T H E U N I V E R S I T Y O F T U L S A THE GRADUATE SCHOOL AND PREDICTIONS. by Risa Okita. A thesis submitted in partial fulfillment of

Transcription

1 T H E U N I V E R S I T Y O F T U L S A THE GRADUATE SCHOOL EFFECTS OF VISCOSITY AND PARTICLE SIZE ON EROSION MEASUREMENTS AND PREDICTIONS by Risa Okita A thesis submitted in partial fulfillment of the requirements for the degree of Masters of Science in the Discipline of Mechanical Engineering The Graduate School The University of Tulsa 2010

2 T H E U N I V E R S I T Y O F T U L S A THE GRADUATE SCHOOL EFFECTS OF VISCOSITY AND PARTICLE SIZE ON EROSION MEASUREMENTS AND PREDICTIONS by Risa Okita A THESIS APPROVED FOR THE DISCIPLINE OF MECHANICAL ENGINEERING By Thesis Committee, Chair Siamack Shirazi, Co-Chair Brenton McLaury Kenneth Roberts Jeremy Edwards Yongli Zhang

3 ABSTRACT Okita, Risa (Master of Science in Mechanical Engineering) Effects of Viscosity and Particle Size on Erosion Measurements and Predictions Directed by Dr. Siamack Shirazi and Dr. Brenton S. McLaury (155 pp., Chapter 8: Future Work) (310 words) In this work, the erosion rates of inconel 625, aluminum 6061-T6 and stainless steel 316 were measured for direct impingement conditions of a submerged jet. Fluid viscosities of 1, 10, 25, and 50 cp and sand particle sizes of 20, 150, and 300 µm were tested. The average fluid velocity of the jet was maintained at 10 m/s. Concurrently, an erosion equation has been generated based on erosion testing of the same material in air at particle velocities of 13, 23 and 42 m/s. The new erosion model has been compared to available models and has been implemented into a commercially available CFD code to predict erosion rates for a variety of flow conditions, flow geometries, and particle sizes. Since particle speed and impact angle greatly influence erosion rates of the material, particle velocities in the areas of interest were measured by Laser Doppler Velocimetry (LDV) and compared to the predicted particle velocities from the CFD simulations. Erosion was measured by weight loss measurements. Erosion data show that erosion rates for the 20 and 150 µm particles are reduced as the viscosity is increased, while the erosion rates for the 300 µm particles do not seem to change much for the higher iii

4 viscosities. For all viscosities considered, larger particles produced higher erosion rates, for the same mass of sand, than smaller particles. Comparisons of LDV measurements and CFD predicted particle velocities reveal that, as the particles penetrate the near wall shear layer, particles in the higher viscosity liquids tend to slow down more rapidly than particles in the lower viscosity liquids. However, CFD predictions, as well as LDV measurements, indicate that the near wall velocities of larger particles are not reduced as much by the increased viscosity as the velocities of smaller particles. This helps explain why the erosion data for larger particles is less sensitive to the increased viscosities. iv

5 ACKNOWLEDGEMENTS The author would like to acknowledge Dr. Shirazi and Dr. McLaury for their support and guidance throughout her studies and research work. The author also would like to thank her family and friends who supported her during this endeavor. v

6 TABLE OF CONTENTS Page ABSTRACT... iii ACKNOWLEDGEMENTS...v TABLE OF CONTENTS... vi LIST OF TABLES...x LIST OF FIGURES... xii CHAPTER 1: INTRODUCTION Background Research Goals and Approach...1 CHAPTER 2: LITERATURE REVIEW Introduction Background of Erosion and Models Erosion Background Erosion Model Background CFD Background Flow Simulation Turbulent Models: Reynolds Stress Model (RSM): k-ε Model: Comparison of RSM, and Standard, RNG, Realizable k-ε models: Level of accuracy of specific classes of problems: Computational time and convergence of models: Near Wall Treatment: Wall Functions: Near Wall Modeling: Particle Tracking Equation of Particle Motion: Discrete Random Walk Model: Erosion Calculation...32 CHAPTER 3: EXPERIMENTAL EROSION DATA...34 vi

7 3.1 Introduction Experimental Facility Electric Resistance (ER) Probe Background Particles Used in Erosion Measurements Erosion Results CMC vs. Glycerin Mixture Inconel 625 Results (ER Probe) Material Coupon Tests Results (Aluminum6061 and Stainless Steel 316)...48 CHAPTER 4: MEASURED AND PREDICTED VELOCITIES Introduction Laser Doppler Velocimetry Background Concept and Procedure: Seeding Particles and Measurement Locations: CFD Approach and Design Input Comparison of Predicted and Measured Velocities Contour of Measured Velocities Comparison of Predicted and Measured Velocities along Z direction Comparison of Fluid Velocities: Comparison of Particle Velocity: Comparison of Predicted and Measured Particle Velocities near the Wall Analysis of Velocity Prediction by CFD Turbulent Model Analysis Grid Size Analysis...75 CHAPTER 5: GENERATION OF EROSION MODELS Introduction Experimental Facility and Test Conditions Particle Velocity Measurement: Erosion Measurements in Air: Results Particle Velocity Results Aluminum Erosion Results in Air Stainless Steel Erosion Results in Air Generation of Erosion Models Aluminum 6061 E/CRC Equation Oklahoma #1 Sand: California 60 Sand: Stainless Steel 316 E/CRC Equation...99 CHAPTER 6: EROSION PREDICTION BY CFD Introduction Comparison of Predicted and Measured Erosion Rates vii

8 6.2.1 Predicted Erosion Rates for Inconel Predicted Erosion Rates for Aluminum Predicted Erosion Rates for Stainless Steel CFD Erosion Prediction Analysis dimensional vs. 2 dimensional axisymmetric Effects of Inlet Configurations Uniform vs. Velocity Profile Effects of Grid Size on Erosion Rates Turbulence Model Analysis Effect of Particle Distribution on Erosion Rates CFD Number of Impact Analysis CHAPTER 7: SUMMARY AND CONCLUSIONS CHAPTER 8: FUTURE WORK REFERENCES APPENDIX A : EROSION MEASUREMENT PROCEDURES A.1 Erosion Measurement A.1 Sand Rate Measurement APPENDIX B: ER PROBE EROSION RESULTS (INCONEL 625) B.1 Raw Erosion Data for 150 µm (Inconel 625) B.2 Raw Erosion Data for 20 µm (Inconel 625) B.3 Unit Conversion and Uncertainty Calculations APPENDIX C: COUPON EROSION RESULTS (LIQUID) C.1 Raw Erosion Data for 300 µm (Aluminum 6061-T3) C.2 Raw Erosion Data for 300 µm (Aluminum 6061-T3) Torab (2009) C.3 Raw Erosion Data for 150 µm (Aluminum 6061-T3) C.4 Raw Erosion Data for 150 µm (Aluminum 6061-T3) Torab (2009) C.5 Raw Erosion Data for 20 µm (Aluminum 6061-T3) Torab (2009) C.6 Raw Erosion Data for 300 µm (Stainless Steel 316) Torab (2009) C.7 Raw Erosion Data for 150 µm (Stainless Steel 316) Torab (2009) C.8 Raw Erosion Data for 20 µm (Stainless Steel 316) Torab (2009) APPENDIX D: MEASURED PARTICLE VELCITY (LDV) D.1 Measured Particle Velocity at Z = 1 mm (LDV) APPENDIX E: COUPON EROSION RESULTS (AIR) E.1 Measured Erosion Rates in Air (Aluminum 6061-T6) 150 µm 13 m/s E.2 Measured Erosion Rates in Air (Aluminum 6061-T6) 150 µm 24 m/s viii

9 E.3 Measured Erosion Rates in Air (Aluminum 6061-T6) 150 µm 42 m/s E.4 Measured Erosion Rates in Air (Aluminum 6061-T6) 300 µm 13 m/s E.5 Measured Erosion Rates in Air (Aluminum 6061-T6) 300 µm 24 m/s E.6 Measured Erosion Rates in Air (Aluminum 6061-T6) 300 µm 42 m/s ix

10 LIST OF TABLES Page 2-1 E/CRC Equations Empirical Constants Empirical Constants in Oka s Equation Erosion Rate for Inconel 625 (ER Probe) for 150 and 20 µm Erosion Results for Al6061 and SS316 (Coupon Tests) Aluminum 6061 Erosion Rates in Air Stainless Steel Erosion Rates in Air by OK#1 (Torabzadeh Khorasani, 2009) Angle Function Variables OK#1 (Aluminum 6061) Empirical Constant C for each test condition OK#1 (Al 6061) Angle Function Variables CA60 (Aluminum 6061) Empirical Constant C for each test condition CA60 (Al 6061) Angle Function Variables (Stainless Steel 316) Empirical Constant C for each test condition (SS 316) Predicted Erosion Rates for Inconel Predicted Erosion Rates for Aluminum Predicted Erosion Rates for Stainless Steel Predicted Erosion Rates for 3D vs. 2D (Aluminum - 150µm 1 cp) Predicted Erosion Rates for Different Inlet Conditions (Aluminum - 150µm) Predicted Erosion Rates for Different Grid Size x

11 (Aluminum - 150µm) Predicted Erosion Rates for Different Turbulent Models (Aluminum - 150µm) Predicted Erosion Rates for Different Sand Size (Inconel cp) Erosion Rates for 1st Impacts (Aluminum µm) xi

12 LIST OF FIGURES Page 1-1 Flow Chart of Erosion Prediction Using CFD Illustration of the Near Wall Region (Fluent 6.3 User s Guide, Chapter 12) Illustration of Particle Impact Schematic of the Experimental Facility Surface of Electrical Resistance Probe Sample Output from Cormon Software Microscopic Picture of California Size Distribution of California Microscopic Picture of Oklahoma # Sand Size Distribution of Oklahoma # Microscopic Picture of Silica Flour Sand Size Distribution of Silica Flour Erosion Rate vs. Viscosity for CMC and Glycerin mixture (V=10 m/s, 300 µm) Erosion Rate vs. Viscosity for CMC and Glycerin mixture (V=5 m/s, 300 µm) Erosion Rate vs. Viscosity for Inconel 625 (ER probe)-150 and 20 µm Schematic of New and Worn Out Probe Head Erosion Rate vs. Viscosity for Inconel 625 (ER probe)-150 µm (Torabzadeh, 2009)...47 xii

13 3-15 Erosion Rate vs. Viscosity for Aluminum with different particle sizes Erosion Rate vs. Viscosity for SS316 with different particle sizes Schematic of LDV System LDV Measurement Location Map CFD Mesh of the Flow Region and Boundary Conditions Measured Particle Velocity at z = 1 mm Contour Map for Measured Velocities of Various Particle Sizes (1 and 100 cp) Measured and Predicted Fluid Velocity vs. Axial Distance at r = 0 mm Measured and Predicted Fluid Velocities vs. Axial Distance at r = 3 mm Measured and Predicted Fluid Velocities vs. Axial Distance at r = 3 to 4 mm (1 cp) Measured and Predicted Fluid Velocities vs. Axial Distance at r = 4mm Measured and Predicted Fluid Velocity vs. Axial Distance at r = 8 mm Measured and Predicted Particle Velocities vs. Axial Distance at r = 0 mm 120 µm Measured and Predicted Particle Velocities vs. Axial Distance at r = 8 mm 120 µm Measured and Predicted Particle Velocities vs. Axial Distance at r = 8 mm 120 µm (Near Wall) Measured and Predicted Particle Velocities along z = 6 mm Measured and Predicted Particle Velocities along z = 12.3 mm Predicted Particle Velocities along z = 12.7 mm (120 and 550 µm) Predicted Velocities at Near Wall (120 µm and 550 µm, 1 and 50 cp)...71 xiii

14 4-18 Fluid Velocity for RSM and LowRe at r = 0 mm Fluid Velocity for RSM and LowRe at r = 4 mm Fluid Velocity for RSM and LowRe at r = 8 mm Diagram of Grid Adaptation Comparison of Predicted Fluid Speeds for Finer and Original Grid (1 and 50 cp) Comparison of Predicted Particle (120 µm) Speeds for Finer and Original Grid (1 and 50 cp) Process of Generating Erosion Models Schematic of LDV Measurement Box Schematic of Erosion Measurements in Air Particle Velocity vs. Fluid Velocity for air - (150 μm) Cumulative Mass Loss vs. Sand Weight for V p = 24 m/s at 15 degrees (Al 6061) Erosion Rate vs. Impact Angle for Al 6061 in Air (OK#1, 150 µm) Erosion Rate vs. Impact Angle for Al 6061 in Air (CA60, 300 µm) Erosion Rate vs. Impact Angle for SS 316 in Air (OK#1, 150 µm) (Torabzadeh Khorasani, 2009) Normalized Erosion Rate vs. Impact Angle in Air 150 µm (Aluminum 6061) Empirical Constant C vs. Impact Velocity for Different Impact Angle OK#1 (Al 6061) Erosion vs. Angle Exp. Data and Models V p = 13 m/s OK#1 (Al 6061) Erosion vs. Angle Exp. Data and Models V p = 24 m/s OK#1 (Al 6061)...93 xiv

15 5-13 Erosion vs. Angle Exp. Data and Models V p = 42 m/s OK#1 (Al 6061) Normalized Erosion Rate vs. Impact Angle in Air 300 µm (Aluminum 6061) Empirical Constant C vs. Impact Velocity for Different Impact Angle CA60 (Al 6061) Erosion vs. Angle Exp. Data and Models V p = 13 m/s CA60 (Al 6061) Erosion vs. Angle Exp. Data and Models V p = 24 m/s CA60 (Al 6061) Erosion vs. Angle Exp. Data and Models V p = 42 m/s CA60 (Al 6061) Normalized Erosion Rate vs. Impact Angle in Air (Stainless Steel 316) Empirical Constant C vs. Impact Velocity for Different Impact Angles (SS316) Erosion vs. Angle Exp. Data and Models V p = 13 m/s (SS 316) Erosion vs. Angle Exp. Data and Models V p = 28 m/s (SS 316) Erosion vs. Angle Exp. Data and Models V p = 42 m/s (SS 316) Predicted Erosion Rate and Experimental Data for Inconel (150 µm) Predicted Erosion Rate and Experimental Data for Aluminum (300 µm) Predicted Erosion Rate and Experimental Data for Aluminum (150 µm) Predicted Erosion Rate and Experimental Data for Aluminum (20 µm) Predicted Erosion Rate and Experimental Data for SS 316 (300 µm) Predicted Erosion Rate and Experimental Data for SS 316 (150 µm) Predicted Erosion Rate and Experimental Data for SS 316 (20 µm) D and 2D Meshes Illustration for Inlet Configurations Predicted Average Impact Speed vs. Radial Location - 50 cp xv

16 6-11 Predicted Average Impact Angle vs. Radial Location - 50 cp Predicted Number of Impacts vs. Radial Location - 50 cp Predicted Averaged Impact Speed vs. Radial Location for Turbulent Models - 50 cp Predicted Number of Impacts vs. Radial Location for Turbulent Models - 50 cp Number of Particle Impacting vs. Number of Impacts for 20, 150, and 300 µm Measured and Predicted Erosion Rates for 1 st Impacts Illustration of Profilometer reading Microscopic Picture of Aluminum Surface Impacted by 150 µm Glass Beads xvi

17 CHAPTER 1 INTRODUCTION 1.1 Background When oil and gas are removed from reservoirs, they usually contain impurities such as sand particles. These particles impinge the wall of the pipes that carry the gas and oil and remove material from the pipe wall. The removal of material by solid particles is called erosion. The erosion damage caused by particles can be very dangerous to an operator since pipes and fittings can rupture suddenly without prior indication of failure. Failures caused by erosion also can be very expensive to fix. In order to save money and increase the safety of an operator, many industries are using erosion models to predict when the pipeline and fittings are susceptible to erosion damage. 1.2 Research Goals and Approach The Erosion/Corrosion Research Center (E/CRC) at The University of Tulsa has conducted research on erosion and corrosion occurring under a range of conditions and pipe geometries. One of the main goals of E/CRC is to develop, validate and expand the software called Sand Production Pipe Saver (SPPS) which can predict erosion for a certain geometry and set of operating conditions. This software can be used as a tool by the oil and gas industries to predict erosion damage and a threshold velocity. Threshold velocity is a flow velocity required to minimize erosion damage. 1

18 Previously, Zhang et al (2006) at E/CRC conducted a series of erosion measurements and calculations to show that erosion equations can be utilized in Computational Fluid Dynamics (CFD) code to predict erosion. They conducted a series of erosion tests in gas and obtained an erosion equation. Then they implemented the erosion equation into a commercially available code and predicted erosion for various gas and liquid cases. However, this study was limited to only one sand particle size and only erosion resulting from sand in either gas or liquid was considered in direct impingement geometry. In order to extend the previous work and predict erosion for various viscous liquids and particle sizes, several investigators including the present author have measured velocities of particles and carrier fluid, as well as erosion rate of the direct impact geometry varying the viscosity of carrier fluid and particle sizes. Miska (2008) measured particle and fluid velocities in the direct impingement geometry utilizing Laser Doppler Velocimetry (LDV). Torabzadeh (2009) and the present author have performed erosion testing of a direct impingement geometry using material coupons and electrical resistance (ER) probes. To predict erosion rate, Computational Fluid Dynamic (CFD) simulations are performed. Gambit 2.3 and Fluent 6.3 are used to create a mesh and to simulate the flow of the direct impingement geometry. Fluent 6.3 is also used to calculate the trajectories of particles after the fluid flow is calculated. User Defined Functions (UDF) created by Zhang (2006) are utilized to perform the erosion calculations in CFD. Figure 1-1 shows the various steps that are used for erosion prediction by CFD. At first, Fluent performs a flow simulation to calculate flow parameters such as fluid pressure and velocity. After the flow calculation is performed, Fluent performs particle tracking which gives particle 2

19 parameters such as particle trajectories, velocity, and number of particle impacts at the wall. For these two stages, results of particle and fluid velocities need to be validated by LDV measurements (Miska, 2008) for selected cases. After the validation using the experimental results, erosion equations are generated which are used to calculate erosion rates in Fluent. The erosion rates calculated through Fluent are once again compared to actual experimental data and validated for selected cases. In the present work, validation of fluid velocity, particle velocity and erosion predictions are performed by comparison of the results to various experimental data. Improvements to the erosion modeling and calculations are examined and the results are compared to data for various fluid viscosities and particle sizes. Figure 1-1: Flow Chart of Erosion Prediction Using CFD In Chapter 2, a brief background is given on erosion mechanisms as well as erosion models used to predict erosion rates in this work. Background on erosion predictions by CFD is also summarized in this chapter. In Chapter 3, experimental results of erosion rates on various materials and fluid conditions are shown and analyzed. In Chapter 4, measured particle and fluid velocities of direct impingement geometry are compared to predicted velocities by CFD. In Chapter 5, a detailed background and 3

20 experimental results of solid particle erosion in gas are shown. These results are used to generate the erosion models which are used to predict erosion rates in CFD. In Chapter 6, using the erosion models developed in Chapter 5, erosion rates of various materials and fluid conditions are predicted and compared to experimental data. Chapter 7 and Chapter 8 are conclusions of this work and proposed future work. 4

21 CHAPTER 2 LITERATURE REVIEW 2.1 Introduction Erosion by solid particles has been of great interest in the last few decades. The mechanisms of solid particle erosion have been studied by numerous researchers. This chapter consists of two sections. First, a background of erosion research as well as the erosion equations used in this work is discussed. Second section, a background of the CFD erosion prediction procedure is summarized. 2.2 Background of Erosion and Models Erosion Background Erosion mechanisms can be very complex, since erosion is influenced by so many factors. Meng and Ludema (1985) studied erosion models and equations in the existing literature at that time and concluded that there is no universal model which works for all flow conditions or materials for practical use. There have been many ideas proposed by researchers on how erosion occurs. Finnie (1972) proposed that ductile material and brittle material have different erosion mechanisms. Finnie described ductile material erosion as a cutting or displacing process. He also listed the factors which may influence the erosion of ductile material. Among 5

22 these factors are particle impact angle, speed, particle size, surface properties, shape of the surface, particle shape, target strength, concentration of particles, and nature of carrier fluids. Levy et al. (1986) published the idea that erosion is caused by a formation of small distressed platelets of the target material. According to Levy, due to shear deformation at the impacting surface, the material gets heated to near the annealing temperature of the metal. The platelets are formed in this hot softened layer. Underneath the soft layer, there is a hard layer which is cold worked by plastic deformation as a result of particle impacts. This hard layer actually increases the efficiency of erosion at the surface of the material. After platelets are formed, consecutive bombardment of numerous particles at the target surface knock off these platelets formed by initial impacts. Particle impact velocity is probably the most important factor for erosion. The effect of particle velocity can easily overshadow the changes in the other factors. There are many publications which explain the relationship of erosion and particle velocity by an empirical power law as shown in Equation 2-1. ER V (2-1) Lindsley and Marda (1999) studied the effect of velocity on erosion rates on brass and Fe-C martensite. Lindsley and Marda reported that the empirical constant n is independent of target material and erosion mechanism but governed by test conditions such as particle characteristics and erosion test apparatus. According to their work, erosion resulted from the brittle cracking mechanism and plastic deformation mechanism showed the exponent n to be 2.9 for both cases even though the erosion mechanisms are 6

23 completely different. Finnie (1978) examined the effect of particle velocity on erosion and found that the exponent n should increase with impact angle for a given range of velocities. He also compared the value of n from other literature and said n ranges from 2.05 to 2.44 depending on test conditions. Particle impact angle is another important factor for erosion. Finnie (1972) derived the angle function from the equation of motion for a rigid abrasive particle striking a ductile surface. For aluminum alloys, the model shows the maximum erosion occurs at 13 degrees and decreases to zero at 0 and 90 degrees. This angle function is in good agreement with experimental data except for high impact angles. As a reason for the discrepancy between measurements and the model, Finnie states that the erosion mechanism at high angles is very different from the one at low angles. At low angles, erosion is mostly due to the cutting mechanism while at high angles, it is due to the surface roughening and low cycle fatigue fracture. Particle properties also greatly affect the erosion of ductile material. For example, difference in angularity of particle shape can cause different erosion mechanisms which yield different erosion rates. Winter and Hutchings (1974) studied the effect of particle orientation at the impact surface. Erosion measurements on mild steel and lead were performed using flat-faced angular particles. They described the different erosion mechanisms based on the angularity of abrasives by a rake angle. The rake angle, by definition, is the angle between the perpendicular to the surface and the leading edge of particle. It is found that cutting is favored when the rake angle is positive or small negative values. At large negative rake angles, ploughing rather than cutting occurs. Since spherical particles always have negative rake angles at impact, ploughing is the 7

24 only possible deformation. On the other hand, most of the abrasives are both round and angular; therefore, the deformation can be either cutting or ploughing. Bahadur and Badruddin (1990) characterized SiC, Al 2 O 3, and SO 2 particles in terms of width to length ratio (W/L) and perimeter squared to area ratio (P 2 /A) and used them as the indicator of particle shape. Erosion rates on 18 Ni (250) maraging steel was studied using these abrasives. It was found that erosion increases with increasing P 2 /A and decreasing W/L for all particles. In the publication, it was noted that angular particles are more likely to engage in cutting and ploughing while circular regular particles engage in only ploughing. Later, Palasamudram and Bahadur (1997) proposed an angularity parameter A n which is a better indicator of angularity than W/L and P 2 /A. A n is calculated based on geometrical parameters of abrasives. They measured erosion rates on 1020 steel and stated that erosion increased with an increase in A n when the particle size is constant and erosion increased with increase of size with constant A n. Particle size also influences erosion of ductile material as much as its shape. Many literatures support the idea that particle size influences erosion rates for smaller sizes: however, after a critical size which is reported to be 100 μm, effect of size on erosion is negligible (Finnie 1972, Tilly and Sage 1970) Erosion Model Background Since there is no erosion equation which works for all materials, there are three distinct erosion equations developed to predict erosion rate for three materials used in this work. Equations 2-2 and 2-3 are called the E/CRC (Erosion/Corrosion Research Center) equation. The equation was originally developed for carbon steel materials. However, 8

25 the same equation can be used for other materials if the constant C and angle function are adjusted based on erosion testing of that material. Therefore F(θ) and the constant C are different depending on material which makes the equation unique for each material. ER F C BH. V F θ (2-2) BH ( ) = H V (2-3) ER is the erosion ratio in kg of material loss over 1 kg of sand through put. F s is a sharpness factor which ranges from 0.2 to 1 depending on the shape of sand particles. Fs is 0.2 for spherical particles, 0.5 for semi-rounded sand, and 1 for sharp sand. C and n are the empirical constants. BH is the Brinnel hardness of the target material calculated based on Vicker's hardness of the material using Equation 2-3. V is the impact particle velocity and F(θ) is the function of impact angle. Equation 2-4 is the angle function obtained for Inconel 625 (Zhang et al., 2006) and Equation 2-5 is the angle function for aluminum and stainless steel. Table 2-1 shows the empirical constants for each material. The variable, θ is the impact angle of particle in radians. Equation 2-4 is a polynomial equation that relates F(θ) to impact angles. The coefficient for each term in Equation 2-4 is developed based on experiments. Equation 2-5, on the other hand has an exponential relationship to impact angles. The factor f is used to normalize the angle function and is only used for aluminum and stainless steel (Equation 2-5). The empirical constants n1, n2 and n3 are also developed based on experiments. The equation for Inconel 625 is developed by Zhang et al. (2006). The equations for Aluminum and Stainless Steel are developed based on data gathered by Torabzadeh (2009) and the present author. 9

26 (2-4) F θ sinθ 1 H 1 sinθ (2-5) Table 2-1: E/CRC Equations Empirical Constants Variables Inconel 625 Al 6061 SS 316 Hv (GPa) n f N/A n1 N/A n2 N/A n3 N/A C 2.17E E E-07 Oka et al. (2005) conducted a comprehensive study of erosion by solid particles. A sand blast type erosion test rig was used to collect erosion rates on various materials with various types of abrasives. Based on these results, a practical and a comprehensive erosion equation model which, according to Oka et al., works for any type of material and impact conditions was proposed. Equations 2-6 and 2-7 provide the erosion model developed by Oka et al. The constants K, k1, k2, and k3 are found based on particle properties and hardness of the target material. the quantity ρ is the density of the target material. The densities of Inconel, aluminum and stainless steel are 8200, 2700, and 7800 kg/m 3 respectively. V and D are the reference values based on experiments (104 m/s and 326 µm, respectively). Values for constants in each equation are shown in Table 2-2. The main difference between the E/CRC equation and Oka s equation is that Oka s equation includes a term that takes into account the effects of particle size while the 10

27 E/CRC equation does not. However, the particle size exponent, k3, is 0.19 and has a small effect on calculated erosion rates. ER K H V V D D ρ F θ (2-6) F θ sinθ 1 H 1 sinθ (2-7) Table 2-2: Empirical Constants in Oka s Equation Variables Values Hv (GPa) 3.43 k 65 k k2 2.3(Hv) k n1 0.71(Hv) 0.14 n2 2.4(Hv) Oka developed the equations based on air testing. The E/CRC equation is also developed based on direct impingement testing in air. The details of how the E/CRC equation is developed are given in Chapter 5. Previous investigators have shown that the erosion equations developed through gas testing can be used to predict erosion for liquid carrier fluids. Using the particle information such as particle speed and angle for each impingement from CFD, total erosion rates of the target material are calculated. 2.3 CFD Background As mentioned in Chapter 1, the CFD erosion prediction procedure has three main steps: flow simulation, particle tracking and erosion calculation. In this section, an overview of the CFD calculation procedure is presented. 11

28 2.3.1 Flow Simulation The first step in CFD erosion prediction is flow simulation. In this step, CFD uses governing equations (Navier-Stoke s equations) to calculate the dynamic properties of fluids such as velocity, pressure, momentum and energy. Since the flow condition is assumed to be turbulent for the direct impingement geometry, time-averaged Navier- Stokes with turbulent models is used in this work, Reynolds Stress Model (RSM) and k-ε turbulent models are used for calculation of flow fields presented. A brief overview of these models is given in the following section. After the selection of turbulence model, boundary conditions as well as fluid parameters such as viscosity, and density are specified (Turbulent Models): Turbulent flow can be distinguished from laminar flow by its velocity fluctuations. While the instantaneous velocity field of steady laminar flow does not change with time, the instantaneous velocity in turbulent flow changes randomly with time. However, it is impossible to directly simulate these fluctuations in order to calculate the flow properties such as velocity, pressure, temperature, and energy for practical cases. In order to save computational time, Navier-Stokes equations used for laminar flow can be time-averaged and be used for turbulent flow. The resulting equations are called Reynolds Averaged Navier-Stokes (RANS) equations. Equations 2-8 and 2-9 are the continuity and momentum equations for the RANS model. 0 (2-8) ρu t ρu u x p μ u u 2 x x x x 3 δ u ρu x x u (2-9) 12

29 As shown above, the RANS equations are very similar to the Navier-Stokes equations except that the momentum equation of the RANS equation has an extra term that represent the Reynolds stresses, -. The Reynolds stress term needs to be modeled in various methods to close the RANS equations. Engineers have proposed inventing many models to close the turbulent flow equations. Among these models, the Reynolds Stress Model (RSM) and k-ε models are very popular models (Reynolds Stress Model (RSM)): The Reynolds Stress Model (RSM) contains seven transportation equations (3D). The RSM model was developed to solve the transport equation for each of the terms in the Reynolds stress tensor, which means Reynolds stresses are assumed to be anisotropic. The model is known to be good in complex flows since it accounts for the effects of rotation, swirl, and change in strain rate. Reynolds stress transport equations are derived by multiplying the momentum equation by fluctuating properties and then taking the time-average of the resulting equations. Equation 2-10 shows the exact transport equation for the Reynolds stresses. t where ' ' ' ' ( u iu j ) ( ρu k u iu j ) ρ + x k = D T,ij + D L,ij + P +φ ij ij +ε ij, (2-10) D T,ij = x k ' ' [ ρu u u i j ' k + ρ( δ kj ' u + δ i ik ' u ) ] j, D L,ij = x k ' ' ( uiu j) ] [ μ x k, 13

30 P ρ u u u u x u u, x P u u, x x and ε 2µ u u. x x The first term on the LHS is called local time derivative term and the second term is the convection term. D T, is the turbulent diffusion term and D L, is the molecular diffusion, P is the stress production term, is the pressure strain term, and ε is the dissipation term. Among the various terms in Equation 2-10, D T,,, and ε need to be modeled to close the equation. The turbulent diffusion term D T, can be modeled by taking the term proportional to the gradient of. As a result, the term becomes: D T, µ u u x σ x (2-11) The turbulent viscosity, µ, is computed as follows: µ ρc µ k ε (2-12) The value of C µ is The value of σ is found to be 0.82 by Lien and Leschziner (1994). The pressure strain term is modeled in Equation The model is called the linear pressure strain model., is called the slow pressure-strain term, and, is called the rapid pressure-strain term. C is 1.8 and C is 0.6, P and C are defined in Equation 2-10 and P = 1/2P kk, C = 1/2C kk.,,, 14

31 , C ρ ε k u u 2 3 δ k, (2-13) and, C P C 2 3 δ P C follows: The dissipation rate ε and the scalar dissipation rate ε can be modeled as ρε t ε 2 3 δ ρε ρu ε x x µ µ σ ε x C 1 2 P ε k C ρ ε k (2-14) The values of constants in Equation 2-14 are σ =1.0, C = 1.44, and C = Turbulent kinetic energy k is obtained using Equation Equation 2-15 is only used for the bulk of the flow. Near the wall region, Equation 2-16 is used to obtain the kinetic energy. Equation 2-16 is derived from Equation 2-10 by taking i = j and summing from i = 1 to 3. σ is ρk t ρu k x x µ µ σ k x 1 2 P ρε (2-15) (2-16) Heat and mass transfer in the flow is modeled using an analogy to momentum transfer. The modeled equation becomes: ρe t x u ρe p x k C µ Pr T x u τ 1 2 P ρε (2-17) τ µ u x u x 2/3µ u x δ 15

32 P rt number is a constant value (k-ε Model): k-ε model consists of three models: standard, RNG, and Realizable k-ε models. RNG and realizable models are improved versions of the standard model. All three models are very similar to each other where they all have transport equations for k and ε. The differences among the three models are the methods of calculating turbulent viscosity and model empirical constants, and the generation and destruction terms in the ε equation. (Standard model): Standard k-ε model is the simplest of the three models. It was proposed by Launder and Spalding (1972). It is a semi-empirical model based on k and ε equations. k-ε model is based on the assumption that the flow is fully turbulent and the effects of molecular viscosity are negligible. Equations 2-18 and 2-19 are the transport equations for kinetic energy k and rate of dissipation ε. ρε t ρk t ρu ε x ρu k x x µ µ σ k x G ρε x µ µ σ ε x C ε k G C ρ ε k (2-18) (2-19) G is the production of turbulence kinetic energy due to the gradients of mean velocity and calculated in Equation G ρu u u x (2-20) 16

33 Turbulent viscosity µ is calculated using Equation The model constants are C =1.44, C =1.92, C µ =0.09, σ =1.0 and σ =1.3. These model constants were determined from experiments. (RNG model): RNG model differs from the standard model since it has an additional term in its ε equation and the effect of swirl is included. It also accounts for low Reynolds number effects. Equations 2-21 and 2-22 are the transport equations for the RNG model. These two equations are very similar to Equation 2-18 and 2-19 except that it has new terms of R and effective viscosity, µ. ρε t ρk t ρu ε x ρu k x x α µ k x G ρε x α µ ε x C ε k G C ρ ε k R (2-21) (2-22) In these equations, α and α are called the inverse effective Prandtl numbers for k and ε. G is the production of turbulence kinetic energy and defined in Equation Effective viscosity in the RNG model can be calculated by integrating Equation This method of solving the effective viscosity allows the RNG model to better handle low-reynolds-number flows and the near wall region. In case of high Reynolds numbers, Equation 2-12 can be used with C µ = d µ 1.72 C dν (2-23) Where ν µ /µ and C

34 One of the advantages of the RNG model over the standard model is that the RNG model accounts for swirl and rotational effects of flow in turbulent viscosity. Equation 2-24 is the modified version of turbulent viscosity. µ µ f α,ω, (2-24) In Equation 2-24, µ is the value of turbulent viscosity calculated from Equation 2-23 or Equation α and Ω are constants. α is called a swirl constant which depends on whether the flow is swirl dominated. For mildly swirling flows, the value is set to 0.07 but a higher value can be used for strongly swirling flows. The main difference between the RNG and standard model is the addition of R term in ε equation and it is given in Equation η=sk/ε, η =4.38 and β= Model constants for the RNG model are C =1.42 and C =1.68. R C µρη η/η 1 βη ε k (2-25) (Realizable k-ε model): This model is called realizable because the model satisfies the mathematical constraints of the Reynolds Stresses, which is consistent with the physics of turbulent flow. It differs from the standard model in that the realizable model contains its own formulation of turbulent viscosity and has a new transport equation for the dissipation rate which has been derived from the transport equation of the vorticity fluctuation. Equations 2-26 and 2-27 are model transport equations for k and ε in the realizable model. ρk t ρu k x x µ µ σ k x G ρε (2-26) 18

35 ρε t ρu ε x µ µ ε ρc x σ x S C ρ ε k νε S, C max 0.43, η η 5, (2-27) η S k ε, and S 2S S. In the equations above, G is the production term of turbulent kinetic energy defined in Equation2-20. C is a constant and σ and σ are the turbulent Prandtl numbers for kinetic energy and dissipation rate. S are user-defined terms. The kinetic energy transport equation in Equation 2-26 is identical to that of standard model while the dissipation rate equation is different from the standard or RNG model. The second term on the RHS of Equation 2-27 is called the production term in the dissipation rate equation and it does not contain the production of k (G k term) in the standard and RNG models. This allows the realized model to better represent the spectral energy transfer. Also, the denominator of the destruction term which is the second term from the last on the RHS does not have any singularity (Equation 2-27). Even if the k value becomes smaller, the denominator does not vanish. This is different from the standard and RNG models which have a singularity due to the k in the denominator (Equations 2-19 and 2-22) The turbulent viscosity can be computed using Equation 2-28 in the realized model. 19

36 k µ ρc µ ε, 1 C µ ku A A, ε U S S Ω Ω, (2-28) Ω Ω 2ε ω, and Ω Ω ε ω. Ω is the mean rate of the rotation tensor. ω is the angular velocity. The model constants are A = 4.04 and A = 6 cos where 1/3 cos 6 W, W S S S, S S S, S 1/2. Note that C µ is no longer constant as it is in the standard and RNG models. In the Realized model, C µ is a function of the mean strain and rotation rates and angular velocity of the system. The model constants for this model are C =1.9, σ =1.0, σ =1.2. For all the k-ε models, turbulent heat transport can be modeled using the Reynolds analogy to momentum transfer. Equation 2-29 is the equation for heat transport equation in the k-ε models. E is the total energy, and k is the effective thermal conductivity. S ρe t ρu E 1 x x k T x u τ S τ µ u x u x 2/3µ u x δ (2-29) 20

37 (Comparison of RSM, and Standard, RNG, Realizable k-ε models): Even though there are various turbulent models that have been developed to predict a variety of turbulent flows, it is known that there is no model which is superior for all problems. Model selection depends on considerations such as physics of the flow, specific class of flow, the level of accuracy required, and computational time available. Some problems are simple; the change in level of accuracy does not necessarily change the results drastically. Some models are good in specific physics of the flow while others do not work well for the specific case. Choice of model for a specific problem will depend on engineering judgment. Some of the important aspects of model selection are level of accuracy for specific problems and the computational time and resources (Level of accuracy of specific classes of problems): Each model has some different characteristics depending on the specific flow situation. One model can be superior for specific physical conditions than others, while another model performs better for a different flow condition. For example, RSM is superior for situations where anisotropy of turbulence has a great effect on the mean flow. Such cases are highly swirling flows, cyclone flows, rotating flow passages and stress driven secondary flows. The limitations of the RSM model is that the modeling of the pressure strain and dissipation terms can be challenging, and these terms become responsible for lowering the accuracy of the performance of RSM. However, among the RANS models, the RSM is said to be the most accurate and reliable model. On the other hand, k-ε models perform well with simpler problems but less accurate than the RSM. However, some improvements and modifications were done on 21

38 the standard model and as a result, the RNG and the realizable models were derived. It is known that the RNG model takes into account the effect of swirl on the turbulence model which results in a better model than the standard model in cases where swirling occurs (Equation 2-24). The additional term in the dissipation rate equation (Equation 2-25) gives more accurate results for rapidly strained flow. Also, while the standard model only works for high Reynolds number flows, the RNG model can perform relatively well in low Reynolds number cases due to the differential formula for effective viscosity (Equation 2-23). Also, the RNG model uses a formula for turbulent Prandtl numbers while the standard model uses constants. These features make RNG model more accurate and reliable for a wider range of problems than the standard model. The realizable model performs superior in cases where the flow involves rotation, free flows including jets and mixing layers, channel and boundary layers under strong adverse pressure gradients, separation, and recirculation. The realizable model is said to be the best model of all the k-ε models. This is because the realizable model satisfies mathematical constrains on the Reynolds stresses which are consistent with the physics of turbulent flow. One limitation of the realizable model is that it produces non-physical turbulent viscosities in situations when the domain contains rotating and stationary fluid zones. Such cases are multiple reference frames and rotating sliding meshes. This is due to the fact that the model includes the mean rotation term in the turbulent viscosity formula (Equation 2-28) (Computational time and convergence of models): Computational time available to solve a case should always be considered in order to achieve a level of accuracy a model can provide. The increased accuracy typically requires more 22

39 computational time. The RSM requires longer computational time than the k-ε models due to the complexity of the model. The RSM also requires additional memory due to the increased number of the transport equations. Also, the RSM requires more iterations to converge than the k-ε models due to the strong coupling between Reynolds stresses and the mean flow. Compared to RSM, k-ε models do not require much computational time. However, the k-ε models do require more computational effort than the other simpler models such as one-equation model or algebraic methods. The realizable model requires slightly more effort than the standard model. The RNG model tends to take 10/15% more computational time than the standard model. This is due to the extra terms and functions in the transport equations and the nature of non-linearity in the model. Also, for solution behavior, the standard model tends to be slightly over diffusive in some cases (Near Wall Treatment): The turbulence models described above are known to be valid only in the bulk of the flow. The existence of a wall greatly influences the nature of flow. In the near wall region, the gradients are much larger than the core flows, and the momentum and other scalar transports occur most actively. Therefore, it is important to accurately represent the flow in the near wall region in order to have successful predictions. Numerous experiments have proven that the near wall region can be divided into three layers. Figure 2-1 is a schematic of the near wall region plotted on semi-log scale. Uτ is the friction velocity defined as. y+ is the non-dimensional distance from the wall and defined as. The innermost layer is called the viscous sub-layer and the 23

40 effect of viscosity is pervasive (y + <5). The outer layer is called the fully turbulent region and turbulence plays a dominant role (y + >30 to 60). Between the viscous sub-layer and the outer layer, there is a buffer region where both viscous and turbulent effects are important (5<y + <30). Figure 2-1: Illustration of the Near Wall Region (Fluent 6.3 User s Guide, Chapter 12) In CFD, there are two approaches to model the near wall region. The wall function approach is commonly used in high Reynolds number flows. Wall functions are semi-empirical formulas used to bridge the viscosity-affected region between the wall and the fully turbulent region. For the wall function approach, the viscosity-affected region does not need to be resolved; therefore, it reduces the computational time and is economical, robust, and reasonably accurate. Another approach is called near wall modeling. In near wall modeling, the turbulence model is modified to enable the viscosity affected region to be resolved with a mesh all the way to the wall, including the viscous sub-layer. Near wall modeling is necessary in situations where low-reynolds-number 24

41 effects are dominant in the flow, since wall functions are no longer valid for these conditions. In this work, both wall functions and near wall modeling approaches are used to accurately predict the flows of interest. In the following sections, wall functions and near wall modeling are described in detail (Wall Functions): Fluent 6.3 provides four choices of wall functions: standard wall functions, non-equilibrium wall functions, enhanced wall treatment, and user defined wall functions. In this work, only standard wall functions are used. Launder and Spalding (1974) published the idea of the standard wall function which is commonly used today. According to their work, near wall mean velocity can be written as (For y + < ), (2-30) and 1/κ (For 30 < y + < 300), (2-31) Where k U UC µ τ ρ y ρc µ k y. µ, (2-32) (2-33) And κ is von Karman constant (= ), E is Empirical constant (= 9.793), C μ is Empirical constant (= 0.09), U is mean velocity of the fluid, k is turbulence kinetic energy, y is distance from the wall, and μ is dynamic viscosity of the fluid. 25

42 Equation 2-30 is valid when y* < and has a linear relationship. The quantity y* is equal to y+ in equilibrium turbulent boundary layers. For locations, where 30 < y* < 300, the logarithmic law is applied (Equation 2-31). In the k-ε models and some cases in the RSM, the k equation is solved on the whole domain including the near wall region. The production of kinetic energy, G k, and its dissipation rate, ε, in the k equation at the wall-adjacent cells are assumed to be equal and computed from and τ G τ κρc / µ k / y, / /. (2-34) (2-35) Standard wall functions are used for RSM and k-ε models in this work. When standard wall functions are used, the first wall adjacent cell s centroid should be located within 30 < y+ < 300. A value of y+ near 30 is desirable. Using an excessively fine mesh near the walls must be avoided since wall functions tend to be invalid near the viscous sub layer. A special consideration needs to be paid to near wall mesh generation in order to achieve successful computations (Near Wall Modeling): When wall functions cease to be valid due to low Reynolds number flow, the near wall modeling approach is required. In this work, the k-ε low Reynolds number model is used as near wall modeling to predict near wall fluid behavior. There are numerous low Reynolds number models proposed in the past. In this work, the k-ε low Reynolds number model proposed by Launder and Sharma (1974) is 26

43 used. Jones and Launder (1973) first presented numerical predictions of various turbulent boundary layer flows in which the viscous sub-layer greatly influences the flow. The new turbulence energy and its dissipation rate equations are calculated simultaneously with the governing equations of the flow. Predictions were in good agreement with measurements. Later, Launder and Sharma (1974) tested the generality of the same model for a flow near a rotating disc. Comparisons with experimental data showed that this new model was able to predict flow and transport quantities accurately for a rotating disc. From their publications, the k-ε low Reynolds number model is provided in the following system of differential and auxiliary equations. Turbulent Viscosity: µ T C µρk ε (2-36) Turbulent kinetic energy equation: ρu k r ρv k y 1 r y r µ µ T k σ y µ T U V y r r y ρε 2µ k / y Turbulent energy dissipation equation: (2-37) ρu ε r ρv ε y 1 r y r µ µ T ε σ y c ε k µ T U V y r r y where c ρε k 2µµ T ρ V y U y r r y / (2-38) 27

44 exp 1, 50 c exp R T, (2-39) (2-40) and (2-41) The turbulent viscosity (Equation 2-36) is identical to the original turbulent viscosity term (Equation 2-12) except C μ is no longer a constant and is dependent on the value of the turbulent Reynolds number R T. Equations 2-37 and 2-38 are also similar to the original kinetic energy and dissipation equation except the last term in each equation. In Equation 2-37, the last term is added for computational reasons. When solving ε computationally, it is advantageous to treat ε as zero at the wall; however, in reality it is not zero. Therefore, the last term was added to the equation to equal the dissipation rate in the vicinity of the wall surface. The same reason goes for the extra term in Equation The last term in the dissipation rate equation is added so that the distribution of kinetic energy within the viscosity affected region would be in accord with experiments. Equations 2-37 and 2-38 are written in cylindrical coordinates explaining the additional terms involving gradients of V θ /r that appear in the equations. For equations written in Cartesian coordinates, please refer to Jones and Launder (1973). As mentioned before, in the low Reynolds number model, C μ and C 2 are no longer constants but are dependent on the turbulent Reynolds number R T which is calculated using Equation Since the low Reynolds number model solves the viscous affected region all the way to the wall, the grids near the wall must be much finer than the ones for the wall 28

45 function approach. Generally, y+ for the first wall adjacent cell s centroid needs to be around 1 or even less Particle Tracking (Equations of Particle Motion): After the flow calculation is completed, particle tracking is performed. In particle tracking, CFD releases virtual particles and computes the trajectories of these particles as well as heat and mass transfer from and to them. Fluent 6.3 uses an Euler-Lagrange approach, in which the fluid phase is treated as a continuum by solving RANS, while the dispersed phase is solved by tracking a large number of particles through the calculated flow field. In this approach, the volume fraction of volume occupied by particles is assumed to be very low. Therefore, interactions between particles are neglected. Fluent uses the following equation to calculate particle trajectories: du dt F D u u g ρ ρ ρ F. (2-42) Equation 2-42 is called the particle equation of motion. Fluent solves a trajectory of a particle by integrating equation This equation equates forces acting on the particle (RHS) with particle inertia (LHS). By default, the gravitational term is set to be zero; however, it can be included in the calculation as an option. u is the fluid velocity and u p is the particle velocity. ρ p is the density of particles and ρ is the density of fluid. F D u u is the drag force per unit particle mass and F D is calculated using Equation In this equation, µ is the viscosity of the fluid and d p is the particle diameter. Re is the relative Reynolds number and is defined as Equation

46 F D µ C D R Re ρd u u µ (2-43) (2-44) F x are additional forces such as forces due to virtual mass (Equation 2-45) and forces due to the pressure gradient in the fluid (Equation 2-46). F 1 ρ d 2 ρ dt u u F ρ ρ u u x (2-45) (2-46) The quantity C D in Equation 2-43 can be calculated by either Equation 2-47 or Equation a1, a2, and a3 are the constants gained from measurements over various ranges of Re number. Equation 2-47 is valid for spherical particles. Equation 2-48 is used when particles are not sphere. In this equation, C D is dependent on the shape factorφ, which is the ratio of s, surface area of a sphere having the same volume as the particle and S, actual surface area of the particle. Re sph is the Reynolds number computed with the diameter of a sphere having the same volume., (2-47) and 24 1, (2-48) where, b1 is exp( ), b2 is , b3 is exp( ), b4 is exp( ), and is S. 30

47 (Discrete Random Walk Model): In Fluent, a particle trajectory is calculated by integrating the trajectory equations for individual particles using the instantaneous fluid velocity u = + u where is the average velocity and u is the velocity fluctuations. Fluent uses a model called discrete random walk (DRW) to determine the instantaneous fluid velocity. In DRW, a particle enters eddies continuously one after another. Each eddy is characterized by its velocity fluctuation and its lifetime. The value of fluctuating fluid velocity u is random but constant over an interval of time given by the characteristic life time of the eddy. The values of u, v, and w are sampled every time a particle enters a new eddy and calculated by the following equations. (2-49) 2 /3 (2-50) Equations 2-49 and 2-50 are used for the k-ε model. ζ is a normally distributed random number and u is the local RMS value of the velocity fluctuations. Since the model assumes isotropy, the RMS fluctuating components are equal to each other and dependent on kinetic energy of turbulence. For RSM, Equation 2-51 is used to calculate the velocity fluctuations. Since the model assumes non-isotropy, the component of fluctuations is different for each component. (2-51) 31

48 The time spent in turbulent motion along the particle path is called the integral time scale T, and is calculated by Equation The value of C L is 0.15 for the k-ε model and 0.30 for the RSM. T L C L k (2-52) The life time scale of an eddy can be calculated using either Equation 2-53 or r in Equation 2-54 is a uniform random number between 0 and 1. τ 2T L (2-53) τ T L log r (2-54) The amount of time required for a particle to pass through an eddy is called the eddy crossing time and is defined in Equation τ is the particle relaxation time, L e is the eddy length sale and u-u p is the magnitude of the relative velocity. ln 1 (2-55) Every time, a particle moves a step forward, Fluent calculates eddy life time and eddy crossing time at that location. When the smaller of the two is reached, the particle leaves the existing eddy and enters a new eddy Erosion Calculation During the particle tracking process, when particles hit the target wall, particle impact information such as particle speed, angle, location of impact, and number of impacts are saved on each cell face on the target wall. Figure 2-2 illustrates the impact information stored in the wall cell. 32

49 Fluid Zone Cell Center Wall Face Cell An impact Particle Stored Particle velocity Particle angle Location of Impact Number of Impact Figure 2-2: Illustration of Particle Impact Erosion rates at the wall are calculated using erosion models for each face on the wall by applying user-defined functions and are stored at the cell center of the face. An erosion rate due to a single impact is calculated using Equation (2-56) ER on the RHS of the equation is the erosion ratio calculated directly from the erosion models based on impact information. In CFD, each particle has its mass flow rate, M. An erosion rate is multiplied by a mass flow rate of the particle impacting and divided by an area of the face being impacted, A f. The resulting erosion rate is in units of mass loss per time and area. The erosion rates from multiple impacts in each cell are summed and reported as an overall erosion rate for that cell. 33

50 CHAPTER 3 EXPERIMENTAL EROSION DATA 3.1 Introduction In order to examine effects of viscosity and particle size on erosion rates, erosion rates for 300, 150, and 20 µm particles impacting on inconel 625, aluminum 6061 and stainless steel 316 are measured with carrier fluid viscosities of 1, 10, 25, and 50 cp. Two different techniques are used to measure the erosion rates. An electric resistance (ER) probe is used to measure the erosion rates on inconel 625. Material coupon tests are used to measure the erosion rates of aluminum and stainless steel. The details on how each technique is utilized in measurements are described in the following section Experimental Facility An experimental facility was constructed to measure erosion rate in carrier fluids with various viscosities and different particle sizes. Figure 3-1 is a schematic of the experimental facility. The viscous liquid is made in a reservoir tank prior to experiments by mixing CMC (Carboxymethyl Cellulose) and water, but the CMC does not change the density significantly. Viscosities of the carrier fluid tested were measured by a viscometer and were approximately 1, 10, 25, 50 cp. The viscosities of the fluids were measured before and after the measurements to ensure that the change in viscosity during testing is negligible. CMC is known to be a non-newtonian fluid; however, at the low 34

51 viscosities of the current test conditions, the CMC-water mixture behaves as a Newtonian fluid. A comparison of erosion rates using CMC-water mixtures and glycerin-water mixtures, which behaves as a Newtonian fluid, is shown in the result section of this chapter. Sand particles are mixed with liquid in the reservoir tank. The volume ratio of sand and liquid is 0.1 % for 150 µm particles for inconel 625, 0.5 % for 150 and 300 µm particles for aluminum % is used for 150 and 300 µm particles for stainless steel. For 20 µm particles, 2 % volume ratio is used for inconel 625 and 1 % is used for aluminum and stainless steel in order to get a measurable erosion rates. The slurry mixer is turned on during the measurement in order to maintain the homogeneity of the mixture. The mixtures of sand and liquid flow from the reservoir tank to the hydraulic pump and from the pump to the straight nozzle in the testing tank. The bypass valve is used to control the flow rates in the system during the measurements. The mixture exits the nozzle and impinges the target wall and drains from the testing tank back to the reservoir tank. The mixture circulates in the system. The nozzle and target wall are completely submerged in the mixture. The nozzle diameter is 8 mm. The distance from the nozzle exit to the target wall is 12.7 mm. The average fluid velocity at the nozzle exit was kept at 10 m/s. The procedure of erosion measurement is described in Appendix A. 35

52 Flowmeter Nozzle Bypass valve Slurry mixer Target ER Probe Reservoir tank Pump (max:8 gpm) Coupon Figure 3-1: Schematic of the Experimental Facility Flat surface coupons as shown in Figure 3-1 as well as electrical resistance probes were used to measure the erosion rates at the target wall. The weight of a coupon was measured before and after the measurements to determine weight loss of material. The weight loss of material is converted to volume loss which is then divided by mass of sand through put in the system to calculate the erosion rates (m 3 /kg). This technique was used to present the erosion rates of aluminum and stainless steel Electric Resistance (ER) Probe Background In this investigation, an electrical resistance (ER) probe was also utilized previously to measure the erosion rates of inconel 625. Figure 3-2 shows a photograph of the probe head. ER probes measure the erosion rates of a material based on the electric resistance of two components made of the same material. The probe head consists of a 36

53 sample element and the reference element. Both components are made of inconel 625. The sand particles are entrained in the fluid and impinge the surface of the probe and scrape off some of the material from the sample element. The change in material volume creates a change in electric resistance of the material. The reference element is covered with epoxy and is protected from sand impacts so that its electrical resistance does not change. By measuring the change in electrical resistance of sample and reference material, the erosion rate is calculated by software that is provided by Cormon, manufacturer of the probe. The diameter of the probe is 1 inch but the diameter of the actual spiral is 0.75 inch as shown in Figure 3-2. Figure 3-2: Surface of Electrical Resistance Probe Figure 3-3 is a screen shot of sample output from the Cormon software for an erosion measurement. The electric resistance data acquired at the probe head is sent to a computer with processing software and then is converted to material thickness loss. The output is the graph of thickness loss vs. time. An erosion rate is calculated simply by 37

54 finding the slope of the curve. Erosion rate, that is the thickness loss over time duration, is calculated between the two cross hairs shown in Figure 3-3, and is converted to mils per year (MPY) and displayed at the bottom of the screen. End of Measurements Beginning of Measurements Slope Sand InjectionStarts Figure 3-3: Sample Output from Cormon Software Particles Used in Erosion Measurements Three different abrasive particles are used for the erosion measurements. California 60 is the biggest size of all three and has sharp edges. Figures 3-4 and 3-5 are the SEM photographs and sand size distribution of California 60. The average sand diameter of California 60 is 300 µm. 38

55 Figure 3-4: Microscopic Picture of California Weight percent [%] Size [microns] Figure 3-5: Sand Size Distribution of California 60 Figures 3-6 and 3-7 are SEM picture and sand size distribution of Oklahoma #1 sand. Oklahoma #1 has an average sand size of 150 µm. The OK#1 sand particles have round edges compared to California sand. 39

56 Figure 3-6: Microscopic Picture of Oklahoma # Volume % Particle Diameter (µm) Figure 3-7: Sand Size Distribution of Oklahoma #1 Lastly, the smallest particle of the three is silica flour. Figures 3-8 and 3-9 are the SEM picture and sand size distribution of silica flour. This sand has an average particle diameter of 20 µm. However, as shown in Figure 3-9, it has a relatively large number of 40

57 particles with sizes less than 20 µm. The edges of these particles are sharp as compared to Oklahoma sand. Figure 3-8: Microscopic Picture of Silica Flour Volume % Particle diameter (µm) Figure 3-9: Sand Size Distribution of Silica Flour 41

58 3.2 Erosion Results CMC vs. Glycerin Mixture CMC-water mixtures are known to be non-newtonian while glycerin-water mixtures are Newtonian fluids; however, at low viscosities, glycerin-water mixtures behave similar to CMC-water mixtures. Figures 3-10 and 3-11 are the erosion measurement results performed during this investigation. Erosion tests were conducted by ER probes with two different liquids having the same fluid viscosities. As shown in the uncertainty bars in Figures 3-10 and 3-11, for the viscosity range of 10, 25, and 45 cp, erosion rates are comparable to each other for CMC and glycerin mixtures. Therefore, in this viscosity range the CMC mixture can be treated as a Newtonian fluid. 3.00E-02 Erosion Rate (mils/lb) 2.50E E E E E E Viscosity (cp) Figure 3-10: Erosion Rate vs. Viscosity for CMC and Glycerin mixture (V=10 m/s, 300 µm) 42

59 Erosion Rate (mils/lb) 1.80E E E E E E E E E E Viscosity (cp) Figure 3-11: Erosion Rate vs. Viscosity for CMC and Glycerin mixture (V=5 m/s, 300 µm) Inconel 625 Results (ER Probe) Erosion rates of 20 and 150 µm particles in liquid viscosities of 1, 10, 25, and 45 cp were measured using an inconel 625 ER probe. The summary of the results are shown in Table 3-1. Each testing data point represents the average of 3 to 6 measurements. The raw data and the result of each measurement are shown in Appendix B. The Cormon software outputs erosion rates in MPY. The erosion rates were converted to mils/lb from MPY by dividing the value by the mass flow rate of sand. Erosion rates must be analyzed in mils/lb instead of MPY since the sand mass flow rate through the system was not constant for each test. The details of the conversions as well as uncertainty calculations 43

60 are shown in Appendix B. From Table 3-1, it can be observed that the erosion rates (mils/lb) of 150 µm are much higher than those of 20 µm. This indicates that erosion rates measured by the ER probe (inconel 625) are influenced greatly by the size of abrasive particles perhaps mostly due to the larger drag force acting on the smaller particles and reducing their impact speed. Table 3-1: Erosion Rate for Inconel 625 (ER Probe) for 150 and 20 µm Erosion Rate for Inconel 625 (ER Probe) Viscosity (cp) ER (MPY) M sand (kg/s) ER (mils/lb) Uncertainty (mils/lb) Oklahoma #1 (150 µm) E E E E E E E E E E E E E E E E-03 Silica Flour (20 µm) E E E E E E E E E E E E E E E E-06 The results shown in Table 3-1 are plotted in Figure As shown in the graph, the erosion rates of 150 µm particles do not change significantly as viscosity increases. On the other hand, 20 µm particles show significant reduction in erosion rates with change in viscosities. This result indicates that for smaller particles, the erosion rates are influenced not only by the particle size but also by viscosity of the carrier fluid. The uncertainty for each condition shows that the experiments are repeatable. 44

61 1.00E-01 Erosion Rate (mils/lb) 1.00E E E-04 Oklahoma #1 (150 µm) Silica Flour (20 µm) 1.00E Viscosity (cp) Figure 3-12: Erosion Rate vs. Viscosity for Inconel 625 (ER probe)-150 and 20 µm Erosion measurements using an inconel 625 ER probe were previously conducted by Okita in spring of 2008 for 150 and 300 µm particles. Erosion measurements with water as a carrier fluid were also performed by Reuterfors (2007). After a careful examination and comparison of the new results with the old erosion measurements performed by Reuterfors (2007) as well as Okita during spring of 2008, it was found that there are significant differences between the new and the old ER probe results. A single ER probe was used by both investigators. However, it appears that the ER probe measurement is very sensitive to the condition of the probe head. As many measurements are gathered over a long period of time, the surface of the probe head starts to erode. The probe head is made of epoxy and the inconel spiral and these two materials erodes at different rates. Therefore after many measurements, the probe head becomes uneven. Since epoxy erodes faster than inconel, the sides of the inconel spiral get exposed to the 45

62 fluid and start to erode from the sides as well as the top surface of the probe. The mechanism of how the probe head surface changes over time is shown schematically in Figure A A Flat surface allows inconel to erode only at the top surface. Erosion Erosion Inconel gets eroded from the sides due to an uneven surface New Surface Epoxy Inconel Old Surface Figure 3-13: Schematic of New and Worn Out Probe Head After it was found that measurements are greatly influenced by the surface of the ER probe head, the epoxy of the existing ER probe head was removed and filled with new epoxy to create a more even surface, but the edges of the ER probe spiral were also rounded. Results shown in Figure 3-12 and Table 3-1 are results of measurements taken after the epoxy is renewed in summer of However, after the new measurements were collected, it was thought that the temperature of the system also affects the measurements. Since the ER probe used by Okita in the summer of 2008 did not have temperature measurements, it was concluded that the results are not reliable. Since the ER probe used for the measurements was old and used, a new ER probe was replaced with old probe to repeat some of the experiments. The temperature function 46

63 was also added to the existing system to acquire more accurate results. The measurements were repeated by Torabzadeh (2009) and this author in spring of The new erosion results of 150 µm particles are shown in Figure The new results show that the erosion rate of 150 µm particles reduces significantly as viscosity is increased while Figure 3-12 showed no change in erosion rate over a range of viscosity. 1.60E-03 Erosion Rate (mils/lb) 1.40E E E E E E E E+00 Test 1 Test Viscosity (cp) Figure 3-14: Erosion Rate vs. Viscosity for Inconel 625 (ER probe)-150 µm (Torabzadeh, 2009) Even after the old ER probe was replaced with a new one and the temperature function was added, there are still some ambiguities in the ER probe results mainly due to unevenness of the surface of the ER probe. Therefore, close to the surface of the ER probe the viscous sub-layer is significantly perturbed and this may affect the turbulence near the wall of the ER probe. There was no simple way to examine how much the change in temperature and the uneven surface affects the results. In order to avoid these inaccuracies, a material coupon technique was utilized. For coupon tests, the actual mass 47

64 loss was measured instead of electric resistance; therefore, the measurements are more physical and accurate. Additionally, the surface is even so this effect is removed. Since inconel is hard material and will take considerably long time to have measurable mass loss, aluminum and stainless steel were used for coupon tests Material Coupon Tests Results (Aluminum6061 and Stainless Steel 316) After it was concluded that the ER probe results are not reliable when comparing different viscosities due to the obstruction of the viscous sub-layer region close to the wall of the ER probe, material coupon tests were conducted to measure the erosion rates of aluminum and stainless steel in this investigation as well as the study by Torabzadeh (2009). Figures 3-15 and 3-16 show the measured erosion rates with change in viscosity of carrier fluid for each material. Table 3-2 summarizes the erosion results for the coupon tests. The measurements were taken more than twice for each condition, and then the data were taken the averaged. The raw data and test results are presented in Appendix C. Figures 3-15 and 3-16 show erosion rates reduce as viscosity increases for both materials and for all of the particle sizes. However, erosion rates of the 300 micron particles are not affected by viscosity as much as the 150 and 20 micron particles. For 300 micron particles, the erosion rates do not change as significantly as viscosity increases. The erosion rate of 20 micron sand declines more significantly than that of 150 micron sand. From Table 3-2 it should be noted that the larger particles tend to have larger erosion rates than smaller particles at any viscosity. It was also observed that aluminum has higher erosion rates than stainless steel for all sizes of particles and all viscosities. 48

65 Table 3-2: Erosion Results for Al6061 and SS316 (Coupon Tests) Viscosity (cp) Aluminum 6061 Erosion Rate (m 3 /kg) 316 Stainless Steel 300 µm 150 µm 20 µm 300 µm 150 µm 20 µm E E E E E E E E E E E E E E E-12 N/A N/A N/A E E E E E E E E-09 Erosion (m 3 /kg) 1.00E E E Viscosity (cp) Figure 3-15: Erosion Rate vs. Viscosity for Aluminum with different particle sizes 49

66 1.00E E-10 Erosion (m 3 /kg) 1.00E E E Viscosity (cp) Figure 3-16: Erosion Rate vs. Viscosity for SS316 with different particle sizes 50

67 CHAPTER 4 MEASURED AND PREDICTED VELOCITIES 4.1 Introduction Although erosion rate is influenced by many factors, particle impact velocity is the biggest factor that affects erosion rate. In order to study the effect of viscosity and particle size on particle velocity, which affects erosion rate, particle velocities of 3, 120 and 550 µm diameter particles were measured and compared to the CFD predicted velocities. The results from the CFD calculations and the predicted particle impact speed and angle is used in Chapter 6 to calculate erosion rates. Therefore it is important to compare calculated fluid velocities and particle velocities with experimental data to make sure that calculated particle velocities match the data. In this chapter, a brief background of the velocity measurement technique is given at first, and then followed by a comparison of measured and predicted fluid and particle velocities. Then, the effect of turbulence models and grid sizes on predicted velocity is examined Laser Doppler Velocimetry Background (Concept and Procedure): Particle and fluid velocities were measured by Miska (2008) with help from the present author using Laser Doppler Velocimetry (LDV). 51

68 LDV utilizes two pairs of laser beams with the same wavelength but different frequencies to create dark and light fringe patterns at the intersection and measures the velocities of seeding particles which pass through the intersection of the beams. The LDV system is composed of several components. The schematic of the LDV system is shown in Figure 4-1. Component 1 creates a laser beam that is sent to a color burst (component 2), where a single laser beam is split into two pairs of green and blue beams. Each pair of beams is used to measure either the axial or radial velocity component. The beams are then sent to a fiber optic probe (component 3) where the beams are emitted towards the test section. The fiber optic probe lens is made so that the two pairs of beams will form an intersection (component 4) creating a fringe pattern. Seeding particles pass through the intersection and create changes in frequency bands. This information is sent back to the optic fiber probe to a color link (component 5). The scattered light information is converted to electrical signals and then sent to IFA 655 where the signals are filtered from noise and sent to a computer for output (component 6). The LDV system comes with software called FIND which allows a user to process the data on the computer. The software outputs the velocity histograms with turbulent intensity and mean velocity calculated. Measurements were collected for 5 different viscosities of 1, 10, 25, 50, and 100 cp (Miska 2008). Since CMC-water mixture is turbid and does not allow laser beams to pass through the measurement section, glycerin was used to mix with water to attain the desired viscosities of the carrier fluids. 52

69 Figure 4-1: Schematic of LDV System (Seeding Particles and Measurement Locations): Aluminum particles with average sizes of 3, 120 and 550 µm were used as seeding particles. 3 µm particles are assumed to travel with liquid with no slip. 120 and 550 µm particles are used to measure the velocities of small and larger particles. A similar flow loop used for erosion rate measurements (Chapter 3) was used for LDV measurements discussed in detail by Miska (2008). Figure 4-2 shows the LDV measurement locations between the nozzle exit and the target wall. The measurements were performed from r = 0 to r = 12 mm and z = 1 to z = 12.3 mm. The particle velocity could not be measured near or on the target surface (z = 12.7 mm) since the measuring section of the LDV (control volume created by laser beams intersections) is about 0.2 mm wide and for any location within 0.2 mm of the wall, the wall would interfere with the measurement. Furthermore, the larger particles have diameters that are larger than 53

70 0.5 mm and their velocity measurements could be effected if only a part of particle would pass through the control volume created by laser beams especially in the near wall region. z axis r axis Figure 4-2: LDV Measurement Location Map CFD Approach and Design Input Computational Fluid Dynamics (CFD) was utilized to predict velocities and evaluate their accuracy by using the LDV measurements. Fluent 6.3 is used for flow simulations. The particle tracking was performed by User Defined Functions created by Zhang et al (2006). The computational mesh of the direct impingement case is shown in Figure 4-3. This geometry is modeled as two-dimensional axi-symmetric. The diameter of the entire flow region is 1.5 inches (38.1 mm) and its length is 1 inch (25.4 mm). The nozzle diameter is 8 mm, and the distance to the wall is 12.7 mm which is the same as the apparatus. In the flow region, the grid gets finer near the target wall. The total number of cells used for this geometry is For the nozzle exit plane velocity, the actual LDV 54

71 data is used as a velocity input. The actual nozzle exit velocity profiles from LDV measurements are shown in Figure 4-4. The Reynolds Stress Model (RSM) is used to calculate the flow field, and the standard wall function is used to simulate the flow near the target wall. 1in 1.5 in Figure 4-3: CFD Mesh of the Flow Region and Boundary Conditions 4.2 Comparison of Predicted and Measured Velocities Figure 4-4 presents the measured particle velocities of 120 and 550 µm particles at z = 1 mm. This location is the first location measureable by LDV. The particle velocities measured at this location are used as boundary conditions for CFD particle tracking simulations. The measured data for 3 µm particles for several viscosities are shown in Appendix D. From Figure 4-4, it is observed that particle velocities in the higher viscosity liquids have higher velocities near the centerline. This is due to the 55

72 reduction in Reynolds number due to the increased viscosity. 550 µm particles tend to travel with slightly lower velocities than 120 µm particles due to slip. Figure 4-4: Measured Particle Velocity at z = 1 mm Contour of Measured Velocities Figure 4-5 displays the contours of the measured particle velocities of 3, 120, and 550 micron particles for 1 and 100 cp. 3 micron particles are assumed to travel with the fluid without slip, therefore they represent fluid velocities. 120 micron particles represent small particles (corresponding to erosion data for 150 microns) and 550 micron particles are used to measure velocity of bigger particles (to interpret erosion data for 300 microns). All the contours show a high velocity near the nozzle exit along the horizontal axis (centerline). The velocities in this region (marked by the red oval) are mostly in the axial directions which flow from nozzle exit toward the wall. For all particles sizes, the velocities near the centerline for the 100 cp fluid are higher than the velocities in the same region for the 1 cp fluid. For the same flow rate, the 100 cp fluids has a laminar 56

73 velocity profile at the nozzle exit while the 1 cp fluid has a turbulent profile; thus the maximum velocity in this region tends to be higher for higher viscosity liquids. However, the particles slow down as they approach the wall due to the reduction in fluid velocity at the stagnation point. As particles move radially away from the centerline along the target wall, there is another location with high particle velocity (shown by the black oval). The speed of particles in this region is high and is mostly from the radial component of velocity which travels outward from the centerline. These high velocities are responsible for the maximum values of erosion rate that occur in this region. A comparison of particle velocities in this region for 1 cp and 100 cp reveals that particle velocities at the wall (impact velocities) in higher viscosity liquids are lower than those in lower viscosity liquids. The comparison of measured and predicted particle velocities in the near wall region is discussed in the next section. Figure 4-5: Contour Map for Measured Velocities of Various Particle Sizes (1 and 100 cp) 57

74 4.2.2 Comparison of Predicted and Measured Velocities along Z direction (Comparison of Fluid Velocities): Figures 4-6 through 4-10 are the comparisons of measured and predicted fluid velocities along the z direction. Only results of 1, 50, and 100 cp are shown in this thesis. The results for the other viscosities are omitted since they are similar to the results of the selected viscosities. From Figure 4-6, it should be noted that along r = 0 mm, the high viscosity liquid has higher velocity as observed in the contour map (Figure 4-5). The fluid velocity decreases as moving towards the wall, having a zero velocity at the wall. At this radial location, CFD predictions match the experimental data, and the fluid velocity is dominated by the axial component with a radial velocity of zero Fluid Velocity (m/s) Exp. Data - 1 cp Exp. Data - 50 cp Exp. Data cp CFD - RSM - 1 cp CFD - RSM - 50 cp CFD - RSM cp Distance from Nozzle Exit z (mm) Target Wall Figure 4-6: Measured and Predicted Fluid Velocity vs. Axial Distance at r = 0 mm 58

75 Figure 4-7 is the fluid velocity along r = 3 mm. At locations away from the target wall, predicted velocities are comparable to the measured velocities for all the viscosities. However, near the wall, CFD tends to under-predict fluid velocities. One of the reasons for the discrepancy between CFD and LDV can be explained by possible misalignment of the experimental apparatus during the LDV measurements. During the LDV measurements, the laser beams are moved from one location to another by a traverse system. However, at the beginning of the measurements, the beams are aligned at the nozzle exit by visual inspection without the aid of additional equipment. Therefore, there is a possibility that the system was misaligned during the measurements. This misalignment may not affect the results much at locations such as r = 0 or r = 8 mm since at these locations, the velocities are either dominated by the axial velocity (at r=0) or dominated by radial velocity (at r=8). On the other hand, at r = 3 mm to r = 4 mm, the velocities start to change from axial to radial dominant since r = 3 or 4 mm coincides with the nozzle wall (radius of nozzle is 4 mm). Therefore, a small misalignment can result in a big difference on the measurements as demonstrated in Figure 4-8. The graph shows the measured fluid velocity for 1 cp along r = 3 mm with predicted fluid velocity at r = 3.0, 3.6 and 4.0 mm. This result reveals that near the wall, the predicted velocity of r = 4 mm matches with measurements better than that of r = 3 mm. One should not rule out the possibility that the CFD and especially the turbulence model, cannot pick up the rapid change of velocity that is observed by the measurements and the problem may be with the CFD predictions. Although the predictions with a different turbulence model (low Reynolds number k-e model) showed the same trend. 59

76 Fluid Velocity (m/s) Exp. Data - 1 cp Exp. Data - 50 cp Exp. Data cp CFD - RSM - 1 cp CFD - RSM - 50 cp CFD - RSM cp Distance from Nozzle Exit z (mm) Target Wall Figure 4-7: Measured and Predicted Fluid Velocities vs. Axial Distance at r = 3 mm 12 Fluid Velocity (m/s) Exp. Data - 1 cp (r=3) CFD - RSM - 1 cp (r=3.0) CFD - RSM - 1 cp (r=3.6) CFD - RSM - 1 cp (r=4.0) Target Wall Distance from Nozzle Exit z (mm) Figure 4-8: Measured and Predicted Fluid Velocities vs. Axial Distance at r = 3 to 4 mm (1 cp) 60

77 Figure 4-9 is the fluid velocity comparison for r = 4 mm. At this location, velocity is low near the nozzle exit, and high near the target wall. The overall profiles are comparable between predictions and measurements. However, very near the wall, CFD tends to under-predict velocity Fluid Velocity (m/s) Exp. Data - 1 cp Exp. Data - 50 cp Exp. Data cp CFD - RSM - 1 cp CFD - RSM - 50 cp CFD - RSM cp Target Wall Distance from Nozzle Exit z (mm) Figure 4-9: Measured and Predicted Fluid Velocities vs. Axial Distance at r = 4mm Lastly, Figure 4-10 displays the results along r = 8 mm. At this radial location, velocity is very small as measured along the nozzle exit but it becomes much larger near the wall. The high velocity in this region is radial dominant. CFD is able to predict the overall trend while close examination reveals that there are under-predictions near the wall. 61

78 16 14 Fluid Velocity (m/s) Exp. Data - 1 cp Exp. Data - 50 cp Exp. Data cp CFD - RSM - 1 cp CFD - RSM - 50 cp CFD - RSM cp Target Wall Distance from Nozzle Exit z (mm) Figure 4-10: Measured and Predicted Fluid Velocity vs. Axial Distance at r = 8 mm (Comparison of Particle Velocity): Detailed comparisons of measured and predicted velocities for 120 µm particles along r = 0 and 8 mm are shown in Figures 4-11 to Results for 550 µm and the other radial locations are omitted here since the comparison of 120 and 550 µm particle velocities will be shown in the following section. The results for r = 3 and 4 mm for these particles sizes are very similar to the results of 3 µm particles (Figures 4-7 and 4-9). As shown in Figure 4-11, particle velocities at the centerline (r = 0 mm) are higher for higher viscosity fluids than that of lower viscosity fluids. As particles approach the wall, velocities decrease and become negligible at the wall. For r = 0 mm, CFD predictions match the measured velocities. 62

79 Particle Velocity (m/s) Exp. Data - 1 cp Exp. Data - 50 cp Exp. Data cp CFD - RSM - 1 cp CFD - RSM - 50 cp CFD - RSM cp Target Wall Distance from Nozzle Exit z (mm) Figure 4-11: Measured and Predicted Particle Velocities vs. Axial Distance at r = 0 mm 120 µm For r = 8 mm, the particle velocities are low at the nozzle exit (z = 0 mm); however, they increase near the wall and reach a maximum velocity, then decrease again very close to the wall (Figure 4-12). Although the particle velocities become smaller as they approach the wall, they never become zero as it was seen for fluid velocities at r = 8 mm. The erosion is caused by this non-zero particle velocity at the target wall. CFD predictions agree with the measurements for a location away from the wall but underpredicts velocities near the wall. 63

80 16 14 Particle Velocity (m/s) Exp. Data - 1 cp Exp. Data - 50 cp Exp. Data cp CFD - RSM - 1 cp CFD - RSM - 50 cp CFD - RSM cp Target Wall Distance from Nozzle Exit z (mm) Figure 4-12: Measured and Predicted Particle Velocities vs. Axial Distance at r = 8 mm 120 µm In order to examine near wall particle behavior, Figure 4-12 is expanded from z = 10 to 12.7 mm (Figure 4-13). Figure 4-13 shows that both measured and predicted particle velocities reach their maximum values near the wall, and then particles slow down as they approach the wall. The location of maximum particle velocity occurs farther away from the wall for higher viscosity liquids than for lower viscosity liquids. This can be explained by the fluid shear layer formed near the wall. The layer tends to be thicker for higher viscosity fluids than lower viscosity fluids. Particle velocities are influenced by these shear layers near the wall, and they slow down quickly as they enter these shear layers. Therefore, particles in higher viscosity liquids tend to slow down starting at a distance farther away from the wall than particles in lower viscosity liquids. 64

81 Another thing to note here is that away from the wall, particle velocities in high viscosity fluids are higher than low viscosity fluids. However very near the wall, particle velocities in lower viscosity fluids are higher than velocities of higher viscosity fluids. As particles enter the shear layer near the wall, the higher viscosity liquids exert more drag on particles than lower viscosity fluids; as a result, particles in higher viscosity liquids slow down more significantly than particles in lower viscosity fluids Particle Velocity (m/s) Exp. Data - 1 cp Exp. Data - 50 cp Exp. Data cp CFD - RSM - 1 cp CFD - RSM - 50 cp CFD - RSM cp Target Wall Distance from Nozzle Exit z (mm) Figure 4-13: Measured and Predicted Particle Velocities vs. Axial Distance at r = 8 mm 120 µm (Near Wall) 65

82 4.2.3 Comparison of Predicted and Measured Particle Velocities near the Wall Figures are comparisons of measured and predicted particle velocities for 120 and 550 µm particles along z = 6, 12.3, and 12.7 mm with carrier fluid viscosities of 1 and 50 cp. Since LDV beams interfere with the wall, there are only CFD predicted particle impact velocities shown for 12.7 mm. Figure 4-14 shows that at z = 6 mm, particle velocity is high near the centerline similar to the trend at z = 1 mm (Figure 4-4). Therefore, most of the velocity is axial and traveling parallel to the centerline. Particle velocities in 1 cp liquid are lower than particle velocities in 50 cp liquid due to the laminar like velocity profile exiting the nozzle for high viscosity liquids. For this location, CFD predicted velocities agree very well with measured velocity for all conditions. As particles move closer to the location near the wall at z = 12.3 mm (Figure 4-15), particle velocities start to form a different profile, which is low at the center line, and high at locations several millimeters away from the centerline. For 120 µm particle velocities, CFD successfully predicts the trend while the magnitude of the peak value of speed is under-predicted for 550 µm particles. Overall, predictions appear to follow the trend of experimental data reasonably well. Lastly, predicted particle velocities for r = 12.7 mm are shown in Figure Unlike z = 12.3 mm, at this location, the particle velocities for 1 cp liquid are higher than particle velocities for the 50 cp liquid. This indicates that particles in 50 cp liquid entered the shear layer close to the wall, where fluid velocity decreases rapidly near the wall, and particles started to slow down. The difference of particle velocity between 1 cp and 50 cp is shown by black arrows in the figure. The comparison of the length of the arrows 66

83 (which represents the differences between the particle velocities) for the 550 and 120 µm particles graphs indicate that the particle velocity does not change as much for 550 micron particles as for 120 micron particles as viscosity of liquid changes from 1 to 50 cp. This is another indication that the larger particles are not affected by the fluid viscosity as much as the smaller particles. The bigger particles have larger inertia than smaller particles, and they penetrate through the shear layer near the wall and do not slow down as much as smaller particles do. This is one of the reasons that erosion rate does not change much with increase in viscosity for 300 µm sand (see Figures 3-15 and 3-16). 67

84 Figure 4-14: Measured and Predicted Particle Velocities along z = 6 mm 68

85 Figure 4-15: Measured and Predicted Particle Velocities along z = 12.3 mm 69

86 120 µm 550 µm Figure 4-16: Predicted Particle Velocities along z = 12.7 mm (120 and 550 µm) In order to see how particle velocity changes as particles approach the wall, the predicted particle velocities at z = 12.3 and 12.7 mm from CFD are plotted on the same graph. The results are shown in Figure The graph on the top is the result for the 1 cp liquid, and the graph on the bottom is the result for 50 cp. For each graph, the data on the left are results for 120 µm particles and the data on the right are results for 550 µm particles. The black arrows indicate how much the particle velocities changed as particles approach the wall from 12.3 mm to 12.7 mm. Comparing the top graph (1 cp) to the bottom graph (50 cp) for each particle size, it is observed that particles slow down more significantly as they approach the wall for higher viscosity liquids (50 cp). This can be explained by the higher viscosity fluids exerting more drag on particles than lower viscosity liquids. Also, since the shear layer, as well as the distance between the 70

87 maximum fluid velocity and the wall, are thicker for higher viscosity liquids, it provides a larger distance for the particles to slow down before they reach the wall. Comparing the graph on the left (120 µm) to the graph on the right (550 µm) for each viscosity (1 and 50 cp) reveals that the black arrows for 120 µm particle velocities are larger than the arrows for 550 µm particle velocities for both viscosities. This indicates that 550 µm particles do not slow down as much as 120 µm particle. Due to higher inertia, bigger particles penetrate through the shear layer and the fluid deceleration region and do not slow down as much as smaller particles as they approach the wall. Figure 4-17: Predicted Velocities at Near Wall (120 µm and 550 µm, 1 and 50 cp) 71

88 4.3 Analysis of Velocity Prediction by CFD CFD calculations are often influenced by the size of grid as well as turbulent models used for calculations. The predicted results from the previous section are based on the RSM model with 4600 cells. In this section of the thesis, the predictions using another turbulence model other than RSM are shown and compared to the experimental data (section 4.3.1). In the following section (4.3.2), a grid size sensitivity study is conducted. The results for the original grid and the finer grid are compared to each other Turbulent Model Analysis Flow simulation results are influenced by the governing equations used during calculations. In this section, RSM and k-ε low Reynolds number models (denoted by LowRe in the figures) are used to calculate the fluid velocity. The comparisons of fluid velocity using each model are shown in the following figures. For the low Reynolds number model, a much finer grid is used in the near wall region to meet the requirement for the wall treatment. y+ of the grid nearest the wall for the low Reynolds number model is approximately 1. Figure 4-18 is the comparison of fluid velocity along r = 0 mm for different viscosity carrier fluids. At this radial location, the fluid velocity calculated from RSM is very similar to one calculated from the low Reynolds number k-ε model for all the viscosities. Since all the viscosities give similar trend, the results are shown for only one viscosity for the next few figures. 72

89 Fluid Velocity (m/s) Exp. Data - 1 cp Exp. Data - 50 cp Exp. Data cp CFD - RSM - 1 cp CFD - RSM - 50 cp CFD - RSM cp CFD - LowRe - 1 cp CFD - LowRe - 50 cp CFD - LowRe cp Distance from Nozzle Exit z (mm) Figure 4-18: Fluid Velocity for RSM and LowRe at r = 0 mm Target Wall Figure 4-19 is the plot of fluid velocity for 50 cp liquid applying the RSM and the low Reynolds number k-ε model at r = 4 mm. Near the wall, the low Reynolds number model gives slightly lower velocities than the RSM and the location of maximum velocity is closer to the wall than the RSM. Farther away from the wall, the low Reynolds number model predicts much higher velocities than the RSM. 73

90 Fluid Velocity (m/s) Exp. Data - 50 cp CFD - RSM - 50 cp CFD - LowRe - 50 cp Target Wall Distance from Nozzle Exit z (mm) Figure 4-19: Fluid Velocity for RSM and LowRe at r = 4 mm From Figure 4-20, it is found that overall, the velocity predicted by the low Reynolds number model is not very different from the velocity predicted by RSM. However, near the wall, it should be noted that the velocities from the low Reynolds number model reaches the maximum velocity at a location closer to the wall than RSM. This means the low Reynolds number model has a thinner fluid layer than RSM at the wall. 74

91 14 12 Fluid Velocity (m/s) Exp. Data cp CFD - RSM cp CFD - LowRe cp Target Wall Distance from Nozzle Exit z (mm) Figure 4-20: Fluid Velocity for RSM and LowRe at r = 8 mm Grid Size Analysis In order to determine the dependency of results on the size of grid, a grid size analysis was performed. After the flow calculation is performed for the original mesh, the grid was made finer by breaking each cell into two cells in the z direction. A diagram of how the original grid is adapted to a finer grid is shown in Figure The last layer of cells adjacent to the wall was kept the same so that it still fulfills the standard wall function criteria. The flow calculation was redone using the finer grid. Figures 4-22 and 4-23 are the fluid and particle velocities of 1 and 50 cp at r = 8 mm for the original and finer grid. To focus on the near wall velocity, the horizontal axis of the plots is set from 6 to 12.7 mm in these figures. From Figure 4-22, it is observed that the flow calculations are independent of grid size for both 1 and 50 cp. Figure 4-23 also shows that particle 75

92 velocity is independent of grid size. Therefore, for this case, the results are not influenced by the size of mesh. The velocities at the other radial locations show the similar results. Cells are split into two cells along horizontal directions Cells next to the wall are kept the same Wall boundary Wall boundary Original Grid Finer Grid Figure 4-21: Diagram of Grid Adaptation Fluid Speed (m/s) CFD (RSMFiner-1cP) CFD (RSM-1cP) CFD (RSMFiner-50cP) CFD (RSM-50cP) Distance from Nozzle Exit z (mm) Target Wall Figure 4-22: Comparison of Predicted Fluid Speeds for Finer and Original Grid (1 and 50 cp) 76

93 Particle Speed (m/s) CFD (RSMFiner-1cP) CFD (RSM-1cP) CFD (RSMFiner-50cP) CFD (RSM-50cP) Target Wall Distance from the nozzle (mm) Figure 4-23: Comparison of Predicted Particle (120 µm) Speeds for Finer and Original Grid (1 and 50 cp) 77

94 CHAPTER 5 GENERATION OF EROSION MODELS 5.1 Introduction In this chapter, the process of generating the E/CRC erosion model described in Chapter 2 is discussed. The erosion model for aluminum 6061 and stainless steel 316 are developed based on direct impingement test results in air. Air is used as the carrier fluid to generate erosion equations since in such low viscosity fluids, the particle speed and direction do not change much as particles approach the target wall (Reuterfors 2007); therefore, it is easy to control particle impact speed and angle. In fact, most erosion models that are developed in the literature use gas as the testing medium (see, for example Oka et al. (2005)). Figure 5-1 describes the process of generating erosion equations. At first, velocities of particles that are flowing out of a straight nozzle are measured by LDV. A plot of particle velocity vs. fluid velocity is generated to provide the necessary information for the actual particle impact velocity during the erosion measurements. In gases, it is common that there is a relative slip velocity between a particle and the fluid. So, the particles leaving the nozzle will be traveling at a lower velocity than the gas at this location. At step 2, erosion measurements of selected materials are conducted in air. The coupon and weight loss method is used for these measurements. The erosion rates of various particle impact angles and velocities are measured to provide enough information 78

95 to develop an erosion equation. At step 3, utilizing the erosion results from step 2 and the particle velocity from step 1, an erosion equation for each material is developed. Step 1 Particle Velocity Measurements in Air Step 2 Erosion Measurements in Air Step 3 Generation of Erosion Model based on Steps 1 and 2 Figure 5-1: Process of Generating Erosion Models Experimental Facility and Test Conditions (Particle Velocity Measurement): LDV is used to measure the particle velocities of 150 μm and 350 µm particles in air for the direct impingement geometry. Glass beads with average particle sizes of 150 μm and 350 µm are used as seeding particles. Glass beads are used instead of Oklahoma #1 sand since glass beads are more reflective of light than sand and more suitable for LDV measurements. Figure 5-2 is a schematic of the LDV measurement facility. A compressor provides the gas flow in the nozzle. The velocity of the gas was controlled by the valve positioned upstream of the flow meter. Since some gas is normally introduced with sand in the sand injection nozzle, the flow meter cannot provide the actual gas flow rate and velocity that is flowing out of the nozzle. Also at the location where the flow meter is installed, the gas pressure is not 79

96 ambient and that affects the flow meter readings. Therefore, since the flow meter is not capable of giving the correct flow rate, a pitot tube is used to measure the actual gas velocity at the nozzle exit. The flow meter was calibrated with the pitot tube measurements and used only as a guide. The pressure drop at the nozzle creates suction in the feeding tube and draws the glass bead particles in the nozzle. The mixture of the glass beads and air flow out of the nozzle, and the particle velocity is measured at the intersection of the LDV beams. The test section is contained in a box to keep particles from scattering and hitting the LDV probe head. A glass panel is provided and attached to a section of the box (as shown in Figure 5-2) so that the LDV beams intersect inside the box at the exit of the nozzle. At the end of the box, there is an outlet for air and particles to escape. Sand Feeder LDV Probe Compressor Valve Feeding Tube Glass Panel Flow Meter Intersection Outlet Nozzle Box Figure 5-2: Schematic of LDV Measurement Box 80

97 The particle velocities were measured for a fluid velocity range of 25 to 104 m/s. The measurements were taken three times at each velocity and the results were averaged. The measurement location was kept at 3 mm away from the nozzle exit at the centerline. In the beginning of the experiments, the particle velocities were measured right at the nozzle exit and also at 10 mm away from the nozzle exit. The results of the velocity measurements were very similar. As discussed previously, the particle velocities in air do not change much as they move away from the nozzle exit. The nozzle diameter is 8 mm, which is the same as the one used for liquid erosion tests (Erosion Measurements in Air): After the particle velocities were measured, the erosion measurements were conducted for aluminum and stainless steel in air. From the LDV measurements, particle velocities of 13, 24, and 42 m/s were used for aluminum and 13, 28 and 42 m/s were used for stainless steel as velocity conditions. At each velocity, the measurements were taken for impact angles of 90, 60, 30, and 15 degrees. At each particle velocity and angle, the measurements were taken at least 3 times with 300 g of Oklahoma #1 (150 μm) sand each time. Figure 5-3 is a schematic of the erosion measurements in air. The test section was contained in a hood during the measurements. Erosion rates are calculated by mass loss of a target coupon divided by the total mass of sand throughput. 81

98 Sand Feeder Compressor Valve Flow Meter Feeding Tube Impact Velocity V p Target Nozzle Impact angle θ Figure 5-3: Schematic of Erosion Measurements in Air 5.2 Results Particle Velocity Results In this section, the particle velocity measurement results for the 150 μm and 350 µm glass beads are shown and plotted against the gas velocity measured with the Pitot tube. Particle velocity was measured by the LDV, and the fluid velocities were measured by the Pitot tube. Figure 5-4 is the graph of particle vs. fluid velocity for the direct impingement geometry. As shown in the graph, the particle velocity is directly proportional to the fluid velocity. A linear equation was used to determine the best fitting curve for the data. The data show that there is more slip between fluid and the particles for the 350 µm particles than the 150 µm particles. The linear equations were used to 82

99 determine the gas velocities necessary to produce the desired particle velocities during the measurements. 60 Particle Velocity (LDV) m/s y = x R² = y = 0.386x R² = microns 150 microns Linear (350 microns) Linear (150 microns) Gas Velocity (from Pitot tube) m/s Figure 5-4: Particle Velocity vs. Fluid Velocity for air - (150 μm) Aluminum Erosion Results in Air Erosion rates are measured for aluminum 6061 in air. Oklahoma #1 (150 μm average diameter) sand and California 60 (300 µm average diameter) sand are used as abrasive particles. A total of 900 g of sand was injected at the nozzle for the erosion tests that are presented in this section. After injecting 300 g of sand, the weight of the coupon was measured and recorded. A sample cumulative mass loss of material is shown with sand weight in Figure 5-5. This figure is for the particle impact velocity of 24 m/s and impact angle of 15 degrees of Oklahoma #1 sand. As shown in the figure, the mass loss 83

100 of material has a linear relationship with the weight of sand injected. All the air test results behave in this manner. The results for the other testing conditions are presented in Appendix E. 12 Cumulative Mass Loss (mg) y = 0.011x R² = Sand Weight (g) Figure 5-5: Cumulative Mass Loss vs. Sand Weight for V p = 24 m/s at 15 degrees (Al 6061) Table 5-1 is the summary of erosion rates for aluminum. Figure 5-6 and Figure 5-7 are the graphs of erosion rate in kg/kg vs. impact angle for three different impact velocities. The impact particle velocities of 13, 24 and 42 m/s, and the impact particle angles of 15, 30, 60, and 90 degrees were tested. (Similar results were gained by Torabzadeh in 2009; therefore, the results of Torabzadeh are omitted here. The results of Torabzadeh will be shown in Figure 5-10 and Table 5-4 in Section ) As shown in the table and the figures, for both particle sizes, higher impact particle velocity yields higher erosion rates for all of the impact angles. From the figures, it is also found that erosion rates are higher for lower impact angles for all the particle velocities. 300 µm particles give higher erosion rates than 150 µm due to their size and shape. The 84

101 microscopic pictures of these particles are shown in Chapter 3. Another thing to be noted here is that the 300 µm particles erosion rate has a trend that is slightly different from that of the 150 µm particles. Erosion rates for the 150 µm particles increase more significantly as the impact angle decreases, while the erosion rates for the 300 µm sand particles do not increase as significantly as for the 150 µm sand particles. The differences in the two types of sand can result in not only a difference in magnitude but also in trend of erosion rate with impact angle (angle function). Table 5-1: Aluminum 6061 Erosion Rates in Air ER (kg/kg) Angle (deg) Impact Velocity V p 13 m/s 24 m/s 42 m/s 150 µm 300 µm 150 µm 300 µm 150 µm 300 µm E E E E E E E E E E E E E E E E E E E E E E E E-04 85

102 1.00E-04 Exp. Data (Vp = 13 m/s) Exp. Data (Vp = 24 m/s) Exp. Data (Vp = 42 m/s) Erosion Rate (kg/kg) 1.00E E E Impact Angle θ (Degrees) Figure 5-6: Erosion Rate vs. Impact Angle for Al 6061 in Air (OK#1, 150 µm) 1.0E-03 Exp. Data (Vp = 13 m/s) Exp. Data (Vp = 24 m/s) Exp. Data (Vp = 42 m/s) Erosion Rate (kg/kg) 1.0E E E Impact Angle (Degrees) Figure 5-7: Erosion Rate vs. Impact Angle for Al 6061 in Air (CA60, 300 µm) 86

103 5.2.3 Stainless Steel Erosion Results in Air Erosion rates for stainless steel 316 were measured by Torabzadeh (2009) in air with particle velocities of 13, 28, and 42 m/s and particle angles of 15, 30, 60, and 90 degrees. Oklahoma #1 sand was used as the abrasive particles. Torabzadeh did not measure particle velocities and was using gas velocity to determine particle velocities. Using her Pitot tube measurements, the particle velocities are calculated from Figure 5-4. The results shown in this section are data measured by Torabzadeh (2009), but the particle velocities are from the present work. Table 5-2 and Figure 5-8 are the summary of erosion results for stainless steel 316. As it was the case for aluminum, for stainless steel, the erosion rates increase with increased particle velocities for all of the impact angles. However, from Figure 5-8, it should be noted the highest erosion rates occur at an impact angle between 30 and 60 degrees for this material, which was not the case for aluminum. Table 5-2: Stainless Steel Erosion Rates in Air by OK#1 (Torabzadeh Khorasani, 2009) Angle (deg) ER (g/g) Impact Velocity V p 13 m/s 28 m/s 42 m/s E E E E E E E E E E E E-05 87

104 1.0E-04 Erosion Rate (kg/kg) 1.0E E-06 Exp. Data (Vp = 13 m/s) Exp. Data (Vp = 28 m/s) Exp. Data (Vp = 42 m/s) 1.0E Impact Angle θ (Degrees) Figure 5-8: Erosion Rate vs. Impact Angle for SS 316 in Air (OK#1, 150 µm) (Torabzadeh Khorasani, 2009) 5.3 Generation of Erosion Models Aluminum 6061 E/CRC Equation (Oklahoma #1 Sand): Utilizing the information gained through erosion measurements in air, the erosion model for aluminum is generated. At first, all the experimental results from Figure 5-6 are normalized and plotted together in Figure 5-9. Since the results are normalized, the results from different particle velocities are close in value to each other which indicate that particle velocity only affects the erosion equations in magnitude and not the shape of the erosion versus impact angle profile. 88

105 The angle function as shown by Equation 5-1 is a modified version of the angle function suggested by Oka et al, (2005) and was used with parameters n1, n2, and n3 which are chosen to fit the experimental data. The Vicker s hardness for aluminum 6061 is approximately 1.12 GPa. n1, n2, and n3 are found based on the experimental data, and for aluminum they are listed in Table 5-3. Since the experimental data are normalized, the angle function must be normalized as well by dividing the function by f, which is the maximum value of the function. The angle function is plotted together with experimental data in Figure 5-9. F θ sinθ 1 Hv 1 sinθ (5-1) Table 5-3: Angle Function Variables OK#1 (Aluminum 6061) n n2 3.6 n3 2.5 Hv (Gpa) f

106 1.2 Normalized ER (-) Vp = 13 m/s Vp = 24 m/s Vp = 42 m/s Angle Function Impact Angle (degrees) Figure 5-9: Normalized Erosion Rate vs. Impact Angle in Air 150 µm (Aluminum 6061) After the angle function is defined, the entire modified erosion equation can be defined based on the earlier work at the E/CRC. Equation 5-2 is the erosion equation developed by Zhang et al. (2006) at the E/CRC is used as an exponent for the particle velocity, which was also used in the case of Inconel (Zhang, 2006). where ER C BH. F V. F θ (5-2) BH H Since Brinnel hardness, sharpness factor (0.5 for Oklahoma sand), impact velocity and angle function are constants for each test condition, an empirical constant C is found by simply dividing the measured erosion rate by these constants for each test condition. Table 5-4 provides the calculated empirical constant C for each test condition for Okita 90

107 and Torabzadeh s data (2009). The results are plotted in Figure The total constant C is calculated by taking an average of the results from the entire test conditions. For aluminum 6061 and OK#1 sand, it is 1.5e-7. Table 5-4: Empirical Constant C for each test condition OK#1 (Al 6061) Okita ER/(HB)-0.59*Fs*f(α)*V p 2.41 Vp (m/s) α=15 α=30 α=60 α=90 AVG E E E E E E E E E E E E E E E-07 C = 1.50E-07 Torabzadeh ER/(HB)-0.59*Fs*f(α)*V p 2.41 Vp (m/s) α=15 α=30 α=60 α=90 AVG E E E E E E E E E E E E E E E-07 C = 1.66E-07 91

108 2.5E-07 ER/(HB)-0.59*Fs*f(α)*Vp E E E E-08 C = 1.5E-7 0.0E Impact Velocity (m/s) α=15 α=30 α=60 α=90 C = 1.50E-7 α=15 (Torabzadeh) α=30 (Torabzadeh) α=60 (Torabzadeh) α=90 (Torabzadeh) Figure 5-10: Empirical Constant C vs. Impact Velocity for Different Impact Angle OK#1 (Al 6061) Figures 5-11 to 5-13 are the measured erosion rates vs. impact angle for each velocity condition plotted with the new modified E/CRC equation and Oka s equation. From the figures, the new E/CRC equation tends to give higher erosion rates at lower angles than Oka s equation. However, at higher angles, from 50 to 90 degrees, erosion rates given by Oka s equation are higher than the E/CRC equation. 92

109 Erosion Rate (kg/kg) 2.5E E E E E-07 Oka's eqn E/CRC eqn Exp. Data 0.0E Angle (degree) Figure 5-11: Erosion vs. Angle Exp. Data and Models V p = 13 m/s OK#1 (Al 6061) Erosion Rate (kg/kg) 1.2E E E E E E-06 Oka's eqn E/CRC eqn Exp. Data 0.0E Angle (degree) Figure 5-12: Erosion vs. Angle Exp. Data and Models V p = 24 m/s OK#1 (Al 6061) 93

110 6.0E E-05 Erosion Rate (kg/kg) 4.0E E E E E+00 Oka's eqn E/CRC eqn Exp. Data Angle (degree) Figure 5-13: Erosion vs. Angle Exp. Data and Models V p = 42 m/s OK#1 (Al 6061) (California 60 Sand): The erosion equation for California 60 mesh sand was generated in the same manner as Oklahoma #1 sand. Angle function variables for this sand are shown in Table 5-5. Figure 5-14 shows the normalized erosion results along with the new angle function. As shown in the figure, the normalized erosion rates all collapse on the same line which indicates the velocity only affects the magnitude but not the shape of the erosion versus impact angle profiles. As discussed previously, the angle function of this sand gives higher erosion rates at lower impact angles than the angle function of OK#1 sand. 94

111 Table 5-5: Angle Function Variables CA60 (Aluminum 6061) n1 0.5 n2 2.5 n3 0.5 Hv (Gpa) f Normalized ER (-) 1.2E E E E E-01 Vp = 13 m/s Vp = 24 m/s Vp = 42 m/s Angle Function 2.0E E Impact Angle (degrees) Figure 5-14: Normalized Erosion Rate vs. Impact Angle in Air 300 µm (Aluminum 6061) After the angle function is developed, the constant C is calculated based on material hardness, impact velocities and impact angles. A sharpness factor of 1 is used for this sand. Values of C for each test condition are summarized and plotted in Table 5-6 and Figure For this sand, the averaged C is 3.28E-7. 95

112 Table 5-6: Empirical Constant C for each test condition CA60 (Al 6061) ER/(HB)-0.59*Fs*f(α)*V p 2.41 Vp (m/s) α=15 α=30 α=60 α=90 AVG E E E E E E E E E E E E E E E-07 C = 3.28E-07 ER/{(HB) *Fs*f(α)*Vp 2.41 } 5.0E E E E E E E E E E E+00 C = 3.28E-7 α=15 α=30 α=60 α=90 C = 1.50E Impact Velocity (m/s) Figure 5-15: Empirical Constant C vs. Impact Velocity for Different Impact Angle CA60 (Al 6061) Figures 5-16 to 5-18 are the graphs of erosion rates versus impact angles for three different velocities for California 60 sand. For this sand, Oka s model gives much lower erosion rates than the new E/CRC equation. This is because Oka s model is using the same equation for California 60 sand and Oklahoma #1. There is no parameter that accounts for sharpness in the Oka s equation. There is a factor, k3, which accounts for the 96

113 size of particle but it is very small, therefore, there is not much difference in erosion rates predicted by Oka s model between Oklahoma sand and California sand in this equation. On the other hand, the new E/CRC equation is based on erosion testing in air by California 60 sand; therefore, it is more accurate than Oka s equation. 1.2E E-05 Oka's eqn E/CRC eqn Exp. Data Erosion Rate (kg/kg) 8.0E E E E E Angle (degree) Figure 5-16: Erosion vs. Angle Exp. Data and Models V p = 13 m/s CA60 (Al 6061) 97

114 Erosion Rate (kg/kg) 5.0E E E E E E E E E E E+00 Oka's eqn E/CRC eqn Exp. Data Angle (degree) Figure 5-17: Erosion vs. Angle Exp. Data and Models V p = 24 m/s CA60 (Al 6061) Erosion Rate (kg/kg) 2.5E E E E E-05 Oka's eqn E/CRC eqn Exp. Data 0.0E Angle (degree) Figure 5-18: Erosion vs. Angle Exp. Data and Models V p = 42 m/s CA60 (Al 6061) 98

115 5.3.2 Stainless Steel 316 E/CRC Equation The E/CRC equation for stainless steel was developed by the same method as aluminum. Only erosion results using Oklahoma #1 are available to generate the erosion equation for the stainless steel. Therefore, only one equation is used for all the sand particles. Utilizing the erosion results obtained from Torabzadeh, angle function parameters were calculated by Fard at E/CRC. Table 5-7 and Figure 5-19 show the values for angle function parameters and the plotted normalized angle function with the experimental data. Unlike the aluminum angle function, the stainless steel angle function has a profile which reaches its maximum around 40 degrees. Table 5-7: Angle Function Variables (Stainless Steel 316) n1 1.4 n n3 2.6 Hv 1.5 (Gpa) f

116 1.2E E+00 Normalized ER (-) 8.0E E E E E+00 Vp = 13 m/s Vp = 24 m/s Vp = 42 m/s Angle Function Impact Angle (degrees) Figure 5-19: Normalized Erosion Rate vs. Impact Angle in Air (Stainless Steel 316) After the angle function is defined, the empirical constant C was found. Table 5-8 and Figure 5-20 are the summary of calculated C values for each test condition. The averaged C is 1.42E-7 in this case. Table 5-8: Empirical Constant C for each test condition (SS 316) ER/(HB) *Fs*f(α)*V p 2.41 Vp (m/s) α=15 α=30 α=60 α=90 AVG E E E E E E E E E E E E E E E-07 C = 1.423E

117 2.5E-07 ER/{(HB )-0.59 *Fs*f(α)*Vp 2.41 } 2.0E E E E E+00 C = 1.42E-7 α=15 α=30 α=60 α=90 C = 1.42E Impact Velocity (m/s) Figure 5-20: Empirical Constant C vs. Impact Velocity for Different Impact Angles (SS316) Figures 5-21 to 5-23 show the E/CRC equation for stainless steel and Oka s equation for stainless steel plotted with experimental data. Unlike aluminum, for stainless steel, Oka s equation gives higher erosion rates than the E/CRC equation at all the angles. The equations developed in this chapter will be used in Chapter 6 to calculate erosion rates caused by particles in CFD. 101

118 3.0E-06 Erosion Rate (kg/kg) 2.5E E E E E E+00 Oka's eqn E/CRC eqn Exp. Data Angle (degree) Figure 5-21: Erosion vs. Angle Exp. Data and Models V p = 13 m/s (SS 316) 1.8E E-05 Erosion Rate (kg/kg) 1.4E E E E E E E E Angle (degree) Oka's eqn E/CRC eqn Exp. Data Figure 5-22: Erosion vs. Angle Exp. Data and Models V p = 28 m/s (SS 316) 102

119 Erosion Rate (kg/kg) 4.5E E E E E E E E E E Angle (degree) Oka's eqn E/CRC eqn Exp. Data Figure 5-23: Erosion vs. Angle Exp. Data and Models V p = 42 m/s (SS 316) 103

120 CHAPTER 6 EROSION PREDICTION BY CFD 6.1 Introduction In this chapter, the results of erosion rates predicted by CFD and erosion equations presented in Chapter 5 are discussed and compared with experimental results presented in Chapter 3. This chapter consists of three sections. At first, the results of predicted erosion rates for inconel, aluminum and stainless steel are compared with measured data. In the second section, a sensitivity study of CFD is performed for aluminum as impacted by 150 um sand particles. Erosion rates are predicted with different dimensions, inlet conditions, turbulence models, grid sizes and sand sizes and compared with original predictions to see how these factors influence the results. In the last section, the number of impacts in CFD is analyzed. The number of impacting particles for each viscosity and particle size for aluminum are studied and compared to each other. Erosion rates considering only the first impact for each particle and all the impacts are also compared to experimental data to examine the effect of the number of impacts on erosion rates. 6.2 Comparison of Predicted and Measured Erosion Rates In this study, instead of using erosion models that are developed for a variety of materials, specific erosion equations are developed based on erosion testing in gas. Then 104

121 specific erosion equations were used to predict erosion rates for inconel, aluminum and stainless steel for a submerged direct impingement flow with liquid. The Reynolds Stress Model is used as the turbulence model for CFD calculations of the flow field and 2-D axisymmetric mesh is created. The CFD simulations used in this chapter are nearly identical to those used in Chapter 4, in terms of the number of grids and turbulence model that is used, but in this chapter, particle impact speed and angle as well as the impact location and frequency are used along with their erosion equations to predict erosion Predicted Erosion Rates for Inconel 625 Table 6-1 shows the predicted and measured erosion rates of inconel 625 impacted by 150 µm particles in mils per pound which was obtained by an ER probe. The measured results are also shown in Chapter 3. The results are plotted in Figure 6-1. From the results, it can be noted that Oka s model tends to predict higher erosion rates than the E/CRC model. Overall, the predicted erosion rates are in good agreement with the measured erosion rates. Both predictions and measurements show erosion rates reduce as viscosity is increased. 105

122 Table 6-1: Predicted Erosion Rates for Inconel 625 Viscosity (cp) Predicted Erosion Rate (mils/lb) Exp Inconel 625 E/CRC Predictions Oka E E E E E E E E E E E E E-02 Exp. Data μm CFD (Oka) μm CFD (E/CRC) μm Erosion Rate (mils/lb) 1.00E E Viscosity (cp) Figure 6-1: Predicted Erosion Rate and Experimental Data for Inconel (150 µm) Predicted Erosion Rates for Aluminum 6061 Table 6-2 and Figures 6-2, 3, and 4 are the measured and predicted erosion rates of aluminum vs. viscosity for three particle sizes in units of m 3 /kg. From Figure 6-2, CFD predicts the erosion rate decreases with increase in viscosity for 300 µm particles, while 106

123 measurements show the erosion rate stays constant across the viscosity change. The erosion rate is also underpredicted by one order of magnitude by CFD for all the viscosities. The E/CRC model predicts better than Oka s model. Erosion rates for 150 µm particles agree better with CFD predictions. Both predictions and measurements have declining profiles and the magnitude of erosion rate is under-predicted only by a factor of 3 or 4. For this particle size, E/CRC and Oka s equations give similar values. For the smallest particles (20 µm), the predictions do not agree with the trend of measurements. Both equations predict that erosion rate decreases from 1 to 10 cp, however, increases from 10 cp to 50 cp, while measurements show the erosion rate is lower for higher viscosities. Also, for 20 µm particles, predictions are lower than measured values. Table 6-2: Predicted Erosion Rates for Aluminum 6061 Viscosity (cp) Predicted Erosion Rate (m 3 /kg) Aluminum 300 µm 150 µm 20 µm E/CRC Oka E/CRC Oka E/CRC Oka E E E E E E E E E E E E E E E E E E E E E E E E

124 1.00E-08 Exp. Data µm CFD (Oka) µm CFD (E/CRC) µm Erosion (m 3 /kg) 1.00E E E Viscosity (cp) Figure 6-2: Predicted Erosion Rate and Experimental Data for Aluminum (300 µm) 1.00E-08 Erosion (m 3 /kg) 1.00E E-10 Exp. Data µm CFD (Oka) µm CFD (E/CRC) -150 µm 1.00E Viscosity (cp) Figure 6-3: Predicted Erosion Rate and Experimental Data for Aluminum (150 µm) 108

125 1E-08 Exp. Data - 20 µm 1E-09 CFD (Oka) - 20 µm CFD (E/CRC) - 20 µm Erosion (m 3 /kg) 1E-10 1E-11 1E Viscosity (cp) Figure 6-4: Predicted Erosion Rate and Experimental Data for Aluminum (20 µm) 109

126 6.2.3 Predicted Erosion Rates for Stainless Steel 316 Table 6-3 and Figures 6-5, 6, and 7 are the measured and predicted erosion rates of stainless steel vs. viscosity for three particle sizes in units of m 3 /kg. Similar to aluminum, stainless steel predictions show that CFD tends to underpredict erosion rates for 300 and 150 µm particles while overpredicting for 20 µm particles. Viscosity (cp) Table 6-3: Predicted Erosion Rates for Stainless Steel 316 Predicted Erosion Rate (m 3 /kg) Stainless Steel 300 µm 150 µm 20 µm E/CRC Oka E/CRC Oka E/CRC Oka E E E E E E E E E E E E E E E E E E E-09 Erosion (m 3 /kg) 1.00E E E-12 Exp. Data µm CFD (Oka) µm CFD (E/CRC) µm Viscosity (cp) Figure 6-5: Predicted Erosion Rate and Experimental Data for SS 316 (300 µm) 110

127 1.00E-09 Exp. Data µm CFD (Oka) µm CFD (E/CRC) µm Erosion (m 3 /kg) 1.00E E E Viscosity (cp) Figure 6-6: Predicted Erosion Rate and Experimental Data for SS 316 (150 µm) 1.00E-09 Exp. Data - 20 µm CFD (Oka) - 20 µm CFD (E/CRC) - 20 µm Erosion (m 3 /kg) 1.00E E E Viscosity (cp) Figure 6-7: Predicted Erosion Rate and Experimental Data for SS 316 (20 µm) 111

128 6.3 CFD Erosion Prediction Analysis Sensitivity of CFD erosion prediction is studied in this section. Erosion rates of aluminum by 150 µm particles predicted under different dimensions, inlet configurations, grid sizes, turbulence models, and sand sizes are analyzed and compared to the original results dimensional vs. 2 dimensional axisymmetric Previously, the direct impingement geometry was modeled as three dimensional (3D). However, in order to increase the efficiency, as well as the necessity to use more computationally expensive models such as near wall modeling, a two dimensional (2D) axisymmetric approach became more reasonable than three dimensional approach for this type of work. Figure 6-8 shows the mesh for 2D and 3D. The reduced number of cells in 2D increases the computational efficiency. 112

129 3 Dimensional 2 Dimensional Axisymmetric Figure 6-8: 3D and 2D Meshes Theoretically, three-dimensional and two-dimensional axisymmetric meshes should be identical and yield comparable results. To verify, two-dimensional erosion and flow calculations are compared to three-dimensional results. Erosion rates of aluminum 113

130 for 150 µm particles in a 1 cp fluid are calculated using both three-dimensional and twodimensional meshes. The results are summarized in Table 6-4. As shown in the table, both E/CRC and Oka s models give very similar values for two-dimensional and threedimensional geometries. The difference between the 2D and 3D models is negligible as compared to differences in calculations and data. This result proves that a twodimensional axis-symmetric can be used in place of a three-dimensional mesh. Table 6-4: Predicted Erosion Rates for 3D vs. 2D (Aluminum - 150µm 1 cp) Predicted Erosion Rate (m 3 /kg) - 1 cp Dimension Aluminum 150 µm E/CRC Oka 2D 1.38E E-10 3D 1.37E E-10 Difference % Effects of Inlet Configurations Uniform vs. Velocity Profile In CFD, particles are released at the nozzle exit (inlet) and the measured particle velocities from LDV at the nozzle exit are used. All the results shown in this chapter as well as others used the LDV particle velocity profile as an inlet condition. As another approach, the inlet velocity can be treated as an uniform velocity, in which the velocity is constant and set equal to the average velocity along the radius of the nozzle exit. An illustration of the inlet configurations is shown in Figure 6-9. Both inlet configurations have the same particle mass flow rate. 114

131 Target Wall z Average Velocity = 10 m/s z r r Nozzle Exit Nozzle Exit Profile Inlet Uniform Inlet Figure 6-9: Illustration for Inlet Configurations To study the effect of inlet configurations on erosion results, erosion rates of aluminum by 150 µm particles are predicted for two different inlet configurations: velocity profile from LDV and uniform inlet at 10 m/s. The results are summarized in Table 6-5. As shown in the table, the differences between these two inlet configurations are trifle. Therefore, the inlet configurations do not affect the erosion rates at the wall. 115

132 Table 6-5: Predicted Erosion Rates for Different Inlet Conditions (Aluminum - 150µm) Predicted Erosion Rate (m 3 /kg) Aluminum µm Viscosity Velocity Profile Const Velocity Difference % (cp) E/CRC Oka E/CRC Oka E/CRC Oka E E E E E E E E Effects of Grid Size on Erosion Rates In Chapter 4, the effects of grid size on fluid and particle velocities were analyzed. The results showed there are no significant differences in particle and fluid velocities calculated from different mesh sizes. In this section, the effects of grid size on erosion rates are studied. Even though grid size does not affect particle velocities, it could affect number of particle impacts at the target wall and therefore, influence the erosion results. The erosion rates are predicted using the same grids used in Chapter 4. Simulations for both grids use the RSM as the turbulence model. The results are shown in Table 6-6. From the table, it should be noted that at 1 cp, both E/CRC and Oka s model give similar values for the original and the finer mesh. However, at 50 cp, both models predict higher erosion rates for the finer grid than the original grid. The differences between two grid sizes are not negligible. 116

133 Table 6-6: Predicted Erosion Rates for Different Grid Size (Aluminum - 150µm) Predicted Erosion Rate (m 3 /kg) Aluminum µm Viscosity Original Finer Difference % (cp) E/CRC Oka E/CRC Oka E/CRC Oka E E E E E E E E In order to understand the cause of the difference between the original and finer grid erosion rates, impact speed, impact angle and number of impacts of 50 cp are plotted along the radial locations. The graphs are shown in Figures 6-10, 11 and 12. As mentioned before, from Figure 6-10, the difference in particle velocities between original and finer grids are negligible. From Figure 6-11, particle angle of the finer mesh is also comparable to that of the original mesh. However, there is a significant difference in number of impacts between the original and the finer mesh. The finer mesh has more impacts especially at r = 10 to 40 mm. This increased number of impacts is the cause of the discrepancy between the original and finer mesh erosion rates. Averaged Impact Speed (m/s) Finer Regular Radial Location r (mm) Figure 6-10: Predicted Average Impact Speed vs. Radial Location - 50 cp 117

134 Averaged Impact Angle (Deg) Finer Regular Radial Location r (mm) Figure 6-11: Predicted Average Impact Angle vs. Radial Location - 50 cp Number of Impacts (-) Finer Regular Radial Location r (mm) Figure 6-12: Predicted Number of Impacts vs. Radial Location - 50 cp 118

135 6.3.4 Turbulence Model Analysis In Chapter 4, particle and fluid velocities are calculated using RSM and low Reynolds number model as turbulence models. In this section, the erosion rates predicted using RSM, k-ε, and low Reynolds number models are compared and analyzed. Results are shown in Table 6-7. As shown in the table, the low Reynolds number model gives much lower erosion rates than the other models. To understand this behavior, a couple of particles were released and particle information for these particles was output along their trajectories. The analysis revealed that particles in the low Reynolds number model behave similar to ones in other models at locations away from the wall. However, as they approach the wall, the particle steps become very small and particles tend to stay in certain cells without leaving the cell and hitting the wall. This is because the cell size gets very small near the wall in the low Reynolds number model mesh, and these smaller cells cause turbulent velocity fluctuations to be small. Since turbulent velocity fluctuations are an important factor that decide the time step of the particles, particle steps also become infinitesimal. In order to fix this problem, commands can be added in User Defined Functions (UDF) so that when turbulent fluctuations get too small near the wall, Fluent will use another method to calculate particle time steps. 119

136 Table 6-7: Predicted Erosion Rates for Different Turbulent Models (Aluminum - 150µm) Predicted Erosion Rate (m 3 /kg) Aluminum µm Viscosity RSM k-ε LowRe (cp) E/CRC Oka E/CRC Oka E/CRC Oka E E E E E E E E E E E E-12 Erosion rates of RSM and the k-ε model are comparable at 1 cp while erosion rates at 50 cp show that the k-ε model tends to give higher erosion rates than RSM. To find out the cause of the difference, impact speeds and number for impacts of 50 cp fluid for each model were plotted along the radial locations in Figures 6-13 and 14. From Figure 6-13, it can be observed that the impact speed is actually higher for RSM than the k-ε model. This is opposite of the trend for erosion rates. In Figure 6-14, however, it is observed that the number of impacts for the k-ε model is much higher than the number of impacts for RSM. This increased number of impacts can cause the erosion rates from the k-ε model to be higher than erosion rates from RSM. As discussed in the Section 6.2.3, number of impacts can affect erosion rates significantly. A careful examination of this effect must be carried out to see why the number of impacts is much higher, and some results will be discussed in a future section. 120

137 Averaged Impact Speed (m/s) Radial Location r (mm) RSM Kε Figure 6-13: Predicted Averaged Impact Speed vs. Radial Location for Turbulent Models - 50 cp Number of Impacts (-) Radial Location r (mm) RSM Kε Figure 6-14: Predicted Number of Impacts vs. Radial Location for Turbulent Models - 50 cp 121

138 6.3.5 Effect of Particle Distribution on Erosion Rates During particle tracking in CFD, usually, the average diameters are used for each size of sand. However, in reality, sand particles are not all at the same size. As shown in Chapter 3, each sand type has its own sand size distribution. Therefore, in order to keep the CFD simulation closer to reality, sand size distribution information was used for sand injections and results are compared to the ones using the average sand size. Table 6-8 summarizes the results. Erosion rates on inconel 625 for 1 cp fluid were predicted using three different particle sizes: 20, 150 and 300 μm. The results show that for bigger particles, the differences in erosion rates between using the average size and sand size distribution are insignificant while there is a significant difference for smaller particles. The reason for the increased erosion rates for the sand size distribution for 20 μm particles is obvious when one looks at its sand size distribution graph (Figure 3-9). For this sand, the average sand size is 20 μm; however, there is a large volume ratio of particles that are much larger than the average sand size. These large particles can cause higher erosion rates. Table 6-8: Predicted Erosion Rates for Different Sand Size (Inconel cp) Sand Size Predicted Erosion Rate (m 3 /kg) Inconel µm 150 µm 20 µm E/CRC Oka E/CRC Oka E/CRC Oka Average 1.87E E E E E E-04 Distribution 1.86E E E E E E-04 Difference %

139 6.4 CFD Number of Impact Analysis Besides particle velocity, the number of impacting particles is another important factor that influences erosion rate. As viscosity changes, the number of particles hitting the wall also changes. In CFD, 10,000 particles are released at the nozzle exit for each case, and the number of particles hitting the wall boundary was recorded. The results are shown in Figure Figure 6-15 shows the number of particles impacting vs. the number of impacts per particle for different particle sizes and different viscosities. Number of impacts is how many times each particle is hitting the wall. Number of particles impacting is how many particles are hitting at each number of impacts. Some particles only hit the wall once or several times and move away from the shear layer near the wall (low impact number) while some particles keep hitting the wall over and over again and are stuck in the shear layer near the wall (high impact number). Figure 6-15 shows that 20 µm particles tend to have much higher impact numbers than 300 and 150 µm particles. For all particle sizes, a greater number of particles are hitting over and over again for higher viscosity liquids (50 cp) than in lower viscosity liquids (1 cp). 123

140 Number of Particle Impacting (-) (300 µm) CFD - 1 cp CFD - 50 cp 300 µm Number of Impacts (-) Number of Particle Impacting (-) (150 µm) CFD - 1 cp CFD - 50 cp 150 µm Number of Impacts (-) Number of Particle Impacting (-) (20 µm) CFD - 1 cp CFD - 50 cp 20 µm Number of Impacts (-) Figure 6-15: Number of Particle Impacting vs. Number of Impacts for 20, 150, and 300 µm 124

141 The impact number for 20 µm particles is very high as compared to other particles. To demonstrate that the number of particles impacting is the source of the difference between the CFD predictions and measurements, the erosion rate for Aluminum was recalculated for 20 µm particles using only the first impact and discarding the rest of the impacts for an individual particle. The results are shown in Table 6-9 and Figure The graph shows the new CFD predictions using the first impact along with experimental data. The predictions using only the first impact agree with the experimental data much better than the original predictions using all of the impacts (Figure 6-4). Table 6-9: Erosion Rates for 1 st Impacts (Aluminum µm) Viscosity (cp) Predicted Erosion Rate (m 3 /kg) Aluminum - 20 µm 1st Impacts Exp. Data E/CRC Oka E E E E E E E E E E E E

142 1E-10 Erosion (m 3 /kg) 1E-11 1E-12 EXP Data CFD Simulation (Oka) CFD Simulation (E/CRC) Viscosity (cp) Figure 6-16: Measured and Predicted Erosion Rates for 1 st Impacts The results shown in this section are only predictions and there is no experimental data regarding the number of particle impacts. The number of particle impacts may be observed experimentally by using glass bead impact tests. Since glass beads are spherical, they leave clear mark of indentation marks, which make it possible to count the number of indentations on the target coupon under SEM. The details of how the experiments can be carried out to observe the number of impacts will be discussed in Chapter

143 CHAPTER 7 SUMMARY AND CONCLUSIONS Erosion rates for Inconel 625, aluminum 6061 and 316 stainless steel occurring from 20, 150, and 300 µm particles with carrier fluids of 1, 10, 25, and 50 cp were measured. It was found that for all the materials, erosion rate decreases as viscosity increases for 20 and 150 µm sand (small particles) while 300 µm sand (large particles) showed no significant change in erosion rate with change in viscosity. LDV measurements were examined in order to study how particles behave near the wall. Fluid and particle velocities for 120 and 550 µm particles in 1, 50, 100 cp fluids were measured by Miska (2008) and present author. The comparison of predicted and measured particle velocities of small and large particles showed that CFD is able to predict velocities comparable to the measurements. Near the wall, however, it was found from CFD that the velocities of large particles are not affected by viscosity as much as that of small particles. Due to larger inertia, large particles penetrate through the shear layer near the wall and slow down but not as much as the small particles which slow down significantly as they enter the shear layer. As a result, erosion rates with large particles do not change as much as small particles as viscosity changes. It was also found that higher viscosity liquids form thicker shear layer near the wall than lower viscosity liquids. Therefore, if particle sizes are the same, particles in higher viscosity fluids reach a maximum velocity farther away from the wall and slow down more rapidly than 127

144 particles in lower viscosity fluids near the wall. Since higher viscosity liquids have a thicker shear layer and exert higher drag on particles, particles impacting the wall have lower velocities in higher viscosity fluids than lower viscosity fluids. This may explain why erosion rate decreases as viscosity increases for each particle size. Predicted fluid and particle velocities using two different meshes were analyzed and compared. It was found that grid sizes do not affect velocities for the meshes investigated. The effects of turbulence model on predicted velocities were also studied. The results showed that overall, velocities predicted by the low Reynolds number model are not very different from those predicted by the RSM. Erosion models were developed based on air testing for aluminum and stainless steel. For aluminum, erosion models were generated for two types of sand: Oklahoma #1 and California 60. Each equation is unique with different empirical constants and angle functions. These newly developed equations were used to predict erosion rates in CFD. CFD was utilized to predict erosion rates for Inconel, aluminum and stainless steel for particle sizes of 20, 150, and 300 µm in carrier fluid of 1, 10, 25 and 50 cp. The predictions are in good agreement with measured erosion rates for Inconel 625. The comparison of predicted and measured erosion rates of aluminum and stainless steel showed that CFD tends to significantly (by a factor of approximately 2 to 10) underpredict erosion rate for 150 and 300 µm particles. For 150 µm particles, the trend of predicted erosion rate is comparable to that of the measured erosion rate. For the 20 µm sand, the predicted erosion rates decrease from 1 to 10 cp but increase from 10 to 50 cp which does not agree with the experimental data. It was also observed that erosion rates are overpredicted for 20 µm particles. 128

145 In order to study the sensitivity of CFD predictions, erosion rates of aluminum by 150 µm particles were predicted for different dimensions, inlet configurations, grid sizes, turbulent models, and sand sizes and compared to the original results. It was found that two-dimensional and three-dimensional meshes yield the same erosion rates. It was also observed that the inlet configurations also do not influence the calculated erosion rates. The grid size influences erosion rates for highly viscous fluids, while erosion rates for 1 cp are nearly the same for the original and finer meshes. Turbulence models also affect erosion rates especially for high viscosity liquids. RSM and the low Reynolds number model give similar erosion rates for 1 cp, while for 50 cp, there is a significant difference in predicted erosion rates. The difference in erosion rates in high viscosity liquids are due to increased number of impacts. The effects of particle sand size distribution were also studied. Erosion rates of Inconel for 1 cp were predicted using an average particle size and sand size distribution for each sand. The results revealed that for bigger particles, the erosion rates were comparable regardless of sand diameter approach. However, for 20 µm particles, calculated erosion rates were much higher (by a factor of two) for calculations using the actual sand size distribution than the calculations using the average particle size. This is due to a relatively large fraction of particles that are much larger than the average sand size. The number of particles impacting the wall was studied using CFD simulations. It was found that particles in higher viscosity fluids impact the wall more frequently than particles in lower viscosity fluid. It was also found that 20 micron particles tend to impinge the target over and over again resulting in large predicted erosion rates while 150 and 300 micron particles only impact a few times and exit the region of interest near the 129

146 wall. The erosion rates of 20 micron particles were recalculated using information from only the first impact of each impacting particle. The predicted erosion rate using only the first impact successfully agrees with the trend of the observed erosion rate of the experimental data. This implies that the number of impacting particles is another important factor for erosion prediction. Although CFD tends to underpredict the measurements for sand in viscous liquids, it is able to predict particle velocity and erosion rates which match the trend of measured velocity and erosion rates. Overall, CFD is capable of being used as a tool to predict erosion rates. It should be mentioned that the erosion equations used in this study were all calibrated with gas data for a range of velocities from 13 to 42 m/s. However, the magnitude of erosion did not match the data for sand in viscous liquids. Therefore, some modification may be needed if there is a fundamental factor causing differences in erosion process in liquids and gases. 130

147 CHAPTER 8 FUTURE WORK In the past, erosion models that were not highly calibrated were used to predict erosion rates in liquids. In some instances, good agreement was observed between calculations and predictions. In this study, however, the erosion equations were calibrated with gas data over a wide range of velocities. Furthermore, the velocity of particles were also measured in gas testing to make sure the erosion models used for aluminum and stainless steel are accurate. However, the erosion calculations in liquid for aluminum and stainless steel did not match the data. But, for Inconel 625 when erosion equations were not calibrated and data was also questionable due to the use of ER probes, the calculations surprisingly appeared to agree with the liquid data. For future work in this area, both experimental and computational work is needed. Further modifications and investigations are needed on CFD modeling so that CFD is able to predict erosion rates that are comparable to experimental data. For example, the drag coefficient used in CFD particle tracking needs to be examined to see whether the shape of particles affects the particle velocity and erosion rates. Different turbulence models also need to be studied. In the current work, only RSM, k-ε, and the low Reynolds number models were used for predictions. The other models such as k-ε RNG and large eddy simulation (LES) as well as different near wall treatments can be examined and studied. 131

148 Another possible work for the future is to collect more comprehensive erosion data in gas to generate more accurate erosion equations. In the current work for aluminum, only one equation is used for silica flour and Oklahoma #1 sand. From the results of California sand, it is obvious that the sharpness affects the angle function. One needs to collect gas testing erosion results for silica flour so that there would be a unique equation for each sand type. Erosion data using glass beads also need to be collected in both air and liquid so that the effect of sharpness factor can be studied. In the current work, erosion rates are measured by simply measuring weight loss of a coupon; however, in this method, one cannot see the erosion pattern on the coupon surface. Using a three-dimensional profilometer, eroded coupon surfaces can be examined. By analyzing the eroded surface in detail, one can compare an erosion pattern on a coupon with the one predicted with CFD. The surface of a coupon needs to be scanned by the profilometer prior to the experiment so that the original surface condition is known. Figure 8-1 is an illustration of profilometer readings before and after the measurements. Prior to measurements, indentation marks are made on the surface and the surface is scanned by profilometer. After the measurements, the surface is scanned again and the indentation marks are used as a guide to compare with the original surface. The difference in depth between the curves for before and after the measurements is the thickness loss created by erosion. 132

149 Indentation Coupon Before Erosion Depth After Erosion Max Erosion Distance Profilometer Reading Indentation Figure 8-1: Illustration of Profilometer reading Number of particle impacts is another area which requires investigations. Impact testing can be performed using glass beads in order to physically count the number of impacts. A very low concentration of glass beads can be released in the system to hit the target wall, and the target wall surface can be examined under SEM to look at the pattern of impingements as well as the number of impacts. Figure 8-2 is a SEM picture of an aluminum surface impacted by glass beads. Glass beads are suitable for this type of work since they are spherical and leave clear indentation marks. In CFD, User Defined Functions may be modified to control the number of impacts according to the experimental results. 133

150 Figure 8-2: Microscopic Picture of Aluminum Surface Impacted by 150 µm Glass Beads 134