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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.
iv
• 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.
v
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.
vi
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
vii
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
viii
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
ix
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
xi
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
xii
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
xiii
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
REFERENCES
1. Algifri, A. H. et. al.: “Eddy Viscosity in Decaying Swirl Flow in a Pipe”, Applied
Scientific Research, Vol. 45, pp. 287-302, 1988.
2. Algifri, A. H. et. al: “Turbulent Measurements in Decaying Swirl Flow in a Pipe”,
Applied Scientific Research, Vol. 45, pp. 233-250, 1988.
3. Arpandi I.A., Joshi A.R., Shoham, O., Shirazi, S. and Kouba, G.E.: “Hydrodynamics
of Two-Phase Flow in Gas-Liquid Cylindrical Cyclone Separators,” SPE 30683
presented at SPE 70th Annual Meeting, Dallas, October 22-26, 1995, SPEJ,
December 1996, pp. 427-436.
4. Bandopadhyay, P.R., Pacifico, G.C. and Gad-el-Hak, M.: “Sensitivity of a Gas-Core
Vortex in a Cyclone-Type Gas-Liquid Separator,” Advanced Technology and
Prototyping Division, Naval Undersea Warfare Center Division, Newport, Rhode
Island, 1994.
5. Barrientos, A., Sampaio, R. and Concha, F.: “Effect of the Air Core on the
Performance of a Hydrocyclone”, XVIII International Mineral Processing Conference,
Sydney, May, 1993. 267-270.
6. Chang, F. and Dhir, V. K: “Turbulent Flow Field in Tangentially Injected Swirl Flows
in Tubes”, Int. J. Heat and Fluid Flow, Vol. 15, pp. 346-356, 1994.
7. Chen, M., Mees, P.A., and Kresta, S.M.: “Characteristics of the Vortex Structure in
the Outlet of a Stairmand Cyclone: Regular Frequencies and Reverse Flow”,
181
Proceedings of the 3rd ASME/JSME Joint Fluids Conference, San Francisco,
Califormia, July 18-23, 1999.
8. Colman, D.A., Thew, M.T., and Lloyd, D.D.: “The Concept of Hydrocyclones for
Separating Light Dispersions and a Comparison of Field Data with Laboratory
Work”, Second International Conference on Hydrocyclones, Paper F2, England, 19-
21 September 1984
9. Crowe, C.: “Multiphase flows with droplets and particles”, CRS Press LLC, 1998.
10. Davies, E.E.: "Compact separators for offshore production," 2nd, New Technology for
the Exploration & Exploitation of Oil and Gas Resources Symposium. Luxembourg,
5 Dec. 1984. London, Eng.,BP Research Centre, 1985, p. 621-629, Proceedings, v. 1.
11. Davies, E.E. and Watson, P.: “Miniaturized Separators for Offshore Platforms,”
Proceedings of the 1st New Technology for Exploration & Exploitation of Oil and
Gas Reserves Symposium, Luxembourg, April 1979, pp. 75-85.
12. Devulapalli, B. and Rajamani, R.K.: “A Comprehensive CFD Model for ParticleSize
Classification in Industrial Hydrocyclones”, Hydrocyclones '96, pp. 83-104.
13. Duineveld, P. C.: “Bouncing and Coalescence of Two Bubbles in Water,” Ph.D.
Dissertation, Twente University, Netherlands 1994.
14. Erdal, F.:“Local Measurements and Computational Fluid Dynamic Simulations in a
Gas-Liquid Cylindrical Cyclone Separators,” Ph.D. Dissertation, The University of
Tulsa, 2001.
182
15. Farchi, D. “A study of Mixers and Separators for Two-phase flow in M.H.D. Energy
Conversion Systems”, M.S. Thesis (in Hebrew), Ben-Gurion University, Israel, 1990.
16. Fekete, Lancelot A.: "Vortex tube separator may solve weight space limitations,”
World Oil (July 1986), p. 40-44.
17. Gomez, L.E.: “A State-of-the Art Simulator and Field Application Design of Gas-
Liquid Cylindrical Cyclone Separators,” M.S. Thesis, The University of Tulsa, 1998.
18. Gomez, L., Mohan, R., Shoham, O., Marrelli, J. D. and Kouba, G.: “Aspect Ratio
Modeling and Design Procedure for GLCC Compact Separators”, ASME Transation,
JERT Journal, March 1999, vol. 121, No. 1, pp. 15-23.
19. Gomez, L., Mohan, R., Shoham, O., and Kouba, G.: “Enhanced Mechanistic Model
and Field Application Design of Gas-Liquid Cylindrical Cyclone Separator”, SPE
Journal, Vol. 5, No 2, June 2000.
20. Hargreaves, J.H. and Silvester, R.S.: “Computational Fluid Dynamics Applied to the
Analysis of Deoling Hydrocyclone Performance”, Trans IChemE, Vol. 68, Part A,
July 1990.
21. Ihme, F., Schmidt-Traud H., Brauer, H., 1972, Chemie-Ingd Tech., Vol. 44, No. 5
pg. 306
22. Ishii, M.: Thermo Fluid Dynamic Theory of Two Phase Flow, Eyrolles, Paris, 1975
23. Ishii, M.: "Interfacial Area Measurement and Interfacial Area Transport Equation,"
FEDSM97-3527, ASME, Vancouver, Canada, June 22, 1997.
183
24. Ishii, M. & N. Zuber 1979 Drag coefficient and relativ velocity in bubbly, droplet or
particulate flows. AIChE J. 25, 843-854.
25. Ito, S., Ogawa, K. and Kuroda, C.: “ Decay Process of Swirling Flow in a Circular
Pipe”, International Chemical Engineering, Vol. 19, No. 4, pp. 600-611, 1979.
26. Kitoh, O.: “Experimental Study of Turbulent Swirling Flow in a Straight Pipe”, J. of
Fluid Mechanics, 1991, Vol. 225, pp. 445-479.
27. Kobayashi, T. and Yoda, M. “Modified κ-ε model for turbulent swirling flow in a
straight pipe”. JSME Intl J. 30, 66. 1987.
28. Kocamustafaogullari and Ishii “Foundation of the interfacial area transport equation
and its closure relations”, Int. J. Heat Mass Transfer. Vol.38, No.3, pp.481-493,
1995.
29. Kouba, G.E., Shoham, O., and Shirazi, S.: “Design and Performance of Gas-Liquid
Cylindrical Cyclone Separators”, Proceedings of the BHR Group 7th International
Meeting on Multiphase Flow, Cannes, France, June 7-9, 1995, pp. 307-327.
30. Kouba, G.E. and Shoham, O.: “A Review of Gas-Liquid Cylindrical Cyclone
(GLCC) Technology,” presented at the “Production Separation Systems”
International Conference, Aberdeen, England, April 23-24, 1996.
31. Kumar, R. and Conover, T.: “Flow Visualization Studies of a Swirling Flow in a
Cylinder” Experimental Thermal and Fluid Science, Elsevier Science Publishing Co.,
1993, pp. 254-262.
184
32. Kurokawa, J.: “Gas-Liquid Flow Characteristics and Gas-Separation Efficiency in a
Cyclone Separator,” ASME FED-Vol. 225, Gas Liquid Flows, 1995, pp. 51-57
33. Lagutkin, M.G., Baranov, D.A., and Markov, A.V.: “Method for Calculation of
Separation Indexes of Suspensions in a Cylindrical Cocurrent Hydrocyclone”,
translated from Khimicheskoe i Neftyanoe Mashinostroenie, No. 4, pp. 20-21, April
1991.
34. Lee, C-H. “Bubble Breakup and Coalescence in Turbulent Gas-Liquid Dispersions”
Chem. Eng. Comm., Vol. 59, pp. 65-84, 1987.
35. Luo, H. and Svendsen, H.: “Theoretical Model for Drop and Bubble Breakup in
Turbulent Dispersions” AIChe Journal, May 1996, vol.42, No. 5, pp. 1225-1233.
36. Magnaudet, J. J.: "The Forces Acting on Bubbles and Rigid Particles," FEDSM,
ASME, Vancouver, Canada, June 22, 1997.
37. Malhotra, A.: “Modelling the Flow in a Hydrocyclone”, The Canadian Journal of
Chemical Engineering, Vol. 72, December 1994.
38. Mantilla, I.: “Bubble Trajectory Analysis in GLCC Separators,” M.S. Thesis, The
University of Tulsa, 1998.
39. Marrelli, J.D. and Revach, F.M.: "Three-phase Fluid Flow Measurement System and
Method", U.S. Patent No. 6,128,962, October 2000.
40. Marti, S., Erdal, F., Shoham, O., Shirazi, S. and Kouba, G.: “Analysis of Gas Carry-
Under in Gas-Liquid Cylindrical Cyclones,” presented at the Hydrocyclones 1996
International Meeting, St. John College, Cambridge, England, April 2-4, 1996.
185
41. Mei R, Klausner and Lawrence “A Note on the history force on a spherical bubble at
finite Reynolds number,” Phys. Fluids, Vol. 6, No.1, January 1994, pp. 418-420.
42. Millington, B.C. and Thew, M.T.: “LDA Study of Component Velocities in Air-
Water Models of Steam-Water Cyclone Separators,” Proceeding of the 3rd
International Conference on Multiphase Flow, The Hague, The Netherlands, May 18,
1987, pp. 115-125.
43. Motta, B.R.F., Erdal, F.M., Shirazi, S.A., Shoham, O. and Rhyne, L.D.: “Simulation
of Single-phase and Two-Phase Flow in Gas-Liquid Cylindrical Cyclone Separators,”
to be presented at the ASME Summer Meeting, Fluid Eng. Division, Vancouver,
Canada, June 22-26, 1997.
44. Nebrensky, N.T., Morgan, G.E. and Oswald, B.J.: “Cyclone for gas/oil separation,”
Proceedings of the International Conference on Hydrocyclones, Churchill College,
Cambridge, UK, 1980, paper No.12, pp. 167-177.
45. Nissan, A.H. and Bresan V.P.: “Swirling Flow in Cylinders”, A. I. Ch. E. Journal,
December 1961, Vol. 7, No.4, pp.543-547.
46. Oranje, I. L.: "Cyclone-type separators score high in comparative tests," Oil & Gas
Journal v. 88., no. 4 (22 Jan. 1990), p. 54-57.
47. Patankar, S.: Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing
Corporation, 1980.
48. Prado, M. G.: “A Block Implicit Numerical Solution Technique for Two-Phase
Multidimensional Steady State Flow,” Ph.D. Dissertation, The University of Tulsa,
1995.
186
49. Prince, M. and Blanch, H.: “Bubble Coalescence and Breakup in Air-Sparged Bubble
Columns Dispersions” AIChe Journal, May 1990, vol.36, No. 10, pp. 1485-1499.
50. Rajamani R.K. and Devulapalli B.: “Hydrodynamic Modeling of Swirling Flow and
Particle Classification in Large-Scale Hydrocyclones”, KONA Powder and Particle
No.12, 1994, pp. 95-104.
51. Reydon, R.F. and Gauvin, W.H.: “Theoretical and Experimental Studies of Confined
Vortex Flow,” The Canadian Journal of Chemical Engineering, vol.59, February
1981, pp. 14-23.
52. Schiller L. and Naumann (1933), VDI Zeits., 77, p.318.
53. Sevilla, E.M. and Branion, R.M.: “Computational Fluid Dynamics Calculations for
Flow in Hydrocyclones”, 81st Annual Meeting, Technical Section, CPPA, 1993
54. Small, D.M. and Thew, M.T.: “The Influence of Swirl and Turbulent Anisotropy on
CFD Modelling for Hydrocyclones”, 1995.
55. Thomas “Bubble Coalescence in Turbulent Flows,” Int. J. Multiphase Flow, vol. 7,
No.6, pp. 709-717, 1981.
56. Trapp, J.A. and Mortensen, G.A.: “A Discrete Particle Model for Bubble-Slug Two
Phase Flows,” Journal of Computational Physics, vol.107, 1993, pp. 367-377.
57. Wang, S.: “Control System Analysis of Gas-Liquid Cylindrical Cyclone Separators”,
M.S. Thesis, The University of Tulsa, 1997.
187
58. Wolbert, D., Ma, B.F. Aurelle, Y. and Seureau, J.: “Efficiency Estimation of Liquid-
Liquid Hydrocyclones Using Trajectory Analysis,” AIChe Journal, June 1995,
vol.41, No. 6, pp. 1395-1402.
59. Yu, S.C.M. and Kitoh O.: “General Formulation for the Decay of Swirling Motion
Along a Straight Pipe”, International Communications in Heat and Mass Transfer,
1994, Vol. 21, No.5, pp. 719-728.
60. Zhikarev, A.S., Kutepov, A.M. and Solov'ev, V.: “Design of a cyclone separator for
the separation of gas-liquid mixtures,” Chemical and Petroleum Engineering v. 21.
no. 3/4 (Mar. 1985): p. 196-198.
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