid turbulent stress tensor [19]. The turbulence models were evaluated using the validation cases discussed earlier. The compatibility of the spray models for LES of flows within combustor was also evaluated as a part of this thesis. 1.3 Simulation Methodology The commercial CFD package ANSYS Fluent was used for the simulations. All the simulations were performed using the pressure-based solver available in ANSYS Fluent [20]. In the pressure-based solver, the velocity field is calculated by manipulating the momentum equations. The continuity and momentum equations are also used to obtain a pressure equation. This pressure equation is further solved to calculate the pressure field [2]. ANSYS Fluent provides two different algorithms for the pressure-based solver, which include a coupled approach and a segregated algorithm. A coupled pressure-based algorithm was used for all the simulations as this is recommended by ANSYS Fluent when

22 Chapter 1. Introduction 6 using the discrete phase model (DPM) to obtain more accurate results. The coupled approach provides advantages over the segregated model by solving the pressure and momentum continuity equations together. Such a coupled scheme is desired when the mesh is not highly refined, or when large time steps are used for the transient simulation [2]. Furthermore, a second-order upwind scheme was used for turbulent kinetic energy and turbulent dissipation rate. The second-order upwind method uses a Taylor series expansion to improve the accuracy of the results at the cell faces [21]. Spray modeling was achieved using DPM which accounts for an Euler-Lagrange approach where the continuous phase is solved using time-averaged Navier-Stokes equations, and the dispersed flow is solved by tracking a number of droplets or parcels through the flow field of the primary phase [2]. Unsteady particle tracking was used to track the droplets. A two-way coupling was used for the interactions between the particles and the gas phase. In the two-way coupled approach, the dispersed flow interacts with the continuous phase by exchanging energy, mass, and momentum. For this approach, the flow field of the continuous phase should first be solved. After achieving a converged solution for the primary phase, the discrete phase can be introduced using the available injection models in ANSYS Fluent. Consequently, ANSYS Fluent recalculates the primary phase flow field and the discrete phase trajectories until a converged solution is obtained. In addition, the droplets resulted from the breakup are assumed to be spherical [18]. 1.4 Thesis Summary The next chapter explains the fundamentals of liquid sprays, introducing the different types of breakup processes that occur during atomization. Chapter 2 concludes with a discussion of common injectors and atomizers used in gas turbine engines. Chapter 3 discusses various treatments for the turbulence within gas turbine engines. Chapter 4 explains the spray models available in ANSYS Fluent and evaluated as part of this study. Chapter 5 presents the simulation results found for the liquid jet in a cross-flow benchmark case. This chapter is followed by Chapter 6, which describes the numerical results obtained for the airblast atomizer case. The results found for the high shear fuel nozzle follow in Chapter 7. Finally, Chapter 8 includes a discussion of conclusions and future recommendations. The current thesis also includes reviews of chemical kinetics,

23 Chapter 1. Introduction 7 radiation, and emission models in ANSYS Fluent, which as previously mentioned are presented in the appendices.

24 Chapter 2 Fundamentals of Liquid Sprays 2.1 Introduction The flow arising from a fuel injector consists of two different regions of multi-phase flow including a dense spray region and a dilute spray region [10]. As is shown in Figure 2.1, the dense spray region consists of an intact liquid core and a multiphase mixing layer where the liquid core is not completely disintegrated. The liquid core consists of a completely intact liquid column and it includes non-atomized fluid elements. The dispersed flow region however includes separate discrete droplets moving in the gaseous phase. The multiphase mixing layer is further developed into a dilute spray region, which consists of smaller droplets. The atomization in a liquid fuel spray experiences a primary breakup as the liquid exits the atomizer or injector. The primary breakup accounts for the breakup of the intact liquid core and leads to formation of irregular liquid elements such as ligaments along the surface of the liquid core. The length of the liquid core is directly related to the primary breakup process. Secondary breakup and droplet collisions also occur in the fuel spray atomization process. Secondary breakup accounts for diameter reduction of the droplets outside the primary breakup length mostly in the dilute spray region [11]. The secondary breakup is due to further irregularities and decrease in the surface tension of droplets. High pressure combustion present in typical atomizers results in conditions where the liquid surface 8

25 Chapter 2. Fundamentals of Liquid Sprays 9 Figure 2.1: Atomization breakup [10]. approaches the thermodynamic critical point. As a consequence, the droplets tend to breakup in the dilute spray region. Figure 2.2 shows the primary and secondary breakups occurring in an atomization process. Furthermore, droplet collisions also occur in both dense and dilute spray regions. In the sections to follow further details of primary and secondary breakup are discussed. This chapter concludes with a discussion of typical atomizers and injectors used in gas turbine engines. 2.2 Primary Breakup The external and internal forces present on the surface of the liquid core create perturbations and oscillations, which can result in the disintegration and breakup of the liquid column into small droplets [1]. This breakup mechanism is referred to as primary breakup. The primary breakup process can be divided into four different categories. These breakup types can be categorized based on three non-dimensional parameters that include the Weber number, the Reynolds number, and the Ohnesorge number. The Weber number in the gas and liquid is defined as the ratio of aerodynamic force to the force generated by surface tension and given by

26 Chapter 2. Fundamentals of Liquid Sprays 10 Figure 2.2: Schematic of the breakup process [11]. We g = u2 ρ g D σ We l = u2 ρ l D σ (2.1) (2.2) where u is the jet velocity, D is the nozzle diameter, ρ is density, and σ represents the surface tension. The Reynolds number is introduced as the ratio between inertial and viscous forces, and is widely used in turbulence calculations. It is given by Re = uρ ld µ l (2.3) where µ is the dynamic viscosity. Finally, the Ohnesorge number is defined as the ratio between viscous forces and surface tension forces and has the form Oh = We l Re = µ l σdρl (2.4) The Ohnesorge number only contains liquid properties and assumes a small and negligible gas viscosity during the breakup process. As mentioned, the primary breakup process is normally divided into four different types based on the breakup regime as defined by the Weber, Reynolds, and Ohnesorge numbers. The four primary breakup regimes are shown in Figure 2.3 and include the Rayleigh regime, the first wind-induced regime, the second wind-induced regime, and the atomization regime [22].

27 Chapter 2. Fundamentals of Liquid Sprays 11 Figure 2.3: Primary breakup regimes [22, 23]. Rayleigh Breakup Regime: Zone A The Rayleigh breakup regime accounts for breakup at low jet velocities. The surface tension plays the most important role in the breakup process of this regime by introducing small perturbations leading to axisymmetric oscillations. These oscillations finally lead to breakup of the liquid core. The Rayleigh breakup introduces droplets with larger diameter than the nozzle. The breakup length is long and it can be increased, by increasing the jet velocity [22]. First Wind-Induced Breakup Regime: Zone B As the Weber number is increased, aerodynamic forces also play a role in the spray breakup process. The Weber number for the first wind-induced breakup regime is directly related to the relative velocity between the liquid and the surrounding gas. The first wind-induced breakup normally leads to droplets with similar diameters to the original nozzle diameter. The breakup length is larger than the nozzle diameter and it can

28 Chapter 2. Fundamentals of Liquid Sprays 12 be decreased by increasing the jet velocity [22]. Second Wind-Induced Breakup Regime: Zone C As the Weber number is further increased it leads to turbulence within the nozzle, instabilities, and growth of short surface waves, which finally result in droplet breakup. The breakup process in this so-called second wind-induced breakup regime is more rapid than that of the first wind-induced breakup regime, resulting in formation of droplets with smaller diameters than the nozzle diameter. The breakup length can be decreased by increasing the jet velocity [22]. Atomization: Zone D Breakup occurs directly at the nozzle orifice for higher Weber numbers. The intact core length is either zero or very short to be detected with modern measurements techniques. The atomization process results in much smaller droplets compared to the original nozzle diameter. Regime Diagram for Primary Breakup As it was mentioned earlier, the preceding regimes for the primary breakup process can be categorized based on the non-dimensional parameters, We, Re, and Oh. The regime diagram of Figure 2.4 is based on the work done by Reitz [24] and shows the four breakup regimes as a function of the Ohnesorge and Reynolds numbers. The primary breakup process is also influenced by the gas density. As the gas density is increased, the atomization is enhanced and the division lines of the chart are shifted to the left. Figure 2.5 shows a chart created by Schneider to categorize the primary breakup process as a function of Reynolds number, Weber number, and gas density [23]. The primary breakup regimes are illustrated in Figure 2.6 for the full three-dimensional parameter space based on the three parameters of gas density, Ohnesorge number, and Reynolds number [25].

29 Chapter 2. Fundamentals of Liquid Sprays 13 Figure 2.4: Primary breakup regimes as a function of Ohnesorge and Reynolds numbers (Zone A=Rayleigh breakup regime, Zone B=first wind-induced breakup regime, Zone C=second wind-induced breakup regime, Zone D=atomization) [22, 24]. Figure 2.5: Primary breakup regimes as a function of Reynolds number and gas density (Zone A=Rayleigh breakup regime, Zone B=first wind-induced breakup regime, Zone C=second wind-induced breakup regime, Zone D=atomization) [22, 23].

30 Chapter 2. Fundamentals of Liquid Sprays 14 Figure 2.6: Primary breakup regimes as a function of Reynolds number, Ohnesorge number, and gas density (Zone A=Rayleigh breakup regime, Zone B=first wind-induced breakup regime, Zone C=second wind-induced breakup regime, Zone D=atomization) [22, 25]. 2.3 Secondary Breakup The fluid particles may experience further breakup and diameter reduction in the dilute spray region due to further irregularities of the liquid elements. This breakup process is referred to as the secondary breakup. Secondary breakup mostly occurs due to the aerodynamic forces and decrease of surface tension [10]. The relative velocity between the droplets and the surrounding gas is the main breakup contributor. The gas Weber number is used to identify the breakup process [4]. With increasing values of the relative velocity, the gas Weber number increases and contributes to increased secondary breakup. This secondary breakup process can be categorized based on the gas Weber number, as is shown in Figure 2.7 [22]. As the gas Weber number is increased, breakup becomes more catastrophic and more droplets are produced. Vibrational Breakup

31 Chapter 2. Fundamentals of Liquid Sprays 15 Figure 2.7: Secondary breakup regimes [22, 26]. Figure 2.8: Rayleigh-Taylor and Kelvin-Helmholtz instabilities [22, 27]. For low gas Weber numbers the main secondary breakup process is referred to as vibrational breakup. The surrounding flow contributes to the oscillation of the droplets, which finally leads to breakup. The droplets are slowly decomposed into fragments creating smaller and smaller droplets [22, 26]. Bag Breakup Bag breakup refers to the secondary breakup process in which the droplets are deflected into a disc before decomposing. The center of the disc is then transformed into a balloon moving parallel to the flow direction. As a result, the balloon experiences breakup creating small droplets. The surrounding ring also decomposes into droplets, which are

32 Chapter 2. Fundamentals of Liquid Sprays 16 mostly larger than the droplets produced by the balloon. Bag breakup is also sometimes referred to as parachute breakup [22]. Bag and Stamen Breakup Bag and stamen breakup is also referred to as umbrella breakup and is similar to bag breakup. However, this breakup process also creates a liquid column at the center of the ring parallel to the flow direction. The liquid column then also disintegrates with the ring [22, 26]. Stripping Breakup As the relative velocity and gas Weber number are further increased, the droplets experience sheet stripping breakup. The shear forces at the equatorial region of the droplets play the most important role in this secondary breakup process by pulling apart the boundary layer. The main difference between sheet stripping breakup and bag breakup is the initiation of the disintegration process, which occurs on the peripheries of the disc for sheet stripping as opposed to the bag breakup where disintegration starts from the center [22]. For larger Weber numbers greater than 350, the droplets may experience wave crest stripping. Large amplitude surface waves with small wavelength play the most important role in the droplet secondary breakup. This type of secondary breakup is due to the pressure difference resulted from an initial perturbation on the droplet surface leading to continuous diameter loss of the droplet. This breakup process is produced by the Kelvin-Helmholtz instability [28]. Catastrophic Breakup The droplets may also experience a catastrophic breakup. For larger amplitude surface waves having short wavelength the perturbations lead to droplet disintegration forming smaller fragments. As a result, these fragments are also further disintegrated. This breakup process is produced by the Rayleigh-Taylor instability [25]. Figure 2.8 illustrates the two physical mechanisms leading to catastrophic breakup [22].

33 Chapter 2. Fundamentals of Liquid Sprays 17 Figure 2.9: Atomizers and injectors [1]. Figure 2.10: Pressure swirl atomizer [2]. 2.4 Atomizers and Injectors Various types of injectors and atomizers are used in gas turbine engines. Examples of some typical injection types are shown in Figures 2.9 and Most of the atomizers consist of single substance pressure nozzles. The pressure swirl atomizer, which is also a

34 Chapter 2. Fundamentals of Liquid Sprays 18 single substance injector, produces a hollow cone as the liquid is pushed against the walls, and it is shown in Figure 2.10 [1]. The swirl atomizer is used in different applications in gas turbine combustors. Other single substance pressure nozzles include flat fan nozzles and full cone injectors [3]. In addition, pneumatic atomizers, which use gases to produce small droplets as a result of high relative velocities, are also becoming popular in gas turbine industry [1]. Twin fluid nozzles, airblast atomizers, and effervescent injectors are some examples of pneumatic atomizers which are used in various industries including biodiesel and gas turbine combustors [29]. Other complex atomizers used in aero-based gas turbine engines include atomizers with propellants, rotary atomizers and liquid jet in a cross-flow [3].

35 Chapter 3 Turbulence Modeling 3.1 Introduction The combustors of gas turbines for aviation and industrial applications all operate with the spray and reactive flows lying well within the turbulent regime and are characterized by high Reynolds numbers. For this reason, the modeling of multi-component fuel spray requires a treatment for the turbulence within both the liquid and gaseous phases. Turbulent flows can be simulated using different approaches. Direct numerical simulation (DNS) accounts for the turbulence by numerically solving the full unsteady Navier- Stokes equations. DNS simulations are computationally very expensive and are therefore mostly used as a research tool while having few practical industrial applications. RANS and LES are more common treatments for the turbulence, which decrease the computational costs relative to those of DNS. Turbulence modeling can be also achieved using hybrid approaches, combining both RANS and LES methods in a single computation, so-called hybrid RANS/LES methods. In this study, the spray models of interest will be assessed for use in conjunction with a range of turbulence models including RANS, LES, and hybrid RANS/LES methods. Each of the methodologies considered are now briefly reviewed. 19

36 Chapter 3. Turbulence Modeling Reynolds-averaged Navier-Stokes (RANS) RANS-based methods are one of the computational approaches that can be used for the numerical treatment of turbulence. RANS methods solve the time-averaged Navier- Stokes equations for the mean motion of the fluid where the turbulence is unresolved and must be modeled. Because of this, RANS methods generally require considerable less time and memory to solve a particular turbulent flow problem; however, in cases involving complex geometries and complex turbulent flows the RANS models may not accurately predict the turbulence. Reynolds averaging basically decomposes the instantaneous Navier-Stokes equations into fluctuating and mean components. For velocity, pressure, or other scalar quantities the Reynolds averaging is defined as follows [2]: u i = ū i + ú i (3.1) φ = φ + φ (3.2) where ū i is the mean velocity, ú i is the fluctuating velocity, and φ represents a scalar such as energy or pressure. Using the preceding definition and applying Reynolds time averaging to the Navier-Stokes equations yields the following set of equations for time averaged equations [2]: ū i = 0 (3.3) x i ū i t + ū ū i j = 1 [ pδ ij + µ( ū i + ū ] j ) τ ij (3.4) x j ρ x j x j x i where δ ij is the Kronecker delta, p is the pressure, µ represents the viscosity, and ρ is the density. The so-called Reynolds stress term, τ ij, is given by: τ ij = ρú j ú i (3.5) This term represents the influence of fluctuations on the mean flow. ANSYS Fluent offers various RANS modeling options. The k-ɛ model is the main RANS model used in this thesis. This model is based on the transport equations for the kinetic energy, k, and the dissipation rate, ɛ [17]. ANSYS Fluent offers different k-ɛ models including the standard, RNG [30], and realizable k-ɛ models [31].

37 Chapter 3. Turbulence Modeling 21 The standard k-ɛ model solves two transport equations to determine a turbulent length and time scale. The standard k-ɛ model has various engineering applications and is reasonably accurate for most of the turbulent flows. The equations describing the transport of the turbulent kinetic energy and its rate of dissipation are [17] ρ k t + ρ x i (ku i ) = ρ ɛ t + ρ x i (ɛu i ) = x j x j [ (µ + µ t ) k ] + G k + G b ρɛ Y M + S k (3.6) σ k x j [ (µ + µ t ) ɛ ] ɛ + C 1ɛ σ ɛ x j k (G k + C 3ɛ G b ) C 2ɛ ρ ɛ2 k + S ɛ (3.7) where G k is the turbulent kinetic energy generated due to mean velocity gradients and G b represents the turbulent kinetic energy generated due to buoyancy. The term Y M represents the dissipation rate due to fluctuating dilatation, and S k and S ɛ are userdefined source terms. σ k and σ ɛ represent turbulent Prandtl numbers [2]. Finally, C 1ɛ C 2ɛ C 3ɛ are constants. The RNG k-ɛ model includes an additional term in its second transport equation. This term is used to improve the accuracy of the model. RANS modeling can be also achieved using the realizable k-ɛ model. The realizable k-ɛ model uses a different expression to predict the turbulent viscosity. Consequently, a modified transport equation is used to predict the dissipation rate [2]. Note that the standard k-ɛ model was used for all of the RANS simulations of this thesis. 3.3 Large Eddy Simulation (LES) LES is one of several other computational methods currently available in ANSYS Fluent for the prediction and modeling of turbulence. LES methods tend to resolve the large eddies directly, while requiring modeling of only the smaller eddies. LES models filter the Navier-Stokes equations into either configuration space or Fourier space. The filtering process filters out the smaller eddies to be modeled, while the larger eddies are directly resolved. The following equations are obtained for filtered solution quantities φ, after filtering the continuity and momentum equations [2]: ū i x i = 0 (3.8)

38 Chapter 3. Turbulence Modeling 22 ū i t + ū ū i j = 1 ( pδ ij + σ ij τ ij ) (3.9) x j ρ x j where σ ij is the stress tensor resulted by molecular viscosity and τ ij represents the LES subgrid-scale stress tensor. The filtering operation results in the subgrid-scale stresses, τ ij, which are unknown and require modeling. The default LES model in ANSYS Fluent uses the Smagorinsky-Lilly approach to model the eddy viscosity as follows [16]: µ t = ρl 2 s 2 S ij s ij (3.10) L s = min(κd, C s V 1/3 ) (3.11) where L s is the mixing rate of the subgrid scales, κ is the von Karman constant, C s is the Smagorinsky constant, V is the volume of the computational cell, and d represents the distance to the closest wall. LES modeling can be also done using a dynamic approach for modeling the eddy viscosity. The dynamic LES or DLES approach is one LES method that will be investigated in this research. DLES uses two filters including a grid LES filter and a test LES filter for resolving the sub-grid turbulent stress tensor [19]. Both the Smagorinsky LES and DLES treatments for the turbulence were investigated in this thesis. 3.4 Hybrid RANS/LES Hybrid RANS/LES methods tend to combine the RANS and LES models in a single computation. In general, hybrid RANS/LES methods can be applied in either a wallbounded or an embedded approach. The wall-bounded method applies a RANS method near walls or in other necessary places and LES methods for other regions. The embedded methods tend to use LES in an unsteady region and RANS for other sections of the flow. The wall-bounded hybrid RANS/LES methods available in ANSYS Fluent include detached-eddy simulation (DES) and delayed DES (DDES) [18]. The RANS region of the DES methods in ANSYS Fluent can be modeled using three different approaches including the Spalart Allmaras model, the realizable k-ɛ method, and the shear stress transport (SST) k-ω model. The Spalart-Allamaras based DES model replaces d in all the equations with a new length scale [32]:

39 Chapter 3. Turbulence Modeling 23 d = min(d, C des max) (3.12) where C des is a constant equal to 0.65, and max represents the largest grid spacing. The realizable k-ɛ based DES model uses an alternative equation for the dissipation term [31]: Y k = ρk 3/2 min(l rke, l les ) (3.13) l rke = k3/2 ɛ (3.14) l les = C des max (3.15) where max represents the maximum local grid spacing, and C des is a constant equal to Finally the SST based DES model uses a modified equation for the dissipation term [33]: where ω is the specific dissipation rate. L t Y k = ρβ kωmax(, 1) (3.16) C des max k L t = (3.17) β ω ANSYS Fluent also offers the delayed DES method, which keeps the simulation in RANS mode for boundary layer [18]. In this work, the SST based DES model in ANSYS Fluent was used for hybrid RANS/LES simulations.

40 Chapter 4 Spray Models in ANSYS Fluent 4.1 Introduction Spray modeling can be done using the discrete phase approach available in ANSYS Fluent. The discrete phase model uses a combination Eulerian-Lagrangian approach where the fluid phase is modeled using Navier-Stokes equations while the dispersed phase is modeled by tracking a number of representative droplets or particles throughout the computational domain. In contrast, with other multiphase models available in ANSYS Fluent, the discrete phase approach assumes low volume fraction for the dispersed second phase. ANSYS Fluent uses the following equation to predict the trajectory of a discrete phase droplet [2]: d u p dt = F D( u u p ) + g(ρ p ρ) ρ p + F (4.1) where u is the fluid velocity, u p represents the particle velocity, ρ is the fluid density, and ρ p represents the particle density. In equation (4.1), F is an additional acceleration term, F D ( u u p ) represents the acceleration due to the drag force, and F D is the drag constant. Droplet collision and secondary breakup models are also available in ANSYS Fluent. Furthermore, ANSYS Fluent offers various spray injection models which can be used to prescribe spray droplet size and velocity distributions associated with various 24

41 Chapter 4. Spray Models in ANSYS Fluent 25 primary breakup models. The spray models in ANSYS Fluent are further discussed in this chapter, as mentioned in the ANSYS Fluent theory and user manuals [2, 18]. 4.2 Droplet Collision Modeling Droplet collision modeling in ANSYS Fluent can be done by tracking the droplets. For modeling collision of N droplets, 1 2 N 2 total collision partners should be considered. AN- SYS Fluent reduces the computational costs by using liquid parcels, each representing several droplets. ANSYS Fluent uses the O Rourke algorithm where two parcels may only collide in the case of being in the same cell of the continuous phase [34]. Moreover, the O Rourke method is second order accurate and can reduce the computational costs of predicting droplet collisions. Furthermore, the collision method in ANSYS Fluent also determines the type of collision to be either bouncing or coalescence. The probability of each collision is found using the collisional Weber number which is dependent on U rel, the relative velocity, and D, the mean diameter of two parcels. The collisional Weber number is given by We c = ρu 2 rel D σ (4.2) The droplet collision model in ANSYS Fluent is suitable for low Weber numbers under about 100 where the effects of droplet shattering can be ignored [2]. 4.3 Secondary Breakup Modeling ANSYS Fluent offers various secondary breakup models for the liquid droplets. The TAB model is mostly used for low Weber numbers. The wave breakup model is recommended for Weber numbers greater than 100. Furthermore, ANSYS Fluent also offers the KHRT and the SSD models. Features of each of these four models are now described TAB Model The Taylor analogy approach models an oscillating and distorting droplet based on a spring mass system according to the surface tension, droplet drag and droplet viscosity

42 Chapter 4. Spray Models in ANSYS Fluent 26 forces [35]. The TAB method which is suitable for low Weber numbers can be modeled using the equation for a damped forced oscillator as follows [36]: F k x d d x dt = md2 x dt 2 (4.3) Using the Taylor analogy and by assuming the breakup requirement for the distortion to be x > C b r, the governing equations for a droplet are then given by y = x C b r (4.4) d 2 y dt = C F ρ g u 2 2 C b ρ l r C kσ 2 ρ l r y C dµ l dy 3 ρ l r 2 dt (4.5) where ρ l is the discrete phase density, ρ g represents the continuous phase density and u is the relative velocity of the droplet. The variable C b is a constant equal to 0.5. Additionally, C F, C k, and C d are also dimensionless constants [37]. It should be noted that breakup occurs when y>1. Furthermore, the size of the child droplet can be also determined using the energy of the child droplet given by [36] E = 4πr 2 σ r r 32 + π 6 ρ lr 5 ( dy dt )2 (4.6) where r 32 represents the Sauter mean radius of the droplet [2] Wave Model The wave droplet breakup model is suitable for higher Weber numbers where the droplet breakup is resulted from the relative velocity between the liquid and gaseous phases. The wave model, which was first proposed by Reitz, accounts for the influence of Kelvin- Helmholtz instabilities [38]. The wave method uses a jet stability analysis for a viscous cylindrical jet with a radius of a, in order to predict the desired dispersion relation [39]. The maximum growth rate, Ω, and the wavelength, δ, found from the wave breakup model analysis are defined by δ = 9.02a ( Oh0.5 )( Ta 0.7 ) ( We ) 0.6 (4.7) Ω = σ( We ) ρ 1 a 3 (1 + Oh)( Ta 0.6 ) (4.8)

43 Chapter 4. Spray Models in ANSYS Fluent 27 where Oh is the Ohnesorge number and Ta represents the Taylor number. Here, ρ 1 is the liquid density and We 2 represents the gas Weber number. The radius of the new droplet is proportional to the wavelength found above and can be written as [2] r = B 0 δ (4.9) where B 0 is a constant usually taken to be 0.61 [38]. In addition, the rate of change in the droplet radius is modeled as da dt = δω(a r) 3.726B 1 a where B 1 is a constant set to a value of 1.73 [37]. (4.10) KHRT Model ANSYS Fluent also offers the KHRT model which combines the wave breakup model with Rayleigh-Taylor instabilities [40]. The KHRT method models droplet breakup by considering breakup to occur as a result of the fastest growing instability. The KHRT approach is suitable for high Weber numbers and assumes the presence of liquid core in the near nozzle region [2]. ANSYS Fluent uses the wave breakup approach within the liquid core, while both KH and RT methods are considered for regions outside the liquid core. The length of the liquid core can be predicted using the theory of Levich as follows [41]: L = C L d 0 ρl ρ g (4.11) where d 0 is the reference nozzle diameter and C L represents the Levich constant. should be noted that the KHRT method uses an effective droplet diameter based on C a, the contraction coefficient, with the effective diameter defined by D e = C a d 0 (4.12) In addition, the frequency of the fastest growing wave and its corresponding wavelength using the RT method are found using [2] 2( g t (ρ p ρ g )) Ω = σ(ρ p + ρ g ) It (4.13) δ = where g t represents the droplet acceleration. gt (ρ p ρ g ) 3σ (4.14)

44 Chapter 4. Spray Models in ANSYS Fluent SSD Model The SSD breakup model uses the Fokker-Planck equation to find a probability distribution of the secondary droplet size [42]. Unlike other secondary breakup models, droplet diameter distribution in the SSD model is a random event and is independent of the diameter of the parent droplet. The SSD model introduces and defines the critical breakup radius and breakup time as r cr = We crσ l ρ g u 2 rel ρl r t bu = B ρ g u rel (4.15) (4.16) where We cr represents the critical Weber number and is originally set to 6. The parameter B is a user-defined constant having a default value of When the droplet radius is larger than the critical radius, the breakup time increases. As the breakup time increases and becomes larger than the critical breakup time, the parent droplet experiences breakup. 4.4 Spray Injection Modeling for Primary Breakup ANSYS Fluent provides 11 different injection types including atomizer and non-atomizer injection models which can be used to represent various types of primary spray breakup behaviour. ANSYS Fluent also offers different particle types for each injection. The available particle types include massless particle, inert, droplet, combusting particle, and multicomponent particle. ANSYS Fluent provides various laws for each particle type. The massless particle has no mass or other physical properties, and it follows the temperature and flow of the continuous phase. The inert particle, which is available for all injections, represents a particle obeying the force balance and the heating or cooling law. Furthermore, a droplet particle also obeys the vaporization and boiling laws in addition to the laws obeyed by an inert particle. Droplet particles are also available where the heat transfer model is active. The combusting particle is a solid particle which obeys the surface reaction law and the devolatilization law in addition to the force balance and heating laws. ANSYS Fluent also offers the wet combustion option which considers evaporation and boiling of the combusting particle. Finally, the multicomponent particle includes several droplet particles and is governed by multicomponent droplets law [2].

45 Chapter 4. Spray Models in ANSYS Fluent 29 ANSYS Fluent provides different approaches for determining the diameter distribution. The diameter distribution modeling in ANSYS Fluent includes the uniform, Rosin- Rammler, and Rosin-Rammler logarithmic approaches. The linear or uniform diameter distribution is the default model in ANSYS Fluent [18]. The Rosin-Rammler method uses the following equation for mass fractions greater than d: Y = e (d/ d) n (4.17) where d represents the size constant and n is the size distribution parameter. Furthermore, the mass fraction for diameters smaller than d are taken to be given by Y = e (d/ d) n 1 (4.18) In addition, ANSYS Fluent also offers stochastic tracking and cloud tracking as turbulent dispersion models. The stochastic model considers the contributions of turbulent velocity fluctuations while the particle cloud tracking accounts for tracking the changes of a cloud consisting of different particles [2]. In what follows, each of these injection models are briefly reviewed in turn Single Injection Model The single injection is used when a single value is desired for each of the initial boundary conditions. The position, velocity, diameter, mass flow rate, and duration of injection are specified as the point properties of single injection Group Injection Model A range of different values are specified for the initial conditions at the particles using the group injection model. ANSYS Fluent uses the first and last points of the position, velocity, diameter, temperature, and flow rate to predict the intermediate values as follows where Φ represents the desired initial condition [18]. Φ i = Φ 1 + Φ N Φ 1 (i 1) (4.19) N 1

46 Chapter 4. Spray Models in ANSYS Fluent Cone Injection Model Hollow spray cone injections in 3D cases are modeled using the cone injection method. The point properties for cone injection include position, diameter, temperature, axis, velocity, cone half angle, radius, and mass flow rate. Swirl fraction is also one of the point properties for the hollow cone injection which specifies the fraction of the swirling velocity of the particles [18] Solid Cone Injection Model The solid cone injection has similar properties to cone injection and is used for solid cones instead of hollow spray cases Surface Injection Model The surface injection available in ANSYS Fluent enables users to model spray injection from a surface. The point properties used in surface injection is similar to single injection except the initial position of the streams which is not defined in the surface injection [18] File Injection Model The file injection in ANSYS Fluent uses an input file containing the specified position, diameter, velocity, temperature and mass flow rate for the droplets introduced for the spray modeling Plain Orifice Atomizer Model ANSYS Fluent provides the modeling of plain orifice atomizer which is the most common form of atomizers in industrial applications. The flow in a plain orifice atomizer may experience a single phase, cavitating, or flipped region [43]. The exit velocity and droplet diameter highly depends on these internal regions. The complex internal regions in a plain orifice atomizer are computationally expensive to model. Consequently, ANSYS Fluent uses models found from previous experimental data for the spray modeling. The list of

47 Chapter 4. Spray Models in ANSYS Fluent 31 governing parameters for the internal regions of the nozzle include nozzle diameter, nozzle length, radius of curvature of the inlet, upstream and downstream pressures, viscosity, density, and vapor pressure, p v [2]. The Reynolds number and cavitation parameter are found using the following expressions: Re = dρ 2(p 1 p 2 ) µ ρ (4.20) K = p 1 p v p 1 p 2 (4.21) where p 1 is the upstream pressure and p 2 represents the downstream pressure. In addition, the coefficient of contraction is found using Nurick s equation [44] C c = 1 C 2 ct r d (4.22) where C ct represents a constant equal to Furthermore, ANSYS Fluent uses the following equation to find the coefficient of discharge based on azimuthal stop angle, Φ stop, and azimuthal start angle, Φ start [2]: C d = 2πṁ A(Φ stop Φ start ) 2ρ(p 1 p 2 ) (4.23) where ṁ is the mass flow rate. ANSYS Fluent uses different equations for the three possible internal regions. The following equations show the exit velocity for a single phase nozzle, cavitating nozzle, and flipped nozzle, respectively [45]: u = ṁeff ρa (4.24) u = 2C cp 1 p 2 + (1 2C c )p v C c 2ρ(p1 p v ) (4.25) u = ṁeff ρc ct A (4.26) where ṁ eff represents the effective mass flow rate. The spray angle, θ, for a flipped nozzle is assumed to be 0.02 [46]. In addition, ANSYS Fluent uses the following equation for predicting the spray angle for single phase and cavitating nozzles: θ = 2tan 1 [ 4π 3 + l 3.6d 3ρg 36ρ l ] (4.27)

48 Chapter 4. Spray Models in ANSYS Fluent 32 Finally, ANSYS Fluent uses the following equation for estimating the droplet diameter for single phase nozzle flows [47]: d 32 = 133 d 8 We 0.74 (4.28) where We is the Weber number. For the case of cavitating flow, the effective diameter of the exiting fluid jet, d eff, replaces d in the equation above. Furthermore, the droplet diameter for a flipped nozzle is obtained using [2] d 0 = d C ct (4.29) Pressure Swirl Atomizer Model The pressure swirl atomizer is also a common type of atomizer used in combustion, oil furnaces and spark ignited automobile engines. The fluid in the pressure swirl atomizer flows through a central swirl chamber where a hollow air cone is created as a result of the liquid moving towards the wall of the chamber [2]. ANSYS Fluent uses the linearized instability sheet atomization (LISA) method first developed by Schmidt as the pressure swirl atomizer model [48]. The LISA model in ANSYS Fluent consists of a film formation section, a sheet breakup section and an atomization section. ANSYS Fluent uses the following equation to determine the effective mass flow rate based on the film thickness, t, and the injector exit diameter, d inj : m eff = πρut(d inj t) (4.30) It should be noted that the axial velocity, u, can be found using the Han approach based on the total velocity, U, and the spray angle, θ, as follows [49]: 2 p u = Ucosθ = k v cosθ ρ (4.31) where k v, the velocity coefficient, is estimated using Lefebvre s method [2]: k v = max[0.7, 4 m eff 1 d 2 0cosθ 2ρ p ] (4.32) Furthermore, ANSYS Fluent uses different approaches for modeling the sheet breakup in a pressure swirl atomizer. analysis as follows [50]: The droplet atomization is also modeled using Weber s d 0 = 1.88d L (1 + 3Oh) 1/6 (4.33)

49 Chapter 4. Spray Models in ANSYS Fluent 33 where d L represents the diameter of ligaments formed at the point of breakup. d L for short waves is related to K s, the wave number of the maximum growth, as follows: d L = 2πC L K s (4.34) where C L represents the ligament constant. In addition, for longer waves the ligament diameter is predicted using the sheet thickness, H, and given by [2] d L = 4H K s (4.35) Airblast Atomizer Model The airblast atomizer introduces an additional air stream to facilitate the droplet breakup and the atomization process. Air assist in the airblast atomizer contributes to sheet instability and may also prevent collisions between droplets. The airblast atomizer uses the same specifications of the pressure swirl atomizer model for short waves with the exception of the sheet thickness which can be specified by the user. In addition, the maximum relative velocity resulted from the sheet and air is also specified in the airblast atomizer [2]. The ligament diameter in the airblast atomizer model is estimated using the same equation for short waves in the pressure swirl model: d L = 2πC L K s (4.36) Flat Fan Atomizer Model The flat fan atomizer is also similar to the pressure swirl atomizer. The flat fan model assumes a flat sheet for droplet breakup instead of using swirl. The flat fan atomizer is only used for three dimensional problems and the origin of the fan should be specified [2]. The ligament diameter for short waves in a flat fan atomizer is estimated using d L = 8H K s (4.37)

50 Chapter 4. Spray Models in ANSYS Fluent Effervescent Atomizer Model ANSYS Fluent also offers the effervescent atomizer model where a super heated liquid is directed to the liquid injected through the nozzle [2]. As a result, the liquid s phase changes rapidly resulting in droplet break up [51]. The initial velocity of the droplets is dependent on the effective mass flow rate and specified using u = ṁeff ρc ct A (4.38) In addition, the droplet size depending on the angle between the injection direction and stochastic trajectory of the droplet, θ, is found using the following equation: d 0 = dmaxe (θ/θs)2 (4.39) dmax = d C ct (4.40) where Θ s represents the dispersion angle multiplier. The dispersion angle can be estimated using the dispersion constant, C eff, and the mass flow rates of vapor and liquid, and written as Θ s = ṁvapor C eff (ṁvapor + ṁ liquid ) (4.41) 4.5 Spray Models Investigated in the Current Thesis As discussed in Chapter 1 of the thesis, the spray modeling capabilities of ANSYS Fluent for applications in the combustors of gas turbine engines were evaluated in this work by considering different benchmark validation cases. Note that not all of the primary spray modeling techniques described above were considered in this thesis. The single injection model was the main primary breakup method used in all of the present simulations. In addition, the airblast atomizer and the plain orifice atomizer models were also evaluated for the experimental cases of interest. Nevertheless, all of the secondary breakup models in ANSYS Fluent, including the TAB, wave, KHRT, and SSD models, were compared and evaluated as part of this thesis.

51 Chapter 5 Numerical Results for Liquid Jet in a Cross-flow 5.1 Introduction The numerical simulation of a liquid jet in a cross-flow (LJIC) was investigated as part of this thesis. ANSYS Fluent was used to model the breakup of the liquid jet. Different breakup and treatments for the turbulence were examined. The problem of liquid jet in a cross-flow has many applications such as afterburners for gas turbines, lean premixed prevaporized ducts and augmentors. As Figure 5.1 shows, the primary breakup occurs as the liquid is injected and consists of a liquid column region which is followed by the formation of large ligaments and droplets. The primary breakup is followed by a dilute spray region consisting of smaller droplets created during secondary breakup. The drag forces generated by the cross-flow bends the liquid jet and contributes to column breakup. The column fracture depends on several parameters including the momentum flux, cavitation in the injection nozzle, pressure fluctuations, and turbulence [15]. Several previous experimental and numerical studies have investigated the breakup of a liquid jet in subsonic or supersonic cross-flows. For example, Wu et al. developed correlations for droplet locations, velocities, and diameters by solving momentum equations for a spherical droplet [52]. Mazaloon et al. and Sallam et al. performed investigations on the primary breakup of the jet using holograph techniques [53]. They found similar- 35

52 Chapter 5. Numerical Results for Liquid Jet in a Cross-flow 36 Figure 5.1: Liquid jet in a cross-flow [52]. ities between breakup of a liquid jet in a cross-flow with secondary breakup of droplets subjected to shock wave disturbances [54]. Leong and Hautman also measured the spray characteristics close to the orifice using Jet-A as the test liquid [55]. Correlations for column waves present along the jet was developed by Sallam et al. [54]. Several studies have also reported satisfactory agreement between the experimental data and simulated results using various sub models for the jet breakup. Madabhushi calculated the water jet atomization using complex sub models and reported reasonable agreement with the experimental data [56]. Madabhushi et al. further enhanced the models developed by Madabhushi and modified the model based on correlations developed by Sallam et al. [15]. The results were also compared with the near field experimental spray data reported by Leong and Hautman [55]. A recent study conducted by researchers at Pratt & Whitney converted the model developed by Madabhushi into a user-defined function (UDF) and applied together with ANSYS Fluent solver to model the breakup process [12]. The focus of the current study is to use ANSYS Fluent to model the experimental setup presented by Leong and Hautman, and compare the results with experimental and numerical data found by Madubhushi and Sen et al.. The experimental setup used by Leong and Hautman is shown in Figure 5.2 [55]. The test facility consisted of a cross-flow air injection system, a test section where the liquid was injected, and an exhaust chamber. The air is injection to the system using a plenum air-feed and bellmouth inlet. The

53 Chapter 5. Numerical Results for Liquid Jet in a Cross-flow 37 Figure 5.2: Experimental setup used by Leong and Hautman [55]. exhaust chamber includes quartz windows having a height of mm and a width of 50.8 mm. For the cases of interest, the liquid injector is located mm away from the entrance of the test section. Two different liquid orifices with diameters of mm and mm are used for the experiment. Both of these orifices have a length of 12.7 mm [15]. Droplet velocities and diameters were measured by Leong and Hautman using phase doppler interferometry (PDI) technique. The measurements were obtained in a plane 25.4 mm downstream the orifice exit. 5.2 Experimental Cases and Computational Setup The experiments performed by Leong and Hautman were conducted under atmospheric temperature and pressure conditions. Experiments were performed for four different test cases. Madubhushi modeled these four cases and compared the results obtained for flow rate, droplet size, and droplet velocity [15]. Sen et al. also used case 3 as described in [15] to validate the UDF model created for the spray breakup [12]. The current thesis focuses on validating both breakup and turbulence models in ANSYS Fluent using three cases originally used by Leong and Hautman for their experiments. Table 5.1 shows the

54 Chapter 5. Numerical Results for Liquid Jet in a Cross-flow 38 Table 5.1: Operating conditions for the three test cases. Case 1 Case 2 Case 3 ṁ l (kg/h) Diameter(mm) V j (m/s) We l Figure 5.3: Mesh 1 (67000 nodes) [15]. details of the conditions for the cases considered. This table also includes the Reynolds and Weber numbers for both the liquid and cross-flow gas. The liquid Reynolds and Weber numbers are found using liquid properties and orifice diameter. The gas Reynolds number is a function of gas properties and the hydraulic diameter of the test section. The gas Weber number is also computed using the gas properties and liquid surface tension. The mesh and computational domain created by Sen et al. was used as the base mesh when modeling the breakup using different spray breakup and turbulence models in ANSYS Fluent. A schematic of the side view of this three dimensional computational domain, referred to here as mesh 1, is shown in Figure 5.3. The test section consists of 364,000 tetrahedral elements and 67,000 nodes. The resolution of the mesh is higher for the region near the fuel injector to capture the primary and secondary breakup procedures. The mesh resolution is sufficient for RANS simulations. However, higher mesh resolutions are needed for LES and hybrid RANS/LES simulations in order to capture the turbulence. Consequently, two finer meshes were created using ICEM CFD. Mesh 2 contains 213,000 nodes while the mesh 3 has the highest resolution with consisting of approximately 866,000 nodes. All the meshes have higher resolution near the fuel orifice.

55 Chapter 5. Numerical Results for Liquid Jet in a Cross-flow 39 Figure 5.4: Mesh 2 ( nodes). Figure 5.5: Mesh 3 ( nodes). Table 5.2: Meshes used for LJIC simulations (dimensions in microns). Mesh 1 Mesh 2 Mesh 3 Number of nodes Minimum grid spacing Number of points in the orifice diameter for a diameter of mm Number of points across the duct at 1 inch downstream the injector Upstream portion of fuel orifice Not included Included Included The details of the three meshes used are shown in Table 5.2. Mesh 1 has a minimum grid spacing of 736 microns, while including 3 points in the orifice diameter. The minimum grid spacings for mesh 2 and 3 are 373 and 75 microns respectively. Mesh 2 includes 6 points in the orifice diameter, while 20 points are present in the orifice diameter of mesh 3. In addition, mesh 2 and 3 also include a discretization of the upstream portion of the

56 Chapter 5. Numerical Results for Liquid Jet in a Cross-flow 40 fuel orifice (the grid is extended 12.7 mm upstream of the orifice). The simulations were performed using the discrete phase model available in ANSYS Fluent, which, as stated previously, uses a Lagrangian-based treatment for the liquid spray. ANSYS Fluent offers various injection and atomizer models for the primary breakup. The breakup models available in ANSYS Fluent were described previously in Chapter 4. The liquid jet in a cross-flow was modeled by injecting several droplets at the liquid orifice using the single injection model as the primary breakup. The plain orifice atomizer model available in ANSYS Fluent was also validated using the previous experimental and numerical data. The simulations were performed using different secondary breakup models including the TAB, wave, KHRT, and SSD model. Additionally, the simulations were performed using RANS, LES, DLES and DES treatments for the turbulence. Furthermore, pressure inlet and pressure outlet were used as boundary conditions of the test section. All the simulations were performed using the computational mesh 1 with the single injection model unless stated otherwise. 5.3 Numerical Results Contours of Velocity Simulations were performed for the three test cases presented by Madubhushi as shown in Table 5.1. Figures 5.6 to 5.9 show and compare the mean axial gas velocity for the first test case on mesh 1 using the various turbulence models. The single injection model with multiple droplets was used to represent the primary breakup and the wave breakup model was used to model secondary breakup and obtain these results. The axial gas velocity reaches a maximum of approximately m/s before decreasing near the liquid orifice. The results obtained from these simulations show similar behavior for the mean velocity of the gas phase. The figures specifically show similar results for LES, DES, and DLES simulations. This result could be due to the coarse mesh used for these simulations. The resolution of this mesh may not be sufficient to capture the turbulence for LES and Hybrid RANS/LES simulations. Simulations were also performed for finer meshes and are described in Section to follow.

57 Chapter 5. Numerical Results for Liquid Jet in a Cross-flow 41 Figure 5.6: Mean axial gas velocity for case 1 using RANS (m/s). Figure 5.8: case 1 using LES (m/s). Mean axial gas velocity for Figure 5.7: case 1 using DLES (m/s). Mean axial gas velocity for Figure 5.9: case 1 using DES (m/s). Mean axial gas velocity for Spatial Variation of the Droplets Figures 5.10 to 5.13 show the spatial variation of the droplets for different secondary breakup models available in ANSYS Fluent. The standard k-ɛ RANS turbulence model on mesh 1 was used to obtain all of the results. These figures are presented to provide a better understanding of the breakup process. The result obtained from the TAB breakup model shows a narrow distribution of the droplets. The results obtained using the wave and KHRT methods are in good agreement. These figures also show the data collection plane 1 inch downstream the orifice used to collect the particle information to be compared with previous experimental and numerical data. The wave breakup model is mostly used for higher Weber numbers, when the breakup is due the relative velocity between the gas and liquid phases. Spanwise distribution of the droplets at the data collection plane is shown for different turbulence models in Figures 5.14 to 5.17, again for mesh 1. These figures again show similar results for different turbulence models.

58 Chapter 5. Numerical Results for Liquid Jet in a Cross-flow 42 Figure 5.10: Topview of the droplets for case 1 using wave model. Figure 5.12: droplets using wave model. Spatial variation of the Figure 5.11: droplets using TAB model. Spatial variation of the Figure 5.13: Spatial variation of the droplets using KHRT model Droplet Diameter The predicted droplet diameter is compared for different secondary breakup and turbulence models. Figure 5.18 shows the previous results found by Sen et al. [12]. Figures 5.19 and 5.20 compare the breakup and turbulence models for the first case. The experimental data show an initial increase in droplet Sauter mean diameter (SMD) as we move away for the wall. Note that the SMD of a droplet is defined as the diameter of a sphere having the same ratio between volume and surface area of the droplet. The overall droplet size increases as the transverse distance is increased. There is slight droplet diameter decrease present at around 10 and 20 mm away from the wall. The initial increase in droplet SMD is because of the thickening of the boundary layer, which results in an

59 Chapter 5. Numerical Results for Liquid Jet in a Cross-flow 43 Figure 5.14: Spanwise distribution of the droplets for RANS. Figure 5.16: Spanwise distribution of the droplets for LES. Figure 5.15: Spanwise distribution of the droplets for DES. Figure 5.17: Spanwise distribution of the droplets for DLES. increase of the wavelength of the surface waves. This trend continues up to the point of column fracture. A wider range of droplet sizes are introduced as the result of column fracture and secondary breakup. Consequently, the droplet diameter slightly decreases before increasing again. The larger droplets having lower accelerations also tend to move to the edge of the spray [15]. The results obtained for the wave and KHRT models show identical results, which are in good agreement with the experimental data. On the other hand, the SSD and TAB models show a narrow distribution of the droplets. The RANS simulation generates better results compared to other turbulence models. The results obtained for finer meshes are compared in Section The wave model when used in conjunction with the RANS turbulence model, produces reasonable results up to around 25 mm away from the wall. These results however fail to predict the presence of larger

60 Chapter 5. Numerical Results for Liquid Jet in a Cross-flow 44 Figure 5.18: Droplet diameter found by Sen et al. [12]. Figure 5.19: Droplet diameter for case 1 using RANS turbulence model. Figure 5.20: Droplet diameter for case 1 using wave breakup model. droplets at the outer edge of the spray. Figures 5.21 and 5.23 compare the results obtained for the second test case using mesh 1. This case accounts for a low momentum jet case where the column fractures occurs close to the liquid orifice. The results again show a narrower distribution of the droplets for TAB and SSD simulations. The numerical results show similar behavior for all the turbulence models. LES and DES results are in good agreement and correctly predict the final decrease in droplet SMD due to presence of large droplets at the edge of the spray. Figures 5.22 and 5.24 illustrate the results obtained for the third case, again with mesh 1. The third case has a larger orifice diameter resulting in a higher momentum

61 Chapter 5. Numerical Results for Liquid Jet in a Cross-flow 45 Figure 5.21: Droplet diameter for case 2 using RANS turbulence model. Figure 5.23: Droplet diameter for case 2 using wave breakup model. Figure 5.22: Droplet diameter for case 3 using RANS turbulence model. Figure 5.24: Droplet diameter for case 3 using wave breakup model. jet. The droplet diameter is mostly underpredicted for different turbulence and breakup models, especially for the region close to the wall. ANSYS Fluent produces similar results for LES, DES, and DLES models. All of the models fail to predict the final increase in droplet SMD Droplet Velocity The predicted distributions of the droplet axial velocity are also compared for different breakup and turbulence models in ANSYS Fluent using mesh 1. All the data is collected at a plane 1 inch downstream the orifice. Figures 5.25 and 5.26 compare the results

62 Chapter 5. Numerical Results for Liquid Jet in a Cross-flow 46 Figure 5.25: Droplet axial velocity for case 1 using RANS turbulence model. Figure 5.26: Droplet axial velocity for case 1 using wave breakup model. obtained for the first test case. The droplet velocity initially decreases up to the point of column fracture. As the air goes around the jet it creates a low velocity wake which results in an initial decrease in droplet velocity. Column flattening, which is present in the wake region results in lower velocities for the droplets. The velocity then starts to increase before a final decrease due the presence of larger droplets at the outer edge of the spray [15]. The increase in droplet velocity after the column fracture is because of the introduction of smaller droplets due to secondary breakup. The wave breakup model is in a better agreement with the experimental data and correctly predicts the initial decrease in droplet velocity, however it fails to predict droplets closer to the outer edge of the spray. The RANS turbulence model shows a lower point for the column fracture, which is in a better agreement with the experimental data as opposed to other turbulence models. The overall droplet velocity is overpredicted for the region close to the wall. Figures 5.27 and 5.29 show the droplet axial velocity for the second test case. The experimental results dont show an initial decrease in droplet velocity. This is due to the fact that column fracture occurs close the wall before the first experimental point. The wave and KHRT models however correctly predict the initial decrease in droplet velocity. Droplet velocity is also compared for the third test case having the highest jet momentum. The results show a narrow distribution of the droplets for the TAB and SSD models while the wave and KHRT models are in better agreement with the experimental data. Near wall predictions of droplet velocity are higher than the experimental measurements. The wake effect may not be properly modeled in ANSYS Fluent, which results in higher

63 Chapter 5. Numerical Results for Liquid Jet in a Cross-flow 47 Figure 5.27: Droplet axial velocity for case 2 using RANS turbulence model. Figure 5.29: Droplet axial velocity for case 2 using wave breakup model. Figure 5.28: Droplet axial velocity for case 3 using RANS turbulence model. Figure 5.30: Droplet axial velocity for case 3 using wave breakup model. velocity values for droplets close to the wall Sensitivity Analysis for Spray Model Constants The wave secondary breakup model was chosen to be the best breakup option based on previous results. As a result, all the following simulations are performed only for the wave secondary breakup model. The wave breakup model includes a constant B1 as given by [2]: τ = 3.726B 1a ΛΩ (5.1)

64 Chapter 5. Numerical Results for Liquid Jet in a Cross-flow 48 Figure 5.31: Droplet diameter for case 1 using wave and RANS models. Figure 5.32: Droplet axial velocity for case 1 using wave and RANS models. where a is the radius of the parent droplet, Λ represents the wavelength of the fastest growing surface wave of the original droplet, τ is the breakup time, and Ω represents the maximum growth rate. The recommended value for B1 is Figures 5.31 and 5.32 show predicted results for the SMD and droplet velocity for a range of values of B1 from 1.73 to 30. Simulations were also performed for B1 values smaller than These values did not improve the results and are not presented in this section. As Figure 5.31 shows, ANSYS Fluent under predicts the overall droplet SMD, as the value of B1 is increased. The results for droplet axial velocity are also in a better agreement with the experimental data when the default value of 1.73 is used Delayed Breakup The single injection model was used as the primary breakup model for all the previous simulations. The single injection model injects particles at the liquid orifice without taking into account the presence of an intact liquid core. All the previous results also fail to show the presence of larger droplets at the outer edge of the spray. Therefore, a delayed breakup mechanism was used in which particles are injected at positions further downstream above the fuel orifice in an attempt to improve the results. Figures 5.33 and 5.34 show the results obtained for this delayed primary breakup for a range of values of initial injection height from to 0.5 mm. Despite showing the presence of droplets

65 Chapter 5. Numerical Results for Liquid Jet in a Cross-flow 49 Figure 5.33: Droplet diameter for case 1 using wave and RANS models (delayed breakup). Figure 5.34: Droplet axial velocity for case 1 using wave and RANS models (delayed breakup). at the edge of the spray, as the initial height of the breakup point is increased, the results do not match the experimental data and the overall droplet velocity is over predicted. ANSYS Fluent also offers a plain orifice atomizer as a primary breakup model. The results obtained using this model is analyzed in the following section Primary Breakup All the previous simulations were conducted using the single injection model, which simply injects a single droplet into the domain. The single injection model does not account for the presence of the intact liquid core. By increasing the number of particle injections however, the number of droplets increases and we obtain a more realistic model for the breakup process. The previous simulations were performed by injecting 37 particles at the orifice at each time step. The simulations were repeated for the third case using the plain orifice atomizer model available in ANSYS Fluent. The plain orifice atomizer is one of the most common atomizers in industrial applications. The plain orifice atomizer is further discussed in Chapter 4. Three different meshes were created as discussed previously in Section 5.2. Mesh 2 and 3 contain the upstream portion of the liquid nozzle to be used in conjunction with the plain orifice atomizer. Figures 5.35 and 5.36 compare the droplet diameter and axial velocity using mesh 2 and 3. The plain orifice model tends to under predict the initial droplet diameter. The results obtained with the single injection

66 Chapter 5. Numerical Results for Liquid Jet in a Cross-flow 50 Figure 5.35: Droplet diameter for case 3 using wave and RANS models. Figure 5.36: Droplet axial velocity for case 3 using wave and RANS models. model are in better agreement with the experimental data. The plain orifice atomizer is unable to properly take into account the wake effect formed behind the jet and under predicts the initial droplet diameter. Based on the results obtained from this section it can be concluded that the single injection model still provides better results for liquid jet in a cross-flow Analysis of Mesh Sensitivity This section investigates and compares the results obtained for mesh 2 and 3. Figures 5.37 to 5.40 show the droplet diameter obtained for the third case using different turbulence models. As the mesh resolution is increased, it is expected that the turbulence of the gaseous phase is captured more accurately. However, the figures show better results for coarser meshes. Mesh 3, which is the finest mesh with containing 866,000 nodes, is unable to produce accurate results. Further evidence for this is provided by Figures 5.41 to 5.44, which compare the droplet axial velocity for the third case. The predictions obtained from mesh 1 and 2 are again in a better agreement with the experimental data. Mesh 1 and 2 correctly predict an increase in droplet velocity after the point of column fracture. Mesh 3 however, shows a continuous decrease in droplet velocity as we move away form the wall. ANSYS Fluent predicts similar results for all the turbulence models. Insight into what may be happening is provided by Table 5.3. The table compares the

67 Chapter 5. Numerical Results for Liquid Jet in a Cross-flow 51 Table 5.3: Mesh analysis (dimensions in microns). Mesh 1 Mesh 2 Mesh 3 Number of nodes Minimum grid spacing Overall droplet SMD Ratio of the maximum droplet size to minimum grid spacing Ratio of the overall droplet SMD to minimum grid spacing particle diameter with the grid size for the three meshes used for the simulations. Mesh 3, which is the finest mesh, has a minimum grid spacing in the range of the droplet diameter. It seems that ANSYS Fluent cannot produce accurate predictions for this case when the particle diameter is on the order of the grid spacing. Therefore, while increased resolution may be required for the accurate prediction of the turbulence, there appears to be limitations in the DPM of ANSYS Fluent when the grid spacing approaches the droplet diameter such that the droplet occupies a significant portion of the computational cell. This casts doubt on the possibility of using Lagrangian-based spray models with LES, DES, and DLES for describing the turbulence within ANSYS Fluent.

68 Chapter 5. Numerical Results for Liquid Jet in a Cross-flow 52 Figure 5.37: Droplet diameter for case 3 using RANS. Figure 5.39: Droplet diameter for case 3 using LES. Figure 5.38: Droplet diameter for case 3 using DES. Figure 5.40: Droplet diameter for case 3 using DLES.

69 Chapter 5. Numerical Results for Liquid Jet in a Cross-flow 53 Figure 5.41: Droplet axial velocity for case 3 using RANS. Figure 5.43: Droplet axial velocity for case 3 using LES. Figure 5.42: Droplet axial velocity for case 3 using DES. Figure 5.44: Droplet axial velocity for case 3 using DLES.

70 Chapter 6 Numerical Results for Airblast Atomizer 6.1 Introduction Airblast atomizers have an additional air stream compared to single substance injectors, to facilitate the breakup of the liquid sheet. The liquid sheet formed by the nozzle is atomized by the additional air stream. The assisting air stream contributes to sheet instability and produces smaller droplets. Most gas turbine engines utilize a prefilming type of airblast atomizer, where the liquid is spread out on a surface to produce a thin sheet. The sheet experiences breakup as it is subjected to the high velocity air. Prefilming atomizers improve the atomization efficiency and reduce the exhaust smoke and soot formation. The airblast atomizer investigated in this thesis consists of two separate airflows to allow atomization of the liquid stream on both sides of the sheet formed in the nozzle. A strong swirling flow is also used to create a conical spray by deflecting the droplets outward in the radial direction [1]. Airblast atomizers have been investigated in previous experimental and numerical studies. A previous experimental study on an airblast atomizer, was decided to be chosen to evaluate the capabilities of spray modeling within ANSYS Fluent. Various relevant experimental cases were reviewed as possible validation cases. Breakup phenomena in a 54

71 Chapter 6. Numerical Results for Airblast Atomizer 55 Figure 6.1: Prefilming airblast atomizer [13]. coaxial airblast atomizer was reviewed by Engelbert et al. [57]. Liu et al. introduced an experimental setup for finding the droplet size distribution of an airblast atomizer using a finite stochastic breakup model (FSBM) as the numerical modeling method for comparison with the experimental results [58]. Dumouchel et al. presented experimental investigation on primary atomization of airblast atomizers [59]. The atomizer model presented by Watanawanyoo et al. also investigated the flow characteristics and droplet size using distilled water as the test liquid [60]. Gurubaran et al. investigated the atomization of a prefilming airblast atomizer in a strong swirling flow [13]. The study conducted by Gurubaran et al. was chosen as the validation case for the airblast atomizer model in ANSYS Fluent. The schematic of the prefilming airblast atomizer used by Gurubaran et al. is shown in Figure 6.1. The experimental setup consisted of an air supply system, an injector, a fuel supply system, and a mechanism to collect particle information. The prefilming airblast atomizer is surrounded by a swirler having an outer diameter of 40 mm, and an inner diameter of 33 mm [13]. 6.2 Experimental and Computational Setup Gurubaran et al. investigated the atomization process using various experimental flow conditions. One of the flow conditions from the original paper, the one for which there

72 Chapter 6. Numerical Results for Airblast Atomizer 56 Figure 6.2: Computational domain. Figure 6.3: Sideview of the airblast mesh. Table 6.1: Meshes used for the airblast atomizer (dimensions in mm). Coarse Mesh Fine Mesh Number of nodes Minimum grid spacing Number of points across the inlets of the atomizer Number of points across the swirler Number of points across the diameter of the duct exists the most experimental data, was selected for the present simulations. For this case, the air is entered the system with a flow rate of 1250 liters per minute. The liquid flow rate is 270 cc/m leading to a 5.43 air to liquid ratio. The air having an initial velocity of 10.4 m/s enters the atomizer via two separate inlets to improve atomization. The atomizer is surrounded by a swirler having a swirl number of 1.09 [13].

73 Chapter 6. Numerical Results for Airblast Atomizer 57 Figure 6.4: Contour of the air velocity magnitude for the fine mesh. Figure 6.5: Contour of the air axial velocity for the fine mesh. Figure 6.6: Computational results for sideview of the droplet breakup using the fine mesh. Figure 6.7: Computational results for spanwise distribution of the droplets using the fine mesh. Several important boundary conditions for the liquid phase are missing from the original paper presented by Gurubaran et al. [13]. Consequently, a sensitivity analysis was performed for these various boundary conditions of the airblast atomizer. In particular, the sensitivity of the predicted spray solutions to the flow rate, spray angle, and film thickness were all investigated. The droplet breakup process and velocity were also investigated for the different spray breakup and turbulence models. Two different meshes were generated and used for this case. The details of these meshes are shown in Table 6.1. The coarse mesh contains 273,000 nodes and has a minimum grid spacing of 0.44 mm. This mesh includes 25 points across the air inlets and 12 points

74 Chapter 6. Numerical Results for Airblast Atomizer 58 Figure 6.8: Experimental droplet axial velocity [13]. Figure 6.9: Axial velocity for the fine mesh (film thickness= m). Figure 6.10: Axial velocity for the fine mesh (film thickness= m). across the swirler. The fine mesh consists of 1,280,000 nodes resulting in a minimum grid spacing of 0.24 mm. For this mesh, the air inlets include 40 points, while the swirler consists of 20 points. The simulations were performed using the DPM model available in ANSYS Fluent. Different turbulence models were validated for discrete phase spray modeling within ANSYS Fluent. The simulations were performed using RANS, LES, DLES and DES turbulence models. The airblast atomizer model available in ANSYS Fluent was used as the primary breakup model. The simulations were performed using different secondary breakup models including wave and KHRT methods.

75 Chapter 6. Numerical Results for Airblast Atomizer 59 Figure 6.11: Axial velocity for the coarse mesh (film Thickness= m). Figure 6.13: Axial velocity for the coarse mesh (film thickness= m). Figure 6.12: Axial velocity for the coarse mesh (film thickness= m). Figure 6.14: Axial velocity for the coarse mesh (film thickness= m). 6.3 Numerical Results Contours of Air Velocity Figure 6.4 shows the contour of air velocity magnitude for the fine mesh. The velocity reaches a maximum of around 51.7 m/s. The recirculation zones created by the swirler are also shown in Figure 6.5. This figure shows the axial air velocity in the mid plane of the domain.

76 Chapter 6. Numerical Results for Airblast Atomizer 60 Figure 6.15: wave model. Droplet axial velocity for Figure 6.16: KHRT model. Droplet axial velocity for Figure 6.17: wave model. Droplet radial velocity for Figure 6.18: KHRT model. Droplet radial velocity for Film Thickness Sensitivity Analysis The liquid atomization and breakup occur as the liquid phase interacts with the surrounding air. The overall breakup process is shown in Figures 6.6 and 6.7. The spanwise distribution of the droplets shows a maximum velocity of 21.5 m/s for the droplets. The droplets velocity tends to increase as we move away in the radial direction. Consequently, droplet velocity reaches a maximum before finally decreasing. Droplet information was collected at five different planes downstream the atomizer. Figure 6.8 shows droplet axial velocity on the downstream planes found by Gurubaran et al. [13]. The experimental data show an initial increase in droplet velocity as we move away from the z axis. The

77 Chapter 6. Numerical Results for Airblast Atomizer 61 velocity then reaches a maximum of around 20 m/s, before decreasing. A sensitivity analysis on the film thickness was performed for both meshes. Figures 6.9 and 6.10 show the results obtained for two different film thicknesses for the fine mesh. The simulations were repeated for the coarse mesh and are shown in Figures 6.11 and The figures show similar results for both meshes. Simulations were also performed for two other film thicknesses shown in Figures 6.12 and The results correctly predict the final decrease in droplet axial velocity, however, they cannot predict the presence of droplets closer to z axis. The overall droplet axial velocity is increased, by decreasing the film thickness. Furthermore, the maximum velocity of 20 m/s is correctly predicted in Figure 6.12 when a film thickness of m is used. The rest of the results are obtained using the coarse mesh Comparison of Breakup Models The previous simulations were all conducted using the wave secondary breakup model. Simulations were repeated with a film thickness of m using the KHRT breakup model. As is shown in Figures 6.15 to 6.18, the KHRT breakup model produces similar results to those found previously with the wave breakup method. The wave breakup model is mostly suitable for higher Weber numbers where the breakup is due to the relative velocity between the liquid and gaseous phases. The rest of the simulations were performed using the wave breakup model Spray Angle Sensitivity Analysis The experimental data predict the presence of droplets close to the z axis. The airblast atomizer model in ANSYS Fluent enables users to specify the spray and the atomizer dispersion angles. The default value for the dispersion angle is 6. A sensitivity analysis was also performed for the spray angle and the dispersion angle. Figures 6.19 to 6.22 show the axial droplet velocity found for different spray angles. The results obtained using a dispersion angle of 45 are in best agreement with the experimental data, correctly predicting the presence of droplets closer to the central axis, a maximum velocity of around 20 m/s, and the final decrease in droplet axial velocity.

78 Chapter 6. Numerical Results for Airblast Atomizer 62 Figure 6.19: Axial velocity (spray angle=45, atomizer dispersion angle=15). Figure 6.21: Axial velocity (spray angle=30, atomizer dispersion angle=15). Figure 6.20: Axial velocity (spray angle=0, atomizer dispersion angle=45). Figure 6.22: Axial velocity (spray angle=0, atomizer dispersion angle=15) Radial and Tangential Velocities Gurubaran et al. also investigated the radial and tangential components of droplet velocity as it is shown in Figures 6.23 and 6.24 [13]. Figures 6.25 and 6.26 show the radial and tangential components of droplet velocity found for a dispersion angle of 45. ANSYS Fluent fails to predict accurate results for the radial and tangential components of velocity. The default airblast atomizer in ANSYS Fluent does not include a model for the swirler. As a result, the tangential component of the initial droplet velocity is neglected. A UDF file was used to add the tangential component of the initial droplet velocity. The results found for this UDF are shown in Figures 6.27 and The airblast atomizer model in ANSYS Fluent still needs modifications to properly model the complex physics

79 Chapter 6. Numerical Results for Airblast Atomizer 63 Figure 6.23: Experimental droplet radial velocity [13]. Figure 6.24: Experimental droplet tangential velocity [13]. Figure 6.25: Radial velocity (spray angle=0, atomizer dispersion angle=45). Figure 6.26: Tangential velocity (spray angle=0, atomizer dispersion angle=45). behind droplet breakup and atomization in a prefilming airblast atomizer Comparison of the Turbulence Modeling The previous simulations were repeated using the first mesh for other turbulence models including LES, DES, and DLES. The results found for all the turbulence models are compared in Figures 6.29 to The figures show similar results for all the turbulence models. The results were obtained using the first mesh which consists of nodes and has a minimum grid spacing of 0.24 mm. Finer meshes are recommended to be used for grid converged RANS, as well as LES, DES, and DLES. However, fine meshes may

80 Chapter 6. Numerical Results for Airblast Atomizer 64 Figure 6.27: Radial velocity using UDF (spray angle=0, atomizer dispersion angle=45). Figure 6.28: Tangential velocity using UDF (spray angle=0, atomizer dispersion angle=45). not produce accurate results when the grid spacing is smaller than the particle diameter Results for Optimal Parameter Selection Figures 6.33 to 6.35 show the most accurate set of results obtained from the previous sections and compare the findings directly with the experimental data. A film thickness analysis was performed and mentioned in details in Section Based on the film thickness analysis, a film thickness of m generates the best results and shows a maximum droplet axial velocity of around 20 m/s in agreement with the experimental data, as is shown in Figure As was mentioned before, most of the models fail to show the precense of droplets close to z axis. However, the results obtained for a dispersion angle of 45, when the atomizer angle is 0, correctly predict the initial increase in droplet axial velocity as we move away in the radial direction. Nevertheless, the overall droplet axial velocity is over-predicted by ANSYS Fluent. Figures 6.34 and 6.35 show the results obtained for the radial and tangential components of the velocity using a UDF to incorporate the initial swirl factor of droplet velocity. In general, the results predict the observed trends for the experimental radial and tangential velocities. However, it would seem that further improvements or modifications to the spray modeling approach in ANSYS Fluent are needed to obtain more accurate results.

81 Chapter 6. Numerical Results for Airblast Atomizer 65 Figure 6.29: Axial velocity using RANS and wave models. Figure 6.31: Axial velocity using LES and wave models. Figure 6.30: and wave models. Axial velocity using DLES Figure 6.32: Axial velocity using DES and wave models.

82 Chapter 6. Numerical Results for Airblast Atomizer 66 Figure 6.33: Comparison of experimental and numerical results for axial velocity [13]. Figure 6.34: Comparison of experimental and numerical results for radial velocity [13].

83 Chapter 6. Numerical Results for Airblast Atomizer 67 Figure 6.35: Comparison of experimental and numerical results for tangential velocity [13].

84 Chapter 7 Numerical Results for High Shear Fuel Nozzle 7.1 Introduction As a last benchmark validation case for the spray modeling study, a high shear fuel nozzle was examined. The high shear fuel nozzle case studied in the present work is based on the work done by Li et ll., who investigated the spray atomization and droplet transport created by a complex nozzle system consisting of different swirlers [14]. Figure 7.1 shows the injector used by Li et al [14]. The injector is surrounded by two swirlers. The inner swirler contributes to the breakup process by increasing the hydrodynamic forces between the air and the liquid, which is injected using six orifices. As a result, the liquid reaches the wall of the swirler creating a thin film. This thin sheet of liquid is further atomized by the second swirling air flow [14]. The swirling air streams also increase the tangential component of the droplets velocity. The two-step atomization produces finer droplets and increases the efficiency. Several previous studies have investigated the physics behind the atomization process for the high shear fuel nozzles. Most of the studies focused on the breakup of the liquid jet in a cross-flowing air. Shedd et al. investigated the atomization of the liquid film by a high velocity air stream [61]. Arienti et al. modeled the wall film formation and droplet breakup using a discrete phase approach [62]. The dynamics of the atomization process 68

85 Chapter 7. Numerical Results for High Shear Fuel Nozzle 69 Figure 7.1: High shear fuel nozzle [14]. Figure 7.2: Computational domain for the high shear fuel nozzle [14]. and liquid jet decomposition were further investigated by Arienti et al. [63]. Becker et al. investigated the breakup process of a kerosene jet in a cross-flowing air at high pressures [64]. Li et al. investigated the physics behind the near-field distribution of the droplets in a liquid jet in a cross-flow configuration [65]. The far-field atomization details for a liquid jet in a cross-flow were also investigated [66]. As mentioned above, the high shear fuel nozzle validation case is based on the work done by Li et al., who investigated the air velocity and spatial variation of the droplets

86 Chapter 7. Numerical Results for High Shear Fuel Nozzle 70 Figure 7.3: Near injector mesh. Figure 7.4: High shear fuel nozzle mesh. for a complex swirler/nozzle configuration [14]. A coupled level set and volume of fluid (CLSVOF) method was used by Li et al. to capture the interactions between the liquid and gaseous phases [67]. This method directly solves the Navier-Stokes equations for incompressible flow, without using LES subgrid models. The complex geometry of the injector was modeled using an embedded boundary approach [68]. The model created by Li et al. also used an adaptive mesh refinement (AMR) method and a ghost of fluid (GF) approach to enhance the accuracy of the results [69]. A Lagrangian-based method was also used to track the droplets. The results obtained by Li et al. were further compared with the experimental results found at the ambient spray facility of United Technologies Research Center (UTRC). A phase doppler interferometry (PDI) technique was used to capture droplet statistics. Furthermore, a mechanical patternator device was used to calculate fuel fluxes [14]. 7.2 Experimental and Computational Setup Figure 7.2 shows the computational domain used for the simulations. Air enters the swirler from two different air inlets with a velocity of 70 m/s. Liquid particles are injected to the system from six orifices using the single injection method available in ANSYS Fluent. The droplets are injected with an initial velocity of 8.43 m/s which results in a momentum flux ratio of 9.4 [14]. The liquid droplets are treated and tracked using a Lagrangian-based method. The liquid droplets can exchange mass, momentum, and energy with the continuous phase. Simulations were repeated for different turbulence and secondary breakup models. Figure 7.2 also shows the two measurement planes located downstream the nozzle.

87 Chapter 7. Numerical Results for High Shear Fuel Nozzle 71 Figure 7.5: Contours of mean velocity magnitude. Figures 7.3 and 7.4 show the unstructured mesh used for the simulations. The mesh consists of 163,000 nodes, and has a minimum grid spacing of 75 microns. This mesh includes around 3 nodes across each of the fuel orifice diameters and approximately 15 nodes across each of the air inlets. As was mentioned earlier in Chapter 5, ANSYS Fluent may not be able to predict accurate results for meshes having smaller grid spacing than the particle diameter. Refining the mesh used for the high shear fuel nozzle, creates smaller grid spacings, which may not be compatible with the Lagrangian-based spray modeling in ANSYS Fluent. For these reasons, a finer mesh was not considered for this case. 7.3 Numerical Results Contours of Gas Velocity Contours of mean gas velocity are shown for the high shear fuel nozzle. For the results shown, the simulations were performed using the wave secondary breakup model and

88 Chapter 7. Numerical Results for High Shear Fuel Nozzle 72 Figure 7.6: Contours of mean axial velocity. Figure 7.7: Experimental air velocity magnitude [14]. a RANS turbulence approach. Figure 7.5 shows the contour for the mean gas velocity magnitude. Air enters the inlets at a velocity of 70 m/s and reaches a maximum of 145 m/s downstream the injector. Figure 7.6 shows the air mean axial velocity clearly showing the recirculation zones where the axial velocity is negative. Li et al. collected the air velocity at two planes downstream the injector [14]. These planes are located 1.1 inch and 1.6 inch away from the injector. Figures 7.7 and 7.8 show the air velocity magnitude found by Li et al. at the data collection planes [14].

89 Chapter 7. Numerical Results for High Shear Fuel Nozzle 73 Figure 7.8: Numerical air velocity magnitude [14]. Figure 7.9: Air velocity for RANS model. Figure 7.10: Air velocity for LES model. The figures on the left show the velocity for the plane 1.1 inch downstream the injector, while the figures on the right show the air velocity 1.6 inch downstream the injector. The results found by Li et al. show an increase in air velocity as we move away from the z axis. The velocity reaches a maximum of around 80 m/s for both planes before finally decreasing. Figure 7.9 shows the results found for the RANS turbulence model. ANSYS

90 Chapter 7. Numerical Results for High Shear Fuel Nozzle 74 Figure 7.11: Spatial variation of the droplets [14]. Figure 7.12: Near-injector particles for the wave model. Fluent slightly over-predicts the air velocity at the downstream planes, however, the results are in a reasonable agreement with previous experimental and numerical results. The results obtained for LES modeling is shown in Figure ANSYS Fluent predicts similar results for both RANS and LES models of the current mesh.

91 Chapter 7. Numerical Results for High Shear Fuel Nozzle 75 Figure 7.13: Numerical results for droplet breakup [14]. Figure 7.14: Experimental results for droplet breakup [14] Spatial Variation of the Droplets Li et al. also investigated the spatial variation of the droplets. Figures 7.11 shows the breakup process presented by Li et al. using experimental and numerical approaches [14]. The near injector particles found using ANSYS Fluent show similar regime for the breakup.

92 Chapter 7. Numerical Results for High Shear Fuel Nozzle 76 Figures 7.13 and 7.14 show the breakup process and the spray angle found by Li et al. The results obtained using RANS and wave models are in rather good agreement with previous experimental and numerical results showing a spray angle of 65. Figure 7.16 shows the spanwise distribution of the droplets and the six orifices used for liquid injection. The swirling air increases the tangential component of the droplet velocity and leads to a counter clockwise rotation of the droplets. The results obtained using the KHRT method show similar predictions for the spray angle and the breakup process. The simulation was also repeated for the LES model. Figure 7.19 show a spray angle of 70 found for this case. The overall breakup process is similar to the results found by RANS modeling. Figure 7.20 shows the breakup process to be more random and/or chaotic compared to the previous results shown above.

93 Chapter 7. Numerical Results for High Shear Fuel Nozzle 77 Figure 7.15: Droplet breakup using RANS and wave models Figure 7.16: Spanwise distribution of the droplets using RANS and wave models.

94 Chapter 7. Numerical Results for High Shear Fuel Nozzle 78 Figure 7.17: Droplet breakup using RANS and KHRT models. Figure 7.18: Spanwise distribution of the droplets using RANS and KHRT models