T H E U N I V E R S I T Y O F T U L S A THE GRADUATE SCHOOL DISPERSED TWO-PHASE SWIRLING FLOW CHARACTERIZATION FOR PREDICTING GAS CARRY-UNDER

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 DISPERSED TWO-PHASE SWIRLING FLOW CHARACTERIZATION FOR PREDICTING GAS CARRY-UNDER IN GAS-LIQUID CYLINDRICAL CYCLONE COMPACT SEPARATORS by Luis Eduardo Gomez A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Discipline of Petroleum Engineering The Graduate School The University of Tulsa 001

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3 ABSTRACT Gomez, Luis E. (Doctor Philosophy in Petroleum Engineering). Dispersed Two-Phase Swirling Flow Characterization for Predicting Gas Carry-Under in Gas-Liquid Cylindrical Cyclone Compact Separators (186 pp. - Chapter VI). Directed by Professor Ovadia Shoham and Professor Ram S. Mohan (355 words) The hydrodynamics of dispersed two-phase swirling flow behavior have been studied theoretically and experimentally for prediction of gas carry-under and evaluating the performance of Gas-Liquid Cylindrical Cyclone (GLCC 1 ) separators. The GLCC operation is limited by two undesirable physical phenomena; one is liquid carry-over (LCO) in the gas stream and the other is gas carry-under (GCU) in the liquid stream. LCO can occur in the gas leg in the form of droplets. GCU is the entrainment of gas bubbles into the exiting liquid stream. Prediction of these two phenomena will allow proper design and operation of the GLCC for the industry. The objective of this study is twofold: to study experimentally the hydrodynamics of dispersed two-phase swirling flow in the lower part of the GLCC; and, to develop a mechanistic model for the characterization of this complex flow behavior, enabling the prediction of gas carry-under in the GLCC. The developed mechanistic model is composed of several sub-models as follows: 1 GLCC - Gas Liquid Cylindrical Cyclone - Copyright, The University of Tulsa, iii

4 Gas entrainment in the inlet region. Continuous-phase swirling flow behavior in the lower part of the GLCC. Dispersed-phase particle (bubbles) motion. Diffusion of dispersed-phase. Coupled Eulerian-Lagrangian analysis. Lagrangian-Bubble Tracking Analysis Simplified Mechanistic Models Integration of the above sub-models yields the amount of gas being carried-under, and the separation efficiency of the GLCC. Two solution schemes are proposed, namely, the Eulerian-Lagrangian Diffusion model (using finite volume method) and Lagrangian- Bubble Tracking model. Simplified mechanistic models for these two approaches are also developed. Large amounts of local measurements of swirling flow data were processed and analyzed to develop correlations for the swirling flow field and the associated turbulent quantities. These correlations are used in the proposed models. Also, experimental data on gas-carry under were acquired for air-water flow. The presented results include the performance of the developed correlations for the swirling flow field and its turbulent quantities. Also presented are the results for both solution schemes and the performance of the mechanistic model. The results presented demonstrate the potential of the proposed approach for predicting the void fraction distribution in dispersed two-phase swirling flow and the associated gas carry-under in GLCC separators. iv

5 ACKNOWLEDGMENTS The author is quite grateful to my advisor Dr. Ovadia Shoham and my Dissertation Co-Chair Dr. Ram Mohan for their personal support and encouragement as well as their supervision and guidance in this study. The author also wishes to thank Dr. Mauricio Prado, Dr. Siamack Shirazi, Dr. Cliff Redus, Dr. Gene Kouba, and Dr. Yehuda Taitel for their willingness to serve as members of the dissertation committee, and for their useful suggestions and assistance. The author is very grateful to the Universidad de Los Andes (ULA) and PDVSA/IINTEVEP for the financial support and opportunity to accomplish this achievement. The author would like to thank the TUSTP members and graduate students for their valuable assistance during this project. Appreciation is also extended to Ms. Judy Teal for her help, support and encouragement. This dissertation is dedicated to my lovely wife Yesenia, my son Gabriel Eduardo and my daughters Mariagustina Danet and Jessica Gabriela. I will always be thankful to them for their support, sacrifices, encouragement and love during my graduate studies at The University of Tulsa. I would also like to dedicate this work to my mother, my family, and especially my brother Tono. v

6 TABLE OF CONTENTS TITLE PAGE APPROVAL PAGE ABSTRACT ACKNOWLEDGMENTS TABLE OF CONTENTS LIST OF FIGURES LIST OF TABLES i ii iii v vi ix xv CHAPTER I: INTRODUCTION 1 CHAPTER II: LITERATURE REVIEW 5.1 Experimental Work and Applications 5. Mechanistic Modeling 9.3 CFD Simulations 10.4 Swirling Flow and Local Measurements 13 CHAPTER III: EXPERIMENTAL PROGRAM Gas Carry-under Experimental Program Gas Carry-under Measurements GLCC Test Facility Gas Carry-under Experimental Results Two-Phase Swirling Flow Visualization 7 3. GLCC Swirling Flow Local Measurements Local Measurement GLCC Test Section 36 vi

7 3.. GLCC Local Measurement Results Straight Pipe Swirling Flow Local Measurements Straight Pipe Swirling Flow Field Analysis Straight Pipe Swirling Flow Turbulent Quantities 75 CHAPTER IV: DISPERSED SWIRLING FLOW MECHANISTIC MODEL Dispersed-Phase Mass Diffusion Model Two-Phase Flow Models Diffusion (Mixture) Model Continuous-phase Flow Field Model Swirl Intensity Decay Number Swirling Flow Velocity Distribution Continuous-Phase Turbulent Quantities Correlations Dispersed-Phase Flow Field Model Dispersed-Phase Particle Velocities Stable Bubble Diameter Mixture Velocity Field Gas Entrainment Calculation Swirling Flow Pattern Prediction Criteria Swirling Flow Patterns Gas Core Diameter Dispersed Two-Phase Swirling Flow Solution Scheme Eulerian-Lagrangian Solution Scheme 19 vii

8 4.7. Lagrangian Bubble Tracking Solution Scheme Simplified Mechanistic Models for Predicting Gas Carry-under139 CHAPTER V: SIMULATION AND RESULTS Continuous-Phase Flow Field Comparison Continuous-Phase Velocity Profiles Continuous-Phase Turbulent Quantities Eulerian-Lagrangian Void Fraction Distribution Simulation Results Performance of Simplified Mechanistic Models Comparison between Simplified Mechanistic Model Predictions and Air-Oil Flow Experimental Results 165 CHAPTER VI: CONCLUSIONS AND RECOMMENDATIONS 171 NOMENCLATURE 174 REFERENCES 179 viii

9 LIST OF FIGURES Figure 1.1 Bulk Separation/Metering Loop for Minas-Indonesia Figure 3.1 Schematic of Metering Section 18 Figure 3. Schematic of GLCC Test Section 19 Figure 3. 3 Percentage of Gas Carry-under in the GLCC Figure 3.4 Void Fraction in the Liquid Leg of the GLCC Figure 3.5 Tangential Inlet Slot Liquid Velocity 3 Figure 3.6 Tangential Inlet Slot to Axial Liquid Velocity Ratio 3 Figure 3.7 Experimental Data for Amount of Gas Carry-under (GCU) for Air-Oil System 6 Figure 3.8 Experimental Data for Percent Gas Carry-under (PGCU) for Air-Oil System 6 Figure 3.9 Dye Injection at Wall and at the Center of the GLCC 7 Figure 3.10 Vortex Interface at the Inlet of GLCC 8 Figure 3.11 Two-Phase Swirling Flow Pattern Visualization Facility 9 Figure 3.1 Two-Phase Swirling Flow Pattern: Stable Gas Core - No Bubble Dispersion 31 Figure 3.13 Two-Phase Swirling Flow Pattern: Whipping Gas Core Low Bubble Dispersion 3 Figure 3.14 Two-Phase Swirling Flow Pattern: Weak Gas Core - High Bubble Dispersion 33 Figure 3.15 Two-Phase Swirling Flow Pattern: No Gas Core - High Bubble Dispersion 34 Figure 3.16 Experimental Swirling Two-Phase Flow Pattern Map 35 ix

10 Figure 3.17 Schematic of GLCC Test Section for Local Measurements (Erdal, 000) 37 Figure 3.18 Axial Velocity for Single Inclined Full Bore Area Inlet Configuration 39 Figure 3.19 Tangential Velocity for Single Inclined Full Bore Area Inlet Configuration 40 Figure 3.0 Axial Velocity for Single Inclined Gradually Reducing Nozzle Area Inlet Configuration 41 Figure 3.1 Tangential Velocity for Single Inclined Gradually Reducing Nozzle Area Inlet Configuration 4 Figure 3. Effect of Reynolds Number on Axial Velocity Profile 45 Figure 3.3 Effect of Reynolds Number on Tangential Velocity Profile 45 Figure 3.4 Variation of Axial Velocity Profile with Axial Position 46 Figure 3.5 Variation of Tangential Velocity Profile with Axial Position 46 Figure 3.6 Axial Velocity of Dual Inclined Inlet Configuration 48 Figure 3.7 Tangential Velocity of Dual Inclined Inlet Configuration 49 Figure 3.8 Turbulent Kinetic Energy for Single Inclined Full Bore Area Inlet Configuration 53 Figure 3.9 Turbulent Kinetic Energy for High Viscosity Single Full Bore Area Inlet Configuration 54 Figure 3.30 Turbulent kinetic Energy for Gradually Reducing Inlet Nozzle Configuration 55 Figure 3.31 Turbulent Kinetic Energy of Dual Inclined Inlet Configuration 56 Figure 3.3 Axial Normal Reynolds Stress Distribution, after Erdal (001) 58 Figure 3.33 Tangential Normal Reynolds Stress Distribution, after Erdal (001) 58 Figure 3.34 Turbulent Kinetic Energy Distribution, after Erdal (001) 59 Figure 3.35 Reynolds Shear Stress Distribution, after Erdal (001) 59 x

11 Figure 3.36 Axial Normal Reynolds Stress Distribution, after Erdal (001) 60 Figure 3.37 Tangential Normal Reynolds Stress Distribution, after Erdal (001) 60 Figure 3.38 Turbulent Kinetic Energy Distribution, after Erdal (001) 61 Figure 3.39 Reynolds Shear Stress Distribution, after Erdal (001) 61 Figure 3.40 Axial Velocity Comparison for Single Inclined Full Bore Area Inlet Configuration 63 Figure 3.41 Tangential Velocity Comparison for Single Inclined Full Bore Area Inlet Configuration 64 Figure 3.4 Turbulent Kinetic Energy Comparison for Single Inclined Full Bore Area Inlet Configuration 65 Figure 3.43 Axial Velocity Distribution After Algifri (1988) 68 Figure 3.44 Axial Velocity Distribution After Kitoh (1991) 68 Figure 3.45 Axial Velocity Distribution After Chang and Dhir (1994) 69 Figure 3.46 Axial Velocity Distribution After Chang and Dhir (1994) 69 Figure 3.47 Radial Velocity Distribution After Algifri (1988) 70 Figure 3.48 Radial Velocity Distribution After Kitoh (1991) 71 Figure 3.49 Radial Velocity Distribution After Chang and Dhir (1994) 71 Figure 3.50 Radial Velocity Distribution After Chang and Dhir (1994) 7 Figure 3.51 Tangential Velocity Distribution After Algifri (1988) 73 Figure 3.5 Tangential Velocity Distribution After Kitoh (1991) 74 Figure 3.53 Tangential Velocity Distribution After Chang and Dhir (1994) 74 Figure 3.54 Tangential Velocity Distribution After Chang and Dhir (1994) 75 Figure 3.55 Axial Normal Stress Distribution After Algifri (1988) 77 xi

12 Figure 3.56 Radial Normal Stress Distribution After Algifri (1988) 77 Figure 3.57 Tangential Normal Stress Distribution After Algifri (1988) 78 Figure 3.58 Axial Normal Stress Distribution After Kitoh (1991) 78 Figure 3.59 Radial Normal Stress Distribution After Kitoh (1991) 79 Figure 3.60 Tangential Normal Stress Distribution After Kitoh (1991) 79 Figure 3.61 Turbulent Kinetic Energy After Algifri (1988) 80 Figure 3.6 Turbulent Kinetic Energy After Kitoh (1991) 81 Figure 3.63 Turbulent Kinetic Energy After Chang and Dhir (1994) 81 Figure 3.64 Turbulent Kinetic Energy After Chang and Dhir (1994) 8 Figure 3.65 Reynolds Shear Stress Figure 3.66 Reynolds Shear Stress Figure 3.67 Reynolds Shear Stress Figure 3.68 Reynolds Shear Stress Figure 3.69 Reynolds Shear Stress Figure 3.70 Reynolds Shear Stress Figure 3.71 Reynolds Shear Stress Figure 3.7 Reynolds Shear Stress Figure 3.73 Reynolds Shear Stress u 'w' Distribution After Algifri (1988) 83 u'v' Distribution After Algifri (1988) 84 v'w' Distribution After Algifri (1988) 84 u 'w' Distribution After Kitoh (1991) 85 u'v' Distribution After Kitoh (1991) 85 v'w' Distribution After Kitoh (1991) 86 u'w' Distribution After Chang and Dhir (1994) 86 u'v' Distribution After Chang and Dhir (1994) 87 v'w' Distribution After Chang and Dhir (1994) 87 Figure 4.1 Schematic of the Swirling flow field and GLCC Coordinate System 94 Figure 4. Variation of Turbulent Kinetic Energy along Axial Direction 103 Figure 4.3 Turbulent Kinetic Energy Prediction 105 xii

13 Figure 4.4 Drag Coefficient Correlations Comparison 111 Figure 4.5 Breakup Frequency Function 119 Figure 4.6 Bubble Coalescence Frequency Function 1 Figure 4.7 Breakup and Coalescence Frequency Events Stable Diameter 13 Figure 4.8 Axisymmetric Control Volume Element 13 Figure 4.9 Control Volume Element in Cylindrical Coordinates 133 Figure 4.10 Control Volume Notation 133 Figure 4.11 Schematic of Bubble Trajectory Path 138 Figure 4.1 Amount of Gas Carry-under Determination 141 Figure 4.13 Oil-Water-Gas Distribution in GLCC (after Oropeza, 001) 14 Figure 5.1 Mean Axial Velocity Comparisons for Algifri Data (1988) 144 Figure 5. Mean Axial Velocity Comparisons for Kitoh Data (1991) 144 Figure 5.3 Mean Axial Velocity Comparisons for Chang and Dhir Data (1994) 145 Figure 5.4 Mean Tangential Velocity Comparisons for Algifri Data (1988) 145 Figure 5.5 Mean Tangential Velocity Comparisons for Kitoh Data (1991) 146 Figure 5.6 Mean Tangential Velocity Comparisons for Chang and Dhir Data (1994) 146 Figure 5.7 Mean Tangential Velocity Comparisons for Chang and Dhir Data (1994) 147 Figure 5.8 Mean Radial Velocity Comparisons for Kitoh Data (1991) 147 Figure 5.9 Mean Radial Velocity Comparisons for Chang and Dhir Data (1994) 148 Figure 5.10 Mean Radial Velocity Comparisons for Chang and Dhir Data (1994) 148 Figure 5.11 Comparison of Turbulent Kinetic Energy Radial Distribution 150 Figure 5.1 Contour Plot Comparison of Turbulent Kinetic Energy Radial Distribution151 xiii

14 Figure 5.13 Comparison of Helical Radial Shifting of the Maximum Turbulent Kinetic Energy with Swirl Intensity 15 Figure 5.14 Maximum and Minimum Turbulent Kinetic Energy Comparison Low Swirling intensity 15 Figure 5.15 Maximum and Minimum Turbulent Kinetic Energy Comparison Different M t /M T 153 Figure 5.16 Maximum and Minimum Turbulent Kinetic Energy Comparison Low and High Reynolds Number 153 Figure 5.17 Turbulent Kinetic Energy Comparison between Correlation and Kitoh (1991) Data 154 Figure 5.18 Reynolds Shear Stress Figure 5.19 Reynolds Shear Stress Figure 5.0 Reynolds Shear Stress Figure 5.1 Reynolds Shear Stress Figure 5. Reynolds Shear Stress Figure 5.3 Reynolds Shear Stress Figure 5.4 Reynolds Shear Stress u 'v' for Kitoh (1991) Data 155 u'v' for Chang and Dhir (1994) Data 156 u 'w' for Kitoh (1991) Data 157 u 'w' for Chang and Dhir (1994) Data 158 u 'w' for Erdal (001) 159 v 'w' for Kitoh (1991) Data 160 v 'w' for Chang and Dhir (1994) Data 161 Figure 5.5 Simulation Results for Void Fraction Distribution 16 Figure 5.6 Bubble Trajectory of d 100 for High Pressure CESSI Data 164 Figure 5.7 Overall Performance of Simplified Bubble-Tracking model 167 Figure 5.8 Experimental Void Fraction Results in Liquid Leg 169 Figure 5.9 Predicted Void Fraction Results in Liquid Leg 169 Figure 5.30 Deviation of Experimental and Predicted Void Fractions in Liquid Leg 170 xiv

15 LIST OF TABLES Table 3.1 Experimental Results of Gas Carry-under for Air-Oil System 4 Table 4.1 Reynolds Stress Coefficients 100 Table 5.1 Simulation Results for Lagrangian-Bubble Tracking for High Pressure Data 164 Table 5. Comparison between Simplified Mechanistic Model Predictions and Air-Oil Flow Experimental Results 166 Table 5.3 A Summary of Liquid Leg Void Fraction Results for Air-Oil Flow 168 xv

16 CHAPTER I INTRODUCTION Compact separators, such as the Gas-liquid Cylindrical Cyclone (GLCC), are becoming increasingly popular as an attractive alternative to conventional separators. Compact separators are simple, compact, possess low weight, low-cost, require little maintenance, have neither moving nor internal parts and are easy to install and operate. The GLCC compact separator is a vertically installed pipe mounted with a downward inclined tangential inlet, with outlets for gas and liquid provided at the top and bottom, respectively. The two phases of the incoming mixture are separated due to the centrifugal/buoyancy forces caused by the swirling motion and the gravity forces. The liquid is forced radially towards the wall of the cylinder and is collected from the bottom, while the gas moves to the center of the cyclone and is taken out from the top. The petroleum industry has recently shown interest in utilizing the GLCC as an alternative to the vessel-type separator due to its wide variety of potential applications, ranging from only partial separation to complete phase separation. GLCCs are used to enhance the performance of multiphase meters, multiphase flow pumps and de-sanders, through control of gas-liquid ratio. It is also used as partial separators, portable well testing equipment, flare gas scrubbers, slug catchers, down hole separators, pre-separators and primary separators (Kouba and Shoham, 1996, Gomez, 1998).

17 Figure 1.1 Bulk Separation/Metering Loop for Minas CALTEX-Indonesia More than 150 GLCC units have already been installed and put to use in the field for various applications in the USA and around the world. Figure 1 shows the largest GLCC in the world, a 5-ft diameter, and 0-ft tall field unit installed in Minas, Indonesia, in a bulk separation/metering loop configuration. Lack of understanding of the complex multiphase hydrodynamic flow behavior inside the GLCC has inhibited complete confidence in its design and prevented its

18 3 widespread application. A fundamental understanding of the hydrodynamics of the flow and of the physical phenomena associated with the separation processes in gravity based separators, centrifugal separators and hydrocyclones is a key for their design and operation with a high degree of reliability. The difficulty in developing accurate performance predictions of these separators is largely due to the complexity of the hydrodynamic flow behavior taking place in the separators. Proper operation of the GLCC is limited by two phenomena, namely, liquid carryover (LCO) in the gas stream and gas carry-under (GCU) in the liquid stream. These phenomena are strongly dependent on the existing flow patterns in the upper part, above the inlet, (LCO), and in the lower part, (GCU), of the GLCC. Very few studies have been published on LCO in the GLCC. These studies enable the prediction of percent LCO occurring in the gas stream. However, no studies have been conducted on the GCU phenomena. This is mainly due to the complex physical phenomena occurring in the lower part of the GLCC, below the inlet, including the swirling flow and the bubble dispersion process that lead to gas carry-under in the outlet liquid stream. This is the need that the present study attempts to address. The objectives of this research are to study experimentally the hydrodynamics of dispersed two-phase swirling flow in the lower part of the GLCC; and, to develop a mechanistic model for the prediction of this complex flow behavior, so as to enable the determination of the gas carry-under in the outlet liquid stream. The significance of this work is on the performance prediction and optimal sizing by understanding the physical phenomena that take place in the GLCC, which enhance the technology and its confident deployment in the field. This provides the petroleum and natural gas industry with an

19 4 effective tool for the GLCC system design and the simulation of its dynamic and/or steady-state performance. Following the introduction in Chapter I, a literature review on the GLCC and swirling flow is given in Chapter II. Chapter III provides details of the experimental program, while Chapter IV presents the modeling of the swirling flow hydrodynamics and the GCU process. The results are discussed in Chapter V, and finally, Chapter VI provides the conclusions and recommendations.

20 5 CHAPTER II LITERATURE REVIEW The use of GLCC separators for gas-liquid separation is a relatively new application in oil and gas industry. Thus, very few studies are available on GLCC experimental data and modeling. Following is an overview of the literature on GLCC separators and swirling flows that are relevant to the present study. This review is divided into following groups: Experimental Work and Applications, Mechanistic Modeling, CFD Simulations, and Swirling Flow/Local Measurements..1 Experimental Work and Applications Since the GLCC technology is relatively new, most of the previous work has been based on experiments. Davies (1984) and Davies and Watson (1979) studied compact separators for offshore production. Their development was aimed for offshore environments where a reduction in size and weight of the production equipment is important. They showed several advantages of using a cyclone separator instead of conventional separator, such as reduction in cost, while improving the separation performance. Based on his experimental results, Fekete (1986) suggested the use of vortex tube separator for gas-liquid separation due to its low weight and space efficiency. Another study by Oranje (1990) also showed that cyclone type separators are suitable for applications on an offshore platform due to their small size and weight. Full-scale performance tests of four types of gas-liquid separators were reported by Oranje. The tests have indicated approximately 100% efficiency for slug catching in a cyclone type separators.

21 6 Bandyopadhyay et al. (1994), at the Naval Weapons Lab, considered the use of cyclone type gas-liquid separators to separate hydrogen bubbles from liquid sodium hydroxide electrolyte in aqueous aluminum silver oxide battery systems. The cyclone used both a tangential inlet as well as a tangential outlet, with an arrangement to change the relative angle between the two. This study showed the gas core configuration, in the center of the separator, to be sensitive to the relative angle between the inlet and outlet and the aspect ratio of the cylinder. Two basic modes of core configuration were observed: straight and helical spiral. The optimum angle for the most stable core was found to be a function of liquid flow rate and the separator geometry. Nebresky et al. (1980) developed a cyclone for gas-oil separation. Their design parameters included a tangential rectangular inlet, equipped with special vane and shroud arrangement to change the inlet area. This allowed them to control the inlet velocity independent of the throughput, which extended their operating range. The cyclone also used a vortex finder for the gas exit. Also, Zikarev et al. (1985) developed a hollow cyclone separator for gasliquid separation with a rectangular and tangential inlet near the bottom of the cyclone. Their procedure is based on theoretical and experimental results, which allows the determination of the geometrical dimensions and operating regimes of the cyclone that correspond to the minimum entrainment of liquid droplets. An experimental investigation with water-air two-phase flow system for a 3 in. GLCC conducted by Wang (1997), where two inlet configurations were used, namely, gradually reduced nozzle with an inlet slot area of 5% of the 3-in. ID inlet pipe, and a concentric reduced pipe configuration with same effective cross sectional inlet area. He found out that the gradually reducing nozzle inlet configuration performs better than the

22 7 concentric reduced pipe, in terms of the operational envelope for liquid carry-over. Wang (1997) concluded that this superior performance is because the concentric reduced pipe inlet causes re-mixing of the two phases before entering into the GLCC, destroying the stratified flow that is promoted by the inclined inlet. On the other hand, the gradually reducing nozzle is capable of maintaining the stratified flow pattern until it reaches the GLCC. Experimental studies on the detailed hydrodynamic flow behavior in the GLCC are scarce. Only a few investigators report local axial and tangential velocity measurements. Millington and Thew (1987) reported local Laser Doppler Anemometer (LDA) velocity measurements in cylindrical cyclone separators. Their studies showed that the distance between the inlet and the outlet controlled the gas carry-under rate. A twin inlet configuration was also used which gave an increased distance between the inlet and outlet, resulting in an improvement of the gas carry-under performance. Millington and Thew suggested the use of twin diametrically opposite inlets for greater axisymmetry and stability of the core and a much improved gas carry-under performance. They made the important observation that the vortex occurring in the cylindrical cyclone separator is a forced vortex with tangential velocity structure. The behavior of the confined vortex flow in conical cyclones was also studied by Reydon and Gauvin (1981). Their studies showed that the magnitude of the inlet velocity does not change the shape of the tangential velocity, axial velocity and static pressure profiles. However, an increase in the inlet velocity increases the magnitude of all of the above quantities. The angle of the tangential inlet with the horizontal plane has no effect on the static pressure profile or the tangential pressure profile, but has a small effect on the axial velocity profile. They also

23 8 concluded that the inclined inlet decreases the symmetry of the flow relative to the axis of the vortex. The fluid velocity in the radial direction was observed to be very small and was neglected for design purposes. In 1990, Farchi made tangential velocity measurements in a cylindrical cyclone with pitot static tubes. His measurements confirmed that a forced vortex occurs in the cyclone. However, as the diameter of the cyclone increases, the velocity distribution tends to match the free vortex velocity profile. Recently, Erdal (001) conducted detailed local measurements in the GLCC, by using a Laser Doppler Velocimeter (LDV). Axial and tangential velocities and turbulent intensities across the GLCC diameter were measured at 4 different axial locations (1.5 to 35.4 below the inlet). Measurements were conducted for different inlet configurations and inlet/outlet orientations. The measurements were conducted for a wide range of Reynolds numbers of about 1500 to 67,000. Measurements were conducted with water at liquid flow rates of 7, 30 and 10 gpm. Also, high viscosity measurements were conducted for flow rates of 54 gpm (7cP), 30 gpm (7cP), and 10 gpm (7cp). However, Erdal (001) did not develop any correlation for turbulent quantities. In this study Erdal s data will be used to develop correlation for the turbulent quantities.. Mechanistic Modeling Mechanistic modeling is based on the physical phenomena of the flow, verified with experimental data. As more data become available, the understanding of the flow behavior is improved. Few mechanistic models have been developed for the GLCC, as

24 9 described next. A discrete particle model was proposed by Trapp and Mortensen (1993), which uses a Lagrangian description for a single dispersed bubble phase and a onedimensional Eulerian description for a single continuous liquid phase, including the compressibility and bubble size effects. Based on experimental and theoretical studies performed at The University of Tulsa, a GLCC mechanistic model has been developed by Arpandi et al. (1995). This mechanistic model is capable of predicting the general hydrodynamic flow behavior in a GLCC, including simple velocity distributions, gas-liquid interface shape, equilibrium liquid level, total pressure drop, and operational envelop for liquid carry-over. However, the model does not address details of the complex flow behavior in the GLCC and related phenomena, such as gas carry-under and separation efficiency. Marti et al. (1996) attempted to develop a mechanistic model for predicting gas carry-under in GLCC separators. The model predicts the gas-liquid interface near the inlet as a function of the radial distribution of the tangential velocity. The interface defines the starting location for the bubble trajectory analysis, which enables determination of gas carry-under and separation efficiency based on bubble size. Mantilla (1998) evaluated and improved the previous published bubble trajectory model for the GLCC using available data and CFD simulations. They also developed correlations for axial and tangential velocities, which are capable of predicting flow reversal (upward flow) in GLCC. However, Mantilla s model was based on empirical information and CFD simulations of swirling flows with multiple tangential inlets. The effects of inclination of the inlets were not included in the models.

25 10 Recently, Gomez et al. (1998) developed a state-of-the-art computer simulator for GLCC design, in an Excel-Visual Basic platform, capable of integrating the different modules of the mechanistic model. Model enhancements include a flow pattern dependent nozzle analysis for the GLCC inlet, an analytical model for the gas-liquid vortex interface shape, a unified particle trajectory model for bubbles and droplets, including a tangential velocity decay formulation and a simplified model for the prediction of the GLCC aspect ratio..3 CFD Simulations With the available experimental methods, obtaining details of the complex hydrodynamic flow behavior in the GLCC is very expensive. However, high-tech fast computers allow the simulation of flow in complex geometries. Computational Fluid Dynamics (CFD) methods for two-phase flow are much less developed than that of single-phase flow. This is mainly due to the constitutive relationships that are still not well understood for two-phase flow. Thus, it is very difficult to obtain a complete picture of two-phase flow behavior within the GLCC. Most of the previous studies are limited to single-phase flow with bubble trajectory analysis. Hargreaves and Silvester (1990) modeled the anisotropic turbulent flow processes occurring in a highly swirling flow regime utilizing a conical hydrocyclone. They proposed a four-equation splicing of Reynolds stress and algebraic turbulence. The results were compared with Laser Doppler Velocity measurements. Estimation of migration probabilities as a function of droplet size and swirl velocity were reported. It was observed that, for the axial velocity, the maximum reverse velocity is not necessarily

26 11 positioned along the cyclone axis. Thus, an axisymmetric model could not simulate this phenomenon. The model developed has a tendency to over-predict the tangential velocity distribution. A Particle Tracking Velocimetry and a three-dimensional computational code, FLUENT, were used by Kumar and Conover (1993). They studied the dynamics of the three-dimensional flow behavior in a cyclone with tangential inlet and tangential exit. Tangential velocities from both experiments and computations were compared showing a good agreement. Sevilla and Branion (1993) used a computational procedure to predict the velocity field and particle trajectories in conical hydrocyclones of different geometries operating under a wide range of flow conditions. The results were compared with available experimental data. They found that the geometry of the hydrocyclones has a significant influence on the magnitude of the axial velocity. Malhotra et al. (1994) used a computational procedure, TEACH Code, to predict the flow field in a hydrocyclone. They included a new formulation of the turbulence dissipation equation. A numerical study was conducted by Bandyopadhyay et al. (1994) to get a better understanding of the mechanism for separating gas bubbles from a bulk liquid in a cyclone separator. The authors first simulated single-phase liquid flow. The simulated liquid flow field was then used to compute the trajectories of a single gas bubble to determine the residence times of bubbles in the separator and to determine gas separation efficiency.

27 1 Rajamani and Devulapalli (1994) modeled the swirling flow and particle classification in hydrocyclones. The results were compared with experimental data that included LDV velocity measurements and particle size distribution in a sump-pump re- circulation system. The numerical solution showed good agreement with the experimental data for both flow field and particle classification. In a follow-up study, Devulapalli and Rajamani (1996) presented a CFD model for industrial hydrocyclones and compared the predicted velocities with LDV measurements. A new conceptual approach called Stochastic Transport of Particles was used to predict the particle concentration gradients inside the hydrocyclone. This technique involves tracking particle clouds rather than individual particles in a Lagrangian frame of reference. Small and Thew (1995) described a method for quantifying turbulence anisotropy in conical hydrocyclones using FLOW-3D simulator. The validity of eddy viscosity models of turbulence, using a Differential Reynolds Stress (DRS) model as a reference, was investigated. The results show that for moderate swirl (swirl number of 0.1 or higher) the k-ε model is unsuitable and must be replaced by a model capable of reproducing anisotropic turbulence effects. Erdal et al. (001) presented CFD simulations utilizing a commercial code called CFX. The simulations included details of the hydrodynamic flow behavior in the GLCC, for both single-phase and two-phase flow. The results verified that axisymmetric simulation (-D with three velocity components) gave good results as compared to the three-dimensional (3-D) simulations. An expression was developed for an equivalent inlet tangential velocity for the axisymmetric model. A sensitivity study on the effects of the ratio of the inlet tangential velocity to the average axial velocity on the flow behavior

28 13 in the GLCC was also carried out. Motta (1997) presented a simplified CFD model for rotational two-phase flow in a GLCC separator. The model assumed an axisymmetric flow but considered three velocity components. The study also presented a comparison between the proposed model and predictions of a commercial CFD code (CFX). Recently, the behavior of small gas bubbles in the lower part of the GLCC, below the inlet, and the related gas carry-under phenomena was investigated by Erdal (001). This investigation was performed by utilizing a commercially available computational fluid dynamics (CFD) code. Simulations of single-phase and two-phase flows were carried out and bubble trajectories were obtained in an axisymmetric geometry that represents the GLCC configuration. The effect of the free interface that forms between the gas and liquid phases on the velocity profiles was examined. The bubble trajectory analysis was used to quantify the effects of the important parameters on bubble carryunder. These include bubble size, ratio of the GLCC length below the inlet to diameter, viscosity, Reynolds number, and inlet tangential velocity..4 Swirling Flow and Local Measurements One of the first experimental studies in this area is by Nissan and Bressan (1961). To generate the swirling flow, water was injected through two horizontal tangential inlets. The flow field was measured with impact probes. The axial velocity distribution showed a region of flow reversal near the center of the tube. Ito et al. (1979) investigated swirl decay in a tangentially injected swirling flow. They used water as the working fluid and a high ratio of tangential momentum to axial momentum, namely, 50. The measurements were carried out with a multi-electrode

29 14 probe. The tangential velocity distribution showed that there were two flow regions: a region of forced-vortex flow near the center of the tube, and a surrounding region of freevortex flow. The swirl was observed to decay with the axial distance, resulting in a decrease in the extent of the solid rotational flow (forced vortex). Colman, Thew and Lloyd (1984) tested a hydrocyclone that was developed at Southampton University under field conditions, using Laser Doppler Anemometer (LDA) to measure the axial velocity profiles in water. They found a narrow core of reverse flow along the axis of the hydrocyclone, with the main flux of downstream moving fluid being near the walls. Millington and Thew (1987) reported local Laser Doppler Anemometer (LDA) velocity measurements in a very short cylindrical cyclone separator. They made the important observation that the vortex that occurs in the cylindrical cyclone separator is a forced vortex with tangential velocity structure. Lagutkin and Baranov (1988, 1991) used cylindrical hydrocyclone to separate solid-liquid mixtures. They developed equations to determine solid removal efficiency and residence time as a function of tangential velocity, turbulent viscosity, densities and dimensions of the cylindrical hydrocyclone. Turbulence in decaying swirling flow through a pipe was studied by Algifri et al. (1988) using a hot-wire probe. Air was used as the working fluid and it was given a swirling motion by means of a radial cascade. The velocity profiles were presented with three components of velocity. They found that for high swirl intensity the Reynolds number strongly affects the velocity distribution. It was suggested that the tangential

30 15 velocity distribution, except in the vicinity of the pipe wall, can be approximated by a Rankine vortex, which is a combination of a free and a forced vortex. Kitoh (1991) studied swirling flows generated with guide vanes. The flow field was measured with X-wire anemometers. It was shown that the swirl intensity decays exponentially. Later, Yu and Kitoh (1994) developed an analytical method to predict the decay of swirling motion in a straight pipe. They indicated that at lower Reynolds numbers the swirl appears to decay at a faster rate than for higher Reynolds numbers. In the study by Chang and Dhir (1994), the turbulent flow field in a tube was investigated by injecting air tangentially into the tube. They used a single rotated straight hot wire and single rotated slanted hot wire anemometers. Profiles for mean velocities in the axial and tangential directions, as well as the Reynolds stresses, were obtained. The axial velocity profile shows the existence of a flow reversal region in the axis of the tube and an increased axial velocity near the wall. Tangential velocity profiles have a local maximum, the location of which moves radially inwards with axial distance. The swirl intensity, defined as the circulation over a cross sectional area, was found to decay exponentially with axial distance. Kurokawa (1995) confirmed the existence of a complex velocity profile by accurate measurements in single-phase liquid flow. The study distinguishes three regions, namely, a forced vortex, generating a jet region with extremely high swirl velocity around the pipe center, a second swirl region formed by a free vortex, and an intermediate region of back flow with high swirl velocity. Using a spiral type cylindrical cyclone for gas-liquid separation, he measured the velocity distribution in the cross

31 16 section of the cyclone. Kurokawa (1995) utilized Laser Doppler Velocimeter (LDV) and a pitot tube probe to characterize swirling flow and gas separation efficiency. He found that the characteristics of liquid swirling flow in a cyclone pipe are influenced considerably by the boundary condition at the downstream. The swirling flow is composed of a jet region with extremely high swirl in the center, a reverse flow region with high swirl, and the outer flow region with low swirl. When the pipe is long enough, the reverse flow region disappears and the swirl in the center region becomes very weak. Recently, Chen et al. (1999) measured tangential and axial velocities using Laser Doppler Anemometer above the top of cyclone outlet tube to achieve a better understanding of the flow phenomena. The effects were investigated for three different outlet diameters. The experiments showed regular periodic motions together with back flow at the center of the cyclone core. As can be seen from the above literature review, no studies, either experimental or theoretical, have been published on gas carry-under in the GLCC separator, based on the understanding of swirling flow phenomena. This is the need that the present study attempts to address.

32 CHAPTER III EXPERIMENTAL PROGRAM An experimental investigation is carried out to study gas carry-under in swirling flow. Detailed experiments are conducted to obtain systematic data and shed light on the physical phenomena. A GLCC test facility is used to gather data on the amount of gas carry under in the outlet liquid stream. Flow visualization is also carried out to classify the existing flow pattern in swirling flow. Additional published data on local flow field measurements of swirling flow are presented and analyzed to develop and validate swirling flow field correlation. 3.1 Gas Carry-under Experimental Program Measurements of gas carry-under in a 3-in ID GLCC, using air and water as fluids, at atmospheric conditions, have been acquired during this study. Following is a description of the test facility, and presentation of the experimental data and pertinent visual observation results Gas Carry-under Measurements in GLCC Test Facility The experimental two-phase flow loop consists of a metering section to measure the single-phase gas and liquid flow rates separately, and a GLCC test section, where all the experimental data are acquired. Following is a brief description of these two sections, as well as the instrumentation and data acquisition system.

33 18 and liquid streams are combined at the mixing tee, and the mixture flows into the GLCC test section. The two-phase mixture downstream of the test section is separated utilizing a conventional separator. Data Acquisition System Air To Test Section T P T Water T P T From Test Section MicroMotion Meter Ball Valve Separator Water Tank Turbine Meter Regulating Valve Orifice Meter Check Valve T Temperature Transducer P Pressure Gauge Figure 3.1 Schematic of Metering Section GLCC Test Section: The test section consisting of a GLCC separator, as shown in Figure 3., is divided into 4 parts: 1. The modular dual inlet section;. The GLCC body; 3. The gas leg, which includes the liquid carry-over trap; and, 4. The liquid leg with the gas carry-under trap.

34 19 LIQUID TRAP MODULAR INLET TWO-PHASE INLET GLCC MICROMOTION GAS TRAP RECOMBINATION POINT TWO-PHASE OUTLET SAMPLING Figure 3. Schematic of GLCC Test Section Dual Inlet: The dual inlet of the GLCC consists of a 3-in. ID lower inlet pipe section, connected to the GLCC with a nozzle having a sector-slot/plate configuration. The nozzle area is 5% of the inlet pipe cross sectional area. The upper inlet section is a reduced pipe configuration, 3 in. by 1.5 in. diameter, with a full bore connection into the GLCC. The GLCC can be configured with a single inlet or a dual inlet by using the appropriate inlet valves. Only the lower inlet was used for the experimental investigations in this study. GLCC body: The GLCC body is 3 in diameter and 8 tall, with the lower inlet located at the middle. It has several ports for conducting local measurements, such as die injections and pitot tube velocity measurements. Gas Leg: The gas leg is in diameter, and includes a gas vortex-shedding meter and a liquid trap. The trap allows accumulation and measurement of liquid carry-over for conditions beyond the operational envelope for liquid carry-over. In the present study no liquid carry-over measurements were conducted.

35 0 Liquid Leg: Prior to recombination of the gas and liquid streams, the liquid phase passes through a barrel trap. This 6 diameter pipe section is provided in order to quantify the amount of gas carry-under into the liquid stream. A Micromotion mass flow meter is also installed on the liquid leg to measure the liquid flow rate. In the present study the barrel trap serves as the main instrument to measure the quantity of gas carryunder. Instrumentation And Data Acquisition System: The GLCC is equipped with a level indicator (sight gauge) installed parallel to the body of the separator, and a differential pressure transducer connected to the gas and liquid legs, which gives a quantified measure of the liquid level. The average pressure of the GLCC is measured by an absolute pressure transducer located in the gas leg. All output signals from the sensors, transducers and metering devices are terminated at a central panel, which in turn is connected to the computer. A data acquisition system setup is built in the computer using LABVIEW software to acquire data from the metering section and test facility Gas Carry-under Experimental Results Air-Water Experimental Data: A large number of experimental runs have been conducted for air-water flow. The operating pressure for these runs was almost atmospheric. Figure 3.3 presents the acquired gas carry-under data in the form of percentage of the inlet gas flow rate that is carried under in the liquid stream (PGCU). The coordinates are the superficial velocities of the gas and liquid phases in the GLCC. The figure also shows the operational envelope for liquid carry-over. Each data point reports the PGCU and the corresponding liquid level and gas liquid ratio (GLR). One can observe that the amount of gas being gathered in the gas trap is an order of magnitude of

36 (ppm) smaller than that of the inlet gas flow rate. The graph also shows a region where the PGCU exhibits the highest values, namely, for 0.3 ft/s < v sl < 0.7 ft/s. Similarly, for the same set of data, the no-slip void fraction in the liquid leg is reported in Fig For completeness of the data reporting, Figs. 3.5 and 3.6 provide, respectively, the prediction of the tangential inlet slot liquid velocity (v t, is ) and the corresponding initial tangential to axial momentum ratio (v t, is / v sl ) for the air-water data. The results are predicted using the inlet analysis model developed by Gomez et al. (001). The contour plot of the tangential inlet slot liquid velocity presented in Fig. 3.5 shows the highest tangential liquid velocity at high superficial liquid velocities in the GLCC, v sl > 0.5 ft/s. In this region, the gas flow rate affects the tangential liquid velocity by accelerating the liquid film in the inlet nozzle. The tangential liquid velocity decreases with decreasing superficial liquid velocity. As can be observed, for low superficial liquid velocities, below 0.5 ft/s, the tangential liquid velocity is independent of the gas flow rate. Figure 3.6 presents initial tangential to axial momentum ratio as given by the ratio of tangential inlet slot liquid velocity to the GLCC superficial liquid velocity (v t, is / v sl ). A clear pattern is observed, where the ratio is maximum at low superficial liquid velocities (equal to 40 at v sl = 0.5 ft/s), and decreases as the superficial liquid velocity increases (reaching a value of 15 for v sl > 0.75 ft/s). One must realize that the high values of v t, is / v sl occurring at low liquid flow rates are due to the fact that the denominator is a fraction. This does not necessarily mean higher swirl intensity under these conditions, as depicted by the low values of the tangential inlet slot liquid velocity shown in Fig. 3.5, which are the lowest under these conditions.

37 Vsl (ft/s) (4.4-34) (4.1-40) (3.6-44) (3.5-57) (3.9-93) 0.4 (3.5-71) Percent Gas Carry-Under in 3-3S GLCC (without Mesh) Operational Envelope 0.1 (3.6-99) ( ) 0.04 (3.3-14) (3.3, 166) (3.3-60) 0.37 ( ) 0.30 ( ) ( ) 0.87 ( ) 3 ID GLCC P = 0 psia Air - Water %PGCU *10 3 (Level - GLR) ( ) 0.06 (3.3-93) ( ) ( ) ( ) Vsg (ft/s) Figure 3.3 Percentage of Gas Carry-under in the GLCC Percent Gas Carry-Under in 3-3S GLCC (without Mesh) 3 ID GLCC P = 0 psia Air - Water Vsl (ft/s) (0.0008) (0.0009) ( ) (0.0038) ( ) 0.4 (0.0031) Operational Envelope 0.1 ( ) ( ) 0.04 ( ) ( ) ( ) 0.37 (0.0133) 0.30 ( ) %PGCU *10 3 (No Slip Void Fraction (%)) ( ) 0.87 ( ) (0.0076) 0.06 (0.0038) (0.0014) (0.0006) ( ) Vsg (ft/s) Figure 3.4 Void Fraction in the Liquid Leg of the GLCC

38 3 Figure 3.5 Tangential Inlet Slot Liquid Velocity Figure 3.6 Tangential Inlet Slot to Axial Liquid Velocity Ratio

39 4 Air-Oil Experimental Data: A total of 0 runs have been conducted for air-oil flow. A mineral oil was used, with a specific gravity of and viscosity ranging from 0 to 5 cp, depending on the operating temperature. The data were acquired in a similar flow loop with a GLCC having exactly the same configuration and dimensions, as in the case of the air-water system. A summary of the experimental data is shown in Table 3.1. Table 3.1 Experimental Results of Gas Carry-under for Air-Oil System Run v sg v sl p T µ q o q gas Measured GCU N o ft/s ft/s psia o F cp bbl/d Mscf/D scf/d PGCU % Figures 3.7 and 3.8 present the amount of gas carry-under (GCU) and the percent gas carry-under (PGCU), respectively, for the air-oil runs given in Table 3.1. The GCU contour plot presented in Fig. 3.7 shows similar trends to the one observed for the airwater GCU results, shown in Fig Three GCU regions are observed, with respect to the superficial liquid velocity, as follows: For low liquid flow rates, v sl < 0.3 ft/s, the GCU values are low, while the highest GCU occurs in the region 0.3 ft/s < v sl < 0.7 ft/s.

40 5 For higher superficial liquid velocities, v sl > 0.7 ft/s, the GCU decreases as the liquid flow rate increases. These trends can be explained based on the physical phenomena, as given below. In the lower region, v sl < 0.3 ft/s, the tangential inlet slot liquid velocity is low (see Fig. 3.5), resulting in low swirl intensity. However, in this region the axial velocity is also low, allowing sufficient residence time for the gas bubbles to separate by gravity. As a result, the GCU in this region is low. In the central region, 0.3 ft/s < v sl < 0.7 ft/s, the tangential inlet slot liquid velocity is considerably higher (see Fig. 3.5). However, for these conditions, the swirl intensity is not sufficiently high to form a well-defined gas core and a high reverse flow region. At the same time, the axial velocity is larger, dragging the dispersed gas bubbles downward. The overall result is the occurrence of maximum GCU in this region. The GCU in this region increases with the superficial gas velocity, probably because of higher gas entrainment rates. Finally, in the upper region, v sl > 0.7 ft/s, the GCU decreases due to the fact that higher tangential inlet slot velocities occur, promoting higher swirl intensity. Consequently, a well-defined gas core is formed with a strong reverse flow, enhancing the separation efficiency. Figure 3.8 shows the same experimental results, as given in Fig. 3.7, presented in terms of the PGCU. This figure can be interpreted as the separation efficiency. As can be seen, the maximum PGCU, around 0.06%, occurs in the central region for low superficial gas velocities, below 3 ft/s. For higher superficial gas velocities, in the same region, the PGCU is low. The reason for this trend is that the PGCU is determined as a ratio of the GCU amount and the inlet gas flow rate.

41 6 Figure 3.7 Experimental Data for Amount of Gas Carry-under (GCU) for Air-Oil System Figure 3.8 Experimental Data for Percent Gas Carry-under (PGCU) for Air-Oil System

42 Two-Phase Swirling Flow Visualization In order to understand the flow mechanism of the physical phenomena taking place in the lower part of GLCC, additional experimental observations were carried out. These observations are used to confirm the hydrodynamic flow behavior of the swirling flow in the lower part of the GLCC, as reported by previous studies. Velocity Distribution: Figure 3.9 demonstrates the complex axial velocity distribution in the GLCC, utilizing die injection. As shown in Fig. 3.9(a), the velocity near the wall is downward, while Fig. 3.9(b) demonstrates the flow reversal region near the centerline, where the flow is upward. (a) Single - Phase Single-Phase Dye Dye Injection Injection Near 1 the Below Wall, Inlet Downward Near the Flow Wall (V sl = 0.83 ft/s, V sg = 0.0 ft/s) 1 VBelow sl = 0.83 Inlet ft/s (b) Two - Phase Two-Phase Dye Injection at the Center, Dye Injection Upward Flow (V4 sl = Below 1.53 ft/s, Inlet Vat sg Pipe = 8.9 center ft/s) 4 Below Inlet V sl = 1.53 ft/s Figure 3.9 Dye Injection at the Wall and at the Center of the GLCC Free Interface Vortex: Figure 3.10 shows the free interface vortex occurring below the GLCC inlet. As can be seen, the gas entrainment increases as gas is introduced into the GLCC. Also, the two-phase flow vortex is more chaotic than that of single-phase liquid flow.

43 8 (a) Single Single-Phase Phase (V sl = 0.83 ft/s, V sg = 0.0 ft/s) V sl = 0.83 ft/s V 00ft/ (b) Two Two-Phase (V Phase sl = 1.53 ft/s, sg 6.89 ft/s) V sl = 1.53 ft/s V 689ft/ Figure 3.10 Vortex Interface at the Inlet of GLCC Two-Phase Flow Patterns in Swirling Flow: The key for deriving appropriate mechanistic models is that the mathematical formulation should capture the main physical mechanism of the flow phenomena. Thus, an investigation to identify the particular flow patterns associated with the swirling flow below the GLCC inlet was conducted in this study. Determination of flow patterns in two-phase swirling flow presents more difficulties than for two-phase pipe flow. This is due to the fact that there is no well-defined interface between the phases. The flow pattern will serve as basis for the developed mechanistic model for gas carry-under. A general view of the facility used for visualization of two-phase swirling flow patterns is given in Fig Figures 3.1 to 3.15, given below, demonstrate that the gas core, which is generated from concentration of bubble at the center, is probably the main mechanism responsible for gas carry-under. The stability of the gas core is also a key for the type of flow patterns occurring in the lower part of the GLCC. Note that the experimental observation of the two-phase swirling flow pattern presented below were carried out keeping the equilibrium liquid level constant, just below the inlet.

44 9 Figure 3.11 Two-Phase Swirling Flow Pattern Visualization Facility Stable Gas Core - No Bubble Dispersion: Figure 3.1 shows that for v sl = 1.ft/s and v sg =.5 ft/s a stable gas core is formed. For this case, low amplitude wavy interface (gas core) with high swirling intensity is formed, stretching all the way to the bottom of the GLCC. The important observation for this flow pattern, related to GCU, is that no bubble dispersion occurs under these conditions. However, gas carry-under might occur due to the gas core reaching the liquid leg exit. Generally, very low values of GCU are observed. Whipping Gas Core - Low Bubble Dispersion: For v sl = 0.7 ft/s and v sg = 5 ft/s, as shown in Figure 3.13, a whipping gas core with high amplitude wavy interface and medium swirling intensity is observed. For this case, the gas core is less stable, breakingup and coalescing with bubbles dispersed in the liquid phase. For these conditions, low bubble dispersion occurs, promoting relatively higher GCU into the liquid leg. This is

45 30 due to the gas core stretching all the way to the bottom of the GLCC, whipping and releasing bubbles into the liquid leg. Moderate GCU amounts occur in this flow pattern. Weak Gas Core - High Bubble Dispersion: Figure 3.14 shows the flow behavior for v sl = 0.4 ft/s and v sg = 10 ft/s with high gas entrainment. For this case, the swirling intensity is weak, forming an unstable wavy interface and a weak gas core. This flow pattern promotes strong dispersion of bubbles from the gas core, which coalesce with the already existing higher bubble dispersion in the liquid phase. Thus, for these conditions the gas core does not stretch to the bottom of the GLCC, but rather disappears as the swirl intensity decays along the lower part of the GLCC. For this flow pattern, higher amount of GCU are observed, with larger bubble size and high bubble dispersion, occurring in the upper section of the GLCC. On the other hand, in the lower section of the GLCC, tiny bubbles are observed. No Gas Core - High Bubble Dispersion: No interface is observed for v sl = 0. ft/s and v sg = 8 ft/s, since for this case the swirl intensity is very low, almost equal to zero. As shown in Figure 3.15, low gas entrainment occurs below the GLCC inlet, resulting in no gas core formation. For this flow pattern, very low GCU is observed, due to the fact that the gas is separated below the GLCC inlet due to gravity segregation. Swirling Two-Phase Flow Pattern Map: The experimental results for swirling two-phase flow patterns (as defined in the previous section) for air-water system at nearly atmospheric conditions are mapped in Fig The flow pattern map provides the transition boundaries between the four different swirling flow patterns, as well as the associated bubble dispersion condition and bubble size.

46 31 Figure 3.1 Two-Phase Swirling Flow Pattern: Stable Gas Core - No Bubble Dispersion

47 3 Figure 3.13 Two-Phase Swirling Flow Pattern: Whipping Gas Core - Low Bubble Dispersion

48 Figure 3.14 Two-Phase Swirling Flow Pattern: Weak Gas Core - High Bubble Dispersion 33

49 Figure 3.15 Two-Phase Swirling Flow Pattern: No Gas Core - High Bubble Dispersion 34

50 Vsl [ft/s] NBD LBD Large Bubble Size Liquid Carry Over Region Stable Gas Core Whipping Gas Core LBD HBD 3" ID GLCC P = 0 psia Air-Water Legend: B : Bubble D : Dispersion H : High N : No L : Low 0.4 HBD Large Bubble Size Weak Gas Core Small Bubble Size HBD Small Bubble Size HBD Large Bubble Size No Gas Core Vsg [ft/s] HBD Small Bubble Size Figure 3.16 Experimental Swirling Two-Phase Flow Pattern Map

51 36 3. GLCC Swirling Flow Local Measurements Swirling flow local measurements data for single-phase swirling flow velocity field and turbulence quantities reported in literature are presented in this section. These data are analyzed and utilized to develop correlations for the corresponding swirling flow characteristics. Erdal (001) measured tangential and axial velocity distributions for liquid flow, as well as their corresponding velocity fluctuations, by using a Laser Doppler Velocimeter (LDV) system, in a test section similar to a GLCC configuration. Analysis of the data was carried out by Erdal (001) only with respect to the flow field. However, neither analysis nor correlations development for the turbulent quantities were conducted. Thus, the Erdal (001) data are used in this study to develop correlations for the turbulent quantities, which are important in the dispersed two-phase phenomena that take place in lower part of the GLCC Local Measurements in GLCC Test Section Experimental studies were conducted by Erdal (001) aiming at local velocity data in swirling flow field in a test section representing the lower part of a GLCC below the inlet, as shown in Fig Single-phase liquid, either water (1 cp) or water-glycerin mixture (7 cp) were used in the experimental program. The liquid flow rates were 7, 30 and 10 gpm, which correspond to Reynolds numbers of 66900, 7900 and 990, respectively, and 4163, 1514 for the case of high viscosity (7cp) experimental runs. Several inclined inlet configurations were tested, namely, single inclined inlet with a full bore pipe area, single inclined inlet with a gradually reduced area (nozzle), and a dual inclined inlet with a full bore pipe area for both inlets. All the different inlets have the

52 37 same total effective cross sectional area and generate the same inlet tangential velocities. The different inlet configurations were tested to check the optimal configuration that provides smoother entrance region with less mixing in order to avoid gas entrainment. Local measurements are conducted along the diameter at different locations in the range between 1.5 in. to 35.4 in. below the inlet, as shown in Fig A total of 4 measurement locations were selected in the measurement plane. At each measurement locations, axial velocity, tangential velocity and turbulent intensities are measured along the diameter by LDV. Inlet Inlet x LDV 1.5 Measurement Plane Flow Direction 4.8 Outlet 35.4 Top View Outlet Side View Figure 3.17 Schematic of GLCC Test Section for Local Measurements (Erdal, 001)

53 GLCC Local Measurements Results In this section the local measurement results of the flow field for single inlet and dual inlet are presented, followed by the results for turbulent quantities, and finally the viscosity effect results. Flow Field for Single Inclined Inlet: The local measurement results of the swirling flow field are presented in the form of contour plots. These plots help to shed more light on the hydrodynamic structure of the swirling flow. Contour Plots: Figures 3.18, 3.19, 3.0, and 3.1 show contour plots, normalized with respect to U av, of the axial and tangential velocity distributions measured at 4 axial locations below the GLCC inlet. The axial velocity contour plots, Figs and 3.0, clearly show an upward flow reversal region, with negative axial velocity, located around the GLCC axis. The flow reversal region is not axisymmetric and has a helical shape. The intensities of both upward and downward flow decay as the flow moves downward. This decay appears to cause a stretch on the vortex as it moves axially downward to the GLCC outlet. These tangential velocity, shown in Figs and 3.1, is positive on the left hand side and is negative on the other side (right). This is due to the rotation of the flow. As can be seen, the tangential velocity is high near the wall region and it decays towards the center. The location of zero or low tangential velocity has also a helical path similar to the one observed in the axial velocity contours. This experimental data reveal that for single inlet configuration, the flow is not symmetric and it has an unstable vortex that has a helical shape. However, data presented by other investigators (referred in this report) show that the flow is axisymmetric.

54 Figure 3.18 Axial Velocity for Single Inclined Full Bore Area Inlet Configuration (Erdal, 001) 39

55 Figure 3.19 Tangential Velocity for Single Inclined Full Bore Area Inlet Configuration (Erdal, 001) 40

56 Figure 3.0 Axial Velocity for Single Inclined Gradually Reducing Nozzle Area Inlet Configuration (Erdal, 001) 41

57 Figure 3.1 Tangential Velocity for Single Inclined Gradually Reducing Nozzle Area Inlet Configuration (Erdal, 001) 4

58 43 For these cases the flow symmetry is achieved utilizing several tangential inlets or vane blades that provide smooth rotation of the flow in entrance region. Although single inlet does not produce symmetry, from careful observation of the contour plots (Figs. 3.0 and 3.1) it can be seen that, the reduced area nozzle configuration presents a more stable helical vortex, and the reverse flow region is closer to the center of the GLCC section. However, the vortex occurring in the full-bore pipe area inlet (Fig and 3.19) is highly unstable. From the contour plots of the local velocity measurement presented above, one may notice that the gradually reduced inlet would provide a benefit of decreasing the whipping of the gas core, resulting in a more stable core that can enhance the separation of gas bubbles below the inlet. Erdal (001) did not consider the effect of inlet inclination angle, since the downward angle of 7 o was kept constant for all experimental runs. The inclination angle may affect the magnitude of the GLCC inlet tangential velocity, which is a component of the inclined inlet velocity. The GLCC tangential velocity that generates the swirling flow would increase as the inclined inlet is moved towards the plane perpendicular to the GLCC axis. The above analysis is for single-phase flow. For two-phase flow, due to downward inclined inlet, additional effects occur, such as promotion of stratified two-phase flow and pre-separation, as demonstrated by Kouba et al. (1995). This causes the impinging liquid stream to spiral below the inlet of the GLCC, preventing the liquid from blocking the flow of gas into the upper part of GLCC, due to a hydraulic jump forming at the nozzle inlet slot. Also, Wang (1997) strongly recommended using the gradually reducing inlet nozzle configuration for wider ranges of operational envelope for liquid carry-over for

59 44 field application of the GLCC. This suggestion is also confirmed by local velocity measurement as described in this analysis. Additional consideration must be taken into account about the turbulent intensity, which causes the bubble dispersion (breakup and coalescence), inlet bubble entrainment and re-mixing at entrance region. The effects of these phenomena are given below. Velocity Profiles: Figures 3. and 3.3 present the effects of Reynolds number on the axial and tangential velocity profiles, respectively. The variation of the axial and tangential velocity profiles with axial position is given in Figures 3.4 and 3.5, respectively. Since Erdal (001) used a two- component LDV system, the radial velocity was not measured and no attempt was made to calculate it from continuity relationship due to the non-symmetry of the flow. As can be seen from Figs 3. and 3.3, both axial and tangential velocities do not show strong dependence on Reynolds number. However, both axial and tangential profile varies along the GLCC axis, mainly due to the decay of the swirl, as evident from Figs. 3.4 and 3.5. In general, the data show that the flow is not symmetric with respect to the pipe axis; where the reverse flow region whips around with a helical shape. This is due to the nonsymmetric inlet of the fluid. When the flow is injected through symmetrical inlet arrangement (e.g. two or four), this helical shape is eliminated as seen in the following section.

60 u/uav z/d = 3.6 Re = Re = r /R Figure 3. Effect of Reynolds Number on Axial Velocity Profile w/uav z/d = 3.6 Re = Re = r/r Figure 3.3 Effect of Reynolds Number on Tangential Velocity Profile

61 u/uav Re = z/d = 3.6 z/d = 5.4 z/d = 6.7 z /d = 8.5 z/d = r/r Figure 3.4 Variation of Axial Velocity Profile with Axial Position w/uav Re = Z/d = 3.6 z/d = 5.4 z/d = 6.7 z/d = 8.5 z/d = r/r Figure 3.5 Variation of Tangential Velocity Profile with Axial Position

62 47 Flow Field for Dual Inclined Inlet: The local experimental measurements presented by Erdal (001) clearly show that flow field for single inclined inlet configuration is not axisymmetric but rather very complex. The flow, near the vortex center is highly unstable and high turbulence levels were generally observed. For a dual inlet configuration, one may anticipate that since the flow is more symmetric, it may be more stable and less turbulent. Contour Plots: Figure 3.6 presents axial velocity contours for flow rates of 7 and 10 gpm for the dual inclined inlet. Both plots show a nearly axisymmetric flow field. Surprisingly, the 7 gpm case shows a downward flow at the center, which is surrounded by a narrow upward flow region. Upward flow maximum velocity for dual inlet is about 3 times higher than the upward flow maximum velocity observed for the single inclined inlet. This behavior is certainly complicated and is not desirable for GLCC design, as it might contribute to more gas carry-under. The 10 gpm case has a wider upward flow region. In GLCC design, this means that there is more room to capture bubbles at the center and elevate them to gas liquid interface for separation. Tangential velocity contours are shown in Figure 3.7. For both flow rates, contour plots show similar and nearly axisymmetric flow fields. However, maximum tangential velocities are higher that that of the single inlet cases. This might be due to the difference in the inlet area, where the single inclined inlet has a higher area and, thus, lower tangential velocity than the dual inclined inlet configuration. Interestingly, the decay of the tangential velocity with Reynolds number and axial distance is not as drastic as in the case of single inclined inlet. This might be due to axisymmetry and higher tangential velocities at the inlet.

63 Figure 3.6 Axial Velocity of Dual Inclined Inlet Configuration (Erdal, 001) 48

64 Figure 3.7 Tangential Velocity of Dual Inclined Inlet Configuration (Erdal, 001) 49

65 50 Turbulent Quantities: The two- component LDV system used by Erdal (001), is also capable of determining the standard deviation of the sampled data, which represents the turbulent fluctuations ( ( u ) and ( w ) ). The statistical quantities such as the mean velocity ( v ) and the standard deviation ( σ ν ) of the data are calculated with the equations given below: vτ v = (3.1) Τ v Τ σ ν = v (3.) Τ where Τ is total burst (measurement) time. Therefore, axial and tangential velocity fluctuations can be directly determined from the LDV data. Measurements showed that fluctuations in the axial and tangential directions have the same order of magnitude. To obtain an estimate of the turbulent kinetic energy, the radial velocity fluctuations are approximately assumed to be the average of the axial and tangential velocity fluctuations. The radial velocity fluctuations and turbulent kinetic energy are calculated by the following equations: 1 = + ( v ) (u ) (w ) (3.3) 1 k = ( u ) + ( v ) + ( w ) (3.4)

66 51 Contour Plots: The calculated turbulent kinetic energy, k, (Equations 3.3 and 3.4) distributions, normalized with U av, are presented in contour plots in Fig. 3.8, 3.9, 3.30 and The data show high k values on the left hand side, right below the inlet near the wall region, for the case of single inclined inlet full bore pipe area, as shown in Figs. 3.8 and 3.9. Also, it can be seen that, the value of k decays downward axially in the near wall region. The high turbulent intensity at the inlet region may contribute to re-mixing and bubble breakup. This process can generate bubbles of smaller sizes, which are much harder to separate. Consequently more gas entrainment may occur under this condition. On the other hand, the case of a single inclined inlet with gradually reducing nozzle area, as shown in Fig 3.30, does not exhibit high k values at wall region below inlet, avoiding the undesired phenomenon of inlet effects. This will also enhance the separation efficiency. The aforementioned comparison demonstrates that the single inclined inlet gradually reducing nozzle area, does not only offer the best performance for liquid carryover, but also the best inlet section configuration for efficient gas carry-under performance. In spite of the high k values at near the pipe wall below the inlet, the turbulent intensity, k, has a similar distribution at the center region with high k values, exhibiting a helical shape, and does not show a strong decay. This high turbulence at the center is due to the instability of the flow at the center region. A maximum local peak value of k occurs around the center, which initially increases axially as the flow moves downward. However, there exists an axial location where the turbulent starts decreasing, and

67 5 eventually the value of the turbulent intensity converge to the value of swirling-free pipe flow. Turbulence due to inlet effects, such the one observed in the single inclined inlet measurements does not appear in the plots given in Fig for dual inclined inlet, which confirms that the flow must be injected tangentially to GLCC wall. However, turbulent kinetic energy decay due to change in the flow rate (Reynolds number) is more obvious and very similar to one observed in single inclined inlet configuration. This high turbulence center region shows the large instability of the flow near the vortex center. This might have a greater impact on the separation of small bubbles below the inlet of GLCC, as they move toward the center due to centrifugal effects. The stability of the gas core is the key to defining the dominant swirling flow pattern, as described previously in this study. The mechanism of the stability of singlephase swirling flow observed in the contour plots can be related to the turbulent intensity. Thus, the turbulent intensity can be used to develop a model to predict the stability of the gas core. One might think that high intensity swirling flow would enhance the gas-liquid separation due to the surge motion of lighter fluid towards the reverse flow region at the center of the pipe, which also become wider as the swirl intensity increases. However, there exist an increment of the turbulent quantities associated with this phenomenon, which will increase the bubble breakup rate producing bubbles with smaller size that are harder to separate. This is due to the fact that the bubble would decrease its motion as bubble size decreases. Therefore, the optimum continuous phase swirling flow for the

68 53 case of gas-liquid separation is compromised for the movement of bubbles towards the center due the centrifugal forces and the bubble breakup into smaller bubbles.

69 Figure 3.8 Turbulent Kinetic Energy for Single Inclined Full Bore Area Inlet Configuration (Erdal, 001) 54

70 Figure 3.9 Turbulent Kinetic Energy for High Viscosity Single Full Bore Area Inlet Configuration (Erdal, 001) 55

71 Figure 3.30 Turbulent kinetic Energy for Gradually Reducing Inlet Nozzle Configuration (Erdal, 001) 56

72 Figure 3.31 Turbulent Kinetic Energy of Dual Inclined Inlet Configuration (Erdal, 001) 57

73 58 Turbulent Intensities: Figures 3.3, 3.33, 3.34 and 3.35 present the turbulent quantities at one axial location, z/d = 3.6 below inlet, for different Reynolds numbers, Re = 900 and Re = Figures 3.3 and 3.33 show the axial and tangential turbulent intensities or normal Reynolds stresses, respectively. Both figures exhibit low (flat) intensity distribution near the annular region and high intensities around the GLCC axis, and both demonstrate the effect of the Reynolds number on the intensity. However, higher turbulent intensities occur in the tangential fluctuation velocity as compare to axial one. As expected, the turbulent kinetic energy distribution, given in Fig exhibits similar behavior. The two-component LDV system used by Erdal (001) enables measurement of only one component of the Reynolds shear stress, namely, u'w', as given in Fig For the turbulent parameter, the Reynolds number has significant effect near the core region. The variations of the turbulent quantities with axial position (decreasing swirl intensity) for one Reynolds number (Re = 55000) are given in Figs 3.36, 3.37, 3.38 and The axial and tangential normal Reynolds stresses are presented in Figs and 3.37, respectively. As can be seen, both stresses show low (flat) intensity in wall region, while at the core region high intensities are observed. The high tangential turbulent intensity, however occur over a wider core range as compared to the normal stress intensity. A very peculiar behavior is exhibited by both turbulent kinetic energy and shear stresses in the core region, as shown in Figs and 3.39, respectively. As can be seen both tend to increase with the axial location. The reason for this behavior is that as swirl decays with axial position, the turbulent dissipation energy increases the energy losses.

74 ( u ) Uav z/d = 3.6 Re = Re = r/r Figure 3.3 Axial Normal Reynolds Stress Distribution, after Erdal (001) ( w ) Uav z/d = 3.6 Re = Re = r/r Figure 3.33 Tangential Normal Reynolds Stress Distribution, after Erdal (001)

75 k/uav z/d = 3.6 Re = Re = r/r Figure 3.34 Turbulent Kinetic Energy Distribution, after Erdal (001) u'w'/uav z/d = 3.6 Re = Re = r/r Figure 3.35 Reynolds Shear Stress Distribution, after Erdal (001)

76 ( u ) Uav Re = z/d = 3.6 z/d = 5.4 z/d = 6.7 z/d = 8.5 z/d = r/r Figure 3.36 Axial Normal Reynolds Stress Distribution, after Erdal (001) ( w ) Uav Re = z/d = 3.6 z/d = 5.4 z/d = 6.7 z/d = 8.5 z/d = r/r Figure 3.37 Tangential Normal Reynolds Stress Distribution, after Erdal (001)

77 6 k/uav Re = z/d = 3.6 z/d = 5.4 z/d = 6.7 z/d= 8.5 z/d = r/r Figure 3.38 Turbulent Kinetic Energy Distribution, after Erdal (001) u'w'/uav Re = z/d = 3.6 z/d = 5.4 z/d = 6.7 z/d = 8.5 z/d = r/r Figure 3.39 Reynolds Shear Stress Distribution, after Erdal (001)

78 63 High Viscosity Effects: In order to understand the effect of Reynolds number and viscosity on the flow field in the GLCC, Erdal (001) also conducted experiments for low Reynolds number with single inclined inlet full bore area configuration. The same procedure is used for the 10 (Re = 1514) and the 30 (Re = 4163) gpm cases. Figures 3.40 and 3.41 show contour plots of the axial and tangential velocity distributions, normalized with respect to U av. These figures show that the velocities decrease with Reynolds number. However, the hydrodynamic structure of the flow remains similar for these wide range of Reynolds numbers. It may be noted that the vortex helical pitch length changes with respect to Reynolds number, and it is longer for low Reynolds numbers. The tangential velocities are much lower than the previous measurements with higher Reynolds numbers. For the value of Reynolds around 1500, one might imply that the flow is laminar, as compared to pipe flow. However, the axial reverse flow still occurs in this case, with low turbulent intensity and the swirling flow prevails with considerable intensity too. Thus, one may conclude that the structure of swirling flow has no similarity with pipe flow hydrodynamics for low Reynolds numbers less than 300, when the swirling flow is present. Turbulent kinetic energy, k, profiles, normalized with U av, are plotted in Figure 3.4. High turbulent kinetic energy region at the center is observed for flow rate of 30 gpm (with 7 cp), which is not present for the case of 10 gpm case. The turbulence that is created at the inlet is rapidly decreasing. Erdal (001) observed that for 10 gpm (7cp), k/ U av is nearly uniform and is equal to 0.. However, below the inlet on the left hand side, there is a relatively high turbulent kinetic energy region, which decays as the tangential velocity approach a value of zero, where the flow behaves similar to pipe flow.

79 Figure 3.40 Axial Velocity Comparison for Single Inclined Full Bore Area Inlet Configuration (Erdal, 001) 64

80 Figure 3.41 Tangential Velocity Comparison for Single Inclined Full Bore Area Inlet Configuration (Erdal, 001) 65

81 Figure 3.4 Turbulent Kinetic Energy Comparison for Single Inclined Full Bore Area Inlet Configuration (Erdal, 001) 66

82 Straight Pipe Swirling Flow Local Measurements Swirling flow through a pipe is a highly complex turbulent flow, characterized by the presence of a tangential velocity component, which is superimposed on the axial flow. Swirling pipe flow exhibits a forced vortex near the region, surrounded by a quasi-free vortex region in the vicinity of the pipe wall region. In the wall region the tangential velocity gradient is quite steep. This type of variation of the tangential velocity is approximated as a Rankine vortex as suggested by Algifri (1988). Associated with this phenomenon, axial flow reversal is also observed. This is due to the centrifugal forces caused by the tangential motion, which tend to move the fluids towards the outer region of the pipe. This radial shift results in a reduction of the axial velocity near the center, where the swirl intensity is sufficiently high to reverse the flow near the center of the pipe. Algifri (1988) pointed out that in a swirling stream, unlike the case of normal pipe flows, the axial velocity will not attain maximum value at the center but at a radius which is governed by the swirling intensity. As a result of swirling intensity decay, variations of the axial velocity component along the axial flow direction, cause a radial velocity component to satisfy continuity conditions. Data from several investigators, namely, Algifri (1988), Kitoh (1991) and Chang and Dhir (1994), are collected and presented here with the purpose of developing correlations or validating existing correlations to characterize and predict swirling flow behavior. A comprehensive set of data was presented by Algifri et al. (1988) with air system apparatus inducing the swirling motion by means of the radial cascade blades. They

83 68 measured the swirling flow field characteristics using a hot-wire anemometer. Kitoh (1991) also measured tangential and axial velocity distributions and Reynolds stress distributions, by means of a hot-wire anemometer, using an air system where the swirling flow is generated with guide vanes. Turbulent flow field in a straight pipe was studied experimentally by Chang and Dhir (1994) utilizing a single rotated straight hot wire, with air being injected tangentially through injectors placed on the periphery of the pipe. Two sets of data were acquired for four and six injectors perpendicular to the test tube Straight Pipe Swirling Flow Field Analysis In this section the data collected from literature as reported by the three previous investigators mentioned above, is presented in terms of the flow field and turbulent quantities, similar to the way Erdal (001) data were presented Axial Velocity Distribution: Figures 3.43, 3.44, 3.45 and 3.46 show the profiles of axial mean velocity, u, for Algifri (1988), Kitoh (1991), Chang and Dhir (1994) for four tangential injectors and Chang and Dhir (1994) for six tangential injectors, respectively. The axial mean velocity, u, is normalized with respect to U av, and given at various locations along the pipe axis. The data show a low or negative upward velocity in the core region surrounded by relatively high downward velocity in the annular region. The presented data show that the flow is approximately axisymmetric and the reverse flow appears at the central region for all cases.

84 Axial Velocity Distribution Re = 5 x 10 4 u/uav z/d=5.7 z/d=1.3 z/d=19.0 z/d=5.7 z/d=39.0 z/d=3.4 z/d= r/r Figure 3.43 Axial Velocity Distribution After Algifri (1988) 1.40 Axial Velocity Distribution Re = 1.7x x10 5 u/uav r/r z/d = 0, z/d = 0, z/d = 0, z/d = 0, z/d = 50, z/d = 50, Figure 3.44 Axial Velocity Distribution After Kitoh (1991)

85 Axial Velocity Distribution Re = 1500, Mt/MT= u/uav r/r z/d=7.06 z/d=8.06 z/d=9.06 z/d=6.06 z/d=10.06 Figure 3.45 Axial Velocity Distribution After Chang and Dhir (1994) Axial Velocity Distribution Re = 1500, Mt/MT= u/uav r/r z/d=7.00 z/d=8.00 z/d=9.00 z/d=6.00 z/d=10.00 Figure 3.46 Axial Velocity Distribution After Chang and Dhir (1994)

86 71 Radial Velocity Distribution: The radial mean velocity distributions, v, estimated from continuity equation and normalized with respect to Uav are given in Figs. 3.47, 3.48, 3.49 and The experimental results indicate that the radial velocity component is of an order 0( ) smaller as compared to the average axial or tangential velocities. It can also be seen that the magnitude of the radial velocity increase with increasing swirl intensity and that the location where the radial velocity is maximum shifts towards the center of the pipe, where the swirl intensity is maximum. The radial velocity occurs due to the variations of the axial velocity in the direction of the flow Radial Velocity Distribution Re = 1.7x x10 5 v/uav r/r z/d = 0 z/d = 0 z/d = 0 z/d = 0 z/d = 50 z/d = 50 Figure 3.47 Radial Velocity Distribution After Algifri (1988)

87 7 Radial Velocity Distribution Re = 5 x v/uav z/d=5.7 z/d=1.3 z/d=19.0 z/d=5.7 z/d=39.0 z/d= r/r Figure 3.48 Radial Velocity Distribution After Kitoh (1991) 0.01 Radial Velocity Distribution Mt/MT = 7.84 Re = v/uav z/d = 7.06 z/d = 8.06 z/d = r/r Figure 3.49 Radial Velocity Distribution After Chang and Dhir (1994)

88 Radial Velocity Distribution Mt/MT =.67 Re = v/uav z/d = 7.00 z/d = 8.00 z/d = r/r Figure 3.50 Radial Velocity Distribution After Chang and Dhir (1994) Tangential Velocity Profiles: The tangential mean velocity, w, normalized with respect to U av, plotted in Figs. 3.51, 3.5, 3.53 and These figures show that the mean tangential velocity increases with radial position in the core region, and reaches a maximum value; thereafter it decreases with radial position in the annular region near the wall. The velocity gradient near the wall is steep, thus, the tangential velocity rapidly decreases to zero at the wall. From these figures, it can also be seen that the tangential velocity indeed has a shape of a Rankine vortex that has a three-region structure consisting of the core, annular and wall regions. The wall region is very thin, with a very narrow boundary layer. Measurement of the tangential velocity is difficult, and thus an extension of the tangential velocity in the annular region is made as an approximation. The annular region is characterized by free vortex, with a fairly large transition region between the core and annular region. The maxima of the tangential velocity are observed

89 74 in the transition region. These maxima shift towards the center with increase in the swirling intensity, thus, shrinking the core region of the forced vortex. The tangential velocity tends to become zero as it approaches the pipe axis, except for the Erdal (001) data. For these the core region exhibits a helical path that varies its pitch or wave length with swirling intensity, and for some conditions, axisymmetric flow is observed when helical pitch becomes straight. w/u av Tangential Velocity Distribution Re = 1.7x x r/r z/d = 0 z/d = 0 z/d = 0 z/d = 0 Figure 3.51 Tangential Velocity Distribution After Algifri (1988)

90 75 Tangential Velocity Distribution Re = 5 x w/uav r/r z/d=5.7 z/d=1.3 z/d=19.0 z/d=5.7 z/d=39.0 z/d=3.4 z/d=1.3 Figure 3.5 Tangential Velocity Distribution After Kitoh (1991) 6.0 Tangential Velocity Distribution Re = 1500, Mt/MT= w/uav z/d=7.06 z/d=8.06 z/d=9.06 z/d=6.06 z/d= r/r Figure 3.53 Tangential Velocity Distribution After Chang and Dhir (1994)

91 76 Tangential Velocity Distribution Re = 1500, Mt/MT= w/uav z/d=7.00 z/d=8.00 z/d=9.00 z/d=6.00 z/d= r/r Figure 3.54 Tangential Velocity Distribution After Chang and Dhir (1994) 3.3. Straight Pipe Swirling Flow Turbulent Quantities Several investigators have studied turbulent swirling flow, most of which confirmed that the nature of swirling flow is highly turbulent with anisotropic behavior. Furthermore, in case of gas-liquid turbulent dispersion, an important key for predicting the multiphase flow behavior is the characterization of the turbulent quantities. Towards this end, a large amount of turbulent data reported by several investigators have been collected, namely, turbulent intensity, turbulent kinetic energy and Reynolds stresses. The data have been used to understand the mechanism and to develop correlations to predict accurately the turbulent flow behavior presented in swirling flow, considering its anisotropic nature as well. The same experimental data reported by previous investigators, as described in the previous section, are also given here for the turbulent intensity and Reynolds stresses. Since, Erdal (001) used a two- component LDV system;

92 77 thus, only u 'w' values were reported, but other investigators have provided a completed set of data of turbulent flow. Turbulent Intensities: Figures 3.55, 3.56 and 3.57 (after Algifri, 1988) and Figs. 3.58, 3.59 and 3.60 (after Kitoh, 1991) show the radial distribution of the turbulent intensity or velocity fluctuation components, u ', v ' and w ', normalized with U av. This is followed by a brief summary of Kitoh s discussion on the turbulent phenomena that takes place in swirling flow, and which are later confirmed by Chang and Dhir (1994) and Erdal (001) data in this study. The data reveal that turbulent intensity has a large magnitude. In a normal (swirlfree) pipe flow all the components of the turbulent intensities are observed to have high values in the vicinity of the pipe wall, whereas the experimental data for swirling flow indicate that the swirling has a tendency to increase these intensities in the region close to the axis of the pipe. Among the three components, v ' shows the most significant increase, becoming three times larger than pipe flow for Kitoh s data. This might be the reason of the enhancement of swirling flow exhibited in heat transfer applications. As a result of high values of v ', the region where u' - v ' > 0 appears in the annular region where the turbulent-energy production terms of v' are also larger than u '. While turbulent intensity in the annular region reduces gradually as the swirl decays, it increases in the core region. In the core region very low-frequency motion prevails, while in the outer regions (annular and wall) the fluctuation include high-frequency motion, as expected in turbulent flow. This peculiar frequency observed in the core region might be the result of an inertial wave generated by the rotating motion, which prevails as the flow

93 78 is non-dissipative. The tangential velocity in swirling flow has a significant influence on the flow structure. u' U av Turbulent Intensities Re =1.5x r/r z/d = 0 z/d = 7.5 z/d = 0 z/d = 50 Pipe flow Figure 3.55 Axial Normal Stress Distribution After Algifri (1988) Turbulent Intensities Re =1.5x10 5 v' U av z/d = 0 z/d = 7.5 z/d = 0 z/d = 50 Pipe flow r/r Figure 3.56 Radial Normal Stress Distribution After Algifri (1988)

94 79 w' U av Turbulent Intensities Re =1.5x r/r z/d = 0 z/d = 7.5 z/d = 0 z/d = 50 Pipe flow Figure 3.57 Tangential Normal Stress Distribution After Algifri (1988) 0.50 Turbulent Intensities Re = u' U av z/d= 1.3 z/d= 5.7 z/d= 1.3 z/d= 19 z/d= 5.7 z/d= 3.4 z/d= r/r Figure 3.58 Axial Normal Stress Distribution After Kitoh (1991)

95 Turbulent Intensities Re = v' U av z/d= 1.3 z/d= 5.7 z/d= 1.3 z/d= 19 z/d= 5.7 z/d= 3.4 z/d= r/r Figure 3.59 Radial Normal Stress Distribution After Kitoh (1991) Turbulent Intensities Re = w' U av z/d= 1.3 z/d= 5.7 z/d= 1.3 z/d= 19 z/d= 5.7 z/d= 3.4 z/d= r/r Figure 3.60 Tangential Normal Stress Distribution After Kitoh (1991)

96 81 Turbulent Kinetic Energy: In this study, the turbulent kinetic energy, k, is also calculated and presented, aiming at the development of turbulent flow correlations, instead of utilization of normal Reynolds stresses. Figures 3.61, 3.6, 3.63 and 3.64 show the turbulent kinetic energy, k, normalized with U av, for Algifri (1988), Kitoh (1991), Chang and Dhir (1994) for four tangential injectors and Chang and Dhir (1994) for six tangential injectors, respectively Turbulent Intensities Re =1.5x10 5 k/u av z/d = 0 z/d = 7.5 z/d = 0 z/d = 50 Pipe flow r/r Figure 3.61 Turbulent Kinetic Energy After Algifri (1988)

97 Turbulent Intensities Re = k/u av z/d= 1.3 z/d= 5.7 z/d= 1.3 z/d= 19 z/d= 5.7 z/d= 3.4 z/d= r/r Figure 3.6 Turbulent Kinetic Energy After Kitoh (1991) Turbulent Intensities Mt/MT = 7.84,Re =1500 k/u av z/d = 6 z/d = 7 z/d = 8 z/d = 9 z/d = r/r Figure 3.63 Turbulent Kinetic Energy After Chang and Dhir (1994)

98 Turbulent Intensities Mt/MT =.67,Re =1500 k/u av r/r z/d = 6 z/d = 7 z/d = 8 z/d = 9 z/d = 10 Figure 3.64 Turbulent Kinetic Energy After Chang and Dhir (1994) Reynolds Stresses: The radial distributions of the Reynolds shear stress u are ' u ' i j shown in Figs. 3.65, 3.66 and 3.67 (after Algifri, 1988), 3.68, 3.69 and 3.70 (after Kitoh, 1991), and 3.71, 3.7 and 3.73 (after Chang and Dhir, 1994). The figures display the dependence of the Reynolds shear stress on the Reynolds number and swirling intensity. The Reynolds stress component u'v' generally decreases in the magnitude as the swirl decays and changes its sign. It is negative near the wall or annular region, where the flow slows down, but it is positive in the core region, where the axial velocity increases in the axial direction. For the case in which the component v'w' does not exist in a swirl-free pipe flow, a change in its sign is observed from the pipe center towards wall. This is due to the nature of flow in the core and the outer regions. The magnitude of v'w' is negative and large in the annular region, while it is small and could be positive in the core

99 84 region. It can also be noticed that the location where v'w' changes its sign has a tendency to move toward the wall as swirl decreases, which is similar to the distribution of the mean tangential velocity given in a previous section. magnitude of Since angular momentum is transferred in the downstream direction, the u'w' should be mostly positive and it decreases as the swirl decays. Also, as can be seen from data, in the region around the center where the forced vortex behavior of the tangential velocity is dominant, u'w' has a large positive value. While in the outer region, where the tangential velocity is of the free-vortex type, small values of u'w' Reynolds Stress Re=1.55x u'w'/u av z/d = 0 z/d = 7.5 z/d = 0 z/d = 50 z/d = r/r u'w' exist. Figure 3.65 Reynolds Shear Stress u 'w' Distribution After Algifri (1988)

100 85 u'v' Reynolds Stress Re=1.55x u'v'/u av z/d = 0 z/d = 7.5 z/d = 0 z/d = 50 z/d = 75 standard r/r Figure 3.66 Reynolds Shear Stress u'v' Distribution After Algifri (1988) v'w' Reynolds Stress Re=1.55x10 5 -v'w'/u av z/d = 0 z/d = 7.5 z/d = 0 z/d = 50 z/d = Figure 3.67 Reynolds Shear Stress r/r v'w' Distribution After Algifri (1988)

101 86 u'w' Reynolds Stress Re = 5 x z/d=1.3 u'w'/u av z/d=5.7 z/d=1.3 z/d=19.0 z/d=5.7 z/d=39.0 Pipe Flow z/d= r/r Figure 3.68 Reynolds Shear Stress u 'w' Distribution After Kitoh (1991) u'v' Reynolds Stress Re = 5 x z/d=1.3 -u'v'/u av z/d=5.7 z/d=1.3 z/d=19.0 z/d=5.7 z/d=39.0 Pipe Flow z/d= r/r Figure 3.69 Reynolds Shear Stress u'v' Distribution After Kitoh (1991)

102 87 v'w' Reynolds Stress Re = 5 x v'w'/u av z/d=1.3 z/d=5.7 z/d=1.3 z/d=19.0 z/d=5.7 z/d=39.0 Pipe Flow z/d= r/r Figure 3.70 Reynolds Shear Stress v'w' Distribution After Kitoh (1991) 0.10 u'w' Reynolds Stress Mt/MT = 7.84 Re = u'w'/u av z/d = 6.06 z/d = 7.06 z/d = 8.06 z/d = 9.06 z/d = Figure 3.71 Reynolds Shear Stress r/r u'w' Distribution After Chang and Dhir (1994)

103 u'v' Reynolds Stress Mt/MT = 7.84 Re = u'v'/u av z/d = 6.06 z/d = 7.06 z/d = 8.06 z/d = 9.06 z/d = Figure 3.7 Reynolds Shear Stress r/r u'v' Distribution After Chang and Dhir (1994) 0.10 v'w' Reynolds Stress Mt/MT = 7.84 Re = v'w'/u av z/d = 6.06 z/d = 7.06 z/d = 8.06 z/d = 9.06 z/d = Figure 3.73 Reynolds Shear Stress r/r v'w' Distribution After Chang and Dhir (1994)

104 89 The eddy viscosities can be calculated using the measured Reynolds stresses, u, ' u ' i j by following relationship: u' v' υ t zr= (3.5) u r v' w' υ t θr = (3.6) ( w / r) r r u' v' υ t θz= (3.7) w z Data presented by Kitoh (1991) and Chang and Dhir (1994) (not given here) shows eddy viscosity distribution. The important observation is that large anisotropic turbulent behavior among the three components is present, where very close to the wall the anisotropy becomes weak. The measured profiles of turbulence quantities presented here can be used to develop correlation or numerical model to properly characterize the swirling flow and its anisotropic turbulent flow nature, which will be given in the next chapter.

105 90 CHAPTER IV DISPERSED TWO-PHASE SWIRLING FLOW MECHANISTIC MODEL A novel mechanistic model is proposed to characterize two-phase swirling flow in a GLCC separator. This model is capable of determining the dispersed-phase distribution in a swirling, continuous-phase, applicable for both heavier swirling mediums, namely liquid phase with bubbles, as well as lighter swirling medium, namely, gas phase with droplets. An Eulerian-Lagrangian approach is adopted to characterize the diffusion of the dispersed-phase in the swirling flow. A Lagrangian particle-tracking model is also used in this study as a second approach, which should provide similar results. Finally, two simplified mechanistic model solution schemes, based on both approaches are proposed. The simplified mechanistic models can be used as an engineering design tool for the prediction of gas carry-under in GLCC separators. 4.1 Dispersed-Phase Mass Diffusion Model The singular characteristic of a two-phase immiscible mixture is the presence of one or several interfaces separating the phases or components. Rigorous mathematical formulation for obtaining solutions for such system is difficult due to the existence of deformable and moving interfaces. Investigators have frequently adopted the Eulerian time and spatial averaging method to formulate models for two-phase flow, as given below.

106 Two-Phase Flow Models Two main rigorous mathematical approaches have been used for the prediction of two-phase flow phenomena, namely, the Two-Fluid Model and the Diffusion (Mixture) Model. The two-fluid model is formulated by considering each phase separately, utilizing mass, momentum and energy transport equations for each phase. Thus, a total of six field equations are included, coupled through jump conditions at the interface. The diffusion model, also known as the Drift Flux Model, on the other hand, is formulated by considering the mixture as a whole. Therefore, the model is more suitable for cases where the two-phases are coupled, such as in dispersed flow. Thus, the model is expressed in terms of three-mixture transport equations, with an additional diffusion equation, which take into account the concentration distribution changes. The main reason that the diffusion model is adopted in this study is because of the strong coupling between the gas and liquid phases that occurs in the dispersed swirling two-phase flow, at the lower part of the GLCC Diffusion (Mixture) Model The starting point of the model derivation is the set of Eulerian time averaged transport equations, as given by Ishii (1975). The model consists of three governing balance equations: the mixture mass balance equation, dispersed-phase diffusion equation and the mixture momentum balance equation, given respectively below. Note that the dispersed-phase diffusion equation is introduced in the model in order to account for the slippage and the corresponding volume fractions of the phases.

107 9 ρ m t + ( ρ u ) = 0 m m, (4.1) α d t ρ d + ( α ρ v ) = Γ ( α ρ v ) d d d d d dm, (4.) ρ u m t m + ( ρ mumum ) = pm + τ m + ρ m g + M m, (4.3) α α = 1 (4.4) c + d where u m and ρ m are the mixture velocity and density, respectively; α d, α c, ρ d, v d, v dm and Γ are the dispersed-phase and continuous-phase void fractions, the dispersedphase density and velocity, the diffusion velocity and mass source. M m is the mixture momentum source due to surface tension effects and τ m is the mixture stress tensor including the viscous, turbulent and diffusion stresses. Dispersed-phase Diffusion Equation: The diffusion equation of the dispersedphase, Eq. (4.), is developed from the dispersed-phase continuity equation utilizing the eddy diffusivity hypothesis and time averaging for velocity-volume fraction fluctuations. Note that the flow is assumed isothermal and that the pressure field variation is assumed to be small. Thus, mass transfer effects and phase density variations are neglected. The diffusion velocity is the velocity of the phase with respect to the center of mass velocity, as given by v dm G = vd (4.5) ρ m

108 93 where G, is the total mass flux. The diffusion velocity can be related either to the relative velocity (slip) between the phases, v s = u - v d, or to the drift velocity, v dj, in a straightforward manner, as follows v dm α ρ = ) ρ ρ c c c ( u vd = vdj (4.6) m ρ m It is common practice in the literature to use the relative velocity or drift velocity rather than the diffusion velocity. This is due to the fact that closure relationships are usually derived from experimental data, and it is more practical to measure the relative velocity rather than the diffusion velocity. For simplicity it is designated that α d is equal to α and α c is equal to (1-α ) from this point on. The diffusion equation of the dispersed-phase can also be expressed in terms of the mass concentration (not used in this study), which is related to the void fraction by c α ρ d = (4.7) ρ m The dispersed-phase diffusion equation results in a general convection-diffusion form. The Eulerian diffusion equation is used in this study to predict the void fraction distribution in swirling flow, and is given in cylindrical coordinates, as follows: ( α ρ d ) 1 ( rα ρ d vdr ) 1 ( α ρ d vd θ ) ( α ρ d vdz ) = t r r r θ z 1 ( rα ρ v ( d v d dmr ) 1 α ρ dmθ ) ( α ρ d v Γ + + r r r θ z dmz ) (4.8)

109 94 For steady-state with no source or sink and axisymmetric flow, the dispersed-phase diffusion equation can be further simplified, as follows: 1 ( rα ρ vdr ) ( α ρ d vdz ) 1 ( rα ρ d vdmr ) ( α ρ d v + = + r r z r r z d dmz ) (4.9) In order to solve the diffusion equation expressions for the diffusion, mixture, continuous-phase and dispersed-phase velocities are required. The mixture continuity and mixture momentum equations can be used to obtain the mixture and continuous-phase velocities. However, in order to achieve these results one must solve numerically the mixture continuity and mixture momentum equations. This requires complex numerical schemes and elaborate computations, without having confidence in the results, as demonstrated by Motta (1997). Instead, an empirical approach is used in this study to determine the continuous flow field, based on single-phase swirling intensity concept, Ω. This correlation is used to determine the axisymmetric flow field by means of the tangential and axial velocities, as presented by Mantilla (1998). 4. Continuous-phase Flow Field Model Several investigators have studied single-phase gas or liquid flow in pipes with tangential injection, reporting a very complex swirling flow field. For example, Ito et al. (1979) indicated that the tangential velocity distribution has two flow regions: forcedvortex flow near the center of the tube and a free-vortex region near the wall. The axial velocity distribution shows a region of flow reversal near the center of the tube. Figure 4.1 shows schematically typical axial and tangential velocity profiles that have been observed for high swirl intensities. Experimental observations carried out in this study

110 95 also confirm these hydrodynamic phenomena, as presented in the experimental program section. Based on several sets of experimental data available in the literature for swirling flows, Mantilla (1998) modified an existing swirl intensity correlation, proposed originally by Chang and Dhir (1994), to predict the flow field, as given in the next section. z r θ Tangential Velocity Axial Velocity Figure 4.1 Schematic of Swirling Flow Field and GLCC Coordinate System 4..1 Swirl Intensity Decay Number The swirling motion decays as a result of wall friction. The swirl intensity concept is used to characterize this decay. For axisymmetric and single-phase flow, the swirl intensity, Ω, is defined as the ratio of the tangential to total momentum flux at any axial location, namely R πρ u u r dr z θ 0 Ω = (4.10) πρ R U av

111 96 where U av is the average axial velocity, R is the pipe radius and ρ is the fluid density. The numerator of Eq. (4.10) corresponds to the tangential momentum flux integrated over the cross section, while the denominator is the total momentum flux based on the average axial velocity. The Mantilla s correlation for the swirl intensity is given by: M Ω = 1.48 M t T I M exp M t T I Re 0.16 z d sep 0.7 (4.11) Recently, Erdal (001) acquired local swirling flow field measurements in an apparatus similar to a GLCC using an LDV. Based on the data, he modified the Mantilla correlation to account for inlet effects and low Reynolds numbers, as follow Ω = 0.67 Re 0.13 M M t T I M exp M t T I Re 0.16 z d sep 0.7 (4.1) where M t is the ratio of the tangential momentum flux to the total momentum flux at the M T inlet, I is an inlet geometry factor, Re is the Reynolds number, z is the axial distance and d sep is the diameter of the GLCC. For the inlet this momentum ratio is: M M t T u = cos β v = U av U L inlet t is av (4.13) where u Linlet is the liquid velocity at the inlet, U av is the bulk (GLCC) average axial liquid velocity and β is the inlet inclination angle. The liquid velocity at the inlet can be calculated by the comprehensive nozzle analysis developed by Gomez (1998), which can then be used to compute the tangential velocity of the liquid at the inlet slot, v t is.

112 97 The Reynolds number in Eqs and 4.1 is defined as for pipe flow, based on the average velocity and the diameter of the GLCC. The inlet factor, I, is assumed to be function of the number of tangential inlets, n, (n = 1 for GLCC), as follow s: n I = 1 exp (4.14) 4.. Swirling Flow Velocity Distribution Mean Axial Velocity Profile: Radial and axial pressure gradients develop as a result of the swirling motion and the tangential velocity in the GLCC. These pressure gradients, in turn, influence the flow field and lead to a complex flow phenomenon. For sufficiently intense swirling motion, a positive pressure gradient in the axial direction may result, which in turn can cause flow reversal in the main flow around the centerline of the GLCC (see Fig. 4.1). At the limit, when the swirl intensity decays to nearly zero, the flow becomes purely an axial pipe flow. The swirl intensity is related, by definition, to the local axial and tangential velocities, as given by Eq Therefore, it is assumed that, for a specific axial location, the swirl intensity prediction can be used to calculate the velocity profiles. Mantilla (1998) developed a correlation for the axial velocity profile, as follows: u U z av = C r R 3 3 C r R , (4.15) C rrev rrev C = , (4.16) R R

113 98 r Ω rev = exp, (4.17) R 0.6 where r rev is the reversal flow radius (or the so called capture radius), where u z is zero. Mean Tangential Velocity Profile: The tangential velocity distribution, except in the vicinity of the wall, can be approximated by a Rankine Vortex type. Algifri et al. (1988) proposed the following equation for the tangential velocity profile: u U θ av = T m 1 exp B r R r R (4.18) where u θ is the local tangential velocity, r is the radial location, T m is related to the maximum moment of the tangential velocity and B is related to the radial location of this maximum velocity. Correlations suggested by Mantilla (1998), based on experimental data, are used to determine the values of T m and B, as follows: T = 0.9Ω 0.05 (4.19) m Ω B = exp (4.0) 0.6 Mean Radial Velocity Profile: The magnitude of the radial velocity, according to experimental data and CFD simulations, is two or three orders of magnitude smaller than the corresponding tangential or axial velocities, and has generally been neglected in the past. There has been no study that attempted to develop a correlation to predict the mean radial velocity distribution. However, although the magnitude of the radial velocity is negligible, as compared to the other components, it is of considerable importance in the

114 99 dispersed-phase diffusion process. This is due to the fact that the magnitude of the particle velocity in the radial direction can be of the same order of the continuous-phase radial velocity, which would promote diffusion between the two phases. Therefore, a correlation for the radial continuous-phase velocity is developed in this study to account for this physical behavior in the mathematical model. As discussed by Algifri (1988) (given in Chapter III), the centrifugal forces caused by the tangential motion tend to move the fluids towards the outer region of the pipe. As a result of the high swirl intensity, a reduction of the axial velocity near the center occurs, that might reverse the axial flow near the center of the pipe. Due to the swirl intensity decay, variations of the axial velocity component cause variations in the radial velocity component to satisfy continuity conditions. Thus, with knowledge of the axial velocity distribution (Eq. 4.15), and using the continuity equation, the mean radial velocity distribution is obtained, as follows: 1 r ( r u ur = r 0 z z ) dr (4.1) M t 4 z d Ω = Re I Ω (4.) z M T dsep 13 Ω drrev = d Ω exp (4.3) rrev rrev rrev 3 drrev dc = drrev R R (4.4) R u U av 4 3 R dc r r r r = (4.5) 0 C R R R R r 7

115 100 where C and r rev /R are the same used in the calculation of the mean axial velocity (Eqs and 4.17) Continuous-Phase Turbulent Quantities Correlations The importance of turbulent flow properties is that they play a key role in the dispersion process. In this study, it is assumed that the turbulent intensity is absorbed or dissipated only in the bubble/droplet breakup and coalescence processes. This justifies the assumption that no forces due to turbulent effects are considered to act on the particle in the Lagrangian approach. Turbulence in swirling flow is considerably high, depending on the initial swirl intensity at the inlet. Several investigators have found that turbulent intensities are higher at the core. With the decay of the swirl, their magnitudes reduce drastically at the core, while they change slightly near the wall. The turbulence exhibits an anisotropic behavior, as discussed in Chapter III. The turbulent quantities of the continuous-phase are required to complete the model calculation, so that the turbulent intensity, eddy viscosity and energy dissipation rate distributions have to be known, to be able to determine the stable bubble or droplet diameter. Reynolds Shear Stresses: Correlations based on data presented in Chapter III were developed in this study for the radial distributions of the Reynolds shear stresses u for the continuous swirling phase. The objective is to use the correlations to ' u ' i j determine the eddy viscosity of the continuous-phase. The correlating parameters of these correlations are based on experimental observations that high anisotropic turbulent behavior occurs in swirling flow among the three Reynolds stress components, u. ' u ' i j This behavior is observed in the core region around the pipe axis where the tangential

116 101 velocity exhibits a forced vortex, affecting the behavior of the Reynolds stresses. Hence, the value of T m and B are selected as correlating parameters, which are related to the maximum magnitude and location of the tangential velocity, respectively. Following are the correlations for the three Reynolds stress components, normalized with respect to the average bulk velocity, av U. The values of the coefficients are given in Table = f d c b a ' ' 3 4 R r R r R r R r B T U v u m av (4.6) + + = n Ω 3 4 f d c b a ' ' e R r R r R r R r B T U w u m av (4.7) + + = f d b a ' ' 3 4 R r R r c R r R r B T U w v m av (4.8) Table 4.1 Reynolds Stress Coefficients a b c d f n 'v' u 'w' u 'w' v Eddy Viscosity Calculation for Swirling Flow: The Boussinesq eddy viscosity hypothesis gives the interaction of the Reynolds stresses and the gradients of the mean velocities. Also, it is well known that the turbulent kinetic energy, k, and its dissipation rate, ε, are related to the turbulent eddy viscosity, t υ, through a dimensional Kolmogorov relationship, which is widely used in the standard k-ε model. For the case of swirling flow, the distribution of the Reynolds stresses components exhibit different magnitude

117 10 and behavior as the swirl decays. This results in different magnitudes of the three eddy viscosity components, causing anisotropic behavior of the turbulent flow. The values of the eddy viscosities are derived from the Boussinesq eddy viscosity model, once the Reynolds shear stresses are known, given by: u' v' υ tzr = (4.9) u z r υt θ r v' w' = u r r r θ (4.30) υt θ z u' w' = uθ z (4.31) Important experimental observations demonstrate large anisotropy turbulent behavior among the three eddy viscosity components, and that close to the wall this anisotropy becomes weak. It is also observed from the data that, in the annular region, the magnitude of υ is larger than υ and also than υ r t. This leads to the conclusion that zr tθz tθ in order to satisfy Kolmogorov theory, a modification has to be made to account for anisotropic turbulent flow. One simple way is to use an ad hoc coefficient, so that the k-ε model relationship can still hold. This coefficient may or may not have functionality with other turbulent parameters, as was demonstrated by Kobayashi and Yoda (1987). Due to high degree of empiricism of these coefficients and without validation, this method is disregarded in the present investigation. Instead, a tensor analysis is carried out, similar to the method of determining the principal stress direction, for calculating an equivalent

118 103 magnitude of the eddy viscosity acting in the principal stress direction. This model is given in the energy dissipation section. Turbulent Kinetic Energy Correlation for Swirling Flow: From the experimental data for the turbulent quantities given in Chapter III, it can be seen (Fig. 4.) that the turbulent kinetic energy exhibits an increasing maximum near the center, as the flow moves downward. However, at some particular location along the axial direction, the magnitude of maximum turbulent kinetic energy starts decreasing. A transition zone occurs between the two regions that is dependant on the swirl intensity and the Reynolds number. As the swirl intensity decreases and decays completely, the turbulent kinetic energy also decreases until it converges to a magnitude similar to pipe flow kinetic energy. It is also observed that these maxima shift location around the GLCC axis in an oscillatory manner. The minimum values of the kinetic energy exhibit an opposite behavior, as compared to the maximum values. The minima have almost a zero magnitude, increasing slowly with axial position as the swirl intensity decreases, until converging to pipe flow values, as well.

119 104 k/uav Re = z/d = 5.4 z/d = r/r Figure 4. Variation of Turbulent Kinetic Energy along Axial Direction The above experimental observations have been used in this study to develop an empirical correlation for the turbulent kinetic energy, normalized with respect to U av, The correlation is dependant on the initial swirl intensity and its decay, and the Reynolds number. The developed correlation also captures the oscillatory phenomenon of the maximum kinetic energy value. The location of the maximum of the turbulent kinetic energy in the radial direction is simulated with a periodical type equation, correlated with experimental data, which can predict the whipping behavior of the core: r shift R = 0. exp [ 0.6 ( ln Ω 0.8) ] sin(3.088 Ω ) (4.3)

120 105 The parameters given below are used to determine the magnitude of the kinetic energy, k(r,z) in the entire flow domain: min [ 1 exp( Ω Re )] Yk = 0.18 (4.33) A K = M exp0. 7 M t T M sin M t T (4.34) { 0.5 tanh[ 5000 ( Ω ) ] 0.5} B = (4.35) K Yk rshift [ 0.83 ( ln Ω 0. ) ] + B Ykmin = R (4.36) 0.45 max AK Re exp 5415 K Ω n = (4.37) Re ( 0. Ω) ϑ = 0.19 exp 0784 (4.38) respect to Fig. 4.3: The final equation for the turbulent kinetic energy correlation, normalized with U av, is given in Eq. 4.39, while a general behavior of this equation is plotted in r r shift k ( ) 1 = Yk max Ykmin exp R R + Ykmin expn U av ϑ r R (4.39)

121 106 k Figure 4.3 Turbulent Kinetic Energy Prediction Turbulent Energy Dissipation Calculation for Swirling Flow: For a complete eddy viscosity turbulent model, at least two turbulent quantities have to be specified. In the present study, the two specified turbulent quantities are the Reynolds shear stresses and the turbulent kinetic energy. These quantities are correlated based on experimental data of the swirl intensity and the Reynolds number. As was discussed above, the k-ε

122 107 model provides a relationship between the turbulent eddy viscosity and the turbulent kinetic energy through the energy dissipation, as given below, where, C µ = k = C (4.40) υ ε µ t The energy dissipation expresses the rate of dissipation of the turbulent kinetic energy throughout the entire flow domain. The importance of the energy dissipation in a two-phase dispersion is manifested in the generation of the interfacial area, namely, breakup and coalescence of bubbles/droplets. A particular problem is presented in swirling flow, due to the anisotropic behavior of the turbulent flow. In order to satisfy Eq. 4.40, a method similar to tensor analysis is adopted, for determining equivalent isotropic turbulent eddy viscosity acting in the principal direction, from the different eddy viscosity values resulting from Eqs. 4-9 to The Reynolds stress tensor is expressed as follows: u' u' v' u' w' = u i ' u j ' u' v' v' v' w' (4.41) u' w' v' w' w' The turbulent kinetic energy is the defined as the sum of the normal Reynolds stresses, and is given below: ( u' + v' w' ) 1 k = + (4.4) An equivalent tensor is defined below to express the eddy viscosity values for the different directions, so that the equivalent value of the eddy viscosity acting in the principal direction can also be obtained.

123 108 = ' ' ' w r z r zr z zr u ij t ξ υ υ υ ξ υ υ υ ξ υ θ θ θ υ θ (4.43) where the parameters used are defined below: av i u R u = ' ξ (4.44) 1 ' ' w u c = and ( ) ' ' 1 ' w u v + = (4.45) The value of c 1 = 1.13 is used in his study, obtained from experiments. The three roots of the cubic polynomial equation, given below, are the three principal equivalent eddy viscosity values, = + I I I δ δ δ (4.46) where the invariants are defined in this study as follows: k U R I av 1 = (4.47) ) ( 1) ( 9 8 1) ( ) ( zr z r av av av k U R c c k U R c k U R c c I υ υ υ θ θ = (4.48) = z av r zr z r z av zr zr r av av k u R k u R c k u R c k u R c c I θ θ θ θ θ θ υ υ υ υ υ υ υ υ υ 3 1) ( ) ( ) ( (4.49) Once the three roots of Eq are obtained, the equivalent turbulent eddy viscosity is defined by the magnitude of the principal direction components:

124 109 υ t eqv = δ1 + δ + δ 3 (4.50) Finally, the energy dissipation rate is determined by the well-known k-ε equation as: k = C (4.51) υ ε µ t eqv Once the continuous flow field and its turbulent quantities are obtained, it is still needed to determine the diffusion velocity, in order to solve the dispersed-phase diffusion equation (Eq. 4.8). Thus, the magnitude of the dispersed-phase velocity is necessary to compute the diffusion velocity from either the drift velocity or relative velocity relationships. In this study, a Langrangian approach is adopted to obtain the dispersedphase (bubble/droplet) flow field, based on a stable particle diameter resulting from the turbulent dispersion. 4.3 Dispersed-Phase Flow Field Model The dispersed-phase is modeled using a Lagrangian approach for the particles with an inertial reference frame. This model is limited to a single, clean (non Marangoni effects), non-deformable bubble/droplet, with a constant mass, as discuss by Magnaudet (1997) and Crowe et al. (1998). The general Lagrangian equation for motion of a particle is given by: dv Du = + g F F F FL Dt (4.5) d m d md g mc + D + H + M + dt where the variables are: m d : mass of the dispersed-phase m c : mass of the displaced continuous-phase v d : dispersed-phase velocity

125 110 u : continuous-phase velocity in absence of the particle (unperturbed velocity) Du/Dt : Lagrangian fluid acceleration, defined as F D : drag force F H : history force F M : added mass force F L : lift force Du Dt u = + u u t Assuming quasi steady-state system with local equilibrium for the particle, the Lagrangian equation is simplified to the external forces acting on the dispersed-phase, as follows: ( m m ) g + m u u + F + F + F + F = 0 (4.53) d c c D L H M Following is a discussion of the different forces given in Eq. (4.5): Drag Force: The steady-state drag force is the force that acts on the particle in a uniform pressure field, where there is no acceleration of the relative velocity between the particle and the conveying fluid. This drag force is always considered in the analysis of particle dynamics, accounting for viscous effects. An expression of the drag force is given based on the relative velocity on the particle interface, v s = u v d, particle (bubble/droplet) diameter, d p, and the drag coefficient, C D, as follows: F D = C D π d p ρ c u vd ( u vd ) (4.54) 8 The above expression is valid for non-deformable spherical particles moving independently in an infinite medium without interaction or vortex shedding. These assumptions correspond typically to particle Reynolds numbers, Re, less than 00, for

126 111 which the sphericity of bubble or droplet remains undeformable, as was demonstrated by Duinaveld (1994). The drag force is one of the most investigated forces, aiming at the prediction of the drag coefficient, C D, as function of the particle Reynolds number. A compilation of four correlations has been selected in this study, from extensive amount of drag coefficient correlations available in the literature, in order to choose the most suitable one for bubble/droplet flow. The correlations of Mei et al. (1994), Sciller Naumann (1933), Ishii and Zuber (1979) and Ihme et al. (197) are given below, respectively, for the viscous regime (Re < 1000). Note that Stoke s regime is also included in these correlations: C = + + ( + 1/ D Re ) (4.55) Re Re [ ] C 4 + D = Re (4.56) Re 0.75 [ ] C 4 + D 3 = Re (4.57) Re C D 4 = Re (4.58) Re The particle Reynolds number, Re, is defined based on relative velocity and continuousphase molecular viscosity as follows:

127 11 ρc u vd d p Re = (4.59) µ c Drag Coefficient Reynolds Number CD-1 CD- CD-3 CD-4 Figure 4.4 Drag Coefficient Correlations Comparison Figure 4.4 shows the results of the four drag coefficients, given in Eqs (CD- 1), 4.56 (CD-), 4.57 (CD-3) and 4.58 (CD-4). As can be seen, all correlations perform similarly at low to moderate Reynolds numbers, or viscous region, namely, (Re < 100). However, for large Reynolds numbers, (Re > 100), Mei et al. (1994) correlation differs from the others. Based on this comparison, the Ihme et al. (197) correlation is adopted for drag coefficient calculations, because of the fact that this correlation tends to predict well the Newtonian regime for large Reynolds number, where C D = 0.44 remains constant. History Force: The history force, also known as Basset force, is due to acceleration of the relative velocity, which describes the force due to lagging boundary

128 113 layer development, because of changes in the relative velocity with time. It also accounts for viscous effects, but under unsteady motion. The value of Basset force depends on the acceleration history-up in the time domain. This term is often difficult to evaluate, although it is important in many unsteady applications. The history force, given below, is much smaller for bubbles than for solid spheres, and can be neglected in most cases. F H = v ( dτ (4.60) t µ u d d p K t τ v ) τ v τ 0 v v where K(t-τ v ) is the kernel function, which depends on the diffusion process of the vorticity. Added Mass Force: When a spherical particle is embedded in a uniform unsteady potential flow, the only force that the bubble experiences is an added mass force caused by the relative acceleration between the dispersed-phase and the continuousphase. Experimental Direct Numerical Simulations (DNS), however, have shown that the added mass force holds for both inviscid and viscous flows. The added mass force, as given below, is due to the fact that the bubble/droplet grows or shrinks, changing its size as well as the amount of the displaced fluid. Du dvd FM = CM mc (4.61) Dt dt where C M is added mass coefficient, namely, C M = 0.5. Lift Force: The lift force on a particle is due to a spinning motion of the particle, moving in a viscous fluid. This rotation may be caused by a velocity gradient of the conveying fluid, known as Saffman Lift force. It also can be imposed by some other

129 114 sources, such us particle contact, rebound from surface, purely rotating motion etc. It is also known as Magnus Lift force. The Saffman Lift force type is important when bubbles/droplets are exposed to a velocity gradient of the continuous-phase flow, causing their migration towards the center from the wall in shear flow, as given by the following expression ( u v ) u = C m ( u v ) ω L = CL mc d L c d F ( ) (4.6) where ω is the vorticity vector and C L is lift coefficient, (C L = 0.5). The lift force is not utilized in this study due to the difficulty of determining the vorticity, since the swirling flow is 3-dimensional with highly complex velocity gradients. Body Forces: Two body forces are considered to act on the particle, as follows: The pressure gradient and buoyancy forces: The effect of the local pressure gradient gives rise to an external force in the direction of the pressure gradient. Furthermore, if this pressure gradient is assumed to be constant over the volume of the particle, it produces a hydrostatic pressure. This implies that the forces are equal to the weight of the displaced continuous-phase fluid, namely, the buoyancy effects. In the GLCC, the particles move in a continuous swirling liquid flow that is subjected to pressure gradients in the vertical direction (buoyancy) as well as the radial direction, due to centrifugal forces. An effective gravitational vector is introduced in this study to take into account both pressure gradient components in the radial direction, as well as vertical direction, defined as: g eff H = g e r r H + g e z z u = r θ H e r H + ge z (4.63)

130 115 where u θ represents the continuous-phase tangential velocity and g is the acceleration due to gravity. Shear Stress Force: Similarly, there exists another force acting on the particle due to the shear stress in the conveying fluid, which has the same order of magnitude as the continuous-phase flow acceleration, Du/Dt (more details are given by Crowe et al., 1998). The shear force is significant when the ratio of the pressure to acceleration forces, expressed by ρ c / ρ d is greater than 1. Since this is the case for bubbly flow, it is considered in this study. Equation 4.53 provides an overall dynamic balance on the dispersed-phase, with which one can simulate accurately the motion of a particle (bubble/droplet). It also allows flexibility of incorporating any of the aforementioned forces, for calculating the appropriate dispersed-phase motion. For example, in vertical pipe flow, the lift force, F L, should be included in the analysis to account for particle rotation induced by the continuous-phase velocity gradient, which leads to the motion of the bubble or droplet towards the center of the vertical pipe Dispersed-Phase Particle Velocities For quasi steady-state conditions with local equilibrium of the particle and neglecting history and lift forces, a set of the particle (bubble or droplet) radial, tangential and axial relative velocities equations are obtained from solving the Lagrangian equation of motion (Eq. 4.53), and are given below, respectively:

131 = z u u r u r u u v C d C r u v C d v r z r r s D p M c d c s D p sr ) ( θ θ ρ ρ ρ (4.64) = z u u r u u r u u v C d C v z r r s D p M s θ θ θ θ ) (1 3 4 (4.65) + + = z u u r u u v C d C v C g d v z z z r s D p M c d c s D p sz ) ( ρ ρ ρ (4.66) The velocity field of the dispersed-phase, v d, can be obtained from the relative velocity (slip velocity) and the continuous-phase velocity, using the following relationship d v s u v = (4.67) Equation 4.68 summarizes all the velocity distributions, namely, for the continuous-phase, relative velocity and dispersed-phase velocity, respectively, given in cylindrical coordinates: + + = + + = + + = z dz d r dr d z sz s r sr s z z r r e v e v e v v e v e v e v v e u e u e u u H H H H H H H H H θ θ θ θ θ θ (4.68) From the above equations, it can be noted that in order to compute the dispersedphase velocities, the particle diameter, d p, is required as input. The stable bubble/droplet diameter is determined using the interfacial area concentration concept, which takes into account the interface growth or decay dispersion mechanisms due to break-up and coalescence processes Stable Bubble Diameter

132 117 Based on a simplified approach of the interfacial area transport equation presented by Kocamustafaogullari and Ishii (1995) and Ishii (1997), the stable particle diameter of the dispersed-phase can be determined assuming that the two-phase flow is fully established, and that quasi steady-state flow assumptions apply. This transport equation, given below, also obeys conservation laws at the interface. The interfacial transfer condition can be obtained from an average of the local jump conditions (Ishii, 1975): a i t +.( a v ) = φ + φ + φ (4.69) i i B C ph where a i is the interfacial area concentration (interfacial area per unit volume); v i is the velocity of the interface; φ B, φ C, and φ ph are the breakup, coalescence and phase change processes, respectively, that represent the source and sink of the interfacial area. Simplification of the above equation, under assumptions of steady-state, fully established two-phase flow with no mass change and no heat transfer (adiabatic flow), leads to the determination of a stable particle diameter that satisfies the equilibrium between the breakup and coalescence. This implies that the net volume change due to break-up and coalescence is zero: φ B = φ C. (4.70) When a fluid particle size exceeds a critical value, the particle interface becomes unstable and break-up is likely to occur. Similarly, when fluid particles are smaller than some critical dimension, coalescence is likely to occur as a result of a series of collision

133 118 events. There exists a unique value of particle diameter, where Eq is satisfied for a given particle dispersion condition, resulting into a stable particle diameter. The key to achieving an accurate prediction of the stable particle diameter depends on the use of the appropriate breakup and coalescence models. These models should apply to the different conditions of the continuous-phase hydrodynamics, namely, turbulent fluctuations, laminar viscous shear, buoyant effect, and interfacial instability or wake entrainment flows. In this study, the breakup model given by Luo and Svendsen (1996) and combination of several coalescence models given by Lee et al. (1987), Prince and Blanch (1990) and Thomas (1981) are adopted. However, any breakup or coalescence models can be used, depending on the occurring dispersion mechanism, namely, turbulent dispersion or shear flow. The models selected were developed particularly for turbulent flow dispersion, such as occuring in the lower part of the GLCC. Breakup Model: An expression for the breakup rate is developed based on the theories of isotropic turbulence and probability parameter by Luo and Svendsen (1996), which is given below d P φ = P V : Vf, λ) ω ( V ) dλ (4.71) B λ min B ( BV B, λ Here, P B (V:Vf BV,λ) is the probability for a particle of size V to break into two particles, one with size (volume) Vf BV, when the particle is hit by an arriving eddy of size λ, and ω B,λ (V) is the arrival (bombarding) frequency of eddies of size (length scale) between λ and λ + dλ. In a turbulent field, the fluctuation of the relative velocity on the surface of a bubble is caused by the arrival of similar eddies, λ, of a spectrum of length

134 119 scales. The inertial sub-range of the isotropic turbulent energy spectrum, E(π/λ) = C ε /3 (π/λ) -5/3, is used to define the mean turbulent velocity or collision frequency of eddies with size λ (eddies in this region have no intrinsic velocity or length scale). For a particular eddy hitting a bubble, the probability for bubble breakage depends not only on the energy contained in the arriving eddy, but also on the minimum energy required by the surface area increase due to particle fragmentation. The breakage volume fraction, f BV, is assumed to be 0.5 in this study, namely, that the breakage produces two bubbles with equal volume. The breakup frequency function is redefined considering the aforementioned assumptions and is given below: 1/ 3 ε 1 (1 + χ) 1.554σ φ B = 0.93 exp dχ (4.7) χ 11/ 3 / 3 5 / 3 11/ 3 min d p χ ρc ε d p χ where λ χ = and d p λ = min µ ρ 3 c 3 c ε 1/ 4. (4.73) Figure 4.5 shows a sketch of the breakup frequency for a case of water-air system with energy dissipation value of ε = 1 m /s 3.

135 10 30 Breakup Frequency (1/s) Bubble Diameter (micron) Figure 4.5 Breakup Frequency Function Coalescence Model: The coalescence model presented by Lee et al. (1987), Prince and Blanch (1990) and Thomas (1981) is based on bubble collisions due to the fluctuating turbulent velocity of the liquid phase. A general expression for the coalescence rate is given below: φ C = ϕ exp( t / τ ) (4.74) where ϕ is the total collision frequency resulting from turbulent motion and buoyant collision rate, t is the time required for coalescence of bubbles of diameter d p1 and d p, while τ is the contact time for the two bubbles. As discussed by Lee et al. (1987), Prince and Blanch (1990), for coalescence of two bubbles/droplets to occur in turbulent field, the bubbles must first collide, trapping small amount of liquid between them, and then remain in contact for sufficient time in order for coalescence to occur through the process of film drainage and reaching a critical film rupture. However, turbulent velocity fluctuations may meanwhile deliver sufficient energy to separate the two bubbles before

136 11 coalescence may occur. Collision may occur due to variety of mechanisms. The two mechanisms considered in this study are collision due to turbulence, ϕ T, and due to buoyancy, ϕ W : ϕ = ϕ T + ϕ W. (4.75) The primary cause of bubble collision is the fluctuating turbulent velocity of the continuous-phase. The frequency of bubble coalescence depends upon the turbulent fluctuations. Thus collision takes place by a mechanism analogous to particle collisions in an ideal gas. The equation given below (Prince and Blanchm, 1990) is used to simulate the turbulent bubble collision: 6 ϕ = + ε +. (4.76) T 1/ 3 / 3 / 3 1/ 0.35 ( d 3 p1 d p ) ( d p1 d p ) d p Collision may also occur from each bubble rise velocity, and is given by expression based on bubble rise velocity, as follows: 3 1 ϕ W = + (4.77) 8 d 1/ ( d 3 p1 d p ) ( vrise 1 vrise ) p where.14σ vrise i = g d ρ d c pi pi is the bubble rise velocity. For the case of droplets this velocity must be redefined. In order to determine whether a given collision will result in coalescence, it is necessary to compute the collision efficiency. Coalescence of two bubbles may occur if they remain in contact for a period of time sufficient for the liquid film to thin to the critical thickness necessary for rupture. This effect can be enhanced if the contact time is

137 1 artificially increased by adding surfactant to the dispersion. In this study the summation of two effects for calculating the coalescence time, namely, inertial thinning, t 1 and viscous thinning, t, is adopted as given below, respectively: t 1 3 r ρ c = 16σ 1/ hi Ln h f (4.78) t 4π µ (4.79) 5 = M σ h f Ah where h i and h f are the initial and final film thickness, respectively. Experimental investigations suggest h i = 1 * 10 5 m and h f = 5 * 10-8 m. The equivalent radius, r, is defined by r = d p 1 d p 1, M is the surface immobility parameter that is dependant on the surfactant, taking values from 0 (no surfactant) to 4, and A h is Hamaker constant, which ranges between 10-0 to joules. The mean contact time of two bubbles depends on the bubble size and the turbulent intensity. High levels of turbulence increase the probability that an eddy will separate the bubbles, reducing the contact time, while large contact area will increase the contact time. An expression for contact time in turbulent flow is given as follows: τ r ε / 3 = (4.80) 1/ 3 Substituting Eqs 4.75 to 4.80 into Eq. 4.74, one can obtain the final coalescence rate equation, as follows: t1 + t C = ( ϕt + ϕw ) exp (4.81) τ φ

138 13 Figure 4.6 shows the coalescence frequency for the case of a water-air system with energy dissipation, with value of ε = 1 m /s 3 and M = Coalescence Frequency (1/s) Bubble Diameter (micron) Figure 4.6 Bubble Coalescence Frequency Function Stable Diameter: Equating Eqs 4.7 and 4.81 and solving iteratively, the stable bubble diameter can be determined. A graphical solution of this procedure is shown in Fig. 4.7, where the stable bubble diameter is defined by the interception between the two curves for a given continuous-phase turbulent field, with ε = 500 m /s 3 and M = , resulting in bubble diameter of approximately 1.5 mm.

139 14 Event Frequencies Coalescence Breakup Bubble Diameter (micron) Figure 4.7 Breakup and Coalescence Frequency Events Stable Diameter In an agitated turbulent dispersion, bubbles or droplets are continuously being brought together and then moved apart by turbulent fluctuations, undergoing pressure fluctuations associated with the turbulence to overcome capillary force, which tend to keep the bubble intact without breakup. On the other hand, the bubble can absorb lowlevel turbulent frequency, causing the bubbles to fluctuate. This might promote contact between bubbles with a thin film, where the drainage behavior of this film promotes coalescence. In this process the continuous-phase turbulent intensity is dissipated, as this energy is absorbed by the interface. The Kolmogorov-Hinze hypothesis is widely used to determine the largest stable diameter (d max, Eq. 4.8) of the bubble function of breakup, and the bubble whose diameter is minimum (d min, Eq. 4.83), which will coalesce upon colliding. The resultant stable particle diameter should be within the range given below, We c σ 3 / 5 / 5 d max ε (4.8) ρc 1/ 4 h σ min d c (4.83) µ c ρc ε

140 15 where We c is a critical Weber number, σ, surface tension and h c is the critical film drainage. 4.4 Mixture Velocity Field Once the void fraction distribution is determined from the solution of the diffusion equation, the unperturbed continuous velocity, u, is corrected based on the distribution of the phases. With this correction, the two way and one way flow coupling between the continuous and dispersed-phases are considered. One way coupling would occur for weak concentration of the dispersed-phase, while two way coupling would occur for large concentrations, which is automatically taken care in the equation of the two-phase mixture given below: u = u α (4.84) m v s The conservation of mass of the mixture, given below, must be satisfied within the entire two-phase flow domain, as the dispersed-phase is diffused throughout the flow field: ρ m t + ( ρ u ) = 0 m m. (4.1)

141 Gas Entrainment Calculation The gas entrained into the liquid-phase below the GLCC inlet is the source of gas carry-under presented at the liquid outlet. It is difficult to determine this parameter even for plunging single-phase liquid jet. Different flow patterns may occur in the GLCC inlet, which strongly affect the gas entrainment mechanism. Hence, quantification of the amount of gas being entrained is dependent on the dominant flow pattern at the inclined inlet for a given flow condition. This is a weak link in the present model, since it is difficult to measure or predict it at the GLCC entrance. At the entrance region, most of the gas splits in a very chaotic manner with some re-mixing due to the swirling motion. Despite the difficulties in measuring or predicting the gas entrainment, a flow pattern dependant approach is proposed in the present study for its determination, as given next. When stratified flow occurs at the GLCC inlet, the liquid entering the GLCC behaves similarly to plunging liquid jet. One correlation, among many, has been selected and modified to be applied to the GLCC, as given below: q ge 3 / 1/ 3 hl v t is ( hinlet heq ) = 8.83 (4.85) Sin β where h inlet and h eq are the height below inlet and the equilibrium liquid level in the GLCC, respectively; h L is the liquid phase film thickness at the inlet slot, v tis is the tangential inlet slot velocity, and β is the inlet inclination angle. When slug flow occurs at the inlet, it is assumed that the source of gas entrainment is the gas bubbles already being carried in the slug body, as defined by the

142 17 liquid holdup in the slug. Thus, the correlation developed by Gomez et al. (000) can be used to determine the gas entrainment due to slugging, as given below: 6 (.4810 ) α = exp (4.86) slug Re LS where Re LS is calculated based on liquid properties (ρ L and µ L ), inlet diameter and mixture inlet velocity. Note that any other correlation for α slug can be used. 4.6 Swirling Flow Pattern Prediction Criteria The gas-core is formed due to the swirling motion of the mixture. Correlations for the gas core configurations are developed, as functions of the swirling flow or tangential velocity and the equilibrium liquid level in the GLCC. Visual observations of the gas-core in swirling two-phase flow have been used to classify the swirling two-phase flow pattern presented in the lower part of the GLCC Swirling Flow Patterns Four swirling two-phase flow patterns have been identified, namely, stable gas core-no bubble dispersion, whipping gas core-low bubble dispersion, weak gas core-high bubble dispersion and no gas core-high bubble dispersion (see section 3.1.3). The stability of the gas core has been selected in this study as a main mechanism of classifying the swirling flow pattern. The importance of the swirling flow pattern is its effect on the gas carry-under through the core region. Weak gas core promotes tiny bubble dispersion in the continuous swirling liquid, which could be dragged into the liquid outlet. On the other hand, stable gas core may stretch all the way to the liquid outlet with large gas core diameter. Under this condition, large gas carry-under may occur. Therefore, stability of the gas core and its characteristics represents an important key for

143 18 the gas carry-under mechanism. The stability of the core can be related to the Raleigh stability criteria, and the core shape can be related to spiral behavior of the turbulent kinetic energy, which is the driving mechanism of bubble dispersion. The Raleigh stability criterion is given below: d ( r u ) dr θ > 0. (4.87) When the above equation is satisfied, the gas core will be stable at location, r. Further simplification can be done for the case of the GLCC, including the tangential velocity correlation given in Eq resulting in the following equation: r r 4 r U av Tm B exp B 1 exp B 0. (4.88) R R The helical shape of the core can be defined by using Eq. 4.3, which also provides the helical shape of the turbulent kinetic energy Gas Core Diameter The diameter of the core can be determined similar to the analysis presented by Barrientos et. al (1993). The Young-Laplace equation can be used to define the normal stresses at the interface (jump conditions), as given below: liquid gas σ Tn n Tn n = (4.89) r= rc r= rc rc Assuming that the gas core interface rotates as a rigid body with an angular velocity ω 1, and that the normal stress at the inner side of the gas core is that of an ideal fluid, while at

144 19 the liquid side the normal stress can be expressed using the radial velocity gradient and the hydrostatic pressure, yielding: Tn n ur gas 1 = ρ L g z + and Tn n = P + = g ρ gω1 rc (4.90) r rc r liquid µ r= rc where σ is the surface tension, g the gravitational acceleration, z the axial position, rc the gas core radius and P g is the GLCC pressure. Combining Eqs 4.89 and 4.90, one can obtain the gas core diameter expression, as given below: 3 1 rc u r ( ) rc σ ρ g utw + = 0 µ L ρ L ρ g g z (4.91) Rsep r r= rc Rsep Rsep where u tw is the tangential velocity at the wall, calculated as suggested by Gomez et. al (1999), as follows: 3 u tw U = av Ω (4.9) The radial velocity gradient can be obtained from the velocity distribution given in Eqs Solving Eq. 4.91, one can obtain the gas core profile along the axial direction. 4.7 Dispersed Two-Phase Swirling Flow Solution Scheme The model building blocks, presented in sections 4.1 to 4.6, need to be integrated in order to predict the hydrodynamics of the swirling flow in the GLCC, and the resulting gas carry-under. Three approaches are proposed in this study, as given below: Eulerian-Lagrangian Diffusion approach, Lagrangian-Bubble Tracking approach Simplified Mechanistic Models for these two approaches.

145 Eulerian-Lagrangian Solution Scheme The process of the dispersed-phase motion described in previous sections applies to a given particle with a constant mass. As a consequence, the particle diameter that defines the interface would also remain constant. However, the turbulent dispersion and the presence of other particles promote distributions of bubbles of different sizes, through their interactions with each other and with the continuous flow. In the present model, this discrepancy is eliminated by means of coupling the Eulerian frame of the continuousphase to the Lagrangian description of the dispersed-phase through interfacial scale (bubble/droplet diameter), at any local position of the Eulerian domain. The dispersion mechanism is provided by the turbulence of the continuous-phase to determine the characteristic particle diameter present at any particular location of the Eulerian frame. Thus, the dispersed-phase model uses the characteristic particle diameter at the same location to calculate the particle (bubble/droplet) motion. The particle diameter distribution is related to the void fraction and interfacial area concentration. The void fraction provides the phase distribution whereas the interfacial area describes the available area for interfacial transfer of mass, momentum and energy. The interfacial area concentration concept accounts for the interface growth or decay due to the break-up and coalescence processes, defining the stable bubble diameter. However, since the continuous-phase changes along the Eulerian domain,

146 131 likewise does its dispersion mechanism; hence different bubble/droplet diameter and dispersed-phase motion can be obtained in the entire flow domain. The Eulerian-Lagrangian coupling is achieved through the dispersed-phase diffusion model, specifically through the relative velocity. This coupling allows determination of the void fraction distribution throughout the entire domain. The discussion given above justifies the reason for not including the turbulent dispersion force in the dispersed-phase flow field model. Instead, the turbulent characteristic of the continuous-phase is used as dispersion mechanism to obtain the stable bubble/droplet diameter. Solution Procedure: The following step-by-step procedure is suggested for determining the gas carry-under by using the Eulerian-Lagrangian solution scheme. Note that the fundamental derivation and pertinent equation for this procedure have already been given in previous sections. 1. Gas Entrainment : Boundary Condition at Top. Continuous-phase Velocity : Swirling Flow Correlations 3. Stable Bubble Diameter : Interfacial Area Equation 4. Particle Relative Velocities : Lagrangian Description of Particles 5. Void Fraction Distribution : Eulerian Diffusion Equation 6. Mixture Velocity Correction : Local Void Fraction 7. Gas Carry-under: Dispersed Mass Flux at Bottom The steps given above can be calculated in a straightforward manner, except for the dispersed-phase diffusion equation, which is discussed in greater details below.

147 13 Governing Equations of Dispersed-Phase Diffusion Model: The dispersedphase diffusion model is applied to the GLCC, assuming steady-state, no source or sink terms, and axisymmetric flow (Eq. 4.8). It is further simplified here by incorporating the coupling of the continuous-phase and the dispersed-phase, as follows: [ rα ρ d ( ur vsr )] [ α d ( u z vsz )] = 1 ρ + r r z 1 r (1 α) r ρ r α N + (1 α) α v (1 α) + z α N ρ + (1 α d sr d v sz ρ ) ρ α (4.93) where, N ρ is the density ratio given by N ρ = ρ d /ρ c. Dispersed-Phase Diffusion Equation Finite Volume Discretization: The governing equation (Eq. 4.93) presented above, can now be discretized in -D or 3-D to enable the determination of the void fraction distribution in the GLCC. Determination of the gas carry-under in the liquid stream can then be obtained by integrating the void fraction at the bottom of the GLCC. The governing equation is integrated over a control volume in order to apply the well-known finite volume method. The governing equation can be re-expressed in the general conservation form, in order to integrate it over control volume and then apply the numerical method based on this integration, namely, the Finite Volume Method, initially introduced by Patankar (1980), as follows:

148 133 SC ( φ u) da = ( Γ φ ). da B. dv ρ. + (4.94) SC VC where φ is the dependent transported variable, Γ is the diffusion coefficient, u is the velocity, and B is the source encompassing all the remaining terms. It can be observed that Eq is nonlinear with respect to the transported variable. This nonlinearity is approximately solved over the control volume by discretizing Eq and assigning the nonlinear term to the source term, B, as follows, VC B dv = SC α (1 α) ρ d v α N ρ + (1 α ) s da (4.95) The dispersed-phase diffusion model can be discretized in an axisymmetric coordinate element, as shown in Fig 4.8, and 3-D cylindrical coordinates, shown in Fig Figure 4.10 shows the control volume notation for the discretization. Figure 4.8 Axisymmetric Control Volume Element

149 134 Figure 4.9 Control Volume Element in Cylindrical Coordinates Figure 4.10 Control Volume Notation Boundary Conditions: Four boundary conditions are established, as follow: 1. Solid wall: no slip condition is specified. α = 0 (4.96) r=r &3. Inlet and Outlet boundaries are specified at top of the equilibrium liquid level in the GLCC, where z = 0, and at the bottom of the GLCC, where z = L. Due to the

150 135 complexity of the swirling flow field, both boundaries exhibit inflow as well as outflow, due to the presence of the reverse flow at core region around the axis. Under this condition, the fluid leaves the calculation domain near the GLCC axis and enters the calculation domain in the annular region near the wall. The flux is corrected to satisfy the overall mixture mass conservation. Thus, the boundary conditions set are zero gradient of the dependant variable across the cross-section of the GLCC: α z z= 0 = 0 α and = 0 z z=l (4.97) 4. Most of the correlations used in this model, namely, velocity profile and turbulent quantities of the continuous-phase, are axisymmetric, so that the dispersed-phase diffusion is driven as axisymmetric solution, too: α r r= 0 = 0 (4.98) Numerical Scheme: As shown in Fig. 4.10, the control volume is divided into adjacent control volumes, where the grid points are located at the center of the respective control volumes. Integration of the governing equation (Eqs ) over the control volume yields the general discretization equation, as given below Apα p = Anbα nb + B (4.99) A p = Anb + Fnb (4.100) Determination of the dependent variables and their respective derivatives at the faces of the control volume, in terms of the values of the variables at the grid point, is

151 136 carried out by assuming a profile between two adjacent grid points, utilizing an upwind differencing scheme for the convective term. Note that the value of A p is determined based on the values of the neighboring faces, A nb (A = ρ d v d ), adding the mixture mass balance term (F = ρ m u m, which should be zero) to enhance the convergence process. Also, the value of the source term, B, is calculated numerically by lagging, using the known parameters from the previous calculation step. The under-relaxation method is used to ensure that the numerical iteration converges, since the governing equation of the dispersed-phase diffusion equation exhibits high nonlinearity. Convergence Criteria: The mixture mass conservation equation is used as the convergence criteria over the control volume and the entire domain. This is done by considering the correction of the unperturbed continuous-phase velocity due the presence of the dispersed phase (two-way coupling). Interpolation at Control Volume Faces: Calculation of the convection flux at the control volume faces is carried out by interpolating the value of the term α(1-α), as suggested by Prado (1995). This enhances the numerical identification of the interface. Gas Carry-under Calculation: The gas void fraction in the liquid outlet and the gas carry-under flow rate can be finally determined by integration of the void fraction distribution at the bottom of the GLCC (z = L) as given, respectively, below: π R 0 0 α = z= L π R α( r,z )r dθ dr 00 r dθ dr (4.101)

152 137 g = v α( r, z) r dθ dr (4.10) GCU z= L π R 00 dz 4.7. Lagrangian Bubble Tracking Solution Scheme The movement of a particle (bubble/droplet) in a swirling flow field can be tracked by means of its relative velocity. The motion of the particle in terms of axial, radial and tangential velocity components are calculated based on Lagrangian description of the particle in an Eulerian frame. In this scheme no wall collisions are considered and only one bubble at a time is tracked in the flow domain. Also, no particle-particle collisions or coalescence are considered. Finally, the bubble/droplet diameter is assumed to remain constant along the entire path. Under the above assumptions, the bubble trajectory exhibits helicoidal path, shown in Fig. 4.11, as it travels within the swirling liquid flow. The path profile traveled by the bubble/droplet can be determined from the following equations, obtained from the dispersed-phase flow field model. Thus, the displaced distance of the bubble/droplet in the axial direction for each increment of r is given as follows: vdz u z vsz z = r r v = dr ur v (4.103) sr The displaced distance in the tangential direction is given by: ( uθ vsθ ) ( u v ) z θ = vd θ t = (4.104) r z sz

153 138 Finally, the helical position of the bubble/droplet can be obtained by adding the successive incremental distances in each coordinates, from the initial location where the bubble/droplet is released. r r r z = z θ = θ r = r (4.105) R R R The Lagrangian model solution for bubble tracking provides a rigorous bubble/droplet mapping, and allows determining whether or not any particular bubble is carried into the liquid (outlet) leg. If the bubble reaches the flow reversal region before reaching the bottom of GLCC, it would be separated. However, if the bubble does not make it to reverse flow region, it would be carried under into liquid stream. The following procedure is suggested to solve numerically the Lagrangian Bubble Tracking scheme. This method requires the number of bubbles to be tracked that can be obtained from the breakup frequency function. 1. Gas Entrainment : Boundary Condition at Top. Number of Bubbles at Inlet: Population Balance and Breakup Function 3. Particle Velocities : Lagrangian Description of Particles 4. Continuous-phase Velocity : Swirling Flow Correlations 5. Bubble Trajectory Tracking : Tracking each Bubble - Constant Diameter 6. Separation at Capture Radius : Bubbles Reaches Reverse Flow Region 7. Gas Carry -under: Population of Bubbles Carry-under

154 Figure 4.11 Schematic of Bubble Trajectory Path 139

155 Simplified Mechanistic Models for Predicting Gas Carry-under In this section, simplification of both the Eulerian-Lagrangian Model and the Lagrangian Bubble Tracking Model are carried out. These simplified models are much easier to solve and can be used for design purposes. Following are the calculation procedures for both simplified models. Simplified Method of Lagrangian-Eulerian Model Simplification of this model is performed by adopting a simple and straightforward numerical scheme, instead of the finite volume scheme. Thus, the calculation of the void fraction distribution (dispersed-phase diffusion model) is carried out only in the radial direction or cross-sectional plane, at each axial position. Hence, the simplified model avoids the long iterative procedure applied to the entire calculation domain, which is carried out in the rigorous Lagrangian-Eulerian model. After, the radial distribution is performed at z i, all parameters needed for the dispersed-phase diffusion model, namely, continuous-phase radial velocity and relative radial velocity for the next step, z i+1, are calculated utilizing the swirl decay. The diffusion in the axial direction is addressed by adopting relatively small values of z. This is justified since the hydrodynamics of the dispersed swirling flow in the radial direction is dominant in comparison to the one in the axial direction. Also, the values of the void fraction at the previous step, z i, are used as the initial guess for the z i+1 step. The calculation is continuously performed until z = L. Following is the calculation procedure:

156 Gas Entrainment : Boundary Condition at Top. Stable Bubble Diameter : Interfacial Area Equation 3. Particle Velocities : Lagrangian Description of Particles 4. Continuous-phase Velocity : Swirling Flow Correlations 5. Void Fraction Distribution : Eulerian Diffusion Equation-radial direction 6. Gas Carry Under: Dispersed Mass Flux at Bottom Simplified Method of Lagrangian Bubble Tracking Model The uncertainty of determining the numbers of bubbles is due to the stochastic models used, which includes the energy spectrum of turbulent characteristics. Thus, in the rigorous Lagrangian Bubble Tracking model, after the number of bubbles is determined, one needs to perform bubble trajectory for each bubble, which results in long computational time. Simplification of this model is performed by using a superposition method, where a particular minimum bubble diameter, d 100, which is tracked until it reaches the reverse flow region, before reaching the liquid outlet (z = L). Thus, bubbles smaller than d 100, are carry-under and larger than d 100, are separated. The amount of gas carry-under is determined using the breakup frequency function, and is given in Fig Integration over the curve given in the figure from d min (Eq. 4.8) to d 100, yields the amount of gas carry-under. When the continuous-phase is composed of oil-water mixture, due to different viscosities of each of the liquid phases (oil, water and oil-water mixture region), the bubble is exerted to different drag forces along its path. Thus, the bubble trajectory calculation for this case depends on the liquid-liquid distribution (see Fig. 4.13), which may introduce uncertainties in the calculation. Hence, the superposition method is also

157 Breakup Frequency (1/s) Gas Carry under d Bubble Diameter (micron) Figure 4.1 Amount of Gas Carry-under Determination used here, as follow. The d 100 calculation is performed three times separately, where it is determined for each liquid phases (oil, water and oil-water mixture region), as if it occupies the entire flow domain. Once the d 100 for water, oil and oil-water mixture are determined separately, a superposition method is carried out based on each of the liquid phase volume fraction. The mixture volume fraction, for the superposition calculations, is formed by mixing 50% volume of the oil and 50% of the water phases. Thus, the water and oil phases volume fraction is 50% of their original volume fraction.

158 143 Following is the calculation procedure for the simplified scheme: 1. Gas Entrainment: Boundary Condition at Top. Continuous-phase Velocity: Swirling Flow Correlations 3. Particle Velocities: Lagrangian Description of Particles 4. Separation at Capture Radius: Two- Phase Reversal Core 5. d 100 Bubble Diameter : BubbleTraj. for each Liq-Phase 6. Each Phase GCU d p < d 100: Breakup Frequency Function 7. Total Gas Carry Under: Superposition Method Wcut = 95% Vsg = 0.75 m/s Vm=0. m/s Vm=0.3 m/s Vm=0.4 m/s Vm=0.5 m/s Vm=0.6 m/s Figure 4.13 Oil-Water-Gas Distribution in GLCC (after Oropeza, 001) The building blocks and the different models for the prediction of gas carry-under in the GLCC have been presented in this chapter. Comparison between the models predictions and the experimental data for gas carry-under, which were given in Chapter 3, will be presented and discussed in the next chapter.

159 144 CHAPTER V SIMULATION AND RESULTS This chapter presents the results for the continuous-phase flow field, namely, the velocity profiles and the turbulent quantities. Also presented are the results of the void fraction distribution and gas carry-under predicted by the rigorous Eulerian-Lagrangian model. Finally, an example of the performance of the simplified mechanistic model for a field application is given. 5.1 Continuous-Phase Flow Field Comparison The local measurement data of Erdal (001) presented in chapter III have been used to develop correlations for swirling flow field and its associated turbulent quantities (see chapter IV). In this section, the developed correlations are tested against data from different studies Continuous-Phase Velocity Profiles The developed swirling flow velocity distribution correlations are given in section 4... These correlations for axial, tangential and radial velocity profiles are evaluated against data presented by Algifri (1988), Kitoh (1991) and Chang and Dhir (1994), using Erdal s (001) modification for the swirl intensity correlation. Mean Axial Velocity Profile: Figures 5.1 to 5.3 present comparisons between the developed correlation and experimental data for the mean axial velocity. Good agreement is observed between the data and the predictions.

160 Prediction: z/d = 0 Data: z/d = 0 Prediction: z/d = 7.5 Data: z/d = 7.5 u/uav r/r Figure 5.1 Mean Axial Velocity Comparisons for Algifri Data (1988) u/uav r/r model Z/D= 3.4 data Z/D= 3.4 model Z/D= 1.3 data Z/D= 1.3 model Z/D= 19 data Z/D= 19 Figure 5. Mean Axial Velocity Comparisons for Kitoh Data (1991)

161 146 M t /M T = u/uav model Z/D= data Z/D= model Z/D= data Z/D= 6.06 r/r Figure 5.3 Mean Axial Velocity Comparisons for Chang and Dhir Data (1994) Mean Tangential Velocity Profile: Comparisons between the developed correlation and experimental data for the mean tangential velocity are shown in Figs 5.4 to 5.7. Very good agreement is observed between the data and the predictions w/uav data z/d = 0 model z/d = 0 data z/d = 7.5 model z/d = r/r Figure 5.4 Mean Tangential Velocity Comparisons for Algifri Data (1988)

162 147 w/uav data z/d = 1.3 model z/d = 1.3 data z/d = 19 model z/d = 19 data z/d = 39 model z/d = r/r Figure 5.5 Mean Tangential Velocity Comparisons for Kitoh Data (1991) 7 M t /M T = w/uav data z/d = 6.06 model z/d = 6.06 data z/d = 8.06 model z/d = 8.06 data z/d = model z/d = r/r Figure 5.6 Mean Tangential Velocity Comparisons for Chang and Dhir Data (1994)

163 148 M t /M T = w/uav data z/d = 6 model z/d = 6 data z/d = 10 model z/d = 10 data z/d = 8 model z/d = r/r Figure 5.7 Mean Tangential Velocity Comparisons for Chang and Dhir Data (1994) Mean Radial Velocity Profile: Figures 5.8 to 5.10 present comparisons between the correlation for the mean radial velocity, developed in this study, against experimental data. The comparisons show fair agreement with respect to both trend and magnitude. 1.0E-03 v/uav 0.0E E E E E-03 model Z/D= 1.3 data Z/D= 1.3 model Z/D= 5.7 data Z/D= 5.7 r/r Figure 5.8 Mean Radial Velocity Comparisons for Kitoh Data (1991)

164 149 M t /M T = E E v/uav -5.0E E-0-1.5E-0 r/r model Z/D= 9 data Z/D= 9 model Z/D= 7 data Z/D= 7 Figure 5.9 Mean Radial Velocity Comparisons for Chang and Dhir Data (1994).E-03 M t /M T = E+00 -.E v/uav -4.E-03-6.E-03-8.E-03-1.E-0 model Z/D= 9 data Z/D= 9 r/r Figure 5.10 Mean Radial Velocity Comparisons for Chang and Dhir Data (1994)

165 Continuous-Phase Turbulent Quantities Turbulent Kinetic Energy: Figures 5.11 and 5.1 present the performance of the developed normalized turbulent kinetic energy correlation with the data of Erdal (001). Figure 5.11 gives the turbulent kinetic energy radial distribution at different axial position (corresponding to decaying swirling intensity). As can be seen, the developed correlation captures the physical phenomenon of the helical shifting of the maximum turbulent kinetic energy along the axis of the GLCC. Figure 5.1 presents the same comparison in contour plots form. Comparison between the entire Erdal (001) data and the developed correlation for the helical radial oscillation of the maximum turbulent kinetic energy around the GLCC axis, as function of the swirl intensity, is shown in Fig The figure demonstrates that for low swirl intensity, high fluctuations occur due to flow instability. However, as the swirl intensity increases the radial oscillation of the maximum turbulent kinetic energy decreases since the flow become more stable. Figures 5.14, 5.15 and 5.16 show the comparison of maximum and minimum magnitudes of the turbulent kinetic energy as function of swirl intensity and Reynolds number. Figure 5.14 shows the comparison for low Reynolds numbers at low swirl intensity, while Fig shows the comparison for high Reynolds numbers. Comparison of the turbulent kinetic energy for the same value of Mt/M T = 10.88, for both low and high Reynolds numbers, is presented in Fig Excellent performance is observed in all three figures. Finally, the developed correlation for the turbulent kinetic energy is compared against the data of Kitoh (1991). Note that these data have not been used in the

166 151 correlation development. As can be seen the correlation performed well against the additional data, capturing the decay of the turbulent kinetic energy as the swirl intensity tends to zero. Data Re = 5488 M t /M T =.5.0 K/U av r/r Swirl I t it Prediction Re = 5488 M t /M T =.5.0 K/U av Swirl Intensity r/r Figure 5.11 Comparison of Turbulent Kinetic Energy Radial Distribution

167 15 Data Prediction k/uav X (mm) R (mm) k k/uav Figure 5.1 Contour Plot Comparison of Turbulent Kinetic Energy Radial Distribution

168 Erdal Data Prediction rshift/r Swirl Intensity Figure 5.13 Comparison of Helical Radial Oscillations of the Maximum Turbulent Kinetic Energy with Swirl Intensity Re 9137 Mt/MT 5.44 Kmax Kmin 0.50 k/u av Swirling Intensity Figure 5.14 Maximum and Minimum Turbulent Kinetic Energy Comparison Low Swirling intensity

169 154 K/U av Kmax Kmin Re 5488 Mt/MT 5.44 Kmax Kmin Re 5488 Mt/MT Swirling Intensity Figure 5.15 Maximum and Minimum Turbulent Kinetic Energy Comparison Different M t /M T Kmax Kmin Re 9137 Mt/MT Kmax Kmin Re 5488 Mt/MT K/U av Swirling Intensity Figure 5.16 Maximum and Minimum Turbulent Kinetic Energy Comparison Low and High Reynolds Number

170 Mt/MT 1 Re Kmax Kmin 0.0 k/u av Swirling Intensity Figure 5.17 Turbulent Kinetic Energy Comparison between Correlation and Kitoh (1991) Data Reynolds Shear Stresses: Comparisons between the developed correlations for the three Reynolds shear stress components and experimental data are presented in this section in Figures 5.18 to 5.4. As can be seen, the good performance of the correlations confirm that the location and the maximum value of the tangential velocity are indeed the proper correlating parameters for the Reynolds shear stress correlations, as proposed in this study. u' v' Component: Figures 5.18 and 5.19 present the comparison of the correlation for this component with Kitoh (1991) and Chang and Dhir (1994) data, respectively, showing a good performance.

171 Data: z/d = 3.0 Prediction: z/d =3.0 Data: z/d = 19.0 Prediction: z/d = Prediction: z/d = 5.7 Data: z/d = 5.7 Data: z/d = Prediction: z/d = 1.3 -u'v'/u av r/r Figure 5.18 Reynolds Shear Stress u 'v' Comparison with Kitoh (1991) Data

172 157 -u'v'/u av Mt/MT = 7.84 Data: z/d = 10 Prediction: z/d = 10 Data: z/d =9 Prediction: z/d = 9 Data: z/d = 8 Prediction: z/d = 8 Data: z/d = 7 Prediction: z/d = 7 Data: z/d = 6 Prediction: z/d = r/r Figure 5.19 Reynolds Shear Stress u'v' Comparison with Chang and Dhir (1994) Data

173 158 u' w' Component: Comparisons of the correlation for this component with the data of Kitoh (1991), Chang and Dhir (1994) and Erdal (001) are shown in Figs. 5.0, 5.1 and 5., respectively. The performance for this component, as shown in the figures, is fairly good u'w'/u av Data: z/d = 1.3 Prediction: z/d = 1.3 Data: z/d = 5.7 Prediction: z/d = 5.7 Data: z/d = 19 Prediction: z/d = r/r Figure 5.0 Reynolds Shear Stress u 'w' Comparison with Kitoh (1991) Data

174 Mt/MT = 7.84 Data: z/d = 6 Prediction: z/d = 6 Data: z/d = 7 Prediction: z/d = 7 Data: z/d = 8 Prediction: z/d = 8 Data: z/d = 9 Prediction: z/d = 9 Data: z/d = 10 Prediction: z/d = 10 -u'w'/u av r/r Figure 5.1 Reynolds Shear Stress u 'w' Comparison with Chang and Dhir (1994) Data

175 160 Mt/MT = Data: z/d = 4.4 Prediction: z/d = 4.4 Data z/d = 5.8 Prediction: z/d = 5.8 Data: z/d = 10 Prediction: z/d = 10 -u'w'/u av r/r Figure 5. Reynolds Shear Stress u 'w' for Erdal (001)

176 161 v' w' Component: The comparison between the prediction for this component with Kitoh (1991) and Chang and Dhir (1994) data are shown in Figs. 5.3 and 5.4, respectively, showing the same good agreement, as for the other components v'w'/u av Data: z/d = 5 Prediction: z/d = 5 Data: z/d = Prediction: z/d = 19 Data: z/d = 5.7 Prediction: z/d = 5.7 Data: z/d = 1.3 Prediction: z/d = 1.3 r/r Figure 5.3 Reynolds Shear Stress v 'w' Comparison with Kitoh (1991) Data

177 16 Mt/MT = v'w'/u av r/r Prediction: z/d = 10 Data: z/d = 9 Data: z/d = 9 Prediction: z/d = 8 Prediction: z/d = 8 Data: z/d = 7 Prediction: z/d = 7 Data: z/d = 6 Prediction: z/d = 6 Data: z/d = 10 Figure 5.4 Reynolds Shear Stress v 'w' Comparison with Chang and Dhir (1994) Data

178 Eulerian-Lagrangian Model Void Fraction Distribution Simulation Results Figure 5.5 shows the simulation results for the rigorous Eulerian-Lagrangian scheme, conducted for a 3-inch ID 8 ft tall GLCC, with a length of 4 ft below the inlet, flowing air and water at standard conditions. The flow rates of the gas and the liquid are 54 Mscf/d and 303 bbl/d, respectively. Shown is the void fraction distribution from a - D simulation, with an initial void fraction of α i = 0.45, inlet tangential velocity of 15 ft/s and axial velocity of 0.6 ft/s. The calculated cross sectional area average void fraction at the bottom of the GLCC is α = 0.1. The calculated gas carry-under flow rate is 0.1 Mscf/d, corresponding to 0.04% of gas carry-under with respect to the inlet gas flow rate. Inlet Outlet Center Wall Figure 5.5 Simulation Results for Void Fraction Distribution