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

2001

iii

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, 1994.

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• 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.

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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.

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TABLE OF CONTENTS

TITLE PAGE i

APPROVAL PAGE ii

ABSTRACT iii

ACKNOWLEDGMENTS v

TABLE OF CONTENTS vi

LIST OF FIGURES ix

LIST OF TABLES xv

CHAPTER I: INTRODUCTION 1

CHAPTER II: LITERATURE REVIEW 5

2.1 Experimental Work and Applications 5

2.2 Mechanistic Modeling 9

2.3 CFD Simulations 10

2.4 Swirling Flow and Local Measurements 13

CHAPTER III: EXPERIMENTAL PROGRAM 17

3.1 Gas Carry-under Experimental Program 17

3.1.1 Gas Carry-under Measurements GLCC Test Facility 17

3.1.2 Gas Carry-under Experimental Results 20

3.1.3 Two-Phase Swirling Flow Visualization 27

3.2 GLCC Swirling Flow Local Measurements 36

3.2.1 Local Measurement GLCC Test Section 36

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3.2.2 GLCC Local Measurement Results 38

3.3 Straight Pipe Swirling Flow Local Measurements 66

3.3.1 Straight Pipe Swirling Flow Field Analysis 67

3.3.2 Straight Pipe Swirling Flow Turbulent Quantities 75

CHAPTER IV: DISPERSED SWIRLING FLOW MECHANISTIC MODEL 89

4.1 Dispersed-Phase Mass Diffusion Model 89

4.1.1 Two-Phase Flow Models 90

4.1.2 Diffusion (Mixture) Model 90

4.2 Continuous-phase Flow Field Model 87

4.2.1 Swirl Intensity Decay Number 88

4.2.2 Swirling Flow Velocity Distribution 96

4.2.3 Continuous-Phase Turbulent Quantities Correlations 99

4.3 Dispersed-Phase Flow Field Model 108

4.3.1 Dispersed-Phase Particle Velocities 114

4.3.2 Stable Bubble Diameter 116

4.4 Mixture Velocity Field 124

4.5 Gas Entrainment Calculation 125

4.6 Swirling Flow Pattern Prediction Criteria 126

4.6.1 Swirling Flow Patterns 126

4.6.2 Gas Core Diameter 127

4.7 Dispersed Two-Phase Swirling Flow Solution Scheme 128

4.7.1 Eulerian-Lagrangian Solution Scheme 129

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4.7.2 Lagrangian – Bubble Tracking Solution Scheme 136

4.7.3 Simplified Mechanistic Models for Predicting Gas Carry-under139

CHAPTER V: SIMULATION AND RESULTS 143

5.1 Continuous-Phase Flow Field Comparison 143

5.1.1 Continuous-Phase Velocity Profiles 143

5.1.2 Continuous-Phase Turbulent Quantities 149

5.2 Eulerian-Lagrangian Void Fraction Distribution Simulation Results 162

5.3 Performance of Simplified Mechanistic Models 163

5.4 Comparison between Simplified Mechanistic Model Predictions and

Air-Oil Flow Experimental Results 165

CHAPTER VI: CONCLUSIONS AND RECOMMENDATIONS 171

NOMENCLATURE 174

REFERENCES 179

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LIST OF FIGURES

Figure 1.1 Bulk Separation/Metering Loop for Minas-Indonesia 2

Figure 3.1 Schematic of Metering Section 18

Figure 3.2 Schematic of GLCC Test Section 19

Figure 3. 3 Percentage of Gas Carry-under in the GLCC 22

Figure 3.4 Void Fraction in the Liquid Leg of the GLCC 22

Figure 3.5 Tangential Inlet Slot Liquid Velocity 23

Figure 3.6 Tangential Inlet Slot to Axial Liquid Velocity Ratio 23

Figure 3.7 Experimental Data for Amount of Gas Carry-under (GCU) for Air-Oil

System 26

Figure 3.8 Experimental Data for Percent Gas Carry-under (PGCU) for Air-Oil System 26

Figure 3.9 Dye Injection at Wall and at the Center of the GLCC 27

Figure 3.10 Vortex Interface at the Inlet of GLCC 28

Figure 3.11 Two-Phase Swirling Flow Pattern Visualization Facility 29

Figure 3.12 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 32

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

x

Figure 3.17 Schematic of GLCC Test Section for Local Measurements (Erdal, 2000) 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 3.20 Axial Velocity for Single Inclined Gradually Reducing Nozzle Area Inlet

Configuration 41

Figure 3.21 Tangential Velocity for Single Inclined Gradually Reducing Nozzle Area Inlet

Configuration 42

Figure 3.22 Effect of Reynolds Number on Axial Velocity Profile 45

Figure 3.23 Effect of Reynolds Number on Tangential Velocity Profile 45

Figure 3.24 Variation of Axial Velocity Profile with Axial Position 46

Figure 3.25 Variation of Tangential Velocity Profile with Axial Position 46

Figure 3.26 Axial Velocity of Dual Inclined Inlet Configuration 48

Figure 3.27 Tangential Velocity of Dual Inclined Inlet Configuration 49

Figure 3.28 Turbulent Kinetic Energy for Single Inclined Full Bore Area Inlet

Configuration 53

Figure 3.29 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 3.32 Axial Normal Reynolds Stress Distribution, after Erdal (2001) 58

Figure 3.33 Tangential Normal Reynolds Stress Distribution, after Erdal (2001) 58

Figure 3.34 Turbulent Kinetic Energy Distribution, after Erdal (2001) 59

Figure 3.35 Reynolds Shear Stress Distribution, after Erdal (2001) 59

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Figure 3.36 Axial Normal Reynolds Stress Distribution, after Erdal (2001) 60

Figure 3.37 Tangential Normal Reynolds Stress Distribution, after Erdal (2001) 60

Figure 3.38 Turbulent Kinetic Energy Distribution, after Erdal (2001) 61

Figure 3.39 Reynolds Shear Stress Distribution, after Erdal (2001) 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 3.42 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) 72

Figure 3.51 Tangential Velocity Distribution After Algifri (1988) 73

Figure 3.52 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

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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 3.62 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) 82

Figure 3.65 Reynolds Shear Stress ''wu Distribution After Algifri (1988) 83

Figure 3.66 Reynolds Shear Stress ''vu− Distribution After Algifri (1988) 84

Figure 3.67 Reynolds Shear Stress ''wv− Distribution After Algifri (1988) 84

Figure 3.68 Reynolds Shear Stress ''wu Distribution After Kitoh (1991) 85

Figure 3.69 Reynolds Shear Stress ''vu− Distribution After Kitoh (1991) 85

Figure 3.70 Reynolds Shear Stress ''wv− Distribution After Kitoh (1991) 86

Figure 3.71 Reynolds Shear Stress ''wu− Distribution After Chang and Dhir (1994) 86

Figure 3.72 Reynolds Shear Stress ''vu− Distribution After Chang and Dhir (1994) 87

Figure 3.73 Reynolds Shear Stress ''wv− Distribution After Chang and Dhir (1994) 87

Figure 4.1 Schematic of the Swirling flow field and GLCC Coordinate System 94

Figure 4.2 Variation of Turbulent Kinetic Energy along Axial Direction 103

Figure 4.3 Turbulent Kinetic Energy Prediction 105

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Figure 4.4 Drag Coefficient Correlations Comparison 111

Figure 4.5 Breakup Frequency Function 119

Figure 4.6 Bubble Coalescence Frequency Function 122

Figure 4.7 Breakup and Coalescence Frequency Events – Stable Diameter 123

Figure 4.8 Axisymmetric Control Volume Element 132

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 4.12 Amount of Gas Carry-under Determination 141

Figure 4.13 Oil-Water-Gas Distribution in GLCC (after Oropeza, 2001) 142

Figure 5.1 Mean Axial Velocity Comparisons for Algifri Data (1988) 144

Figure 5.2 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 5.12 Contour Plot Comparison of Turbulent Kinetic Energy Radial Distribution151

xiv

Figure 5.13 Comparison of Helical Radial Shifting of the Maximum Turbulent

Kinetic Energy with Swirl Intensity 152

Figure 5.14 Maximum and Minimum Turbulent Kinetic Energy Comparison–Low

Swirling intensity 152

Figure 5.15 Maximum and Minimum Turbulent Kinetic Energy Comparison – Different

Mt/MT 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 ''vu for Kitoh (1991) Data 155

Figure 5.19 Reynolds Shear Stress ''vu for Chang and Dhir (1994) Data 156

Figure 5.20 Reynolds Shear Stress ''wu for Kitoh (1991) Data 157

Figure 5.21 Reynolds Shear Stress ''wu for Chang and Dhir (1994) Data 158

Figure 5.22 Reynolds Shear Stress ''wu for Erdal (2001) 159

Figure 5.23 Reynolds Shear Stress ''wv for Kitoh (1991) Data 160

Figure 5.24 Reynolds Shear Stress ''wv for Chang and Dhir (1994) Data 161

Figure 5.25 Simulation Results for Void Fraction Distribution 162

Figure 5.26 Bubble Trajectory of d100 for High Pressure CESSI Data 164

Figure 5.27 Overall Performance of Simplified Bubble-Tracking model 167

Figure 5.28 Experimental Void Fraction Results in Liquid Leg 169

Figure 5.29 Predicted Void Fraction Results in Liquid Leg 169

Figure 5.30 Deviation of Experimental and Predicted Void Fractions in Liquid Leg 170

xv

LIST OF TABLES

Table 3.1 Experimental Results of Gas Carry-under for Air-Oil System 24

Table 4.1 Reynolds Stress Coefficients 100

Table 5.1 Simulation Results for Lagrangian-Bubble Tracking for High Pressure Data 164

Table 5.2 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

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).

2

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 20-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

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 carry-

over (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

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.

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.

2.1 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.

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 gas-

liquid 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 25% 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

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

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 (2001) 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 24 different axial locations (12.5″

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 72, 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 (2001) did not develop any correlation for turbulent quantities. In this study Erdal’s

data will be used to develop correlation for the turbulent quantities.

2.2 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

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 one-

dimensional 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.

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.

2.3 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

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.

12

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. (2001) 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 (2-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

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 (2001).

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 carry-

under. These include bubble size, ratio of the GLCC© length below the inlet to diameter,

viscosity, Reynolds number, and inlet tangential velocity.

2.4 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

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 free-

vortex 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

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

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.

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.

3.1.1 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.

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.

Figure 3.1 Schematic of Metering Section

GLCC Test Section: The test section consisting of a GLCC separator, as shown

in Figure 3.2, is divided into 4 parts:

1. The modular dual inlet section;

2. 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.

T P

P TT

P TT

Air

Water

To Test Section

From Test SectionSeparator

Turbine Meter

Orifice Meter

Temperature Transducer

MicroMotion Meter

Data Acquisition System

Water TankBall Valve

Regulating Valve

Check Valve

Pressure Gauge

19

Figure 3.2 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 25% 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 2” 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.

TWO-PHASEINLET

TWO-PHASEOUTLET

GAS TRAP

LIQUID TRAP

GLCC

RECOMBINATIONPOINT

SAMPLING

MODULAR INLET

MICROMOTION

20

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 carry-

under.

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.

3.1.2 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

21

106 (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 < vsl < 0.7 ft/s. Similarly,

for the same set of data, the no-slip void fraction in the liquid leg is reported in Fig. 3.4.

For completeness of the data reporting, Figs. 3.5 and 3.6 provide, respectively, the

prediction of the tangential inlet slot liquid velocity (vt, is) and the corresponding initial

tangential to axial momentum ratio (vt, is / vsl) for the air-water data. The results are

predicted using the inlet analysis model developed by Gomez et al. (2001). 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, vsl > 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 (vt, is / vsl). A clear pattern is

observed, where the ratio is maximum at low superficial liquid velocities (equal to 40 at

vsl = 0.25 ft/s), and decreases as the superficial liquid velocity increases (reaching a value

of 15 for vsl > 0.75 ft/s). One must realize that the high values of vt, is / vsl 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.

22

Figure 3.3 Percentage of Gas Carry-under in the GLCC

Figure 3.4 Void Fraction in the Liquid Leg of the GLCC

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 4 8 12 16 20 24 28 32 36

Vsg (ft/s)

Vsl (

ft/s)

0.059

(4.4 - 34)

0.048(4.1 - 40) 0.077

(3.9 - 93)

0.469(3.6 - 44)

0.318(3.5 - 57)

0.242(3.5 - 71)

0.221(3.6 - 99)

0.073(3.3, 166)

0.141

(3.5 - 176)

0.204(3.3 - 214)

0.110(3.3 - 260)

0.157(3.3 - 416)

0.287(3.1 - 446)

0.004(2.9 - 1137)

0.302(3.2 - 347)0.327

(3.3 - 314)

0.006(3.2 - 612)

0.018(3.3 - 397)0.062

(3.3 - 293)0.306

(3.4 - 141)

Operational Envelope

Percent Gas Carry-Under in 3-3S GLCC(without Mesh)

%PGCU *103

(Level - GLR)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 4 8 12 16 20 24 28 32 36

Vsg (ft/s)

Vsl (

ft/s)

0.059

(0.00028)0.048

(0.00029) 0.077

(0.00098)

0.469(0.00359)

0.318(0.00328)

0.242(0.00312)

0.221(0.00357)

0.073( 0.00142)

0.141

(0.00363)

0.204(0.00703)

0.110(0.00387)

0.157(0.00665)

0.287(0.01054)

0.004(0.00063)

0.302(0.01437)0.327

(0.01332)

0.006(0.00062)

0.018(0.00124)0.062

(0.00328)0.306

(0.00762)

Operational Envelope

Percent Gas Carry-Under in 3-3S GLCC(without Mesh)

%PGCU *103

(No Slip Void Fraction (%))

3” ID GLCC

P = 20 psia

Air - Water

3” ID GLCC

P = 20 psia

Air - Water

23

Figure 3.5 Tangential Inlet Slot Liquid Velocity

Figure 3.6 Tangential Inlet Slot to Axial Liquid Velocity Ratio

24

Air-Oil Experimental Data: A total of 20 runs have been conducted for air-oil

flow. A mineral oil was used, with a specific gravity of 0.845 and viscosity ranging from

20 to 25 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

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 air-

water GCU results, shown in Fig. 3.3. Three GCU regions are observed, with respect to

the superficial liquid velocity, as follows: For low liquid flow rates, vsl < 0.3 ft/s, the

GCU values are low, while the highest GCU occurs in the region 0.3 ft/s < vsl < 0.7 ft/s.

Run p T µ µ µ µ qgas

No ft/s ft/s psia oF cp bbl/D Mscf/D scf/D PGCU %1 2.0 0.4 23.9 79.0 25.0 302.1 13.3 9.48 0.07132 2.0 0.6 23.5 79.0 25.0 453.2 13.1 5.75 0.04393 2.0 0.8 24.0 75.6 26.7 604.2 13.4 6.01 0.04474 2.0 1.0 24.0 76.0 26.5 755.3 13.4 10.87 0.08095 4.0 0.2 23.9 80.0 24.6 151.1 26.6 3.54 0.01336 4.0 0.4 23.6 79.5 24.8 302.1 26.3 10.91 0.04167 4.0 0.6 23.6 80.6 24.3 453.2 26.2 9.88 0.03778 4.0 0.8 24.0 82.6 23.4 604.2 26.5 6.06 0.02289 4.0 0.9 24.0 83.7 22.9 679.8 26.5 5.67 0.0214

10 8.0 0.2 23.7 84.5 22.5 151.1 52.2 3.36 0.006411 8.0 0.4 23.8 82.7 23.3 302.1 52.6 8.96 0.017012 8.0 0.6 23.7 82.8 23.3 453.2 52.4 9.84 0.018813 8.0 0.8 24.0 83.2 23.1 604.2 53.0 7.31 0.013814 12.0 0.2 24.0 82.0 23.6 151.1 79.7 4.77 0.006015 12.0 0.4 24.1 84.9 22.4 302.1 79.6 12.31 0.015516 12.0 0.6 24.2 85.7 22.0 453.2 79.8 10.37 0.013017 12.0 0.8 24.0 86.4 21.7 604.2 79.1 9.21 0.011618 16.0 0.2 24.4 84.9 22.4 151.1 107.5 7.31 0.006819 16.0 0.4 24.4 86.4 21.7 302.1 107.2 12.40 0.011620 16.0 0.6 24.6 86.7 21.6 453.2 108.0 15.68 0.0145

vsg vsl qo Measured GCU

25

For higher superficial liquid velocities, vsl > 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, vsl < 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 < vsl < 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,

vsl > 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.

26

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

27

3.1.3 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.

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.

Single-Phase Dye InjectionNear the Wall, Downward Flow(Vsl= 0.83 ft/s, Vsg= 0.0 ft/s)12” Below Inlet

Two-Phase Dye Injectionat the Center, Upward Flow(Vsl= 1.53 ft/s, Vsg= 8.9 ft/s)24” Below Inlet

(b) Two - Phase

Dye Injection 24” Below Inlet at Pipe center

Vsl = 1.53 ft/s

(a) Single - Phase

Dye Injection 12” Below Inlet Near the Wall

Vsl = 0.83 ft/s

28

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. 3.11. Figures 3.12 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.

Single-Phase(Vsl= 0.83 ft/s, Vsg= 0.0 ft/s)

Two-Phase(Vsl= 1.53 ft/s, Vsg= 6.89 ft/s)

(b) Two –

Phase Vsl = 1.53 ft/s

V 6 89 ft/

(a) Single –

Phase Vsl = 0.83 ft/s

V 0 0 ft/

29

Figure 3.11 Two-Phase Swirling Flow Pattern Visualization Facility

Stable Gas Core - No Bubble Dispersion: Figure 3.12 shows that for vsl = 1.2ft/s

and vsg = 2.5 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 vsl = 0.7 ft/s and vsg = 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, breaking-

up 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

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 vsl = 0.4 ft/s and vsg = 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 vsl = 0.2 ft/s

and vsg = 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. 3.16. 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.

31

Figure 3.12 Two-Phase Swirling Flow Pattern: Stable Gas Core - No Bubble

Dispersion

32

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

Dispersion

33

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

34

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

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 5 10 15 20 25

Vsg [ft/s]

Vsl

[ft/s

]

No Gas Core

Weak Gas Core

Liquid Carry Over Region

Whipping Gas Core

Stable Gas Core

NBD

LBDLBD

HBD

HBD

HBD

HBD

HBD

3" ID GLCC P = 20 psia Air-Water

Legend: B : Bubble D : Dispersion H : High N : No L : Low

Large Bubble Size

Large Bubble Size

Large Bubble Size

Small Bubble Size

Small Bubble Size

Small Bubble Size

Figure 3.16 Experimental Swirling Two-Phase Flow Pattern Map

36

3.2 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 (2001) 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 (2001) only with respect to the flow field. However,

neither analysis nor correlations development for the turbulent quantities were conducted.

Thus, the Erdal (2001) 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.

3.2.1 Local Measurements in GLCC Test Section

Experimental studies were conducted by Erdal (2001) 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. 3.17. Single-phase liquid, either water (1 cp) or water-glycerin

mixture (7 cp) were used in the experimental program. The liquid flow rates were 72, 30

and 10 gpm, which correspond to Reynolds numbers of 66900, 27900 and 9290,

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

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 12.5 in. to 35.4 in. below the inlet, as shown in Fig 3.17. A total of 24

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.

LDV Measurement Plane

Top View

Inlet

3.5″

1.25″

2″

Outlet

x

4.8′

Side View

Inlet

Outlet

FlowDirection

12.5″

35.4″

LDV Measurement Plane

Top View

Inlet

3.5″

1.25″

2″

Outlet

x

4.8′

Side View

Inlet

Outlet

FlowDirection

12.5″

35.4″

x

4.8′

Side View

Inlet

Outlet

FlowDirection

12.5″

35.4″

Figure 3.17 Schematic of GLCC Test Section for Local Measurements (Erdal, 2001)

38

3.2.2 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, 3.20, and 3.21 show contour plots, normalized

with respect to Uav, of the axial and tangential velocity distributions measured at 24 axial

locations below the GLCC inlet.

The axial velocity contour plots, Figs. 3.18 and 3.20, 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. 3.19 and 3.21, 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.

39

Figure 3.18 Axial Velocity for Single Inclined Full Bore Area Inlet Configuration (Erdal, 2001)

40

Figure 3.19 Tangential Velocity for Single Inclined Full Bore Area Inlet Configuration (Erdal, 2001)

41Figure 3.20 Axial Velocity for Single Inclined Gradually Reducing Nozzle Area Inlet Configuration (Erdal, 2001)

42Figure 3.21 Tangential Velocity for Single Inclined Gradually Reducing Nozzle Area Inlet Configuration (Erdal, 2001)

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. 3.20 and

3.21) 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. 3.18 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 (2001) did not consider the effect of inlet inclination

angle, since the downward angle of 27o 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

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 3.22 and 3.23 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 3.24 and 3.25,

respectively. Since Erdal (2001) 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 3.22 and 3.23, 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.

3.24 and 3.25. 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.

45

Figure 3.22 Effect of Reynolds Number on Axial Velocity Profile

Figure 3.23 Effect of Reynolds Number on Tangential Velocity Profile

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

r /R

u/U

av

Re = 55000Re = 9200

z/d = 3.6

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

r/R

w/U

av

Re = 55000Re = 9200

z/d = 3.6

46

Figure 3.24 Variation of Axial Velocity Profile with Axial Position

Figure 3.25 Variation of Tangential Velocity Profile with Axial Position

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

r/Ru/

Uav

z/d = 3.6z/d = 5.4z/d = 6.7z /d = 8.5z/d = 10.1

Re = 55000

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

r/R

w/U

av

Z/d = 3.6z/d = 5.4z/d = 6.7z/d = 8.5z/d = 10.1

Re = 55000

47

Flow Field for Dual Inclined Inlet: The local experimental measurements

presented by Erdal (2001) 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 3.26 presents axial velocity contours for flow rates of 72

and 10 gpm for the dual inclined inlet. Both plots show a nearly axisymmetric flow field.

Surprisingly, the 72 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 3.27. 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.

48

Figure 3.26 Axial Velocity of Dual Inclined Inlet Configuration (Erdal, 2001)

49Figure 3.27 Tangential Velocity of Dual Inclined Inlet Configuration (Erdal, 2001)

50

Turbulent Quantities: The two- component LDV system used by Erdal (2001),

is also capable of determining the standard deviation of the sampled data, which

represents the turbulent fluctuations ( 2)u( ′ and 2)w( ′ ). The statistical quantities

such as the mean velocity ( v ) and the standard deviation ( νσ ) of the data are calculated

with the equations given below:

ΤΤ

=v

v (3.1)

−

ΤΤ

= 2

2

vv

νσ (3.2)

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:

′+′=′ 222 )w()u(21)v( (3.3)

′+′+′= 222 )()()(21 wvuk (3.4)

51

Contour Plots: The calculated turbulent kinetic energy, k, (Equations 3.3 and 3.4)

distributions, normalized with 2avU , are presented in contour plots in Fig. 3.28, 3.29, 3.30

and 3.31. 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. 3.28

and 3.29. 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 carry-

over, 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

52

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. 3.31 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 single-

phase 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

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.

54Figure 3.28 Turbulent Kinetic Energy for Single Inclined Full Bore Area Inlet Configuration (Erdal, 2001)

55

Figure 3.29 Turbulent Kinetic Energy for High Viscosity Single Full Bore Area Inlet Configuration (Erdal, 2001)

56

Figure 3.30 Turbulent kinetic Energy for Gradually Reducing Inlet Nozzle Configuration (Erdal, 2001)

57Figure 3.31 Turbulent Kinetic Energy of Dual Inclined Inlet Configuration (Erdal, 2001)

58

Turbulent Intensities: Figures 3.32, 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 = 9200 and Re = 55000. Figures 3.32 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. 3.34 exhibits

similar behavior. The two-component LDV system used by Erdal (2001) enables

measurement of only one component of the Reynolds shear stress, namely, ''wu− , as

given in Fig 3.35. 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

3.39. The axial and tangential normal Reynolds stresses are presented in Figs. 3.36 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. 3.38 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.

59

Figure 3.32 Axial Normal Reynolds Stress Distribution, after Erdal (2001)

Figure 3.33 Tangential Normal Reynolds Stress Distribution, after Erdal (2001)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1r/R

Re = 55000Re = 9200

av

2

U)u( ′′′′

z/d = 3.6

0

0.2

0.4

0.6

0.8

1

1.2

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1r/R

Re = 55000Re = 9200

av

2

U)w( ′′′′

z/d = 3.6

60

Figure 3.34 Turbulent Kinetic Energy Distribution, after Erdal (2001)

Figure 3.35 Reynolds Shear Stress Distribution, after Erdal (2001)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1r/R

k/U

av2

Re = 55000Re = 9200

z/d = 3.6

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

r/R

u'w

'/Uav

2

Re = 55000Re = 9200

z/d = 3.6

61

Figure 3.36 Axial Normal Reynolds Stress Distribution, after Erdal (2001)

Figure 3.37 Tangential Normal Reynolds Stress Distribution, after Erdal (2001)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

r/R

z/d = 3.6z/d = 5.4z/d = 6.7z/d = 8.5z/d = 10.1

av

2

U)u( ′′′′

Re = 55000

0

0.2

0.4

0.6

0.8

1

1.2

1.4

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1r/R

z/d = 3.6z/d = 5.4z/d = 6.7z/d = 8.5z/d = 10.1

av

2

U)w( ′′′′

Re = 55000

62

Figure 3.38 Turbulent Kinetic Energy Distribution, after Erdal (2001)

Figure 3.39 Reynolds Shear Stress Distribution, after Erdal (2001)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1r/R

k/U

av2

z/d = 3.6z/d = 5.4z/d = 6.7z/d= 8.5z/d = 10.1

Re = 55000

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

r/R

u'w

'/Uav

2

z/d = 3.6z/d = 5.4z/d = 6.7z/d = 8.5z/d = 10.1

Re = 55000

63

High Viscosity Effects: In order to understand the effect of Reynolds number

and viscosity on the flow field in the GLCC, Erdal (2001) 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 Uav. 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 2300, when the swirling flow is present.

Turbulent kinetic energy, k, profiles, normalized with 2avU , are plotted in Figure

3.42. 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 (2001) observed that for 10 gpm (7cp),

k/ 2avU is nearly uniform and is equal to 0.2. 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.

64

Figure 3.40 Axial Velocity Comparison for Single Inclined Full Bore Area Inlet Configuration (Erdal, 2001)

65

Figure 3.41 Tangential Velocity Comparison for Single Inclined Full Bore Area Inlet Configuration (Erdal, 2001)

66

Figure 3.42 Turbulent Kinetic Energy Comparison for Single Inclined Full Bore Area Inlet Configuration (Erdal, 2001)

67

3.3 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

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.

3.3.1 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 (2001) 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 Uav, 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.

69

Axial Velocity DistributionRe = 1.7x104-1.55x105

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

0.00 0.20 0.40 0.60 0.80 1.00

r/R

u/U

av

z/d = 0,z/d = 0,z/d = 0,z/d = 0,z/d = 50,z/d = 50,

Figure 3.43 Axial Velocity Distribution After Algifri (1988)

Figure 3.44 Axial Velocity Distribution After Kitoh (1991)

Axial Velocity DistributionRe = 5 x 104

-1.00

-0.50

0.00

0.50

1.00

1.50

0.00 0.20 0.40 0.60 0.80 1.00r/R

u/U

av

z/d=5.7z/d=12.3z/d=19.0z/d=25.7z/d=39.0z/d=32.4z/d=12.3

70

Figure 3.45 Axial Velocity Distribution After Chang and Dhir (1994)

Figure 3.46 Axial Velocity Distribution After Chang and Dhir (1994)

Axial Velocity DistributionRe = 12500, Mt/MT=7.84

-2.0

-1.0

0.0

1.0

2.0

3.0

0.00 0.20 0.40 0.60 0.80 1.00

r/R

u/U

av z/d=7.06 z/d=8.06 z/d=9.06 z/d=6.06 z/d=10.06

Axial Velocity DistributionRe = 12500, Mt/MT=2.67

-2.0

-1.0

0.0

1.0

2.0

3.0

0.00 0.20 0.40 0.60 0.80 1.00

r/R

u/U

av

z/d=7.00 z/d=8.00 z/d=9.00z/d=6.00 z/d=10.00

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 3.50. The experimental results indicate that the radial velocity

component is of an order 0(100-1000) 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.

Figure 3.47 Radial Velocity Distribution After Algifri (1988)

Radial Velocity DistributionRe = 1.7x104 - 1.55x105

-0.01

0.01

0.03

0.05

0.07

0.09

0.11

0.13

0.00 0.20 0.40 0.60 0.80 1.00r/R

v/U

av

z/d = 0z/d = 0z/d = 0z/d = 0z/d = 50z/d = 50

72

Figure 3.48 Radial Velocity Distribution After Kitoh (1991)

Figure 3.49 Radial Velocity Distribution After Chang and Dhir (1994)

Radial Velocity DistributionRe = 5 x 104

-0.0050

-0.0025

0.0000

0.0025

0.00 0.20 0.40 0.60 0.80 1.00

r/R

v/U

av

z/d=5.7z/d=12.3z/d=19.0z/d=25.7z/d=39.0z/d=32.4

Radial Velocity DistributionMt/MT = 7.84 Re = 12500

-0.02

-0.01

0.00

0.01

0.00 0.20 0.40 0.60 0.80 1.00

r/R

v/U

av

z/d = 7.06z/d = 8.06z/d = 9.06

73

Figure 3.50 Radial Velocity Distribution After Chang and Dhir (1994)

Tangential Velocity Profiles: The tangential mean velocity, w, normalized with

respect to Uav, plotted in Figs. 3.51, 3.52, 3.53 and 3.54. 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

Radial Velocity DistributionMt/MT = 2.67 Re = 12500

-0.02

-0.01

0.00

0.01

0.00 0.20 0.40 0.60 0.80 1.00

r/R

v/U

av

z/d = 7.00z/d = 8.00z/d = 9.00

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 (2001)

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.

Figure 3.51 Tangential Velocity Distribution After Algifri (1988)

Tangential Velocity DistributionRe = 1.7x104 - 1.55x105

0.000.100.200.300.400.500.600.700.800.901.00

0.00 0.20 0.40 0.60 0.80 1.00

r/R

w/U

av

z/d = 0z/d = 0z/d = 0z/d = 0

75

Figure 3.52 Tangential Velocity Distribution After Kitoh (1991)

Figure 3.53 Tangential Velocity Distribution After Chang and Dhir (1994)

Tangential Velocity DistributionRe = 5 x 104

0.00

0.50

1.00

1.50

2.00

0.00 0.20 0.40 0.60 0.80 1.00

r/R

w/U

av

z/d=5.7z/d=12.3z/d=19.0z/d=25.7z/d=39.0z/d=32.4z/d=12.3

Tangential Velocity DistributionRe = 12500, Mt/MT=7.84

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.00 0.20 0.40 0.60 0.80 1.00

r/R

w/U

av

z/d=7.06z/d=8.06z/d=9.06z/d=6.06z/d=10.06

76

Figure 3.54 Tangential Velocity Distribution After Chang and Dhir (1994)

3.3.2 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 (2001) used a two- component LDV system;

Tangential Velocity DistributionRe = 12500, Mt/MT=2.67

0.0

1.0

2.0

3.0

0.00 0.20 0.40 0.60 0.80 1.00

r/R

w/U

av

z/d=7.00z/d=8.00z/d=9.00z/d=6.00z/d=10.00

77

thus, only ''wu 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, 2'u , 2'v and 2'w , normalized with

Uav. 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 (2001) data in this study.

The data reveal that turbulent intensity has a large magnitude. In a normal (swirl-

free) 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, 2'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 2'v , the region where 2'u - 2'v > 0 appears in the annular

region where the turbulent-energy production terms of 2'v are also larger than 2'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

78

is non-dissipative. The tangential velocity in swirling flow has a significant influence on

the flow structure.

Figure 3.55 Axial Normal Stress Distribution After Algifri (1988)

Figure 3.56 Radial Normal Stress Distribution After Algifri (1988)

Turbulent Intensities

Re =1.5x105

0.0000.0200.0400.0600.0800.1000.1200.1400.1600.1800.200

0.00 0.20 0.40 0.60 0.80 1.00

r/R

z/d = 0z/d = 7.5z/d = 20z/d = 50Pipe flow

avUu 2'

Turbulent Intensities

Re =1.5x105

0.000

0.050

0.100

0.150

0.200

0.250

0.300

0.00 0.20 0.40 0.60 0.80 1.00

r/R

z/d = 0z/d = 7.5z/d = 20z/d = 50Pipe flow

avUv 2'

79

Figure 3.57 Tangential Normal Stress Distribution After Algifri (1988)

Figure 3.58 Axial Normal Stress Distribution After Kitoh (1991)

Turbulent Intensities

Re =1.5x105

0.0000.0200.0400.0600.0800.1000.1200.1400.1600.1800.200

0.00 0.20 0.40 0.60 0.80 1.00

r/R

z/d = 0z/d = 7.5z/d = 20z/d = 50Pipe flow

avUw 2'

Turbulent IntensitiesRe = 50000

0.000

0.050

0.100

0.150

0.200

0.250

0.00 0.20 0.40 0.60 0.80 1.00r/R

z/d= 12.3z/d= 5.7z/d= 12.3z/d= 19z/d= 25.7z/d= 32.4z/d= 39

avUu 2'

80

Turbulent IntensitiesRe = 50000

0.000

0.050

0.100

0.150

0.200

0.250

0.300

0.350

0.00 0.20 0.40 0.60 0.80 1.00r/R

z/d= 12.3z/d= 5.7z/d= 12.3z/d= 19z/d= 25.7z/d= 32.4z/d= 39

avUv 2'

Figure 3.59 Radial Normal Stress Distribution After Kitoh (1991)

Figure 3.60 Tangential Normal Stress Distribution After Kitoh (1991)

Turbulent IntensitiesRe = 50000

0.000

0.050

0.100

0.150

0.200

0.250

0.300

0.00 0.20 0.40 0.60 0.80 1.00r/R

z/d= 12.3z/d= 5.7z/d= 12.3z/d= 19z/d= 25.7z/d= 32.4z/d= 39

avUw 2'

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, 3.62, 3.63 and 3.64 show

the turbulent kinetic energy, k, normalized with 2avU , for Algifri (1988), Kitoh (1991),

Chang and Dhir (1994) for four tangential injectors and Chang and Dhir (1994) for six

tangential injectors, respectively.

Figure 3.61 Turbulent Kinetic Energy After Algifri (1988)

Turbulent IntensitiesRe =1.5x105

0.000

0.020

0.040

0.060

0.080

0.00 0.20 0.40 0.60 0.80 1.00

r/R

k/U

2 av

z/d = 0z/d = 7.5z/d = 20z/d = 50Pipe flow

82

Figure 3.62 Turbulent Kinetic Energy After Kitoh (1991)

Figure 3.63 Turbulent Kinetic Energy After Chang and Dhir (1994)

Turbulent IntensitiesRe = 50000

0.000

0.020

0.040

0.060

0.080

0.100

0.00 0.20 0.40 0.60 0.80 1.00r/R

k/U

2 av

z/d= 12.3z/d= 5.7z/d= 12.3z/d= 19z/d= 25.7z/d= 32.4z/d= 39

Turbulent IntensitiesMt/MT = 7.84 ,Re =12500

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.00 0.20 0.40 0.60 0.80 1.00r/R

k/U

2 av

z/d = 6z/d = 7z/d = 8z/d = 9z/d = 10

83

Figure 3.64 Turbulent Kinetic Energy After Chang and Dhir (1994)

Reynolds Stresses: The radial distributions of the Reynolds shear stress ''ji uu are

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, 3.72 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 ''vu− 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 ''wv− 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 ''wv− is

negative and large in the annular region, while it is small and could be positive in the core

Turbulent IntensitiesMt/MT = 2.67,Re =12500

0.000

0.020

0.040

0.060

0.080

0.100

0.120

0.00 0.20 0.40 0.60 0.80 1.00r/R

k/U

2 av

z/d = 6z/d = 7z/d = 8z/d = 9z/d = 10

84

region. It can also be noticed that the location where ''wv− 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.

Since angular momentum is transferred in the downstream direction, the

magnitude of ''wu− 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, ''wu− has a large positive value. While in the

outer region, where the tangential velocity is of the free-vortex type, small values of

''wu− exist.

Figure 3.65 Reynolds Shear Stress ''wu Distribution After Algifri (1988)

u'w' Reynolds Stress Re=1.55x105

0.000

0.001

0.001

0.002

0.002

0.003

0.00 0.20 0.40 0.60 0.80 1.00r/R

u'w

'/U2 av

z/d = 0z/d = 7.5z/d = 20z/d = 50z/d = 75

85

Figure 3.66 Reynolds Shear Stress ''vu− Distribution After Algifri (1988)

Figure 3.67 Reynolds Shear Stress ''wv− Distribution After Algifri (1988)

u'v' Reynolds Stress Re=1.55x105

-0.002

0.000

0.002

0.004

0.006

0.008

0.010

0.00 0.20 0.40 0.60 0.80 1.00

r/R

-u'v

'/U2 av

z/d = 0z/d = 7.5z/d = 20z/d = 50z/d = 75standard

v'w' Reynolds Stress Re=1.55x105

-0.090

-0.060

-0.030

0.000

0.030

0.060

0.090

0.00 0.20 0.40 0.60 0.80 1.00

r/R

-v'w

'/U2 av

z/d = 0z/d = 7.5z/d = 20z/d = 50z/d = 75

86

Figure 3.68 Reynolds Shear Stress ''wu Distribution After Kitoh (1991)

Figure 3.69 Reynolds Shear Stress ''vu− Distribution After Kitoh (1991)

u'w' Reynolds Stress Re = 5 x 104

-0.008

-0.003

0.002

0.007

0.00 0.20 0.40 0.60 0.80 1.00r/R

u'w

'/U2 av

z/d=12.3z/d=5.7z/d=12.3z/d=19.0z/d=25.7z/d=39.0Pipe Flowz/d=32.4

u'v' Reynolds Stress Re = 5 x 104

-0.008

-0.003

0.002

0.007

0.00 0.20 0.40 0.60 0.80 1.00r/R

-u'v

'/U2 av

z/d=12.3z/d=5.7z/d=12.3z/d=19.0z/d=25.7z/d=39.0Pipe Flowz/d=32.4

87

Figure 3.70 Reynolds Shear Stress ''wv− Distribution After Kitoh (1991)

Figure 3.71 Reynolds Shear Stress ''wu− Distribution After Chang and Dhir (1994)

v'w' Reynolds Stress Re = 5 x 104

-0.010

-0.005

0.000

0.005

0.00 0.20 0.40 0.60 0.80 1.00r/R

-v'w

'/U2 av

z/d=12.3z/d=5.7z/d=12.3z/d=19.0z/d=25.7z/d=39.0Pipe Flowz/d=32.4

u'w' Reynolds Stress Mt/MT = 7.84 Re = 12500

-0.05

0.00

0.05

0.10

0.00 0.20 0.40 0.60 0.80 1.00

r/R

-u'w

'/U2 av

z/d = 6.06z/d = 7.06z/d = 8.06z/d = 9.06z/d = 10.06

88

Figure 3.72 Reynolds Shear Stress ''vu− Distribution After Chang and Dhir (1994)

Figure 3.73 Reynolds Shear Stress ''wv− Distribution After Chang and Dhir (1994)

v'w' Reynolds Stress Mt/MT = 7.84 Re = 12500

-0.05

0.00

0.05

0.10

0.00 0.20 0.40 0.60 0.80 1.00

r/R

-v'w

'/U2 av

z/d = 6.06z/d = 7.06z/d = 8.06z/d = 9.06z/d = 10.06

u'v' Reynolds Stress Mt/MT = 7.84 Re = 12500

-0.05

0.00

0.05

0.10

0.00 0.20 0.40 0.60 0.80 1.00

r/R

-u'v

'/U2 av

z/d = 6.06z/d = 7.06z/d = 8.06z/d = 9.06z/d = 10.06

89

The eddy viscosities can be calculated using the measured Reynolds stresses, ''ji uu ,

by following relationship:

ruvu

zrt

∂∂

−= ''υ (3.5)

rrwr

wvrt

∂∂

−=)/(

''θυ (3.6)

zwvu

zt

∂∂

−= ''θυ (3.7)

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.

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.

91

4.1.1 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.

4.1.2 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.

92

( ) 0=⋅∇+∂

∂mm

m ut

ρρ , (4.1)

( ) ( )dmddddddd vv

tραραρα

⋅∇−Γ=⋅∇+∂

∂ , (4.2)

( ) mmmmmmmmm Mgpuu

tu

++⋅∇+−∇=⋅∇+∂

∂ ρτρρ , (4.3)

1=+ dc αα (4.4)

where mu and mρ are the mixture velocity and density, respectively; dα , cα , dρ , dv ,

dmv and Γ are the dispersed-phase and continuous-phase void fractions, the dispersed-

phase density and velocity, the diffusion velocity and mass source. Mm is the mixture

momentum source due to surface tension effects and mτ is the mixture stress tensor

including the viscous, turbulent and diffusion stresses.

Dispersed-phase Diffusion Equation: The diffusion equation of the dispersed-

phase, Eq. (4.2), 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

mddm

Gvvρ

−= (4.5)

93

where G, is the total mass flux. The diffusion velocity can be related either to the relative

velocity (slip) between the phases, vs= u - vd, or to the drift velocity, vdj, in a

straightforward manner, as follows

djm

cd

m

ccdm vvuv

ρρ

ρρα

=−−= )( (4.6)

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 dα is equal to α and cα 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

m

dcρρα

= (4.7)

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:

∂∂

+∂

∂+

∂∂

−Γ

=∂

∂+

∂∂

+∂

∂+

∂∂

zvv

rrvr

r

zvv

rrvr

rt

dmzddmddmrd

dzddddrdd

)()(1)(1

)()(1)(1)(

ραθ

ραρα

ραθ

ραραρα

θ

θ

(4.8)

94

For steady-state with no source or sink and axisymmetric flow, the dispersed-phase

diffusion equation can be further simplified, as follows:

∂∂

+∂

∂−=

∂∂

+∂

∂zv

rvr

rzv

rvr

rdmzddmrddzddrd )()(1)()(1 ραραραρα (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).

4.2 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: forced-

vortex 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

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

TangentialVelocity

AxialVelocity

rθ

Figure 4.1 Schematic of Swirling Flow Field and GLCC Coordinate System

4.2.1 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

220

2

av

R

z

UR

drruu

πρ

πρ θ=Ω (4.10)

96

where Uav 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:

−

=Ω −

7.0

16.035.0

493.0

2 Re21exp48.1

sepT

t

T

t

dzI

MMI

MM

(4.11)

Recently, Erdal (2001) 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 −

7.0

16.035.0

493.0

213.0 Re21expRe67.0

sepT

t

T

t

dzI

MMI

MM

(4.12)

where T

t

MM is the ratio of the tangential momentum flux to the total momentum flux at the

inlet, I is an inlet geometry factor, Re is the Reynolds number, z is the axial distance and

dsep is the diameter of the GLCC. For the inlet this momentum ratio is:

av

ist

av

inletL

T

t

Uv

Uu

MM

=

=

βcos (4.13)

where uLinlet is the liquid velocity at the inlet, Uav 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, vt is.

97

The Reynolds number in Eqs. 4.11 and 4.12 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:

−−=2

exp1 nI (4.14)

4.2.2 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. 4.10. 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:

17.032 23

++

−

=CR

rCR

rCU

u

av

z , (4.15)

−

−

= 7.0232

Rr

RrC revrev , (4.16)

98

Ω−−=6.0

exp65.05.0R

rrev , (4.17)

where rrev is the reversal flow radius (or the so called capture radius), where uz 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:

−−

=

2

exp1RrB

Rr

TUu m

av

θ (4.18)

where uθ is the local tangential velocity, r is the radial location, Tm 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 Tm and B, as follows:

05.09.0 −Ω=mT (4.19)

Ω−+=6.0

exp206.3B (4.20)

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

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:

drzur

ru

r zr ∂

∂=0

)(1 (4.21)

Ω

−=Ω −

7.035.0416.0Re35.0

sepT

t

dzI

MM

zd (4.22)

Ω−Ω=6.0

exp1213 ddRrev (4.23)

revrev

revrevrev dR

RrdR

Rr

RrdC

2

2232

−

−

= (4.24)

+

−

−

−=Rr

Rr

Rr

Rr

CdCR

Uu

av

r 711606420

234

2 (4.25)

100

where C and rrev /R are the same used in the calculation of the mean axial velocity (Eqs.

4.16 and 4.17).

4.2.3 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

''ji uu for the continuous swirling phase. The objective is to use the correlations to

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, ''ji uu .

This behavior is observed in the core region around the pipe axis where the tangential

101

velocity exhibits a forced vortex, affecting the behavior of the Reynolds stresses. Hence,

the value of Tm 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, 2avU . The values of the coefficients are given in Table 4.1.

−

⋅+

⋅+

⋅−

⋅⋅=− fdcba'' 234

2 Rr

Rr

Rr

Rr

BT

Uvu m

av

(4.26)

⋅+

⋅−

⋅+

⋅−

⋅⋅=− Ω⋅n234

2 fdcba'' eRr

Rr

Rr

Rr

BT

Uwu m

av

(4.27)

+

⋅−

⋅+

⋅−

⋅⋅=− fdba'' 234

2 Rr

Rrc

Rr

Rr

BT

Uwv m

av

(4.28)

Table 4.1 Reynolds Stress Coefficients

a b c d f n

''vu 3.304 10-1 6.158 10-1 1.177 10-1 1.295 10-1 5.987 10-3 -

''wu 7.935 10-1 2.0297 100 1.8388 100 6.549 10-1 3.520 10-2 3.143 10-2

''wv 1.2954 100 2.4614 100 1.3188 100 1.942 10-1 1.639 100 -

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, tυ , 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

102

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:

ruvuz

tzr

∂∂

−= ''υ (4.29)

∂∂

−=

ru

rr

wvrt

θθυ '' (4.30)

zuwu

zt

∂∂

−=θ

θυ '' (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 ztθυ is larger than rtθυ and also than zrtυ . This leads to the conclusion that

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

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. 4.2)

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.

104

Figure 4.2 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 2avU ,

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:

( )[ ] 02274.0)091.10088.23sin(8.0ln6.0exp22.0 2 −−Ω⋅⋅−Ω⋅−⋅−=R

rshift (4.32)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1r/R

k/U

av2

z/d = 5.4z/d = 10.1

Re = 55000

105

The parameters given below are used to determine the magnitude of the kinetic

energy, k(r,z) in the entire flow domain:

( )[ ]00979.0min Re5467.0exp118.0 −⋅Ω⋅−−⋅=Yk (4.33)

3

35

1023.30238.0908.0sin

10342.370exp10202.3

−

−−

⋅+

−

⋅

⋅−

⋅⋅⋅=

T

t

T

tK

MM

MM

.A (4.34)

( )[ ] 5.025000tanh5.0126.1 +−Ω⋅⋅⋅=KB (4.35)

( )[ ] min

2245.0

max 5415.0ln83.0expRe YkR

rBAYk shift

KK +

+−Ω⋅−⋅= (4.36)

Re009.133 Ω=n (4.37)

( )Ω⋅−⋅= 0784.0exp1292.0ϑ (4.38)

The final equation for the turbulent kinetic energy correlation, normalized with

respect to 2avU , is given in Eq. 4.39, while a general behavior of this equation is plotted in

Fig. 4.3:

( )

⋅⋅+

−

−⋅−=2

min

2

minmax2 exp21exp

RrnYkR

rRr

YkYkU

kshift

av ϑ (4.39)

106

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

k

107

model provides a relationship between the turbulent eddy viscosity and the turbulent

kinetic energy through the energy dissipation, as given below, where, Cµ = 0.09.

t

kCυ

ε µ

2

= (4.40)

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. 4-29 to 4.31. The Reynolds stress tensor is expressed as

follows:

=2

2

2

'''''

'''''

'''''

''

wwvwu

wvvvu

wuvuu

uu ji (4.41)

The turbulent kinetic energy is the defined as the sum of the normal Reynolds stresses,

and is given below:

( )222 '''21 wvuk ++= (4.42)

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.

108

=

2

2

2

'

'

'

wrz

rzr

zzru

ijt

ξυυ

υξυ

υυξ

υ

θθ

θυ

θ

(4.43)

where the parameters used are defined below:

av

i

uRu ⋅

=2'ξ (4.44)

2

2

1''

wuc = and ( )222 ''

21' wuv += (4.45)

The value of c1 = 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,

0322

13 =−+− III δδδ (4.46)

where the invariants are defined in this study as follows:

kU

RIav

21 = (4.47)

)()1(9

8

)1(1

98

)1(916

22222

2

1

1

22

2

1

22

2

21

12

zrzrav

avav

kUR

cc

kUR

ck

UR

ccI

υυυ θθ ++−⋅+

+⋅+

+⋅+

=

(4.48)

−+

−

+

+

−

++=

zav

rzrzrzav

zrzr

ravav

kuRk

uR

c

kuR

ck

uR

ccI

θθθθθ

θ

υυυυυυυυ

υ

32

)1(1

34

)1(1

98

)1(34

1

222

2

11

13

(4.49)

Once the three roots of Eq. 4.46 are obtained, the equivalent turbulent eddy viscosity is

defined by the magnitude of the principal direction components:

109

23

22

21 δδδυ ++=eqvt (4.50)

Finally, the energy dissipation rate is determined by the well-known k-ε equation as:

eqvt

kCυ

ε µ

2

= (4.51)

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 dispersed-

phase (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:

LMHDcdd

d FFFFgDtDumgm

dtdv

m ++++

−+= (4.52)

where the variables are:

md : mass of the dispersed-phase

mc : mass of the displaced continuous-phase

vd : dispersed-phase velocity

110

u : continuous-phase velocity in absence of the particle (unperturbed velocity)

Du/Dt : Lagrangian fluid acceleration, defined as uutu

DtDu ∇⋅+

∂∂=

FD : drag force

FH : history force

FM : added mass force

FL : lift force

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:

0)( =++++∇⋅+− MHLDccd FFFFuumgmm (4.53)

Following is a discussion of the different forces given in Eq. (4.52):

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, vs = u – vd, particle

(bubble/droplet) diameter, dp, and the drag coefficient, CD, as follows:

)(8

2

ddp

cDD vuvud

CF −−=π

ρ (4.54)

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 200, for

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, CD, 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. (1972) are given below, respectively, for the

viscous regime (Re < 1000). Note that Stoke’s regime is also included in these

correlations:

( )

+++=−

−1

2/11 Re315.31

21

Re81

Re16

DC (4.55)

[ ]687.02 Re15.01

Re24 +=DC (4.56)

[ ]75.03 Re1.01

Re24 +=DC (4.57)

36.0Re48.5Re24 573.0

4 ++= −DC (4.58)

The particle Reynolds number, Re, is defined based on relative velocity and continuous-

phase molecular viscosity as follows:

112

c

pdc dvuµ

ρ −=Re (4.59)

Figure 4.4 Drag Coefficient Correlations Comparison

Figure 4.4 shows the results of the four drag coefficients, given in Eqs. 4.55 (CD-

1), 4.56 (CD-2), 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. (1972) 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 CD = 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

1 10 100 1 .103 1 .104 1 .1051 .10 3

0.01

0.1

1

10

100

CD-1CD-2CD-3CD-4

Reynolds Number

Dra

g C

oeff

icie

nt

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.

v

t

v

d

vvpH d

vutKdF τττ

τµ

∂∂

−∂∂−=

0

)( (4.60)

where K(t-τv) 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 continuous-

phase. 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.

−=dt

dvDtDumCF d

cMM (4.61)

where CM is added mass coefficient, namely, CM = 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

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

( ) ( ) ω×−=×∇×−= dcLdcLL vumCuvumCF )( (4.62)

where ω is the vorticity vector and CL is lift coefficient, (CL = 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:

zrzzrreff eger

uegegg +=+=2θ (4.63)

115

where uθ 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 ρc / ρd 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, FL,

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.

4.3.1 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:

116

∂∂

+−∂∂+

−

−=

zuu

ru

ruu

vCdC

ru

vCd

v rz

rr

sD

pM

c

dc

sD

psr

22 )1(34

34 θθ

ρρρ

(4.64)

∂∂

++∂

∂+−=

zuu

ruu

ruu

vCdC

v zr

rsD

pMs

θθθθ

)1(34 (4.65)

∂∂

+∂∂+

−

−=

zuu

ruu

vCdC

vCdg

v zz

zr

sD

pM

c

dc

sD

psz

)1(34

34

ρρρ

(4.66)

The velocity field of the dispersed-phase, vd, can be obtained from the relative

velocity (slip velocity) and the continuous-phase velocity, using the following

relationship

sd vuv −= (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:

++=++=

++=

zdzdrdrd

zszsrsrs

zzrr

evevevvevevevv

eueueuu

θθ

θθ

θθ

(4.68)

From the above equations, it can be noted that in order to compute the dispersed-

phase velocities, the particle diameter, dp, 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.

4.3.2 Stable Bubble Diameter

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):

phCBiii va

ta φφφ ++=∇+∂∂

).( (4.69)

where ai is the interfacial area concentration (interfacial area per unit volume); vi is the

velocity of the interface; φB, φC, and φph 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:

CB φφ = . (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

118

events. There exists a unique value of particle diameter, where Eq. 4.70 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

=Pd

BBVBB dVVfVPmin

)(),:( ,λ

λ λωλφ (4.71)

Here, PB(V:VfBV,λ) is the probability for a particle of size V to break into two

particles, one with size (volume) VfBV, when the particle is hit by an arriving eddy of size

λ, and ωB,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

119

scales. The inertial sub-range of the isotropic turbulent energy spectrum, E(2π/λ) = C ε2/3

(2π/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, fBV,

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

3/113/53/23/11

23/1

min

554.1exp)1(923.0χ

χχερ

σχ

χεφ ddd pcp

B (4.72)

where

pdλχ = and

4/1

3

3

min 4.11

=

ερµλ

c

c . (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 m2/s3.

120

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:

)/exp( τϕφ tC −= (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 dp1 and dp2,

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

0 1000 2000 3000 4000 5000 6000 7000

10

20

30

Bubble Diameter (micron)

Bre

akup

Fre

quen

cy (1

/s)

121

coalescence may occur. Collision may occur due to variety of mechanisms. The two

mechanisms considered in this study are collision due to turbulence, ϕT, and due to

buoyancy, ϕW :

WT ϕϕϕ += . (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:

2/13/22

3/21

3/12213 )()(635.0 pppp

pT dddd

d++= εϕ . (4.76)

Collision may also occur from each bubble rise velocity, and is given by

expression based on bubble rise velocity, as follows:

2/121

2213 )()(1

83

riseriseppp

W vvddd

−+=ϕ (4.77)

where pipic

irise dgd

v 505.014.2 +=ρ

σ 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

122

artificially increased by adding surfactant to the dispersion. In this study the summation

of two effects for calculating the coalescence time, namely, inertial thinning, t1 and

viscous thinning, t2, is adopted as given below, respectively:

=

f

ic

hhLnrt

2/13

1 16σρ

(4.78)

2522 24 −= hf AhMt µσπ (4.79)

where hi and hf are the initial and final film thickness, respectively. Experimental

investigations suggest hi = 1*10–5 m and hf = 5*10-8 m. The equivalent radius, r, is defined

by 1

21

225.0−

+=

pp ddr , M is the surface immobility parameter that is dependant on the

surfactant, taking values from 0 (no surfactant) to 4, and Ah is Hamaker constant, which

ranges between 10-20 to 10-19 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:

3/1

3/2

ετ r= (4.80)

Substituting Eqs 4.75 to 4.80 into Eq. 4.74, one can obtain the final coalescence

rate equation, as follows:

( )

+−+=τ

ϕϕφ 21exp ttWTC (4.81)

123

Figure 4.6 shows the coalescence frequency for the case of a water-air system with

energy dissipation, with value of ε = 1 m2/s3 and M = 0.034.

Figure 4.6 Bubble Coalescence Frequency Function

Stable Diameter: Equating Eqs 4.72 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 m2/s3 and M = 0.00014,

resulting in bubble diameter of approximately 1.5 mm.

0 100 200 300 400 500 600 700 800 900 1000

500

1000

1500

Bubble Diameter (micron)

Coa

lesc

ence

Fre

quen

cy (1

/s)

124

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 low-

level 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 (dmax, Eq. 4.82) of the bubble function of breakup,

and the bubble whose diameter is minimum (dmin, Eq. 4.83), which will coalesce upon

colliding. The resultant stable particle diameter should be within the range given below,

5/25/3

max−

≈ ε

ρσ

c

cWed (4.82)

4/122

min

≈

ερµσ

cc

chd (4.83)

0 500 1000 1500 2000 2500 3000

2000

4000

6000

8000

Bubble Diameter (micron)

Even

t Fre

quen

cies

Coalescence

Breakup

125

where Wec is a critical Weber number, σ, surface tension and hc 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:

sm vuu α−= (4.84)

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:

( ) 0=⋅∇+∂

∂mm

m ut

ρρ. (4.1)

126

4.5 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:

βSinhhh eqinletistvL

geq3/122/3

2 )(83.8

−= (4.85)

where hinlet and heq are the height below inlet and the equilibrium liquid level in the

GLCC, respectively; hL2 is the liquid phase film thickness at the inlet slot, vtis 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

127

liquid holdup in the slug. Thus, the correlation developed by Gomez et al. (2000) can be

used to determine the gas entrainment due to slugging, as given below:

( )LSslug Re1048.2exp0.11 6−−=α (4.86)

where ReLS is calculated based on liquid properties (ρL and µL), inlet diameter and

mixture inlet velocity. Note that any other correlation for αslug 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.

4.6.1 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

128

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:

( )0

2

>drurd θ . (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. 4.18 resulting in the following equation:

0exp1exp422

22 ≥

−−

−RrB

RrBBTUr mav . (4.88)

The helical shape of the core can be defined by using Eq. 4.32, which also

provides the helical shape of the turbulent kinetic energy.

4.6.2. 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:

rcnTnnTn gas

rcr

liquid

rcr

σ=⋅−⋅==

(4.89)

Assuming that the gas core interface rotates as a rigid body with an angular velocity ω1,

and that the normal stress at the inner side of the gas core is that of an ideal fluid, while at

129

the liquid side the normal stress can be expressed using the radial velocity gradient and

the hydrostatic pressure, yielding:

ruzgnTn r

Lliquid

rcr ∂∂+−=⋅

=µρ 2 and

+−=⋅=

2212

1 rcPnTn gggas

rcrωρ (4.90)

where σ is the surface tension, g the gravitational acceleration, z the axial position, rc the

gas core radius and Pg is the GLCC pressure. Combining Eqs 4.89 and 4.90, one can

obtain the gas core diameter expression, as given below:

0)(221

3

2 =−

−−

∂∂+

= sepsepgL

rcr

rL

septwg RR

rczgr

uRrcu σρρµρ (4.91)

where utw is the tangential velocity at the wall, calculated as suggested by Gomez et. al

(1999), as follows:

Ω= avtw Uu23 (4.92)

The radial velocity gradient can be obtained from the velocity distribution given in Eqs.

4.22 - 4.25. 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.

130

4.7.1 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 continuous-

phase 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,

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

2. 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.

132

Governing Equations of Dispersed-Phase Diffusion Model: The dispersed-

phase 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:

[ ] [ ]=

∂−∂

+∂

−∂z

vur

vurr

szzdsrrd )()(1 ραρα

−+−

∂∂+

−+−

∂∂

szsr vNz

vrNrr dd αρ

ααααρ

ααα

ρρ )1()1(

)1()1(1 (4.93)

where, Nρ is the density ratio given by Nρ = ρd /ρc.

Dispersed-Phase Diffusion Equation Finite Volume Discretization: The

governing equation (Eq. 4.93) presented above, can now be discretized in 2-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:

133

( ) ( ) dVBdAdAuVCSCSC

... +∇Γ= φφρ (4.94)

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. 4.93 is nonlinear with respect to the transported variable. This nonlinearity is

approximately solved over the control volume by discretizing Eq. 4.93 and assigning the

nonlinear term to the source term, B, as follows,

⋅

−+−

=⋅SC

sd

VC

dAvN

dVB)1(

)1(αα

ραα

ρ

(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.

4.9. Figure 4.10 shows the control volume notation for the discretization.

Figure 4.8 Axisymmetric Control Volume Element

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.

0==Rr

α (4.96)

2&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

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:

00

=∂∂

=zzα and 0=

∂∂

=Lzzα (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:

00

=∂∂

=rrα (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. 4.93 – 4.95) over the

control volume yields the general discretization equation, as given below

+= BAA nbnbpp αα (4.99)

+= nbnbp FAA (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

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 Ap is determined

based on the values of the neighboring faces, Anb (A = ρd vd), adding the mixture mass

balance term (F = ρm um, 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

π

θ

θαα 2

0 0

2

0 0R

R

Lz

drdr

drdr)z,r( (4.101)

137

==

π

θα2

0 0

),(R

dzLzGCU drdrzrvg (4.102)

4.7.2 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:

rvuvu

rvv

zsrr

szz

dr

dz ∆

−−

=∆

=∆ (4.103)

The displaced distance in the tangential direction is given by:

( )( )szz

sd vur

vuztv

−−∆

=∆=∆ θθθθ (4.104)

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

Rzz ∆=

r

Rθθ ∆=

r

Rrr (4.105)

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

2. 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

139

Figure 4.11 Schematic of Bubble Trajectory Path

140

4.7.3 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 zi, all parameters needed for the dispersed-phase diffusion

model, namely, continuous-phase radial velocity and relative radial velocity for the next

step, zi+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, zi, are used as the initial guess for the zi+1 step. The calculation is

continuously performed until z = L. Following is the calculation procedure:

141

1. Gas Entrainment : Boundary Condition at Top

2. 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, d100, which is tracked until it

reaches the reverse flow region, before reaching the liquid outlet (z = L). Thus, bubbles

smaller than d100, are carry-under and larger than d100, are separated. The amount of gas

carry-under is determined using the breakup frequency function, and is given in Fig. 4.12.

Integration over the curve given in the figure from dmin (Eq. 4.82) to d100, 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

142

Figure 4.12 Amount of Gas Carry-under Determination

used here, as follow. The d100 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 d100 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.

5000 1 .104 1.5 .104 2 .1040

10

20

30

40

50

60

70

80

Bubble Diameter (micron)

Bre

akup

Fre

quen

cy (1

/s)

Gas Carryunder d100

143

Following is the calculation procedure for the simplified scheme:

1. Gas Entrainment: Boundary Condition at Top

2. Continuous-phase Velocity: Swirling Flow Correlations

3. Particle Velocities: Lagrangian Description of Particles

4. Separation at Capture Radius: Two- Phase Reversal Core

5. d100 Bubble Diameter : BubbleTraj. for each Liq-Phase

6. Each Phase GCU dp < d100: Breakup Frequency Function

7. Total Gas Carry Under: Superposition Method

Figure 4.13 Oil-Water-Gas Distribution in GLCC (after Oropeza, 2001)

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.

Vm=0.2 m/s Vm=0.3 m/s Vm=0.4 m/s Vm=0.5 m/s Vm=0.6 m/sVm=0.2 m/s Vm=0.3 m/s Vm=0.4 m/s Vm=0.5 m/s Vm=0.6 m/s

Wcut = 95% Vsg = 0.75 m/s

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 (2001) 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.

5.1.1 Continuous-Phase Velocity Profiles

The developed swirling flow velocity distribution correlations are given in section

4.2.2. 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 (2001) 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.

145

Figure 5.1 Mean Axial Velocity Comparisons for Algifri Data (1988)

Figure 5.2 Mean Axial Velocity Comparisons for Kitoh Data (1991)

-0.5

0.0

0.5

1.0

1.5

2.0

0.0 0.2 0.4 0.6 0.8 1.0

r/R

u/U a

v

Prediction: z/d = 0Data: z/d = 0Prediction: z/d = 7.5Data: z/d = 7.5

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

0.0 0.2 0.4 0.6 0.8 1.0

r/R

u/U a

v

model Z/D= 32.4data Z/D= 32.4model Z/D= 12.3data Z/D= 12.3model Z/D= 19data Z/D= 19

146

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.

Figure 5.4 Mean Tangential Velocity Comparisons for Algifri Data (1988)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.2 0.4 0.6 0.8 1.0r/R

w/U

av

data z/d = 0

model z/d = 0

data z/d = 7.5

model z/d = 7.5

Mt/MT = 7.84

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

0.0 0.2 0.4 0.6 0.8 1.0

r/R

u/U

av

model Z/D= 10.06data Z/D= 10.06model Z/D= 6.06data Z/D= 6.06

147

Figure 5.5 Mean Tangential Velocity Comparisons for Kitoh Data (1991)

Figure 5.6 Mean Tangential Velocity Comparisons for Chang and Dhir Data (1994)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0.0 0.2 0.4 0.6 0.8 1.0r/R

w/U

av

data z/d = 12.3model z/d = 12.3data z/d = 19model z/d = 19data z/d = 39model z/d = 39

Mt/MT = 7.84

0

1

2

3

4

5

6

7

0 0.2 0.4 0.6 0.8 1r/R

w/U

av

data z/d = 6.06

model z/d = 6.06

data z/d = 8.06

model z/d = 8.06

data z/d = 10.06

model z/d = 10.06

148

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.

Figure 5.8 Mean Radial Velocity Comparisons for Kitoh Data (1991)

-4.0E-03

-3.0E-03

-2.0E-03

-1.0E-03

0.0E+00

1.0E-03

0.0 0.2 0.4 0.6 0.8 1.0

r/R

v/U a

v

model Z/D= 12.3data Z/D= 12.3model Z/D= 25.7data Z/D= 25.7

Mt/MT = 2.67

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.2 0.4 0.6 0.8 1r/R

w/U

av

data z/d = 6model z/d = 6data z/d = 10model z/d = 10data z/d = 8model z/d = 8

149

Figure 5.9 Mean Radial Velocity Comparisons for Chang and Dhir Data (1994)

Figure 5.10 Mean Radial Velocity Comparisons for Chang and Dhir Data (1994)

Mt/MT=2.67

-1.5E-02

-1.0E-02

-5.0E-03

0.0E+00

5.0E-03

0.0 0.2 0.4 0.6 0.8 1.0

r/R

v/U a

v

model Z/D= 9data Z/D= 9model Z/D= 7data Z/D= 7

Mt/MT=7.84

-1.E-02

-8.E-03

-6.E-03

-4.E-03

-2.E-03

0.E+00

2.E-03

0.0 0.2 0.4 0.6 0.8 1.0

r/R

v/U a

v

model Z/D= 9data Z/D= 9

150

5.1.2 Continuous-Phase Turbulent Quantities

Turbulent Kinetic Energy: Figures 5.11 and 5.12 present the performance of the

developed normalized turbulent kinetic energy correlation with the data of Erdal (2001).

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 5.12 presents the same comparison in

contour plots form.

Comparison between the entire Erdal (2001) 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 5.13. 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. 5.15 shows the

comparison for high Reynolds numbers. Comparison of the turbulent kinetic energy for

the same value of Mt/MT = 10.88, for both low and high Reynolds numbers, is presented

in Fig 5.16. 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

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.

Figure 5.11 Comparison of Turbulent Kinetic Energy Radial Distribution

0.0

0.5

1.0

1.5

2.0

2.5

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0r/R

K/U

2 av

2.86 2.84 2.83 2.82 2.80 2.79 2.78 2.76 2.75 2.74 2.72 2.722.70 2.69 2.67 2.64 2.62 2.60 2.57 2.55 2.49 2.42 2.36 2.30

Swirl I t it

DataRe = 54828Mt/MT =

0.0

0.5

1.0

1.5

2.0

2.5

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0r/R

K/U

2 av

2.86 2.84 2.83 2.82 2.80 2.79 2.78 2.76 2.75 2.74 2.72 2.722.70 2.69 2.67 2.64 2.62 2.60 2.57 2.55 2.49 2.42 2.36 2.30

Swirl Intensity

PredictionRe = 54828Mt/MT =

152

Data Prediction

Figure 5.12 Contour Plot Comparison of Turbulent Kinetic Energy Radial Distribution

-41 0 41

350

400

450

500

550

600

650

700

750

800

850

900

R (mm)

X(mm)

0.1 0.4 0.7 1.0 1.4 1.7

k/Uav2

k/Uav2

k

153

Figure 5.13 Comparison of Helical Radial Oscillations of the Maximum Turbulent

Kinetic Energy with Swirl Intensity

Figure 5.14 Maximum and Minimum Turbulent Kinetic Energy Comparison–Low Swirling intensity

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0 2 4 6 8 10

Swirling Intensity

k/U

2 av

Re 9137

Mt/MT 5.44

Kmax

Kmin

-0.3

0

0.3

0 1 2 3 4 5 6 7 8 9 10 11 12

Swirl Intensity

r shi

ft/R

Erdal DataPrediction

154

Figure 5.15 Maximum and Minimum Turbulent Kinetic Energy Comparison – Different

Mt/MT

Figure 5.16 Maximum and Minimum Turbulent Kinetic Energy Comparison – Low and High Reynolds Number

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00

Swirling Intensity

K/U

2 av

Kmax

Kmin

Re 54828Mt/MT 5.44

Kmax

Kmin

Re 54828Mt/MT 10.88

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00

Swirling Intensity

K/U

2 av

Kmax

Kmin

Re 9137Mt/MT 10.88

Kmax

Kmin

Re 54828Mt/MT 10.88

155

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 5.24. 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.

'vu' 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.

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 1 2 3

Swirling Intensity

k/U

2 av

Mt/MT 1Re 50000KmaxKmin

156

Figure 5.18 Reynolds Shear Stress ''vu Comparison with Kitoh (1991) Data

-0.008

-0.006

-0.004

-0.002

0.000

0.002

0.004

0.006

0.008

0.0 0.2 0.4 0.6 0.8 1.0

r/R

-u'v

'/U2 av

Data: z/d = 32.0

Prediction: z/d =32.0

Data: z/d = 19.0

Prediction: z/d = 19.0

Prediction: z/d = 5.7

Data: z/d = 5.7

Data: z/d = 12.3

Prediction: z/d = 12.3

157

Figure 5.19 Reynolds Shear Stress ''vu Comparison with Chang and Dhir (1994) Data

Mt/MT = 7.84

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.0 0.2 0.4 0.6 0.8 1.0

r/R

-u'v

'/U2 av

Data: z/d = 10Prediction: z/d = 10Data: z/d =9Prediction: z/d = 9Data: z/d = 8Prediction: z/d = 8Data: z/d = 7Prediction: z/d = 7Data: z/d = 6Prediction: z/d = 6

158

'wu' Component: Comparisons of the correlation for this component with the

data of Kitoh (1991), Chang and Dhir (1994) and Erdal (2001) are shown in Figs.

5.20, 5.21 and 5.22, respectively. The performance for this component, as shown in

the figures, is fairly good.

Figure 5.20 Reynolds Shear Stress ''wu Comparison with Kitoh (1991) Data

-0.010

-0.008

-0.006

-0.004

-0.002

0.000

0.002

0.0 0.2 0.4 0.6 0.8 1.0

r/R

-u'w

'/U2 av

Data: z/d = 12.3

Prediction: z/d = 12.3

Data: z/d = 5.7

Prediction: z/d = 5.7

Data: z/d = 19

Prediction: z/d = 19

159

Figure 5.21 Reynolds Shear Stress ''wu Comparison with Chang and Dhir (1994) Data

Mt/MT = 7.84

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.0 0.2 0.4 0.6 0.8 1.0

r/R

-u'w

'/U2 av

Data: z/d = 6Prediction: z/d = 6Data: z/d = 7Prediction: z/d = 7Data: z/d = 8Prediction: z/d = 8Data: z/d = 9Prediction: z/d = 9Data: z/d = 10Prediction: z/d = 10

160

Figure 5.22 Reynolds Shear Stress ''wu for Erdal (2001)

Mt/MT = 5.44

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

r/R

-u'w

'/U2 av

Data: z/d = 4.4Prediction: z/d = 4.4 Data z/d = 5.8Prediction: z/d = 5.8Data: z/d = 10Prediction: z/d = 10

161

'wv' Component: The comparison between the prediction for this component

with Kitoh (1991) and Chang and Dhir (1994) data are shown in Figs. 5.23 and 5.24,

respectively, showing the same good agreement, as for the other components.

Figure 5.23 Reynolds Shear Stress ''wv Comparison with Kitoh (1991) Data

-0.01

-0.01

-0.01

0.00

0.00

0.00

0.00

0.00

0.0 0.2 0.4 0.6 0.8 1.0

r/R

-v'w

'/U2 av

Data: z/d = 25

Prediction: z/d = 25

Data: z/d = 19

Prediction: z/d = 19

Data: z/d = 5.7

Prediction: z/d = 5.7

Data: z/d = 12.3

Prediction: z/d = 12.3

162

Figure 5.24 Reynolds Shear Stress ''wv Comparison with Chang and Dhir (1994) Data

Mt/MT = 7.84

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.0 0.2 0.4 0.6 0.8 1.0

r/R

-v'w

'/U2 av

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

163

5.2 Eulerian-Lagrangian Model Void Fraction Distribution Simulation Results

Figure 5.25 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

254 Mscf/d and 303 bbl/d, respectively. Shown is the void fraction distribution from a 2-

D simulation, with an initial void fraction of αi = 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 5.25 Simulation Results for Void Fraction Distribution

164

5.3 Performance of Simplified Mechanistic Model

In this section the simulation results of the Lagrangian – Bubble Tracking

simplified mechanistic model for a high pressure field study are presented. The

experimental data were collected at the Colorado Engineering Experiment Station Inc.

(CEESI) facility in Colorado, utilizing a 6 inch ID 11-ft tall GLCC, with a length of 5 ft

below the inlet. The operating pressure was 500 psia, and the working fluids were natural

gas and oil. For the simulation run, the inlet flow rates were vSG = 5.98 ft/sec and vSL =

0.38 ft/s. The amount of gas carry-under flow rate measured was 5.2 Mscf/d.

Figure 5.26 shows the d100 bubble trajectory. For this case d100 = 0.085 mm.

Table 5.1 presents the output of the model with the detailed results. As can be seen, the

calculated gas carry-under flow rate is 4.84 Mscf/d, corresponding to PGCU of 0.13%.

As compared the calculated GCU of 4.84 Mscf/d to the measured value of 5.2 Mscf/d,

results in 6.92% of error. These results are encouraging, showing the potential

performance and impact of the proposed models.

.

165

Figure 5.26 Bubble Trajectory of d100 for High Pressure CEESI Data

Table 5.1 Simulation Results for Lagrangian-Bubble Tracking for High Pressure Data

GLCC Below Inlet

0

1

2

3

4

5

6

7

0 2 4

Radial Position [in]

Axi

al P

ositi

on [f

t]

Bubble Traj Vortex

GCU - Bubble Trajectory and Superposition MethodBubble Diameter [mm]

Smallest LargestWeber No

8.0 30.0

Velocity dmin dmax

Liq. Velocity @ GLCC [ft/s] 0.38 15.249 57.186Liquid Tang. @ Nozzle [ft/s] 15.00 0.010 0.036

Bubble Diameter [mm]d1 d99 davg STD

Bubble Diameter 0.010 57.186 0.057 0.045

Cumulative Probability 0.000 1.000Error 0.001 -0.001Least Error Function 0.000002

Void Fraction Calculations Gas Carry-UnderFree Water Free Oil Mixture GCU Qg GCU

d100 Separated Bubble [mm] 0.000 0.085 0.085 [α] [MScf/D]Cumulative Probability 0.000 1.000 1.000 Scenario 1 0.320 4.84Scenario 1: LVF/Liq. Phase 0.000 1.000 0.000 Scenario 2 0.320 4.84

Scenario 2: LVF/Liq. Phase 0.000 1.000 0.000Scenario 1: GVF/Liq Phase 0.000 0.320 0.000Scenario 2: GVF/Liq. Phase 0.000 0.320 0.000Scenario 1: GCU [α]/Phase 0.000 0.320 0.000Scenario 2: GCU [α]/Phase 0.000 0.320 0.000Liquid Holdup @ Flow Line 0.680

166

5.4 Comparison between Simplified Mechanistic Model Predictions and Air-Oil

Flow Experimental Results

An overall evaluation of the Lagrangian – Bubble Tracking simplified mechanistic

model against the experimental GCU data collected for the air-oil flow is presented in this

section. The experimental data are given in Table 3.1, section 3.1.2. The simplified

model predictions for the 20 experimental runs, along with the experimental results, are

shown in Table 5.2. The table provides the measured PGCU, the predicted PGCU and

the error for all runs. The average error for all the runs is –21.05%, while the absolute

error is 39.70%. This is a reasonable error for the complex multiphase hydrodynamics

exhibited by the GCU process. Note that for this comparison the gas entrainment is not

calculated based on the impinging jet correlation (Eq. 4.83), but rather based on

correlation for the liquid holdup in the slug body (Eq. 4.84). It was found out that the

Gomez et al. (2000) slug liquid holdup correlation performed well for high superficial

liquid velocities, vsl > 0.2 ft/s. For low superficial liquid velocities, vsl ≤ 0.2 ft/s, it is

recommended to use the Gregory et al. (1978) slug liquid holdup, as it gives better results

for the PGCU predicted by the model. The overall performance of the simplified

mechanistic model is shown in Fig. 5.27.

Run p T µ µ µ µ qgas Error Abs. ErrorNo ft/s ft/s psia oF cp bbl/D Mscf/D scf/D PGCU % scf/D PGCU % % %1 2.0 0.4 23.9 79.0 25.0 302.1 13.3 9.48 0.0713 2.90 0.0218 -69.42 69.422 2.0 0.6 23.5 79.0 25.0 453.2 13.1 5.75 0.0439 4.40 0.0336 -23.42 23.423 2.0 0.8 24.0 75.6 26.7 604.2 13.4 6.01 0.0447 7.70 0.0573 28.17 28.174 2.0 1.0 24.0 76.0 26.5 755.3 13.4 10.87 0.0809 12.10 0.0901 11.31 11.315 4.0 0.2 23.9 80.0 24.6 151.1 26.6 3.54 0.0133 3.70 0.0139 4.62 4.626 4.0 0.4 23.6 79.5 24.8 302.1 26.3 10.91 0.0416 1.90 0.0072 -82.59 82.597 4.0 0.6 23.6 80.6 24.3 453.2 26.2 9.88 0.0377 4.50 0.0172 -54.44 54.448 4.0 0.8 24.0 82.6 23.4 604.2 26.5 6.06 0.0228 8.40 0.0316 38.72 38.729 4.0 0.9 24.0 83.7 22.9 679.8 26.5 5.67 0.0214 11.30 0.0427 99.46 99.46

10 8.0 0.2 23.7 84.5 22.5 151.1 52.2 3.36 0.0064 4.70 0.0090 39.91 39.9111 8.0 0.4 23.8 82.7 23.3 302.1 52.6 8.96 0.0170 2.00 0.0038 -77.67 77.6712 8.0 0.6 23.7 82.8 23.3 453.2 52.4 9.84 0.0188 4.80 0.0092 -51.20 51.2013 8.0 0.8 24.0 83.2 23.1 604.2 53.0 7.31 0.0138 8.90 0.0168 21.77 21.7714 12.0 0.2 24.0 82.0 23.6 151.1 79.7 4.77 0.0060 4.40 0.0055 -7.74 7.7415 12.0 0.4 24.1 84.9 22.4 302.1 79.6 12.31 0.0155 2.10 0.0026 -82.94 82.9416 12.0 0.6 24.2 85.7 22.0 453.2 79.8 10.37 0.0130 5.20 0.0065 -49.86 49.8617 12.0 0.8 24.0 86.4 21.7 604.2 79.1 9.21 0.0116 9.40 0.0119 2.10 2.1018 16.0 0.2 24.4 84.9 22.4 151.1 107.5 7.31 0.0068 5.90 0.0055 -19.27 19.2719 16.0 0.4 24.4 86.4 21.7 302.1 107.2 12.40 0.0116 2.20 0.0021 -82.26 82.2620 16.0 0.6 24.6 86.7 21.6 453.2 108.0 15.68 0.0145 5.30 0.0049 -66.21 66.21

Average -21.05 39.70

vsg vsl qo Calculated GCU Measured GCU

Table 5.2 Comparison between Simplified Mechanistic Model Predictions and Air-Oil Flow Experimental Results

168

Figure 5.27 Overall Performance of Simplified Bubble-Tracking model

The void fraction in the liquid leg is an important design parameter related to the

gas carry-under phenomena in the GLCC. Table 5.3 presents the experimental and

predicted values of the gas void fraction in the liquid leg for the same data set presented

in Table 5.2. The experimental values are calculated based on the measured amount of

gas carry-under, assuming no-slip flow condition in the liquid leg. Contour plots of the

experimental and predicted void fractions in the liquid leg are given in Figures 5.28 and

5.29, respectively. Both figures show that the region for the highest void fraction is

located at high gas and low liquid flow rate conditions. The comparison between Figures

5.28 and 5.29, as well as the comparison give in Table 5.3, reveal good agreement

between the measured and predicted gas void fractions in the liquid leg.

The good agreement between the measured and predicted gas void fractions in the

liquid leg is further demonstrated in Figure 5.30. In this figures the difference between

the measured and predicted void fractions, namely, ∆α, is plotted for all the experimental

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0.00 0.02 0.04 0.06 0.08 0.10Measured PGCU (%)

Cal

cula

ted

PGCU

(%)

c

169

runs. As can be seen, the deviation between the measured and predicted void fraction

values is minimal. This is a reflection of the model being able to capture the physical

phenomena. Also, it demonstrates that the model can be used with confidence to design

GLCCs upstream of multiphase flow meters, aiming at the “sweet spots” of the meters.

Table 5.3

A Summary of Liquid Leg Void Fraction Results for Air-Oil Flow (See Table 5.2)

Run Measured CalculatedNo

Ft/s Ft/s αααα αααα1 2.0 0.4 0.00355 0.001092 2.0 0.6 0.00146 0.001123 2.0 0.8 0.00112 0.001434 2.0 1.0 0.00162 0.001805 4.0 0.2 0.00266 0.002786 4.0 0.4 0.00414 0.000727 4.0 0.6 0.00251 0.001148 4.0 0.8 0.00114 0.001589 4.0 0.9 0.00095 0.00189

10 8.0 0.2 0.00257 0.0035911 8.0 0.4 0.00339 0.0007612 8.0 0.6 0.00250 0.0012213 8.0 0.8 0.00138 0.0016814 12.0 0.2 0.00358 0.0033015 12.0 0.4 0.00462 0.0007916 12.0 0.6 0.00259 0.0013017 12.0 0.8 0.00174 0.0017818 16.0 0.2 0.00541 0.0043719 16.0 0.4 0.00461 0.0008220 16.0 0.6 0.00386 0.00131

VSLVSG

170

Figure 5.28 Experimental Void Fraction Results in Liquid Leg

Figure 5.29 Predicted Void Fraction Results in Liquid Leg

171

Figure 5.30 Deviation of Experimental and Predicted Void Fractions in Liquid Leg

-0.020

-0.015

-0.010

-0.005

0.000

0.005

0.010

0.015

0.020

0 2 4 6 8 10 12 14 16 18 20

Run

∆α

∆α

∆α∆α

172

CHAPTER VI

CONCLUSIONS AND RECOMMENDATIONS

The hydrodynamics of dispersed two-phase swirling flow in the lower part of the GLCC

were studied both experimentally and theoretically. Following are the main conclusions

of the study:

Experiments have been conducted to obtain systematic data and shed light on the

gas-carry-under physical phenomena. A GLCC facility has been used to gather

data on the amount of gas carry-under in the outlet liquid stream. Flow

visualization studies have also been carried out to classify the existing flow

pattern in swirling flow.

Published local LDV measurements for swirling flow field have been analyzed

and utilized to develop and validate GLCC swirling flow field prediction

correlations. The correlations include the axial, tangential and radial velocity

distributions, and the turbulent kinetic energy and Reynolds shear stresses.

The building block sub-models for the gas carry-under phenomena have been

developed, as follows:

Gas entrainment in the inlet region

Continuous-phase swirling flow field

Dispersed-phase particle (bubbles) motion

Diffusion of dispersed-phase

173

The sub-model building blocks have been integrated in order to predict the

hydrodynamics of the swirling flow in the GLCC, and the resulting gas carry-

under. Three approaches have been proposed, as given below:

Eulerian-Lagrangian Diffusion approach,

Lagrangian-Bubble Tracking approach

Simplified Mechanistic Models for above two approaches

The developed correlations for the continuous-phase swirling flow field have been

tested against data from other studies, not used in the development of the

correlations. All the correlations, including the axial, tangential and radial

velocity distributions, and the turbulent kinetic energy and Reynolds shear stresses

show good agreement with the data. The correlations have been integrated into

the models of the present study.

The Eulerian-Lagrangian rigorous model has been used to simulate the flow in a

GLCC. The results for the void fraction distribution capture the physical

phenomena of the swirling dispersed flow, showing the bubble migration towards

the GLCC center line with a high void fraction, and a low void fraction at the wall

region.

The simplified Lagrangian – Bubble tracking model predictions have been

verified against field GLCC experimental data. The simulation results for the gas

carry-under are in good agreement with the measured value, showing the potential

performance and impact of the proposed models.

The developed models can be used for the design of GLCC field applications,

capable of predicting the gas carry-under from first principles.

The following recommendations are for future studies:

174

Develop more realistic flow field correlations, taking into account the non-

axisymmetric nature of the flow in the GLCC.

Run additional systematic experiments with different physical properties and real

crudes. Use the data to verify and refine the models.

Develop control strategies for GVF control in the liquid leg so as to enable GLCC

operation at the sweet spot of multiphase meters equipped in the liquid leg as

described in the patent by Marelli and Revach (2000).

Develop hardware aimed at minimization or elimination of gas carry-under. One

possibility, shown in the figure below, is to suck the gas core to the inlet section,

circulating the gas entrained in the GLCC centerline. This configuration can also

control the amount of gas carry-under for downstream multiphase meter.

175

NOMENCLATURE

A = cross sectional area ( ft2 )

B = related to the radial location of the maximum velocity

c = mass concentration

C = coefficient

d = diameter (ft)

F = force (lbf)

g = acceleration due to gravity ( ft s/ 2 )

gc = unit conversion constant (32.2 lbm.ft/lbf. 2s )

G = total mass flux ( sftlbm ⋅2/ )

h = height (ft)

Hl = liquid holdup

I = inlet geometry factor

k = kinetic energy ( ft2/s2))

L = length (ft)

m = mass (lbm)

M = momentum (lbf/ft2)

n = number of tangential inlets

P = pressure (lbf/ft2)

q = volumetric flow rate (ft3/s)

r = radial direction of cylindrical coordinates

R = pipe radius (ft)

176

Re = Reynolds number

t = time (s)

Tm = related to the maximum momentum

u = axial and continuous-phase velocity (ft/s)

U = mean velocity (ft/s)

v = radial and dispersed-phase velocity (ft/s)

w = tangential velocity (ft/s)

Vp = velocity vector of the particle (ft/s)

Weqv = equivalent width of the slot area

z = axial direction of cylindrical coordinates

Greek Letters

α = void fraction

β = inclination angle measured from horizontal

δ = film thickness

∆ = Incremental deviation

φ = change process

ϕ = collision rate

ε = kinetic energy dissipation rate ( ft2/s3)

λ = eddy length scale

Γ = mass source

µ = viscosity (lbf s/ft2)

π = 3.1415926

54

177

θ = tangential direction

ρ = density (lbm/ft 3 )

σ = surface tension (lbf/ft)

Τ = total burst time (s)

τ = shear stress (lbf/ft2)

tυ = turbulent eddy viscosity (lbm/ft.s)

ω = angular velocity (1/s)

Ω = swirl intensity

Superscripts

= mean value of the variable

' = turbulent disturbance

Subscripts

100 = 100% separation efficiency

av = average

B = breakup

c = continuous-phase

cN = average gas core velocity at the nozzle

C = coalescence

d = disperse-phase

dm = diffusion

dj = drift

D = drag

178

e = entrainment

eff = effective

eq = equilibrium

eqv = equivalent

f = film

g = gas

H = history

i = interface

in = inlet

is = inlet slot

l = liquid

L = lift

max = maximum

min = minimum

m = mixture

M = added mass

p = particle

ph = phase

r = radial direction

rev = reversal flow

s = slug body

sep = separator

sg = superficial gas

179

shift = maximum of the turbulent kinetic energy

sl = superficial liquid

t = tangential

T = total

u = slug unit

w = pipe wall

W = buoyancy

z = axial direction

Abbreviations

GLCC = gas-liquid cylindrical cyclone

TUSTP = Tulsa University Separation Technology Projects

GCU = gas carry-under

PGCU = percent of gas carry-under

180

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