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Benchmark Data and Analysis of Dilute Turbulent Fluid-Particle Flow in Viscous and Transitional Regimes

Permanent Link: http://ufdc.ufl.edu/UFE0041580/00001

Material Information

Title: Benchmark Data and Analysis of Dilute Turbulent Fluid-Particle Flow in Viscous and Transitional Regimes
Physical Description: 1 online resource (197 p.)
Language: english
Creator: Pepple, Mark
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: doppler, flow, laser, liquid, multiphase, slurry, solid, turbulence, velocimetry
Chemical Engineering -- Dissertations, Academic -- UF
Genre: Chemical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The effects of flow rate and solids concentration of a liquid-solid flow consisting of water and glass spheres 0.5, 1.0, or 1.5 mm in diameter are varied to investigate the viscous, transitional, and collisional flow regimes in a vertical three inch pipe. The flow is highly turbulent, with single-phase Re from 2.0x10^5 to 5.0x10^5 and solids concentration from 0.7% to 3% by volume. These conditions span a wide range of Stokes and Bagnold numbers. Laser Doppler velocimetry is used to measure the mean and fluctuating velocities of the two phases simultaneously, while the phase Doppler method is used to measure particle size and thus discriminate between the phases. The detailed, non-intrusive velocity measurements under the conditions investigated provide a unique data set by which multiphase computational fluid dynamics (CFD) models can be validated. For all particle sizes, Re, and solids concentrations the mean fluid velocity profile is very similar in shape to that of the single-phase fluid. The slip between the fluid and 0.5 mm particles is very small. The 1.0 mm particles exhibit an increase in slip as solids concentration increases. The fluctuating velocity measurements show trends characteristic of both collision-dominated and viscous-dominated flow, clearly showing the flow is in a transitional regime. In all cases, the effects of changing the Re are greater than the effects of changing the concentration of solids. There is a reduction in turbulence of both phases across the pipe with increasing Re. However, at the highest Re there is an increase in both fluid and solid turbulence, which can be explained by an increase in vortex shedding at Rep > 300. The solid fluctuating velocity of the 1.0 mm particles is significantly greater than that of the 0.5 mm particles for all conditions. At each respective Re, the solids fluctuations for the 1.0 mm particles are greater than those of the fluid in their presence, except very near the wall where they become similar. Conversely, the solids fluctuations for the 0.5 mm particles are less than those of the fluid in their presence. The difference in turbulence between the two phases decreases with increasing Re. The turbulence of both phases becomes increasingly flat near the center of the pipe with increasing Re and solids concentration. This is in agreement with the flat profiles of both fluid and solid turbulence in inertia-dominated gas-solid flows. In general, the 0.5 mm particles damp the fluid turbulence while the 1.0 mm and 1.5 mm particles are either neutral or enhance the turbulence. These data give insight into the fluid-particle interactions over a wide range of flow conditions.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Mark Pepple.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Curtis, Jennifer S.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0041580:00001

Permanent Link: http://ufdc.ufl.edu/UFE0041580/00001

Material Information

Title: Benchmark Data and Analysis of Dilute Turbulent Fluid-Particle Flow in Viscous and Transitional Regimes
Physical Description: 1 online resource (197 p.)
Language: english
Creator: Pepple, Mark
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: doppler, flow, laser, liquid, multiphase, slurry, solid, turbulence, velocimetry
Chemical Engineering -- Dissertations, Academic -- UF
Genre: Chemical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The effects of flow rate and solids concentration of a liquid-solid flow consisting of water and glass spheres 0.5, 1.0, or 1.5 mm in diameter are varied to investigate the viscous, transitional, and collisional flow regimes in a vertical three inch pipe. The flow is highly turbulent, with single-phase Re from 2.0x10^5 to 5.0x10^5 and solids concentration from 0.7% to 3% by volume. These conditions span a wide range of Stokes and Bagnold numbers. Laser Doppler velocimetry is used to measure the mean and fluctuating velocities of the two phases simultaneously, while the phase Doppler method is used to measure particle size and thus discriminate between the phases. The detailed, non-intrusive velocity measurements under the conditions investigated provide a unique data set by which multiphase computational fluid dynamics (CFD) models can be validated. For all particle sizes, Re, and solids concentrations the mean fluid velocity profile is very similar in shape to that of the single-phase fluid. The slip between the fluid and 0.5 mm particles is very small. The 1.0 mm particles exhibit an increase in slip as solids concentration increases. The fluctuating velocity measurements show trends characteristic of both collision-dominated and viscous-dominated flow, clearly showing the flow is in a transitional regime. In all cases, the effects of changing the Re are greater than the effects of changing the concentration of solids. There is a reduction in turbulence of both phases across the pipe with increasing Re. However, at the highest Re there is an increase in both fluid and solid turbulence, which can be explained by an increase in vortex shedding at Rep > 300. The solid fluctuating velocity of the 1.0 mm particles is significantly greater than that of the 0.5 mm particles for all conditions. At each respective Re, the solids fluctuations for the 1.0 mm particles are greater than those of the fluid in their presence, except very near the wall where they become similar. Conversely, the solids fluctuations for the 0.5 mm particles are less than those of the fluid in their presence. The difference in turbulence between the two phases decreases with increasing Re. The turbulence of both phases becomes increasingly flat near the center of the pipe with increasing Re and solids concentration. This is in agreement with the flat profiles of both fluid and solid turbulence in inertia-dominated gas-solid flows. In general, the 0.5 mm particles damp the fluid turbulence while the 1.0 mm and 1.5 mm particles are either neutral or enhance the turbulence. These data give insight into the fluid-particle interactions over a wide range of flow conditions.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Mark Pepple.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Curtis, Jennifer S.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0041580:00001


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1 BENCHMARK DATA AND ANALYSIS OF DILUTE TU RBULENT FLUID-PARTICLE FLOW IN VISCOUS AND TRANSITIONAL REG IMES By MARK PEPPLE A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF TH E REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 20 10

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2 20 10 Mark Pepple

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3 To my family and friends for their encouragement throughout graduate school If you wait for perfect conditions, you will never get anything done Ecclesiastes 11:4 Not to us, O Lord, not to us but to your name be the glory, because of your love and faithfulness Psalm 115:1

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4 ACKNOWLEDGMENTS My sincere appreciation goes to my advisor, Jennifer Sinclair Curtis for her guidance, encourag ement, and support. I am most grateful for the eternal perspective she exuded in the midst of a demanding professional career. I am indebted to Dr. Caner Yurteri for instructing me on LDV my first two years and entertaining all my subsequent questions. I thank my parents for their love, support, and encouragement throughout the trials of graduate school. I also want to remind them that graduate school was initially their idea. I am grateful for my many friends without whom I would not hav e survived or enjoyed the last fiveplus years. Allyn and Eric, thanks for the weekly lunches and book discussions, they were always a welcomed interruption. O fficemates thank you for putting up with me and sharing in the ups and downs of graduate school.

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5 TABLE OF CONTENTS ACKNOWLEDGMENTS ...................................................................................................... 4 page LIST OF TABLES ................................................................................................................ 8 LIST OF FIGURES ............................................................................................................ 10 LIST OF ABBREVIATIONS .............................................................................................. 13 ABSTRACT ........................................................................................................................ 18 CHAPTER 1 INTRODUCTION AND BACKGROUND .................................................................... 20 Introduction ................................................................................................................. 20 Background .......................................................................................................... 21 Stokes number .............................................................................................. 22 Bagnold number ............................................................................................ 23 Mean Flow ................................................................................................................... 25 Collision -Dominated Flow .................................................................................... 25 Viscous -Dominated Flow ..................................................................................... 28 Turbulence Modulation ............................................................................................... 30 Collision -Dominated Flow .................................................................................... 30 Viscous -Dominated Flow ..................................................................................... 31 Turbulence Modulation Correlations ................................................................... 32 Radial Solids Con centration Profile ........................................................................... 34 Two -Phase Flow Measurement Techniques ............................................................. 35 Two -Phase Flow Modeling ......................................................................................... 37 Motivation .................................................................................................................... 39 2 EXPERIMENTAL SETUP AND METHODS .............................................................. 44 Experimental Setup .................................................................................................... 44 Experimental Particles ......................................................................................... 47 Laser Doppler Velocimetry .................................................................................. 49 Basic principles .............................................................................................. 49 Phase Doppler anemometry ......................................................................... 52 Solids concentration ...................................................................................... 54 Experimental Procedures ........................................................................................... 56 LDV/PDPA System .............................................................................................. 56 Phase Discrimination ........................................................................................... 58 Data Limitations ................................................................................................... 59 Exclusion of 1.5 mm solid data ..................................................................... 59 Limited radial penetration in slurry of 0.5 mm particles ............................... 60

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6 Procedural Obstacles ........................................................................................... 60 Flow control and air bubbles ......................................................................... 60 Excessive tur bulence .................................................................................... 61 Phase discrimination and particle selection ................................................. 63 Other improvements ...................................................................................... 66 Equipment/instrumentation issues ................................................................ 67 Error Analysis ....................................................................................................... 68 Velocity and size measurements .................................................................. 68 Radial location ............................................................................................... 69 Solids concentration ...................................................................................... 70 Pressure measurements ............................................................................... 71 3 TWO -PHASE MODEL ................................................................................................ 85 Kinetic Theory of Granular Flow ................................................................................. 85 Governing Equations .................................................................................................. 86 Boundary Conditions and Model Solution .................................................................. 88 Results ........................................................................................................................ 88 4 PRESSURE LOSS IN PIPE BENDS OF LARGE CURVATURE AT HIGH RE ....... 91 Introduction ................................................................................................................. 91 Experimental ............................................................................................................... 95 Results and Discussion .............................................................................................. 96 Influence of Downstream Tangent: Configuration A ........................................... 97 Influence of Downstream Tangent: Configuration B ........................................... 99 Conclusion ................................................................................................................ 100 5 SINGLE PHASE VALIDATION ................................................................................ 108 In troduction ............................................................................................................... 108 Experimental ............................................................................................................. 109 Scaling ....................................................................................................................... 110 Results ...................................................................................................................... 111 Effect of Re ......................................................................................................... 112 Turbulence Measurements in Air using Hot Wire ............................................. 112 LDV v s Hot wire Measurements in Air Flow ..................................................... 113 Turbulence Measurements in Water ................................................................. 114 Conclusion ................................................................................................................ 115 6 LIQUID -SOLID FLOW .............................................................................................. 124 Pressure Drop ........................................................................................................... 124 Correlations ........................................................................................................ 125 Bartosik ........................................................................................................ 125 Littman and Paccione .................................................................................. 127 Ferre and Shook .......................................................................................... 128 Results ................................................................................................................ 129

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7 Experimental ................................................................................................ 129 Correlations ................................................................................................. 131 V elocity Measurements ............................................................................................ 132 Fully Developed Flow and Reproducibility of Data ........................................... 133 Mean Velocity ..................................................................................................... 134 Fluctuating Velocity ............................................................................................ 135 Effect of Re .................................................................................................. 135 Effect of solids concentration ...................................................................... 137 Error Analysis ..................................................................................................... 140 Conclusion ................................................................................................................ 141 7 CONCLUSIONS AND RECOMMENDATIONS ....................................................... 165 APPENDIX A EXPERIMENTAL VELOCITY DATA ........................................................................ 169 Two -Phase Flows ..................................................................................................... 169 0.5 mm Particles ................................................................................................ 169 1.0 mm Particles ................................................................................................ 172 1.5 mm Particles ................................................................................................ 177 Reproducibility .................................................................................................... 181 Fully Developed Flow ........................................................................................ 182 Single -Phase Flows .................................................................................................. 182 B EXPERIMENTAL PRESSURE DATA ...................................................................... 184 Two -Phase Flows ..................................................................................................... 184 Single -Phase Flows .................................................................................................. 184 LIST OF REFERENCES ................................................................................................. 188 BIOGRAPHICAL SKETCH .............................................................................................. 197

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8 LIST O F TABLES Table page 1 -1 Mean velocity behavior for collision-dominated flow ............................................. 41 1 -2 Mean velocity behavior for viscous -d ominated flow ............................................. 41 1 -3 Fluctuating velocity behavior for collision -dominated flow .................................... 42 1 -4 Fluctuating velocity behavior for viscous dominated flow ..................................... 42 2 -1 LDV/PDPA settings ................................................................................................ 80 4 -1 Published experimental pressure loss data in pipe bends ................................. 102 4 -2 Total bend loss coefficient ................................................................................... 107 5 -1 Turbulence measurements in air ......................................................................... 117 5 -2 Turbulence measurements in water .................................................................... 118 5 -3 Comparison of friction velocity values ................................................................. 119 5 -4 Ratio of mean to maximum velocity, power law exponent .................................. 119 5 -5 DNS turbulence data ............................................................................................ 119 6 -1 Experimental parameters in dimensionless numbers ......................................... 146 A-1 Fluid and solid velocity measurements for 0.7% solids at Re=2.0x105.............. 169 A-2 Fluid and solid velocity measurements for 1.7% solids at Re=2.0x105.............. 169 A-4 Fluid and solid velocity measurements for 0.7% solids at Re=3.35x105............ 170 A-5 Fluid and solid velocity measurements for 1.7% solids at Re=3.35x105............ 170 A-6 Fluid and solid velocity measurements for 3% solids at Re=3.35x105 ............... 171 A-7 Fluid and solid velocity meas urements for 0.7% solids at Re=5.0x105.............. 171 A-8 Fluid and solid velocity measurements for 1.7% solids at Re=5.0x105.............. 171 A-9 Fluid and solid velocity measurements for 3% solids at Re=5.0x105 ................. 172 A-10 Fluid and solid velocity measurements for 0.7% solids at Re=2.0x105.............. 172 A-12 Fluid and solid velocity measurements for 3% solids at Re=2.0x105 ................. 173

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9 A-14 Fluid and solid velocity measurements for 1.7% solids at Re=3.35x105............ 174 A-16 Fluid and solid velocity measurements for 0.7% solids at Re=5.0x105.............. 175 A-18 Fluid and solid velocity measurements for 3% solids at Re=5.0x105 ................. 176 A-19 Fluid velocity measurements for 0.7% solids at Re=2.0x105 ............................. 177 A-20 Fluid velocity measurements for 1.7% solids at Re=2.0x105 ............................. 177 A-22 Fluid velocity measurements for 0.7% solids at Re=3.35x105 ........................... 178 A-24 Fluid velocity measurements for 3% solids at Re=3. 35x105 .............................. 179 A-26 Fluid velocity measurements for 1.7% solids at Re=5.0x105 ............................. 180 A-28 Three measurements of solids fluctuating velocity for 1.0 mm particles at 0.7% solids at Re=2.0x105 ................................................................................... 181 A-29 Solid mean and fluctuating velocity at two radii and two axial locations for 0.5 mm particles at 0.7% solids at Re=2.0x105 ......................................................... 182 A-30 Mean and fluctuating velocity of single phase water .......................................... 182 B-3 Pressure gradient for 0.5 mm particles ............................................................... 184 B-3 Pressure gradient for 1.0 mm particles ............................................................... 184 B-3 Pressure gradient for 1.5mm particles ................................................................ 184 B-1 Pressure along vertical pipe and bend with sudden expansion at downstream tangent (Configuration A) ..................................................................................... 18 5 B-2 Pressure along vertical pipe and bend with steel pipe at downstream tang ent (Configuration B) .................................................................................................. 186 B-3 Pressure along vertical pipe and bend with sudden expansion at downstream tangent (Configuration A) with vertical adjustment ............................................. 187 B-4 Pressure along vertical pipe and bend with steel pipe at downstream tangent (Configuration B) with vertical adjustment ........................................................... 187

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10 LIST OF FIGURES Figure page 1 -1 Gas -solid pressure drop ......................................................................................... 43 2 -1 Flow loop ................................................................................................................ 74 2 -2 Venturi eductor ....................................................................................................... 75 2 -3 Configuration of pressure tap ................................................................................ 75 2 -4 Vertical pipe dimensions ........................................................................................ 76 2 -5 Experimen tal particles ............................................................................................ 77 2 -6 Resolving directional ambiguity with frequency shift ............................................ 78 2 -7 LDV probe volume fringes ..................................................................................... 79 2 -8 Experimental probe volume dimensions ............................................................... 79 2 -9 Light scattering intensity for 1 mm sphere for 514 nm light .................................. 81 2 -10 Frequency and phase measurements of a Doppler burst .................................... 81 2 -11 Signal processing flowchart ................................................................................... 82 2 -12 Phase Doppler setup .............................................................................................. 83 2 -13 Sampling rate of Doppler burst. ............................................................................. 84 3 -1 Solid fluctuating velocity of gas -solid flow of 243 m polystyrene particles at Re ~ 2.2x104 ........................................................................................................... 90 3 -2 Solid fluctuating velocity of liquid -solid flow of 2.32 mm glass particles at Re = 6.7x104................................................................................................................. 90 4 -1 Loss coefficient profiles ........................................................................................ 103 4 -2 Bend geometry and discharge configurations ..................................................... 104 4 -3 Loss coefficient upstream of bend entrance ....................................................... 105 4 -4 Loss coefficient through bend .............................................................................. 106 5 -1 Effect of Reynolds number in air measurements ................................................ 120 5 -2 Effect of Re in water measurements ................................................................... 121

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11 5 -3 Effect of pipe diameter ......................................................................................... 122 5 -4 LDV vs. hot wire measurements in air ................................................................ 122 5 -5 Turbulence measurements in water .................................................................... 123 5 -6 Turbulence measurements in air and water ........................................................ 123 6 -1 Pressure drop with 0.5 mm particles ................................................................... 143 6 -2 Pressure drop with 1.0 mm particles ................................................................... 144 6 -3 Pressure drop with 1.5 mm particles ................................................................... 145 6 -4 Dimensionless parameters of experiments ......................................................... 147 6 -5 Full y developed flow ............................................................................................. 148 6 -6 Linear pressure profile ......................................................................................... 148 6 -7 Reproducibility of measurements ........................................................................ 149 6 -8 Fluid mean velocity at 0.7% solids ...................................................................... 150 6 -9 Flu id mean velocity at 1.7% solids ...................................................................... 151 6 -10 Fl uid mean velocity at 3% solids .......................................................................... 152 6 -11 Solid mean velocity at 0.7% solids ...................................................................... 153 6 -12 Solid mean velocity at 1.7% solids ...................................................................... 154 6 -13 Solid mean velocity at 3% solids ......................................................................... 155 6 -14 Fluid fluctuating velocity at 0.7% solids ............................................................... 156 6 -15 Fluid fluctuating velocity at 1.7% solids ............................................................... 157 6 -16 Fluid flu ctuating velocity at 3% solids .................................................................. 158 6 -17 Solid fluctua ting velocity at 0.7% solids ............................................................... 159 6 -18 Solid fluctuating velocity 1.7% solids ................................................................... 160 6 -19 Solid flu ctuating velocity at 3% s olids .................................................................. 161 6 -20 Fluid fluctuating veloci ty error based on ensemble size ..................................... 162 6 -21 Evolution of uf with data count ............................................................................ 162

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12 6 -22 Evolution of us with data count ............................................................................ 163 6 -23 Fluid fluctuating velocity error based on standard deviation of uf after 250 measurements ...................................................................................................... 164

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13 LIST OF ABBREVIATION S A cross-sectional area of probe volume [m2] Ba Bagnold number C0 correction factor based on length of downstream tangent Cd coefficient of drag Cf correction factor based on pipe roughness CRe corr ection factor based on Re c1 k turbulence model constant c2 k turbulence model constant c3 k turbulence model constant D pipe diameter [m] DL laser beam diameter [m] d particle diameter [m] d30 volume average particle diameter [m] Ept pseudo thermal energy [m2 s2] F focal length [mm] FD drag force of fluid on particle FKS interfacial energy flux by fluid-solid interactions FMOD fluid particle interaction term Fr Froude Number fD Doppler frequency [s1] ff fluid phase friction factor fs solid-phase friction factor fx flux norma l to probe volume cross section f1 k turbulence model constant

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14 f2 k turbulence model constant g gravity [m s2] if hydraulic gradient of fluid im hydraulic gradient of two phase flow K pressure loss coefficient Ki inertial coefficient in Bagnolds s Kv viscous coefficient in Bagnolds s k turbulent energy production [m2 s2] kr surface roughness [m] kt total bend loss coefficient kt* kt at Re = 106 le length of most energetic eddy [m] N ensemble size n number of particles P pressure, including height adjustment if needed [Pa] Pmeas raw pressure [Pa] Pref pressure 37 diameters upstream of bend entrance [Pa] qpt pseudo thermal energy conductive flux R absolute pipe radius [m] Rb radius of bend curvature Re Reynolds number = D f/ Ref Reynolds number based on mean fluid velocity in two phase flow Rep particle Reynolds number = d urf/ r pipe radius [m] St turbulent Stokes number

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15 SzP standard error in pressure drop T period of signal [s] t time [s] tf fluid response time [s] tp particle response time [s] Uf mean fluid velocity [m s1] Um mean slurry velocity [m s1] Us mean solid velocity [m s1] Ut friction velocity [m s1] U instantaneous velocity [m s1] y ur absolute value of slip velocity [m s1] ut shear induced turbulen ce in single -phase flow [m s1] ux velocity normal to LDV fringes [m s1] V probe volume [m3] W uncertainty in pressure drop X* location downstream of bend where pressure gradient is equal to that upstream of bend z vertical distance [m] zc confidence coef ficient Greek function of (R/r) in kt shear rate [s1] pt pseudo thermal energy dissipation rate vertical distance [m] t total pressure change due to bend [Pa] time between signal detection at multiple receivers [s]

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16 f fringe spacing [m] x pr obe volume length in x direction [m] y probe volume length in y direction [m] z probe volume length in z direction [m] turbulent energy dissipati on error in the population mean s ensemble mean half the angle of intersecting laser beams b total an gle of bend deflection wavelength [m] L linear concentration in Ba s constant in Prandtls universal l aw of friction for smooth pipes w linear concentration based on the solids concentration near wall fluid viscosity [kg m1s1] ef effective fluid viscosity [kg m1s1] T turbulent eddy viscosity [kg m1s1] solids volume fraction 0 maximum soli ds volume fraction in Ba = 0.64 f fluid density [kg m3] m slurry density [kg m3] s solid density [kg m3] standard deviation e ensemble standard d eviation s particle stress tensor f fluid shear stress

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17 m slurry shear stress s solid shear stress phase difference turbulence modulation parameter of Hosokawa and Tomiyama [25] r angle of receiver angle created by the plane that bisects the two photo detectors in PDPA

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18 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy BENCHMARK DATA AND ANALYSIS OF DILUTE TU RBULE NT FLUID-PARTICLE FLOW IN VISCOUS AND TRANSITIONAL REG IMES By Mark Pepple May 20 10 Chair: Jennifer S. Curtis Major: Chemical Engineering The effects of flow rate and solids concentration of a liquid -solid flow consisting of water and glass spheres 0.5, 1.0, or 1.5 mm in diameter are varied to investigate the viscous, transitional and collisional flow regimes in a vertical three inch pipe. The flow i s highly turbulent, with single -phase Re from 2.0x105 to 5.0x105 and solids concentration from 0.7% to 3% by volume. These conditions span a wide range of Stokes and Bagnold numbers. Laser Doppler velocimetry i s used to measure the mean and fluctuating velocities of the two phases simultaneously, while the phase Doppler method i s used to measure particle si ze and thus discriminate between the phases. The detailed, non -intrusive velocity measurements under the conditions investigated provide a unique data set by which multiphase computational fluid dynamics ( CFD ) models can be validated. For all particle s izes, Re, and solids concentrations the mean fluid velocity profile is very similar in shape to that of the singlephase fluid. The slip between the fluid and 0.5 mm particles is very small. The 1.0 mm particles exhibit an increase in slip as solids conc entration increases. The fluctuating velocity measurements show trends characteristic of both collision dominated and viscous -dominated flow, clearly showing

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19 the flow is in a transitional regime. In all cases, the effects of changing the Re are greater t han the effects of changing the concentration of solids. There is a reduction in turbulence of both phases across the pipe with increasing Re. However, at the highest Re there is an increase in both fluid and solid turbulence, which can be explained by an increase in vortex shedding at Rep > 300. The solid fluctuating velocity of the 1.0 mm particles is significantly greater than that of the 0.5 mm particles for all conditions. At each respective Re, the solids fluctuations for the 1.0 mm particles are greater than those of the fluid in their presence, except very near the wall where they become similar. Conversely, the solids fluctuations for the 0.5 mm particles are less than those of the fluid in their presence. The difference in turbulence between the two phases decreases with increasing Re. The turbulence of both phases becomes increasingly flat near the center of the pipe with increasing Re and solids concentration This is in agreement with the flat profiles of both fluid and solid turbulence in inertia -dominated gas -solid flows. In general, the 0.5 mm particles damp the fluid turbulence while the 1.0 mm and 1.5 mm particles are either neutral or enhance the turbulence. These data give insight into the fluid particle interactions over a wide range of flow conditions.

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20 CHAPTER 1 INTRODUCTION AND BACKGROUND Introduction Fluid -solid twophase flows can be found in various settings including industrial processes (pneumatic/hydraulic conveying and fluidized bed reactors ), natural phenomena (sand/sediment in oceans and other bodies of water), and biolog y (blood flow). Fluid -solid flows are found in the mining, chemical, oil, pharmaceutical, and food industries. Fundamental understanding of fluid-solid flows is necessary for the accurate design o f pumps, pipelines, reactors, separation processes, heat exchangers, and any other operation involving fluid-solid materials. The presence of a solid-phase can have a significant impact on momentum, heat, and mass transfer and accordingly necessitates a f undamental understanding of fluid-particle interactions. From an industrial perspective liquid -solid flows, or slurries, are typically classified as either settling or non -settling. This demarcation depends on particle density and size, fluid viscosity, and slurry velocity. Non-settling slurries are usually composed of particles m and can be considered homogeneous. This homogeneity allows for the determination of an effective viscosity which is required for design of reacting and transporting operations. Settling slurries are comprised of two distinct phases and cannot be characterized by an effective viscosity. They have a minimum transport, or deposition, velocity and in horizontal pipes exhibit a non axisymmetric solids profile. The two phas es that compose non -settling slurries interact; the solids can undergo direct collisions and also be influenced via the fluid. These interactions are often complex and are not fully understood.

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21 Th is complexity results in significant challenges in the de sign, scale up, and optimization of multi phase systems. These difficulties could be largely remedied by accurate predictive computer models. However, reliable simulation models do not exist, and consequently design is often based on large expensive physi cal models or other similar existing equipment. These methods are not reliable due to the complexity of multiphase systems and result in significant downtime for many two -phase operations (Merrow [1 ] and Bell [2] ). The development of accurate computer mo dels requires detailed experimental data by which the models can be verified. Model validation requires mean and fluctuating velocities of both phases and solids concentration profiles at varying flow rates and solids concentrations. These detailed measurements are vital to the development of constitutive relationships that link the solids motion and material properties with stress, kinetic energy produc tion, and energy dissipation. A nonintrusive measurement technique is essential for acquiring meanin gful experimental data in multiphase flows. The solid-phase can damage intrusive measurement techniques and any intrusive device will inherently disrupt the flow. Laser Doppler velocimetr y (LDV) has been used to obtain detailed velocity data in multiphas e flows and jets fo r various particle sizes and Re, including gas -solid (Maeda et al. [ 3 ], Lee and Durst [ 4 ] Tsuji et al. [ 5 ] Sheen et al. [ 6 ] van de Wall and Soo [7 ] Jones [ 8 ] Hadinoto et. al. [ 9 ] ), gas -liquid (Theofanous and Sullivan [ 10 ] and Wang et al. [11] ), liquid -liquid (Hu et al. [1 2 ] ), and liquid-solid (Zisselmar and Molerus [1 3 ] Abbas a nd Crowe [14] Nouri et al. [1 5 ] et al. [16 ] and Assad et al. [1 7 ] ). Background Fluid particle flows can be categorized into two flow regimes In cases where viscosity dominates inter particle momentum and energy transfer occur via the fluid.

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22 F luid particle systems where the densities of the two phases are nearly equal, the solids are very small, or the flow rate is very low are typically in the m acroviscous regime. Alternatively when particle collisions and particle inertia dominate, particles interact directly and transfer energy and momentum through direct collisions, unaffected by the interstitial fluid This is known as the graininer tia regime and is characteristic of flows of l arge particles with densities greater than the fluid. Between these two extremes, both collisional and viscous forces are significant. Viscous -d ominated flow typically includes gas -solid and liquid-solid flows with small particles. Additionally, liquid -solid flows that have low solid concentrations low velocities, or a neutrally buoyant solidphase also tend to be viscous d ominated flows, (Koh et al. [1 8 ] Averbakh et al. [1 9 ], Zisselmar and Molerus [1 3 ] a nd Nouri et al. [15 ] ) Collision d ominated flows are usually gas -solid flows with larger and denser particles, and may include high velocities and high solids loadings where solids loading are defined as the ratio of solid flux to fluid flux (Tsuji et al. [ 5 ] Lee and Durst [ 4 ] and Sheen et al [6 ] ) Stokes n umber T wo common methods exist f or qualifying particle forces in multiphase flows. The first is the Stokes number. According t o Hardalupas et al. [2 0 ] the turbulent Stokes number can be used to describe a particles responsiveness to fluid phase turbulence fluctuations. Stokes number s less than 1 characterize responsive particles while numbers greater than one are unresponsive the particle fluctuating motion does not follow the fluid fluctuation s. The turbulent Stokes number is defined as: f pt t St (1 -1 )

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23 w here tp and tf are the particle and fluid response times, respectively 18 d ts 2 p (1 -2 ) f fU D t (1 -3 ) where Uf is the mean fluid velocity D the p ipe diameter, d the particle diameter, s the The work of Simonin et al. [ 21] and Yamamoto et al [22 ] suggest that particles with Stokes numbers larger than 1 will engage in particle -particle collisions, even at very low solids concentrations. Further more, these collisions have a significant influence on the solid fluctuating motion and the radial concentration profile. Bagnold number The second common method of classification is the Bagnold number. Bagnold [ 23 ] defined two flow regimes, the macroviscous and grain inertia regime s, with the ir differentiation defined by the Bagnold number which is a ratio of viscous and inertial forces d d Ba2 / 1 L 2 f 2 / 3 2 2 L 2 f (1 -4 ) where f is the density of the fluid shear rate, estimated as the mean fluid velocity divided by the pipe radius L is the linear concentration defined as: 1 3 / 1 0 L1 (1 -5 ) where is the solids volume fraction and 0 the maximum solids concentration, which in the case of spheres is 0.64. Bagnold numbers greater than 450 are said to be

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24 characteristic of flows dominated by solid -solid interactions and Bagnold numbers less than 40 are characteristic of viscous flow. Between these two n umbers, both collisional and viscous forces are relevant and it is this region that is the focus of this research. The 1954 work of Bagnold [23] in which he identified the macro viscous and graininertia flow regimes has been critiqued extensively, w ith a complete review of his experiments offered by Hunt et al. [2 4 ]. Bagnold [ 23 ] stated that the rate of collisions and the momentum change per collision are both proportional to the shear rate and thus the stress is proportional to the square of the sh ear rate. Bagnolds scaling has been observed numerically by Silbert et al. [ 2 5 ] for granular flow down an incline. However, Hunt et al [ 2 4 ] argue d that Bagnolds [ 23 ] recorded shear stress measurements were influenced by the end walls of his rotational cylinder, effects Bagnold ignored in his paper. The experiments of Hunt et al. [2 4 ] resulted in a shear stress dependence on the shear rate to the 1.5 power rather than the second power. Furthermore, Hunt et al. [2 4 ] suggest ed that the changes Bagnold [ 23 ] identified as the macro viscous and grain inertia flow regimes were a change from a linea r shear flow to a flow dominated by the boundary layer along the rotating end walls. A further crit ique was offered by Wilson [26 ] who contended that data obtained from rotating cylind ers can accurately predict dense flows with many particle collisions but is not suitable for predicting more dilute flows, like those often found in pipes because there are fewer particle collisions. Admittedly, the exact numbers off ered by Bagnold [ 23 ] for denoting his various flow regimes may not precisely describe slurry flow in a vertical pipe. However, this is not of concern. Both viscous and collisional forces exist in a two -phase flow and their relative magnitudes are examine d and

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25 manipulated in this work through the variation of fluid velocity and solids concentration. The experimental conditions investigated in this dissertation were selected such t hat they encompass both collision -d ominated and viscous -d ominated flows. M ean Flow CollisionD ominated Flow There are more experimental data available for twophase flows in the grain-inertia flow regime than the macroviscous flow regime. This is due largely to the fact that phase discrimination and experimental access is easer in gas -solid flows which tend to be dominated by collisions. Some of the most significant gas -solid work in this flow regime include Maeda et al [3 ] Tsuji et al [ 5 ] Lee and Durst [ 4 ] Sheen et al [ 6], Jones [8 ] and Hadinoto et al [ 9 ] and in liqui d et al [1 6 ] Tsuji et al [ 5 ] utilized particles ranging in size from 200 m to 3 mm over a range of Re from 1.6 x 104 to 3.3 x 104. In all cases the flow was in the collisional regime, though the smallest particles were n earing the lower limit, according to the Bagnold number. The large particles were found to have a minor flattening effect on the mean fluid flow. However, the smaller particles (500 m and 200 m) created a concave fluid velocity profile the maximum velo city was located away from the pipe center in addition to an overall flattening of the profile. The mean velocity profile of the particles was flat except in the case of the 200 m particles which continued to show some curvature. Sheen et al [ 6 ] and Maeda et al [3 ] also found concave velocity profiles for both phases. Sheen et al [ 6 ] observed concave velocity profiles for both phases with polystyrene particles ranging in size from 225 m to 675 m at Re of approximately 2.7x104, with the degree of co ncavity increasing with solids loading. Concavity was not found for 800 m particles.

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26 Hardalupas et al [20 ] investigated the effects of particle loading on relative slip velocities in a gas -solid jet at constant Re and found that the slip velocity decr eased with increasing solids loading. Kulick et al [2 7 ] examined the influence of particle density in gas -solid channel flow at constant Re and found that changes in particle density did not affect the mean fluid velocity. Sheen et al [ 6 ] found that the particle mean velocity lagged that of the fluid for all cases and all locations except for the smallest particles (275 m) near the wall in which case the negative slip velocity increased with increasing solids loading. This phenomenon was also observed by Lee and Durst [4 ] for 100 m and 200 m glass spheres at Re = 1.3 x 104. The relative size of this region decreased with increasing particle size such that it was not observed for 400 m and 800 m p articles by Lee and Durst [ 4 ] nor Maeda et al [ 3 ] for 475 m and larger particles. Jones [ 8 ] investigated gas -solid flow with solids loadings up to 30 with glass spheres 70 m and 200 m in diameter and found the fluid mean velocity became flat and then mildly concave with increased solids loading. However, no concavity was noticed in the solids mean velocity. The slip velocity between the two phases was found to decrease with increasing solids loading and increase with increasing Re. Hadinoto et al [ 9 ] found that the fluid mean velocity became increasi ngly flat with increasing Re for 200 m particles, but not for 70 m particles. The larger particles are clearly in a collisional regime, while the smaller particles are in, or approaching, the transitional flow regime, depending on the Re. Hadinoto et al [ 9 ] also showed that the slip velocity decreased with increasing Re for both particle sizes at a constant solids concentration.

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27 In liquid -solid flow et al [16] found that on average the slip velocity decreased and the point at which the s lip velocity went to zero moved toward the center of the pipe with increasing mass flux. The decrease in slip velocity with increasing Re was opposite that reported by Jones [ 8 ]. Hosokawa and Tomiyama [28 ] used LDV to measure the mean and fluctuating vel ocity of 1, 2.5, and 4 mm ceramic particles at two solids loadings in water at Re = 1.5x103 in a 30 mm diameter pipe. Under these conditions the Bagnold number varied from approximately 70 to 1200. However, insufficient data were presented to establish t rends in the transitional flow regime and the fluid velocity in the presence of the solid was not measured. They found a decrease in the flattening of the mean solid velocity profile with increasing particle size and loading. To summarize, at the level of mean velocity the solid velocity is relatively flat with the degree of flatness increasing with particle size, density, and loading. The mean fluid velocity in the presence of small particles has been found by some to be concave to various degrees wit h the maximum fluid velocity occurring away from the pipe center. The concavity increases with solids loading and decreases with increasing particle size. The mean fluid velocity has been found to be greater than the mean solids velocity across the major ity of the pipe from the center to near the wall. As the wall is approached the slip velocity decreases such that the solid velocity exceeds that of the fluid. The magnitude of the slip velocity increases with increasing particle size and density, causin g the location of the slip velocity sign change to move closer to the wall. The slip velocity decreases with increasing solids loading and Rep. At constant particle size, density, and loading, increasing the Re results in increased flattening of the mean

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28 fluid velocity profile for sufficiently large particles. The mean solid velocity also becomes increasi ngly flat with increasing Re. See Table 11 for a summary of these trends in the flow behavior. Viscous D ominated Flow Only a limited amount of the t urbulent liquid-solid experimental data captures both the solid velocity in the presence of the fluid and the fluid velocity in the presence of the solid. More commonly, the solid velocity in the presence of the fluid is compared to the single phase fluid velocity, for exam ple Chemloul and Benrabah [2 9 ] Other liquid -solid experiments matched the index of refraction of the two phases and are thus only able t o give solidphase velocities (Zisselmar and Molerus [13] and A bbas and Crowe [14] ). In addition t o matching the index of refraction of the two phases, the densities are also often matched, Nouri et al [1 5 ] Averbakh et al [1 9 ] Koh et al [1 8 ] and Lyon and Leal [30 ] In the cases where the densities are matched no slip velocity is observed. Where a slip velocity is expected to be present, it is often redefined as the difference in solid velocity and single phase fluid velocity at a constant volumetric flow rate. This modified slip velocity has been shown to decrease with increasing flow rate. No uri et al. [15 ] used 270 m particles and matched their index of refraction to the liquid at solids concentrations up to 14% in a pipe at Re = 3 965 x104. The mean particle velocity was found to be greater than that of the single phase liquid and became in creasingly flat with increasing solids concentration. However, they did observe that the mean particle velocity profile shape changes with particle concentration; the particle velocity peaked at the centerline at low solids concentration and then decreased with increasing solids concentration.

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29 Abbas and Crowe [1 4 ] looked at silica gel particles 96 m and 210 m in diameter at solids concentrations up to 30% by volume at Re from 1.2 x 103 to 3.0 x 104. At Re < 2.4x103 the solids profile remained parabolic cor responding to laminar flow regardless of solids concentration. At Re > 2.4 x 103 the solids profiles were characteristic of turbulent flow. Koh et al [1 8 ] and Lyon and Leal [ 30 ] used small particles (70 m and 95 m) and low flow rates (< 0.1 m/s). Thei r single phase experiments exhibited the expected parabolic profile of laminar flow. This profile remained for the smaller particles at the lowest flow rate, but became progressively flat with increasing particle diameter and solids concentration. The mean solid velocity profile for a given particle concentration did not change with changes in the flow rate. Mishra et al. [ 31] measured the mean velocity and solids concentration profile for copper tailings in water in a 4 inch horizontal pipe at flow vel ocities between 1.67 and 2.95 m/s and solids concentrations between approximately 1% and 4.5% by volume. They found that the mean solid velocity profile was largely independent of flow rate and solids concentration Despite the high density particles, th e slurry was clearly in the viscous flow regime because the average particle size was only 71 m. Additionally, they used an intrusive impact probe to make their measurements. Kiger and Pan [ 32 ] used particle image velocimetry (PIV) to measure mean and fluctuating velocities of 200 m glass particles in a horiz ontal water channel at Re = 9.6x103, developing an image separation technique to distinguish between the two phases. The mean particle velocity lagged the fluid, most noticeably in the middle of the profil e. Chemloul and Benrabah [ 29 ] obtained mean velocities of water and glass

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30 spheres (0.5 mm and 1.0 mm in diameter) in a vertical pipe and found that the slip velocity decreased with increasing Re for a given particle size and concentration a tre nd opp osite that found by Jones [ 8 ] et al [1 6 ] The slip velocity was also the greatest at the pipe center and decreased across the pipe. The mean solids profile became increasingly flat with increasing solids concentration. See Table 1-2 for a summary of these trends in the flow behavior. Turbulence Modulation CollisionD ominated Flow Of greater importance than the mean velocity profile is how the presence of a second phase affects the turbulence of the fluid. This effect is known as turbul ence modulation. Typically, a flatter mean velocity profile corresponds with a flatter turbulence profilethe turbulence energy is spread out. However, whether the dispersed phase increases or decreases the magnitude of fluid turbulence depends on a number of factors. Furthermore, the solid phase turbulence is related to the solids concentration profile and mean velocities. Maeda et al. [ 3 ] found an increase in two phase fluid-phase turbulence intensity for all particle sizes examined, 45 to 136 m at Re = 2 0 x 104. Lee and Durst [4] investigated larger particles and found an increase in fluidphase turbulence intensity with 800 m particles at Re = 8 0 x 103. Tsuji et al [ 5 ] found fluidphase turbulence enhancement for larger particles and turbulence d amping for smaller particles, with an increase in the corresponding affect with increasing solids loading. Kulick et al. [2 7 ] found that fluid fluctuations were damped by the particles, with greater damping by the 50 and 90 m glass particles than the 70 m copper particles. Hadinoto et al. [9 ]

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31 studied the effect of Re on 70 m and 200 m glass particles and found that for both particles, the normalized fluid -phase fluctuations increase with increasing Re. Hadinoto et al. [ 9 ] also found that the normali zed solid-phase fluctuations decrease with increasing Re. et al. [1 6 ] found a flat solid -phase turbulence profile at low mass flow rates that became less flat with increasing mass fluxes for both ceramic and polystyrene particles. Indeed, the re was little change in the magnitude of the solid phase turbulence near the pipe center with changes in flow rate. However, Alajb et al. [1 6 ] varied both the solids loading and Re in each experimental, making qualification of the results difficult. Furthermore, the single phase fluid turbulence was not included in the comparison with the two-phase fluid phase turbulence plots making turbulence enhancement or damping speculativ e. Hosokawa and Tomiyama [2 8 ] found that the solids fluctuating velocity increased with both increasing particle size and solids loading. See Table 1-3 for a summary of these trends in the flow behavior. Viscous D ominated Flow Liu and Singh [3 3 ] offer the only turbulence data of both phases simultaneously, but did not conduct a thorough investigation of variables. In general they found that the particles < 200 m in diameter, damped the turbulence in comparison with singlephase flow. The magnitude of the solidphase turbulence was similar to the liquidphase turbulence, except at the center where the solid fluctuations were approximately 30% greater. However, their maximum solids concentration was 0.5% by volume and the maximum Re was 2.0x104. Other experimental work only compares the solid fluctuations to the single-phase liquid fluctuations. Zisselmar and Molerus [13] found that 53 m particles damped the

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32 turbulence with respect to the single-phase away from the wall. In these cases the solid fluctuations have been found to decrease with increasing solids loading in some cases (Nouri et al [1 5 ] and Chemloul and Benrabah [29 ] ) while in others the solids fluctuations were found to be independent of solids loading except near the wall where they increased with soli ds loading (Lyon and Leal [30 ] ). Nouri et al [1 5 ] a nd Chemloul and Benrabah [29 ] both used larger particles in comparison with Lyon and Leal [ 30 ] Nouri et al [1 5 ] showed that the solid -phase turbulence decreased with increasing solid diameter, for neutrally buoyant particles. The particle fluctuating v elocity was found to be less than that of the single -phase liquid, with the difference increasing wit h increasing solids loading. At a constant solids concentration of 20% Abbas and Crowe [1 4 ] found that the centerline axial turbulence intensity increased with particle diameter (96 m and 210 m) and slightly with Re for a nonneutrally buoyant particle. Kiger and Pan [ 32] found an increase in fluid fluctuating velocity in the axial direction in the presence of their solid-phase on the order of 10% acros s the bulk of the channel. Near the wall the fluid fluctuations were damped (y+ < 30) or were not significantly influenced (30 < y+ < 100) by the solid-phase The solid-phase fluctuations exceeded the fluid phase in the center region of the channel (y/h > 0.4) but were less than the fluid closer to the wa ll; y/h < 0.4. See Table 1-4 for a summary of these trends in the flow behavior. Turbulence Modulation Correlations In an attempt to understand and summarize the increasing amount of turbulence modulat ion data, Gore and Crowe [3 4 ] and Hetsroni [3 5 ] examined available experimental data mainly gas -solid and gas liquid but also liqu id -solid. Gore and Crowe [3 4 ] concluded that the particle diameter was the determining factor on the

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33 turbulence modulation in a twophase flow. The ratio of particle diameter to the characteristic length of the most energetic eddy in single phase flow was identified as the criteria for turbulence enhancement or dampening. The length of the most energetic eddy was defined by Hu tchinson et al. [3 6 ] as (le 0.2R). When this ratio was greater than 0.1 turbulence is enhanced by the solid phase and conversely a ratio of less than 0.1 would result in turbulence dampening. Small particles would follow the most energetic eddies and t hus diminish their energy while larger particles would create vortices in their wakes thus increasing th e fluid turbulence. Crowe [3 7 ] went on to argue that increasing the amount of solids present in the flow would augment the particle diameter dependent turbulence modulation be it enhancement or suppression. Hetsroni [35] also surveyed available experimental data and argued the particle Reynolds number determined the turbulence modulation: Rep greater than about 400 enhanced turbulence. The particle Re ynolds number is defined as f r pdu Re (1 -6 ) where ur is the absolute value of the slip velocity The work of Sheen et al [6 ] corroborated the f indings of Gore and Crowe [34 ] while exhibiting the turbulence modulat ion described by Hetsroni [3 5 ] at Rep velocity increased with increasing particle size, thus increasing vortex shedding and turbulence enhancement. Furthermore, because the slip velocity in the radial direction is minimal, radial turbulence damping will oc cur for all particles, regardless of particle size Hosokawa and Tomiyam a [28] contend that the ratio of eddy viscosity of the twophase flow to that of an analogous single phase flow is an appropriate parameter to

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34 correlate turbulence modulation with no m odulation occurri ng at unity. Their [3 4 ] with the ratio of turbulence intensity caused by the dispersed phase to that caused by shear: e t rl u d u (1 -7 ) w here ut the shear induced turbulence in single -phase flow. The additional terms appeared to refine the sc atter of data in comparison to that p roposed by Gore and Crowe [3 4 ] However, as clearly shown by Hadinoto et al [ 9 ] the correlations espoused by Gore and Crowe [34 ] and Hetsroni [35 ] ar e insufficient. The present data will offer additional insight into turbulence modulation under conditions not previously investigated. Radial Solids Concentration Profile The radial concentration of the solidphase also changes with flow conditions and is related to the turbulence and mean flow profiles. Typically, a greater number of particle collisions will occur in regions of higher solids density; which in turn decreases the solids fluc tuating velocity through energy dissipation via inelastic colli sions. In collision -dominated flow at low flow rates and solids concentrations, the radial concentration profile is relatively flat the solids are evenly distributed across the pipe. As the flow rate or solids loading increases, the solids move toward th e center of the pipesuch that areas near the pipe wall have been found void of particles (Maeda et al [ 3 ] Lee and Durst [ 4 ] et al [16]) Mishra et al [ 31 ] found that the solids moved from the wall toward the center of the pipe, makin g the distribution more uniform as the flow rate increased at low flow rates a high density of particles were present in the bottom of the pipe. Similar to collision -d ominated flow, Koh et al [18 ] and

PAGE 35

35 Lyon and Leal [30 ] found that the radial solids conce ntration profile shows increased solids in the center of the channel with increasing solids concentration. The concentration profile is not affected by particle size (Lyon and Leal [ 30 ] at 50% solids). Two Phase Flow Measurement Techniques There is a v oid of non -intrusive data that captures both liquid velocities in the presence of solids and solid velocities in the presence of the fluid for flows in the transitional flow regime. The effects of particle size, particle concentration, inlet flow conditions, flow geometry and other variables on the two-phase flow need to be determined. In addition constitutive relationships that link the turbulent stress, kinetic energy, and energy dissipation to the solids motion and material properties are needed. Thus, the mean velocity and fluctuations of both phases need to be measured simultaneously. Intrusive measurement techniques like hot wires, pito t tubes, and isokinetic probes have been used extensively and have shown some success in many fluidmechanical s ystems. However, these methods are known to disturb the flow around the point of data collection. Hot wires and pitot tubes are not able to discriminate between solid and liquid veloc ity and require calibration. Isokinetic probes provide local concentration data but do not measure velocity. Additionally, the solid -phase can damage intrusive measurement devices. Chaouki et al. [3 8 ] surveyed noninvasive measurement methods which rely on either radioactive or optically active particles. Nuclear particle tracking techniques offer limited spatial resolution at high flow rates, > 23 m/s. High speed cameras have also been used to capture solidphase velocity and solid profiles in two -phase flows, but because the particles must be counted, this technique is laborious and only suitable for very dilute flows (Sakaguchi et al. [39] ). Capacitance probes and

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36 Gamma rays have also been used to measure average radial densities in pipes, but are not capable of measuring particle velocities. Non intrusive laser based techniques offer the best combination of temporal and spatial resolution. Particle image velocimetry (PIV) creates a laser plane and captures a cross section of the flow, calculating average velocity vectors by measuring particle displacement between consecutive light pulses. PIV has the ability to measure an entire plane simultaneously but LDV offers better temporal and spatial resolution. Additional complimentary features have been added to PIV which allow for particle siz ing and/or phase discriminat ion p article tracking via planer laser induced florescence (PIV/PLIF) and particle sizing via a global sizing velocimeter (GSV). Both of these techniques and nuclear magnetic resonance ( NMR ) have some of the needed abilities, but are limited in particl e sizing, resolution, and introduce additional complications for large experiments. Laser Doppler velocimetry when used in conjunction with phase discrimination provides the required mean and fluctuating velocit ies of both phases When the velocity di fference between the two phases is large enough, two distinct velocity peaks can be obtained, making phase discrimination simpl e This is typically the case in gas -solid flows. This method does not work when the two phases respective velocity histograms overlap as is often the case in liquid-solid flows. Several inhouse techniques have been used to discriminate LDV data in these cases. For example the transit -time method of et al [1 6 ] the discriminator LDV of Muste et al [40 ] and the l aser Doppler split -phase measuring t echnique of Liu and Singh [3 3 ] The transit -time

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37 method of et al [1 6 ] was attempted but not found to be reliable. The lat t er two methods involve significant additional signal processing. A significantly more established and commercially available method is phase Doppler anemometry (PDA or PDPA), which measures the size of spherical particles. Each particle measurement contains both size and velocity data, making discrimination based on size straight forw ard. The availability and demonstrated reliability of the LDV/PDA technique made it the instrument of choice. PDPA has also been used to estimate t he radial s olids concentration profile in twophase flows This method, and its errors, has been the subj ect of several papers and will be addressed in more detail in C hapter Two The large particle size, relatively low solids concentration, and highly onedimensional flow are advantageous conditions for concentration profile measurements with PDPA. However the large pipe radius requires a significant penetration depth which results in significant signal attenuation. Fin ally, t he sampling of the entire flow to determine the overall solids concentration allows for verification of the PDPA resul t. Thus, the present work also examine s the validity of PDPA solids flux measurements. Two Phase Flow Modeling There exist many avenues for modeling multi phase systems. The most important factor in determining the best method is the Re. When the Re is very small v iscous models can be used to model fluid-particle systems. For example, Stokesian dynamics (Brady and Bossis [ 41] ) gives very accurate solutions for spheres with no appreciable inertia. Each particle has an equation of motion which includes fluid forces, but there is no explicit equation for fluid motion. Stokesian dynamics is not inherently restricted by particle size, but as soon as any inertial forces become significant the simulation is no

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38 longer valid. Analogous models can be formulated for particles of other shapes. These models can be used to determine macroscopic behavior from microscopic material properties and mechanics. Brownian dynamics is a simplified form of Stokesian dynamics a nd has been widely used to simulate the settling of particles in a quiescent fluid (Brady and Bossis [41]) Stokesian Dynamics utilizes a more robust description of hydrodynamic forces and is consequently often used in shear flows (Brady and Bossis [41]) Although potentially very accurate, these viscous models ar e limited to systems with no inertial forces and total particles on the order of 103. Consequently, a different kind of model is needed to predict the behavior of a liquid-solid flow where both viscous and inertial forces are significant. Inertial model s can be categorized as either Eulerian of Lagrangian. Lagrangian models solve an equation of motion for each particle in the system, tracking their interactions in a specific geometry. A major advantage of the Lagrangian method is that each particle can have its own physical properties size, shape, and density. However, the scope of simulations is limited by the number of particles in the system. The discrete element method (DEM) is an example of Lagrangian principles and has been used to model a wide range of systems. When the particles simulated are large and dense in comparison with the surrounding fluid and their mean flow is not driven by a fluid dry (no fluid) particle simulations are sufficient. When viscous forces become significant, the Lagr angian method can include fluid forces or be coupled with traditional computational fluid dynamic (CFD) models. This later technique is known as the EulerianLagrangian method. However, the limitations in terms of number of particles that restrict tradit ional Lagrangian methods remain in Eulerian-Lagrangian models

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39 To overcome this restriction the particles can be treated as a continuum. When this approach is utilized it is known as a two-fluid or simply an Eulerian model. The advantages of this approach are its ability to handle an infinite number of particles and be applied to any geometry. It is also significantly less computationally expensive to model large systems than when individual particles are considered. However, because the solids are treat ed as a continuum equations of motion for the fluid and solid phase s are based on the seminal work of Anderson and Jackson [ 42 ], and individual particle characteristics are ignored and replaced by volume averaged quantities Stress in the solid-phase can be described in various ways though the most popular method is the kinetic theory of granular flow. This theory utilizes a granular or pseudo t emperature energy balance equation, similar to the thermal temperature in gas molecules, to describe the behav ior of the solid phase fluctuations. Particle-particle and particle wall collisions are described by a coefficient of restituti on. Two fluid models have successfully simulated a variety of multiphase flows including gas -solid, gas -liquid, liquid -solid, and liquid -liquid, and have been applied to two and three dimensions. An Eulerian models ability to capture both viscous and collisional forces without restraint on the number of particles makes it the ideal method for simulating flows of practical inter est. Motivation There is clearly a dearth of detailed, non-intrusive experimental data for a twophase flow in the viscous -d ominated and transitional flow regimes. A systematic investigation into the effects of Re, particle size/density, and solids conc entration on both mean and fluctuating velocities and radial solids concentration profiles is needed Additionally, there is no data for liquid -solid two -phase flows at Re > 5 x 104. Therefore,

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40 it is the intent of this dissertation to present mean and fluc tuating velocity data for a t wo phase flow at Re between 2 .0x 105 and 5.0 x 105. Furthermore, we will show a transition from inertial flow dominated by particle collisions to a viscous -dominated flow regime. The experimental data can be used to validate a computer model. Figure 1 -1 is representative of the inability of current stateof -the art multiphase flow model s which neglect lubrication effects, to capture pressure drop i n fluid -solid flows in the transitional flow regime. In Figure 1 -1 A the model a ccurately predicts t he pressure drop for the large 2 00 m particles. As the particle diameter decreases viscous effects become more significant and the model over predict s the pressure drop (Figure 1 1B ) By manipulating experimental conditions to map th e transition from collision -d ominated to viscous d ominated flow, the present data provide s a standard by which future models can be assessed.

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41 Table 1 1 Mean v elocity b ehavior for c ollision -d ominated f low Increasing Particle Diameter d Increasing Pa rticle Density s Increasing Solids Concentration Increasing Re Fluid Maximum away from center with small particles, with effect decreasing with increasing d No effect Conflicting Increasing flatness Solid I ncreasing flatness I ncreasing flatnes s I ncreasing flatness I ncreasing flatness Solids Conc. Profile Conflicting Flat at low concentrations, move toward center with increasing Flat at low Re, move toward center with increasing Re Slip Velocity Increase Increase Decreases Con flicting Table 1 2 Mean v elocity b ehavior for v iscous d ominated f low Increasing Particle Diameter, d Increasing Particle Density, s Increasing Solids Increasing Re Fluid Not yet studied Not yet studied Not yet studied Increasingl y flat Solid Increasing flat ness Increasing flat ness I ncreasing flatness Independent Solids Conc. Profile No Effect Not yet studied Conflicting Solids become more evenly distributed Slip Velocity Increases Increases Increases Decreases

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42 Table 1 3 Fluctuating v elocity b ehavior for c ollision d ominated f low Increasing Particle Diameter, d Increasing Particle Density, s Increasing Solids Increasing Re Fluid Increases Increases Increases or Decreases; Effect of particles is augmented Increases Solid Increases Increases near wall Increases Increases near wall Table 1 4 Fluctuating v elocity b ehavior for v iscous -d ominated f low Increasing Particle Diameter, d Increasing Particle s Increasing Solids Increasing Re Fluid Decrease Little Change Decrease Decreases Solid Decreases (neutrall y buoyant) increases Decrease Conflicting Increases

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43 M a s s L o a d i n gP r e s s u r e D r o p / S i n g l e P h a s e P r e s s u r e D r o p0 0 5 1 1 5 2 1 1 2 1 4 1 6 1 8 2E x p M o d e l A M a s s L o a d i n gP r e s s u r e D r o p / S i n g l e P h a s e P r e s s u r e D r o p0 0 5 1 1 5 2 1 1 2 1 4 1 6 1 8 2B Figure 1 1 Gas -solid pressure drop A) d = 200 m and B) d = 70 m

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44 CHAPTER 2 EXPERIMENTAL SETUP AND METHODS Experimental Setup The experiments were conducted in a pilot -scale flow loop which allowed for the study of the effects of particle concentration and slurry velocity on vertical fully developed turbulent pipe flow. A diagram of the flow loop can be seen in Figure 2 1. The setup was designed in -house and much time was devoted to ensuring the accuracy and precision of the experimental measurements. The loop was constructed from nominal 3 inch (78 mm) schedule 40 type 304 stainless steel. The flow was driven by a 50 hp centrifugal pump and controlled by a variable frequency drive (ABB mo del number ACH550 -UH-072A -4) which allowed for flow control with reproducibility error less than 2% by volumetric flow rate at all speeds The flow could be controlled from a minimum at the particle deposition velocity to a maximum of over 8 m/s (at this velocity the jet within the venturi was removed) An electromagnetic flow meter gave a volumetric flow rate and was used to reproduce flow conditions The water in the system was replaced approximately onc e a month during experiments. The optical purit y of the water decreased over time due to the presence of dirt, dust, and other small matter in the room housing the flow loop. The large size, 0 .5 mm to 1 .5 mm, of the particles necessitated their removal from the flow prior to the pump and re-introduct ion post pump. Separation was achieved by gravity and entrainment via a ventur i eductor see Figure 2 -2 The increased velocity caused by the jet on the entrance side of the eductor induces a low pressure region that entrains the flow from above. Opening the eductor introduced the solids into the flow while closing the eductor resulted in their collection in the pipe below the particle

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45 separator. The loop could be operated in singlephase and two-phase conditions. Two phase conditions were defined by t he presence of the 0.5, 1.0, or 1.5 mm particles at any concentration greater than approximately 0.01% by volume. For experiments at Re > 5.0x105, based on pipe diameter and mean fluid velocity, the particles were removed from the system and the jet nozzl e of the eductor was removed. Removing the nozzle reduced the pressure drop across the eductor making the operation more efficient. Furthermore, a longer pipe at the point of discharge into the particle separator was used for single phase experiments at Re > 5.0 x 105. The longer pipe was submerged in the particle separator making flow smoother and reducing splashing. See C hapter Four for more details. The cylindrical test section was made of borosilicate glass with a wall thickness of 4.75 mm and was 12 pipe diameters (0.91 m) in length with an ID of 76 mm. The liquid entered the test section after traveling 51 vertical pipe diameters. The measurements were then taken approximately 1 diameter below the end of the test section, allowing for a total of 62 diameters for the flow to become fully developed. The small diameter difference (2.0 mm) between the nominal 3 inch schedule 40 pipe and the glass test section created a small increase in the turbulence at the wall immediately after their connection. This increase in turbulence was mapped vertically with the LDV and was found to dissipate within a few pipe diameters. Pressure taps were placed every 5 diameters along the vertical steel pipe. The pressure taps were 1.0 mm in diameter. Threaded coupli ngs were welded over the holes and pressure gauges were screwed into the couplings. The pipe wall thickness was over 5 times the tap diameter, so the water in contact with the gauge was assumed

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46 to be quiescent see Figure 2 -3 The gauges (CeComp model DP G1000B15PSIG -5 HA) had a range of 0 15 PSI (0 103 kPa) with an accuracy of 0.1% of the full scale. The pressure d istribution was measured at each flow rate and provided one of two methods used to verify fully developed flow. The second method required comparing fluctuating velocity profiles at vary ing developmental lengths. Axi symmetric flow was also verified by comparing fluctuating velocity profiles at differing azimuthal locations. Fully developed and axisymmetric flow was verified for both single and two-phase flows at a single flow rate. The solids concentration in the slurry was determ ined by sampling approximately 5 0 gallons of the entire flow. After a series of experiments, the valve on the bottom of the small tank on top of the particle sep arator was closed. Once the tank was appropriately full, the threeway valve was adjusted, routing the flow around the tank. The tank was calibrated such that the total volume could be determined by the height of slurry in the tank. The water was then drained and the particles were collected, dried in an oven and weighed. Based on the particle density a particle volume and solids volume concentration was determined. The total volume sampled was ensured to be less than the minimum well mixed slurry in the loop. This minimum volume was estimated by assuming the particle separator was a continuation of the nominal 4 inch pipe used from the particle separator to the eductor a volume of approximately 110 gallons. The solids that were removed were then add ed back into the loop to e nsure a constant solid concentration. This method proved to be very reliable once the minimum fluidization velocity was obtained.

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47 The friction velocity was needed to validate single-phase flow and was determined from the pressure drop with f f t2 R g dz dP U (2 -1) where R is the pipe radius, g gravity, and f the fluid density. See Figure 24 for a detailed diagram of the vertical pipe. This value was also compared with the friction velocity calculated through wall shear -stress measurements via law of -the wall correlations similar to a Clauser Chart (Tavou laris [ 4 3 ] ) t t fU u log B U u A 1 u y log (2 -2 ) w here u is the velocity at point y in the logarithmic sublayer, B=5.0, and A = ln (10)/ =5.9. Additionally, these two values were compared with that obtained through Prandtls universal law of friction for smoot h pipes ( Prandtl [ 4 4 ] ): 8 0 D U log 0 2 1s f f s (2 -3 ) where Uf is the mean (bulk) velocity, D the pipe diameter, and s is related to the friction velocity by 8 U U2 f s t (2 -4 ) The three methods produced v alues of Ut that were within 10% at Re = 5.0 x 105. L aser Doppler velocimetr y (LDV) was used to measure the liquid velocities. Experimental Particles For the two -phase experiments the particles were 1 .0 mm and 0.5 mm glass (borosilicate) spheres purchas ed from Mo -Sci and 1.5 mm glass (boros ilicate) spheres

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48 purchased from Jay -go. Photographs of the three sets of particles can be found in Figure 25 The particle size dis tributions were 0.4 0.6 mm, 0.8 1.2 mm and 1.3 1.7 mm for the 0.5, 1.0 and 1 .5 mm particles, respectively The pa rticles were highly spherical and reflected light very well. The difference in refractive index of the liquid and solid -phase was sufficient for the Phase Doppler Particle Analyzer ( PDPA) to accurately measure particle diameter. Seed particles were added to increase the visibility of the liquid phase. The seed particles were 10 m silver coated hollow glass spheres, designed for liquid laser Doppler applications and purchased from Dantec Dynamics. A number of seed particles were tried with the above pa rticles proving to be the best. Light incident on a transparent particle will undergo both reflection and refraction, while a highly reflective opaque particle will reflect the vast majority of the incident light. Utilizing the Mie Parameter dM (2 -5) where d is the particle diameter and the wavelength of light, particles with M > 10 scatter light proportional to the square of the particle diameter Albrecht et al [ 4 5 ]. For the seed particles M = 61. Since the diameter of the dispersed phase particles are nearly two orders of magnit ude greater than the seed particles, a highly reflective seed particle was needed due to the large amount of light scattered by the dispersed phase. Using equations 1 -1 through 1 -3 t he 1.0 mm glass particles had a response time of approximately 0.14 sec onds while the fluid response time ranged from approximately 0.076 to 0.015 seconds, yielding Stokes number s between 1.9 and 9.5. The response

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49 time of the 10 m particles was on the order of 106 seconds which clearly shows the seed particles will follow the fluid. Laser Doppler Velocimetry Basic p rinciples LDV is a non-intrusive, laser -based, technique capable of making instantaneous and timeaveraged velocity measurements with high spatial resolution (Albrecht et al [46]) LDV is based on the Doppler Effect the phenomenon whereby the frequency of a wave is dependent on the velocity of the wave source and/or point of observation. An acoustic example of the Doppler Effect is the sound from a siren on an ambulance increases in frequency as it approaches and decreases as it becomes farther away. This effect can be utilized to determine the velocity of the wave, given other parameters. Multiple configurations of LDV have been successfully demonstrated, including systems with one laser beam and two scattering angles or a referencebeam. However, the most prominent arrangement consists of crossing two beams of equal intensity with one or more receivers (Albrecht et al [4 6 ] ). Typically, a single beam of coherent laser light is split in to two beams using a beam splitter with one beam undergoing a frequency shift via a Bragg-cell. A Bragg -cell is a n acousto optic modulator that shifts the frequency of light using sound waves. An oscillating electric signal activates a piezoelectric transducer that is atta ched to an optically transparent material, such as glass. The vibrations of the glass create acoustic waves which cause the index of refraction of the glass to change. These changes in index of refraction scatter light. The frequency of the scattered li ght has been shifted by a frequency equal to the acoustic vibrations of the glass. A frequency shift on the order of 40 MHz is common in LDV.

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50 The frequency shift is often needed to determine the direction of the flow. A particle passing through the probe volume normal to the fringes will produce a signal identical to that of a particle passing in the opposite direction. In oscillating or highly turbulent flows this can result in directional ambiguity. The Bragg -cell introduc es a negative frequency off set so that the minimum detectable frequency will necessarily correspond with a negative velocity and the maximum detectable frequency will necessarily correspond with a po sitive velocity, s ee Figure 2 -6 Upon exiting the Bragg-cell, the two beams travel through a lens that focuses them at the designated point or volumethe probe volume. As the two beams of coherent light intersect the ir wave fronts constructively and destructively interact to form a series of equally spaced lines or fringes. Lines of c onstructive interference are lit while lines of des tructive interference are dark, see F igure 2-7 As the particle crosses the fringes light is alternatively scattered and then not scattered. A photodetector will receive scattered light at a frequency pr oportional to the distance between the fringes. This distance is determined through the wavelength of light and optics used to cross the beams sin 2 f (2 -6) section of the two laser beams. Finally the velocity of the particle is calculated as the product of the distance (fringe spacing) and frequency. The geometry of the probe volume can be calculated geometrically, assuming the laser beam has a Gaussian intensity (1/e2 of the maximum). This results in an ellipsoid with the following dimensions:

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51 sin D F 4L z (2 -7 ) cos D F 4L x (2 -8 ) L yD F 4 (2 -9 ) F is the focal length of the transmitting optics and DL the diameter of the laser beam see Figure 28 Finally the Doppler frequency can be calculated: sin u 2 fx D (2 -12) where ux is the velocity normal to the fringes. Table 5 1 lists the probe volume characteristics. In determining the Doppler frequency, it is assumed that the particle velocity is constant as it travels through the volume and the fringes composing the sample volume are of uniform spacing. The magnitude and direction of scattered light depends on the relative refractive index of the dispersed and continuous phases and the wavelength of light and can be determined through Mie scattering theory. Figure 29 shows the relative intensity of light scattered from 1. 0 mm glass spheres in water as a function of angle for 514 nm light. The scattered light is collected through a combination of lenses and typically focused through a pinhole aperture onto either a photomultiplier tube or a photodiode. The pinhole is need ed to eliminate extraneous light from other particles in the system from entering the photo detector (Goldstein [47 ] ) Furthermore, the pinhole allows only light nearest the core of the probe volume to be detected. This central core of laser

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52 light is t he most planer. Finally, a photo detector transforms the laser light oscillations into an electrical signal. As mentioned above, the Bragg-cell shifts the frequency of only one beam, so that the detected signal is that of the Doppler frequency plus the f requency shift. This signal is typically electronically downmixed to a lower frequency via a process known as heterodyning (Albrecht et al [4 5 ] ). Let 1 be the Doppler frequency and Bragg-cell induced frequency shift and 2 the designated downmixing frequency. Since the photo detector measures intensity, which is the square of the signal, the sum of the two frequencies is squared: (sin 1t + sin 2t)2 = (sin 1t )2 + 2(sin 1t x sin 2t) + (sin 2t)2 (2 -1 3) Only the middle term on the right side of the equation can be detected by the detector. U tilizing the following trigonometric identity on the middle term 1t x 2 1 2)t + co 1 2)t] (2 -1 4) the difference frequency can be found. Again, t he sum component is too high to be detected. Thus, the detected signal is equal to th e Doppler frequency plus the difference in 1 and 2 (Goldstein [4 7 ] ). The downmixing frequency can be adjustable and is dependent on the Bragg-cell frequency shift and the flow characteristics. S ee Figure 210. Phase Doppler a nemometry Phase Doppler anemometry was originally de veloped by Durst and Zare [4 8 ] and is now widely used and commercially available. Size measurements are determined from the difference in phase of a single Doppler signal detected at two positions separated by a known distance assuming a spherical particle. A thorough background can be found in Albrecht et al [4 6 ] For two photo detectors that are symmetric about a

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53 bisecting plane, and located at an off r, and in the case of reflective particles, the difference in phase of the signal observed at the two detectors is sin sin cos cos cos 1 sin sin cos cos cos 1 2 d 2 (2 -1 5) r is the angle of the receiver Albrecht et al [4 6 ] See Figure 21 1 The PDPA uses the ratio of the time lag between the signals detected at the two the signal, T (see Figure 2-1 2 ) T t 2 (2 -1 6 ) c omb in ing equations 2 -15 and 21 6 the particle diameter is: sin sin cos cos cos 1 sin sin cos cos cos 1 T 2 t d (2 -1 7 ) When particles are not perfect spheres the calculated diameter will contain error. The amount of error depends on the non-sphericity of the particle and the random particle orientation while traversing the probe volume. Typically, multiple phase calculations are made from multiple photo detectors. A non-spherical particle will result in different ph ases and thus different diameters. Particles that exhibit phases greater than a set value can then be rejected. In the present case three photo detectors are used (A, B, and C) to calculate two phases for each particle AB and AC. When the phase measurem ents between AB and AC differed by more than 8% the size measurement w as rejected.

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54 Solids c oncentration LDV/PDPA system s have been used to determine the solids concentration by relating the number and size of measured particles to the total volumetric flu x through the probe volume over a period of time. The use of laser Doppler and phase Doppler techniques in the determination of solids concentration profiles and mass flux continues to be the subject of much research due to the many sources of er ror in su ch measurements, Dullenkopf et al. [4 9 ] Reliable concentration measurements depend on several factors, including particle velocity, size, tr ansit time, and trajectory (A s a et al [ 50 ] Roisman and Tropea [5 1 ] ). Additionally, the effective size of the p robe volume is dependent on laser beam intensity, particle size, collection angle, and width of the focusing slit. The use of laser beams with Gaussian intensities has the effect of biasing PDPA measurements toward larger p articles, Qiu and Sommerfeld [52 ]. The beam is less intense at the edge, potentially allowing smaller particles, which scatter less light, to pass through the edge of the beam undetected. A larger particle traveling through the same portion of the probe volume would scatter more light and consequently is more likely to be detected. This results in a probe volume or probe volume cross -section that is a function of particle size. Qui and Sommerfeld [52 ] have identified errors stemming from sign al -to noise and trigger levels. F urther er rors have been identified from the simultaneous presence of multiple particles in the probe volume (Roisman and Tropea [5 1 ] ) and from counting a single particle as multiple (V an den Moortel et al [5 3 ] ). In the latter, an overestimation known as burst -spl itting, fluctuations in beam intensity at the level of individual bursts result in a single burst having multiple peaks and its subsequent interpretation as

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55 multiple particles. The fluctuations can come from many sources, i.e. beam interruptions in dense flows. Recently, several post -processing algorithms have been developed with the aim of mitigating these errors ( V an den Mortal et al [5 3 ] Bergenblock et al [5 4 ] and Sommerfeld and Q i u [55 ] ). Unfortunately, these algorithms require signal processing not available wit h the PDPA presently used. Fortunately, the experimental conditions are fairly ideal (Saffman [ 56 ]) in that the flow is largely 1 dimensional (pipe flow in contrast to a jet) and relatively dilute. Various methods exist for determining mass flux with phase Doppler techniques (Dullenkopf et al. [4 9 ] and Roisman and Tropea [5 1 ]) In all approaches the particle velocity a nd size are measured. The main difference s lie in the determination of the experimental probe area or volumethe area or volume created by the crossing of the two laser beams. In the present case t he probe volume area is automatically corrected for particle size. The experimental volume is defined as: UtA V (2 -18) w here A is the diameter dependent experimental cross section, t is time, and U the mean velocity In determining the cross section, the laser beam i s assumed to have a Gaussian power distribution and the intensity of light scattered by the particles is assumed to be proportional to the square of its diameter. Thus, the solids concentration is: UtA 6 d n3 30 (2 -19) where n is the total number of validated particles after all validation requirements are satisfied and d30 the volumeaverage diameter.

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56 3 n 1 i 3 i 30n d d (2 -20) T he solids concentration measured with the PDPA was compared to that determined by sampling the flow and found to be unreliable at time over predicting the solids concentration and at other times under predicting it. At the highest solids concentration th e measured solids concentration near the wall was 2 orders of magnitude greater than that measured in the center of the pipe, indicating an almost total lack of particles in the center. However, it was clear from watching the slurry that particles were in deed traveling through the center of the pipe. The discrepancies most likely come from decreasing signal quality and data rate as the probe volume approaches the center of the pipe Consequently, the radial solids concentration profile s as measured with the PDPA w ere not included in the results. Experimental Procedures LDV/PDPA System A two -component Laser Doppler Velocimeter/Phase Doppler Particle Analyzer (LDV/PDPA) was used to measure the mean and fluctuating velocity component s of the solid and liquid as well as the particle size The system utilizes a n Argon-Ion laser and a Bragg-cell to avoid directional uncertainty. The transmitting optics, receiving optics, and real -time signal analyzers were manufactured by TSI/Aerometrics. The optics are mounted on a traversing mechanism that can be positioned within 0.0001 inches. The relevant optical parameters of the LDV/PDPA s ystem are summarized in Table 21. A 50 0 mm focal length lens was used to measure the seed particles and 0.5 mm solids, allowing both phases to be measured simultaneously. For the 1 .0 and 1.5 mm

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57 particles two traverses across the pipe radius were made. The first measured the solidphase and the second the fluidphase. The 1 .0 and 1.5 mm particles required a larger fringe spacing for accurate size measurements. This was accomplished through a beam contractor that reduced the initial beam separation from 40 mm to 20mm. The receiver utilized a 520 mm focal length lens and housed three photo detectors which give two phase determinations. If the two phase calculations differ ed by more than 8%, the particle was rejected. The experiments with 1.0 mm and 1.5 mm particles were conducted with a Coherent 5W Argon laser. A new laser (Spectra -Physics Stabilite 2017 6W Argon) was purchased prior to the 0.5 mm experiments. The power of each laser beam at the probe was 1020 mW with the Coherent laser and 6090 mW with the new laser. T he voltage of the photomultiplier tubes (PMTs) was adjusted as needed to compensate for signal attenuation as the probe volume penetrated the slurry. The PMTs were maintained between approximately 450 5 50 V and 375 450 V for the old and new lasers, respectively. The best voltage was determined by balancing maximum data rate with minimum noise, as judged by monitoring t he Doppler bursts on an oscilloscope. A 20 MHz high -pass filter was used to remove the pedestal from the raw signal The burst threshold was maintained at 0.2 mV. The mixer frequency for the axial velocity and size measurements was 36 MHz, while the sampling rate and low -pass filter were 10 MHz and 5 MHz, respectively, for the runs at the two lower flow rates. For the highest flow rate the sampling rate and low pass filters were doubled to 20 MHz and 10 MHz, respectively. This change was necessary because the highest velocity measurable at the combination of 10 MHz sampling and the optics employed was less

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58 that needed to avoid aliasing. See Table 2 -1. Data rates varied from over 100 Hz for the solid particles near the wall to less than 0 .1 Hz for the liquid at the pipe center. The individual validation rates of the 1.0 and 0.5 mm particles ranged from 40 % to 10 %, depending on location in the pipe. Data was collected at 14 points across the pipe, with a greater density of points near the pipe wall. Due to refractive index changes, the closest measurements could be made to the wall was at r/R of approximately 0.95 Phase Discrimination The discrimination of the solid and liquid was based on particle size. Established techniques based o n signal amplitude differences between the two phases do not generally work in liquid -solid flow (Assar [57 ] and Chen and Kadambi [ 5 8 ]) because the slip velocity between the two phases is too small. Axial velocity and particle diameter data was collected. The data was collected under software coincidencemeaning each particle diameter measurement was associated with a specific particle velocity. The seed particles were two orders of magnitude smaller than the particles composing the solid-phase Thus, two distinct and easily distinguishable diameter peaks were obs erved by the PDPA. The 0 .5 mm particles h ad an average particle diameter according to the PDPA of 0 48 mm and all coincident particles between 375 and 600 m were collected. The 1.0 mm part icles had an average diameter of a pproximately 985 m and all coincident particles between 750 and 1200 m were included in the solid -phase data. In both cases, a minimum of 1000 size velocity coincident measurements were collected at each point. However in most cases several thousand points were obtained. In the case of the 1.5 mm particles, only the fluid was measured. For the liquid measurements, all particles from the optically limited

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59 minimum of 2 .4 8 m to 100 m were included in the liquid -phase statistics. Averages of 500 samples were collected for the liquid phase Data Limitations Exclusion of 1.5 mm s olid d ata The velocity measurements of the solids phase of the slurry composed of 1.5 mm particles were excluded from the results because they were determined to be inaccurate. The fluctuating velocity of the 1.5 mm particles was measured to be significantly greater (approximately double) than that of the 1.0 mm parti cles at each set of conditions. The 1.5 mm particles were measured with a 750 mm focal length lens (with the 0.5x beam contractor) not manufactured or specifically designed for LDV because an appropriate lens could not be purchased. A 1000 mm focal length lens with the 0.5x beam contractor was available and had the capability to s ize the particles, but the probe volume was too large. Additionally, lenses that precisely fit the current system could not be found and thus the 750 mm lens was had to be carefully fitted to the housing of the LDV probe. The diameter of the 750 mm lens was slightly less than needed. Duct tape was carefully wrapped about the circumference of the lens until the lens fit securely. A razor blade was used to trim the tape and ensure the tape and lens thickness was uniform. The beams passing through the 75 0 mm lens passed all alignment and convergence checks, and the data rate and signal quality appeared equal to that of the lens used to measure the 1.0 mm particles. However, upon comparing the solids velocity fluctuations, the 750 mm lens with the 0.5x be am contractor was used to measure the 1.0 mm particles. The fluctuating velocity measurements were significantly inflated over those measurements obtained with the 500 mm lens with beam contractor. After

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60 additional investigation it was decided that eithe r the 750 mm lens or the method of securing it in the LDV probe housing was unreliable, and the data was discarded. However, the measurements of the fluid in the presence of the 1.5 mm particles are still reliable as they were made with the same lens as all fluid measurements. Limited radial penetration in slurry of 0.5 mm particles At the highest solids concentration, 3% by volume, solid and liquid measurements of the 0.5 mm particles were limited to r/R 0.5. This is due to increased signal attenuati on by the increased number of particles in the slurry. For a given volumetric solids concentration, there are 8 times the number of 0.5 mm particles as 1.0 mm particles. Consequently, there is a significant increase in the number of particles the scatter ed light must pass through before reaching the receiver. This scatters and weakens the signal as light is reflected and refracted at each fluidparticle interface. Increasing the laser power and/or the PMT voltage did not increase the maximum penetration depth. Procedural Obstacles The design of the slurry flow loop was begun in January 2005 and completed in March of 2006. The fabrication was completed by Met Pro Supply of Bartow, FL and delivered in May 2006. A number of modification/improvements ha ve been made since the system was originally constructed. Flow control and air bubbles Flow control was initially attempted via a bypass by connecting a pipe in a T junction just after the pump, leading directly back to the water tank. This method did n ot provide adequate control or reproduc ibility of flow. B efore the variable frequency drive was installed, the pump could only be operated at full power. Under full power air

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61 bubbles were present in the test section most likely from cavitation. However, in the process of troubleshooting the air bubbles it was hypothesized that air was being entrained through the water tank. The water discharge from the particle separator into the tank resulted in a large amount of splashing. To address this a pipe ext ension was attached to the discharge. The extens ion submerged the dischar g e, split the single pipe into two, and routed the flow up through two U bends. The objective was to route any entrained air up to the surface and decrease the flow rate to increase the residence time in the pipe, giv ing air more time to rise to the surface. This pipe was eventually found to be unnecessary. In attempt to mitigate the cavitation in the ventur i eductor two additional orifices were constructed from Delrin (a hard an d smooth plastic) on a la the. The orifices had larger openings than the orifice that came with the venturi eductor. The larger diameter would increase the pressure and hopefully eliminate the cavitation. The two inhouse orifices were successful in incr easing the pressure in the ventur i but the failure of the bypass to control the flow necessitated the VFD, and the two inhouse orifices were not needed once the VFD was installed. Delivery and instillation of the VFD required a couple months. Excessiv e turbulence Once the flow was under the control of the VFD the first attempted measurements were of single -phase water. Initial fluctuating velocity measurements were noticeably larger than literature values. An initial hypothesis was that the velocity fluctuations were influenced by the pipe vibrations. When running, the entire loop vibrated, with the vibrations increasing with increasing flow rate/pump speed. To mitigate this, vibration damping clamps were placed in several locations upstream and dow nstream of the test

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62 section and anchored to the building by a network of steel strut s This was effective in reducing the pipe vibration but its effect on the velocity fluctuations was uncertain. T o better understand the vibrations accelerometer measurements of the test section, pump, and scaffolding were taken. These measurements showed a primary vibra tion frequency equal to the pump driving frequency supplied by the VFD, and then a series of harmonics that corresponded to the six v eins of the pump imp eller. In all cases the frequencies of vibrations were less than 1 kHz. This frequency of vibration was deemed insignificant in comparison with the D oppler frequency measurements because the scattered light signal is several orders of magnitude larger th an the vibrations. Furthermore, the high pass filter used to remove the signal pedestal would also remove any contribution from the vibrations. However, the excessive fluid turbulence remained. The turbulence intensity differed depending on the radius measured for example, north, south, or east radius of pipe. In the original design the test section consisted of two glass windows each 6 inches in length. The two windows were separated by 8 pipe diameters of stainless steel pipe. Nominal 3 inch s tainl ess steel pipe has an internal diameter of 3.068 inches. The glass windows were 3.0 inches. It was hypothesized that this step was increasing the level of turbulence at the wall. Further measurements confirmed this. The turbulence at the pipe center wa s consi stent with literature values while there was an increase in wall turbulence at the bottom of the window vs. the top. The two 6 inch windows and pipe were replaced with a single window 12 pipe diameters (36 inches) in length. This new window allowed any increase in turbulence fostered by the pipe diameter difference to dissipate and fluid wall turbulence measurements confirmed this.

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63 Between 3 and 5 pipe diameters, depending on Re, were needed for the increased wall turbulence to dissipate to that expected in fully developed pipe flow. Approximately six months elapsed from the first single phase measurements to when those same measurements accurately matched literature values across all radii. Phase d iscrimination and p article s election The two me thods outlined above were based solely on laser Doppler measurements velocity measurements only Measuring the particle size via phase Doppler measurements was not initially deemed feasible due to the large particle size. The refractive nature of the glass particles required a forward scattering angle. At the recommended angle of 30 sizing 1.0 mm particles required a 1000 mm focal length lens and the 0.5x beam contractor. This resulted in a probe volume with length of 94 mm ; more than double the pipe radius This lack of resolution resulted in attempting measurements without the PDPA The method outlined by et al [ 16] was the intended method of distingui shing the solid and liquid. et al [16 ] utilized 2.3 mm glass particles and found their transit time was significantly larger than the seed particles, claiming two distinguishable peaks in a histogram of time spent in the probe volume. However, the probe volume is ellipsoidal and thus large particles passing through the edge will have short transit times. A series of i deal measurements conducted outside the pipe, consisting of droppi ng particles of various sizes from a set height though the center of the probe volume did not show any repeatable correlation between size and transit time. Several months were spent working with this method before it was rejected. The next method of disc rimination attempted was that typically used in gas -solid flows. The increased slip found in gas -solid flows results in two distinguishable velocity

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64 peaks. Adjusting the laser power/PMT power appropriately less power for large particles, more power for s mall seed particles has been shown to give good phase discrimination (Jones [8]) The glass particles were replaced with 2 mm stainless steel shot. Two peaks were visible but largely overlapping. Larger stainless steel spheres 3/16 inches in diameter ( 4.76 mm) were then attempted. These larger particles were tested, in part, to prove that the method would work. Clearly their size and density would result in a collision-d ominated regime. Although two peaks were identifiable, the results were of low quality, most likely due to the large size of the particles. While working with the stainless steel particles, whose scatter ing is entirely reflective, it was realized that at a reflective angle the largest diameter measurable by the PDPA increased. Cons equently, stainless steel shot approximately 600 m in diameter was purchased. The smaller diameter and increased density, in comparison with glass, resulted in very similar Bagnold numbers (see equation 1 4). The smaller diameter allowed the PDPA to mea sure the size of the particles and distinguish the phases based on diameter. However, it was found that shot is not spherical enough to meet the requirements of the PDPA. The signal was very noisy and resulted in a very low quality diameter histogram. B oth traditional and conditioned cut wire shot were tried with low quality results. Finally, glass beads, which have a much higher sphericity than steel shot, were tried with the receiver in a reflective position at 30 from backscatter This arrangemen t proved to be the best arrangement and was used for all experiments. Ultimately over a year was spent in determining a suitable particle and phase discrimination technique.

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65 Several seed particles were also tried before the 10 m silver coated hollow g lass spheres, mentioned above, were selected. Unfiltered tap water, with its inherent contaminants was found to provide a good signal during single phase experiments. The seed was added in hopes of improving the data rate of the fluid in the presence of the solid phase 10 m h ollow glass spheres, 20 m polyamide particles and TiO2 particles were also tried. Filtering the tap water and then adding seed was also tried an inline water filtering line was built. The filter removed material > 20 m. How ever, it was found that filtering did not have an effect on the fluid data rate. Laser Doppler measurements in round pipes of small diameter can often be biased by refraction effects from the curved surface. These effects are typically overcome by const ructing a planar front to the pipe, such that the laser beams are normal to a flat surface that is matched in index of refraction to the pipe, and in some cases, the fluid. This error was deemed negligible under the present conditions due to the relativel y large pipe diameter and the fact the measurements were limited to 1D axial profiles. The two laser beams were aligned with the axis of the pipe; t he degree of curvature over the width of the laser beam at the point i t entered the pipe was determined to be less than 1 for all radial locations across the pipe. When a second signal processor was still working, making 2D measurements tenable, a planar front was constructed The box had a glass front and silicone sealant was used to attach it to the glas s pipe. T he interstitial space was filled with a matched index of refraction liquid (a concentrated solution of NaI). The planar front was ultimately found to be disadvantageous because the data rate decreased due to the deep yellow color of the NaI solu tion.

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66 Other i mprovements The paddlewheel flowmeter was replaced with an electromagnetic flowmeter. The original location of the flowmeter was upstream of the ventur i thus making its measurement not representative of the flow through the test section. It was then moved immediately upstream of the test section. This location was eventually deemed problematic due to an increase in wall turbulence fostered by the slight differences in pipe diameter between the stainless steel pipe, flow meter, and glass test section. Ultimately the flow meter was moved to its final location approximately 5 pipe diameters downstream of the first longradius bend. Additional pressure taps were added to the original design, which had only 3 taps around the test section see Chapter 4. Initially the holes into the pipe were made without regard to their diameter. However, after surveying the literature regarding pressure loss measurements, the effect of diameter was discovered. This required drilling of precise 1.0 mm ho les through the pipe wall and repeating the measurements. The original design provided for concentration sampling via the 3way valve located immediately after the first long-radius bend. However, it was realized that due to the openness of the system, routing the flow out the 3way value rather up the vertical pipe into the test section necessarily changed the pressure drop and thus the flow rate. After much thought it was recognized that any change in the flow during sampling over the flow conditions during data acquisition would necessarily change the flow. This awareness led to the final flow through design, where the flow discharged through the sampling tank and the 3way valve was used to route the flow around the tank after sampl ing. A 100 gallon tank was modified to attach a 4 inch bulkhead. A 3 inch bulkhead was initially tried and found to be too small to accommodate higher flow

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67 rates. A 4 inch ball valve was attached to the bulkhead and was closed to fill the tank during sampling. Chang ing flow meters, moving the flow meter, and moving the 3way valve resulted in pipe length mismatches. These mismatches were remedied by constructing spacers from 0.75 inch thick sheets of acrylic. A 3 inch flow hole and corresponding holes for flange bo lts were cut into squares of acrylic. The squares were then inserted between flange connections. Additionally, c hlorine was added to the water each time it was replaced after mold began growing in the loop, requiring a thorough cleaning of the loop. The chlorine was designed for swimming pools and came in a granular form. Equipment/instrumentation issues The final velocity measurements included only the axial direction. Originally both axial and radial mean and fluctuating velocity profiles were desired. The LDV/PDPA is a 3-D system. However during the course of troubleshooting both LDV signal processors ultimately failed. Both processors power suppl ie s failed at some point, with one requiring replacement. Ultimately the LDV signal processors were shown to be unreliable, though their failure was not catastrophic. All told, several months were spent attempting to understand and diagnosis the erratic behavior of the processors before they were finally deemed un usable Unfortunately, due to their age they could not be fixed and 1-D measurements were completed. Finally, p rior to being found unreliable and being replaced, the paddlewheel flow meter also abruptly stopped working and was serviced.

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68 Error Analysis Velocity and size m easurements Laser Do p pler velocimetry makes a direct measurement and requires no calibration. Statistical errors arise based on the number of samples used to determine the mean and fluctuating velocities of the two phases. Following the work of Yanta and Smith [ 5 9 ], the error in the ensemble mean is U u N z2 c e (2 -21) where is the error in the population mean, s the ensemble mean, N the ensemble size, and zc the confidence coefficient The ratio of the standard deviation to the mean is the turbulence intensi ty. However, the error in the fluctuating velocity is independent of flow conditions N 2 zc e (2 -2 2 ) w here is the population standard deviation and s the ensemble standard deviation. For example, an ensemble of 1000 points at 95% confi dence and a turbulence intensity of 0.05 will have 4.4% random error in the fluctuating vel ocity measurements The velocity histogram at each point was analyzed and out lying points were removed using a method analogous to the Thompson-Tau technique. A p oint was determined to be an outlier if it was not connected to either tail of the distribution and was more than three standard deviations from the mean. In the case of long tails, points had to be at least four standard deviations away from the mean and appear to be extraneous. After each point was removed, the mean and standard deviation was recalculated prior to removing any additional points. Additionally, a scatter of velocity vs.

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69 diameter was consulted to give additional information regarding the potential validity of the velocity measurement before it was discarded. The range of particle diameters used in the statistics did not have a significant impact on the velocity statistics. For example, changing the upper or lower limit by 10% would typi cally change the mean velocity by < 0.1% and the fluctuating velocity by < 1%. When the probe volume was close to the wall a secondary peak at zero m/s would often appear. These points were removed in all cases T his was easily accomplis hed for the higher speed flows, while f or the lowest velocity much care was taken to ensure that all relevant measurements were included. Additionally, t he lowest possible sampling rate and low pass filter (LPF) combination was used in each case. It was found that usi ng a higher sampling rate inflated the turbulence statistics A higher sampling rate will obtain all its velocity data in a few er number of cycles, increasing the uncertainty of the measurement, s ee Figure 2 -1 3 Radial location Measurements were always begun at the pipe wall and finished at the pipe center The optics were positioned under single phase flow to make alignment easier. To ensure that the laser was normal to the pipe, the beams entering the pipe were aligned vertically with their reflectio n off the back wall. The receiving probe has a magnifying lens that allows the user to see the crossing beams and focus the spatial filter in the center of the probe volume. The location where the beams cross from the glass pipe to the water is also visi ble. In each case the spatial filter was placed as close to the wall as possible while retaining a highquality signal. There is a small degree of uncertainty in this starting location. The distance from the first measurement to the second was 500 steps on the traverse (1.7 mm in water).

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70 Based on the appearance of this distance in the receiving probes magnifying glass, it can be assumed that the uncertainty in the initial starting location is 100 steps (0.34 mm in water). This uncertainty can be ap plied to all radial locations across the pipe. Near the pipe wall where the velocity gradients are the largest the radial uncertainty can contribute to the uncertainty in the fluctuating velocity measurements. Near the pipe center the gradients are much less steep and any contribution to the error in the turbulence measurements based the radial uncertainty is negligible. It is also important to focus the receiving optics on the center of the probe volume. The center can be determined by sliding the rec eiving probe slightly forward and backward and ensuring the beams cross at their individual waists (narrowest point). This produces a bow -tie where the beams converge and diverge evenly. With a small probe volume, the center is easy to determine. When measuring the 1.0 mm particles great care was taken to ensure that the spatial filter wa s centered in the probe volume. As the pipe radius was traversed the receiving optics were adjusted to maintain alignment on the probe center. Near the pipe center u nder higher solids concentrations the crossing of the laser beams w as more difficult to see. In such cases, the venturi was temporarily closed, removing the particles from the loop, making the beams visible and alignment easier before re introducing the p articles into the loop. Solids c oncentration The error in the determination of the solids concentration was found to be less than 5 %. The determination o f the total slurry sampled was calculated from the height of slurry in the sampling tank. The height was measured from the top of the bulkhead fitting at the bottom of the tank to the water line. A wooden broom handle was slowly inserted into the tank and then removed. The water line was then easily measured. The

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71 error in this height measurement was est imated to be 3 mm, which translated into a total volume error of about 1%. The volume of the tank below the bulkhead was estimated mathematically based on its dimensions. The second source of error was in the determination of the volume of the particles The sampling tank was drained over a sieve which collected particles in the bottom of the valve The bulkhead was not flush with the bottom of the tank, keeping settled particles from simply washing out upon draining. These particles were carefully co llected by tilting the sampling tank onto its side collecting the majority of them by hand, and then washing out the tank while passing the washout through a sieve. Some loss of particles was inevitable in this process, and thus an y error resulted in an underestimation of the total solids. The amount of loss is difficult to estimate, though it can be safely assumed to be less than 5%. Based on rep eatability the sampling procedure was found to be accurate within 5%. Pressure m easurements The single gr eatest manifestation of error was the in the determination of the two phase friction veloci ty from the hydraulic gradient. Turbulent flow is inherently random and this randomness will result in some degree of pressure fluctuations. Furthermore, the magni tude of the fluctuations will increase with increasing Re. This was found to be true for both single phase and twophase flow. However, t he addition of the solid particles increased the variability of the pressure measurements with the magnitude increas ing with increasing solids concentration. The particle diameter did not appear to influence the pressure fluctuations significantly. The following analysis is in regard to the 1.0 mm particles.

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72 Accordingly, the least amount of error was in the run at R e = 2.0 x 105 at a solids concentration of 0.7% by volume. The overall pressure change was from 5. 25 to 2. 20 PSI Based on observation the pressure fluctuated from 5.1 to 5.4 PSI and 2.05 to 2.35 PSI for the lowest and highest taps, respectively. Most of the fluctuations were about a small er interval, and consequently the mean values could be fairly well established. The error could be safely assumed to be less than 0.05 PSI, or 1.0% and 2.3%, respectively. The largest pressure fluctuations were found in the run at Re = 5.0 x 105 at a solids concentration of 3% by volume. In this case the pressure ranged from 7.8 to 4.3 PSI. However, the fluctuations ranged from 3.8 to 4.8 PSI and 7.3 to 8.3. These were extremes with the majority of the fluctuati ons on the order of 0.25 PSI with an uncertainty interval of 0.15 PSI, or 1.9% and 3.5% respectively. This error does not appear significant, and the R2 values in the linear regression of all six pressure readings reflected this. The lowest value of th e 1.0 mm particles was 0.9958, for Re = 3.35 x 105 at 1.7% solids. This relatively small amount of uncertainty, however, can have a significant impact on the friction velocity and consequently the two-phase fluctuating velocity measurements were scaled by the centerline fluid velocity. For each set of conditions the uncertainty of dP/dz at 95% confidence was determined: n 1 i 2 i zP 2 nz z 1 S t W (2 -2 3 ) where tn 2 is the 95% confidence correlation parameter, z the height of pressure tap, z (bar) is the a verage height, and SzP is the standard error:

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73 2 n P P Sn 1 i 2 i zP (2 -2 4 ) where P is the measured pressure and P is the estimated value according to the best -fit linear regression. The standard error is a measure of the scatter about the best -fit lin e The standard error assumes there is no erro r in the independent variable, in this case the height of the tap, z Although the statistics show a significant uncertainty, the dilute nature of the slurry suggests it should not show a dramatic change in dP/dz over th e single phase. The twophase frictional velocity was also calculated to give an additional comparison with the single-phase flow. The similarity in the two phase friction velocity to that of the single -phase via both pressure drop and a meas urement of the near wall velocity gradient bolsters confidence in the two phase pressure drop. .

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74 Figure 21. Flow loop A) water tank, B) pump, C) venturi eductor, D) electromagnetic flow meter, E) test section, F) by -pass, G) sa mpling tank, H) particle screen and I) particle separator A B C F E D G 1.22 m 1.22 m 3.65 m 7.01 m 4.79 m 3.84 m 0.96 m 2.56 m 1.52 m H I

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75 Figure 22. Venturi eductor A ) single phase inlet, B ) solids entrainment and mixing and C ) s lurry exit Figure 23. Configuration of pressure tap Pipe Wall Pipe Wall Pressure Sensor Water 1 mm 5. 5 mm B C 3 in. 4 in. A 4 in.

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76 Figure 24. Vertical pipe dimensions Glass T est Section Developmental Length 0 0 26 1.98 51 3.89 63 4.80 Pipe Diameters m 46 3.51 41 3.12 36 2.74 31 2.36 Pressure Taps 14 1.59 Electromagn etic Flowmeter

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77 A B C Figure 25. Experimental particles A) 0.5 mm, B) 1.0 mm and C) 1 .5 mm

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78 Figure 26 Resolving directional ambiguity with frequency shift u f D f min f max u min u min u max u max Shift No Shift

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79 Figure 27 LDV probe volume fringes Figure 28 Experimental probe volume dimensions z x X Z f

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80 Table 2 1. LDV/PDPA s ettings Liquid 1.0 mm Particles 0 .5 mm Particles Transmitting Optics 514.5 514.5 514.5 Focal Length (mm) 500 500 5 0 0 f 6.4 12.9 6.4 Laser Beam Diameter (mm) 1.4 1.4 1.4 Laser Beam Intersection Angle 4.59 2.29 4.59 Laser Beam Separation (mm) 40 20 4 0 234 4 68 234 z (mm) 5.85 23.4 5. 85 x (mm) 0.234 0.468 0. 234 y (mm) 0.234 0.468 0. 234 Receiving Optics 521 521 521 400 400 400 Colle ction Angle 150 150 150 Software Settings High Pass Filter (MHz) 20 20 20 Frequency Shift (MHz) 36 36 36 Sampling Rate (MHz) 10, 20 10, 20 10, 20 Low Pass Filter (MHz) 5, 10 5, 10 5, 10 Burst Threshold (mV) 0.2 0.2 0.2

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81 Figure 29 Light scattering intensity for 1 mm sphere for 514 nm light Figure 210 Frequency and p hase measurements of a Doppler burst

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82 Figure 211 Signal processing flowchart High Pass Filter : 20 MHz Removes low frequency pedestal Downmixing: 40 MHz for LDV 36 MHz for PDPA Heterodyning technique combines input and reference signals Signal Input Low Pass Filter: 5 or 10 MHz Eliminates high frequency component Analog to Digital Converter (ADC): 10 or 20 MHz Digitizes signal Computer: Discrete Fourier Transforms (DFT) Transform signal from frequency domain to time domain Data: f req uency, phase, SNR, etc.

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83 Figure 2 1 2 Phase D oppler setup A) laser beams converging to probe volume, B) receiving probe and C) multiple photo detectors required to determine phase shift r = 30 from backscatter Side View Overhead View Receiver Bisecting Plane M ultiple photo detectors in receiver Scattered Light Scattered Light Overhead View Probe Volume Transmitter Probe Volume

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84 Figure 21 3 Sampling r ate of Doppler b urst A) 64 points at rate X and B) 64 points at rate 2X. A B

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85 C HAPT ER 3 TWO -PHASE M ODEL Kinetic Theory of Granular Flow State of -the art turbulent two phase model s involve mass and momentum balances for each phase and a fluctuating energy balance for the particle assembly. The mass and momentum balances originate from th e work of Anderson and Jackson [42 ] and Lun and Savages [60, 6 1 ] kinetic theory of granular flow is used for the particle stress and v iscosity. The most rigorous treatment in two-fluid models employ Myong and Kasagis [ 62 ] two equation k modified for the presence of a dilute particle phase. The original kinetic theory of granular flow of Lun et al [63 ] describes the transfer of momentum and kinetic energy between particles while neglecting the effects of the interstitial fluid. Lun and Savage [ 60 6 1 ] later includes these effects by incorporating an additional stress exerted by the fluid on the particle through long-range interactions by means of fluid fluctuations. The theory of Lun et al. [ 63 ] was incorporated into a twofluid model of a lam inar gas -particle flow by Sinclair and Jackson [ 64 ] L ater, the kinetic theory of granular flow and gas turbulence were incorporated into a two-fluid model by Louge et al [ 65 ] who used a oneequation turbulence model. This work was extended to a twoequation k model by Bolio et al [6 6 ] The Bolio et al [6 6 ] model was validated for various kinds of particles and particle sizes by the data of Tsuji et al [ 5 ] Tsuji [6 7 ] and Jones [8 ] However, the model has not been validated for liquid-solid flows in an inertia dominated regime. When two particles in a fluid collide, two particle-particle interactions occur direct collisions and interactions through the fluid. The direct collisions transfer momentum

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86 and energy by elastic plastic defo rmations while the fluid interactions occur via the fluid velocity gradient and pressure disturbances generated by the random motions of the particles. These random motions transfer momentum and energy through the fluid to neighboring particles. In Lun and Savage [60 ] particle particle interactions occur through direct collisions only. Additionally, a particle undergo ing an inelastic collision loses some of its fluctuating kinetic energy to heat. Further energy is dissipated into the fluid as the parti cle must expend energy to displace the fluid between the two particles. The coefficient of restitution in a vacuum, es, can be measured experimentally with particle image tracking velocimetry, LDV, and other non-intrusive techniques The velocities and trajectories of i ndividual particles are tracked before and after collision. Values of es depend on the material properties of the colliding objects and are available for common materials Governing Equations D etailed explanation of two -fluid models tha t incorporate particle -particle interactions can be found in Bolio et al [6 6 ] Brief descriptions of the governing equations are outlined below. T he fluid and solid continuity are given as 0 U 1 t 1f f f (3 -1) 0 U t s s s (3 -2) wh f s are the fluid and solid density, and Uf and Us are the fluid and solid velocity, respectively. Momentum balances are given as g F P U U t Uf D f f f f f (3 -3)

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87 g g F U U t Us f D s s s s s (3 -4) The terms on the r ight side of the equation 3 3 are the pressure gradient, the fluid shear stress containing both viscous and Reynolds stress, the drag force of the fluid on the solids, and the gravitational force on the fluid, respectively. The terms on the right side of equation 3 -4 are the particle stress, drag, buoyancy force and gravitational force Equation 3 5 is the fluid turbulent kinetic energy k balance. Diffusion, generation by mean shear flow, and viscous -d issipation are the first three terms on the right s ide. The last term is the turbulence modulation that includes both collisional ( Lun and Savage [60 ] ) and fluctuating drag forces ( Bolio et al [6 6 ] ). MOD f T f REY f k T ef f fF 1 U : 1 k 1 k U t k 1 (3 -5) MOD 2 3 2 f 2 2 T f REY f 1 1 T ef f fF k f c k 1 f c U : 1 k f c 1 U t 1 (3 -6) The terms on the right s ide of equation 3 -6 represent the same contributions as in the k equation The cis and fis represent constants and functions, respectively, and are given in Myong and Kasagi [ 62 ] The particle phase str ess, s, depends on the granular temperature, T, and this can be found from a kinetic energy balance associated with the particle velocity fluctuations. This kinetic energy balance (or granular temperature balance or pseudo thermal energy balance) can be found in Sinclair and Jackson [ 64] :

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88 KS pt s s pt pt s pt sF U : q E U t E (3 -7) where qpt is the pseudo-s is the particle stress tensor, pt the pseudo thermal energy dissipation rate, and FKS the interfacial energy flux by fluid -solid inter actions. The detailed expression for these terms can be found in Lun et al [ 63 ] and Lun and Savage [ 60 ,6 1 ] Boundary Conditions and Model Solution No -slip boundary conditions are used at confining wall for the mean fluid velocity and the fluid turbulent kinetic energy k. The wall boundary condition for the turbulent kinetic energy dissipat boundary condition, see Bolio et al. [66] The particle phase mean velocity boundary condition is determined by equating the lateral momentum flux t ransmitted to the wall by particle wall collisions with the tangential stress in the particle phase next to the wall ; Bolio et al. [6 6 ] Similar to the particle velocity, the wall boundary condition for the pseudo-thermal temperature T is determined by eq uating the energy conducted to the wall by particleparticle collisions with the energy dissipation due to the inelastic particlewall collisions and the energy generat ed by particle slip at the wall; Johnson and Jackson [ 68 ] An adaptation of the implicit finite volume technique created by Patankar [ 69] can be used to solve the system of equations. Results Figure 31 compares the Bolio model (which neglects lubrication effects) for predictions of the solids fluctuating velocity with the gas -solid experi mental data of Tsuji [ 5 ] The flow was comprised of 243 m particles with a density of 1020 kg/m3 at a

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89 loading of 3. 4 and Re ~ 2.0x105. This results in Ba gnold and Stokes number s of approximately 1 50 0 and 58, respectively. The model does a good job predicting the solid turbulence under these conditions, wh ich are dominated by the inertial forces of the solid particles. Figure 32 compares the model solids fluctuating velocity with the liquid -solid experimental data of [ 16 ] at Re = 6.7x104. In this case the solid phase is glass particles of densi ty 2500 kg/m3of and diameter of 2.32 mm. Under these conditions t he Bagnold number is approximately 1000 and the Stokes number 38 The model now significantly over predicts the solid phase turbulence due to the increase in viscous forces. As the flow moves more into a transitional regime where viscous forces become more significant, the model is no longer able to predict the flow. These two figures display the need for improved models and the experimental data with which they can be validated.

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90 r / Rus' / Uf c0 0 2 0 4 0 6 0 8 1 0 0 0 2 0 0 4 0 0 6 0 0 8 0 1 0 1 2B o l i o M o d e l E x p o f T s u j i Figur e 31 Solid fluctuating velocity of gas -solid flow of 243 m polystyrene particles at Re ~ 2.2x104 (Tsuji et al. [ 67 ]) r / Rus' / Uf c0 0 2 0 4 0 6 0 8 1 0 0 0 2 0 0 4 0 0 6 0 0 8 0 1 0 1 2M o d e l o f B o l i o E x p o f A l a j b e g o v i c Figure 32. Solid fluctuating velocity of liquid -solid flow of 2.32 mm glass particles at Re = 6.7x104 ( )

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91 CHAPTER 4 PRESSURE LOSS IN PIPE BENDS OF LARGE CURVATURE AT HIGH RE Introduction Curved pipes are ubiquitous in industrial and laboratory settings. Understanding fluid flow in bends is relevant to heating and air conditioning systems, engine intake and exha ust, heat exchangers, commercial pipelines, and blood flow through arteries. In comparison to a straight pipe, flow through a bend may experience a greater pressure drop over an equivalent pipe length due to flow separation. This flow separation is marke d by secondary flow that moves the faster moving fluid to the outside of the bend and the slower to the inside as dictated by an increase in pressure along the outer wall of the bend and a decrease in pressure along the inner wall. The sharper the bend, t he more dramatic the flow separation, such that in very long radius bends, wall friction dominates and flow separation has a negligible effect on pressure loss. Over intermediate radii of curvature, both factors wall friction and flow separation are s ignificant. The flow through a bend is a function of the Reynolds number Re and the radius of curvature, Rb/ R (In this paper, bend describes both elbows with Rb/ R < 20, as well as curved pipes with Rb/ R > 20.) Laminar and turbulent flow through pipe bends has been reviewed by Berger et al [7 0 ] and Ito [ 7 1 ]. P ressure loss in a pipe bend is often characterized by the pressure loss coefficient K defined as 2 f f refU 5 0 P P K (4 -1)

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92 where Uf f the fluid density, and Pref is a reference pressure measured upstream from the bend. Another method of characterizing pressure loss in a bend is the total bend loss coefficient kt 2 f t tU h g 2 k (4 -2) t is the change in pressure associated with points D and F on Fig ure 4 1 and g is gravity. Point F is the pressure at some location X* downstream of the bend where the pressure gradient is the same as the pressure gradient upstream of the bend. Point D is the pressure at the same location X* if the bend were not present. K and kt are two different conventions for describing pressure loss in a pipe bend. The pressure loss coefficient K and the total bend loss coefficient kt are employed in the present work t o be consistent with other studies of flow in pipe bends, particularly Ito [ 7 2 ]. Fig ure 4 -1 is included to give a physical description of kt and is modeled after a similar figure in Ito [ 7 2 ]. kt gives a total bend loss and can be used to measure pressure loss as a function of Re, Rb/R or degree of bend. kt is also the pressure loss computed in numerical correlations. The pressure loss coefficient K is a method of normalizing pressure data and shows th e pressure profile in a bend. Various experimental correlations have been proposed for the total bend loss coefficient. The empirical correlation of Ito [ 7 2 ] gives the total bend loss coefficient for Re(r/R)2 > 91 as 84 0 b 17 0 b tr R 00241 0 k. .Re (4 -3) where l factor which depends on the radius of curvature. For large curvature bends, Rb/rR 72 ]

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93 correlation is based on data in pipe bends with large curvature (up to 58) and Re < 3 x 105. In addition, the c orrelation proposed by Miller [73 ] estimates kt as f o Re t tC C C k k (4 -4) where kt* is a function of Rb/ R Re = 106 and CRe, Co, and Cf are correction factors based on Re, length of the downstream tangent, and pipe roughness, respectively. According to Miller [ 7 3 ], this correlation can be applied for pipe curvature Rb/ R < 20 over a range of Re (< 107). Both the Ito [ 7 2 ] and the Miller [ 7 3 ] correlation predict that the total bend loss coefficient increases with increasing pipe curvature and decreasing Re. Another well kn own correlation for kt, published by the Crane Company [ 7 4 ], predicts Re independence, assuming fully turbulent flow. Table 4 1 gives a summary of published experimental data on flow in 90 and 180 pipe bends. Based on these data, a number of conclusions about flow and pressure loss in pipe be nds have been developed. Ito [ 7 2 ] observed a decrease in the total bend loss coefficient kt with increasing Re at a given radius of curvature, and an increase in kt with increasing radius of curvature for a given Re. The length of the upstream and downstream tangents was also investigated, and 50 pipe diameters after the bend were required for the flow to return to a fully developed state, regardless of the bend geometry. Ito [ 7 2 ] also found that the total bend l oss coefficient increased with increasing length of upstream tangent, with a minimum of 20 pipe diameters required for consistency with his empirical correlation given in equation 4 3. Rowe [75 ] mapped total pressure and fluid velocity in and downstream o f a pipe bend. The pressure at the outside of the pipe bend was higher than on the inside of the pipe bend. Secondary flows reached a maximum at 30 and then decreased until 90, where some local flow

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94 reversal was observed. Anwer et al [7 6 ], Anwer and So [7 7 ], and Sudo et al [ 78, 79 ] investigated upstream effects associated with pipe bends. In each of these studies, only one set of operating conditions (Re and pipe curvature) was studied. Anwer et al [7 6 ] observed mean flow asymmetry and an increase in all three components of the normal stress over the pipe one pipe diameter upstream of the ben d. In addition, Anwer and So [77 ] identified the beginning of a nonlinear pressure gradient developing about 4 pipe diameters upstream of the bend, in line wit h the outside of the bend. Sudo et al [ 78 79 ] showed mean flow asymmetry and pressure gradient nonlinearity developing between 1 and 0.5 diameters upstream of a bend. Crawford et al. [ 8 0 ] also investigated upstream effects but over range of Re and pipe curvatures. They concluded that a nonlinear pressure gradient begins about five pipe diameters upstream of the bend, regardless of the radius of curvature. Crawford et al. [ 80 ] also found that the length of straight pipe required for fully developed flow in the downstream tangent increased with decreasing bend curvature ratio. Finally, their experimental data for total bend loss coefficient exceed ed predictions based on Itos [ 7 2 ] correlation. Coffield et al. [8 1 ] investigated flow in pipe bends at higher Reynolds numbers (up to 2.5 x 106) than previous investigations. They found significant deviation between their measurements of total bend loss coefficients and predictions based on existing correlations (such as equation 4 -3) which are designed for flows with lower Reynolds numbers. Hawthorne [ 8 2 ] determined that secondary flows in pipe bends are oscillatory, marked by periodic changes i n the direction of circulation. Despite all o f these previous investigations, there is a lack of experimental data for flow in pipe bends of large curvature at high Reynolds number (Re > 3x 105). While

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95 Coffield et al. [ 8 1 ] investigated high Re flow in pipe bends, the radius of curvature in their experiments was low (< 3). In addition, Coffield et al. [ 8 1 ] did not study upstream effects as in th is present work. Furthermore, t h e present study looks into the influence of a sudden expansi on at the outlet of a pipe bend as opposed to a continuation of straight pipe section. Experimental Water flow was investigated in a 180 vertical bend consisting of two 90 bends, each with Rb/R = 24. The water was unfiltered tap water at a temperature of 23C. The two 90 bends were connected by a straight horizontal section seven pipe diameters in length. The pipe was three inch nomi nal (78 mm) schedule 40 stainless steel. The pipe bends were made by the roll bending method which produces very little cross sectional distortion. A diagram of the experimental setup is given in Figure 42. The Re was varied from 3.68 x 105 to 8.50 x 105. Pressure taps were placed on the insid e and outside of the first 90 bend at its entrance and every 18 thereafter or approximately every four pipe diameters throughout the bend. Additionally, inside and outside taps were placed two diameters upstream, and two and seven diameters downstream, of the first 90 bend. Finally, taps were placed inline with the outside of the bend every 5 diameters upstream of the first 90 bend and provided pressure measurements up to 37 pipe diameters upstream. Before enter ing the bend, 67 pipe diameters allow the flow to become fully developed; this was confirmed via LDV measurements. Pressure taps were 1.0 mm in diameter. Threaded couplings were welded over the holes, and pressure gauges were screwed into the couplings. The pipe wall thickness was over 5 times the tap diameter, so the water in contact with the gauge was assumed to be quiescent. The gauges had a range of 0 15 PSI (0 103 kPa) with a

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96 digital readout to the hundredths place, an accuracy of 0.1% of the full scale and readings occurring at 3 Hz (smaller than the data point size on Figure s 4 -3 and 4 -4). The pressure was determined by taking an average over 30 seconds. Pressure fluctuations increased with increasing Re, and were consistently less than 4%. The Re was determined by a magnetic flow meter. Fluctuations in the flow meter reading were always less than 2% of the mean flow. A 50 HP centrifugal pump pumped the water and was controlled via a variable frequency drive. Experiments were conducted wi th two different pipe configurations downstream of the second 90 bend. Configuration A involved a continuation of the 78 mm I.D. stainless steel pipe used throughout the flow loop. Configuration B utilized a PVC pipe that expanded in diameter from 78 mm to 156 mm via two bushings, discharging the fluid to atmosphere. In both cases, the downstream tangent was 22 pipe diameters in length Results and Discussion Pressure measurements in Figures 4 -3 and 4 -4 are presented as pressure loss coefficients K with Pref equal to the pressure 37 pipe diameters upstream of the first 90 bend. The pressure measurements are also adjusted to take int o account the vertical z g P Pf meas (4 -5) where Pmeas is the measured tap pressure. Fig ure 4 3A shows pressure loss coefficients upstream of the first 90 pipe bend as a function of Re for downstream Configuration A (contin uation of the straight pipe section). At the lowest Re investigated, the pressure gradient is linear approaching the

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97 first 90 bend and upstream effects are minimal, consistent with previous investigations. However, as the Re starts to increase, the loss coefficient profile begins to flatten approaching the bend. Hence, upstream effects (i.e. deviations from the linear pressure gradient associated with fully developed flow) become pronounced, increase significantly with increasing Re, and extend well bey ond a few pipe diameters upstream of the bend. This result is in stark contrast with the results of previous investigations at lower Re which are summarized by Ward-Smith [ 8 3 ] variations in pressure due to the presence of the bend start to occur in the upstream tangent at a valueof between 1 and 2 [pipe diameters]. Fig ure 4 3B gives the pressure loss coeffi cients upstream of the first 90 pipe bend for downstream Configuration B (sudden expansion at the outlet); these pressure loss coefficients are v irtually identical to those with Configuration A. Hence, upstream effects significantly increase with increasing Re, regardless of downstream configuration. As seen in Figures 4 -3 and 4 4, the trend of increasing K as a function of Re is consistent with equation 4 -1; t here is a second order dependence on mean velocity in the pressure in the numerator. When combined with a first order dependence between pressure and velocity as described by the Navier -Stokes equation, an inversely linear relationship bet ween Re and K results. Influence of Downstream Tangent: Configuration A Fig ure 4 A presents the loss coefficients through the pipe bend for downstream Configuration A. The vertical lines in the figure indicate the entrance and exit points of the bend. Throughout the pipe bend, the pressure on the inside of the pipe is less than that on the outside. This pressure difference is also present at the entrance to the bend. Previousl y published results (Crawford [ 8 0 ]) show that this pressure difference is

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98 la rgely a function of pipe curvature; the present results also indicate a weak dependence on Re. The pressure difference between the inside and outside of the pipe increases slightly with increasing Re. This difference between the inside and outside pressur e decreases significantly approaching the bend exit. In the connecting pipe, the inside pressure becomes greater than the outside pressure. The reversal in pressure difference is likely associated with a reversal in the direction of the secondary flow, a s identified by Rowe [ 7 5 ] and Hawthorne [ 8 2 ]. The present results indicate that this pressure difference downstream of the bend has a weak dependence on Re; the pressure difference increases slightly with decreasing Re. Despite the pressure drop evidence for the existence of secondary flow, there is a minimal contribution from the pipe curvature to the total bend pressure loss. The loss coefficient profile follows the pressure change associated with points B and E on Fig ure 4 -1; the pressure gradient is approximately linear throughout the bend, regardless of Re. This r esult is consistent with Rowe [75 ] who observed secondary flows in pipe bends with large curvature (Rb/ R = 24) at a given (lower) Re, but noted that secondary flows did not contribute to the total bend pressure loss. Comparisons of the measured total bend loss coefficient to the predictions from the empirical correlations of Ito [ 7 2 ], Miller [ 7 3 ], and the Crane Comp any [7 4 ] are displayed in Table 4 -2 The total bend loss coefficients were d etermined via regression using an average of the inside and outside pressure at each location downstream from the bend entrance. All correlations significantly under predict the total bend loss. The correlations of Ito [ 7 2 ] and Miller [ 7 3 ] and the experi ments show a decrease in total

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99 bend loss coefficient with increasing Re, but the significant variation is not captured by the correlation. At the range of Re investigated in the present work, the correlations predict only a very slight decrease in kt with increasing Re (Ito [ 7 2 ] and Miller[ 7 3 ]) or none at all (Crane Company [74 ]). Ito [ 74 ] found good agreement with experiments in bends of 45, 90, and 180 at Re from 2x104 to 4x105 and Rb/R values from 3.7 to 25. However, the Re range of the present in vestigation is outside the range of experimental data on which the correlation of Ito [ 7 2 ] is based. In addition, the pipe curvature employed in the present study, Rb/ R = 24, is outside the range of the Miller [ 7 3 ] correlation. Unfortunately, Miller [ 7 3 ] and the Crane Company [74 ] did not compare their respective correlations with experimental data. From previous investigations (Ito [ 7 2 ]), it is known that kt increases with increasing curv ature. Crawford et al. [ 8 0 ] investigated larger pipe curvatures and also found that the correlation of Ito [ 7 2 ] under predicted the total bend loss coefficient. Influence of Downstream Tangent: Configuration B Fig ure 4 4 B presents the loss coefficients through the bend for Configuration B the case where the water is allowed to freefall from the second 90 bend. The pressure measurements are consistent with those in Configuration A upstream of the bend and up to four diameters through the bend. However, at this point in the bend, the pressure on the inside of the pip e increases, such that it surpasses the pressure on the outside of the pipe by eight diameters through the bend. By the next pressure tap, twelve diameters through the bend, the inside pressure is again lower than that on the outside. Finally, at sixteen pipe diameters through the bend, the inside pressure surpasses that on the outside and remains larger through the end of the bend and into the downstream tangent. This unusual pattern of pressure

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100 reversal is likely associated with a highly complex secon dary flow pattern in the bend. Since the pressure measurements in Configuration A (Fig ure 4 4 A) and Configuration B (Fig ure 4 4 B) were obtained at the same Re, the difference in flow behavior is associated with the change in the downstream configuration. In Configuration B, the loss coefficient based on an average of the inside and outside pressures of the bend also varies linearly throughout the bend as with Configuration A. Thus, even though the flow disruptions propagate throughout the bend, the secon dary flows do not affect the overall pressure drop in the bend in a significant way. Conclusion Pressure data are presented for flow in pipe bends at a novel combination of conditions large pipe curvature with high Re. A number of interesting observations associated with these conditions are made: Upstream effects occur well beyond a few pipe diameters prior to a pipe bend provided the Re is sufficiently high. Through the pipe bend, as well as downstream of the pipe bend, the pressure difference between the outside and the inside of the pipe is weakly dependent on Re. Correlations for total bend pressure loss significantly under predict the pressure drop in the bend and fail to capture a decrease in kt with increasing Re. In addition, the following conclusions result from the investigation of two different exit configurations: Upstream effects are not dependent on the downstream exit configuration. A sudden expansion downstream of a bend is associated with a complex outside and inside pressure pattern in t he pipe bend. Independent of exit configuration, the pressure on the outside of the bend increases, surpassing that of the pressure on the inside of the bend, at the bend exit and downstream of the bend.

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101 Independent of exit configuration, the loss coeffici ent varies linearly throughout the bend, signifying that the effective length of the pipe is equal to its actual length, and wall friction is the dominant process contributing to pressure loss in bends of R/r 24.

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102 Table 4 1. Published experimental pre ssure loss data in pipe bends Author Re R b /R In Bend Angular Position Upstream Locations Downstream Locations Ito [ 74 ] 2x10 4 to ~3.5x105 2 3.66 6.59 3.68 6.52 90 90 90 180 180 0 0 /2 0 /3 inside, outside, top, bottom 0, 7.8, 15.0, 22.2, 30.8 0, 9.3, 1 7.8, 27.6, 41.4, 54.3, 61.6, 71.6 Rowe [ 7 7 ] 2.36x105 24 90 180 /4 /6 constant 0 1, 5, 29, 61 Anwer et al. [ 7 8 ] & Anwer and So [ 7 9 ] 5.0x104 13 180 6 total inside, outside 0, 1, 4, 18 9 total, up to 50 Sudo et al. [ 80 ] 6.0x104 4 90 /3 inside, outside, bottom 0, 0.5, 1 0, 0.5, 1, 2, 5 Sudo et al. [81 ] 6.0x104 4 180 /12 inside (90 45), outside (90 45), bottom 0, 0.5, 1 0, 0.5, 1, 2, 5 Crawford et al. [ 82 ] 2.0x104 to 1.26x10 5 1.3 5 20 90 90 90 /2 /2 /4 ins ide, outside 0, 5, 10, 50, 90 0, 5, 10, 20, 30, 40, 50, 60, 70, 90 Coffield et al. [ 8 3 ] 1x105 to 2.5x106 2.4 3 90 90 /4 /4 inside, outside, bottom 0, 1, 2, 5, 10, 15, 19 0, 1, 4, 7, 10, 15, 20, 25, 20 Hawthorne [84 ] 1.7x105 3 10 90 180 0 /6 constant every 30 0 0 0, 2.7, 7.3, 10, 16 0, 4.2

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103 Fig ure 4 1 Lo ss coefficient profiles: (.) n o bend present; ( ) n o additional pressure loss due to bend; ( .. .. -) a dditional pressure loss due to bend Bend Downstream Tangent Upstream Tangent D E A B C F 0 X Pipe Diameters from Bend Entrance

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104 Fig ure 42 Bend geometry and discharge configurations Pressure Taps 7 straight diameters R b / R = 24 R b / R = 24 Downstream Tangent 940 mm 940 mm R b 2 R r = 39 0d +20d +16d +12d +27d +22d 7d 17d 12d 2d 22d 27d 32d 37d Pref Configuration A Configuration B

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105 P i p e D i a m e t e r s f r o m B e n d E n t r a n c eK-3 0 2 0 1 0 0 -3 2 5 -2 1 5 -1 0 5 0R e = 3 6 8 0 0 0 R e = 5 0 0 0 0 0 R e = 6 1 6 0 0 0 R e = 7 3 6 0 0 0 R e = 8 5 0 0 0 0 A Fig ure 43. Loss coefficient upstream of bend entrance A) C onfiguration A and B) C onfiguration B P i p e D i a m e t e r s f r o m B e n d E n t r a n c eK3 0 2 0 -1 0 0 -3 2 5 -2 1 5 -1 0 5 0R e = 3 6 8 0 0 0 R e = 5 0 0 0 0 0 R e = 6 1 6 0 0 0 R e = 7 3 6 0 0 0 R e = 8 5 0 0 0 0 B

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106 P i p e D i a m e t e r s F r o m B e n d E n t r a n c eK0 1 0 2 0 3 0 -6 -5 -4 -3 -2 -1R e = 3 6 8 0 0 0 I n s i d e R e = 3 6 8 0 0 0 O u t s i d e R e = 5 0 0 0 0 0 I n s i d e R e = 5 0 0 0 0 0 O u t s i d e R e = 6 1 6 0 0 0 I n s i d e R e = 6 1 6 0 0 0 O u t s i d e R e = 7 3 6 0 0 0 I n s i d e R e = 7 3 6 0 0 0 O u t i d e R e = 8 5 0 0 0 0 I n s i d e R e = 8 5 0 0 0 0 O u t i d e A P i p e D i a m e t e r s f r o m B e n d E n t r a n c eK0 1 0 2 0 3 0 -6 -5 -4 -3 -2 -1R e = 3 6 8 0 0 0 I n s i d e R e = 3 6 8 0 0 0 O u t s i d e R e = 5 0 0 0 0 0 I n s i d e R e = 5 0 0 0 0 0 O u t s i d e R e = 6 1 6 0 0 0 I n s i d e R e = 6 1 6 0 0 0 O u t s i d e R e = 7 3 6 0 0 0 I n s i d e R e = 7 3 6 0 0 0 O u t i d e R e = 8 5 0 0 0 0 I n s i d e R e = 8 5 0 0 0 0 O u t i d e B Figure 4 4 L oss coefficient through bend. A) C onfiguration A and B) C onfiguration B

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107 Table 4 2. Total bend loss coefficient comparison between experimental results and predictions from correlations Re k t (Present Work) k t (Ito [ 74 ]) k t (Miller [ 75 ]) k t (Crane [76 ]) 3.68 x 10 5 1.81 0.35 0.31 0.61 5.00 x 10 5 1.0 9 0.34 0.30 0.61 6.16 x 10 5 0.82 0.33 0.29 0.61 7.35 x 10 5 0.64 0.32 0.28 0.61 8.50 x 10 5 0.54 0.31 0.28 0.61

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108 CHAPTER 5 SINGLE PHASE VALIDATION Introduction The veracity of current research investigating multiphase flow is often predicated on a single phas e base -case. This base -case validation has resulted in frequent citations of the work of Laufer [ 8 4 ] and other benchmark single-phase turbulence papers (Perry and Abell [ 8 5 ], Lawn [ 8 6 ], Schildknecht et al. [ 8 7 ]). Single phase turbulence data are also available as base -case conditions for prominent twophase investigations, both in gas (Tsuji [ 5 ], Lee and Durst [ 4 ]) and in liquid (Nouri et al. [ 15 ] and Theofanous and Sullivan [ 10 ]). Turbulence measurements using PIV (Van Doorne and Westerweel [ 88 ] and F ujiwara et al. [ 89 ]) have been made in lower Re flows and compared with available DNS data (Eggels et al. [ 9 0 ], W u and Moin [ 9 1 ]). More recently, Zhao and Smits [ 9 2 ] and Morrison et al. [ 9 3 ] have conducted single-phase turbulence studies over a large rang e of Re, with a focus on the wall region. Table s 5 -1 and 52 summarize the key publications which report singl e phase turbulence measurements in air and water flows, respectively. Perry and Abell [ 8 5 ] identified significant differences between the repor ted single phase turbulence measurements currently available in the literature. They cited inconsistent hot wire measurement techniques, among other factors, as the reason for these discrepancies. Since that time, a host of improved turbulence measuremen t techniques have been developed most notably, the non intrusive methods based on the Doppler Effect. In this paper, we present an up-to -date review of turbulence measurements in single phase flow in round pipes and show that significant differences in t he reported

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109 values of turbulent intensity persist. In fact, the variation between single-phase turbulence measurements can greatly exceed the magnitude of turbulence modulation, a common and important theme in many two-phase flow research studies. It is the aim of this paper to analyze the variations in these single-phase measurements and extract any common features based on experimental conditions. We focus on the central region of the pipe where the influence of Re and wall effects are minimized. Addi tionally, we supplement the published singlephase turbulence data by including laser Doppler velocimetry (LDV) measurements of single phase flow in water at Re higher than previously investigated. Experimental Laser Doppler velocimetry (LDV) was used to make single-phase flow experiments in water at five Re: 1.5x105, 2.27x105, 3.36x105, 5.0x105, and 6.16x105. All the data were collected in a backscatter configuration. However, the distance from the wall was calibrated via a series of forward scatter ex periments conducted to determine the wall shear stress and corresponding friction velocity. A lens of f ocal length 250 mm w as used, resulting in a probe volume length (in water) of approximately 2 mm, depending on its location in the pipe. At Re = 5.0x105 measurements were taken along three different radial chords, 90 degrees apart, and then repeated at two different vertical positions, separated by 8 pipe diameters, to verify that the flow was fully developed. The reproducibility between experiments wa s at least 95% at the fluctuating velocity level. Furthermore, the pressure gradient was constant at the entrance to the test section. Tap water produced an adequate measurement signal without extra seeding. Data were collected at 16 radial positions, w ith a greater density near the pipe wall. The friction velocity was

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110 determined experimentally from wall shear stress measurements and pressure drop profiles and compared to a low Re k for smooth pipes (P randtl [ 4 4 ]), see Table 5 3 Scaling Unfortunately, the turbulence measurements from the various published works use different scaling to nondimensionalize their results. Hence, in order to compare one published work with another, a uniform scaling must be adopted. Here, the friction velocity is used since it is the most common scaling for turbulence measurements. In published works where the mean, centerline or local velocity are used to scale the turbulence measurements, rather than the friction velo city, its value is deduced from the reported Re using friction factor correlations. The friction velocity is defined as f 0 tU (5 -1) where f is the fluid density and 0 is the wall shear stress, defined as: 8 U 2 f f s 0 (5 -2) Here s is the Darcy friction factor and Uf is the mean fluid velocity. C ombining equations 51 and 5-2 8 U U2 f s t (5 -3) The friction factor s can be estimated via Prandtls universal law of friction for smooth pipes (Prandtl [ 4 4 ]). 8 0 D U log 0 2 1s f f s (5 -4)

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111 where D (=2R) is the pipe diameter and is the fluid viscosity. Conditions were assumed to be standard ambient conditions when they were not reported 1 atm pressure and 20 C. In the cases where the measurements of the turbulent velocity were scaled by the local fluid velocity or the maximum fluid velocity, those values were estimated from the standard turbulent velocity profile (Schlichting [ 94]). n 1R r U u max (5 -5) where u is the local mean fluid velocity at radial position r. The value of n is a relatively weak function of Re as given in Table 5-4 From equation 5 -5, the ratio of the mean to maximum fluid velocity can be derived: 1 n 2 1 n n 2 U U2 max (5 -6) While the friction velocity affects the magnitude of t he reported turbulence measurements, it does not influence the shape of the turbulent velocity fluctuation profiles. By normalizing the scaled fluctuating velocity profiles with their respective centerline values, the shape of the turbulent velocity fluct uation profiles can be easily compared. Results The measurements presented in Tables 51 and 52 encompass a range of experimental techniques including hot wire, LDV, particle image velocimetry (PIV), 3-D conical probe, and hot -film anemometry. Table 55 lists two well known DNS results to which the experimental data was compared. Pipe diameters range from 15 mm to 302 mm. While the number of radial measurements varies among these published works,

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112 most report an increase in measurement density near the w all and a value for the centerline turbulence intensity. We use various factors to compare and analyze these published data whether the measurements were made in air or water, whether the measurement were made using intrusive or non-intrusive experimental techniques, as well as other factors including Re and pipe diameter. Effect of Re Figures 5 1 A and B present axial turbulent velocity measurements in air as a function of distance from the wall y (y=R -r) based on the work of Laufer [8 4 ] and Zhao and Smits [ 9 2 ], respectively. Both of these studies show negligible effect of Re on the magnitude of the scaled turbulent velocity fluctuations in the far wall region. The measurements of Perry and Abel [85 ] (not shown) are also consistent with this observation. However, in the singlephase flow of water, this observation of Re independence is not the case. Figures 5 2A B, and C present axial turbulent velocity measurements in water as a function of radial position r based on the work of Wang et al [11], Hu et al [12] and the present study. Although there is no consistent trend in the magnitude of the turbulent velocity fluctuations as a function of Re, in general, the scaled turbulent fluctuations tend to decrease with increasing Re. Unfortunately, the turb ulence measurements in water of Toonder and Niewstadt [ 9 5 ] are inconclusive in this regard as their measurements do not uniformly extend into the pipe core. Turbulence Measurements in Air using Hot -Wire Although the reported magnitude of the scaled gas t urbulent velocity fluctuations in the far wall region does not vary with Re for a given investigation, there are significant variations in the magnitude of the scaled fluctuations between investigations in the

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113 various published works. Figure 5 -3 presents measurements of the turbulent veloci ty profile in air using only hot wire. In this figure, no estimation for the friction velocity was necessary as all the published works scaled their turbulence measurements with Ut. The specific measurements shown are those conducted at the highest Re for each investigation. Also included in this plot are the direct numerical simulation (DNS) results of Wu and Moin [ 91 ] at Re = 4.4 6 x104. Between hot wire investigations, there is considerable deviation in the magnitude of the scaled turbulent velocity. The level of these deviations exceed the typical error (5 -6%) associated with turbulence velocity measurements using hot wire (Comte -Bellot [95]) In addition, the level of these deviations are on the order of or greater than the magnitude of the turbulent modulation often investigated in multiphase research studies. The deviations in the reported magnitude of the turbulent velocity do not show any trend with pipe diameter or Re. The DNS results exhibit the lowest velo city fluctuations with the measurements of Laufer [ 84] at Re = 5.0x105 most closely following the DNS results. LDV vs Hot wire Measurements in Air Flow Figure 54 shows hot wire measurements of Figure 5-3 (in gray) along with the LDV measurements in air. Overall, the axial fluctuations measured with LDV are lower than those obtained with hot wire. This is especially true in the middle of the radius, resulting in velocity profiles obtained using LDV tending to be flatter than profiles obtained using hot wi re. The turbulent velocity data obtained using LDV are more consistent, except for the LDV measurements of Tsuji [ 5 ]. Nevertheless, the variation b etween all of these sets of data is outside of the range of the typical error ass ociated with LDV measurements of fluctuating velocity (4 %) (Yanta and Smith [ 5 8 ]). In addition, these LDV data are not in line with the DNS results, except for the measurements of

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114 Tsuji. LDV validation and post processing techniques are likely responsible for these variations in the data. The validation and post processing greatly affect which individual seed velocity measurements are included in the final reported measurement for the turbulent velocity. Turbulence Measurements in Water Figure 5 5 displays the turbulent velocity profiles in water from nine different sets of measurements. There is significant variation between these measurements at all radial locations. The level of these variations exceeds those in turbulent gas flow measurements. The scaled fluctuations in wat er vary from 0.8 to 1.2 at the centerline and from 1.4 to 2.0 at r/R=0.6, with more inconsistency in the measurements at the pipe centerline. The SPIV (stereoscopic PIV) data of Van Doorne and Westerweel [ 88 ] are very similar to the DNS data of Eggels et al. [ 92 ] at Re = 5.3 x 103 with the lowest centerline turbulence. However, the PIV data of Fujiwara et al. [ 9 0 ] at Re = 1.1x104 are significantly different, with a scaled centerline turbulence velocity that is 44% greater than the measurements of van Doorne and Westerweel [ 88 ]. The profiles obtained via a hot -film device by Shawkat et al. [ 9 7 ] and Hu et al. [12] are significantly less smooth than the turbulence profiles obtaining using other experimental techniques. The LDV measurements of Theofanous and Sullivan [ 10] and Nouri et al. [ 15 ] produced the largest values for the turbulent velocity, with the data of Theofanous and Sullivan [10] being well outside the range of all other experimental measurements. Both of these sets of LDV measurements report considerably larger turbulence velocities than the present LDV data; the present data are in the middle of the range of previous investigations. For the LDV data sets, which report turbulence

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115 measurements scaled with the friction velocity, the variations in the turbulence measurements are likely due to the difficulty of measurement of the friction velocity in water. Typically, pressure drop measurements are used to determine the friction velocity. For example, in vertical flow, pressure drop measurement s in water are subject to more variations than in air since the wall shear stress contributes much less to the overall pressure drop due to the gravitational force. The importance of an accurate determination of the friction velocity Ut has also been noted by van Doorne and Westerweel [ 88 ] and Eggels et al. [ 9 0 ] among others, because the measurement of Ut systematically influences the magnitude of the reported measurements. Figure 5 6 combines all of the turbulence measurements those conducted in air den oted by pink lines and those conducted in water denoted by blue lines. The DNS results of Wu and Moin [ 9 1 ] are represented with a black line. In general, measurements of turbulent velocity fluctuations in water flow are higher than in air flow. Conclus ion There is significant variation in the reported values of single phase gas turbulence intensity among the commonly cited references of these measurements. In both gas and liquid flow, this variation exceeds typical errors associated with the flow measu rement techniques. The magnitude of the turbulence velocity fluctuations in water is consistently higher than in air at the same Re. In addition, the magnitude of the variations in the measurements of turbulent velocity is greater in liquid versus gas fl ow. In air, the turbulent velocity exhibits no Re dependence far from the wall; in water, there is a Re dependency. Finally, due to the intrusive nature of the hot wire probes, there is a bias in the LDV versus hot wire measurements. In air, turbulent v elocity profiles

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116 measured using LDV are consistently flatter than those obtained from hot wire measurements. Based on these conclusions the singlephase measurements were deemed to be in agreement with established values, proving the suitability of the exp erimental flow facility and instrumentation for two-phase experiments.

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117 Table 5 1 Turbulence m easurements in a ir Re Pipe D. (mm) Fluid Method Scaling Quantity Zhao and Smits [ 92 ] 6,100,000 4,300,000 1,100,000 480,000 230,000 140,000 110,000 129 Air Hot Wire U t Laufer [ 84] 500,000 50,000 254 Air Hot Wire Ut Perry and Abell [ 85 ] 257,000 173,000 133,000 78,000 111 Air Hot Wire Ut Lawn [ 86 ] 250,000 164,000 90,000 38,000 144.3 Air Hot Wire Ut Schildknecht et al. [87 ] 17,250 50 Air Hot Wire & Pitot Ut Sheen et al. [ 6 ] 32,500 52 Air LDV Mean Velocity Tsuji et al. [5] 22,000 30 Air LDV Center line Velocity Maeda et al. [3 ]. 20,000 56 Air LDV Local Velocity Lee and Durst [ 4 ] 13,000 41.8 Air LDV Centerli ne Velocity

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118 Table 5 2 Turbulence measurements in water Re Pipe D. (mm) Fluid Method Scaling Quantity Present Data 610,000 500,000 360,000 220,000 110,000 76 Water LDV Ut Shawkat et al. [9 7 ] 148,000 43,500 200 Water Hot -film Local Velocity Nouri et al. [15] 59,200 25.4 Water LDV Mean Velocity Hu et al. [12] 57,000 38,000 38 Water Hot -film Centerline Velocity Toonder and Nieuwstadt [ 95 ] 24,600 17,800 10,000 4,900 40 Water LDV Ut Wang et al. [11] 44,000 34,000 23,000 57.15 Water 3 -D Conical Probe None Theofanous and Sullivan [10] 14,000 57 Water LDV Local Velocity Fujiwara et al. [ 89 ] 11,000 44 Water PIV/LIF Ut Van Doorne and Westerweel [ 88 ] 5,300 40 Water SPIV Ut

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119 Table 5 3. Comparison of friction velocity values Re dp/dz (m/s) Law of Wall (m/s) Prandtl [44] (m/s) 2.2x10 5 0.112 0.108 0.112 3.6x10 5 0.185 0.168 0.181 5.0x10 5 0.255 0.225 0.239 6.1x10 5 0.313 0.268 0.293 Table 5 4 Ratio of mean to maximum velocity power law exponent n=f(R e) 6 7 8 9 10 U/Umax 0.791 0.817 0.837 0.852 0.865 Table 5 5. DNS t urbulence d ata Re Pipe D. (mm) Fluid Method Scaling Quantity Eggels et al. [9 0 ] 5,300 DNS DNS DNS U t Wu and Moin [91 ] 44,600 DNS DNS DNS U t

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120 y/R Figure 51 Effect of Reynolds number in air measurements A) Laufer [84] and B) Zhao and Smits [92 ] A B

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121 r / Ru / Ut0 0. 2 0. 4 0. 6 0 0. 5 1 1. 5 2R e =2 3 x 1 04R e =2 3 x 1 04R e =2 3 x 1 04 A r / Ru / Ut0 0 2 0 4 0 6 0 0 5 1 1 5 2R e = 3 8 x 1 04R e = 5 7 x 1 04 B r / Ru / Ut0 0 2 0 4 0 6 0 0 5 1 1 5 2R e = 1 1 x 1 05R e = 2 2 x 1 05R e = 3 6 x 1 05R e = 6 1 x 1 05R e = 5 0 x 1 05 C Figure 52 Effect of Re in w ater measurements A) Wang et al. [11], B) Hu et al. [12] and C) present d ata

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122 r / Ruf' / Ut0 0 2 0 4 0 6 0 8 1 1 2 1 4 1 6R e = 6 1 x 1 06D = 1 2 9 m m [ 9 2 ] R e = 5 0 x 1 05D = 2 5 4 m m [ 8 4 ] R e = 2 5 7 x 1 05D = 1 1 1 m m [ 8 5 ] R e = 9 0 x 1 04D = 1 4 4 m m [ 8 6 ] R e = 1 7 2 5 x 1 04D = 5 0 m m [ 8 7 ] R e = 4 4 x 1 04[ 9 1 ] Figure 53 Effect of pipe d iameter r / Ruf' / Ut0 0 2 0 4 0 6 0 8 1 1 2 1 4 1 6R e = 6 1 x 1 06[ 9 2 ] R e = 5 0 x 1 05[ 8 4 ] R e = 2 5 7 x 1 05[ 8 5 ] R e = 9 0 x 1 04[ 8 6 ] R e = 3 2 5 x 1 04L D V [ 6 ] R e = 2 2 x 1 04L D V [ 5 ] R e = 2 0 x 1 04L D V [ 3 ] R e = 1 7 2 5 x 1 04[ 8 7 ] R e = 1 3 x 1 04L D V [ 4 ] R e = 4 4 x 1 04D N S [ 9 1 ] R e = 5 3 x 1 03D N S [ 9 0 ] Figure 5 4 LDV vs hot wire measurements in air

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123 r / Ruf' / Ut0 0 2 0 4 0 6 0 8 1 1 2 1 4 1 6 1 8 2 2 2R e = 5 0 x 1 05P r e s e n t D a t a R e = 1 4 8 x 1 05[ 9 7 ] R e = 5 9 2 x 1 04[ 1 5 ] R e = 5 7 x 1 04[ 1 2 ] R e = 2 4 6 x 1 04[ 9 5 ] R e = 2 3 x 1 04[ 1 1 ] R e = 1 4 x 1 04[ 1 0 ] R e = 1 1 x 1 04[ 8 9 ] R e = 5 3 x 1 03[ 8 8 ] Figure 55 Turbulence measurements in water r / Ruf' / Ut0 0 2 0 4 0 6 0 8 1 1 2 1 4 1 6 1 8 2 2 2R e = 6 1 x 1 06[ 9 2 ] R e = 5 0 x 1 05[ 8 4 ] R e = 2 5 7 x 1 05[ 8 5 ] R e = 3 2 5 x 1 04[ 6 ] R e = 2 2 x 1 04[ 5 ] R e = 2 0 x 1 04[ 3 ] R e = 5 3 x 1 03[ 4 ] R e = 5 0 x 1 05P r e s e n t D a t a R e = 5 9 2 x 1 04[ 1 5 ] R e = 2 4 6 x 1 04[ 9 5 ] R e = 1 4 x 1 04[ 1 0 ] R e = 1 1 x 1 04[ 8 9 ] R e = 5 3 x 1 03[ 8 8 ] R e = 4 4 x 1 04[ 9 1 ] Figure 5 6 Turbulence measurements in air (pink) and water (blue)

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124 CHAPTER 6 LIQUID -SOLID FLOW Pressure Drop The pressure drop per unit le ngth of a fu lly developed single -phase fluid in a pipe can be defined as g i D 4 dz dPf f f (6 -1 ) w here if is the hydraulic gradient in length of fluid per length of pipe and f is the wall shear stress. Various methods exist to measure the wall shear stress but of greater interest here is the ability to infer the wall shear stress, and thus the pressure drop, based on mean flow properties. This is well established in singlephase flows via well known friction factors. In two -phase flows, however, both the measurement of the wall shear stress and the development of correlations to predict the pressure drop, are more challenging. Although there is no established method of pr edicting two-phase pressure drop, v arious co rrelations have been formulated. Bagnold [ 23 ] decomposed the total shear stress of the two-phase mixture into fluid and solid components s f m (6 -2 ) And assumed the two-phase pressure can be determined by g i D 4 dz dPm m m m (6 -3) where m is the volume average density of the two-phase flow. Assuming the fluid is Newtonian, the fluid shear stress is wall f fdr dU (6 -4 )

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125 The shear stress of the solid-phase is more difficult t o determine and requires certa in assumptions. Based on his experimental results, Bagnold [ 23 ] proposed that the solid stress varies based on the flow -regime 40 Ba dr dU Kwall s 2 / 3 w v s (6 -5 ) 450 Ba dr dU d Kwall 2 s 2 w 2 s i s (6 -6 ) w here w is the linear concentrati on at the wall, defined in equation 1 5. Bagnold [ 23] determined the viscous and inertial coefficients, Kv and Ki, to be 0.013 and 2.2, respectively. However, Bagnolds [ 23 ] experiments were conducted in a rotatin g c ouette device with a rotating outer cyl inder. Correlations Bartosik Sumner et al. [ 98 ] performed slurry -flow experiments in vertical pipe s utiliz ing a wide range of particles, varying density, diameter, and concentration, in vertical pipes. They found that slurries of particles less than 0. 8 mm in diameter at solids concentrations less than about 20% by volume exhibited no increase in pressure drop over the single-phase fluid. Additional radial solids concentration measurements revealed a very low concentration of particles n ear the wall, m aking the two phase wall shear stress equivalent to that of the single-phase, which helped to explain the lack of increase in the pressure drop. However, Sumner et al. [ 98 ] found that at particle diameters greater than 1 mm and at higher solids concentrat ions, the slurry pressure drop increased over that of the single phase flow. To investigate these differences, Shook and Bartosik [ 99 ] conducted experiments with sand and polystyrene particles

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126 between 1.37 and 3.4 mm in diameter in vertical pipes. They f ound that the total slurry wall shear stress was equal to that of the single -phase fluid under conditions with particle diameters of approximately 1.5 mm at solids concentration Shook and Bartosik [ 99 ] found no enhancement of the wall shear stress under conditions in t he macro viscous regime varying particle diameter, concentration, and flow rate. Enhancement occurred in the inertial regime but exhibited a Re dependence. To account for this they modified equation 6 -6 replacing Ki with 8 1 fA.Re (6 -7 ) where Ref is the Re based on the mean fluid velocity. Additionally, they simplified equation 6-6 by proposing that the solid velocity gradient be equal to t he fluid velocity gradient at the wall. This assumption was partly motivated by the difficulty of obtaining reliable solid velo city measurements at the wall. Furthermore, this assumption eliminates the need to measure the fluid velocity gradient at the w all by relating the two phase hydraulic gradient to that of the singlephase and then substituting f wall fdr dU (6 -8 ) Equation 67 was further modified Bartosik [ 10 0 ] to the form 317 2 f 7 210 x 3018 8 D A.Re (6 -9 ) Bartosik also assumed that the fl uid density and slurry density were equal and substituted Bagnolds linear concentration near the wall ( w 2) with that of the bulk slurry (L 1.5). Combining equations 6 -1 6 -2 6 6 6 -8 and 6 -9 yields the hydraulic gradient for the slurry obtained by Bartosik [ 10 0 ]

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127 317 2 f 2 f 3 f 2 3 L 2 s 7 fm4 i gD d 10 x 3018 8 1 i i. /Re (6 -10 ) w here im and if are the hydraulic gradient for the twophase mixture and single-phase fluid (in units of length of slurry or fluid per length of pipe) respectively The pressure drop can then be determined with equation 6-3. Matouek [10 1 ] found that this correlation significantly under predicted the increase i n pressure drop caused by sand particles > 0.4 mm in diameter over that of single phase water. Matouek [ 10 2 ] concluded that under these conditions the solid -phase a ffected the wall shear stress directly though collisions with the wall and not simply thro ugh an increase density of the two-phase fluid over that of the fluid alone. Littman and Paccione Another correlation was developed by Littman and Paccione [ 103 ] who derived a solid-phase friction factor fs, based on the assumption that it is a function of the Froude number 2 sU gD Fr (6 -1 1 ) and a turbulence response parameter r t f f s d e Ru U D d 5 0 C 3 40 t t (6 -12 ) where tR and te are the particle relaxation time and the lifetime of the most energetic eddy, respectively. Ut is the friction veloc ity and Cd is the coefficient of drag 687 0 p p d15 0 1 24 C.Re Re (6 -1 3 ) and UT the terminal velocity

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128 gd C 3 4 Uf f s d T (6 -1 4 ) Their final correlation takes the form e Rt 30 t 2 T f f s s 25 0 f d f me 1 U U d D Re C 295 0 v 1 dz dP dz dP (6 -1 5 ) The two-phase pressure drop is equal to the single -phase multiplied by a correction factor weighted by the concentration of the solidphase. Ferre and Shook The two previous c orrelations are based on mean flow properties but still require the hydraulic gradient of the single-phase flo w. Ferre and Shook [ 105 ] developed a m ethod of predicting the pressure drop in slurry flow that does not require a measurement of the single-phase pressure drop by utiliz ing friction factors for both phases. s s f f 2 m mf f U 5 0 (6 -1 6 ) where ff and fs a re the fluid and solid friction factors, respectively. The fluid friction factor can be estimated from the Re and surface roughness following the correlation of Churchill [ 10 4 ] 12 1 5 1 12 fB A 8 2 f .Re (6 -1 7 ) With and A and B defined as 16 r 9 0D k 27 0 7 457 2 A Re ln .. (6 -1 8 )

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129 1637530 B Re (6 -1 9 ) where kr is the surface roughness. The solid -phase friction factor was derived by Ferre and Shook [ 10 5 ] who measured 1.8 and 4.6 mm glass particles in water and ethylene glycol in a 40.9 mm diameter verti cal pipe 31 1 L 99 0 36 0 s m s D d dU 0428 0 f (6 -20 ) Their final correlation can be found by combining equations 6 -2 6 3, and 6 -1 6 through 6 -20 They found that the slurry wall friction diverged from that of the single phase fluid only at solids concentrations above 25% by volume for the 1.8 mm particles while differences were noticeable at the lowest concentration, 9%, for the 4.6 mm particles. Results Experimental The hydraulic gradient as a function of mean fluid velocity for each solids concentration and particl e diameter can be found in Figures 6 1 through 6 3 Each figure displays the experimental results as well as the pressure predicted by the correlations of Ferre and Shook [ 10 5 ], Bartosik [ 10 0 ], and Littman and Paccione [ 1 0 3 ] The error bars on the experi mental data represent a 95% confidence interval. The experimental results and correlations are all very similar at the lower two Re for all concentrations, except for the 0.5 mm particles where the correlation of Littman and Paccione [ 103] significantly over predicts the pressure. This over prediction is the result of very small Rep resulting from a very small slip velocity. At the highest velocity the experimental results for the 1.0 mm particles at 0.7% and 1.7% solids are significantly lower that predicted. This was true to a lesser extent

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130 for the 0.5 mm particles under the same conditions, though the prediction was within a 95% confidence. In light of this the pressure drop measurements for the 1.0 mm particles at the highest Re were repeated, with very similar results. The radial solids concentration profiles of et al. [ 16 ] show the solid phase moving toward the pipe center with increasing Re at solids concentrations of approximately 2.3% by volume. As the particles move toward the pipe center there is a decrease in the solids contribution to the wall friction. However, the same results should then be expected for the 1.5 mm particles, but w ere not observed. W hy the two-phase pressure is less than that of the clear fluid at the highest Re is not certain, but could be an example of drag reduction. D rag reduction is a well documented phenomenon in solid-liquid systems when the solid phase is high aspect ratio fibers or with the addition of polymers or solvents. However, drag reduction has also been observed in water -solid flows with more spherical pa rticles. Sifferman and Greenkorn [ 10 6 ] found drag reduction in sandwater flows of about 1% sand by volume, average diameter of 350 m, at Re from 5x104 to 4x105. Zandi [ 10 7 ] found drag reduction in solidliquid flows over a range of solid concentrations of clay, coal, fly ash, and activated charcoal slurries with a maximum of 57% reduction for clay approximately 500 m in diameter at Re = 1.0x105. Many other examples of drag-reduction at specific Re have also been observed (Radin et al. [ 108]). Drag r eduction has also been observed for smooth spherical particles in gas -solid systems. In these cases the particle diameter is typically much smaller than the particles presently tested. Radi n et al. [ 1 0 8 ] tested a range of spherical particles in water wit h diameters up to 420 m, at solids concentrations up to about 1% by volume

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131 a nd Re up to 3.94x105, but found no drag reduction. Where the current experimental conditions overlap with the experiments of Radin et al. [ 10 8 ] namely at the lower Re, no drag r eduction was observed. However, no data exits for liquid-solid flow of spherical particles at Re 5.0x105. Also noteworthy is that Sifferman and Greenkorn [ 10 6 ] found certain oil water -sand mixtures to be drag enhancing at low Re and drag reducing at hi gh Re, clearly showing a Re dependence. It is consistent with theory that the apparent reduction occurred at lower solids concentrations and at higher Re. Consequently, the possibi lity of drag reduction under these conditions exist s and further investiga tion is needed to quantify the phenomena. Correlations No correlation accurately predicts all the experimental results. The correlation of Ferre and Shook [ 10 5 ] consistently over predicts dP/dz for the 1.0 mm particles. However, for the 1.5 mm particle s the correlation of Bartosik [ 100 ], with its D3 term, over predicts the pressure drop at the lower two Re. Overall, the correlation of Littman and Paccione [1 0 3 ] does the best job of predicting the pressure drop over the range of conditions. The correlations of Littman and Paccione [ 1 0 3 ] and Bartosik [ 10 0 ] utilize the experimental single phase hydraulic gradient while that of Ferre and Shook [ 10 5 ] does not. This helps explain while the values predicted by Ferre and Shook [ 10 5 ] show greater deviation than the other two correlations. The large error bars can be misleading. As explained in the error analysis section of Chapter 2, the dilute nature of the two-phase flow suggests it should be similar to single phase flow as the correlations of Littman and Paccione [ 1 0 3 ] and Bartosik [ 10 0 ] clearly show. Single -phase pressure drop is well understood and can be accurately predicted. Our experimental single-phase measurements were very similar to

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132 established values. Additionally, the single -phase friction velocity determined via the pressure profile was in good agreement with that determined via LDV measurements of the near wall velocity gradient. Velocity Measurements A total of 27 mean and fluctuating velocity profiles were completed. T hree particles sizes, 0.5 mm, 1.0 mm, and 1.5 mm; at three flow rates, Re = 2.0x105, 3.35x105, and 5.0x105; and three solids concentrations, 0.7%, 1.7%, and 3% solids by volume. Only the fluid mean and fluctuating velocities were obtained for the slurry composed of 1.5 mm particles. Additionally, measurements of the 0.5 mm solids and the fluid in their presence were limited to r/R 0.45. In all cases the raw velocity i s normalized by the mean fluid centerline velocity Ufc. In the case of the 0.5 mm particles at 3% soli ds, where the measurements were limited to r/R 0.45, the mean centerline fluid in the presence of the 0.5 mm partic les i s estimated by assuming the ratio of fluid centerline velocity to fluid velocity at r/R = 0.46 for the 0.5 mm particles i s equal to th at of the 1.0 mm particles, at each respective Re. Table 6 1 outlines these conditions and gives Bagnold, Stokes, and particle Reynol ds numbers for all conditions. Determination of Rep requires a mean solid velocity and i s consequently not calculated fo r the 1.5 mm particles and the 0.5 mm particles at 3% solids Figure 64 presents the data in T able 6 1 and shows that the Bagnold and Stokes numbers increase continuously with no significant overlap as conditions change for the 0.5 mm and 1.0 mm particle s; first for increasing solids concentration for a given Re and particle diameter, then by increasing Re, and lastly by particle diameter. The Bagnold and Stokes numbers of the 1.5 mm particles at the lowest Re overlap with those of the 1.0 mm particles at the highest Re. Particle

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133 Reynolds numbers experience the greatest change with changing conditions (specifically particle diameter) and are consequently plotted on a log scale. Fully Developed Flow and Reproducibility of Data Measurements of the solid and liquid velocity over two radii, 90 apart, and at two axial locations, separated by 6 pipe diameters were made to verify that the slurry was fully developed. T he solid phase was composed of 0.5 mm particles at a concentration of 0.7% by volume and at Re = 2.0x105. The results can be found in Figure 65 Ad ditionally, the pressure at six vertical locations prior to the test section at these same conditions can be found in Figure 6-6 A linear regression through these six points is how the hydraulic gradient was determinedfor this specific case R2=0.9999. The profile is clearly linear, another indication that the flow is fully developed. Additionally, t he reproducibility of the measurements was examined. The measurements of the velocity of the 1.0 mm particles at 0.7% solids and Re = 2.0x105 were repeated three times. The results can be found in F igure 6-7 A Run 1 was conducted almost a year prior to runs 2 and 3. Runs 2 and 3 were completed hours apart, though the pump and LDV were shutdown bet ween measurements. The figure depicts the high degree of reproducibility of the measurements. Figure 6-7 B shows the average value with the error bars representing one stand ard deviation. The 3 runs along with all other measurements, were conducted at the top of the pipe over the north radius. The small amount of variation in the velocity measurements in Figures 6-5 and 6-7 are less than the effects observed by manipulating the experimental variables. Consequently, changes in the mean and fluctuatin g velocity profiles observed when

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134 adjusting particles size, solids concentration, and Re can be confidently regarded as the result of that adjustment. Mean Velocity Figures 6 8 through 6 -10 show the effects of Re and solids loading on the mean fluid velo city for all particle sizes The maximum velocity of both phases was always found at the pipe center. Examining the shape of the profiles shows that the mean fluid velocity is very similar in shape to that of the single phase fluid for all flow conditions The profiles have the flat shape characteristic of turbulent flow. This shape does not change significantly with chan ges in Re, Ba, or St. The mean solid velocity profiles are presented in Figures 61 1 through 613 The most obvious difference is t he increased slip velocity, the velocity difference between two phases, between the 0.5 mm and 1.0 mm particles. As expected, the larger particles have a larger slip. The slip between the fluid and 0.5 mm particles is very small; no more than 1% in all c ases with no significant trends as conditions were changed. Additionally, as evident by the small slip, the profile of the 0.5 mm particles is also very similar to that of the single-phase fluid. Tsuji et al. [5] also found that 200 m particles exhibite d a curved profile while 500 m were flat. However, Tsujis 200 m particles were still in the graininertia flow regime, according to the Bagnold number. The 1.0 mm particles exhibit a flatter, more linear profile across the pipe radius. The degree of flatness increases slightly with increasing solids loading. In some cases, like in Figure 6 -13 A the solid velocity exceeds that of the fluid near the wall. Th e negative slip is the result of solid slip near the wall, while the fluid does not slip. No p rominent trends regarding the negative slip near the wall were found. The 1.0 mm particles exhibit an increase i n slip as solids concentration increase s a result opposite

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135 that of Hardalupas [20]. Interestingly, there is a decrease in slip from Re = 2. 0x 105 to Re = 3.35 x 105 and then an increase again at Re = 5.0x105. Overall, t he slip at the highes t Re is greater than at the lowest Re which is in agreement with the results of Jones [8] However, this is the opposite of the result of Chemloul and Benrabah [29] who found a decrease in slip with increasing Re with 0.5 mm and 1.0 mm glass particles at Re between 9.4x103 and 2.48x104. Thus the lack of a trend regarding the impact of Re on particle slip in the present data is consistent with the various findi ngs in the literature. Increasing the solids concentration has a greater effect than increasing the Re on the slip velocity in t he range of conditions tested. However, the solids concentration has a significantly small er influence on Ba, St, and Rep, tha n Re or particle diameter, indicating that these parameters fail to capture the flow behavior under conditions of increasing solids. Fluctuating Velocity Effect of Re Figures showing the fluctuating velocity of the liquid in the presence of each particl e size are presented in Figures 614 through 6-16. The fluctuating velocity of the 0.5 m and 1.0 mm solidphases are shown in Figures 6 -17 through 6 -19. Generally, the fluid fluctuations increase with increasing particle size especially near the wall The effect of particle size on fluid fluctuations diminish es as the center of the pipe is approached. Increasing fluid fluctuations with increasing particle size is characteristic of collision -dominated flow and opposite that of viscous -dominated flow. The fluid fluctuations decrease with increa sing Re across the pipe which is characteristic of viscous dominated flow and opposite that of collisiondominated flow. The fluid fluctuating velocity becomes more flat at r/R < 0.5 as Re increases, such that at Re =

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136 5. 0x105 there is very little change in this region of the pipe. The presence of the solidphase damps the fluid turbulence near the pipe center at the lower two Re and slightly enhances it at the highest Re, for all particles sizes. The solid fluctuating velocity of the 1.0 mm particles is significantly greater than that of the 0.5 mm particles for all conditions a trend found in both viscous dominated and collision -dominated flow In comparison with the single phase fluid, the 1.0 mm particle f luctuating velocity is always greater, while that of the 0.5 mm particles is less than or equal, except very near the wall. At each respective Re, the solids fluctuations for the 1.0 mm particles are greater than those of the fluid in their presence exce pt very near the wall where they become similar. Conversely, the solids fluctuations for the 0.5 mm particles are less than those of the fluid in their presence. The difference in turbulence between the two phases decreases with increasing Re. The soli d phase turbulence profile also becomes increasingly flat with increasing Re at the lower two solids concentrations for both particles sizes. For example, at 1.7% solids the turbulence of both phases changes very little at Re = 5.0x105 at r/R < 0.5. At 3 % solids, increasing the Re increases the turbulence of the solid phases in the middle of the radius This has the effect of decreasing the flatness of the profile. It is reasonable to expect a flat profile to develop at r/R < 0.5 with increasing Re for the 0.5 mm particles as it did at 1.7% solids Similar to the decrease in slip at Re = 3.35x105, the magnitude of the solid turbulence at the pipe center decreases as the Re is increased from 2.0x105 to 3.35x105, and then increases again at Re = 5.0x105. The magnitude at the two Re extremes are similar. This is true for both particles sizes at 0.7% and 1.7% solids. The

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137 centerline solid turbulence of the 1.0 mm particles at 3% solids at all three Re are similar. These findings could be explained by a reduction in turbulence with increasing Re by a redistribution of the solids more evenly across the pipe. However, at the highest Re, there is a significant increase in Rep, from < 200 to > 300 for all loadings. This increase in Rep is indicative of an increase in slip. The increase is slip suggests a significant increase in vortex shedding that enhances both fluid and solid fluctuations. Effect of solids c oncentration The effects of altering the solids concentration on the fluid turbulence are most p rominent at the lowest Re. At the two higher Re, there is little change in the fluid turbulence across the pipe. There are two main exceptions to this both at Re = 5.0x105; the fluid in the presence of the 0.5 mm particles increas es and becom es flat as solids concentration increases and near the wall there is an increase in fluid turbulence in the presence of the 1.0 and 1.5 mm particles with increasing solids concentration. At Re = 2.0x105 the fluid fluctuations near the wall decrease with increasing solids concentration for the 0.5 mm and 1.0 mm particles. This decrease includes a change from turbulence enhancement to turbulence damping with respect to the single-phase fluid The fluid in the presence of the 1.5 mm particles shows an increase in tur bulence near the wall at the h ighest loading. The fluid turbulence near the center of the pipe increases and becomes more flat with increasing solids content at the lowest Re a trend consistent with collision-dominated flow and opposite that of viscous -d ominated flow This increase at the pipe center again includes a change from minor turbulence damping to minor enhancement. At Re = 3.35x105 the two -phase fluid turbulence is very similar to that of the single phase turbulence. Minor enhancement occurs at the

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138 wall and damping near the pipe center. At Re = 5.0x105 the presence of the solidphase enhances the turbulence at the wall and center. The effects of changing the solids concentration on the solid turbulence are most evident at the lowest Re, 2.0 x105. At this Re the solid fluctuations of the 1.0 mm particles decrease with increasing solids concentration, except near the pipe center, where it remains relatively constant. At the higher two Re the decrease in solid turbulence in only evident near t he wall. The solid fluctuations near the wall for the 0.5 mm particles decrease with increasing solids concentration and remain largely unchanged away from the wall. The only increase in solid fluctuations with increasing solids concentration occurs at 3% solids and Re = 5.0x105. The increase in solid turbulence under these conditions is indicative of a collision -dominated flow, which makes sense considering these conditions represent the highest Bagnold number at which solid velocity data was gained. The solid turbulence profile becomes more flat with increasing solids concentration for the 1 .0 mm particles At the pipe center the solid turbulence does not change significantly with solids loading. This constant level, when combined with an overall de crease in turbulence throughout the middle of the radius results in the profile becoming more flat with increasing solids content at each Re. The solid turbulence profiles at 0.7% and 1.7% are similar in shape With the 1.0 mm particles the solid fluctuations are similar in magnitude to that of the fluid near the center of the pipe. Otherwise, the solid fluctuations are greater than the fluid fluctuations. In the case of the 0.5 mm particles, increasing the solids concentration decreases the difference in turbulence between the two phases.

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139 To summarize, the results show trends characteristic of both collision -dominate and viscous dominated flow, clearly showing the flow is in a transitional regime. F or both particle sizes, t he effects of changing the Re are greater than the effects of changing the solids loading as expected, because increasing the Re results in a greater change in Stokes and Bagnold numbers than increasing the solids loading. The most significant changes occur at the highest Re and solids concentration for the 1.0 mm particles. This is expected, because under these conditions the B agnold and S tokes numbers are largest. The similarity in the fluid and solid profiles for the 0.5 mm particles, at both the mean and fluctuating level ar e also as expected. The Stokes numbers for the 0.5 mm particles range from 1.3 to 3.2, in dicat ing a solidphase that is not totally independent of the fluid. T he Bagnold n umbers range from 25 to 90, indicative of viscous -d ominated flow. The 1.0 mm parti cles experience a greater change in turbulence profile over the solids loadings and Reynolds numbers tested, which is again expected as they cover the greatest range of Bagnold numbers, from 94 to 299. Gore and Crowe [34] stated that when d/0.2R > 0.1 f luid turbulence enhancement should be expected. Based on this ratio, the 0.5 mm particles should damp turbulence while the 1.0 and 1.5 mm particles should enhance the fluid turbulence. The results show that this trend is generally truethe larger particles have a greater tendency to enhance turbulence but not a sufficient predictor. Hetsroni [ 35 ] suggested that the Rep was a better predictor and argued that Rep > 400 will result in turbulence enhancement via vortex shedding and wake formation Sheen et al. [ 6 ] found t his to be

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140 true at Rep > 100. The present data suggest that turbulence enhancement via wake formation occurred at Rep > 300. However, th e results also show that predicting changes in the fluid turbulence is more complicated than either of th ese two predictors. For example, near the wall, where the slip between the two phases is generally small, producing a small Rep, significant turbulence enhancement is found, even in the presence of the 0.5 mm particles. Likewise, increased slip (larger R ep) does not necessarily producer greater turbulence enhancement. At the pipe center the 1.0 mm particles at 1.7% solids and Re = 2.0x105 and 5.0x105 have similar slip (Figure 6-1 2 A,C), but the fluid turbulence at the lower Re is slightly damped while at the higher Re it is slightly enhanced (Figure 6 1 5 A,C). Finally, t he results also show a clear Re dependence, in agreement with Hadinoto et al. [ 9 ]. Error Analysis Based on equation (2-21) there is negligible error in the mean velocity measurements. Fo r example, with turbulence intensity of 0.1 and an ensemble size of 500 measurements at 95% confidence the error is 0.88%. Based on equation (2-2 2 ) the error in the fluctuating velocity measurements depends only on the number of data points. For example, a t 95% confidence 500 data points results in an uncertainty of 6.2%. Figure 6 20 shows the fluid fluctuating velocity with error bars based on equation (2 -21) for 1 mm particles at r/R = 0.82 for Re = 5.0x105 and 3% solids. Furthermore, Figure 62 1 de picts the evolution of the standard deviation with data count, showing that the standard deviation is flat and no significant changes would be expected with additional hits. There were generally several thousand measurements for each solid velocity, making their error very small, on the order of the size of the data point. To

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141 fur ther illustrate this, Figure 6-2 2 shows the evolution of the standard deviation for 0.5 mm particles at r/R = 0.91 for 0.7% solids and Re = 3.35x105. Under these conditions more than 2.0x104 velocity measurements were recorded. The figure shows the small changes in us/Ufc after various data counts. Another method of quantifying error in the fluctuating velocity measurements is to calculate the standard deviation of the fluctuating velocity after a certain minimum number of measurements are recorded in this case 250. Figure 62 3 represents the same conditions as Figure 6-20 except the error bars denote one standard deviation of uf/Ufc determined from velocity measurements 2 51 and above. In almost all cases the error bars are smaller than the data markers. Conclusion Measurements of the mean and fluctuating velocity of a turbulent liquid-solid flow composed of 0.5, 1.0, or 1.5 mm glass spheres in water at solids concentrat ions of 0.7%, 1.7%, and 3% and Re of 2.0x105, 3.35x105, and 5.0x105 were made with LDV/PDPA. Additionally, the hydraulic gradient as a function of Re was measured for each particle size and solids concentration. The data constitute a unique contribution to the field of multiphase flow, as the range of conditions measured span the transition from a viscous -dominated to an inertiadominated flow. The major results are: Drag reduction for the 1.0 mm particles at the highest Re occurs while the other pressu re gradient for the other two-phase conditions is similar to each respective single phase flow. For all particle sizes, Re, and solids concentrations the mean fluid velocity is very similar in shape to that of the single -phase fluid. The slip between t he fluid and 0.5 mm particles is very small while the 1.0 mm particles exhibit an increase in slip as solids concentration increases.

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142 Trends characteristic of both collisiondominate and viscous -dominated flow are evident, clearly showing the flow is in a transitional regime. Generally, the 0.5 mm particles damp the fluid turbulence while the 1.0 mm and 1.5 mm particles are either neutral or enhance the turbulence. The solid turbulence of the 1.5 mm particles exceeds that of the fluid in their presence, while the solidphase turbulence of the 0.5 mm particles is less than the fluid in their presence. The turbulence of both phases becomes increasingly flat near the center of the pipe with increasing Re and solids loading. This is in agreement with the f lat profiles of both fluid and solid turbulence in inertia dominated gas -solid flows. There is a decrease in turbulence with increasing Re until vortex shedding and wake formation increases turbulence at Rep > 300. The effects of changing the Re are greater than the effects of changing the solids loading.

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143 M e a n V e l o c i t y ( m / s )d P / d z ( k P a / m )0 2 4 6 8 6 8 1 0 1 2 1 4 1 6P r e s e n t D a t a F e r r e a n d S h o o k B a r t o s i k L i t t m a n a n d P a c c i o n e S i n g l e P h a s e A M e a n V e l o c i t y ( m / s )d P / d z ( k P a / m )0 2 4 6 8 6 8 1 0 1 2 1 4 1 6P r e s e n t D a t a F e r r e a n d S h o o k B a r t o s i k L i t t m a n a n d P a c c i o n e S i n g l e P h a s e B M e a n V e l o c i t y ( m / s )d P / d z ( k P a / m )0 2 4 6 8 6 8 1 0 1 2 1 4 1 6P r e s e n t D a t a F e r r e a n d S h o o k B a r t o s i k S i n g l e P h a s e C Figure 61. Pressure drop with 0.5 mm p articles A) 0.7% solids, B ) 1.7% solids and C) 3% Solids

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144 M e a n V e l o c i t y ( m / s )d P / d z ( k P a / m )0 2 4 6 8 6 8 1 0 1 2 1 4 1 6P r e s e n t D a t a F e r r e a n d S h o o k B a r t o s i k L i t t m a n a n d P a c c i o n e S i n g l e P h a s e A M e a n V e l o c i t y ( m / s )d P / d z ( k P a / m )0 2 4 6 8 6 8 1 0 1 2 1 4 1 6P r e s e n t D a t a F e r r e a n d S h o o k B a r t o s i k L i t t m a n a n d P a c c i o n e S i n g l e P h a s e B M e a n V e l o c i t y ( m / s )d P / d z ( k P a / m )0 2 4 6 8 6 8 1 0 1 2 1 4 1 6P r e s e n t D a t a F e r r e a n d S h o o k B a r t o s i k L i t t m a n a n d P a c c i o n e S i n g l e P h a s e C Figure 6 2 Pressure drop with 1 .0 mm p articles A) 0.7% solids, B ) 1.7% solids and C ) 3% Solids

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145 M e a n V e l o c i t y ( m / s )d P / d z ( k P a / m )0 2 4 6 8 6 8 1 0 1 2 1 4 1 6P r e s e n t D a t a F e r r e a n d S h o o k B a r t o s i k L i t t m a n a n d P a c c i o n e S i n g l e P h a s e A M e a n V e l o c i t y ( m / s )d P / d z ( k P a / m )0 2 4 6 8 6 8 1 0 1 2 1 4 1 6P r e s e n t D a t a F e r r e a n d S h o o k B a r t o s i k L i t t m a n a n d P a c c i o n e S i n g l e P h a s e B M e a n V e l o c i t y ( m / s )d P / d z ( k P a / m )0 2 4 6 8 6 8 1 0 1 2 1 4 1 6P r e s e n t D a t a F e r r e a n d S h o o k B a r t o s i k L i t t m a n a n d P a c c i o n e S i n g l e P h a s e C Figure 6 3 Pressure drop with 1.5 mm p articles A) 0.7% solids, B ) 1.7% solids and C ) 3% Solids

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146 Table 6 1. Experimental parameters in dimensionless numbers Re % Solids d p (mm) Ba St Re p 2.0x10 5 0.7 0. 5 25 1.3 2.6 2.0x10 5 1.7 0.5 31 1.3 0.3 2.0x10 5 3 0.5 38 1.4 3.35x10 5 0.7 0. 5 42 2.2 6.3 3.35x10 5 1.7 0.5 49 2.1 3.4 3.35x10 5 3 0.5 58 2.1 5.0x10 5 0.7 0. 5 62 3.2 6.7 5.0x10 5 1.7 0.5 77 3.3 14.0 5.0x10 5 3 0.5 87 3.2 Re % Solids d p (mm) Ba St Re p 2.0x10 5 0.7 1 .0 97 5.6 21 2.0x10 5 1.7 1.0 122 5.7 155 2.0x10 5 3 1 .0 139 5.5 90 3.35x10 5 0.7 1 .0 163 9.4 87 3.35x10 5 1.7 1.0 205 9.4 124 3.35x10 5 3 1 .0 221 9.3 175 5.0x10 5 0.7 1 .0 259 15.4 306 5.0x10 5 1.7 1.0 303 14.5 334 5.0x10 5 3 1 .0 341 14.2 596 Re % Solids d p (mm) Ba St Re p 2 .0x10 5 0.7 1 5 230 13.3 2.0x10 5 1.7 1. 5 276 13.1 2.0x10 5 3 1 5 305 12.6 3.35x10 5 0.7 1 5 385 22.5 3.35x10 5 1.7 1. 5 461 21.9 3.35x10 5 3 1 5 516 21.5 5.0x10 5 0.7 1 5 570 33.3 5.0x10 5 1.7 1. 5 677 32.5 5.0x10 5 3 1 5 763 31.7

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147 R e y n o l d s N u m b e r ( 1 03)B a g n o l d N u m b e r0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 00 5 m m 0 7 % 1 0 m m 0 7 % 1 5 m m 0 7 % 0 5 m m 1 7 % 1 0 m m 1 7 % 1 5 m m 1 7 % 0 5 m m 3 % 1 0 m m 3 % 1 5 m m 3 % A R e y n o l d s N u m b e r ( 1 03)S t o k e s N u m b e r0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 0 5 1 0 1 5 2 0 2 5 3 0 3 50 5 m m 0 7 % 1 0 m m 0 7 % 1 5 m m 0 7 % 0 5 m m 1 7 % 1 0 m m 1 7 % 1 5 m m 1 7 % 0 5 m m 3 % 1 0 m m 3 % 1 5 m m 3 % B R e y n o l d s N u m b e r ( 1 03)P a r t i c l e R e y n o l d s N u m b e r0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 1 001 011 021 030 5 m m 0 7 % 1 0 m m 0 7 % 0 5 m m 1 7 % 1 0 m m 1 7 % 1 0 m m 3 % C Figure 64. Dimensionless parameters of experiments. A) Bagnold number, B) Stokes number and C) particle Reynolds Number

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148 r / Rus' / Uf c0 0 2 0 4 0 6 0 8 1 0 0 0 2 0 0 4 0 0 6 0 0 8 0 1 0 1 2N o r t h T o p E a s t T o p E a s t M i d d l e Figure 65 Fully developed flow, s olid fluctuating velocity at two radii and two developmental lengths for 0.5 mm particles at 0 .7% solids a nd Re = 2.0x105 D e v e l o p m e n t a l L e n g t hP r e s s u r e ( k P a )0 1 2 3 4 5 0 1 0 2 0 3 0 4 0y = 1 0 6 1 x + 5 6 3 8 3 R2= 0 9 9 9 9 Figure 66 Linear pressure prof ile for 0 .5 mm particles at 0 .7% solids and Re = 2.0x105

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149 r / Rus' / Uf c0 0 2 0 4 0 6 0 8 1 0 0 0 2 0 0 4 0 0 6 0 0 8 0 1 0 1 2 1 2 3 A r / Rus' / Uf c0 0 2 0 4 0 6 0 8 1 0 0 0 2 0 0 4 0 0 6 0 0 8 0 1 0 1 2B Figure 67 Reproducibility of measurements; solid fluctuating velocity of 1.0 mm particles at 0.7% solids and Re = 2.0x105. A) individual measurements B) average and standard deviation

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150 r / RUf/ Uf c0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 10 5 m m L i q u i d 1 m m L i q u i d 1 5 m m L i q u i d S i n g l e P h a s e A r / RUf/ Uf c0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 10 5 m m L i q u i d 1 m m L i q u i d 1 5 m m L i q u i d S i n g l e P h a s e B r / RUf/ Uf c0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 10 5 m m L i q u i d 1 m m L i q u i d 1 5 m m L i q u i d S i n g l e P h a s e C Figure 68 Fluid mean velocity at 0.7% solids A) Re = 2.0x105, B) Re = 3.35x105 and C) Re = 5.0x105

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151 r / RUf/ Uf c0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 10 5 m m L i q u i d 1 m m L i q u i d 1 5 m m L i q u i d S i n g l e P h a s e A r / RUf/ Uf c0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 10 5 m m L i q u i d 1 m m L i q u i d 1 5 m m L i q u i d S i n g l e P h a s e B r / RUf/ Uf c0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 10 5 m m L i q u i d 1 m m L i q u i d 1 5 m m L i q u i d S i n g l e P h a s e C Figure 69 Fluid mean velocity at 1.7% solids A) Re = 2.0x105, B) Re = 3.35x105 and C) Re = 5 .0x105

PAGE 152

152 r / RUf/ Uf c0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 10 5 m m L i q u i d 1 m m L i q u i d 1 5 m m L i q u i d S i n g l e P h a s e A r / RUf/ Uf c0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 10 5 m m L i q u i d 1 m m L i q u i d 1 5 m m L i q u i d S i n g l e P h a s e B r / RUf/ Uf c0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 10 5 m m L i q u i d 1 m m L i q u i d 1 5 m m L i q u i d S i n g l e P h a s e C Figure 610 Fluid mean velocity at 3% solids A) Re = 2.0x105, B) Re = 3.35x105 and C) Re = 5.0x105

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153 r / RUs/ Uf c0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 10 5 m m S o l i d 1 m m S o l i d S i n g l e P h a s e A r / RUs/ Uf c0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 10 5 m m S o l i d 1 m m S o l i d S i n g l e P h a s e B r / RUs/ Uf c0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 10 5 m m S o l i d 1 m m S o l i d S i n g l e P h a s e C Figure 6 1 1 Solid mean velocity at 0.7% solids A) Re = 2.0x105, B) Re = 3.35x105 and C) Re = 5.0x105

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154 r / RUs/ Uf c0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 10 5 m m S o l i d 1 m m S o l i d S i n g l e P h a s e A r / RUs/ Uf c0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 10 5 m m S o l i d 1 m m S o l i d S i n g l e P h a s e B r / RUs/ Uf c0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 10 5 m m S o l i d 1 m m S o l i d S i n g l e P h a s e C Figure 61 2 Solid mean velocity at 1.7% solids A) Re = 2.0x105, B) Re = 3.35x105 and C) Re = 5.0x105

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155 r / RUs/ Uf c0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 10 5 m m S o l i d 1 m m S o l i d S i n g l e P h a s e A r / RUs/ Uf c0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 10 5 m m S o l i d 1 m m S o l i d S i n g l e P h a s e B r / RUs/ Uf c0 0 2 0 4 0 6 0 8 1 0 0 2 0 4 0 6 0 8 10 5 m m S o l i d 1 m m S o l i d S i n g l e P h a s e C Figure 613 Solid mean velocity at 3% solids A) Re = 2.0x105, B) Re = 3.35x105 and C) Re = 5.0x105

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156 r / Ruf' / Uf c0 0 2 0 4 0 6 0 8 1 0 0 0 2 0 0 4 0 0 6 0 0 8 0 1 0 1 20 5 m m L i q u i d 1 0 m m L i q u i d 1 5 m m L i q u i d S i n g l e P h a s e A r / Ruf' / Uf c0 0 2 0 4 0 6 0 8 1 0 0 0 2 0 0 4 0 0 6 0 0 8 0 1 0 1 20 5 m m L i q u i d 1 0 m m L i q u i d 1 5 m m L i q u i d S i n g l e P h a s e B r / Ruf' / Uf c0 0 2 0 4 0 6 0 8 1 0 0 0 2 0 0 4 0 0 6 0 0 8 0 1 0 1 20 5 m m L i q u i d 1 0 m m L i q u i d 1 5 m m L i q u i d S i n g l e P h a s e C Figure 61 4 Fluid fluctuating velocity at 0.7% solids A) Re = 2. 0x105, B) Re = 3.35x105 and C) Re = 5.0x105

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157 r / Ruf' / Uf c0 0 2 0 4 0 6 0 8 1 0 0 0 2 0 0 4 0 0 6 0 0 8 0 1 0 1 20 5 m m L i q u i d 1 0 m m L i q u i d 1 5 m m L i q u i d S i n g l e P h a s e A r / Ruf' / Uf c0 0 2 0 4 0 6 0 8 1 0 0 0 2 0 0 4 0 0 6 0 0 8 0 1 0 1 20 5 m m L i q u i d 1 0 m m L i q u i d 1 5 m m L i q u i d S i n g l e P h a s e B r / Ruf' / Uf c0 0 2 0 4 0 6 0 8 1 0 0 0 2 0 0 4 0 0 6 0 0 8 0 1 0 1 20 5 m m L i q u i d 1 0 m m L i q u i d 1 5 m m L i q u i d S i n g l e P h a s e C Figure 61 5 Fluid fluctuating velocity at 1.7% solids A) Re = 2.0x105, B) Re = 3.35x105 and C) Re = 5.0x105

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158 r / Ruf' / Uf c0 0 2 0 4 0 6 0 8 1 0 0 0 2 0 0 4 0 0 6 0 0 8 0 1 0 1 20 5 m m L i q u i d 1 m m L i q u i d 1 5 m m L i q u i d S i n g l e P h a s e A r / Ruf' / Uf c0 0 2 0 4 0 6 0 8 1 0 0 0 2 0 0 4 0 0 6 0 0 8 0 1 0 1 20 5 m m L i q u i d 1 m m L i q u i d 1 5 m m L i q u i d S i n g l e P h a s e B r / Ruf' / Uf c0 0 2 0 4 0 6 0 8 1 0 0 0 2 0 0 4 0 0 6 0 0 8 0 1 0 1 20 5 m m L i q u i d 1 m m L i q u i d 1 5 m m L i q u i d S i n g l e P h a s e C Figure 61 6 Fluid fluctuating velocity at 3% solids A) Re = 2.0x105, B) Re = 3.35x105 a nd C) Re = 5.0x105

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159 r / Rus' / Uf c0 0 2 0 4 0 6 0 8 1 0 0 0 2 0 0 4 0 0 6 0 0 8 0 1 0 1 20 5 m m S o l i d 1 0 m m S o l i d S i n g l e P h a s e A r / Rus' / Uf c0 0 2 0 4 0 6 0 8 1 0 0 0 2 0 0 4 0 0 6 0 0 8 0 1 0 1 20 5 m m S o l i d 1 0 m m S o l i d S i n g l e P h a s e B r / Rus' / Uf c0 0 2 0 4 0 6 0 8 1 0 0 0 2 0 0 4 0 0 6 0 0 8 0 1 0 1 20 5 m m S o l i d 1 0 m m S o l i d S i n g l e P h a s e C Figure 61 7 Solid fluctuating velocity at 0.7% solids A) Re = 2.0x105, B) Re = 3.35x105 and C) Re = 5.0x105

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160 r / Rus' / Uf c0 0 2 0 4 0 6 0 8 1 0 0 0 2 0 0 4 0 0 6 0 0 8 0 1 0 1 20 5 m m S o l i d 1 0 m m S o l i d S i n g l e P h a s e A r / Rus' / Uf c0 0 2 0 4 0 6 0 8 1 0 0 0 2 0 0 4 0 0 6 0 0 8 0 1 0 1 20 5 m m S o l i d 1 0 m m S o l i d S i n g l e P h a s e B r / Rus' / Uf c0 0 2 0 4 0 6 0 8 1 0 0 0 2 0 0 4 0 0 6 0 0 8 0 1 0 1 20 5 m m S o l i d 1 0 m m S o l i d S i n g l e P h a s e C Figure 61 8 Solid fluctuating velocity 1.7% solids A) Re = 2.0x105, B) Re = 3.35x105 and C) Re = 5.0x105

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161 r / Rus' / Uf c0 0 2 0 4 0 6 0 8 1 0 0 0 2 0 0 4 0 0 6 0 0 8 0 1 0 1 20 5 m m S o l i d 1 m m S o l i d S i n g l e P h a s e A r / Rus' / Uf c0 0 2 0 4 0 6 0 8 1 0 0 0 2 0 0 4 0 0 6 0 0 8 0 1 0 1 20 5 m m S o l i d 1 m m S o l i d S i n g l e P h a s e B r / Rus' / Uf c0 0 2 0 4 0 6 0 8 1 0 0 0 2 0 0 4 0 0 6 0 0 8 0 1 0 1 20 5 m m S o l i d 1 m m S o l i d S i n g l e P h a s e C F igure 61 9 Solid fluctuating velocity at 3% s olids A) Re = 2.0x105, B) Re = 3.35x105 and C) Re = 5.0x105

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162 r / Ruf' / Uf c0 0 2 0 4 0 6 0 8 1 0 0 0 2 0 0 4 0 0 6 0 0 8 0 1 0 1 20 5 m m L i q u i d 1 m m L i q u i d 1 5 m m L i q u i d S i n g l e P h a s e Figure 620 Fluid fluctuating velocity error based on ensemble size for 3% solids at Re=5.0x105 D a t a C o u n tuf' / Uf c2 0 0 4 0 0 6 0 0 8 0 0 0 0 0 2 0 0 4 0 0 6 0 0 8 0 1 Figure 62 1 Evolution of uf with data count for 1 mm particles at r/R=0.82 for 3% solids at Re=5.0x105

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163 D a t a C o u n tus' / Uf c0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 00 0 0 2 0 0 4 0 0 6 0 0 8 0 1 D a t a C o u n tus' / Uf c0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 00 0 0 2 0 0 4 0 0 6 0 0 8 0 1 D a t a C o u n tus' / Uf c0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 00 0 0 2 0 0 4 0 0 6 0 0 8 0 1 D a t a C o u n tus' / Uf c0 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 00 0 0 2 0 0 4 0 0 6 0 0 8 0 1 D a t a C o u n tus' / Uf c0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 00 0 0 2 0 0 4 0 0 6 0 0 8 0 1 D a t a C o u n tus' / Uf c0 5 0 0 0 1 0 0 0 0 1 5 0 0 0 2 0 0 0 0 2 5 0 0 00 0 0 2 0 0 4 0 0 6 0 0 8 0 1 Figure 62 2 Evolution of us with data count for 0.5 mm particles at r/R=0.91 for 0.7% solids at Re=3.35x105

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164 r / Ruf' / Uf c0 0 2 0 4 0 6 0 8 1 0 0 0 2 0 0 4 0 0 6 0 0 8 0 1 0 1 20 5 m m L i q u i d 1 m m L i q u i d 1 5 m m L i q u i d S i n g l e P h a s e Figure 62 3 Fluid fluctuating velocity error based on standard deviation of uf after 250 measurements for 3% solids at Re=5.0x105

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1 65 CHAPTER 7 CONCLUSIONS AND RECO MMENDATIONS The main goal of this dissertation was the acquisition of benchmark multiphase flow datanonintrusive mean and fluctuating velocity measurements of a tu rbulent liquid -solid pipe flow These data map the transition from a viscous d ominated to an inertial or collisiond ominated flow. The experiments were designed such that a range of particle sizes, solids concentrations, and flow rates could be i nvestiga ted. The data are needed in the validation of computational fluid dynamic (CFD) models which can be used to predict flow and transport properties of multiphase flows in relevant industrial settings. Current models which are built on kinetic theory concep ts are incapable of predicting the flow behavior as viscous forces become significant. Prior to the addition of the solid -phase, a single -phase base needed to be established. This consisted of velocity and pressure measurements. These two sets of measu rements each reve a led interesting phenomena not previously documented. The first was the acquisition of p ressure data for flow in pipe bends at a novel combination of conditions large pipe curvature at high Re It was found that u pstream effects occur we ll beyond a few pipe diameters prior to a pipe bend provided the Re is sufficiently high. The pressure difference between the outside and the inside of the pipe in the bend, as well as downstream of the pipe bend, is weakly dependent on Re. Existing c orr elations for total bend pressure loss significantly under predict the pressure drop in the bend and fail to capture a decrease in kt with increasing Re. Finally, independent of exit configuration, the loss coefficient varies linearly throughout the bend, signifying that the effective length of the pipe is equal to its actual length, and wall friction is the dominant process contributing to pressure loss in bends of Rb/R 24.

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166 The second involved a significant variation in the reported values of single-phase gas turbulence intensity among the commonly cited references of these measurements. In both gas and liquid flow, this variation exceeds typical errors associated wi th the flow measurement techniques. The magnitude of the turbulence velocity fluctuations in water is consistently higher than in air at the same Re. In addition, the magnitude of the variations in the measurements of turbulent velocity is greater in liquid versus gas flow. In air, the turbulent velocity exhibits no Re dependence far from the wall; in water, there is a Re dependency. In air, turbulent velocity profiles measured using LDV are consistently flatter than those obtained from hot wire measurements. Based on these results the single phase measurements were deemed to be in agreement with established values, proving the suitability of the experimental flow facility and instrumentation for two phase experiments. Finally, the solid phase was add ed to the experimental facility and two-phase measurements of velocity and pressure were obtained. The pressure results indicate little change over the singlephase pressure gradients except at 0.7% and 1.7% at Re = 5.0x105 where drag reduction was observ ed. Further measurements at Re > 5.0x105 are necessary to see if the drag reduction persists over a wider range of Re and if it occurs at higher Re with the other particle sizes. The velocity results show an increase in particle independence from the fl uid with increasing Bagnold and Stokes number. In general, the 0.5 mm particles damp the fluid turbulence while the 1.0 mm and 1.5 mm particles are either neutral or enhance the turbulence. The solid turbulence of the 1.0 mm particles exceeds that of the fluid in their presence, while the solidphase turbulence of the 0.5 mm particles is less than the

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167 fluid in their presence. The turbulence of both phases becomes increasingly flat near the center of the pipe with increasing Re and solids loading. This i s in agreement with the flat profile s of both fluid and solid turbulence in inertia dominated gas -solid flows The results reveal the need for further investigation into turbulence enhancement as a function of Re and particle size. Specifically, at what Re and/or Rep does vortex shedding and wake formation occur and how does this balance with the decrease in turbulence with increasing Re. Other recommendations for future work include t he acquisition of the particle velocity for the 1.5 mm particles, whi ch constitute Bagnold numbers from the upper -transitional to the lower grain-inertia regime. These measurements can be obtained with the proper LDV/PDPA lenses which are available for the new LDV/PDPA that has been purchased. The new LDV/PDPA will also allow for radial velocity measurements data that will be beneficial for the validation of CFD models. This validation includes the analysis of current CFD models to examine their ability to predict the experimental results and the subsequent development of new constitutive relationships that better capture fluidparticle interactions. The current data are also limited to solids concentrations of 3% by volume or less. However, industrial slurries are typically composed of a higher volume of solids. Increasing the solids concentration would require the matching of index of refraction of the solid and liquid. A solution of sodium -iodine is a potential candidate for the fluid which can be manipulated to match that of the current glass particles. Increasing the fluid velocity to accommodate a larger range of Re is also possible. This can be achieved by increasing the pump speed and also by increasing the temperature of the water. The two methods, when combined would allow for the investigation of Re > 106.

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168 Other potential investigations, which do not require any modifications to the current experimental setup, include measuring the effects of a bi modal particle size distribution.

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169 APPENDIX A EXPERIMENTAL VELOCIT Y DATA Two Phase Flows 0.5 mm Particles Ta ble A -1. Fluid and solid velocity measurements for 0.7% solids at Re=2.0x105 r/R U f (m/s) u f (m/s) U s (m/s) u s (m/s) 0.955 2.199 0.329 2.215 0.324 0.911 2.344 0.281 2.382 0.282 0.866 2.461 0.266 2.447 0.248 0.821 2.587 0.263 2.607 0.245 0.777 2.644 0.245 2.624 0.223 0.732 2.658 0.216 2.648 0.209 0.643 2.775 0.205 2.794 0.190 0.554 2.825 0.191 2.818 0.182 0.464 2.904 0.172 2.919 0.164 0.375 3.005 0.160 3.002 0.150 0.286 3.076 0.153 3.077 0.138 0.196 3.078 0.137 3.069 0.132 0.107 3.097 0.132 3 .090 0.120 0.018 3.122 0.128 3.103 0.119 Table A -2. Fluid and solid velocity measurements for 1.7% solids at Re=2.0x105 r/R U f (m/s) u f (m/s) U s (m/s) u s (m/s) 0.955 2.311 0.282 2.327 0.285 0.911 2.462 0.267 2.476 0.255 0.866 2.562 0.263 2.578 0.2 36 0.821 2.633 0.252 2.649 0.230 0.777 2.692 0.230 2.708 0.228 0.732 2.749 0.246 2.728 0.221 0.643 2.782 0.213 2.783 0.213 0.554 2.891 0.181 2.873 0.186 0.464 2.966 0.182 2.964 0.166 0.375 3.048 0.161 3.042 0.156 0.286 3.119 0.146 3.083 0.143 0.19 6 3.136 0.150 3.112 0.140 0.107 3.149 0.147 3.127 0.131 0.018 3.168 0.155 3.163 0.146

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170 Table A -3. Fluid and solid velocity measurements for 3% solids at Re=2.0x105 r/R U f (m/s) u f (m/s) U s (m/s) u s (m/s) 0.955 2.463 0.309 2.430 0.288 0.911 2.565 0 .288 2.546 0.281 0.866 2.647 0.253 2.659 0.243 0.821 2.725 0.237 2.732 0.217 0.777 2.789 0.238 2.802 0.218 0.732 2.853 0.228 2.839 0.210 0.643 2.982 0.216 3.000 0.210 0.554 3.049 0.226 3.048 0.196 0.464 3.108 0.206 3.106 0.202 Table A -4. Fluid and solid velocity measurements for 0.7% solids at Re=3.35x105 r/R U f (m/s) u f (m/s) U s (m/s) u s (m/s) 0.955 3.716 0.414 3.730 0.386 0.911 3.889 0.415 3.902 0.394 0.866 4.036 0.389 4.028 0.377 0.821 4.205 0.347 4.250 0.355 0.777 4.271 0.328 4.235 0.32 6 0.732 4.390 0.321 4.375 0.306 0.643 4.516 0.307 4.445 0.283 0.554 4.588 0.271 4.560 0.259 0.464 4.696 0.229 4.680 0.223 0.375 4.774 0.213 4.781 0.207 0.286 4.857 0.199 4.842 0.191 0.196 4.878 0.180 4.866 0.170 0.107 4.904 0.172 4.897 0.161 0.018 4.933 0.171 4.924 0.161 Table A -5. Fluid and solid velocity measurements for 1.7% solids at Re=3.35x105 r/R U f (m/s) u f (m/s) U s (m/s) u s (m/s) 0.955 3.645 0.441 3.687 0.411 0.911 3.814 0.437 3.868 0.393 0.866 4.022 0.413 4.045 0.400 0.821 4.146 0.411 4.127 0.390 0.777 4.206 0.356 4.142 0.360 0.732 4.254 0.350 4.223 0.327 0.643 4.454 0.318 4.418 0.314 0.554 4.580 0.274 4.572 0.271 0.464 4.757 0.250 4.766 0.244 0.375 4.877 0.264 4.841 0.247 0.286 4.920 0.224 4.903 0.192 0.196 5.031 0.212 5. 004 0.191 0.107 5.013 0.187 4.986 0.172 0.018 5.096 0.197 5.076 0.188

PAGE 171

171 Table A -6. Fluid and solid velocity measurements for 3% solids at Re=3.35x105 r/R U f (m/s) u f (m/s) U s (m/s) u s (m/s) 0.955 3.579 0.457 3.587 0.435 0.911 3.828 0.440 3.798 0.414 0.866 4.003 0.397 3.988 0.385 0.821 4.210 0.379 4.212 0.365 0.777 4.333 0.353 4.298 0.353 0.732 4.399 0.352 4.407 0.337 0.643 4.554 0.312 4.538 0.306 0.554 4.662 0.287 4.681 0.275 0.464 4.804 0.263 4.786 0.254 Table A -7. Fluid and solid velocity measurements for 0.7% solids at Re=5.0x105 r/R U f (m/s) u f (m/s) U s (m/s) u s (m/s) 0.955 5.308 0.649 5.302 0.598 0.911 5.792 0.556 5.788 0.546 0.866 5.962 0.550 5.921 0.526 0.821 6.116 0.489 6.095 0.507 0.777 6.197 0.487 6.180 0.485 0.732 6.346 0. 455 6.310 0.452 0.643 6.453 0.423 6.447 0.417 0.554 6.738 0.362 6.720 0.344 0.464 6.581 0.381 6.575 0.369 0.375 6.816 0.337 6.824 0.325 0.286 6.910 0.311 6.927 0.307 0.196 7.015 0.293 7.030 0.278 0.107 7.115 0.267 7.106 0.255 0.018 7.144 0.255 7.11 8 0.252 Table A -8. Fluid and solid velocity measurements for 1.7% solids at Re=5.0x105 r/R U f (m/s) u f (m/s) U s (m/s) u s (m/s) 0.955 5.409 0.652 5.378 0.631 0.911 5.649 0.605 5.656 0.591 0.866 5.978 0.559 5.918 0.538 0.821 6.026 0.543 5.971 0.534 0.777 6.179 0.488 6.117 0.457 0.732 6.247 0.444 6.246 0.432 0.643 6.538 0.406 6.538 0.394 0.554 6.580 0.397 6.537 0.381 0.464 6.603 0.344 6.589 0.328 0.375 6.868 0.333 6.870 0.331 0.286 7.024 0.310 7.008 0.312 0.196 7.144 0.326 7.118 0.296 0.107 7 .000 0.322 6.957 0.315 0.018 7.032 0.284 7.015 0.303

PAGE 172

172 Table A -9. Fluid and solid velocity measurements for 3% solids at Re=5.0x105 r/R U f (m/s) u f (m/s) U s (m/s) u s (m/s) 0.955 5.389 0.654 5.475 0.588 0.911 5.735 0.583 5.713 0.560 0.866 5.970 0.563 5.969 0.527 0.821 6.195 0.504 6.191 0.478 0.777 6.303 0.492 6.301 0.454 0.732 6.354 0.476 6.396 0.445 0.643 6.510 0.432 6.532 0.398 0.554 6.764 0.397 6.755 0.376 0.464 6.904 0.387 6.916 0.393 1.0 mm Particles Table A -10. Fluid and solid velocity measurements for 0.7% solids at Re=2.0x105 r/R U f (m/s) u f (m/s) U s (m/s) u s (m/s) 0.955 2.173 0.369 2.289 0.431 0.911 2.340 0.339 2.331 0.409 0.866 2.397 0.310 2.396 0.386 0.821 2.502 0.279 2.459 0.351 0.777 2.573 0.282 2.516 0.332 0.688 2.662 0.2 57 2.630 0.292 0.598 2.760 0.225 2.714 0.263 0.509 2.855 0.206 2.778 0.244 0.420 2.923 0.197 2.890 0.229 0.330 3.007 0.177 2.954 0.210 0.241 3.053 0.169 2.931 0.221 0.152 3.092 0.147 3.018 0.194 0.063 3.110 0.135 3.057 0.178 0.027 3.107 0.146 3.057 0.190

PAGE 173

173 Table A -11. Fluid and solid velocity measurements for 1.7% solids at Re=2.0x105 r/R U f (m/s) u f (m/s) U s (m/s) u s (m/s) 0.955 2.258 0.297 2.207 0.327 0.911 2.404 0.270 2.269 0.297 0.866 2.477 0.237 2.317 0.291 0.821 2.535 0.237 2.373 0.283 0.777 2.600 0.231 2.420 0.271 0.732 2.646 0.209 2.449 0.267 0.643 2.722 0.201 2.577 0.214 0.554 2.790 0.183 2.638 0.198 0.464 2.833 0.163 2.697 0.181 0.375 2.910 0.147 2.749 0.188 0.286 2.954 0.137 2.780 0.186 0.196 2.979 0.119 2.815 0.168 0.107 3.007 0.124 2.837 0.164 0.018 3.020 0.135 2.855 0.156 Table A -12. Fluid and solid velocity measurements for 3% solids at Re=2.0x105 r/R U f (m/s) u f (m/s) U s (m/s) u s (m/s) 0.955 2.337 0.342 2.482 0.279 0.911 2.430 0.289 2.544 0.274 0.866 2.538 0.2 54 2.578 0.271 0.821 2.622 0.229 2.619 0.266 0.777 2.679 0.227 2.636 0.261 0.732 2.727 0.212 2.625 0.273 0.643 2.799 0.216 2.718 0.247 0.554 2.874 0.203 2.802 0.212 0.464 2.912 0.194 2.876 0.198 0.375 2.967 0.186 2.919 0.196 0.286 3.070 0.169 2.951 0.176 0.196 3.126 0.164 2.982 0.177 0.107 3.141 0.153 3.007 0.177 0.018 3.158 0.153 3.022 0.173

PAGE 174

174 Table A -13. Fluid and solid velocity measurements for 0.7% solids at Re=3.35x105 r/R U f (m/s) u f (m/s) U s (m/s) u s (m/s) 0.955 3.625 0.475 4.058 0.42 7 0.911 3.889 0.464 3.963 0.478 0.866 4.080 0.413 4.040 0.449 0.821 4.211 0.414 4.149 0.431 0.777 4.315 0.370 4.183 0.456 0.688 4.476 0.330 4.304 0.436 0.598 4.617 0.316 4.487 0.377 0.509 4.699 0.273 4.583 0.340 0.420 4.827 0.242 4.650 0.323 0.330 4.898 0.260 4.768 0.278 0.241 4.983 0.208 4.790 0.301 0.152 5.030 0.196 4.870 0.235 0.063 5.056 0.190 4.929 0.206 0.027 5.041 0.191 4.964 0.190 Table A -14. Fluid and solid velocity measurements for 1.7% solids at Re=3.35x105 r/R U f (m/s) u f (m/s) U s (m/s) u s (m/s) 0.955 3.890 0.440 3.783 0.441 0.911 3.969 0.429 3.927 0.410 0.866 4.144 0.389 4.058 0.374 0.821 4.251 0.374 4.144 0.370 0.777 4.380 0.368 4.251 0.365 0.732 4.466 0.331 4.328 0.365 0.643 4.581 0.303 4.442 0.341 0.554 4.660 0.316 4 .547 0.328 0.464 4.786 0.270 4.650 0.296 0.375 4.864 0.256 4.718 0.264 0.286 4.938 0.228 4.769 0.238 0.196 4.971 0.201 4.818 0.226 0.107 4.994 0.187 4.835 0.213 0.018 5.032 0.211 4.865 0.215

PAGE 175

175 Table A -1 5 Fluid and solid velocity measurements for 3 % solids at Re=3.35x105 r/R U f (m/s) u f (m/s) U s (m/s) u s (m/s) 0.955 3.519 0.429 3.338 0.431 0.911 3.657 0.390 3.515 0.410 0.866 3.751 0.355 3.614 0.402 0.821 3.867 0.353 3.682 0.385 0.777 3.962 0.340 3.768 0.359 0.732 4.055 0.320 3.880 0.346 0.6 43 4.197 0.292 4.016 0.320 0.554 4.289 0.286 4.116 0.312 0.464 4.385 0.266 4.254 0.312 0.375 4.479 0.235 4.341 0.295 0.286 4.539 0.224 4.428 0.286 0.196 4.605 0.203 4.502 0.264 0.107 4.651 0.170 4.548 0.257 0.018 4.079 0.159 4.599 0.241 Table A -16 Fluid and solid velocity measurements for 0.7% solids at Re=5.0x105 r/R U f (m/s) u f (m/s) U s (m/s) u s (m/s) 0.955 5.190 0.643 5.354 0.696 0.911 5.511 0.579 5.510 0.670 0.866 5.813 0.505 5.658 0.655 0.821 5.903 0.508 5.761 0.637 0.777 6.044 0.465 5.846 0.595 0.732 6.151 0.463 5.925 0.569 0.643 6.265 0.434 6.185 0.518 0.554 6.484 0.387 6.371 0.500 0.464 6.599 0.352 6.505 0.467 0.375 6.721 0.373 6.644 0.436 0.286 6.873 0.361 6.794 0.397 0.196 6.938 0.347 6.881 0.390 0.107 7.058 0.352 6.922 0. 400 0.018 7.055 0.348 6.952 0.391

PAGE 176

176 Table A -17. Fluid and solid velocity measurements for 1.7% solids at Re=5.0x105 r/R U f (m/s) u f (m/s) U s (m/s) u s (m/s) 0.955 5.366 0.597 5.270 0.656 0.911 5.560 0.571 5.388 0.624 0.866 5.770 0.550 5.505 0.611 0 .821 5.896 0.540 5.570 0.589 0.777 6.026 0.513 5.636 0.603 0.732 6.186 0.493 5.805 0.570 0.643 6.320 0.429 5.955 0.538 0.554 6.451 0.341 6.161 0.491 0.464 6.587 0.311 6.267 0.443 0.375 6.708 0.327 6.366 0.406 0.286 6.791 0.322 6.453 0.359 0.196 6.8 54 0.306 6.541 0.357 0.107 6.956 0.333 6.573 0.368 0.018 7.043 0.333 6.656 0.350 Table A-18. Fluid and solid velocity measurements for 3% solids at Re=5.0x105 r/R U f (m/s) u f (m/s) U s (m/s) u s (m/s) 0.955 5.202 0.702 4.905 0.752 0.911 5.381 0.665 5.036 0.766 0.866 5.570 0.595 5.073 0.746 0.821 5.757 0.527 5.197 0.694 0.777 5.927 0.475 5.370 0.666 0.732 5.989 0.480 5.482 0.652 0.643 6.174 0.397 5.639 0.651 0.554 6.378 0.356 5.708 0.625 0.464 6.521 0.321 5.808 0.597 0.375 6.559 0.325 5.941 0. 534 0.286 6.696 0.320 6.083 0.473 0.196 6.740 0.312 6.229 0.426 0.107 6.817 0.319 6.334 0.415 0.018 6.830 0.318 6.424 0.366

PAGE 177

177 1.5 mm Particles Table A -19. Fluid velocity measurements for 0.7% solids at Re=2.0x105 r/R U f (m/s) u f (m/s) 0.955 2.222 0 .323 0.911 2.336 0.300 0.866 2.404 0.302 0.821 2.482 0.286 0.777 2.565 0.245 0.732 2.583 0.258 0.643 2.664 0.253 0.554 2.731 0.264 0.464 2.770 0.203 0.375 2.858 0.167 0.286 2.906 0.158 0.196 2.940 0.136 0.107 2.992 0.135 0.018 2.961 0.126 Ta ble A -20. Fluid velocity measurements for 1.7% solids at Re=2.0x105 r/R U f (m/s) u f (m/s) 0.955 2.211 0.325 0.911 2.321 0.267 0.866 2.400 0.255 0.821 2.463 0.251 0.777 2.486 0.250 0.732 2.535 0.223 0.643 2.616 0.202 0.554 2.661 0.193 0.464 2.708 0.180 0.375 2.769 0.170 0.286 2.829 0.160 0.196 2.886 0.160 0.107 2.949 0.182 0.018 2.905 0.160

PAGE 178

178 Table A -21. Fluid velocity measurements for 3% solids at Re=2.0x105 r/R U f (m/s) u f (m/s) 0.955 2.093 0.301 0.911 2.183 0.307 0.866 2.276 0.303 0 .821 2.381 0.276 0.777 2.407 0.271 0.732 2.422 0.234 0.643 2.544 0.192 0.554 2.619 0.190 0.464 2.627 0.175 0.375 2.642 0.166 0.286 2.706 0.161 0.196 2.751 0.158 0.107 2.763 0.160 0.018 2.788 0.155 Table A -22. Fluid velocity measurements for 0. 7% solids at Re=3.35x105 r/R U f (m/s) u f (m/s) 0.955 3.655 0.444 0.911 3.830 0.400 0.866 3.967 0.341 0.821 4.096 0.342 0.777 4.170 0.328 0.732 4.254 0.314 0.643 4.423 0.299 0.554 4.498 0.282 0.464 4.494 0.261 0.375 4.613 0.230 0.286 4.692 0.193 0.196 4.747 0.187 0.107 4.766 0.189 0.018 4.784 0.189

PAGE 179

179 Table A -23. Fluid velocity measurements for 1.7% solids at Re=3.35x105 r/R U f (m/s) u f (m/s) 0.955 3.691 0.413 0.911 3.888 0.400 0.866 3.937 0.398 0.821 4.032 0.374 0.777 4.130 0.344 0.73 2 4.188 0.326 0.643 4.319 0.308 0.554 4.396 0.264 0.464 4.478 0.239 0.375 4.593 0.213 0.286 4.654 0.217 0.196 4.669 0.180 0.107 4.734 0.178 0.018 4.758 0.183 Table A -24. Fluid velocity measurements for 3% solids at Re=3.35x105 r/R U f (m/s) u f ( m/s) 0.955 3.453 0.415 0.911 3.649 0.373 0.866 3.776 0.392 0.821 3.901 0.341 0.777 3.976 0.325 0.732 4.029 0.323 0.643 4.160 0.275 0.554 4.317 0.271 0.464 4.308 0.242 0.375 4.403 0.217 0.286 4.537 0.193 0.196 4.571 0.194 0.107 4.613 0.179 0.0 18 4.638 0.164

PAGE 180

180 Table A -25. Fluid velocity measurements for 0.7% solids at Re=5.0x105 r/R U f (m/s) u f (m/s) 0.955 5.505 0.662 0.911 5.773 0.579 0.866 5.973 0.579 0.821 6.025 0.529 0.777 6.167 0.471 0.732 6.280 0.419 0.643 6.439 0.406 0.554 6.55 4 0.394 0.464 6.762 0.374 0.375 6.774 0.365 0.286 6.901 0.318 0.196 7.002 0.315 0.107 6.924 0.310 0.018 6.956 0.311 Table A -26. Fluid velocity measurements for 1.7% solids at Re=5.0x105 r/R U f (m/s) u f (m/s) 0.955 5.138 0.667 0.911 5.443 0.631 0.866 5.738 0.599 0.821 5.830 0.579 0.777 5.925 0.576 0.732 5.965 0.581 0.643 6.198 0.461 0.554 6.363 0.410 0.464 6.583 0.345 0.375 6.636 0.334 0.286 6.699 0.329 0.196 6.776 0.324 0.107 6.842 0.301 0.018 6.905 0.274

PAGE 181

181 Table A -27. Fluid veloci ty measurements for 3% solids at Re=5.0x105 r/R U f (m/s) u f (m/s) 0.955 4.938 0.713 0.911 5.265 0.700 0.866 5.504 0.672 0.821 5.696 0.617 0.777 5.871 0.543 0.732 6.019 0.509 0.643 6.286 0.449 0.554 6.350 0.386 0.464 6.517 0.358 0.375 6.632 0.343 0.286 6.718 0.332 0.196 6.847 0.312 0.107 6.924 0.320 0.018 6.919 0.282 Reproducibility Table A -28. Three measurements of solids fluctuating velocity for 1.0 mm particles at 0.7% solids at Re=2.0x105 r/R 1 u s 1 r/R 2 u s 2 r/R 3 u s 3 0.955 0.117 0.955 0.119 0.955 0.123 0.911 0.121 0.911 0.115 0.911 0.120 0.866 0.109 0.866 0.110 0.866 0.114 0.821 0.103 0.821 0.104 0.821 0.111 0.777 0.097 0.777 0.102 0.777 0.102 0.732 0.091 0.732 0.094 0.688 0.091 0.643 0.088 0.643 0.087 0.598 0.083 0.554 0. 083 0.554 0.080 0.509 0.078 0.464 0.082 0.464 0.083 0.420 0.072 0.375 0.076 0.375 0.076 0.330 0.068 0.286 0.071 0.286 0.072 0.241 0.071 0.196 0.063 0.196 0.066 0.152 0.062 0.107 0.060 0.107 0.063 0.063 0.057 0.018 0.058 0.018 0.060 0.027 0.057

PAGE 182

182 Fully Developed Flow Table A -29. S olid mean and fluctuating velocity at two radii and two axial locations for 0.5 mm particles at 0 .7% solids at Re=2.0x105 North Top East Top East Middle r/R U s u s U s u s U s u s 0.955 2.215 0.324 2.277 0.293 2.152 0.3196 0.911 2.382 0.282 2.38 0.2662 2.339 0.3049 0.866 2.447 0.248 2.512 0.2376 2.417 0.2893 0.821 2.607 0.245 2.599 0.2282 2.541 0.2294 0.777 2.624 0.223 2.693 0.2156 1.581 0.2322 0.732 2.648 0.209 2.763 0.2112 2.669 0.2008 0.643 2.794 0.190 2.821 0.1957 2.824 0.1991 0.554 2.818 0.182 2.888 0.1859 2.864 0.184 0.464 2.919 0.164 2.989 0.1661 2.945 0.167 0.375 3.002 0.150 3.067 0.1549 3.006 0.1435 0.286 3.077 0.138 3.112 0.1405 3.045 0.1355 0.196 3.069 0.132 3.146 0.1338 3.099 0.1349 0.107 3.090 0.120 3 .142 0.1251 3.139 0.1384 0.018 3.103 0.119 3.146 0.123 3.098 0.1398 Single Phase Flows Table A -30. Mean and fluctuating velocity of single phase water Re=2.0x10 5 Re=3.35x10 5 Re=5.0x10 5 r/R U f (m/s) u f (m/s) U f (m/s) u f (m/s) U f (m/s) u f (m/s) 0.9 64 2.219 0.275 3.737 0.454 5.428 0.541 0.938 2.332 0.268 3.877 0.415 5.520 0.529 0.893 2.439 0.250 4.049 0.395 5.719 0.513 0.848 2.516 0.245 4.188 0.369 5.862 0.487 0.804 2.584 0.238 4.287 0.352 6.075 0.477 0.759 2.643 0.233 4.389 0.330 6.170 0.467 0 .714 2.699 0.224 4.445 0.334 6.290 0.452 0.625 2.774 0.210 4.579 0.311 6.511 0.409 0.536 2.852 0.198 4.669 0.293 6.617 0.381 0.446 2.906 0.196 4.763 0.276 6.793 0.357 0.357 2.973 0.168 4.854 0.247 6.928 0.325 0.268 3.019 0.165 4.920 0.226 7.036 0.302 0.179 3.053 0.157 4.965 0.208 7.088 0.281 0.089 3.068 0.140 4.976 0.199 7.102 0.263 0.000 3.077 0.139 4.973 0.186 7.155 0.249

PAGE 183

183 Table A -31. Fluctuating velocity of single phase water Re=2.2x10 5 Re=3.6x10 5 Re=5.0x10 5 Re=6.1x10 5 r/R u f (m/s) u f (m/s ) u f (m/s) u f (m/s) 0.973 0.241 0.553 0.610 0.698 0.955 0.241 0.454 0.562 0.671 0.929 0.234 0.415 0.544 0.626 0.893 0.231 0.395 0.503 0.616 0.848 0.220 0.369 0.480 0.581 0.804 0.212 0.352 0.470 0.562 0.759 0.197 0.330 0.448 0.536 0.714 0.193 0.33 4 0.439 0.526 0.625 0.187 0.311 0.393 0.500 0.536 0.174 0.293 0.358 0.464 0.446 0.163 0.276 0.335 0.439 0.357 0.149 0.247 0.307 0.399 0.268 0.142 0.226 0.285 0.361 0.179 0.140 0.208 0.266 0.337 0.089 0.132 0.199 0.255 0.333 0.000 0.124 0.186 0.247 0.318

PAGE 184

184 APPENDIX B EXPERIMENTAL PRESSURE DATA Two Phase Flows Table B -3. Pressure gradient for 0.5 mm p articles Solids Concentration (Volume) Re 0.7% (kPa/m) 1.7% (kPa/m) 3% (kPa/m) 2.0x10 5 10.61 10.775 10.951 3.35x10 5 11.432 11.716 5.0x10 5 12.802 13.009 Table B -3. Pressure gradient for 1.0 mm p articles Solids Concentration (Volume) Re 0.7% (kPa/m) 1.7% (kPa/m) 3% (kPa/m) 2.0x10 5 10.548 10.848 11.147 3.35x10 5 11.727 11.851 12.114 5.0x10 5 12.425 12.166 12.942 Table B -3 Pressure gradient for 1.5mm particles Solids Concentration (Volume) Re 0.7 % (kPa/m) 1.7% (kPa/m) 3% (kPa/m) 2.0x10 5 10.625 10.651 11.142 3.35x10 5 11.463 11.282 11.365 5.0x10 5 13.893 13.686 13.195 Single Phase Flows

PAGE 185

185 Table B -1. Pressure along vertical pipe and bend with sudden ex pansion at downstream tangent (C onfiguration A) Distance from Bend Entrance (Diameters) Re = 3.68x10 5 Re = 5.0x10 5 Re = 6.16x10 5 Re = 7.36x10 5 Re = 8.5x10 5 Inside (PSI) Outside (PSI) Inside (PSI) Outside (PSI) Inside (PSI) Outside (PSI) Ins ide (PSI) Outside (PSI) Inside (PSI) Outside (PSI) 37 4.19 5.86 8.15 10.65 13.40 32 3.58 5.25 7.60 10.02 12.76 27 3.00 4.63 6.95 8.88 12.05 22 2.39 3.92 6.17 8.57 11.13 17 1.65 2.98 5.06 7.42 9.40 12 0.91 2.24 4.02 6 .15 7.95 7 0.30 1.46 3.14 5.18 6.74 2 0.20 0.86 2.81 4.87 6.54 0 0.53 0.46 0.42 0.58 2.26 2.54 4.23 4.64 5.74 6.22 4 0.95 0.93 0.13 0.04 1.60 1.90 3.47 3.95 4.76 5.48 8 1.29 1.30 0.48 0.33 1.25 1.58 3.12 3.73 4.45 5.39 12 1.8 2 1.74 1.15 0.91 0.41 0.77 2.09 2.65 3.15 3.99 16 2.03 2.06 1.40 1.25 0.04 0.50 1.48 2.35 2.45 3.74 20 2.12 2.21 1.49 1.51 0.13 0.25 1.33 1.14 2.20 2.16 22 2.06 2.35 1.35 1.67 0.05 0.34 1.56 1.09 2.51 2.07 27 2.29 2.56 1.67 1.96 0.23 0.73 1.25 0.55 2.18 1.38

PAGE 186

186 Table B -2. Pressure along vertical pipe and bend with steel pipe at downstream tangent (C onfiguration B) Distance from Bend Entrance (Diameters) Re = 3.68x10 5 Re = 5.0x10 5 Re = 6.16x10 5 Re = 7.36x10 5 Re = 8.5x10 5 Inside (PSI) Outside (PSI) Inside (PSI) Outside (PSI) Inside (PSI) Outside (PSI) Inside (PSI) Outside (PSI) Inside (PSI) Outside (PSI) 37 4.19 5.86 8.15 10.65 13.40 32 3.64 5.34 7.68 10.30 13.10 27 2.93 4.54 6.71 8.40 11.70 22 2.35 3.90 6.00 8.14 10.95 17 1.64 3.04 4.98 7.12 9.45 12 0.90 2.36 3.96 5.88 8.08 7 0.30 1.64 3.10 4.95 6.95 2 0.20 1.06 2.77 4.65 6.75 0 0.52 0.46 0.63 0.78 2.23 2.50 4.03 4.42 6.00 6.45 4 0.92 0.90 0.13 0.29 1.62 1.92 3.28 3.8 0 5.05 5.80 8 1.26 1.25 0.22 0.03 1.27 1.65 2.94 3.63 4.75 5.74 12 1.78 1.67 0.86 0.58 0.45 0.86 1.97 2.62 3.55 4.44 16 1.99 1.97 1.10 0.86 0.07 0.65 1.35 2.39 2.85 4.27 20 2.08 2.08 1.18 1.05 0.10 0.01 1.20 1.35 2.60 2.94 22 2.02 2.22 1.05 1.20 0.08 0.10 1.43 1.30 2.90 2.85 27 2.26 2.43 1.37 1.48 0.21 0.48 1.10 0.78 2.56 2.20

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187 Table B -3 Pressure along vertical pipe and bend with sudden ex pansion at downstream tangent (C onfiguration A) with vertical adjustment Distance from Bend Entrance (Diameters) Re = 3.68x10 5 Re = 5.0x10 5 Re = 6.16x10 5 Re = 7.36x10 5 Re = 8.5x10 5 Inside (PSI) Outside (PSI) Inside (PSI) Outside (PSI) Inside (PSI) Outside (PSI) Inside (PSI) Outside (PSI) Inside (PSI) Outside (PSI) 4 0.95 0.93 0.1 3 0.03 1.59 1.89 3.46 3.94 4.75 5.47 8 1.34 1.36 0.53 0.39 1.20 1.53 3.07 3.67 4.40 5.33 12 1.99 1.92 1.32 1.10 0.24 0.58 1.92 2.47 2.98 3.81 16 2.42 2.49 1.79 1.67 0.35 0.08 1.09 1.93 2.06 3.32 20 2.85 3.00 2.22 2.30 0.86 1.04 0.60 0.35 1.47 1.37 22 2.79 3.14 2.08 2.46 0.68 1.14 0.83 0.30 1.78 1.27 27 3.02 3.35 2.40 2.75 0.96 1.53 0.51 0.25 1.45 0.59 Table B -4. Pressure along vertical pipe and bend with steel pipe at downstream tangent (C onfiguration B) with vertical adjustment Distance from Bend Entrance (Diameters) Re = 3.68x10 5 Re = 5.0x10 5 Re = 6.16x10 5 Re = 7.36x10 5 Re = 8.5x10 5 Inside (PSI) Outside (PSI) Inside (PSI) Outside (PSI) Inside (PSI) Outside (PSI) Inside (PSI) Outside (PSI) Inside (PSI) Outside (PSI ) 4 0.93 0.91 0.12 0.28 1.61 1.91 3.27 3.79 5.04 5.79 8 1.31 1.31 0.27 0.09 1.22 1.59 2.89 3.57 4.70 5.68 12 1.95 1.86 1.03 0.77 0.28 0.67 1.80 2.43 3.38 4.25 16 2.38 2.39 1.49 1.28 0.32 0.23 0.96 1.97 2.46 3.85 20 2.81 2.87 1.91 1. 84 0.83 0.80 0.47 0.56 1.87 2.15 22 2.75 3.01 1.78 1.99 0.65 0.89 0.70 0.51 2.17 2.06 27 2.99 3.22 2.10 2.27 0.94 1.27 0.37 0.01 1.83 1.41

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188 LIST OF REFERENCES [ 1] Merrow, E.W. 2000, "Problems and Progress in Particle Processing," Chemical Innovation, 30 pp. 34 -41. [2] Bell, T.A., 2005, "Challenges in the Scale Up of Particulate Processes -an Industrial Perspective," Powder Tech., 150, pp. 60 71. [3] Maeda, M., Hishida, K., and Furutani, T., 1980, Optical Measurements of Local Gas and Particle Velocity in an Upward Flowing Dilute Gas -Solids Suspension, Polyphase Flow Transport Technology San Francisco, CA [4] Lee, S., and Durst, F., 1982, On the Motion of Particles in Turbulent Duct Flows, Int. J. Multiphase Flow, 8 (2), pp. 125-14 6. [5] Tsuji, Y., Morikawa,Y., and Shiomi, H., 1984, LDV Measurements of an Air -Solid Two -Phase Flow in a Vertical Pipe, J. Fluid Mech., 139, pp. 417 -434. [6] Sheen, H., Chang, Y., and Chiang, Y., 1993, Two -Dimensional Measurements of Flow Structure i n a Two -Phase Vertical Pipe Flow, Proc. Natl. Sci. Counc. ROC(A), 17(3), pp. 200 -213. [7] van de Wall, E., and Soo, S., Relative Motion between Phases of a Particular Suspension, Powder Tech. 95 pp. 153-163. [8] Jones, E.N., 2001, "An Experimental I nvestigation of Particle Size Distribution Effects in Dilute -Phase Gas -Solid Flow," Ph.D. Thesis, Purdue University, West Lafayette, IN. [9] Hadinoto, K., Jones, E.N., Yurteri, C., and Curtis, J.S., 2005, "Reynolds Number Dependence of Gas -Phase Turbulenc e in Gas -Particle Flows," Int. J. Multiphase Flow, 31 pp. 416-434. [10] Theofanous, T. and Sullivan, J., 1982, Turbulence in Two-Phase Dispersed Flows, J. Fluid Mech 116, pp. 343362. [11] Wang, S., Lee, S., Jones Jr., O., and Lahey Jr., R., 1987, 3 -D Turbulence Structure and Phase Distribution Measurements in Bubbly Two -Phase Flows, Int. J. Multiphase Flow, 13(3), pp. 327-343. [12] Hu, B., Mata, O., Hewitt, G. and Angeli, P., 2007, Mean and Turbulent Fluctuating Velocities in Oil -Water Vertical Dispersed Flows, Chem. Eng. Sci., 62, pp. 11991214. [13] Zisselmar, R. and Molerus, O., 1979, "Investigation of SolidLiquid Pipe Flow with regard to Turbulence Modification," Chem Eng. J., 18 pp. 233239.

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197 BIOGRAPHICAL SKETCH Mark Pepple was born in 1979 in Park Ridge, Illinois. The second of two sons, he grew up in Elmhurst, Illinois, graduating from York High School in 1998. He then enrolled at the University of Illinois, Urbana-Champaign (UIUC) where he graduated with a B achelor of Science in chemical engineering in December 2002. While at UIUC he was a member of the cross country and track and field teams and was extensively involved with Intervarsity Christian Fellowship. Before beginning his Ph.D. in chemical engineering at the University of Florida in August 2004, he held positions at the Illinois State Geological Survey and ChemSensing Inc., volunteered with Intervarsity Christian Fellowship, and began a M aster of Arts in religion at Trinity Evangelical Divinity School. While working toward his doctorate Mark attempted to balance his life with other activities. This included running up to 80 miles a week, posting personal records from 3k to 10k, and competing at the 2009 USA T rack and F ield club cross country national championship. Additionally, he was a member of the Graduate Christian F ellowship, a student organization, serving as president for two years.