dissolution of si in molten al with gas injection · dissolution of si in molten al with gas...

Dissolution of Si in Molten Al with Gas Injection

by

Mehran Seyed Ahmadi

A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy

Graduate Department of Materials Science and Engineering University of Toronto

© Copyright by 2014 by Mehran Seyed Ahmadi

ii

ABSTRACT

Dissolution of Si in Molten Al with Gas Injection

Mehran Seyed Ahmadi Doctor of Philosophy

Graduate Department of Materials Science and Engineering University of Toronto

2014 Silicon is an essential component of many aluminum alloys, as it imparts a range of desirable

characteristics. However, there are considerable practical difficulties in dissolving solid Si in

molten Al, because the dissolution process is slow, resulting in material and energy losses. It

is thus essential to examine Si dissolution in molten Al, to identify means of accelerating the

process.

This thesis presents an experimental study of the effect of Si purity, bath temperature,

fluid flow conditions, and gas stirring on the dissolution of Si in molten Al, plus the results of

physical and numerical modeling of the flow to corroborate the experimental results. The

dissolution experiments were conducted in a revolving liquid metal tank to generate a bulk

velocity, and gas was introduced into the melt using top lance injection. Cylindrical Si

specimens were immersed into molten Al for fixed durations, and upon removal the

dissolved Si was measured. The shape and trajectory of injected bubbles were examined by

means of auxiliary water experiments and video recordings of the molten Al free surface.

The gas-agitated liquid was simulated using the commercial software FLOW-3D. The

simulation results provide insights into bubble dynamics and offer estimates of the

fluctuating velocities within the Al bath.

The experimental results indicate that the dissolution rate of Si increases in tandem with

the melt temperature and bulk velocity. A higher bath temperature increases the solubility of

Si at the solid/liquid interface, resulting in a greater driving force for mass transfer, and a

higher liquid velocity decreases the resistance to mass transfer via a thinner mass boundary

iii

layer. Impurities (with lower diffusion coefficients) in the form of inclusions obstruct the

dissolution of the Si main matrix. Finally, dissolution rate enhancement was observed by gas

agitation. It is postulated that the bubble-induced fluctuating velocities disturb the mass

boundary layer, which increases the mass transfer rate.

Correlations derived for mass transfer from solids in liquids under various operating

conditions were applied to the Al–Si system. A new correlation for combined natural and

forced convection mass transfer from vertical cylinders in cross flow is presented, and a

modification is proposed to take into account free stream turbulence in a correlation for

forced convection mass transfer from vertical cylinders in cross flow.

iv

ACKNOWLEDGEMENTS

I wish to express my sincere gratitude to my supervisors Professors S. A. Argyropoulos

and M. Bussmann. Thank you for giving your support and guidance during these few years. I

especially thank you for taking the time to discuss the many and varied aspects of this

project.

I would like to thank the members of my advisory committee members Professors N.

Ashgriz and M. Barati for taking time out of their busy schedule to meet with me and give

insightful suggestions. I would also like to thank Professors T. Coyle and M. Hasan for

attending my final exam and for their valuable comments. Special acknowledgements also go

to Dr. D. Doutre with whom I had many fruitful discussions.

A special thank you to those who helped in so many ways with love and words of

encouragement, especially: Dad, Mom, and my sister and brother.

Financial assistance is also acknowledged and appreciated from: the Natural Science and

Engineering Research Council of Canada (NSERC), the Government of Ontario, Novelis

Global Technology Centre, and Department of Materials Science and Engineering at the

University of Toronto.

v

To my dear parents, Mojtaba and Maryam, whose love, support and encouragement have accompanied me throughout my life

vi

CONTENTS

ABSTRACT ________________________________________________________________________________ ii

ACKNOWLEDGEMENTS ___________________________________________________________________ iv

LIST OF TABLES ___________________________________________________________________________ ix

LIST OF FIGURES __________________________________________________________________________ x

NOMENCLATURE ________________________________________________________________________ xvi

INTRODUCTION ___________________________________________________________________________ 1

1.1 Background Theory _____________________________________________________________________ 4

1.2 Objectives _____________________________________________________________________________ 5

1.3 This Thesis ____________________________________________________________________________ 6

BACKGROUND ____________________________________________________________________________ 7

2.1 Dissolution of Solid Additions in Molten Al __________________________________________________ 9

2.1.1 Assimilation mechanism of solid additions ________________________________________________ 9

2.1.2 Diffusion coefficient of solid additions in liquids __________________________________________ 11

2.1.3 Natural and forced convection mass transfer _____________________________________________ 12

2.1.4 Effect of intermetallics on mass transfer _________________________________________________ 13

2.2 Dissolution of Solid Additions in Two-phase Flow ____________________________________________ 17

2.2.1 Fluid mechanics of bubbly systems ____________________________________________________ 17

2.2.1.1 Bubble formation and trajectory _____________________________________________________________ 19

2.2.1.2 Bubble-induced velocity field in the liquid ____________________________________________________ 20

2.2.2 Mass transfer in two-phase flow systems ________________________________________________ 23

2.2.2.1 Mass transfer from small particles ___________________________________________________________ 24

2.2.2.2 Mass transfer from large solid additions _______________________________________________________ 26

DISSOLUTION OF SOLID Si CYLINDERS IN MOLTEN Al: SINGLE-PHASE FLOW _______________ 34

3.1 Pure Diffusion of Si in Al ________________________________________________________________ 34

3.2 Experimental Methodology ______________________________________________________________ 36

3.2.1 Materials _________________________________________________________________________ 36

3.2.2 Experimental set-up ________________________________________________________________ 37

3.2.3 Experimental procedure _____________________________________________________________ 40

3.3 Results and Discussion __________________________________________________________________ 40

3.3.1 Natural convection experiments _______________________________________________________ 40

vii

3.3.1.1 Heat transfer after immersion _______________________________________________________________ 42

3.3.1.2 Isothermal mass transfer ___________________________________________________________________ 46

3.3.1.3 Effect of impurities _______________________________________________________________________ 50

3.3.2 Forced convection experiments ________________________________________________________ 56

3.3.2.1 Local variation of dissolution rate ___________________________________________________________ 59

3.3.2.2 Comparison with a forced convection correlation _______________________________________________ 59

3.3.2.3 Comparison with a combined natural and forced convection correlation _____________________________ 61

3.4. Relationship Between Bath Temperature and Bulk Velocity ____________________________________ 64

3.5 Summary _____________________________________________________________________________ 65

FLUID DYNAMICS OF GAS-AGITATED LIQUID _____________________________________________ 67

4.1 Bubble Formation and Trajectory in an Air–Water System ______________________________________ 67

4.2 Bubble Formation and Trajectory in a N2–Al System __________________________________________ 76

4.2.1 Bubble size _______________________________________________________________________ 78

4.2.2 Bubble trajectory ___________________________________________________________________ 81

4.3. Numerical Modeling of Gas-Agitated Tank _________________________________________________ 82

4.3.1 Simulation set-up and parameters ______________________________________________________ 83

4.3.2 Temporal- and spatial-averaged velocities _______________________________________________ 89

4.3.3 Experimental validation with the air–water system ________________________________________ 90

4.3.4 Results and Discussion ______________________________________________________________ 96

4.3.4.1 Bubble distribution within the liquid Al _______________________________________________________ 96

4.3.4.2 Non-rotating tank ________________________________________________________________________ 98

4.3.4.3 Rotating tank ___________________________________________________________________________ 107

4.4 Summary ____________________________________________________________________________ 119

DISSOLUTION OF SOLID Si CYLINDERS IN MOLTEN Al: TWO-PHASE FLOW ________________ 121

5.1 Experimental Procedure ________________________________________________________________ 121

5.2 Results and Discussion _________________________________________________________________ 123

5.2.1 Effect of bulk velocity at a given gas flow rate ___________________________________________ 124

5.2.2 Effect of gas flow rate ______________________________________________________________ 131

5.2.3 Effect of lance location _____________________________________________________________ 133

5.2.4 Correlating single- and two- phase flows _______________________________________________ 137

5.3 Comparison with a Correlation for Mass Transfer in a Gas‐stirred Tank ___________________________ 140

5.4 Comparison with a Correlation for Mass Transfer in Turbulent Cross Flow ________________________ 141

viii

5.5 Relationship Between Mass Transfer Coefficient and Energy Input into the Liquid in Single and

Two-phase Flows ________________________________________________________________________ 145

5.6 Summary ____________________________________________________________________________ 146

SUMMARY, CONCLUSIONS AND FUTURE WORK __________________________________________ 148

6.1 Summary ____________________________________________________________________________ 148

6.2 Conclusions _________________________________________________________________________ 149

6.3 Contributions ________________________________________________________________________ 154

6.4 Recommendations for Future Work _______________________________________________________ 155

LIST OF REFERENCES ___________________________________________________________________ 157

APPENDIX A: CORRELATIONS FOR MATERIAL PROPERTIES ______________________________ 168

A.1 Diffusion Coefficient of Si into liquid Al __________________________________________________ 168

A.2 Density and Viscosity of Liquid Al _______________________________________________________ 169

APPENDIX B: IMPROVING THE REPRODUCIBILITY OF Si DISSOLUTION ____________________ 170

ix

LIST OF TABLES

Table 2-1: Si content, attractive properties, and applications of some common cast Al–Si alloys [16]. 8

Table 2-2: Dissolution studies of stationary solid additions in liquid Al. 14

Table 2-3: Dissolution studies of rotating solid additions in liquid Al. 15

Table 2-4: Heat and mass transfer correlations based on cold model studies of gas-agitated metallurgical ladles. 32

Table 2-5: Heat and mass transfer correlations based on hot model studies of gas-agitated metallurgical ladles. 33

Table 3-1: Overall chemical analysis (in wt.%) of the various batches of Si used in this study. 37

Table 3-2: Results of Energy Dispersive X-ray analysis at points shown in Figure 3-11 (b) and Figure 3-12 (b). 53

Table 3-3. Dimensionless parameters involved in the combined convection from a Si vertical cylinder in liquid Al cross flow. 62

Table 4-1: List of FLOW‐3D simulations for the N2–Al system. 96

Table 4-2: Comparison of experimental measurements and FLOW-3D predictions for the equivalent bubble diameter at the lance exit in the N2–Al system (bulk velocity = 0). 97

Table 5-1: Mean mass transfer coefficient of MGSi–II specimens, mk , and estimated mass boundary layer thickness, δm, at various operating conditions. 131

Table 5-2: Predicted mass transfer coefficients using the general combining law for Equation (5-6) and natural convection, and a comparison with experimental values (bulk velocity = 0, θ = 30°). 144

Table 5-3: Predicted mass transfer coefficients using the general combining law for Equation (5-8) and natural convection, and a comparison with experimental values (θ = 30°). 144

x

LIST OF FIGURES

Figure 2-1: Equilibrium Al–Si phase diagram [19]. 9

Figure 2-2: Schematics of (a) bottom stirring and (b) top lance injection. 18

Figure 2-3: (a) He bubble in water, and (b) He bubble in a liquid metal (mercury), both at the end of a stainless steel lance [60]. 20

Figure 3-1: Cylinder radius vs. time, considering only pure diffusion. 36

Figure 3-2: Schematic of a bilge-shaped crucible shows the location of thermocouples to examine the effect of preheating the specimen. All dimensions are in cm. 38

Figure 3-3: (a) The RLMT with solid Al charge, (b) top view shows the rotation direction and location of the immersed Si specimen and AA´ is perpendicular to the xy-plane and passes through the Si sample, and (c) side view with the Si sample at the AA´ plane. All dimensions are in cm. 39

Figure 3-4: MGSi–I specimens after natural convection dissolution for 3 min in an Al bath at various superheats. 41

Figure 3-5: The effect of bath superheat on the dissolved fraction, md/mi, of MGSi–I specimens after natural convection dissolution for 3 min. 42

Figure 3-6: Formation of an Al shell on MGSi–I cylinders immersed for short periods in an Al bath at SPH = 40 K. 43

Figure 3-7: Temperature history of a MGSi–I cylinder immersed into liquid Al (a) initially at room temperature, (b) preheated for 3 min prior to immersion. 45

Figure 3-8: Comparison of the dissolved fraction with and without preheating, for MGSi–I at SPH = 40 K. 46

Figure 3-9: Comparisons between measured and predicted natural convection mass transfer for liquid Al at (a) SPH = 40 K and (b) SPH = 80 K. 49

Figure 3-10: Effect of bath superheat on the dimensionless radius, r/r0, of MGSi–I, MGSi–II and EGSi specimens immersed for 3 min in liquid Al under natural convection. 50

Figure 3-11: (a) Secondary electron image of a MGSi–I specimen prior to immersion, (b) a higher magnification of the outlined area in (a). 51

Figure 3-12: (a) Secondary electron image of a MGSi–II specimen prior to immersion, (b) a higher magnification of the outlined area in (a). 52

xi

Figure 3-13: Backscattered electron image of a MGSi–I specimen with an attached Al after quenching in water from 973 K to 293 K. 53

Figure 3-14: Si specimens after natural convection dissolution for 3 min at SPH = 80 K; captions on top indicate the batch of Si. 55

Figure 3-15: Effect of bulk velocity on the dissolved fraction after 3 min immersion, (a) SPH = 40 K and (b) SPH = 80 K. 57

Figure 3-16: Dissolution of MGSi–I under natural and forced convection conditions; (a) SPH = 40 K and (b) SPH = 80 K. 58

Figure 3-17: Variation of local dissolution of MGSi–II cylindrical specimens in a cross flow of liquid Al at various bulk velocities (SPH = 40 K, immersion time = 3 min). 59

Figure 3-18: Comparison of experimental and estimated dimensionless radii for pure forced convection mass transfer from vertical Si cylinders immersed for 3 min in a liquid Al cross flow. 61

Figure 3-19: Comparison of experimental and estimated dimensionless radii for combined convection mass transfer from vertical Si cylinders immersed for 3 min in a liquid Al cross flow. 63

Figure 3-20: Comparison of experimental and estimated dimensionless radii for combined convection mass transfer from vertical Si cylinders immersed in a liquid Al cross flow at a bulk velocity of 7 cm s−1. 64

Figure 3- 21: Mass transfer coefficient vs. SPH (shown on the bottom abscissa) superimposed on mass transfer coefficient vs. bulk velocity (shown on the top abscissa) (MGSi–II, immersion time = 3 min). 65

Figure 4-1: (a) The transparent water tank on a rotating table, (b) top view shows the rotation direction and location of the gas injection lance, and AA´ represents a plane perpendicular to the xy-plane passing through the lance, (c) side view of the water tank and the lance at AA´. All dimensions are in cm. 68

Figure 4-2: Typical output voltage of the pressure transducer used to measure bubble formation frequency (air–water system, bulk velocity = 0). 69

Figure 4-3: Formation and rise of single bubbles in the air–water system (gas flow rate = 0.3 SLPM, bulk velocity = 0). 70

Figure 4-4: Formation of single bubbles and coalescence of two consecutive bubbles during rise in the air–water system (gas flow rate = 0.6 SLPM, bulk velocity = 0). 71

Figure 4-5: Formation of doublets in the air–water system (gas flow rate = 1.0 SLPM, bulk velocity = 0). 72

Figure 4-6: Equivalent bubble diameter vs. gas flow rate in the air–water system. 73

xii

Figure 4-7: Equivalent bubble diameter in the air–water system with and without cross flow. 74

Figure 4-8: Effect of bulk liquid velocity on the equivalent bubble diameter in the air–water system (db normalized by the bubble diameter when the bulk velocity = 0). 75

Figure 4- 9: Comparison of bubble trajectories at various bulk velocities (gas flow rate = 1 SLPM). 76

Figure 4-10: Schematic of the RLMT shows the rotation direction and location of the immersed Si specimen and the gas injection lance. (a) Top view where AA´ represents a plane perpendicular to the xy-plane passing through the lance, (b) side view of the RLMT. All dimensions are in cm. 78

Figure 4-11: Typical output voltage of the pressure transducer used to measure the frequency of bubble formation (N2–Al at SPH = 40 K, bulk velocity = 0). 79

Figure 4-12: Bubble size in liquid Al at bulk velocities of 0 and 7.0 cm s−1, and a comparison with the available correlation for a (Chlorine/N2)–Al system [57]. 80

Figure 4-13: Bubble arrival at liquid Al surface (bulk velocity = 0, gas flow rate = 0.50 SLPM, θ = 30º, the coated lance diameter is approximately 0.725 cm). 81

Figure 4-14: Bubble arrival at the liquid Al surface (bulk velocity = 3.5 cm s−1, gas flow rate = 0.50 SLPM, θ = 30º, the coated lance diameter is approximately 0.725 cm). 82

Figure 4-15. Cylindrical domain for the FLOW-3D simulations of the N2–Al system. All dimensions are in cm. 84

Figure 4-16: (a) Top view of the mesh planes, and (b) the mesh around the lance. 85

Figure 4-17. (a) Overall liquid kinetic energy of liquid per unit mass of liquid, Kl, and (b) ldK dt vs. time (bulk velocity = 0, gas flow rate = 0.50 SLPM, solid line is the sliding 1 s average). 88

Figure 4-18: Instantaneous liquid velocity magnitude (bulk velocity = 0, gas flow rate = 0.50 SLPM, r = 13.5 cm, θ = 30°, z = 11 cm: 4 cm below the free surface of liquid Al coincides with the center of an imaginary Si cylinder). 90

Figure 4-19: Qualitative comparison of air-water bubble formation (bulk velocity = 0, gas flow rate = 0.3 SLPM). 93

Figure 4-20: Qualitative comparison of air-water bubble formation (bulk velocity = 0, gas flow rate = 1.0 SLPM). 94

Figure 4-21: Quantitative comparison of the formation and rise time of many bubbles over a time period of 4 s as predicted by a FLOW‐3D simulation, and measured in the

xiii

air–water experiments, at gas flow rates of (a) 0.3 SLPM and (b) 1.0 SLPM (bulk velocity = 0). 95

Figure 4-22: Predicted instantaneous bubble distributions at gas flow rates of (a) 0.50 SLPM and (b) 1.00 SLPM (3D view of the lance vicinity, bulk velocity = 0). 98

Figure 4-23: (a) Predicted instantaneous bubble-induced velocity magnitude in the θz-plane passing through the lance center, (b) the tangential velocity at various rz-planes, and (c) the vertical velocity at various rθ-planes (bulk velocity = 0, gas flow rate = 0.50 SLPM, t = 9.00 s). 101

Figure 4-24. Spatially averaged (a) absolute mean velocity, and (b) rms velocity fluctuations in the r, θ, and z directions (bulk velocity = 0, gas flow rate = 0.50 SLPM, θ = 30°). 103

Figure 4-25: Comparison of spatially-averaged (a) mean velocity and (b) rms velocity fluctuations at various angular positions relative to the lance (bulk velocity = 0, gas flow rate = 0.50 SLPM). 105

Figure 4-26: Comparison of spatially-averaged (a) mean velocity and (b) rms velocity fluctuations at various gas flow rates (bulk velocity = 0, θ = 30°). 106

Figure 4-27: Instantaneous (a) tangential velocity, uθ, and (b) vertical velocity, uz, on the θz-plane passing through the center of the lance (bulk velocity = 3.5 cm s−1, gas flow rate = 0.50 SLPM, t = 9.00 s). 108

Figure 4-28: Instantaneous tangential velocity on two rθ‐planes (bulk velocity = 3.5 cm s−1, gas flow rate = 0.50 SLPM, t = 9.00 s). 109

Figure 4-29: Instantaneous velocity magnitude, V, at various rz‐planes (bulk velocity = 3.5 cm s−1, gas flow rate = 0.50 SLPM, t = 9.00 s). 109

Figure 4-30: Spatially-averaged absolute mean velocity in the r, θ, and z directions (bulk velocity = 3.5 cm s-1, gas flow rate = 0 SLPM, θ = 30°). 110

Figure 4-31: Spatially-averaged rms velocity fluctuations and turbulence intensity (bulk velocity = 3.5 cm s−1, gas flow rate = 0 SLPM, θ = 30°). 111

Figure 4-32: Spatially-averaged (a) absolute mean velocity, and (b) rms velocity fluctuations in the r, θ, and z directions (bulk velocity = 3.5 cm s−1, gas flow rate = 0.50 SLPM, θ = 30°). 112

Figure 4-33: Comparison of spatially-averaged rms velocity fluctuations at various bulk velocities (gas flow rate = 0.50 SLPM, θ = 30°). 113

Figure 4-34: Comparison of spatially-averaged turbulence intensity in the rotating tank (gas flow rate = 0.50 SLPM, θ = 30°). 114

xiv

Figure 4-35: Comparison of spatially-averaged absolute mean velocities in the (a) r, (b) θ, and (c) z directions at various gas flow rates (bulk velocity = 3.5 cm s−1, θ = 30°). 116

Figure 4-36: Comparison of spatially-averaged rms velocity fluctuations in the (a) r, (b) θ, and (c) z directions at various gas flow rates (bulk velocity = 3.5 cm s−1, θ = 30°). 117

Figure 4-37: Comparison of spatially-averaged (a) mean velocity, and (b) rms velocity fluctuations at various angular positions relative to the lance (bulk velocity = 3.5 cm s−1, gas flow rate = 0.50 SLPM). 118

Figure 5-1: The furnace lid includes various holes to immerse a thermocouple, Si specimens, and the lance into the liquid Al. 122

Figure 5-2: Dissolved MGSi–II cylindrical specimens at various gas flow rates (immersion time = 3 min, SPH = 40 K, bulk velocity = 3.5 cm s−1, θ = 30°). 123

Figure 5-3: Dissolved fraction of MGSi–II at SPH = 40 K vs. bulk velocity (immersion time = 3 min, gas flow rate = 0.50 SLPM, θ = 30°). 125

Figure 5-4: (a) ΔDF, and (b) EF for dissolution for MGSi–II vs. bulk velocity at a gas flow rate = 0.50 SLPM (immersion time = 3 min, θ = 30°, the lines indicate average values). 127

Figure 5-5: (a) ΔDF, and (b) EF for dissolution for MGSi–II vs. bulk velocity at a gas flow rate = 1.00 SLPM (immersion time = 3 min, θ = 30°, the lines indicate average values). 128

Figure 5-6: (a) ΔDF and (b) EF for MGSi–I vs. gas flow rate (immersion time = 3 min, bulk velocity = 3.5 cm s−1, θ = 30°, the lines indicate average values). 134

Figure 5-7: (a) ΔDF and (b) EF for MGSi–II vs. gas flow rate (immersion time = 3 min, bulk velocity = 3.5 cm s−1, θ = 30°, the lines indicate average values). 135

Figure 5-8: ΔDF vs. the relative positions of the gas injection lance and Si specimen for (a) MGSi–I, SPH = 40 K and (b) MGSi–II, SPH = 80 K (immersion time = 3 min, bulk velocity = 3.5 cm s−1, gas flow rate = 1.00 SLPM, the filled symbols indicate average values). 136

Figure 5-9: Mass transfer coefficient vs. gas flow rate (shown on the top abscissa) superimposed on mass transfer coefficient vs. bulk velocity (shown on the bottom abscissa) for (a) SPH = 40 K and (b) SPH = 80 K (MGSi–II, immersion time = 3 min, θ = 30°, error bars indicate the standard deviations). 138

Figure 5-10: Mass transfer coefficient vs. gas flow rate at a bulk velocity of 3.5 cm s−1 (shown on the top abscissa) superimposed on mass transfer coefficient vs. bulk velocity (shown on the bottom abscissa) for (a) SPH = 40 K and (b) SPH = 80 K

xv

(MGSi–II, immersion time = 3 min, θ = 30°, error bars indicate the standard deviations). 139

Figure 5-11: Normalized mass transfer coefficient for single-phase and two-phase flows vs. normalized liquid kinetic energy per unit mass of liquid. 146

Figure A-1: Diffusion coefficient of Si into Al as a function of temperature. 168

Figure A-2: Kinematic viscosity of liquid Al as a function of temperature. 169

Figure B-1: MGSi–I as‐drilled specimens after natural convection dissolution for 5 min in liquid Al at SPH = 40 K. 171

Figure B-2: Effect of sample surface preparation on the dissolved fraction of MGSi–I specimens immersed for 5 min in liquid Al under natural convection at SPH = 40 K. 171

xvi

NOMENCLATURE

Acronyms AA Aluminum Association

ASTM American Society for Testing and Materials

BOF Basic Oxygen Furnace

CFD Computational Fluid Dynamics

DF Dissolved Fraction

DNS Direct Numerical Simulation

EDX Energy Dispersive X-ray spectroscopy

EF Enhancement Factor

EGSi Electronic Grade Silicon

ICP Inductively Coupled Plasma mass Spectrometry

LDV Laser Doppler Velocimetry

LES Large Eddy Simulation

LPD Liquid Phase Diffusion

MAC Marker-and-Cell

MGSi Metallurgical Grade Silicon

NLPM Normal Liter per Minute

RLMT Revolving Liquid Metal Tank

SLPM Standard Liter per Minute

SPH Superheat

SEM Scanning Electron Microscopy

VoF Volume of Fluid

English symbols Ac cross section area of lance or nozzle, m2

C concentration, kg m−3

C1 coefficient appears in the equation of Re based on energy dissipation rate, Equation (2-3)

D diffusion coefficient, m2 s−1

d diameter of a cylindrical or spherical specimen, m

d0 initial diameter of a cylindrical or spherical specimen, m

xvii

db bubble diameter, m

db0 bubble diameter at zero bulk velocity, m

(db)max maximum stable bubble diameter, m

dlance,ID inner diameter of a lance or nozzle, m

dlance,OD outer diameter of a lance or nozzle, m

dp particle diameter, m

EK gas kinetic power, W

EB power due to buoyancy force of rising bubbles, W

Grm,l mass transfer Grashof number [ 3 Sat b 2Si T Si Sig( C ) l (C C )= ∂ρ ∂ − ρν ]

FB buoyancy force, N LDF lateral drag force, N

f frequency of bubble formation, s−1

g gravitational acceleration, m s−2

H liquid height inside a tank, m

I coefficient appears in the equation for mass flux from rotating disk, Equation (2-1)

j mass flux, kg m−2 s−1

k specific turbulent kinetic energy, m2 s−2

Kl liquid kinetic energy per unit mass of liquid, m2 s−2

km local mass transfer coefficient, m s−1

mk mean combined convection mass transfer coefficient, m s−1

Nmk mean natural convection mass transfer coefficient for vertical cylinder, m s−1

Fmk mean forced convection mass transfer coefficient for vertical cylinder in cross

flow, m s−1

L distance from the nozzle/ lance exit to the bath surface, m

Lv downward migration of gas upon injection from lance, m

l length of cylindrical specimen, m

lc characteristic length, m

M total number of data used in time-averaging

m exponent appears in the equation for mean Sh of natural convection, Equation (3-6)

md dissolved mass of cylindrical Si specimen, kg

mi immersed mass of cylindrical Si specimen, kg

xviii

NV number of cells in a volume representing a Si cylinder

n coefficient appears in the equation for mean Sh of natural convection, Equation (3-6)

Nu mean Nusselt number

P static pressure of liquid at the lance/nozzle tip, Pa

P0 atmospheric pressure, Pa

Pr Prandtl number [= ν/α]

p exponent appears in the equation of the general combining law

Q gas flow rate at the lance exit, m3 s−1

QS gas flow rate at standard temperature and pressure

(273.15K and 100 kPa), m3 s−1

Ri inner diameter of a liquid tank, m

Ro outer diameter of a liquid tank, m

Re Reynolds number

ReT Reynolds number based on rms velocity fluctuations

r radius of a cylindrical specimen, or radial direction, m

r0 initial radius of a cylindrical specimen, m rot

S ir radial distance from the center of the tank to the point of immersion of a Si cylinder centerline, m

S location of solid/liquid interface, m

S0 initial location of solid/liquid interface, m

Sc Schmidt number [= ν/D]

Sh mean Sherwood number

T temperature, K

Tu turbulence intensity

t time, s

Ub bulk velocity of liquid normal to the centerline of a vertical cylinder or an injection lance, m s−1

ub bubble rise velocity, m s−1

up peripheral velocity of a rotating cylinder, m s−1

Up velocity of upward liquid flow in a ladle, m s−1

u rms velocity fluctuations, m s−1

ur, uθ, uz velocity components in cylindrical coordinates, m s−1

ru , uθ , zu time-averaged velocity components in cylindrical coordinates, m s−1

xix

ru′ , uθ′ , zu′ velocity fluctuation components in cylindrical coordinates, m s−1

V instantaneous velocity magnitude, m s−1

V mean velocity of liquid, m s−1

Vg gas entry velocity, m s−1

v volume, m−3

X, Y, Z general variables

x, y, z Cartesian coordinates

Greek symbols α thermal diffusivity, m2 s−1

δ momentum boundary layer thickness, m

δm mass boundary layer thickness, m

φ general quantity

ε energy dissipation rate per unit mass, m2 s−3

θ relative angular position with respect to a lance or a Si specimen, deg

θc contact angle, deg

λ ratio of interface velocity to mass transfer coefficient

μ dynamic viscosity, kg s−1 m−1

μ0 dynamic viscosity at the solid surface, kg s−1 m−1

ν kinematic viscosity, m2 s−1

ρ density, kg m−3

σ surface tension, N m−1

Ω rotational speed of a rotating disk, rad s−1

ω rotational speed of a liquid Al tank, rad s−1

Subscript 0 initial condition

Al liquid Al

c centerline of a cylindrical ladle

g gas

l liquid

Si solid Si

Superscript

b bulk liquid

xx

F forced convection

N natural convection

ref reference condition

rms root mean square

Sat saturation

Other | | absolute value

< > spatial averaging

1

CHAPTER 1

INTRODUCTION

Aluminum (Al) is ubiquitous: in the buildings we live in, the trains we take to work, the

networks that connect us, and the packaging that protects our food and drink. Al is in high

demand for several reasons: it is a light metal, has good corrosion resistance, high electric

and thermal conductivity, and Al is highly recyclable, which is crucial from an

environmental standpoint [1].

The direct use of pure Al is limited because of lack of strength and castability. To

improve on pure Al properties, the requirements for any particular application, including

formability, strength, and wear resistance must be taken into account. This necessitates the

addition of alloying elements. Al alloys with silicon (Si) as the major alloying element are of

great importance as they are characterized by excellent castability and good weldability. Si

levels in unalloyed Al are very low (typically 0.05 to 0.15 wt.%). When added in

combination with Mg, Si yields heat treatable casting alloys such as 356 (6 wt.% Si, 0.4 wt.%

Mg, widely used for wheels and suspension components), and wrought alloys of the 6000

series which can be extruded or rolled. Very high levels of Si are present in many die casting

alloys where the Si provides strengthening, resistance to hot tearing and wear resistance. Si is

also a major component of the 4000 series brazing alloys, where typical

CHAPTER 1. INTRODUCTION

2

Si levels range from 5 to 13%.

Al is produced by the electrolysis of alumina extracted from bauxite ore (primary Al), or

by recycling (secondary Al). Secondary Al accounted for 60% of the metal produced in

North America in 2011 [2]. Al properties are not compromised by recycling [3] and the

energy required to produce secondary Al is only 5% of that required to produce primary Al

[1]. Despite the energy savings associated with using recycled scrap, remelting is

nevertheless an energy intensive process, with a total energy consumption of about

10-20 GJ/tonne [4].

There is no "standard process" for the production of Al alloys. Every plant has certain

resources, and they exercise the most efficient ways to achieve the specific compositions of

their products. For example, to produce Al–Si alloys, one major producer of primary Al adds

lumps of Si to an empty furnace and then transfers hot Al from the reduction cells to the

furnace. Because of the high temperature of the melt (~900°C), the solubility of Si is very

high, and with a bottom-mounted electromagnetic stirrer, Si can be dissolved even before all

of the molten metal has been transferred [5]. At the end of the cycle, only melt refining

measures must be taken to reach an acceptable tolerance for composition and homogeneity.

Needless to say, such a process requires a separate source of hot metal.

In Al processing plants without a smelter (e.g. Novelis, the sponsor of this project at one

of its North American plants), metal in the form of unalloyed Al ingots from a smelter or

scrap Al is charged into melting or holding furnaces, to which alloying elements are added

[5]. Batch sizes are typically 20 to 50 tonnes, which represents an addition of several tonnes

of Si. At this scale, there are considerable practical difficulties in dissolving and mixing Si

into Al. The melting time for Al can vary significantly, but roughly speaking, it takes 2 to 4

hours to melt 20-50 tonnes of Al (700-740°C), and then an additional 20 to 30 minutes to

dissolve Si in the liquid Al. To make Al–Si alloys, Metallurgical Grade Si (MGSi) is

generally used in the form of crushed pieces (5 to 10 cm) which are dropped onto the surface

of the molten Al. The solid Si floats on the Al, but is mostly submerged (ρSi/ρAl = 0.98 at


3

700°C [6,7]). Some form of stirring is required to continuously expose the pieces to molten

Al, to speed up the dissolution process and obtain a uniform melt composition. This stirring

is most commonly carried out by a large steel rake attached to a fork truck, which requires

opening the furnace doors during the process. This results in heat loss, and the continuous

exposure of fresh liquid Al to the atmosphere forms dross.

The addition of Si can be a lengthy process, resulting in lost production time, energy loss

as heat when adding Si and stirring the melt, and material losses due to dross formation.

Significant savings could be achieved if the dissolution time could be reduced. This is the

motivation for this thesis: to examine Si assimilation in liquid Al, to identify means of

improving productivity.

The assimilation rate of a solid addition in melting/holding furnaces can be improved by

a number of means. One can raise the flame temperature of the furnace, as this increases the

solubility of Si into Al. However, this approach has many drawbacks: it can cause

overheating of the metal near the flame, leading to excessive oxidation and increasing the

metal loss. Also, increasing the flame temperature not only heats the metal, but also the roof

refractories and chimney system, which can significantly reduce thermal efficiency.

Another approach to accelerating the rate of Si dissolution is mechanical stirring using a

steel blade or an impeller to circulate the molten metal. This produces a bulk velocity in the

liquid; however, the use of either device entails considerable energy loss. In the case of

stirring with a blade, the estimated heat loss corresponds to approximately 10% of the total

energy used during the entire melt cycle [5], and as mentioned earlier, mechanical agitation

causes metal loss due to dross formation, which can be as important as the energy cost. A

more sophisticated method is electromagnetic stirring with the furnace doors closed, which

can be very efficient, but this is costly for new installations, and difficult to retrofit on old

furnaces [8].

Another method to increase the dissolution rate of Si is gas injection: light bubbles move

quickly through the liquid, agitating the flow, and resulting in bubble-induced stirring. Gas


4

stirring can be used by itself or with mechanical stirring. Gas injection is relatively

economical, and has been extensively used in the steelmaking industry for homogenization

and inclusion removal [9,10]. The implementation of gas injection is feasible in the Al

industry, as evidenced by the fact that, for example, hydrogen is removed from liquid Al by

purging with Ar and/or N2 through a simple tube [3], and using an inert gas, the pneumatic

injection of powdered alloying elements (e.g. Fe, Mn and Cr) into molten Al is practiced

[11].

1.1 Background Theory

Si has a higher melting temperature than Al, and so it dissolves rather than melts. For solid Si

dissolving in liquid Al, the dissolution rate is controlled by mass transfer through a mass

boundary layer between the solid addition and the liquid. The mass flux of the solute can be

expressed by Fick’s law of diffusion as j = −DSi/Al (dC/dx) at the interface. The rate of

dissolution of Si in Al is slow owing to low solute (Si) diffusivity (DSi/Al ≈ 10−8 m2 s−1). The

kinetics of dissolution can be improved by stirring the melt which will increase concentration

gradient, dC/dx, and so can be an effective method of enhancing the mass transfer rate.

Stirring drives convection, and then the mass flux is expressed as j = km (CSat − Cb) [12],

where km is the convective mass transfer coefficient. Assuming that the solute concentration

varies linearly over a thickness δm from the saturation value to the bulk value, then km is

inversely proportional to δm. The higher the liquid velocity, the thinner the mass boundary

layer, which results in a higher km.

The flow field and accordingly the liquid velocity depends on the stirring method. While

impellers generate a bulk velocity, injected bubbles induce a liquid bulk motion plus an

agitation that results in an effectively thinner mass boundary layer adjacent to any dissolving

Si. This study compares bubble-induced agitation with a uniform bulk velocity as a means of

accelerating Si dissolution.


5

In general, the assimilation kinetics of alloying additions in Al as a function of flow

conditions have not been sufficiently studied, although the assimilation process can be a rate

limiting step which affects the production rate of Al alloys. Specifically, no one has

examined Si dissolution in liquid Al with and without gas agitation. The only study of Si

alloying of Al showed that Si granules (0-1.2 cm) dissolved faster by a factor of two to three

than Si chunks (1-10 cm) [13]. However, the authors did not describe the Al flow and its

effect on the dissolution rate. Despite the more rapid dissolution of granules than chunks,

industry tends to dissolve larger pieces of Si so as not to lower recoveries [5], because small

pieces float on top of the molten metal and so tend to end up in dross.

The Al industry will benefit from this study, and there is the potential to apply the

methodology to the processing of other metals as well. The development of this technology

will yield economic and environmental benefits, by increasing production capacity, and

lowering the energy requirement.

1.2 Objectives

This thesis presents a quantitative comparison of the dissolution rate of Si in molten Al

without and with gas agitation, referred to as single-phase and two-phase flow conditions,

respectively. The specific objectives of the study were to:

• conduct a series of experiments to quantify the dissolution rate under natural and

forced convection without gas agitation;

• examine the effect of gas stirring on the enhancement of dissolution, and correlate the

effect of the gas flow rate to an equivalent bulk velocity associated with single-phase

flow;

• investigate the influence of impurity levels of Si specimens on the dissolution rate;


6

• study the shape and trajectory of injected bubbles, by means of auxiliary cold model

experiments;

• simulate gas agitation using commercial Computational Fluid Dynamics (CFD)

software, to visualize the bubble dynamics and to estimate the velocity field within

the opaque Al bath.

1.3 This Thesis

The rest of the thesis is organized as follows:

Chapter 2 begins with a review of the dissolution of high melting point additions in

single-phase flow, and is followed by a review of the fluid dynamics of bubbly systems, and

mass transfer from additions in a two-phase flow.

In chapter 3, the dissolution of solid Si in molten Al is presented as a function of molten

metal temperature and velocity, and the level of impurities present in the Si. The experiments

were conducted for a range of Al bath velocities, providing a quantitative comparison of the

dissolution rate under natural and forced convection conditions.

In chapter 4 results are presented of three studies of gas injection: (i) observations of the

molten Al free surface, as well as measurements of N2 bubble frequency in molten Al; (ii)

bubble characteristics upon injection from a downward lance in an analogous air–water

system; and (iii) simulation results of the gas-agitated liquid, to obtain estimates of the

bubble-induced velocities.

In chapter 5, the dissolution enhancement of cylindrical Si specimens in gas-agitated

molten Al is presented as a function of gas flow rate, injection lance position, uniform bulk

velocity, and bath temperature.

Chapter 6 concludes the thesis.

7

CHAPTER 2

BACKGROUND

Al alloys can be categorized as wrought or cast, and whether or not they are heat treatable.

Wrought alloys generally contain smaller amounts of alloying additions than cast alloys [14].

Wrought alloy products include plates, sheets, foils and wires used in beverage cans,

radiators, paneling and window frames. Even though most wrought Al products are alloyed,

there are applications such as electrical cables where near-to-pure Al is used [3].

Cast Al alloys are widely used in the transportation sector for engine blocks, cylinder

heads, pistons and wheels. Cast parts produced from Al alloys exhibit a unique high strength

to density ratio which make them desirable for the aerospace and automobile industries,

where structural weight is a critical property. Substituting steel and iron with light weight Al

is an accepted strategy to improve fuel economy and reduce CO2 emissions [3]. Pure Al has a

density of only 2700 kg m−3, approximately one-third that of steel (7830 kg m−3), while

alloying with precipitation-hardening elements generates mechanical properties equivalent to

those of steel.

In general, the physical and mechanical characteristics required of a part determine the

alloying elements that must be added to molten Al before casting. Si, Cu, Mg and Zn are the

main commercial alloying elements to Al. Among cast Al alloys, the Al–Si family makes up

85% or more of all Al cast parts [15]. The addition of Si promotes fluidity and low shrinkage

CHAPTER 2. BACKGROUND

8

in casting, brazing and welding applications, and so makes Al–Si alloys commercially

feasible.

Cast Al alloys are categorized based on their chemical compositions. They are numbered

according to a four digit system adopted by the Aluminum Association (AA) and approved

by the American Society for Testing and Materials (ASTM). The first digit indicates the

major alloying element in the group. For instance, 4xxx refers to Al–Si alloys and 3xxx

refers to Al–Si (+Cu or Mg) alloys [16]. Cast Al–Si alloys can be classified into three groups

[17]: (i) hypoeutectic (5-10 wt.% Si), (ii) eutectic and near eutectic (l0-13 wt.% Si), and (iii)

hypereutectic (13-25 wt.% Si). The composition of some common Si-containing alloys, along

with common applications, is given in Table 2-1 [16]. Note that there are applications of Al–

Si alloys with up to 18 wt.% Si.

Table 2-1: Si content, attractive properties, and applications of some common cast Al–Si alloys [16].

Alloy Si content (wt.% Si) Attractive properties Application

443.0 4.5-6 Good corrosion resistance Cooking utensils

332.0 8.5-10.5 Good wear resistance Pulleys and sheaves

413.0 11-13 Excellent castability Marine equipment

A390.0 16-18 Low thermal expansion, high hardness and good wear resistance

Engine pistons, compressor cylinders

Although wrought Al alloys generally contain smaller amount of additions, there are

wrought Al alloys with high Si concentration (e.g. AA4004 with 9.0-10.5 wt.% Si [18]),

because the Si lowers the melting point. These alloys commonly form part of a clad package

consisting of a high melting point core covered with a layer of the low melting point 4xxx

alloy. Such clad alloys are used for brazing applications, where the 4xxx alloy serves as the

brazing filler that seals and holds the finished assembly together.


9

The thermodynamics of the Al–Si system have been well studied. The Al–Si binary

system is a simple eutectic, as shown in Figure 2-1 [19]. The eutectic temperature is

577 ± 1°C and the eutectic composition is 12.6 ± 1 wt.% Si. Si has a high solubility in molten

Al but its solubility in solid Al is low. The saturation concentration of Si in liquid Al can be

obtained from the liquidus curve.

Figure 2-1: Equilibrium Al–Si phase diagram [19].

2.1 Dissolution of Solid Additions in Molten Al

2.1.1 Assimilation mechanism of solid additions

This thesis focuses on the kinetics of Si assimilation in liquid Al. This section introduces

different dissolution routes for the melting/dissolution of additions in metallic systems, and

then identifies the route specific to the Al–Si system.

The assimilation of a solid addition into a liquid metal can occur as melting or

dissolution: the former takes place when the melting temperature of the addition is below that

of the liquid, whereas the latter occurs when the solid addition has a melting temperature


10

higher than the liquid temperature. Solid additions to liquid metals can be categorized into

three groups [20]. Group I is characterized by melting; adding scrap Al to liquid Al is an

example. Group II is characterized by dissolution. Group III includes exothermic additions

with melting points higher than the liquid metal temperature. These exothermic additions

release substantial amounts of heat resulting in mass transfer that begins as dissolution and

progresses to melting. Mn in liquid Al is an example of a Group III addition [21].

Si has a melting point higher than that of Al, and so it dissolves in liquid Al, rather than

melts. When Si is added to liquid Al, there is negligible exothermicity, so it belongs to the

Group II of additions, for which assimilation takes place as two steps [22]:

Step I: Interface reaction at the solid/liquid interface: atoms migrate from the solid phase into

the melt. The absence of a relationship between dissolution rate and liquid agitation indicates

that the dissolution rate is controlled by this step.

Step II: Transport of dissolved species from the interface to the bulk liquid metal: the

dissolved species diffuses from the solid/liquid interface into the bulk liquid Al. The

liquid-side interface concentration of the dissolving species is defined by the liquidus curve

on the phase diagram at the melt temperature. When dissolution is controlled by liquid phase

diffusion (LPD), the flow in the vicinity of the addition will have a significant influence on

the dissolution rate. In this case, the mass transfer coefficient depends on the fluid flow

conditions.

The author is unaware of any systematic work on the dissolution of Si in Al under

different fluid flow conditions, but the dissolution of other high melting point additions in Al

has been investigated. These studies can be categorized based on whether the solid addition

was stationary or rotating, corresponding to natural and forced convection, respectively.

Studies of stationary solid additions, summarized in Table 2-2, were conducted to compare

the dissolution kinetics of different additions in liquid Al [23-25], investigate natural

convection mass transfer in liquid metal systems [24,26,27], and characterize the types of

intermetallic layers formed at interfaces [25]. Experiments using rotating disks [28-35] or


11

cylinders [23,36] of the addition, summarized in Table 2-3, were conducted to measure solute

diffusion coefficients and identify the dependence of dissolution rate on fluid flow

conditions. In the following, we focus on the findings of: (i) the diffusion coefficient of solid

additions in liquid metals, as this value for the Al–Si system is required in order to compare

dissolution rates to dimensionless correlations for mass transfer; (ii) the dissolution behavior

under natural and forced convection, to study spatial and temporal dissolution patterns, the

mass transfer rate in different convection regimes, and discrepancies between experimental

results and available correlations; and (iii) intermetallics as a resistance to mass transfer.

2.1.2 Diffusion coefficient of solid additions in liquids

To obtain reliable measurements of solute diffusion coefficients, the thickness of the mass

boundary layer must be constant on the entire dissolving surface. Levich [37] showed that

this condition is achieved only by a rotating disk. Therefore, the rotating disk method has

been used to study the dissolution of high melting point alloying elements in many liquid

metals, including Al and steel.

In rotating disk experiments, by periodically sampling the melt, the mass transfer

coefficient and mass flux of the material can be calculated at various rotation speeds. The

rotation speed is chosen to ensure a laminar flow. To calculate the diffusion coefficient, the

equation formulated by Levich and modified by Kasnar [38] can be used, that is appropriate

for the range of Sc encountered in liquid metal systems,

1 2/3 1/6 1/2 Sat bj 0.544I D (C C )− −= ν Ω − (2-1)

I is a function of Sc. At a constant temperature, a linear dependence of dissolution rate on the

rotation speed of the disk implies that the dissolution mechanism is LPD-controlled, which is

the case for most additions. For these additions, the diffusion coefficient, solubility and

dissolution rate are described by Arrhenius-type equations [31,32].


12

The diffusion coefficient for Si in liquid Al used in the current study is that of

Ershov et al. [39], albeit without the modification of Kasnar [38]. Even though the value is

different than earlier measurements [40], it is deemed more reliable as it was obtained by the

rotating disk method.

2.1.3 Natural and forced convection mass transfer

The solubility of elements in liquid Al determines relative dissolution rates. For example, Ti,

V, Cr, Fe, Co, and Ni dissolve in molten Al at rates that increase in the listed order [23]. The

radius of a cylindrical specimen varies linearly with time during the early stages of

dissolution [27], and the dissolution rate varies from the top to the bottom of an immersed

cylinder. For example, Ni [27] and Fe [26] cylinders in liquid Al dissolve more quickly at the

top than the bottom; Zn and Sn cylinders in liquid Hg dissolve more quickly at the bottom

[26]. This is because the mass boundary layer thickness across which diffusion takes place

varies along a specimen, which confirms that dissolution takes place under natural

convection [26,27]. Based on the available literature, the dissolution of stationary cylinders

was compared to dimensionless correlations developed for natural convection. In these

studies, the correlations assumed a fixed interface, by assuming a low mass transfer rate.

Pekguleryuz et al. [24] explained a discrepancy in the mass transfer coefficient on the lack of

reliable values for the diffusion coefficient. In another study, Kosaka et al. [26] modified the

general form of a Sherwood number correlation for turbulent natural convection to fit their

data, rather than ascribe the uncertainty to measured values of the diffusion coefficient.

To investigate the effect of forced convection on dissolution, rotating cylinder

experiments are usually conducted. Forced convection correlations for rotating cylinders

underpredict the dissolution of commercially pure iron, S45C, Fe–Cr, and Fe–Si in liquid Al

[36]. It was suggested that the higher dissolution rates were caused by either natural

convection effects at lower rotating speeds, or turbulent flow at the rough surfaces of the


13

dissolving specimens at higher speeds. However, a velocity at which the transition from

natural convection to forced convection occurs was not identified.

2.1.4 Effect of intermetallics on mass transfer

In contrast to the Al–Si system which forms no intermetallic phase [19], the assimilation of

some additions in Al involves formation of intermetallics at the addition/liquid interface. It

has been reported that these intermetallic phases can retard the dissolution of a stationary

addition by resisting mass transfer [25].

Rotating specimens have been used to analyze intermetallic layer growth. In rotating

cylinder experiments, the intermetallic layers are thinner than those that form on stationary

samples [36]. Tunca et al. [31] showed that the thickness of the intermetallic phase depends

on the type of addition. Nevertheless, the dissolution of Mo, Nb and Cr rotating disks in

unsaturated liquid Al is LPD-controlled regardless of the thickness and number of

intermetallic layers at the solid/liquid interface [31].


14

Table 2-2: Dissolution studies of stationary solid additions in liquid Al.

Sample type

Solid addition

Diameter (mm) Length (mm)

Al purity wt.%

Al bath size (mm)

Al bath mass or volume

Temperature (°C)

Sample preheating

Dissolution rate measurement Intermetallics Reference

Cylinder

Ti, 99.96 wt.% 31

12.7 immersed 99.996 Not reported

Not reported 705-818

1 hour, 2.5 cm above the

melt Mass loss Not reported [23]

V, 99.5 wt.% 31 Cr, High purity 25 Ni, 99.96 wt.% 31

Co, 99.816 wt.% 31 Fe, 99.885 wt.% 31

Al 90 wt.%–10wt.% Sr

15-18 20-30 99.99 Not reported 10 kg 675-775 Not reported Chemical analysis

of melt samples

Al4Sr

[24] Al 76 wt.%–Sr 10 wt.%–Si 14 wt.% SrAl2Si2

Al 45 wt.%–Sr 55 wt.% Al4Sr–Al2Sr Fe–Si

5 50 (30 immersed) 99.8 45.1 ID,

140.6 depth 350 gr 700-800 Not reported Mass loss FeAl3–Fe2Al5 [25] Fe–Ni Fe–Cu Fe–Mn Fe–C

Fe, 98.3 wt.% 0.6-1 4.1-8.35 immersed 99.3 53 ID,

100 depth 600 ± 10 gr 710-820 Above the melt Mass loss Not reported [26]

Ni, 99.7 wt.% 6.05 2.5 pure 3.5 ID, 6.35 depth 120 gr 675

Above the melt to reach

a required temperature

Diameter along the length Not reported [27]


15

Table 2-3: Dissolution studies of rotating solid additions in liquid Al.

*mc = monocrystalline, **pc = polycrystalline

Sample type

Solid addition

Diameter (mm)

Length (mm)

Rotational speed (rpm)

Al purity wt.%

Al bath size (mm)


Temperature (°C)

Sample preheating


Disk

Cr, 99.94 wt.% 12 ± 0.5 5 63-351 99.995 Not reported Not reported 700-900 Not reported Chemical analysis of melt samples

(12-90 min) Al7Cr, Al11Cr2 [28]

Rh, mc*, 99.8 wt.% 12 ± 0.5 5 63-351 99.995 Not reported Not reported 700-900 Not reported Chemical analysis of melt samples

(18-90 min) Not reported [29]

Fe, 99.99 wt.%

12 ± 0.5 5

63-351

99.995 Not reported Not reported 700-900 Not reported

Chemical analysis of 6 melt samples regular intervals

(6-8 hours)

FeAl3(Fe2Al5)

[30] CO, 99.98 wt.% 63-351 Co2Al9

Ni, 99.97 wt.% 59-591 NiAl3, Ni2Al3

Mo (pc** 99.99 wt.%)

12.7 Not reported 95-306 99.999 45 ± 1 ID 150 g

735-915 Not reported

Chemical analysis of melt samples

(ICP)

Al8Mo3, Al17Mo4, Al22Mo5, Al4Mo

[31] Nb (99.997 wt.%) NbAl3

Cr (99.997 wt.%) Δ, γ, β phases

Y (99.9 wt.%) 700-800 Al3Y, Y-rich (68 wt.%)

Nb (pc, 99.5 wt.%)

(mc, 99.88 wt.%)

12 Not reported 38-382 99.995 36 ± 1 ID 100 g 700-850 Not reported

Chemical analysis of 6 melt samples regular intervals

(7.5 hours)

NbAl3

[32] Ta (mc, 99.99 wt.%) TaAl3

Mo (pc 99.95 wt.%)

(mc 99.994 wt.%) Al4Mo

W (mc, 99.999 wt.%) WAl5

Ti, 99.7 wt.% 10 10 0-960 99.6 Not reported Not reported 800-1300 Not reported Mass loss (30-60 min) Not reported [33]

Armco Fe, 99.0 wt.% 11 50 8.5-615.4 99.99 Not reported 100 ± 5 g 700-800 To reach

close to bath temperature


FeAl3, Fe2Al5, FeAl2, Fe3Al,

Fe2Al5 [34]

Fe–Ni (5 to 90 wt.% Fe) 11.28 ± 0.01 6 62-787 99.995 Not reported 0.1 lit 700 To the

required temperature


(150-2400 s) Not reported [35]


16

Table 2-3: (Continued)

Sample type

Solid addition

Diameter (mm) Length (mm)

Rotational speed (rpm)

Al purity wt.%

Al bath size (mm)


Temperature (°C)

Sample preheating


Cylinder

Ti (99.96 wt.%) 31

12.7 immersed

21.6 (11.1 mm from the axis of

rotation) 99.996 Not reported Not reported 705-818

1 hour, 2.5 cm above the

melt Mass loss Not reported [23]

V(99.5 wt.%) 31 Cr (High purity) 25 Ni (99.96 wt.%) 31

Co (99.816 wt.%) 31

Fe (99.885 wt.%) 31

9-34 (11.1 mm from the axis of

rotation) Fe (99.6 wt.%)

5 50 (30 immersed)

7-130 (around the

addition axis)

99.8 45.1 ID, 140.6 depth 350 gr 700-800 Not reported Mass loss

(0-2500 s) FeAl3–Fe2Al5 [36] Fe–3C (2.94 wt.% C) Fe–Cr (2.94 wt.% Cr)

S45C Fe–Si (3 wt.% Si)


17

2.2 Dissolution of Solid Additions in Two-phase Flow

Quantifying the effect of gas agitation for enhancing the dissolution rate of alloying additions

in liquid Al has been largely neglected in the literature. We refer to flow phenomena with

injected gas as "two-phase flow".

Dissolution is a localized phenomenon, and predicting the rate of the process requires an

estimate of the velocity field. Since we consider gas agitation as a means of dissolution

acceleration, the behavior of bubbles and characteristics of the bubble-induced velocity field

are of interest. Lance and Bataille [41] argue that rising bubbles induce a random velocity

field in the liquid that they refer to as "pseudo-turbulence", that is different than the

shear-induced turbulence or "true turbulence" of the liquid phase. Pseudo-turbulence can be

generated by liquid stirring due to the motion of bubbles, in addition to turbulence due to

vortex shedding in the wake of bubbles, and the deformation of gas/liquid interfaces.

2.2.1 Fluid mechanics of bubbly systems

The introduction of gas at moderate velocities into liquid metals is common in ladle refining

processes. In this case, bubbles move due to buoyancy (bubbling regime), as opposed to the

initial gas momentum (jetting regime). An example of the jetting regime is gas injection in

Basic Oxygen Furnaces (BOFs), where the gas flow rate can be on the order of

10,000 NLPM, an order of magnitude higher than in refining furnaces [42]. In this case, the

gas released from the lance does not form bubbles, but rather blows into the liquid metal as a

continuous jet.

Within the bubbling regime, bottom stirring and top lance injection, shown in Figure 2-2,

are widely practiced in furnaces, ladles, and other transfer vessels, to homogenize

temperature and composition. These two approaches can differ in the number and size of

bubbles [43]. In bottom stirring, a bubble plume forms that leads to rapid bubble break up


18

and coalescence, resulting in a distribution of bubble size along and across the container. In

top lance injection, generally fewer large bubbles agitate the liquid, although generating a

bubble plume similar to bottom stirring is possible via higher gas flow rates and increased

lance immersion depth.

Bubble plumes, typically generated by bottom stirring, are so common in ladle

metallurgy that numerous investigations have characterized bubble formation [44-46], the

subsequent rise behavior [43-45,47,48], and the velocities within [47,49-52] and outside [49-

53] of the two-phase region. A good review of the fluid dynamics, heat and mass transfer in

these ladles is presented in [9,10].

(a) (b)

Figure 2-2: Schematics of (a) bottom stirring and (b) top lance injection.

By comparison, there exist comparatively few studies of two-phase flow by top lance

injection, where the lance intrudes on the rise trajectory of individual bubbles. This is the

injection type adopted in the current study, and so relevant knowledge of bubble formation

and rise is required. In addition, as top lance injection can result in a column of large bubbles,

previous experimental and numerical studies of the liquid velocity field induced by an

unhindered stream of large bubbles may be relevant, although the presence of the lance may

limit their direct applicability.


19

2.2.1.1 Bubble formation and trajectory

Information on the size and distribution of bubbles is required to understand their interaction

with the surrounding liquid. Using top lance injection, bubble frequency and size have been

studied by visual observation in transparent liquids [54-56] and with indirect measurements

(e.g. pressure transducers, acoustic devices) in opaque liquid metals [46,57].

When gas is injected vertically downward into a liquid, the bubbles initially travel

downwards a distance, Lv, before beginning to rise. Using water experiments, Iguchi et al.

[58] proposed a correlation for Lv as a function of 2 5g l lance,IDρ Q (ρ gd ) and showed that for the

bubbling regime, this vertical migration is negligible.

The non-wetting characteristic of liquid metals must be considered in metallurgical

bubbling systems, and so water experiments must be interpreted carefully [59]. The contact

angle, θc, is used to quantify the wettability. For the case of a liquid drop on a solid surface,

liquid wets the solid when 0 < θc < 90º, and does not wet it when 90º < θc < 180º. As clearly

illustrated in Figure 2-3 [60], a He bubble forms in water at the end of a lance because the

water/stainless steel contact angle is small (θc < 90º). On the other hand, mercury does not

wet stainless steel (θc > 90º) and so the bubble wets the outer surface of the lance.

For a downward facing lance, non-wetting behavior combined with the upward buoyancy

force results in more rapid bubble detachment and rise, as the bubbles wick up onto the lance

and so experience a smaller drag force. As a result, Irons and Guthrie [46] reported 10 times

smaller bubbles (by volume) using a vertical downward facing nozzle than an upward facing

one, in pig iron. Using a poorly wetted lance in water, it was shown that Ar bubbles along the

lance rise faster than away from it [61]. Fu et al. [57] found that Cl2–Ar bubbles in liquid Al

wicked up onto a top submerged alumina lance; however, they were unable to measure the

bubble rise velocity using a two-microphone detection system, as the noise of bubbles

breaking close to lance was not distinct. Although the rise velocity of bubbles in liquid Al

was not reported in this case, its lower limit may be estimated using measurements from a


20

J-shaped top submerged lance [57]. For flow rates and equivalent bubble diameters pertinent

to this study (1-2 cm), the rise velocity was measured to be 0.35-0.55 m s−1 [57,62].

(a) (b)

Figure 2-3: (a) He bubble in water, and (b) He bubble in a liquid metal (mercury), both at the end of a stainless steel lance [60].

The bubble arrival frequency at the melt free surface can be different than the bubble

detachment frequency, for two reasons: the formation of double bubbles, or "doublets", at the

lance exit [44,46], and bubble coalescence during rise. In liquid Al, using a radiographic

technique, the coalescence of Ar bubbles was observed at the exit of an upward facing nozzle

[62].

A liquid flow in the transverse horizontal direction relative to the nozzle results in an

early detachment of bubbles because of the shear force exerted at the lance exit [63]. An

investigation of a cross-flow on a top injection lance in water showed that by increasing the

transverse velocity at the lance exit, the bubble formation frequency begins to increase when

( )0.5blance,IDU gd > 0.204 , provided the generated bubble is not partially engulfed in the wake

of the lance, which usually occurs at higher flow rates [55].

2.2.1.2 Bubble-induced velocity field in the liquid

In a confined column of liquid, with bubbles rising individually as a chain along the center,

the liquid velocity field depends on the trajectory of the bubbles [64]: (a) rigid bubbles that

follow a straight line establish a bulk recirculating flow, (b) moderately wobbling bubbles

that follow a 2D zigzag path add uneven counter-rotating vortex pairs, and (c) violently


21

wobbling bubbles that follow a spiral trajectory further generate cross flow and large

irregular circular flow. In a water tank including a free surface, large scale structures of a

bubble-induced flow were examined [65] using time-resolved image velocimetry. Aside from

mean recirculating flow and source-and/or sink-like flow related to bubble wakes, an

up-and-down motion of the free surface was identified as another dominant flow structure.

A superposition of the bubble-induced motions results in a random flow field with

velocity fluctuations that have been referred to as pseudo-turbulence [41]. It has been shown

that larger bubbles, associated with a higher gas flow rate, do not significantly alter the

recirculating mean velocity field; however, the turbulence is greatly enhanced [65].

Increasing the gas flow rate by a factor of 5 yielded only a 2.5 times increase in the overall

kinetic energy, while increasing the turbulent kinetic energy by a factor of 5.7. It was

postulated that the energy transfer from the bubbles to the liquid is non-linear due to the

oscillation of the free surface [65]. Laser Doppler Velocimetry (LDV) measurements of

bubble plumes in water confirmed a uniform turbulent energy in the bulk, but significantly

higher values in the two-phase region and near the free surface [49,52]. Because of gas/liquid

interaction the turbulence intensity in the plume region can be 0.5, much higher than the

turbulence intensity of typical single-phase flows (<0.2) [49]. A comparison of vertical and

horizontal velocity fluctuations showed anisotropy of turbulence skewed towards the vertical

direction due to flow entrainment in the wakes of bubbles [49,66].

Numerical modeling of gas–liquid two-phase flows: The above‐mentioned studies have

characterized bubble-induced flow; however, the quantitative results (e.g. bulk velocity and

velocity fluctuations) cannot be easily extrapolated to other studies, given that the flow is a

function of numerous parameters including the gas/liquid density ratio, the gas flow rate, the

size and distribution of bubbles, and the geometry of the tank or column. In particular, there

is a lack of data of bubble-induced velocity fields in high temperature liquid metals, in which

velocities cannot be easily measured. For such systems, CFD can be used to estimate local

velocities in a flow field, which is especially important when one seeks to quantify a


22

localized rate phenomenon such as dissolution. Mathematical/numerical models used to

simulate two-phase flow are summarized below, including shortcomings and advantages as

they relate to the system of interest.

In early work, the liquid velocity field in a ladle with a central plume of many small

bubbles was approximated analytically by prescribing a Gaussian distribution for bubble

distribution and liquid velocity [67]. Then, simple quasi-single phase models were developed

that assumed a predetermined axisymmetric plume, with the buoyancy force acting on the

surrounding liquid. These models predicted the velocity field outside the plume satisfactorily

with little computation [68], assuming the free surface to be flat. For flows with larger

bubbles, such quasi-single phase models cannot be used, as the bubbles are larger than the

mesh size [43].

In turbulent multiphase flows, when none (k-ε model [69]) or only some (Large Eddy

Simulation or LES [70]) of the turbulent structures are resolved, turbulence closures must be

included to model mean turbulent quantities. It has been shown that k-ε model predictions of

fluctuating velocities agree with LES predictions and experimental measurements only when

extra source terms are added to the k and ε equations [70]. The source term for turbulent

kinetic energy is simply the work done by the bubbles (the interfacial force multiplied by the

slip velocity) [69].

In the last two decades, direct numerical simulations (DNS) of multiphase flows have

become the state-of-the-art. These simulations solve the governing equations on a sufficiently

fine grid so that all time and length scales are fully resolved (for laminar flow and more

recently for turbulent flows (e.g. [71,72])), using one of the following approaches: the

Eulerian-Lagrangian approach, or the Eulerian or "one-fluid" approach [73].

The Eulerian-Lagrangian method for computing multiphase flows refers to the use of

moving Lagrangian grids in conjunction with an Eulerian stationary grid [73]. Fluid

interfaces are represented by unstructured grids that move and deform over the Eulerian grid.


23

This is a complex approach as the interaction of the Lagrangian grids with the stationary grid

must be managed, and the Lagrangian grids reconstructed dynamically (e.g [74]).

In the Eulerian models, a single set of Navier-Stokes equations is solved on a stationary

grid covering the entire domain, and different fluids are identified by a marker function that

is advected across the Eulerian grid, and that is in turn used to calculate fluid densities and

viscosities. Examples of Eulerian models are the Marker-and-Cell (MAC) method [75], the

Volume of Fluid (VoF) method developed by Hirt and Nichols [76], and the Level-Set

method introduced by Osher and Sethian [77]. Among these models, the VoF method is

relatively simple to implement and has demonstrated its usefulness for a large number of

problems. For example, using a 3-D VoF method, bubble-bubble interaction [78] and the

effect of cross flow on bubble formation [79] has been satisfactorily modeled. The VoF

method is widely used, and a number of commercial software packages employ it to

represent and track interfaces and free surfaces. In the VoF method, a volume fraction is

identified in each cell as the fraction of the volume of that cell filled with one of the two

fluids. As interfaces move with the flow, the volume fractions are advected, either by a

geometric reconstruction/advection scheme (e.g. [80]), or by any of a number of algebraic

schemes.

2.2.2 Mass transfer in two-phase flow systems

Dimensionless correlations for convective heat and mass transfer from solids to liquids are

based on boundary layer theory. When the fluid motion is generated by an external source (as

opposed to natural convection caused by thermal and density gradients), the classical

dimensionless mass transfer correlations (e.g. Ranz-Marshall correlation) are functions of Re

and Sc [81]:

( )Sh f Sc,Re= (2-2)


24

This type of correlation is only applicable when the level of turbulence in the flow is very

low. However, ladle metallurgical processes involve the agitation of liquid in a large domain,

characterized by high Re that indicate very turbulent flow [10]. The effect of turbulence can

be taken into account by (i) modifying the definition of Re for a stirred flow, or by (ii)

introducing a new dimensionless number into a correlation, similar to what has been done for

heat and mass transfer phenomena in flows with grid generated turbulence [82-84]. In

metallurgical reactors, the choice of approach depends on the size of the alloying addition.

Mass transfer may occur from solid particles (e.g. Mn and Fe powder in liquid Al, with

particles smaller than 0.06 cm [11]) or from large additions (e.g. Si in liquid Al with lumps

larger than 1 cm). Approach (i) has been used for small particles, and approach (ii) for larger

additions. In the following, a brief review of the former is provided, for the sake of

completeness, and then the latter is discussed in more detail.

2.2.2.1 Mass transfer from small particles

The rate of dissolution of small particles is a function of the relative velocity between the

particles and the turbulent liquid flow. Unfortunately, that relative velocity cannot be simply

measured for erratically moving small particles due to the random velocity fluctuations

superimposed on the mean bulk flow velocities [11].

In a turbulent flow, larger eddies extract energy from the bulk flow and transfer it to

smaller eddies; smaller eddies in turn transfer their energy to even smaller eddies, and so on,

until the eddies are of the Kolmogroff length scale, and energy is dissipated by viscous

losses. During this cascade, the directional information of the large eddies (with a length

scale of the main flow) is gradually lost as the energy transfers from larger to smaller eddies

in multiple directions. Thus, at scales much smaller than the scale of the main flow, the

turbulence is isotropic, and this is referred to as Kolmogoroff’s theory of local isotropic

turbulence. For a small particle, mass transfer is a function of the flow in the small volume


25

around the particle, and so average statistical properties of the turbulent flow can be

determined by proposing a Re based on the local energy dissipation rate [85]:

p

1/3 4 3p

d 1l

dRe C

ε=

ν (2-3)

where ε is the energy dissipation rate per unit mass of liquid. To estimate the energy

dissipation rate in turbulent stirred systems, it is assumed that the rate of energy supplied is

equal to the rate of energy dissipated [11]. The energy can be supplied either by impellers or

by injecting bubbles.

The energy input rate of impellers is typically estimated by measuring the torque on the

motor [11]. For instance, for two different impellers in a turbulent stirred Al bath, the

dissolution of suspended fine particles of Fe and Mn (equivalent spherical diameter less than

0.06 cm) was correlated to pdRe [11].

Injecting gas into a liquid adds energy in two ways [10]: as gas kinetic power,

3K g c gE = 0.5ρ A V , and due to the bubbles displacing the liquid. There are various expressions

to describe the latter [9]; a widely used one calculates the work done on the surrounding

liquid by the upward movement of a known gas volume [86,87]:

lB

0

gLE 854QT log(1 )Pρ

= + . (2-4)

In the bubbling regime in ladle metallurgy, the energy due to buoyancy is dominant

[9,88], and the gas kinetic power is generally neglected. Using the rate of energy input due to

buoyancy per unit mass of liquid, Kolmogoroff’s theory of local isotropic turbulence can be

employed to correlate the mass transfer rate of particles to the fluid properties and energy

dissipation rate. For instance, a cold model study (benzoic acid/water) was used to

investigate the assimilation of Direct Reduced Iron (DRI) particles charged into the slag layer

in electric furnaces, as a function of the rate of gas energy input [89].


26

2.2.2.2 Mass transfer from large solid additions

When additions are in the form of larger pieces, as is of interest here, the associated length

scales are more similar to the dimensions of the main flow, and so the above approach cannot

be employed. This means the size of eddies which contribute to convective mass transfer lie

outside the range of isotropic turbulence, so that the convective mass transfer coefficients for

large solid additions will be affected by both the dimensions of the system and the means of

agitation. Therefore, both the bulk flow velocity and the intensity of turbulence must be

identified in the vicinity of the addition.

In a bubble-induced flow, the instantaneous flow variables are random and vary with time

either due to the pseudo-turbulence or shear-induced turbulence, even though in practice

these effects cannot be isolated [41]. In such a flow the velocity at any location can be

expressed in terms of a mean value and a fluctuating value. For instance, in cylindrical

coordinates:

r r ru u (r, , z, t) u (r, , z, t)′= θ + θ , (2-5)

u u (r, , z, t) u (r, , z, t)θ θ θ′= θ + θ , (2-6)

z z zu u (r, , z, t) u (r, , z, t)′= θ + θ , (2-7)

where ru , u θ , and zu are time-averaged velocities at the point (r, θ, z). The velocity

fluctuations are represented by ru′ , uθ′ , and zu′ . The kinetic energy of the turbulent

fluctuations per unit mass is then defined as [90]:

2 2 2r z

1k (u u u )2 θ′ ′ ′= + + (2-8)

which is half of the trace of the Reynolds stress tensor. Note that pseudo-turbulence

contributes to the kinetic energy and to the Reynolds stress tensor, and so the bubble-induced

flow can be categorized as a turbulent flow.

As mentioned earlier, in a turbulent flow, mass transfer processes are functions of the

detailed flow and turbulence characteristics near the solid addition. However, the dependence


27

cannot be easily predicted from first principles due to the complex nature of turbulent

transport [91]. Various models have been developed based on many simplifying assumptions.

As discussed extensively by Mathpati and Joshi [91], Direct Numerical Simulation (DNS)

and Large Eddy Simulation (LES) represent the state of the art for critically evaluating the

assumptions behind heat and mass transfer models, and are capable of providing detailed

information on turbulent flow structures in the vicinity of an interface. However, to date such

methods are limited to low values of Re and Sc, as they are computationally intensive.

Simpler models fall into two categories: one category (referred to as analytical) is based on

turbulent viscosity, and the other on heuristic arguments.

The so-called analytical approach generally results in correlations for transport rates with

parameters obtained from experimental results; such models are semi-empirical in nature,

and do not necessarily help to understand the underlying physics of transport near solids. On

the other hand, heuristic models are useful to visualize the transport phenomena, but are

limited in applicability. Heuristic models suggest that fluid elements, referred to as eddies,

intermittently move from a turbulent core of the flow to a solid surface, periodically

renewing the interface by introducing fresh liquid. For example, the Random Eddy

Penetration (or Surface Rejuvenation) Model [92,93] may be used to understand the

enhancement of heat and mass transfer rates by gas agitation. According to this theory,

eddies from a bulk liquid intermittently travel sufficiently close to a solid to sweep away

some of the solute in a mass boundary layer [93]. The contact time, and the distance these

eddies travel with respect to the solid/liquid interface, are random. The eddies remove

accumulated solute in the concentration boundary layer from the approach distance out to

infinity and replace it with fresh fluid [93], causing a steep concentration gradient at the

approach point. Between the random encroachment of eddies, mass transfer in the boundary

layer is controlled by diffusion [93]. The net effect is an increase in the mass transfer rate.

Although heuristic models such as this describe a picture of mass transfer near the interface,


28

they are not widely used because parameters such as the size, time and distance distributions

of the penetrating eddies are not well-developed.

Consequently, following an empirical approach that is appropriate for engineering

applications, mass transfer coefficients can be estimated by superimposing turbulent effects

on the bulk flow (Re) and fluid properties (Sc), by introducing a new dimensionless variable,

ReT [84,94]:

cT

ulRe =ν

, (2-9)

where u represents the root mean square (rms) velocity fluctuations [95,96]:

2 2 2

r zu u uu3θ′ ′ ′+ +

= (2-10)

(Note that for isotropic turbulence: 2 2 2r zu u u u 2 / 3kθ′ ′ ′= = = = ).

Similar to the pioneering work of Lavender and Pei [84], who studied heat transfer in

unidirectional grid-generated turbulent flow, mass transfer from solid additions immersed in

gas-agitated ladles is described as:

( )TSh f Sc,Re,Re= . (2-11)

In the above equation, ReT can be replaced by turbulence intensity, where the rms

velocity fluctuations are normalized by the local mean velocity [97,98]:

uTuV

= . (2-12)

A mean value of the local motion near a solid addition can be calculated by taking into

account the influence of multi-dimensional flow as in a gas-agitated system [96-98]:

2 2 2r zV(r, , z, t) u u uθθ = + + . (2-13)

Different transport correlations have been developed for gas-agitated systems; lists are

presented in Table 2-4 and Table 2-5. These correlations require flow velocities, which are

determined using one of three methodologies: analytical approaches based on an energy


29

balance; solving the Navier-Stokes equations in conjunction with a turbulence model; and

LDV.

Several studies have utilized water modeling to correlate heat or mass transfer

coefficients from solid additions to either a bulk velocity or to the local mean and fluctuating

velocities of recirculating flow generated by gas injection (similar to Figure 2-2 (a)).

Tanguchi et al. [99] used an energy balance approach to estimate the upward bulk velocity. A

comparison of their results with the Whitaker [100] correlation (applicable to turbulent flows

with low turbulence intensities) was satisfactory.

In a study of the melting rate of horizontal ice rods [101], the heat transfer coefficients

were correlated to the measured (also computed elsewhere [52]) local mean velocity and

turbulence intensity based on the mean velocity at the centerline of the ladle. Iguchi et al.

[102] showed that for a bottom blowing water jet (single-phase flow) and bubbling jet

(two-phase flow), the measured turbulence intensity in the latter flow was much higher

around a melting ice sphere. The results for both single-phase and two-phase flow were

correlated by modifying the empirical correlation of Whitaker [100], by introducing Tu as a

new dimensionless number, to account for turbulence intensities higher than 5%. However,

the turbulence intensity was calculated based on the vertical velocity of the plume centerline.

In the spirit of the Lavender and Pei correlation [84], Mazumdar et al. [97] proposed a

dimensionless equation for the dissolution of solid benzoic acid cylinders in a gas-agitated

water ladle taking into account local mean and fluctuating velocities.

Although most studies have used cold models, there have been some attempts to

investigate gas agitation on heat and mass transfer phenomena in high temperature liquid

metals, presented in Table 2-5.

Argrypoulos et al. [103] examined the melting rate of Al cylinders in liquid Al without

(single-phase flow) and with gas agitation (two-phase flow) in a bottom stirred ladle. They

used an average plume velocity as the characteristic velocity of the two-phase flow. At a Re


30

similar to that of a single-phase flow, higher heat transfer coefficients were obtained for the

two-phase flow owing to the higher velocity fluctuations.

Extending their ice/water study, Taniguchi et al. [104] compared the melting and

dissolution rates of Al spheres in Al and Al/Si baths with available correlations for heat [100]

and mass [105] transfer in room temperature fluids. The agreement was unsatisfactory

because they used the average plume velocity instead of local velocity values, neglected the

turbulence intensities, and as Argyropoulos et al. [106] argue, the classical heat transfer

correlations appropriate for high values of Pr are likely inadequate for metallic systems.

Szekely et al. [98] developed an axisymmetric numerical model for a cylindrical plume to

compute a velocity profile in an Ar-stirred steel ladle. Applying the bulk velocity values to

the modified Lavender and Pei correlation [84] for cylinders, and assuming a constant

turbulence intensity of 0.3, they demonstrated satisfactory agreement with the measured mass

transfer coefficient from graphite cylinders. Following a similar approach, but this time

prescribing a conical-shaped plume, Mazumdar et al. [107] predicted the local mean

velocities and rms velocity fluctuations in a 25 kg gas agitated melt [88], and showed that

using their previously-derived correlation for a cold system demonstrated good agreement

with the experimental data of Wright [88].

Wright [88] attempted to deduce the average plume velocities by measuring the mass

transfer rate from steel cylinders in a Fe–C melt. However, they used a correlation that had

been proposed for the dissolution of cylinders rotating at a certain peripheral velocity [108].

Thus, the analysis yielded equivalent peripheral velocities for steel cylinders based on their

dissolution rate. This, of course, did not provide information on the plume bulk velocity or

the level of overall turbulence in the gas-stirred ladle.

Finally, El-Kaddah et al. [109] dissolved graphite cylinders in a 4-tonne inductively

stirred melt of molten steel. The dissolution of the cylinders depended both on the mean

velocity and turbulence intensity. While the source of agitation was different than a


31

gas-stirred melt, the study confirmed the significance of local mean velocities and velocity

fluctuations on the mass transfer process.

In general, the variety of dimensionless correlations that have been used, and the

sometimes poor agreement with measured data [97], suggest that they may be very specific

to the conditions used to derive them. In addition, none of the above studies directly

compared mass transfer in a single-phase forced convection system to mass transfer in a

gas-agitated one. The current study was undertaken for that reason: to investigate the effect

of gas injection on a constant bulk flow, and to describe the effect of gas agitation on the

mass transfer as an increment to the bulk velocity.


32

Table 2-4: Heat and mass transfer correlations based on cold model studies of gas-agitated metallurgical ladles. Equation Description Method to estimate velocities Reference

( ) ( )1 41 2 2 3 0.4d d b 0

Nu 2

0.4 Re 0.06Re Pr

− =

+ μ μ

sphere

l pd

l

U d3.5 Re 76000

ρ≤ = <

μ0.71 Pr 380< <

( )b 01 3.2< μ μ <

Photography of tracers, macroscopic energy balance [99]

( )0.8 1 3d

Nu

0.388 Re Tu Pr

=

horizontal cylinder 2 2

l r zd

l

u u d100 Re 2000

ρ +≤ = ≤

μ

z,c

uTu 0.15u

= >

Pr 10=

Numerical solution of Navier-Stokes equation or

LDV measurements, both presented in [52]

[101]

( ) ( )1 41 2 2 3 0.4 1.36d d b 0

Nu 2

0.4Re 0.06Re Pr (1 Tu)

− =

+ μ μ +

sphere

l cd

l

u d1500 Re 16000ρ≤ = <

μ

2z,c

z,c

uTu 0.5

u

′= ≤

5.7 Pr 9.2< <

( )b 00.46 0.7< μ μ <

LDV measurements [102]

( ) ( ) ( )0.25 0.32 0.33d T

Sh

0.73 Re Re Sc

=

vertical cylinder 2 2

l r zd

l

u u d100 Re 3000

ρ +≤ = <

μ

lT

l

ud100 Re 800ρ≤ = <

μ

u 2 3k=

Sc 500=

Numerical solution of Navier-Stokes equation [97],

LDV measurements [110] [97,110]


33

Table 2-5: Heat and mass transfer correlations based on hot model studies of gas-agitated metallurgical ladles. Equation Description Method to estimate velocities Reference

( ) ( )1 41 2 2 3 0.4d d b 0

Nu 2

0.4 Re 0.06Re Pr

− =

+ μ μ

sphere

l pd

l

U d3.5 Re 76000

ρ≤ = <

μ0.71 Pr 380< <

( )b 01 3.2< μ μ <

Macroscopic energy balance [104]

( )0.621 2NSh Sh 0.374 ReSc= + 1/ 2

d1 Re Sc 500000≤ <

1 2 1 4 1 3TSh 2 0.72Re Re Sc= +

vertical cylinder 2 2

l r zd

l

u u dRe

ρ +=

μ

lT

l

udRe ρ=

μ

Numerical solution of Navier-Stokes equation for ru and zu [98]

0.33 0.644md

p

k0.1121Re Scu

− =

vertical cylinders

l pd

l

u d100 Re 10000

ρ< = <

μ Estimated from dissolution data [88]

( )0.8 1 3dSh 0.388 Re Tu Sc=

vertical cylinders 2 2

l r zd

l

u u dRe

ρ +=

μ

c,max

uTuu

=

u 2 3k=

Numerical solution of Navier-Stokes equation [109]

34

CHAPTER 3

DISSOLUTION OF SOLID Si CYLINDERS IN MOLTEN Al: SINGLE-PHASE FLOW

A study of Si dissolution in molten Al in single-phase flow is presented. We begin by

estimating the maximum time scale associated with the dissolution of Si in Al based on pure

diffusion. Then, we present experimental results of the dissolution rate of Si in Al as a

function of impurity levels of the solid Si, the Al bath temperature, and flow conditions. The

experimental results are compared with available natural and forced convection correlations.

3.1 Pure Diffusion of Si in Al

A one-dimensional model was developed to examine the pure diffusion of a Si cylinder into

liquid Al, to evaluate an upper bound on the total dissolution time. A one-dimensional, radial

mass diffusion equation was solved.

Consider a pure cylindrical Si addition (as used in the experimental study) immersed in

molten Al. The diffusion of the solid occurs due to the driving force of a concentration

gradient. The change in Si concentration at any point (r) in the infinite medium is then

determined by:

Chapter 3. DISSOLUTION OF SOLID Si CYLINDERS IN MOLTEN Al: SINGLE-PHASE FLOW

35

2

2Si/Al

1 C C 1 CD t r r r

∂ ∂ ∂= +

∂ ∂ ∂ (3-1)

The radius of the cylinder decreases as the Si diffuses, as described by the following

boundary condition,

SatSi Si Si/Al

r S(t )

dS C(C ) Ddt r =

∂−ρ = −

∂ (3-2)

Equation (3-1) was solved numerically for the Al–Si system, where S0 = 0.95 cm (the

initial radius of the specimens used in the experimental study), Sat 3SiC 504 kg m−= [19] (the

saturation concentration of Si in Al at T = 973 K), ρSi = 2331 kg m−3 [7], and DSi/Al = 1.25 ×

10−8 m2 s−1 [39]. The initial Si concentration in the liquid is assumed to be zero, and the

concentration of Si at the interface reaches the equilibrium value, SatSiC , instantaneously.

Figure 3-1 shows that the time required for the complete dissolution of the cylinder is

approximately 6 hours. This is the maximum possible total dissolution time; under natural or

forced convection conditions the overall mass transfer coefficient will be higher. The

variation of cylinder radius with time is not linear. Early on, dissolution proceeds at a fast

rate due to a higher concentration gradient (dC/dr), and then decelerates as the solute diffuses

into the infinite medium. The rate of dissolution accelerates again as the radius of the

specimen decreases. The dissolution rate is proportional to the concentration gradient at an

interface. For a given value of saturation concentration at an interface, the concentration

gradient as a function of distance from the interface decreases more sharply from a

cylindrical interface than a planar one. This is because in a cylindrical domain the area

through which the solute diffuses is proportional to r. When the specimen shrinks, this effect

leads to a higher dissolution rate as the interfacial area becomes very small.


36

Figure 3-1: Cylinder radius vs. time, considering only pure diffusion.

3.2 Experimental Methodology

An experimental setup was developed to study the effect of natural and forced convection on

the dissolution of cylindrical Si specimens.

3.2.1 Materials

Al ingots were of commercial purity with a typical composition of 99.87 wt.% Al,

0.04 wt.% Si and 0.09 wt.% Fe. Two different batches of metallurgical grade Si were used,

with higher and lower levels of impurities, referred to as the MGSi–I and MGSi–II

respectively; a few experiments were also conducted with monocrystalline electronic grade

Si, referred to as EGSi. Table 3-1 lists the main impurities in each batch, determined using

Inductively Coupled Plasma (ICP) mass spectrometry.


37

Table 3-1: Overall chemical analysis (in wt.%) of the various batches of Si used in this study.

The Si arrived in large pieces from which cylinders were core drilled to a diameter of

approximately 1.87 cm and a length of between 9 and 10 cm. The specimens were ground

with emery paper and cleaned in acetone before use1. Each Si specimen was weighed to

±0.1 gr.

In a few of the experiments, the specimen temperature was monitored by a K-type

thermocouple placed in a hole (0.6 cm diameter and 2.5 cm deep), drilled into the center top

of the cylinder. The hole was filled with tin (melting point of 231.9°C) which upon melting,

ensures proper thermal contact between the thermocouple and the specimen) drilled into the

center of the cylinder. A K-type thermocouple was also placed adjacent to the Si specimen

surface at the middle of the immersed length, recording the Al–Si interface temperature.

Thermocouple readings were unaffected by the heat of solution of Si in Al, which is low

(−1.6 kJ mol−1) [111].

3.2.2 Experimental set-up

Two different electric resistance furnaces were used.

Furnace A with stationary bath: A bilge-shaped graphite crucible (18 cm top ID, 13 cm

bottom ID, 25 cm deep) was filled with 11 kg of Al and placed in the furnace. A schematic of

1 Following this preparation procedure carefully played an important role in reducing the variability of the

experimental data. In an initial stage of this work, more than 300 Si dissolution experiments, with and without gas agitation, were carried out. To prepare the cylindrical Si specimens, the only measure taken was to use acetone to remove dirt prior to immersion; these were referred to as "as-drilled" specimens. Varying the operating parameters (i.e. temperature, velocity, gas flow rate, and immersion time), some trends could be deduced from the experimental results, but the scatter in the data was large. More accurate conclusions about the effect of the operating parameters were obtained by adding the grinding step (for more details see Appendix B). The results of the as-drilled specimens do not appear in this thesis.

Al Ca Fe Mn Ti MGSi–I 0.131 ± 0.017 0.083 ± 0.014 0.896 ± 0.136 0.012 ± 0.005 0.064 ± 0.009MGSi–II 0.081 ± 0.008 0.011 ± 0.001 0.233 ± 0.021 0.011 ± 0.002 0.026 ± 0.002

EGSi 0.001 <0.0001 0.001 <0.0001 <0.0001


38

this crucible is shown in Figure 3-2. The Si specimens were immersed in to the center of the

crucible for the natural convection experiments. The temperature of the furnace was

controlled with two K-type thermocouples connected to an electric control device, that

allowed the bath temperature to be controlled to ±2K. The bath temperature was monitored

by another K-type thermocouple immersed approximately 1.5 cm away from the crucible

wall and 3 cm beneath the Al free surface.

Figure 3-2: Schematic of a bilge-shaped crucible shows the location of thermocouples to examine the effect of preheating the specimen. All dimensions are in cm.

Furnace B with Revolving Liquid Metal Tank (RLMT): Figure 3-3 shows an image and

schematics of the RLMT (35 cm ID, 23.8 cm deep), with a usable capacity of 35 kg of Al. In

an effort to protect the crucible from the Al bath, the walls of the RLMT were painted with

boron nitride. The tank was placed inside a furnace and rotated by a variable speed motor.

The rotational speed of the tank could be controlled to ±0.5 rpm for the forced convection

experiments. A heavily insulated lid was used to minimize heat loss from the furnace top.

More detailed information on the furnace specifications is available from [112]. Through a

hole in the lid, the Si specimens were immersed at a radial distance of 13.5 cm from the

center of the tank. A single K-type thermocouple was placed at the center of the tank, 5 cm


39

beneath the molten metal free surface. The temperature of the liquid metal was controlled to

±2 K by manually adjusting the power to the furnace.

(a)

(b)

(c)

Figure 3-3: (a) The RLMT with solid Al charge, (b) top view shows the rotation direction and location of the immersed Si specimen and AA´ is perpendicular to the xy-plane and passes through the Si sample, and (c) side view with the Si sample at the AA´ plane. All dimensions are in cm.


40

3.2.3 Experimental procedure

A holding assembly was employed to immerse cylindrical specimens into the liquid Al in

both furnaces. For the RLMT, when the liquid Al reached the desired melt temperature, the

tank was rotated for a sufficient length of time prior to cylinder immersion to attain solid

body rotation. That time was estimated by ( )0.52AlH /ν ω [113], where H is the height of

liquid, νAl is the kinematic viscosity of the liquid Al, and ω is the RLMT rotational speed.

Approximately 11 min was required to spin up the tank to 1 rpm.

Once the Al reached the desired temperature and rotational speed, a Si cylinder was

immersed 8 cm into the liquid; after a certain duration, the cylinder was withdrawn and

allowed to cool. The solid Al that remained attached to the sample was removed by using a

38 vol.% HCl solution, which left the Si intact [114]. Then the partially dissolved Si

specimen was weighed to ±0.1 gr to determine the dissolved mass in the liquid Al. The data

presented in this thesis usually represents three experiments. The standard deviation of the

dissolved fraction measurements is represented by error bars.

With each Si cylinder immersion the Si level in the liquid Al increased. Whenever the Si

level in the Al bath exceeded 1.5 wt.% Si, the bath was discarded and replaced.

3.3 Results and Discussion

The results are presented in two parts: Si dissolution experiments under natural convection

conditions (without mechanical stirring) in Furnace A, and Si dissolution experiments under

forced convection conditions (by rotating the liquid metal) in Furnace B.

3.3.1 Natural convection experiments

The bath temperature was set to superheats (SPH) of 20, 40 60, 80 and 100 K for different

experimental runs. Figure 3-4 depicts typical MGSi–I samples after immersion for 3 min at


41

various bath superheats, and illustrates that after dissolution the sample lengths remained

unchanged.

Figure 3-4: MGSi–I specimens after natural convection dissolution for 3 min in an Al bath at various superheats.

Figure 3-5 depicts the dissolved fraction of MGSi–I specimens as a function of bath

superheat after 3 min immersion. The results show that the dissolved fraction increases

significantly with increasing bath superheat. The dissolution of the MGSi–I specimen at the

lowest superheat of 20 K is negligible, while approximately 50% of the sample dissolved at

the highest superheat of 100 K. In the industrial practice of Al–Si alloy making, the Al bath

temperature is typically in the range of 973-1013 K (700-740°C). Therefore, in the remainder

of this chapter, experimental data is only presented for superheats of 40 K and 80 K.


42

Figure 3-5: The effect of bath superheat on the dissolved fraction, md/mi, of MGSi–I specimens after natural convection dissolution for 3 min.

3.3.1.1 Heat transfer after immersion

When a Si addition, initially at room temperature, is first immersed into the liquid metal, an

Al shell solidifies around the cylinder. In the experiments, as shown in Figure 3-6, the

formation of an Al shell was confirmed by removing the solid Si from the Al bath after a

relatively short immersion time. As can be seen, the Al shell forms within a few seconds and

then melts back as the immersion time increases. The heat absorbed by the solid Si cylinder

upon immersion leads to a local temperature drop in the melt, that forms the shell. As the

temperature of the Si increases, the solidified layer melts back and eventually thermal

equilibrium is established between the Si cylinder and the liquid Al. Referring again to

Figure 3-6, as the shell melts back, it is likely that some of any remaining shell slips off of

the cylinder during withdrawal. As such, the portion of the Al shell that remains attached to

the cylinder upon withdrawal is likely less than the amount that was on the cylinder while

still submerged in the melt.


43

Figure 3-6: Formation of an Al shell on MGSi–I cylinders immersed for short periods in an Al bath at SPH = 40 K.

To investigate the influence of heat transfer after immersion on the onset and rate of

dissolution, experiments were run where the Si cylinder (and the specimen holding assembly)

was preheated above the Al free surface. The bath temperature, Al/Si interface temperature,

and the internal temperature of the cylinder were monitored, as shown in Figure 3-2.

Figure 3-7 (a) and (b) show typical temperature measurements without and with

preheating, respectively. The insets magnify the thermocouple readings near the initial bath

temperature. Without preheating, the specimen prior to immersion was at room temperature,

indicated by points A and F in Figure 3-7 (a), while the specimen centerline temperature

reached 793 K (520°C) after preheating for 3 min, shown by segment F´F´´ in Figure 3-7 (b).

Note that in Figure 3-7 (b), the kink at about 230°C on the Si centerline temperature is

associated with the melting point of the tin used to fill the specimen hole.

Figure 3-8 compares the dissolved fraction of Si with and without preheating at

SPH = 40 K. An extrapolation of the experimental data (linear regression) indicates that

preheating reduced the incubation time (the time to the onset of dissolution) from about 66 s


44

to about 10 s. The preheating not only shortens the incubation time, but also increases

slightly the subsequent dissolution rate by avoiding the initial large decrease in the liquid Al

temperature in the vicinity of the Si sample, as illustrated in the insets of Figure 3-7 (a) and

(b). Without preheating, the Al/Si interface temperature is 6 K lower than the liquid Al initial

temperature even after 3 min (point E in Figure 3-7 (a)); with preheating, the Al/Si interface

temperature is only 2 K lower than the initial bath temperature (point E´ in Figure 3-7 (b)).

Finally, Figure 3-7 (b) shows that the temperatures at the Al/Si interface and at the

specimen center (shown by segments A´B´B´Ć´DÉ´ and F´F´´G´HÍ´, respectively) do not

exceed the initial temperature of the Al bath. This confirms that there is no appreciable

exothermicity involved in the dissolution process.


45

(a)

(b)

Figure 3-7: Temperature history of a MGSi–I cylinder immersed into liquid Al (a) initially at room temperature, (b) preheated for 3 min prior to immersion.


46

Figure 3-8: Comparison of the dissolved fraction with and without preheating, for MGSi–I at SPH = 40 K.

3.3.1.2 Isothermal mass transfer

The isothermal dissolution of Si makes the adjacent liquid denser, because Si T( ρ C ) =0.14∂ ∂

[116]. This means that upon dissolution, the fluid next to the Si cylinder flows downward,

which establishes a natural convection flow.

Since Si dissolution in liquid Al is LPD-controlled [39], the following equation describes

the steady-state rate of change of the cylindrical specimen mass at an instantaneous cylinder

radius:

( )2

Si N Sat bm Si Si

d r lk (2 r l) C C

dtρ π

⎡ ⎤= − π −⎣ ⎦ (3-3)

Further assuming that the Si bulk concentration bSiC =0 , and Siρ and l are constants,

Equation (3-3) reduces to:

Sat

N Sim

Si

Cdr kdt

= −ρ

(3-4)


47

Under the assumption that there is a negligible effect of curvature on the mass transfer

coefficient, Nmk , the radius of the Si specimen will vary according to the following equation:

Sat

N Si0 m

Si

Cr r k t= −ρ

(3-5)

To estimate the natural convection mass transfer coefficient, Nmk , a general form of a

dimensionless correlation is employed:

( )mm ,lSh n Gr Sc= , (3-6)

where Grm,l is defined as [117]:

3 Sat b

l Si T Si Sim,l 2

l l

g( C ) l (C C )Gr ∂ρ ∂ −=

ρ ν, (3-7)

and

l

Si/Al

ScDν

= . (3-8)

In the current study 8 8m,l5.5×10 < Gr < 7.4×10 , and 42 > Sc > 29. For this range of Sc,

the momentum boundary layer is thicker than the mass boundary layer and accordingly the

fluid properties are evaluated at the bulk concentration [108,118]. For 9 12m,l10 < Gr Sc <10 ,

two independent experimental studies [119,120] also involving mass transfer in liquid metals

suggest values of n that vary from 0.11 to 0.129, and m = 1/3, and so we adopt these values

as well.

As dissolution proceeds, the specimen radius decreases, and so the thickness of the mass

boundary layer changes with time and is truly transient [10]. In addition, when the densities

of solid and liquid phases are different, this induces a fluid velocity normal to the moving

interface (i.e. transpiration flow) [115]. In this thesis, these two effects are neglected when

predicting mass transfer rates:

(i) The effect of specimen shrinkage on the mass transfer rate is relatively independent of

bulk flow velocity, and has been characterized by the ratio of interface velocity to the mean


48

mass transfer coefficient with no transpiration and constant specimen radius [115]:

( ) mdr / dt kλ = − . The mass transfer coefficient for a shrinking specimen at large values of λ

will be lower than for a specimen of constant radius. When this ratio is large the solute

accumulates near the interface. In the current study 0.22 < λ < 0.25, for which the results of

[115] suggest that neglecting the effect of specimen shrinkage will overpredict the mass

transfer coefficient by less than 15%.

(ii) As mentioned in Chapter 1, solid Si in liquid Al is neutrally buoyant, and so the effect of

transpiration is negligible.

The experimental results of dissolved fraction were converted into changes in average

radius. A dimensionless cylinder radius after immersion (non-dimensionalized by the initial

radius of the cylinder) was calculated as:

d

0 i

mr 1r m= − (3-9)

Figure 3-9 shows comparisons of the predicted and measured cylinder radius versus

immersion time, at different bath superheats, where the incubation times determined from the

experimental results have been incorporated into the model predictions. The correlation

clearly overpredicts the rate of dissolution of the MGSi–I, while the rates of dissolution of

the MGSi–II and EGSi are much better predicted. A detailed discussion of the effect of

impurities is presented in the next section. Regardless of Si purity, increasing the temperature

of the liquid Al, which increases the saturation concentration at the solid/liquid

interface, SatSiC , increases the dissolution rate of the specimen, as shown in Figure 3-10.


49

(a)

(b)

Figure 3-9: Comparisons between measured and predicted natural convection mass transfer for liquid Al at (a) SPH = 40 K and (b) SPH = 80 K.


50

3.3.1.3 Effect of impurities

Figure 3-10 displays the effect of Al bath superheat on the dimensionless radius after 3 min,

for the three types of Si specimens: MGSi–I, MGSi–II, and EGSi. The specimens with fewer

and no impurities, MGSi–II and EGSi respectively, dissolved faster in liquid Al than the

specimens with more impurities. Similar trends were observed by Yeremenko et al. [32] who

showed that 99.994% pure polycrystalline Mo dissolved more quickly in molten Al than

99.95% pure Mo, and that there was no difference in the dissolution rates of mono and

polycrystalline Mo of the same purity.

Figure 3-10: Effect of bath superheat on the dimensionless radius, r/r0, of MGSi–I, MGSi–II and EGSi specimens immersed for 3 min in liquid Al under natural convection.

Further support for the finding that the level of impurities in an alloy may impact on

dissolution rate is provided by another study involving liquid steel as solvent. In that case,

two different grades of Ferroniobium (35 wt.% Fe, 65 wt.% Nb) with very different levels of

impurities dissolved at very different rates [121]. The FeNb with lower levels of impurities

dissolved more quickly than the FeNb with more impurities. The author postulated that the


51

impurities form various high melting point phases, that retard the FeNb dissolution rate

[121].

To characterize the distribution of impurities in the MGSi–I and MGSi–II samples, the

microstructure of a number of Si specimens was examined by Scanning Electron Microscopy

(SEM) equipped with Energy Dispersive X-ray (EDX) spectroscopy. (A similar analysis of

the EGSi microstructure found no distinct phases.) Figure 3-11 and Figure 3-12 illustrate

secondary electron images of MGSi–I and MGSi–II specimens, respectively. In both cases,

the microstructures shown are prevalent over the entire specimen sections. Figure 3-11 (b)

and Figure 3-12 (b) depict a higher magnification of the outlined areas in Figure 3-11 (a) and

Figure 3-12 (a), respectively.

(a) (b)

Figure 3-11: (a) Secondary electron image of a MGSi–I specimen prior to immersion, (b) a higher magnification of the outlined area in (a).

+3

+2

+1


52

(a) (b)

Figure 3-12: (a) Secondary electron image of a MGSi–II specimen prior to immersion, (b) a higher magnification of the outlined area in (a).

The corresponding results of the EDX analysis are listed in Table 3-2, and show

randomly distributed inclusions contain impurities that the ICP analysis also detected

(Table 3-1). The dominant elements are consistent with those found by other studies on

metallurgical grade Si [122,123]. However, the compositions vary from those in the

literature, as they do between MGSi–I and MGSi–II. The inclusions are primarily silicide

phases with formation temperatures above 1255 K (982°C), as reported by Meteleva-Fischer

et al. [123]; this temperature is higher than the liquid Al temperature in the current

experiments. Thus, these phases do not melt in liquid Al, but rather assimilation must take

place by the dissolution of the constituents into the molten metal. Figure 3-13 shows a

backscattered electron image of Al attached to a dissolving MGSi–I specimen, that was

obtained by quenching in water from 973 K to 293 K. This figure illustrates that the

inclusions do not melt (in accordance with the above discussion) or dissolve more quickly

than Si, but rather the inclusions migrate into the molten Al as the surrounding Si dissolves.

+1

+2

+3


53

Figure 3-13: Backscattered electron image of a MGSi–I specimen with an attached Al after quenching in water from 973 K to 293 K.

As presented in Table 3-2, different compositions of similar elements were identified in

the MGSi–I and MGSi–II batches. The area fraction of the inclusions is higher in MGSi–I

(implying a higher level of impurities) than in MGSi–II, as seen in Figure 3-11 (a) and

Figure 3-12 (a). Image analysis of the microstructures at a low magnification of ×30 showed

that the area fraction of inclusions was 4.6 ± 0.5 % in MGSi–I and only 0.8 ± 0.2 % in

MGSi–II.

Table 3-2: Results of Energy Dispersive X-ray analysis at points shown in Figure 3-11 (b) and Figure 3-12 (b).

Batch Element Point

1 2 3 Composition wt.%

MGSi–I

O 0.7 – – Al – 2.8 1.1 Si 99.3 50.0 32.2 Ca – 0.5 – Ti – – 29.0

Mn – – 0.9 Fe – 46.7 36.8

MGSi–II

O 0.4 – – Al – 23.9 4.5 Si 99.6 30.6 27.8 Ca – 7.7 0.6 Ti – – 29.1

Mn – 1.3 2.1 Fe – 36.5 35.9

Attached Al Solid Si


54

The major elemental impurities, including Fe, Mn, and Ti, have lower diffusion

coefficients in liquid Al than Si [23,39]. The uneven presence of these impurities as

inclusions obstructs the dissolution of the Si matrix. In other words, Si cannot dissolve

evenly from a specimen surface, resulting in the lower dissolution rate of the MGSi–I

cylinders, as well as rougher surfaces after dissolution, illustrated in Figure 3-14. Although

the impurity levels of the two batches are not dramatically different, the presence of the

impurities likely impedes the development of a two-dimensional convective flow along the

specimen length, and alters the dissolution pattern. The mass boundary layer is likely more

local and three-dimensional at a solid Al/Si interface with more inclusions, because when

liquid Al encounters an inclusion at the specimen surface, it will not dissolve as quickly as

the solid Si. Instead, liquid Al must dissolve the Si surrounding the inclusion, until the

inclusion transfers into the liquid Al, as shown in Figure 3-13.

The effect of impurities is more pronounced at a lower superheat due to the larger

difference between the diffusion coefficients of Si and the impurities in liquid Al. For

example, according to Ershov et al. [39], DSi/Al/DFe/Al decreases from 6 to 4.5 as the Al bath

temperature increases from 973 K (700°C) to 1013 K (740°C). This is qualitatively consistent

with the decrease in the variation of r/r0 with increasing bath superheat, as depicted in

Figure 3-10.


55

Figure 3-14: Si specimens after natural convection dissolution for 3 min at SPH = 80 K; captions on top indicate the batch of Si.

The dissolved surfaces become smoother as the impurities decrease, as shown in

Figure 3-14. This clearly indicates that reducing the level of impurities provides a more

accessible surface for the diffusion of Si. The necking at the top of the samples is most

evident for the EGSi specimen. This confirms that the liquid Al becomes denser upon

dissolution of Si, ( )l Si Tρ C > 0∂ ∂ [116], and that the leading edge of the natural convection

mass transfer boundary layer is located at the top of the specimen. Figure 3-14 also shows

that the local dissolution rate is nearly constant along the MGSi–II and EGSi specimen

surfaces. Natural convection mass transfer from a vertical cylinder in a turbulent regime

produces uniform dissolved surfaces, as was also observed during the dissolution of steel

specimens in a Fe–C melt [88]. The value of m,lGr Sc for the results presented here is in the

turbulent range, which is taken into account by the exponent m = 1/3 in Equation (3-6), and

indicates that the dissolution rate is independent of the immersed length.


56

3.3.2 Forced convection experiments

The RLMT was rotated at 1, 2.5, 5, 7, 10, and 15 rpm, and the bath superheat set to 40 K and

80 K. When rotating the liquid Al in the RLMT, the flow pattern at steady state is a solid

body rotation with zero velocity at the center of the tank and maximum velocity at the wall.

The tangential velocity of liquid metal at the position of the Si cylinder can be calculated as:

rot rotSi Siu (r r ) rθ = = ×ω (3-10)

where rotSir = 13.5 cm is the distance from the center of the tank to the point of immersion of

the cylinder center line. Therefore, the aforementioned rotational speeds of the RLMT

correspond to tangential velocities of 1.4, 3.5, 7.0, 9.9, 14.0, and 21.0 cm s−1, respectively.

These velocities change by only ±6% across the initial cylinder radius, and so from here on

the tangential velocity at the point of immersion is simply referred to as the bulk velocity, Ub.

Under forced convection conditions, two sets of tests were carried out, one varying the

bulk velocity while immersing specimens for 3 min, and the other varying the immersion

time at a constant bulk velocity. Figure 3-15 depicts the dissolved fractions of MGSi–I and

MGSi–II after 3 min at various bulk velocities, with liquid Al at 40 K and 80 K SPH. These

figures indicate that the dissolution rate increases in tandem with bulk velocity and bath SPH.

Figure 3-16 (a) and (b) show r/r0 versus time for the dissolution of MGSi–I at a bulk velocity

of 7.0 cm s−1 compared to natural convection dissolution, at bath superheats of 40 K and

80 K, respectively. The incubation time is not significantly affected, but the rate of

dissolution clearly increases by the forced convection.


57

(a)

(b)

Figure 3-15: Effect of bulk velocity on the dissolved fraction after 3 min immersion, (a) SPH = 40 K and (b) SPH = 80 K.


58

(a)

(b)

Figure 3-16: Dissolution of MGSi–I under natural and forced convection conditions; (a) SPH = 40 K and (b) SPH = 80 K.


59

3.3.2.1 Local variation of dissolution rate

Although the average mass transfer rate from the entire surface of a specimen is of primary

interest, the dissolution patterns of dissolved specimens reflect the local transfer rates.

Figure 3-17 demonstrates that the dissolution rate is highest at the stagnation point, and

lowest at the back of cylinder. It is also evident that the higher the Reynolds number

bd AlRe (= U d ν ) , the higher both the local and average transfer rates. The variation of the

local mass transfer around the periphery of a cylinder has been experimentally studied by

several investigators [124,125]. Among those, Bošković-Vragolović et al. [125] used the

adsorption method to measure mass transfer rates from a cylinder for 38 < Red < 3614. They

showed Sh to be a maximum at the stagnation point and decrease significantly around the

cylinder, in agreement with the current findings.

Figure 3-17: Variation of local dissolution of MGSi–II cylindrical specimens in a cross flow of liquid Al at various bulk velocities (SPH = 40 K, immersion time = 3 min).

3.3.2.2 Comparison with a forced convection correlation

An estimate of the dissolution of a Si cylinder in a cross flow of liquid Al can be obtained

from Equation (3-4). However, in this case a forced convection mass transfer coefficient


60

must be estimated from a reliable dimensionless mass transfer correlation. Such a correlation

has been proposed by Churchill and Bernstein using heat and mass transfer data [126]:

( )

4/55/81/2 1/3d d

1/42/3

0.62 Re Pr ReNu 0.3 12820001 0.4 Pr

⎡ ⎤⎛ ⎞= + +⎢ ⎥⎜ ⎟⎝ ⎠⎡ ⎤ ⎢ ⎥⎣ ⎦+⎣ ⎦

(3-11)

This equation is applicable for Re Pr > 0.2. The authors [126] presumed that

Equation (3-11) also holds for mass transfer, with Nu replaced by Sh and Pr by Sc. The

applicability of the mass transfer version of Equation (3-11) for the dissolution of horizontal

cylinders of benzoic acid in water has been established [127].

In the current study, the applicability of Equation (3-11) was examined. The

characteristic length for dRe is the diameter of the Si addition (for an initial diameter d0,

0d510 < Re < 3800 ). As the dissolution of the Si specimen progressed, the diameter

decreased, and so Red decreased accordingly.

Figure 3-18 displays a comparison of experimental data with estimates of the

dimensionless radii based on Equation (3-11), that only accounts for forced convection mass

transfer. The correlation predicts the MGSi–II data reasonably well, while the MGSi–I

cylinders dissolved much more slowly. The agreement between experimental and estimated

radii is especially good at higher liquid Al velocities. At lower velocities, the correlation

predicts a slower rate of dissolution than was measured experimentally, presumably due to

the fact that Equation (3-11) does not take into account natural convection effects that are

relatively more dominant at lower liquid Al velocities (i.e. < 3 cm s−1).


61

Figure 3-18: Comparison of experimental and estimated dimensionless radii for pure forced convection mass transfer from vertical Si cylinders immersed for 3 min in a liquid Al cross flow.

3.3.2.3 Comparison with a combined natural and forced convection correlation

For the vertical cylinders immersed in the RLMT, the buoyant force is normal to the cross

flow. Thus, the combined natural and forced convection is three-dimensional, for which a

mass transfer correlation is unavailable. A correlation for this type of combined convection

was developed as part of this work.

The characteristic length associated with the forced convection is the cylinder diameter,

and with the natural convection is the cylinder length. An asymptotic solution for buoyancy

effects on a boundary layer along an infinite cylinder in a cross flow [128] suggests that the

strength of the two convection regimes on heat or mass transfer is determined by the

magnitude of ( ) ( )4 2m,l dd l Gr Re⎡ ⎤

⎣ ⎦ . This criterion is different than the Richardson number

( )2m,d d= Gr Re , which is the expansion parameter for combined free and forced convection


62

from a horizontal cylinder in cross flow [129], and even ( )2m,l lGr Re , which quantifies the

effect of buoyancy on forced convection along a vertical cylinder [130].

The values of Grm,l and 0dR e for the experiments of this study are given in Table 3-3.

Notice that the values of ( ) ( )4 2m,l dd l Gr Re⎡ ⎤

⎣ ⎦ are equal to or larger than unity at bulk

velocities of 1.4 and 3.5 cm s−1, which implies that natural convection must be taken into

account to evaluate the mass transfer from the dissolving specimens at these velocities.

A general combining law for transfer processes which vary uniformly between two

known limiting solutions is given by [131]:

p p 1/pZ (X Y )= + , (3-12)

where X and Y are the limiting solutions for asymptotically small and large values of an

independent variable (i.e. ( ) ( )4 2m,l dd l Gr Re⎡ ⎤

⎣ ⎦ ). For the current problem the mass transfer

coefficient when the combined convection variable is zero is given by FmX = k . When the

independent variable goes to infinity, NmY = k represents the asymptotic solution. As for the

exponent, [132] recommends p = 4 for spheres and for cylinders in a flow normal to the

buoyant force. Hence, incorporating the mass transfer coefficient for combined free and

forced convection in Equation (3-4) yields:

Table 3-3. Dimensionless parameters involved in the combined convection from a Si vertical cylinder in liquid Al cross flow.

L (cm)

d0 (cm)

SPH (K) Sc Grm,l

Ub

(cm s−1) 0dRe ( ) ( )0

4 20 m,l dd l Gr Re

8 1.87

40 42 5.5 x 108 1.4 510 6.5 3.5 1260 1.0 7.0 2530 0.2 9.9 3540 0.13

80 29 7.4 x 108 1.4 540 7.4 3.5 1360 1.2 7.0 2710 0.3 9.9 3800 0.15


63

( ) ( )

Sat1/44 4N F Sim m

Si

Cdr k kdt

⎡ ⎤= − +⎢ ⎥⎣ ⎦ ρ (3-13)

Figure 3-19 shows the estimated change in radius based on the combined convection

correlation, compared to the experimental data, which now predicts the dissolution of the

MGSi–II specimens within the experimental error even at lower bulk velocities.

Figure 3-19: Comparison of experimental and estimated dimensionless radii for combined convection mass transfer from vertical Si cylinders immersed for 3 min in a liquid Al cross flow.

Figure 3-20 shows the dimensionless radius as a function of time at a bulk velocity of

7.0 cm s−1 using the combined convection correlation. (Recall that the correlation estimates

include the experimentally-measured incubation times.) The correlation predicts the

acceleration of dissolution with time that was observed in the experiments, by incorporating

the change in cylinder diameter when calculating the forced convection mass transfer

coefficient. The acceleration of the shrinkage rate with decreasing radius was also observed

for the melting of steel scrap specimens in liquid steel [133]. As expected, the correlation

underpredicts the MGSi–I experimental data for various superheats, due to the presence of


64

impurities, but predicts the dissolution of the higher purity MGSi–II with very good

agreement.

Figure 3-20: Comparison of experimental and estimated dimensionless radii for combined convection mass transfer from vertical Si cylinders immersed in a liquid Al cross flow at a bulk velocity of 7 cm s−1.

3.4. Relationship Between Bath Temperature and Bulk Velocity

For the ranges of bath SPH and bulk velocity examined, the two effects can be correlated via

mass transfer coefficients. The experimental mass transfer coefficients were deduced for

natural and forced convection from the dissolution of specimens immersed for 3 min,

incorporating the incubation times:

0 Sim Sat

Si

(r r)kt C− ρ

= . (3-14)

Figure 3- 21 superimposes plots of forced convection mass transfer coefficients vs. bulk

velocity (on the top abscissa) at two SPH, and natural convection mass transfer coefficients

vs. SPH (on the bottom abscissa). To demonstrate the use of this graph; consider the


65

following example. The mass transfer coefficient associated with natural convection at SPH

= 100 K (TT'), mk = 8.2 × 10−5 m s−1, can also be obtained at lower SPHs, of 40 K and 80 K,

by introducing bulk velocities of 6.1 (LL') and 3.9 cm s−1 (HH'), respectively. This figure is

of practical importance as it quantifies the extent to which mechanical stirring and increasing

bath temperature each contribute to a higher dissolution rate.

Figure 3- 21: Mass transfer coefficient vs. SPH (shown on the bottom abscissa) superimposed on mass transfer coefficient vs. bulk velocity (shown on the top abscissa) (MGSi–II, immersion time = 3 min).

3.5 Summary

The dissolution of solid Si in liquid Al was studied as a function of bath temperature, fluid

flow conditions, and Si purity. The delay in the onset of mass transfer (incubation time) was

reduced by preheating the addition prior to immersion. With no external stirring, the

dissolution process occurred under turbulent natural convection. The experimental data for

high purity Si showed a good agreement with a dimensionless correlation for vertical

cylinders; the dissolution was slower for Si with a higher level of impurities. For the forced


66

convection conditions, the mass transfer rate was fitted with a dimensionless correlation for a

cylinder in cross flow, and at higher bulk velocities, predicted the experimental results very

well. At lower bulk velocities (< 3 cm s−1) natural convection effects cannot be neglected. A

newly-developed correlation for combined forced and natural convection yields very good

predictions of the dissolution of high purity Si at all bulk velocities. This correlation offers a

method to estimate the mass transfer coefficient in similar liquid metal systems,

8 8m,l5.5×10 < Gr < 7.4×10 ,

0d510 < Re < 3800 , and 29 < Sc < 42 .

67

CHAPTER 4

FLUID DYNAMICS OF GAS-AGITATED LIQUID

This chapter considers the fluid dynamics of a gas-agitated tank. First, bubbling behavior

(size, frequency and trajectory) in non-rotating and rotating liquids is considered, both in an

air–water system, and based on observations of the molten Al free surface and measurements

of N2 bubble frequency. Then, CFD simulation results are presented to estimate

bubble-induced velocities in the opaque liquid Al.

4.1 Bubble Formation and Trajectory in an Air–Water System

Air–water experiments were conducted to characterize the two-phase flow (e.g. bubble

plume vs. individual bubbles) that results from top lance injection. The experiments were

carried out to investigate the formation and trajectory of air bubbles in water, as a function of

gas flow rate and the bulk velocity of the water. To perform the experiments, a transparent

acrylic tank filled with water was placed on a rotating table, shown in Figure 4-1. Top lance

injection (Ti tube with 4.37 mm ID and 6.25 mm OD) was used to blow air bubbles 10 cm

below the free surface of an 11 cm deep bath.

CHAPTER 4. FLUID DYNAMICS OF GAS–AGITATED LIQUID

68

(a)

(b)

(c)

Figure 4-1: (a) The transparent water tank on a rotating table, (b) top view shows the rotation direction and location of the gas injection lance, and AA´ represents a plane perpendicular to the xy-plane passing through the lance, (c) side view of the water tank and the lance at AA´. All dimensions are in cm.

A pressure transducer was used to measure the frequency of bubble formation at the lance

exit. When no gas was blown the output voltage from the transducer was constant. Bubble

frequency was measured by processing a uniform pattern of pressure fluctuations in the gas


69

delivery line caused by the formation and release of bubbles. Figure 4-2 shows typical output

voltage variations vs. time for gas flow rates up to 1.0 SLPM. For a given gas flow rate, QS,

and bubble frequency, f, and assuming spherical bubbles, the equivalent diameter of each

bubble, db, is:

1/3

S 0 lb

6Q P Tdf P 273

⎛ ⎞= ⎜ ⎟π⎝ ⎠. (4-1)

This equation is more appropriate at lower gas flow rates [44], (e.g. 0.3 and 0.6 SLPM in

Figure 4-2), where each repeating pattern is clearly associated with a single bubble.

Figure 4-2: Typical output voltage of the pressure transducer used to measure bubble formation frequency (air–water system, bulk velocity = 0).

The frequency of bubble formation was also determined using a high speed camera (210

frames per second). The videos illustrate not only bubble formation but also bubble-bubble

interactions. Three different regimes were detected. In the first regime (< 0.5 SLPM,

Figure 4-3), individual bubbles form and rise to the free surface without coalescing or

breaking up.


70

Figure 4-3: Formation and rise of single bubbles in the air–water system (gas flow rate = 0.3 SLPM, bulk velocity = 0).

In the second regime (0.5 SLPM < QS < 0.7 SLPM, Figure 4-4), bubbles form

individually at the lance exit but coalesce during rise. The distance between two consecutive

bubbles decreases as the bubbles rise because the trailing bubble rises in the wake of the

leading one. This is consistent with [134], which shows that for a chain of bubbles rising

through a quiescent liquid, the velocity of a bubble is equal to the velocity of an isolated

bubble in a liquid of infinite extent, plus the wake velocity of bubbles ahead of it.

Lance

Ruler


71

(i) first bubble forms (ii) second bubble forms

(iii) two bubbles coalesce

Figure 4-4: Formation of single bubbles and coalescence of two consecutive bubbles during rise in the air–water system (gas flow rate = 0.6 SLPM, bulk velocity = 0).

In the third regime (0.7 SLPM < QS < 1.0 SLPM, Figure 4-5), two consecutive bubbles

combine into a single bubble near the exit of the lance. This affects the shape of the bubbles:

the first bubble is flatter while the second one elongates at the lance exit. This phenomena is

referred to as formation of "doublets" and is caused by the reduced pressure in the wake of

the leading bubble [44,46].


72

(i) leading bubble forms (ii) trailing bubble forms

(iii) two bubbles coalesce (iv) forming a single bubble

Figure 4-5: Formation of doublets in the air–water system (gas flow rate = 1.0 SLPM, bulk velocity = 0).

From the videos, bubble size was estimated with a standard deviation less than ±7% db,

and is plotted vs. gas flow rate at the lance exit in Figure 4-6. In the first regime, all the

bubbles are the same size at a given gas flow rate. In the second regime, the trailing bubbles

are slightly smaller than leading ones (less than 7% by diameter, and the size of the leading

bubble is plotted in Figure 4-6). In the third regime, the trailing bubble is 15‐20% smaller (by

diameter) than the leading bubble, but then the two bubbles coalesce at the lance exit to form

a larger bubble. Goda et al. [55] also measured bubble formation frequency in water using

top lance injection and suggested a correlation for a range of gas flow rates


73

0.3 LPM < Q < 3 LPM with −20% to +30% scatter, but did not comment on bubble

coalescence. As seen in Figure 4-6, in the absence of coalescence at the lance exit, the

correlation adequately predicts the current experimental results, where at higher flow rates

the correlation underpredicts the bubble size by neglecting the coalescence. Nevertheless, the

coalescence of air bubbles in water at the exit of a top injection lance has also been reported

by Tseuge et al. [54] at gas flow rates higher than a "critical value".

Figure 4-6: Equivalent bubble diameter vs. gas flow rate in the air–water system.

The transition from single bubbles to doublets (regime III) with increasing gas flow rate

helps interpret the pressure transducer data. At lower gas flow rates, Figure 4-2 shows peaks

of equal height, while at higher flow rates, the peaks are uneven which implies bubble size

variation. One would underestimate the size of bubbles in the liquid by processing only the

output voltage data, as the coalescence of bubbles at the lance exit or during rise would not

be taken into account.

The effect of a liquid cross flow at 20 cm s−1 on bubble size at various gas flow rates is

presented in Figure 4-7. Due to the lateral force, bubble size decreases (in agreement with the

experimental study of [55]) and the transitions between the bubble formation regimes shift to


74

lower flow rates. As seen in Figure 4-7, when the bulk velocity is 20 cm s−1, the transition

from single bubbles to doublet formation at the lance exit occurs at a lower gas flow rate (0.5

SLPM) than in the absence of a bulk flow (0.7 SLPM).

Figure 4-7: Equivalent bubble diameter in the air–water system with and without cross flow.

Figure 4-8 further illustrates the effect of cross flow, by plotting bubble size vs. Relance,OD,

the liquid Reynolds numbers at the lance exit. At 0.3 SLPM single bubbles formed, and at 0.8

SLPM doublets formed, independent of bulk velocity. For these cases, the bubble size

monotonically decreases with increasing bulk velocity.


75

Figure 4-8: Effect of bulk liquid velocity on the equivalent bubble diameter in the air–water system (db normalized by the bubble diameter when the bulk velocity = 0).

Bubble trajectory during rise depends on bubble size and bulk flow velocity; bubbles

nevertheless do not wet the lance. Without a bulk velocity, smaller single bubbles of

ellipsoidal shape wobble along a zig-zag path, in agreement with [135]. The path of larger

doublets is rectilinear with more dramatic changes in shape. In cross flow, the rising bubbles

move laterally and undergo large deformation, particularly at higher gas flow rates. As seen

in Figure 4- 9, bulk velocities of 10, 20, and 30 cm s−1 result in lateral displacements of

3.6 dlance,OD, 7.1 dlance,OD, and 9.1 dlance,OD respectively, by the time the bubbles reach the free

surface.


76

Bulk velocity = 0 Bulk velocity = 10 m s−1

Bulk velocity = 20 m s−1 Bulk velocity = 30 m s−1

Figure 4- 9: Comparison of bubble trajectories at various bulk velocities (gas flow rate = 1 SLPM).

4.2 Bubble Formation and Trajectory in a N2–Al System

The opacity of liquid Al precludes the direct observation of the formation and trajectory of

bubbles similar to the air–water system, and so we only measured the pressure fluctuations in

the gas delivery line, and video recorded the free surface of the liquid Al.

It should be noted first that suggesting relationships to relate bubble behavior in the air–

water and N2–Al systems is complex and beyond the scope of the current study, for two

reasons. First, as mentioned in Section 2.2.1.1, bubbles wet the injection lance in liquid Al,

but they do not in water; this significantly changes the formation and detachment

9.1 dlance,OD

3.6 dlance,OD

7.1 dlance,OD


77

characteristics of bubbles in the two liquids. Second, for water, the heat transfer between the

gas and the liquid is negligible; therefore, knowing the gas temperature at the lance entrance,

the actual gas flow rate can be accurately calculated from Equation (4-1). For liquid Al, the

temperature of the gas at the lance exit can only be approximated by assuming heat transfer

between the immersed cylindrical lance and the liquid Al as a function of gas flow rate. This

introduces uncertainty into the gas flow rates calculated at the lance exit (i.e. +5-8 % in the

reported values for every ΔT = +50 K error in the estimated exit temperature). Nevertheless,

the air–water experimental results are employed to interpret the pressure transducer data and

the observations of the liquid Al free surface.

To carry out two-phase flow experiments in molten Al, the gas flow rate of industrial

grade N2 was controlled to 0.01 SLPM using a mass flow controller. Tygon tubing delivered

N2 to the top of a straight Ti lance (the same used in the air–water experiments) immersed

10 cm below the molten Al surface (L/H = 2/3), as shown in Figure 4-10. The Ti lance was

coated with boron nitride of approximately 0.5 mm thickness. The lance was positioned in

the melt at the same radial distance as the Si specimen; however, its angular position relative

to the Si cylinder (shown by θ in Figure 4-10) was varied.


78

(a)

(b)

Figure 4-10: Schematic of the RLMT shows the rotation direction and location of the immersed Si specimen and the gas injection lance. (a) Top view where AA´ represents a plane perpendicular to the xy-plane passing through the lance, (b) side view of the RLMT. All dimensions are in cm.

4.2.1 Bubble size

Figure 4-11 shows a typical pressure transducer measurement. Similar to the air–water

system (Figure 4-2), at lower flow rates (e.g. 0.50 SLPM), the pattern is more uniform and

each peak can be associated with the formation of a uniform size bubble at the lance exit.

Although the pressure transducer data implies the formation of single bubbles at the lance

exit, bubbles may coalesce during the rise period, which cannot be confirmed in the liquid

Al. This means that at lower flow rates, the N2 bubbles are in Regime I or II as identified in

the air–water experiments.


79

At higher flow rates (e.g. 1.00 SLPM), consecutive bubbles appear to coalesce at the

lance exit, as implied by the uneven peaks and the irregular pattern. As such, the size of

bubbles at the lance exit may be larger than what is predicted from the pressure transducer

data, as was also the case in the air–water system in Regime III.

Figure 4-11: Typical output voltage of the pressure transducer used to measure the frequency of bubble formation (N2–Al at SPH = 40 K, bulk velocity = 0).

The pressure transducer data was used to obtain the bubble frequency and then the bubble

size was estimated (single bubbles) using Equation (4-1). Figure 4-12 depicts the equivalent

bubble diameter after detachment vs. volume flow rate at the lance exit, and a comparison

with a correlation of Fu et al. [57] based on measurements of bubble frequency of

Chlorine/N2 injection into molten Al. Based on the earlier discussion, the size of rising

bubbles can be underestimated by up to 26% (by diameter) if one neglects the coalescence of

two same size bubbles during rise. This may occur at gas flow rates higher than 0.50 SLPM

in Figure 4-12, where the pattern of pressure data is non-uniform.

Figure 4-12 also illustrates that the bubble size decreases slightly (i.e. 3-5%) by rotating

the tank (Ub = 7 cm s−1). Comparing this reduction to the results of the air–water system


80

(Figure 4-8), the effect of the lateral drag force due to the bulk flow in the molten Al is less

pronounced. This may be because the bubbles that form in liquid Al encompass the lance

(Figure 2-3 (b) and as will be shown in Section 4.2.2), while the bubbles in water form at the

lance tip (Figure 2-3 (a)), and therefore, can be more easily pinched off.

To decide whether N2 bubbles break into smaller ones before reaching the Al free

surface, we estimate the bubble size at the free surface with no coalescence. Assuming an

isothermal expansion, the diameter of an ascending bubble remains approximately

unchanged (+3%). A very conservative upper limit for the diameter of a stable N2 bubble in

liquid Al is [135],

( )b max Al Al g(d ) 4 g -= σ ρ ρ (4-2)

Using this equation, (db)max = 2.2 cm, much larger than any of the bubble size in

Figure 4-12. Therefore, the bubbles likely do not disintegrate. This is confirmed by images of

the liquid Al free surface (Figure 4-13), which vaguely show a bubble diameter on the order

of 1 cm.

Figure 4-12: Bubble size in liquid Al at bulk velocities of 0 and 7.0 cm s−1, and a comparison with the available correlation for a (Chlorine/N2)–Al system [57].


81

4.2.2 Bubble trajectory

Information on the trajectory of the bubbles was also obtained by visual examination of the

melt free surface. Figure 4-13 shows the lance and Si specimen 30º apart (this corresponds to

an arc distance of 7.1 cm). At zero bulk velocity (non-rotating tank), the bubbles rise along

the lance and break the free surface adjacent to the lance. In the rotating tank, Figure 4-14

also shows the bubbles at the free surface next to the lance, very different than what was

observed in the air–water system at a similar Relance,OD (Figure 4- 9). This is because of the

larger buoyancy force exerted on the rising bubbles in liquid Al (ρAl/ρwater ≈ 2.4), as well as

the higher wettability of the lance. A comparison of the buoyancy force, FB, for a bubble

diameter of 1-2 cm, and the lateral drag force LDF exerted on the bubbles by the bulk liquid

(at velocities of 1.4-7 cm s−1), reveals that the former is dominant ( LD BF F < 0.02 ). More

important, N2 bubbles wet the lance during rise, which strongly opposes their detachment and

transport downstream.

Figure 4-13: Bubble arrival at liquid Al surface (bulk velocity = 0, gas flow rate = 0.50 SLPM, θ = 30º, the coated lance diameter is approximately 0.725 cm).


82

Figure 4-14: Bubble arrival at the liquid Al surface (bulk velocity = 3.5 cm s−1, gas flow rate = 0.50 SLPM, θ = 30º, the coated lance diameter is approximately 0.725 cm).

Although bubbles do not appear to contact the dissolving Si specimen in the experiments,

the displacement of liquid by the rising bubbles induces velocities within the liquid Al. These

velocities will be estimated in the next section.

4.3. Numerical Modeling of Gas-Agitated Tank

Not only can one not directly observe bubbles in the melt, but it is hardly possible to measure

the bubble-induced liquid Al velocities. Hence, the commercial software FLOW-3D was

used to predict the bubble distribution beneath the free surface, and estimate the velocity

field. In the simulations, a pragmatic approach was adopted to estimate mean velocities and

turbulence intensities, rather than attempt to fully resolve the flow field. Considering the

large scale of the problem, this would require for more computational resources than were

available.


83

This section presents information on model set-up (domain and mesh), the initial and

boundary conditions, and the stopping criterion. The assumptions and simplifications are

clearly stated. Next, the model is validated by comparing with results of the air–water

experiment in the non-rotating tank. Then, the results of simulations of the N2–Al system, of

bubble frequency, bubble distribution and the flow field characteristics, are presented.

Finally, for both the non-rotating and rotating tanks, time and spatial averages of bubble-

induced velocities are computed at various gas flow rates and angular positions of the lance.

4.3.1 Simulation set-up and parameters

The simulations were time-varying, and started by blowing gas into a liquid at t = 0. The

flow was assumed to be isothermal, and as mass transfer was not considered, energy and

species balance equations were not solved. The liquid Al properties (density, viscosity, and

surface tension) were evaluated at 700°C, and the specified gas flow rate was adjusted for the

temperature and pressure at the lance exit.

The Navier‐Stokes equations were solved along with the standard two equation k-ε model

to account for the turbulent properties of the flow. Bubble/liquid interactions and the liquid

free surface motion were simulated with the volume of fluid (VoF) method [76]. The

interaction of bubble/liquid/lance was taken into account by a surface tension model and by

specifying an appropriate contact angle. Equations were solved iteratively with a minimum

time step of 10−6 s. The simulations were set up with the FLOW-3D Graphical User Interface

(GUI), version 10.0.3.1, and the flow variables were solved with solver version 10.0.3.5.

Domain: FLOW‐3D uses the VoF method to track interfaces, and the simulations were run

using the "one‐fluid" model that only solves for flow within the liquid phase, and not within

the air above the tank. The computational domain included the top injection lance and the

tank, with enough room above the liquid to allow for free surface fluctuations (Figure 4-15).

The Si cylinder was not modeled. Rather, the results of the simulations were used to assess


84

mean and fluctuating velocities at the various positions up and downstream of the lance

where Si cylinders were positioned in the experiments. A similar approach has been adopted

by other studies (e.g. [97,98,101,107,109,110]) in which flow was predicted in the absence of

an immersed melting or dissolving specimen.

Figure 4-15. Cylindrical domain for the FLOW-3D simulations of the N2–Al system. All dimensions are in cm.

Mesh: The computational domain was discretized with a 3D cylindrical mesh (the radial,

angular and vertical coordinates denoted by r, θ, and z, respectively), as shown in

Figure 4-15. The mesh was refined selectively within regions of interest (Figure 4-16 (a)).

Figure 4-16 (b) illustrates the extra mesh refinement around the lance to capture bubble

formation.

FLOW-3D uses an explicit approach to solve for fluid advection, and so the time step is

directly proportional to the control volume size; very small cells adversely affect the runtime.

To eliminate the very small cells at the center of the cylindrical domain (r = 0), a core of

4 cm radius (i.e. 5.2% of the liquid volume) was removed, and the mesh size in the radial

direction was gradually increased near the core to avoid very small cells.


85

(a)

(b)

Figure 4-16: (a) Top view of the mesh planes, and (b) the mesh around the lance.


86

Initial conditions: For a non-rotating tank, the entire velocity field began at rest. For the

rotating tank, the fluid velocity was initialized to the corresponding solid body rotation

velocity profile in the positive θ direction (counterclockwise).

Boundary conditions: The boundary conditions were specified based on the experimental

conditions. The gas volume flow rate was imposed as an inflow condition at the lance exit.

No-slip boundary conditions were imposed at the bottom (i.e., rθ-plane: z = 0), inside

(θz-plane: r = Ri) and outside tank walls (θz-plane: r = R0). When simulations were run of a

rotating-tank, appropriate velocities were specified at those walls. The pressure at the melt

surface (rθ-plane: z = H, H changes with time because of the free surface fluctuations) was

specified as the atmospheric pressure, P0.

Although the flow was modeled in the entire tank (0° ≤ θ ≤ 360°), FLOW-3D

nevertheless requires that one define a pair of boundaries in the angular direction (i.e. a pair

of rz‐planes). For the non-rotating tank, a periodic boundary condition was specified for the

pair of rz-plane, so that the liquid flow that leaves a periodic plane re-enters the other one.

These boundaries were located 180° from the lance to minimize the potential impact on

bubble generation and the flow in the vicinity of the lance.

For the rotating tank, the pair of rz-plane boundaries was set differently. A solid body

rotation velocity profile was imposed as the inflow condition at rz-plane 90° upstream of the

lance, and an outflow boundary condition was specified at the rz-plane 270° downstream.

This is a simplification of the experiments: it neglects the changes in free stream bulk

velocity, by assuming the solid body velocity profile is recovered far downstream of the

lance.

Stopping criterion: For a full domain simulation, the combination of the large number of

cells (~3.2 x 106) and small time steps (~10−6-10−5 s) resulted in very lengthy simulations.

The simulation runtimes were between 1 to 2 months on an Intel i7-4770 CPU @ 3.40 GHz

with 8 cores and 32 GB of RAM. The simulations were run until a quasi‐steady state was

reached, evaluated by monitoring a sliding 1 s average of the overall liquid kinetic energy per


87

unit mass of liquid, lK . The stopping criterion was when ldK dt was reduced by a factor of

5 from its initial value, as shown in Figure 4-17. This occurred at about 9 s of simulation time

for the non-rotating tank. For consistency, the simulations in the rotating tank were run for

the same time period.


88

(a)

(b)

Figure 4-17. (a) Overall liquid kinetic energy of liquid per unit mass of liquid, Kl, and (b) ldK dt vs. time (bulk velocity = 0, gas flow rate = 0.50 SLPM, solid line is the sliding 1 s average).


89

4.3.2 Temporal- and spatial-averaged velocities

The simulation results were used to obtain time- and spatial-averaged velocities. The results

were averaged over time to capture the effect of many bubbles without overlooking the

transient response of the system, and then they were averaged over a volume representing the

Si cylinder.

As mentioned in Section 2.2.2, instantaneous velocities at any location vary with time.

Figure 4-18 illustrates the velocity magnitude at the midpoint of an imaginary cylinder

immersed at θ = 30° relative to the lance. As the simulations are transient and start from the

onset of bubble injection, even the mean velocities are time-dependent. Time-averaged mean

velocities and the rms values of fluctuating components in each direction were calculated as

follows:

Mi

r ri 1

1u (r, , z, t) uM =

θ = ∑ , M

i

i 1

1u (r, , z, t) uMθ θ

=

θ = ∑ , M

iz z

i 1

1u (r, , z, t) uM =

θ = ∑ ; (4-3)

and,

( )2iMr r2

ri 1

u uu

M=

−′ = ∑ ,

( )2iM2

i 1

u uu

Mθ θ

θ=

−′ = ∑ ,

( )2iMz z2

zi 1

u uu

M=

−′ = ∑ . (4-4)

where M is the number of liquid velocity data. Substituting Equations (4-3) into Equation

(2-13) and Equations (4-4) into Equation (2-10) yields the mean velocity, V, and the rms

velocity fluctuations, u .

Time-averaging must be performed over a time period that is sufficiently longer than the

duration of any velocity fluctuation [12]. Therefore, a sliding temporal average was

calculated for a period of 1 s, during which about 30 bubbles were released, based on data at

every 0.005 s (i.e. M = 200), that is much larger than the typical time step (~ 10−5 s).

Sampling the data every 0.05 s (non-rotating Al tank at θ = 30° with a gas flow rate of 0.50

SLPM) yielded very similar time-averaged results.


90

In the experimental study, the focus was on the overall dissolution rate of Si cylinders,

and so spatial averages of mean and rms velocity fluctuations were calculated within the

volume that encompasses an imaginary Si specimen. Assuming an equal weight for each cell

in the volume:

v

vN

ϕ< ϕ >=

∑, (4-5)

where φ is a general quantity and vN is the number of cells (i.e. 15000-45000) in the

imaginary cylinder.

Figure 4-18: Instantaneous liquid velocity magnitude (bulk velocity = 0, gas flow rate = 0.50 SLPM, r = 13.5 cm, θ = 30°, z = 11 cm: 4 cm below the free surface of liquid Al coincides with the center of an imaginary Si cylinder).

4.3.3 Experimental validation with the air–water system

FLOW-3D was used to simulate the air–water visualization experiments in the non-rotating

tank. Water wets Ti, and so a contact angle of 58.5° was specified, as suggested by [136].


91

The simulation results predict a periodic bubble formation and a noticeable shift from

single bubbles (0.3 SLPM, Regime I) to doublets (1.00 SLPM, Regime I) by increasing the

gas flow rate, in agreement with the experiments (Section 4.1). Although the formation of

doublets was dominant at the highest flow rate, single bubble formation was also observed.

In addition, a simulation at a gas flow rate of 0.6 SLPM (Regime II) was run that predicted

bubble coalescence closer to the lance exit than is shown in Figure 4-4.

Figure 4-19 and Figure 4-20 compare the predicted evolution of bubbles at the lance exit

to images from the experiments, at gas flow rates of 0.30 and 1.00 SLPM, respectively. The

results were compared at various time intervals from the appearance of a single

bubble/doublet at the lance exit to its detachment. At each instant of time in Figure 4-19 and

Figure 4-20, the top and bottom images correspond to the experiment and simulation,

respectively. The lance is omitted from the simulation images to more clearly show the

bubbles; what appears as a section of the lance attached to the bubbles is in fact the inside of

the lance (4.37 mm ID).

Figure 4-19 shows the single bubble formation belonging to Regime I. The simulation

results, in accordance with the experiments, predict a bubble evolution consisting of three

distinct stages. Initially, the bubble emerges at the lance exit as the momentum of the gas

overcomes the liquid pressure, and the bubble grows in line with the lance centerline

(0-0.035 s). Then the bubble, while continuing to grow, moves preferentially towards one

side of the lance (0.035-0.070 s). Finally, the bubble detaches as the buoyancy force

increases with bubble size (0.07-0.105 s). The same evolution stages, with very similar

images, are reported in the experimental study of [137]. Note that liquid flow instabilities due

to the periodic formation and release of bubbles cause each bubble to move towards different

side of the lance.

Figure 4-20 depicts the doublet formation belonging to Regime III. The formation of the

leading bubble (0-0.08 s) is similar to the single bubble formation described above. However,

the bubble is larger because of the higher gas flow rate, and so the bubble forms more


92

quickly. At the lower flow rate, the leading bubble has a negligible effect on the trailing

bubble. In contrast, the effect of the leading bubble at the higher flow rate is clearly observed

in the experiments, and is well-predicted by the simulation. As shown in Figure 4-20, the

large leading bubble reduces the trailing bubble growth time, leading to a smaller bubble and

deforming it (0.08-0.12 s). This is because the leading bubble wake influences the formation

of the trailing bubble as the distance between the two bubbles is short [138]. FLOW-3D

satisfactorily predicts both the quicker detachment and the elongation of the trailing bubble.

In addition to a "picture norm" comparison, the FLOW-3D predictions were evaluated

quantitatively, by comparing the average formation time of the single bubbles (at 0.30

SLPM), and of the leading and trailing bubbles of the doublets (1.00 SLPM) over a time

period of 4 s, to the corresponding experimental results. The time for the bubble to reach the

free surface was also calculated and compared. This time was defined as follows: for a single

bubble, from detaching from the lance exit to exiting the liquid; for the doublets, from the

leading bubble detaching from the lance exit to the doublet exiting the liquid. Figure 4-21

shows the comparison at gas flow rates of 0.30 SLPM and 1.00 SLPM. The FLOW-3D

predictions and experimental results agree within the standard deviations. Overall, the

prediction of the numerical model is quite satisfactory, and so the validated model was used

to investigate the characteristics of the N2–Al system.


93

t = 0 s t = 0.035 s

t = 0.070 s t = 0.105 s

Figure 4-19: Qualitative comparison of air-water bubble formation (bulk velocity = 0, gas flow rate = 0.3 SLPM).


94

t = 0 t = 0.04 s

t = 0.08 s t = 0.10 s

t = 0.12 s

Figure 4-20: Qualitative comparison of air-water bubble formation (bulk velocity = 0, gas flow rate = 1.0 SLPM).


95

(a)

(b)

Figure 4-21: Quantitative comparison of the formation and rise time of many bubbles over a time period of 4 s as predicted by a FLOW‐3D simulation, and measured in the air–water experiments, at gas flow rates of (a) 0.3 SLPM and (b) 1.0 SLPM (bulk velocity = 0).


96

4.3.4 Results and Discussion

Table 4-1 lists the full tank FLOW-3D simulations of the N2–Al system. The results of these

cases are presented in the following section.

Table 4-1: List of FLOW‐3D simulations for the N2–Al system.

Bulk velocity of liquid at the lance exit (cm s−1)

Gas flow rate (SLPM)

Non-rotating tank 0 0.50 0.75 1.00

Rotating tank

1.4 0.50

3.5 0

0.50 1.00

7.0 0.50

4.3.4.1 Bubble distribution within the liquid Al

In the N2–Al experiments, the Ti lance was coated with boron nitride, which molten Al does

not wet. As a result, the N2 bubbles appear to wet the lance and rise along it, as confirmed

earlier in Figure 4-13.

FLOW-3D simulations in a non-rotating tank were run at both 0.50 and 1.00 SLPM, with

the Al/lance contact angle set to 160° [139,140]. Unlike both the air–water and N2–Al

experiments, the simulations predicted a less clear transition from single bubble (Regimes I

and II) to doublet (Regime III) formation, as both single bubbles and doublets formed at both

0.50 and 1.00 SLPM. Nevertheless, the average bubble size was reasonably well predicted by

FLOW-3D, as indicated in Table 4-2. At both flow rates the predicted bubble size was a few

percent (~8%) higher than the measured values, and the variations in the predicted bubble

size were higher than the experimental values obtained via pressure transducer data. The

simulations for a gas flow rate of 0.50 SLPM were also run with the contact angle set to 150°

and 170°. As expected, average bubble size increased and decreased, respectively. At 170°


97

and gas flow rate = 0.50 SLPM, the average size was 1.22 ± 0.18 cm, just slightly larger than

the measured size. Given the uncertainties: the contact angle, the temperature-adjusted gas

flow rate at the lance exit, and the transport properties (density, viscosity, and surface

tension) at high temperatures, the FLOW-3D results are surprisingly good.

Table 4-2: Comparison of experimental measurements and FLOW-3D predictions for the equivalent bubble diameter at the lance exit in the N2–Al system (bulk velocity = 0).

Gas flow rate (SLPM)

Bubble equivalent diameter (cm) Experimental

(Estimated from pressure transducer data)

FLOW-3D (Counting formed bubbles

at the lance exit) 0.50 1.16 ± 0.01 1.26 ± 0.15 1.00 1.47 ± 0.02 1.59 ± 0.20

Finally, Figure 4-22 shows sample results for gas flow rates of 0.50 and 1.00 SLPM, that

illustrate the bubbles rising along the lance. For a gas flow rate of 0.50 SLPM, bubbles rise

with a velocity of 0.63 ± 0.05 m s−1, higher than that of unhindered bubbles of a similar size

[57,62]. The attachment of the ascending bubbles to a poorly wetted lance has been

previously reported [60,61] in water model studies, and Watanabe and Iguchi [61] showed

that such bubbles rise more quickly than those away from a lance.


98

(a) (b)

Figure 4-22: Predicted instantaneous bubble distributions at gas flow rates of (a) 0.50 SLPM and (b) 1.00 SLPM (3D view of the lance vicinity, bulk velocity = 0).

4.3.4.2 Non-rotating tank

The simulation results of the RLMT provide insights into the behavior of the bubble-induced

bulk flow, and quantify the velocity field. This section presents the liquid flow characteristics

and estimated velocities in the non-rotating tank.

Fluid flow characteristics: Prior to gas injection the liquid is at rest; when the bubbles are

introduced, the gas/liquid interaction induces a flow in the melt. The general characteristics

of the gas-agitated flow are inferred from velocity profiles. Figure 4-23 shows contour plots

of instantaneous velocities at various planes in the cylindrical domain. The characteristics of

the flow field are similar on both sides of the lance. However, the flow field is not entirely

symmetric because of the non-linear instabilities due to the bubbly flow. The simulation

results indicate that the assumption of axisymmetric flow adopted in most previous studies of

gas injection in ladles (e.g. [43,52,97,98,107,141-143]) may not be appropriate, especially

where the lance is located off-center in a metallurgical reactor.


99

Figure 4-23 (a) is a contour plot of the instantaneous velocity magnitude in the θz-plane

that passes through the center of the lance (r = 13.5 cm). The velocity values are highest

adjacent to the lance, decreasing with a sharp gradient in the θ direction. The release of

bubbles at the free surface of the liquid leads to higher velocities in this region, while in the

zone beneath the lance, the flow is weak and nearly stagnant, as also reported by [58,141].

This is presumably due to the negligible downward movement of the bubbles.

Figure 4-23 (b) plots the tangential velocity, uθ, in a series of rz-planes. At smaller θ

values (e.g. θ = 30°), uθ is towards the lance as the liquid is drawn into the wake of the rising

bubbles. A strong outflow passes across the top surface and outside wall, which establishes a

recirculating bulk flow on each side of the lance, similar to what was observed

experimentally for top lance injection in a water ladle [144], albeit for a bubble plume instead

of individual bubbles. The entrainment of liquid becomes less significant as θ increases

(θ = 70° and 120°), evidenced by less flow towards the lance (negative tangential velocity),

and is negligible far from the lance, on the opposite side of the tank (θ = 180°).

As the bubbles rise, they displace the liquid above, inducing a vertical velocity.

Figure 4-23 (c) depicts the vertical velocity, uz, at two rθ-planes, at the exit of the lance (z =

5 cm), and 1 cm below the free surface (z = 14 cm). On the lower plane, there is an upward

bulk flow in the neighborhood of the lance due to momentum transfer from the rising bubbles

[141]; the flow then moves downwards near the wall. On the upper plane, no distinct bulk

flow can be detected due to the highly agitated free surface. An up-and-down motion at the

liquid Al free surface was also observed experimentally (i.e. the uneven surface in

Figure 4-13), that is an indication of higher turbulence intensities. The magnitude of velocity

fluctuations at the top surface may have been overpredicted, as the formation of dross

observed experimentally was not considered in the simulations. This oxide layer with a high

melting point likely damps the agitation of the free surface. Note that many previous studies

of gas-agitated ladles (e.g. [43,52,97,98,107,141-143]) assumed a flat free surface;


100

nevertheless, they observed higher values of turbulent kinetic energy (turbulence intensity) at

the free surface than in the bulk of the liquid [52].


101

(a)

(b)

(c)

Figure 4-23: (a) Predicted instantaneous bubble-induced velocity magnitude in the θz-plane passing through the lance center, (b) the tangential velocity at various rz-planes, and (c) the vertical velocity at various rθ-planes (bulk velocity = 0, gas flow rate = 0.50 SLPM, t = 9.00 s).


102

Velocity estimates: As mentioned in Section 2.2.2, both mean velocities and rms velocity

fluctuations affect localized mass transfer phenomena, and so are of interest. The simulation

results were used to estimate these velocities as functions of relative position to the lance,

and gas flow rate. In Chapter 5 these velocities will be used to develop correlations for mass

transfer in gas-agitated systems. 416 871 0222

In the dissolution experiments in the non-rotating tank, the Si cylinder was immersed at

θ = 30° with respect to the lance. Figure 4-24 shows a spatial average of the absolute mean

velocity and the rms velocity fluctuations in the r, θ, and z directions at this position, for a

gas flow rate of 0.50 SLPM. Figure 4-24 (a) illustrates the multidimensionality of the mean

flow: although the velocity components are of the same order of magnitude, the mean

tangential velocity is the largest, followed by the vertical and radial components. This result

shows that the approach [97,98,110] of assuming an axisymmetric flow relative to the lance,

and neglecting the velocities perpendicular to the plane that passes through the solid addition

and the lance, leads to an underestimation of the mean velocity. Figure 4-24 (b) shows that

the velocity fluctuations are appreciable in all directions, although the tangential and vertical

components are greater than the radial one, which implies a deviation from isotropic

turbulence. This is in accordance with the results of [145].


103

(a)

(b)

Figure 4-24. Spatially averaged (a) absolute mean velocity, and (b) rms velocity fluctuations in the r, θ, and z directions (bulk velocity = 0, gas flow rate = 0.50 SLPM, θ = 30°).


104

Figure 4-25 compares the mean velocity and rms velocity fluctuations as a function of θ,

and illustrates a stronger mean flow and turbulence closer to the gas/liquid region. As θ

increases from 5° to 10°, both < V > and < u> change abruptly (consistent with the sharp

velocity gradient near the lance shown in Figure 4-23), decreasing by factors of 2.6 and 4.3,

respectively. Further increasing θ from 10° to 30°, the velocities gradually decrease. At

θ = 5°, a portion of the volume over which the spatial averaging was performed encompasses

the gas and liquid mixture. The increase in velocity is in general agreement with the

prediction of Mazumdar et al. [97], who reported that the mean and fluctuating velocities

outside an axisymmetric plume (of a conical shape with specified gas volume fraction as a

function of bath height) are significantly lower than inside it.

Figure 4-26 shows the mean velocities and rms velocity fluctuations at various gas flow

rates in the non-rotaing tank. By increasing the gas flow rate from 0.50 to 1.00 SLPM, when

the startup period has passed, < V > is essentially the same, but < u> increases by 70%,

indicating that a higher gas flow rate yields a greater liquid agitation rather than a stronger

mean flow. This observation is in agreement with the experimental findings of [65].


105

(a)

(b)

Figure 4-25: Comparison of spatially-averaged (a) mean velocity and (b) rms velocity fluctuations at various angular positions relative to the lance (bulk velocity = 0, gas flow rate = 0.50 SLPM).


106

(a)

(b)

Figure 4-26: Comparison of spatially-averaged (a) mean velocity and (b) rms velocity fluctuations at various gas flow rates (bulk velocity = 0, θ = 30°).


107

4.3.4.3 Rotating tank

The tank rotation generates a liquid bulk velocity. As discussed in the N2–Al experiments,

this causes a small decrease in the bubble size and a shift of the rising bubbles to the

downstream side of the lance. FLOW-3D predicts these behaviors satisfactorily. By

increasing the bulk velocity from 0 to 3.5 cm s−1, at gas flow rates of 0.50 SLPM and 1.00

SLPM, the average bubble size decreases slightly from 1.26 cm to 1.24 cm, and from 1.49

cm to 1.48 cm, respectively. These reductions are negligible compared to the standard

deviations associated with the equivalent bubble diameter; a similar conclusion was drawn

from the pressure transducer measurements. Figure 4-27 illustrates that the bubbles rise

adjacent to the lance downstream of the bulk flow, in accordance with Figure 4-14.

Fluid flow characteristics: With the predicted bubble behavior in qualitative agreement with

experiments, the bubble-induced field can be examined. Figure 4-27 (a) shows a contour plot

of the tangential velocity. Downstream of the lance, the wakes behind rising bubbles cause

tangential velocities opposite to the bulk flow direction. Of course the magnitude of these

bubble-induced velocities decreases with distance from the lance. Upstream of the lance, the

approaching flow is significantly disturbed, as the bubbles generate both inward and outward

flows along the lance. Figure 4-27 (a) also shows that in the rotating tank the approaching

flow below the lance is accelerated in the presence of the two-phase region, in contrast to the

flow in the non-rotating tank, in which the liquid below the injection lance is nearly

unaffected (Figure 4-23 (a)).

Bubbles also induce velocities in the vertical direction. Figure 4-27 (b) is a contour plot

of the vertical velocity on the θz-plane passing through the lance. The rise of bubbles

downstream of the lance causes upward velocities skewed towards the direction of the bulk

flow. This yields a non-symmetric flow around the lance, where vertical velocities are

induced mostly in the downstream flow.


108

(a)

(b)

Figure 4-27: Instantaneous (a) tangential velocity, uθ, and (b) vertical velocity, uz, on the θz-plane passing through the center of the lance (bulk velocity = 3.5 cm s−1, gas flow rate = 0.50 SLPM, t = 9.00 s).

The bubble-induced velocities also vary vertically within the bath. Figure 4-28 is a

contour plot of tangential velocity at two heights. Both upstream and downstream flow

disturbances are magnified near to the free surface. At the lance exit, the tangential velocity

profile resembles the initial solid body rotation, while at 1 cm below the free surface the flow

pattern is more agitated.


109

Figure 4-28: Instantaneous tangential velocity on two rθ‐planes (bulk velocity = 3.5 cm s−1, gas flow rate = 0.50 SLPM, t = 9.00 s).

The variation of velocity in the flow direction is of interest because it illustrates how the

effect of gas injection is convected throughout the domain. Figure 4-29 is a contour plot of

velocity magnitude on various rz-planes (where the Si cylinders were immersed in the

experiments). Large velocity gradients are observed adjacent to the lance (Figure 4-27); the

velocity profiles are more similar on the planes further from the lance. Nevertheless, higher

velocities are predicted on the downstream planes near the free surface, due to the release of

bubbles.

Figure 4-29: Instantaneous velocity magnitude, V, at various rz‐planes (bulk velocity = 3.5 cm s−1, gas flow rate = 0.50 SLPM, t = 9.00 s).


110

Velocity estimates: Before quantifying mean and fluctuating velocity components due to gas

agitation in the rotating tank, it is instructive to consider the influence of the lance on the

flow field without injecting gas, since the simplifying assumption of solid body rotation is

not valid in the presence of the lance. Such a simulation offers an estimate of the velocity

fluctuations due to pure shear-induced turbulence. Figure 4-30 shows absolute mean

velocities at θ = 30° averaged over the imaginary cylinder volume. The tangential velocity

decreases from the initial 3.5 cm s−1 to a steady 2.5 cm s−1 due to the drag force exerted by

the lance. There are also small radial and vertical velocities (an order of magnitude less than

the tangential velocity) due to flow disturbances created by the lance. Figure 4-31 shows the

rms velocity fluctuations and turbulence intensity corresponding to the mean velocity. The

spatially-averaged turbulence intensity, <Tu>, is about 11% at steady state. This value is in

the expected range for single-phase flows [103,145].

Figure 4-30: Spatially-averaged absolute mean velocity in the r, θ, and z directions (bulk velocity = 3.5 cm s-1, gas flow rate = 0 SLPM, θ = 30°).


111

Figure 4-31: Spatially-averaged rms velocity fluctuations and turbulence intensity (bulk velocity = 3.5 cm s−1, gas flow rate = 0 SLPM, θ = 30°).

Figure 4-32 (a) shows the spatially-averaged mean velocity components at θ = 30° and a

gas flow rate of 0.50 SLPM. The results demonstrate radial and vertical velocities of the

same order of magnitude, albeit much smaller than the tangential velocity in the bulk flow

direction. This is a crucial distinction from previous studies on heat and mass transfer from

vertical cylinders in cross flow with grid-generated turbulence [82-84,146,147]. These

experiments were conducted in wind tunnels where the mean velocity was one-dimensional

and constant along the test section; correlations derived from such experiments would be

difficult to apply to a system with gas agitation as the source of velocity fluctuations

(pseudo-turbulence).

Figure 4-32 (b) indicates that the rms velocity fluctuations are significant in all

directions; fluctuations in the tangential direction are slightly higher than in the vertical and

radial directions because of the interaction of the bulk and bubble-induced flows. (This also

indicates a deviation from the isotropic turbulence present in grid-generated turbulence.)


112

(a)

(b)

Figure 4-32: Spatially-averaged (a) absolute mean velocity, and (b) rms velocity fluctuations in the r, θ, and z directions (bulk velocity = 3.5 cm s−1, gas flow rate = 0.50 SLPM, θ = 30°).


113

A comparison of Figure 4-24 (b) and Figure 4-32 (b) reveals that the rms velocity

fluctuations at θ = 30° in the rotating tank are generally higher than those in the non-rotating

one. This is further illustrated in Figure 4-33, which plots u< > at θ = 30° downstream of

the lance (where the dissolution of Si cylinders was examined in the experiments) for various

bulk velocities. Increasing the bulk velocity from 0 to 3.5 cm s−1, u< > increases by more

than 60% after the startup period (4.5 s < t < 9.0 s). The much higher rms velocity fluctuation

in the rotating tank indicates that the effect of gas agitation is further extended into the

domain when a bulk flow is present. Further doubling the bulk velocity; however, the rms

velocity fluctuation only increases by another 25%. As a result, the turbulence intensity,

<Tu>, decreases at the higher bulk velocity. Figure 4-34 shows the turbulence intensities at

two bulk velocities; the simulation results reveal a 40% decrease in <Tu> as the bulk velocity

increases from 3.5 cm s−1 to 7.0 cm s−1.

Figure 4-33: Comparison of spatially-averaged rms velocity fluctuations at various bulk velocities (gas flow rate = 0.50 SLPM, θ = 30°).


114

Figure 4-34: Comparison of spatially-averaged turbulence intensity in the rotating tank (gas flow rate = 0.50 SLPM, θ = 30°).

Figure 4-35 and Figure 4-36 show a comparison of mean velocities and rms velocity

fluctuations at various gas flow rates (0, 0.50, and 1.00 SLPM), respectively. Injecting

bubbles into the melt significantly enhances liquid bulk motion and agitation, as evidenced

by a comparison of single-phase and two-phase flow simulations.

As the gas flow rate increases from 0.50 SLPM to 1.00 SLPM, larger bubbles form at the

lance exit (Table 4-2), displacing a larger volume of liquid that leads to changes in the mean

flow and a higher degree of agitation (turbulence intensity). As demonstrated in

Figure 4-35 (b), in the downstream flow the mean tangential velocity decreases near the

lance due to the effect of larger bubble wakes, but the absolute mean velocities increase in

the radial (Figure 4-35 (a)) and in particular the vertical directions (Figure 4-35 (c)).

Increasing the gas flow rate from 0.50 to 1.00 SLPM, when the mean velocities become

nearly steady (4.5 s < t < 9.0 s), the mean tangential velocity decreases by about 10%, while

the absolute mean radial and vertical velocities increase 30% and 50%, respectively. This

implies that for transport phenomena taking place in bubble-induced flows, neglecting the


115

three-dimensionality of the velocity field may lead to inconsistencies in correlating the

operating parameters (e.g. gas flow rate) to the transfer rate (e.g. mass transfer).

Nevertheless, the net effect of the aforementioned changes in the components of mean

velocity is a negligible change in the mean velocity, < V >.

As shown in Figure 4-36, increasing the gas flow rate from 0.50 SLPM to 1.00 SLPM

increases the intensity of turbulence in all directions. The components of rms velocity

fluctuations increase in the radial, tangential and vertical directions by approximately 30%,

20%, and 20%, respectively, and so the overall rms velocity fluctuations, < u>, also increase

by 20%. This demonstrates that an increase in mass transfer rates at higher gas flow rates is

primarily associated with the enhanced velocity fluctuations.

Finally, Figure 4-37 (a) compares the mean velocity as a function of θ, and illustrates that

even in upstream locations, especially closer to the lance (θ = −30°) where liquid is drawn

into the wakes of rising bubbles, the mean velocity can be even higher than in the

downstream. Figure 4-37 (b), of the rms velocity fluctuations, shows that introducing bubbles

into a bulk flow can significantly disturb even the approaching liquid, yielding velocity

fluctuations in the upstream flow that are similar or higher than in the downstream.


116

(a)

(b)

(c)

Figure 4-35: Comparison of spatially-averaged absolute mean velocities in the (a) r, (b) θ, and (c) z directions at various gas flow rates (bulk velocity = 3.5 cm s−1, θ = 30°).


117

(a)

(b)

(c)

Figure 4-36: Comparison of spatially-averaged rms velocity fluctuations in the (a) r, (b) θ, and (c) z directions at various gas flow rates (bulk velocity = 3.5 cm s−1, θ = 30°).


118

(a)

(b)

Figure 4-37: Comparison of spatially-averaged (a) mean velocity, and (b) rms velocity fluctuations at various angular positions relative to the lance (bulk velocity = 3.5 cm s−1, gas flow rate = 0.50 SLPM).


119

4.4 Summary

The size and trajectory of bubbles were evaluated using air–water experiments and video

recordings of the N2–Al free surface. In liquid Al, large buoyancy‐driven bubbles (with an

equivalent diameter of 1‐2 cm) are formed at a frequency of approximately 33-38 s−1, and

rise adjacent to the lance in both rotating and non-rotating tanks. These bubbles induce

velocities in the neighboring liquid, rather than come into contact with the dissolving Si.

The commercial CFD software FLOW-3D was used to characterize the bubble-induced

flow and quantify the velocities. The simulation results were validated by comparison with

the air–water results (bubble formation and rise times). The simulation and experimental

results agreed within the respective standard deviations. In the N2–Al simulations, the

equivalent bubble diameters were overpredicted slightly (by about 8%), where the

experimental bubble size was evaluated via pressure transducer data.

In the non-rotating tank, simulations revealed bubble-induced flows that are similar but

not symmetric around the lance, and that the entrainment of the liquid due to the rising

bubble wakes establishes a recirculating flow around the lance. The results showed that mean

velocity and turbulence intensities increase sharply near the lance, and beyond the two-phase

region the velocities decrease gradually. At the position of the Si cylinder outside the

two-phase region, a two-fold increase in the gas flow rate yielded a 70% increase in the rms

velocity fluctuations, but only a very small increase (< 10%) in the mean velocity.

In the rotating tank, the bubble-induced flow patterns are more complicated because of

the interaction between the bulk flow and the wakes of the rising bubbles, especially close to

the proximity of the lance. The bubbles accelerate the flow in the upstream and create

velocities in the opposite direction to the bulk flow in the downstream. Since the bubbles rise

just downstream of the lance, the vertical velocities are highest in this region, especially near

the free surface. Although gas agitation increases both mean velocity and turbulence intensity

compared to a single-phase flow, increasing the gas flow rate by a factor of two mainly


120

affects the rms velocity fluctuations (which increase by 20% at the location of the Si

cylinder), while the mean velocity remains unchanged. A higher bulk velocity further

convects the effect of gas agitation throughout the entire tank. Finally, the bubble-induced

motion and agitation are significant both upstream and downstream of the lance.

121

CHAPTER 5

DISSOLUTION OF SOLID Si CYLINDERS IN MOLTEN Al: TWO-PHASE FLOW

The results of a study of the effect of gas agitation on the dissolution of Si in molten Al are

reported, examining the dissolution enhancement of cylindrical Si specimens in a two-phase

flow. Mass transfer coefficients with and without gas injection are compared, to correlate the

effect of gas injection as an equivalent bulk velocity. Finally, the mass transfer coefficients

with gas agitation are compared to available correlations for mass transfer from solids in

gas-agitated liquids (i.e. non-rotating tank), and in the cross flow of a turbulent liquid (i.e.

rotating tank), incorporating the predicted velocities of Chapter 4 into various dimensionless

groups.

5.1 Experimental Procedure

Similar to the forced convection single-phase flow experiments, Al was melted inside the

RLMT, as described in Chapter 3. As shown in Figure 5-1, the furnace lid has three

Chapter 5. DISSOLUTION OF SOLID Si CYLINDERS IN MOLTEN Al: TWO-PHASE FLOW

122

types of holes. The hole at the center was used to insert a bath thermocouple and the large

hole to immerse Si specimens. The remaining holes were used to insert a gas injection lance

at different angular positions with respect to the Si cylinder. The two-phase flow

experimental setup included a gas delivery system with a flow controller.

Figure 5-1: The furnace lid includes various holes to immerse a thermocouple, Si specimens, and the lance into the liquid Al.

Metallurgical grade Si specimens (both MGSi–I and MGSi–II) were used in the

two-phase flow experiments. A detailed discussion of the differences between the two

batches is reported in Chapter 3. The size of the specimens, the preparation method, and the

immersed length were the same as in the single-phase flow experiments.

Preparation for a typical two-phase flow experiment was similar to that described in

Section 3.2.3, up to the point that the melt reached a solid body rotation. Then the lance was

inserted into the melt, the gas was turned on, and N2 bubbles began to form. After adjusting

the gas flow rate to the desired value, a Si cylinder was immersed into the liquid. After

immersion, the specimens were treated in the same way as in the single-phase flow

experiments. As before, dissolution data presented in this chapter usually represents three

experiments, and the standard deviation of these measurements is represented by error bars.


123

5.2 Results and Discussion

The single-phase flow experiments (Chapter 3), and the studies of bubble behavior and liquid

flow (Chapter 4), allow us to understand and quantify the impact of gas injection on Si

dissolution.

Figure 5-2 illustrates the effect of gas agitation on the dissolution of the cylindrical Si

specimens. The overall dissolution rate increases with increasing gas flow rate, and the rate

of dissolution is highest near the top of each specimen, facing the bulk flow. This is

consistent with the simulation predictions which revealed higher bubble-induced velocities

and a more vigorous agitation near the Al bath surface.

Figure 5-2: Dissolved MGSi–II cylindrical specimens at various gas flow rates (immersion time = 3 min, SPH = 40 K, bulk velocity = 3.5 cm s−1, θ = 30°).

In the two-phase flow experiments, the effect of the following parameters was examined

by immersing cylinders for 3 min: (1) bath temperature (SPH = 40 and 80 K), (2) bulk

velocity (0, 1.4, 3.5, and 7.0 cm s−1), (3) gas flow rate (0 to 2.00 SLPM), and (4) the position

of the lance relative to the Si cylinder (θ = −50° to +70°, negative denotes a downstream


124

position, positive an upstream position with respect to the Si specimen). The effect of each

parameter is examined while keeping the others constant.

5.2.1 Effect of bulk velocity at a given gas flow rate

Figure 5-3 illustrates the effect of changing bulk velocity; at a given gas flow rate, superheat,

and lance position, and shows that for the entire range of bulk velocities tested, the

introduction of gas leads to higher dissolved fractions. The injected gas produces relatively

large bubbles that agitate the liquid, as confirmed by the observed rippling of the liquid Al

free surface (Figure 4-13). The bubble-induced bulk fluid motion and increase in turbulence

intensity (estimated in Chapter 4) result in a decrease in mass transfer resistance adjacent to

the dissolving cylinder. This finding may be explained heuristically by, for example, the

Random Eddy Penetration (or Surface Rejuvenation) Model of Harriott [93], introduced in

Section 2.2.2. According to this model, turbulent eddies from regions of uniform solute

concentration will regularly penetrate the mass boundary layer, sweeping away some of the

accumulated solute. In between arrival of these eddies, the mass transfer in the mass

boundary layer is by diffusion. Overall, this agitation of the boundary layer increases the

mass transfer rate.


125

Figure 5-3: Dissolved fraction of MGSi–II at SPH = 40 K vs. bulk velocity (immersion time = 3 min, gas flow rate = 0.50 SLPM, θ = 30°).

The increased rate of dissolution due to gas agitation can be expressed as an increase in

the dissolved fraction, ΔDF = DFwith gas − DFwithout gas. The relative enhancement of the

dissolution rate is then defined as:

without gas

DFEnhancement factor (EF) = 100DFΔ

× . (5-1)

EF expresses the percent increase in the dissolved fraction due to gas agitation.

Figures 5-4 (a) and 5-5 (a) illustrate ΔDF vs. bulk velocity for gas flow rates of 0.50 and

1.00 SLPM; the corresponding EF are shown in Figures 5-4 (b) and 5-5 (b). In general, two

regions can be identified in Figures 5-4 (a) and 5-5 (a), at lower and higher bulk velocities.

At lower velocities where natural convection is dominant, ΔDF is roughly constant. As the

bulk velocity increases there is a noticeable increase in ΔDF, corresponding to the forced

convection regime.

Whether there is no bulk velocity, or bulk velocity matters little (bulk velocity < 3

cm s−1), natural convection is the dominant mode of mass transfer, and the effect of gas


126

injection on the flow around the dissolving Si is similar. Therefore, the velocity fluctuations

induced by the same degree of gas agitation result in a comparable ΔDF. For instance, as

shown in Figure 5-5 (a), at SPH = 40 K and a gas flow rate of 1.00 SLPM, ΔDF is 0.065 and

0.06 at bulk velocities of 0 and 1.4 cm s−1, respectively.

When the bulk flow is sufficiently strong to shift the primary mode of mass transfer to

forced convection (bulk velocity > 3 cm s−1), agitating the flow by gas injection significantly

augments ΔDF and thus EF. For example, as shown in Figure 5-5 (a), at SPH = 40 K, a gas

flow rate of 1.00 SLPM, and a bulk velocity of 3.5 cm s−1, ΔDF = 0.13 is twice the value as

when natural convection is dominant. This indicates that gas agitation is more effective in the

presence of forced convection, which convects the agitation downstream. The FLOW-3D

results confirm this: Figure 4-23 (a) illustrates flow in a non-rotating tank and shows that the

agitation is limited to a small region near the lance. In a rotating tank, (Figure 4-27), the

agitated region is much larger. The simulation results also show this quantitatively: u< > at

the location of a Si cylinder 30° downstream of a lance is 0.46 in the non-rotating tank, and

0.76 in the rotating one (bulk velocity = 3.5 cm s−1) as shown in Figure 4-33.

Figures 5-4 (a) and 5-5 (a) also show that as the bulk velocity increases beyond

3.5 cm s−1, the enhancement of mass transfer rate does not increase. For instance, at SPH =

40 K and a gas flow rate = 1.00 SLPM, ΔDF is a relatively constant 0.12 at velocities of 3.5

and 7.0 cm s−1. As the bulk velocity increases, the turbulence intensity decreases,

(Figure 4-34) which leads to a smaller dissolution enhancement. This is in accordance with

describing the enhancement of heat or mass transfer rate as a function of Re1/2Tu [83] or

Tu [102].


127

(a)

(b)

Figure 5-4: (a) ΔDF, and (b) EF for dissolution for MGSi–II vs. bulk velocity at a gas flow rate = 0.50 SLPM (immersion time = 3 min, θ = 30°, the lines indicate average values).


128

(a)

(b)

Figure 5-5: (a) ΔDF, and (b) EF for dissolution for MGSi–II vs. bulk velocity at a gas flow rate = 1.00 SLPM (immersion time = 3 min, θ = 30°, the lines indicate average values).


129

Figures 5-4 and 5-5 also show that the effect of gas agitation on ΔDF and EF decreases

with an increase in the bath superheat, in particular in the forced convection regime (bulk

velocity > 3 cm s−1). Comings et al. [82] show that the effect of turbulence intensity on heat

transfer from cylindrical specimens decreases as the thickness of the boundary layer

increases. Since gas agitation disturbs the mass boundary layer, the observed trend may be

associated with how the thickness of the boundary layer varies with the liquid temperature.

The boundary layer thickness can be estimated from the mass transfer coefficients

deduced from the experimental results. Adjusting for incubation times associated with the

single-phase flow experiments (and acknowledging that these may be longer than the

incubation times in two-phase flow), a mean mass transfer coefficient for the entire

immersion period , mk , can be calculated from Equation (3-14), and then the mass boundary

layer thickness can be estimated as [23,108]:

Si/Alm

m

Dk

δ ≅ (5-2)

where DSi/Al increases with temperature [39]. The estimates of δm, from the MGSi–II

experimental data are presented in Table 5-1: they range from 0.11-0.24 mm. This range is of

the same order of magnitude as found by Kim and Pehlke [108], who estimated a boundary

layer thickness in the range of 0.48-0.86 mm for Sh pertinent to the current study.

Table 5-1 also shows that a higher temperature generally yields a slightly thicker mass

boundary layer. For instance, at a bulk velocity of 3.5 cm s−1 the mass boundary layer in

single-phase flow at SPH = 80 K is about 10% thicker than at SPH = 40 K. This is simply

because of a higher diffusion coefficient, DSi/Al, at a higher SPH.

When natural convection is dominant (bulk velocity < 3 cm s−1), the single-phase flow

experiments suggest that the mass boundary layer thickness at a higher temperature

(SPH = 80 K) remains relatively unchanged compared to a lower temperature (SPH = 40 K);

therefore, when gas is injected, the variation of ΔDF with temperature is less significant.


130

A dimensional analysis of the effect of transport properties on the mass boundary layer

supports the effect of liquid Al temperature. For simplicity assume a single-phase flow and a

laminar boundary layer around a cylinder (which is plausible, as Red based on the bulk

velocity is less than 2710). Then the momentum boundary layer thickness can be described

by [117] as:

1/2Re−δ ∼ (5-3)

and the mass boundary layer thickness can be estimated as [117]:

1/3m 1 Sc1.026

−δ=

δ. (5-4)

Combining Equations (5-3) and (5-4) at a given bulk velocity and a characteristic length

yields:

1/6 1/3m Si/AlDδ ν ×∼ (5-5)

Taking into account the variations of Al and Si transport properties as a function of

temperature (correlations in Appendix A were used to calculate the transport properties), the

mass boundary layer thickness increases by 10% when SPH increases from 40 K to 80 K

similar to the increase observed experimentally.

The above analyses suggest that when a thinner mass boundary layer (i.e. at lower SPH)

is disturbed by bubble-induced agitation, a relatively larger increase in the dissolved fraction

is obtained. Following the argument of Harriott [93]: δm~D1/3, and so at a lower temperature,

indicating a lower diffusion coefficient, eddies must come closer to the surface to remove

solute. However, following each solute removal, the time required to re-establish a steady

state gradient is proportional to D−1. This implies that the effect of relatively fewer eddies is

greater when the diffusion coefficient is lower.


131

Table 5-1: Mean mass transfer coefficient of MGSi–II specimens, mk , and estimated mass boundary layer thickness, δm, at various operating conditions.

SPH (K)

Bulk velocity, (cm s−1)

Gas flow rate, (SLPM)

Mass transfer coefficient, × 5

mk 10 (m s−1)

Estimated boundary layer thickness, δm

(mm)

40

0 0 5.17 ± 0.25 0.24

0.50 6.04 ± 0.25 0.20 1.00 6.48 ± 0.24 0.19

1.4 0 6.05 ± 0.01 0.20

0.50 6.77 ± 0.24 0.18 1.00 7.26 ± 0.07 0.17

3.5

0 6.42 ± 0.38 0.19 0.25 6.85 ± 0.44 0.18 0.50 8.36 ± 0.26 0.15 0.75 8.94 ± 0.45 0.14 1.00 9.08 ± 0.35 0.13

7.0 0 8.82 ± 0.35 0.14

0.50 11.00 ± 0.13 0.11 1.00 11.52 ± 0.19 0.11

80

0 0 6.93 ± 0.33 0.24

0.50 7.58 ± 0.33 0.22 1.00 7.87 ± 0.27 0.21

1.4 0 7.31 ± 0.25 0.22

0.50 7.82 ± 0.26 0.21 1.00 8.36 ± 0.13 0.20

3.5

0 7.92 ± 0.80 0.21 0.25 8.19 ± 0.26 0.20 0.50 8.85 ± 0.31 0.19 0.75 9.23 ± 0.51 0.18 1.00 9.84 ± 0.62 0.17

7.0 0 10.76 ± 0.56 0.15

0.50 11.64 ± 0.22 0.14 1.00 12.85 ± 0.40 0.13

5.2.2 Effect of gas flow rate

A higher gas flow rates imparts a higher energy to the liquid. While the addition of gas

kinetic energy is insignificant, the displacement of liquid due to the relative motion of the


132

rising bubbles plays an important role in dissolution enhancement. By changing the gas flow

rate from 0.25 to 1.00 SLPM, EB is in the range of 0.13-0.47 W (Equation (2-4)), while EK is

in the range of 10−6-10−4 W.

Figures 5-6 and 5-7 illustrate that ΔDF and EF increase with an increase in the gas flow

rate, regardless of the type of MGSi and bath temperature. Injecting gas at a higher flow rate

produces larger bubbles at roughly the same frequency, as shown in Figure 4-12 and

discussed in Section 4.3.5.1. The displacement of a larger volume of liquid significantly

increases turbulence intensity but not mean velocity, as evidenced by the FLOW-3D

simulations (Section 5.3.5.2) and by LDV measurements in water [65]. Nevertheless, as Sh is

a function of both Red based on the mean velocity component, and ReT based on the rms

velocity fluctuations at the position of the dissolving object [97], there is a noticeable

enhancement in mass transfer by increasing the gas flow rate.

A comparison of Figure 5-6 (b) and Figure 5-7 (b) also reveals that the EF for MGSi–I

are much higher than for MGSi–II at the same operating conditions, even though the

corresponding ΔDF values in Figure 5-6 (a) and Figure 5-7 (a) are similar. This is because

the MGSi–I specimens dissolved more slowly than the MGSi–II in a single-phase flow,

resulting in a much smaller denominator in Equation (5-1).

As mentioned, gas agitation increased the dissolved fraction of MGSi–I and MGSi–II to a

similar extent. By contrast, in the single-phase experiments, increasing the bulk velocity

increased the dissolution rate of Si specimens with fewer impurities (MGSi–II) more than the

rate of specimens with more impurities (MGSi–I). This may be because the MGSi–I

specimens dissolved more non-uniformly (e.g. Figure 3-14), and the solid Si/liquid Al mass

transfer interface was thus much more three-dimensional due to the presence of randomly

located inclusions. The bubble‐induced velocities associated with gas injection are

appreciably more three-dimensional (e.g. Figure 4-32 (a)) and it may be that this type of flow

was better suited to dissolving a more complex interface structure.


133

Finally, Figure 5-7 shows that at various gas flow rates, the relative effect of gas agitation

on dissolution enhancement decreases with increasing temperature, for the same reasons

mentioned previously.

5.2.3 Effect of lance location

The effect of the relative position of the lance with respect to the Si cylinder on the

dissolution rate was examined. As illustrated in Figure 5-8, although the mass transfer

enhancement decreases slightly with increasing distance between the lance and specimen, it

appears that the velocity fluctuations generated by the bubbles are convected throughout the

tank. This is in accordance with the simulation results (Figure 4-27 and Figure 4-28).

It is especially noteworthy that even when the lance is downstream of the Si specimen

(i.e. θ < 0), a higher mass transfer is achieved compared to the single-phase flow

experiments. This is also in agreement with the results of simulations, that predicted similar

mean velocity and rms velocity fluctuations both at upstream and downstream locations

(Figure 4-37). This is one of the characteristics of turbulent flow, that the motion at any

location can strongly affect the motion at other locations [148].


134

(a)

(b)

Figure 5-6: (a) ΔDF and (b) EF for MGSi–I vs. gas flow rate (immersion time = 3 min, bulk velocity = 3.5 cm s−1, θ = 30°, the lines indicate average values).


135

(a)

(b)

Figure 5-7: (a) ΔDF and (b) EF for MGSi–II vs. gas flow rate (immersion time = 3 min, bulk velocity = 3.5 cm s−1, θ = 30°, the lines indicate average values).


136

(a)

(b)

Figure 5-8: ΔDF vs. the relative positions of the gas injection lance and Si specimen for (a) MGSi–I, SPH = 40 K and (b) MGSi–II, SPH = 80 K (immersion time = 3 min, bulk velocity = 3.5 cm s−1, gas flow rate = 1.00 SLPM, the filled symbols indicate average values).


137

5.2.4 Correlating single- and two- phase flows

Chapter 4 presented CFD predictions of the effect of gas injection on both bulk velocity and

velocity fluctuations in liquid Al. Here from the experimental data, single-phase and

two-phase flow mass transfer coefficients are compared to correlate the effect of gas

injection (i.e. two-phase flow) to an equivalent bulk velocity (i.e. single-phase flow). Each of

Figure 5-9 (a) and (b) superimposes two plots: (i) two-phase mass transfer coefficients vs.

gas flow rate (on the top abscissa) at different bulk velocities, and (ii) single-phase mass

transfer coefficients vs. bulk velocity (on the bottom abscissa). Bubble-induced velocities can

then be interpreted as an equivalent increment to the bulk velocity of the liquid.

To illustrate this, Figure 5-10 is a simpler version of Figure 5-9, with the single-phase

flow results plotted against only the two-phase flow experiments at 3.5 cm s−1. At a SPH of

40 K and a two-phase bulk velocity of 3.5 cm s−1 (Figure 5-10 (a), dotted line with the open

circles), when gas is injected at a flow rate of 1.00 SLPM (TT'), the mass transfer coefficient

is about 9 × 10−5 m s−1; this same mass transfer coefficient is obtained in a single-phase flow

moving at about 7.3 cm s−1 (SS'). At the higher SPH of 80 K (Figure 5-10 (b)), for the same

two-phase flow bulk velocity and gas flow rate as above (TT"), the equivalent single-phase

flow bulk velocity (SS") is only 5.9 cm s−1. Figure 5-9 may be used in a similar manner at

other operating conditions to correlate the effect of gas injection on mass transfer rate to an

increase in the bulk velocity.


138

(a)

(b)

Figure 5-9: Mass transfer coefficient vs. gas flow rate (shown on the top abscissa) superimposed on mass transfer coefficient vs. bulk velocity (shown on the bottom abscissa) for (a) SPH = 40 K and (b) SPH = 80 K (MGSi–II, immersion time = 3 min, θ = 30°, error bars indicate the standard deviations).


139

(a)

(b)

Figure 5-10: Mass transfer coefficient vs. gas flow rate at a bulk velocity of 3.5 cm s−1 (shown on the top abscissa) superimposed on mass transfer coefficient vs. bulk velocity (shown on the bottom abscissa) for (a) SPH = 40 K and (b) SPH = 80 K (MGSi–II, immersion time = 3 min, θ = 30°, error bars indicate the standard deviations).


140

5.3 Comparison with a Correlation for Mass Transfer in a Gas‐stirred Tank

For the non-rotating tank, the results of the two-phase flow dissolution experiments are

compared to the correlation of Mazumdar et al. [97,107] for mass transfer from vertical

benzoic acid cylinders in a gas-stirred water tank [97], and vertical steel cylinders in

gas-stirred carbon saturated iron [107], both inside and outside the plume region:

( ) ( ) ( )0.25 0.32 0.33d TSh 0.73 Re Re Sc= . (5-6)

Red and ReT are based on local mean and rms velocity fluctuations, respectively.

Table 5-2 shows that Equation (5-6) underestimates the mass transfer coefficients, mk , by

27% and 17% at gas flow rates of 0.50 and 1.00 SLPM, respectively. The reason may be that

in [97,107], both V and u at the location of the dissolving specimens are much higher

(benzoic acid cylinders in water: 5 cm s−1 < V < 32 cm s−1, 1.1 cm s−1 < u < 7.5 cm s−1 [97];

steel cylinders in carbon saturated iron: 18 cm s−1 < V < 43 cm s−1, 1.3 cm s−1 < u < 5.0 cm

s−1 [107]) than the values predicted numerically in the current study (Figure 4-26 and

Table 5-2). As a result, natural convection effects were less important in those studies. To

take into account natural convection in the current study, the Mazumdar correlation values

were combined with the experimentally-deduced natural convection mass transfer

coefficients. Using the general combining law described in Section 3.3.2.3 yields a much

better agreement with the experimental data. The differences between the combined

correlation predictions and the experimental results are −5% and −3% at gas flow rates of

0.50 and 1.00 SLPM, respectively.

The small discrepancy may be associated with the prescribed incubation time. To

estimate the two-phase flow experimental mass transfer coefficients, the dissolution data was

used while taking into account the incubation times from the single-phase flow experiments.

It is very possible that the incubation times were shorter in the two-phase flow experiments.


141

By overestimating the incubation times, the experimental mass transfer coefficients would be

overpredicted.

5.4 Comparison with a Correlation for Mass Transfer in Turbulent Cross Flow

The Mazumdar correlation was also applied to the rotating tank (e.g. bulk velocity = 3.5

cm s−1, in which the gas-agitated velocity field was predicted in Chapter 4). However, even

when considering natural convection, the correlation underpredicts the experimental results

by 19% and 23% at gas flow rates of 0.50 SLPM and 1.00 SLPM, respectively. This is

because the Mazumdar fluid flow configuration with respect to the cylindrical specimen

[97,107] is different than in the rotating tank. For that reason, an effort was made to compare

the two-phase flow experimental results to a more appropriate turbulent flow configuration.

As mentioned in Section 4.3.4.3, there are a fair number of correlations that predict heat

and mass transfer from spheres and cylinders in cross flow, but usually in a gas phase

characterized by low turbulence intensities. In studies of liquid phase cross flow (i.e. water),

Iguchi et al. [102] and Szekely et al. [101] proposed a correlation for heat transfer based on

the melting rate of ice spheres and horizontal cylinders in a bottom stirred cylindrical water

tank, respectively. Iguchi et al. [102] defined Tu based on axial mean and rms velocity

fluctuations along the plume centerline; Szekely et al. [101] normalized the local velocity

fluctuations based on gas entry velocity. As a result, these correlations are not based on

appropriate local velocities, and so their general use is not possible. To the best of the

author’s knowledge, only Sandoval-Robles et al. [149] proposed a correlation for mass

transfer from solid spheres in a liquid phase cross flow with high turbulence intensities. In

that case, the turbulence was generated by a porous plate. They used the mean and rms

velocity fluctuations at the location of the solid to calculate Re and ReT (330 < Red < 1720


142

and 0.04 < Tu < 0.3, in the range of Red and Tu of the current study). They describe the mean

velocity by 1/2dRe , and account for the turbulence effect by 0.066

TRe .

This suggests that for a turbulent stream, ReT with the same exponent may be

incorporated into the Churchill and Bernstein correlation [126] for heat and mass transfer

from cylinders in cross flow (Equation (3-11)), rewritten here for mass transfer,

( )

4/55/81/2 1/3d d

1/42/3

0.62 Re Sc ReSh 0.3 12820001 0.4 / Sc

⎡ ⎤⎛ ⎞= + +⎢ ⎥⎜ ⎟⎝ ⎠⎡ ⎤ ⎢ ⎥⎣ ⎦+⎣ ⎦

(5-7)

Recall that the predictions of this correlation when combined with natural convection

were in a satisfactory agreement with the single-phase flow experiments (Section 3.3.2.3).

Therefore, Equation (5-7) may be adapted as follows:

( )

4/55/81/2 1/30.066d dT1/42/3

0.62 Re Sc ReSh 0.3 1 Re2820001 0.4 / Sc

⎡ ⎤⎛ ⎞= + +⎢ ⎥⎜ ⎟⎝ ⎠⎡ ⎤ ⎢ ⎥⎣ ⎦+⎣ ⎦

(5-8)

Table 5-3 presents a comparison of mass transfer coefficients obtained from

Equation (5-8) (based on the initial diameter of the cylinder, and combined with a natural

convection correlation) with experimental values. The agreement is much better than with the

Mazumdar correlation, yet the experimental data are under-predicted at lower velocities and

overpredicted at higher velocities.

The correlation may underpredict the experimental data for either of two reasons. The

first is associated with the incubation time, as described in Section 5.3. The second reason is

due to the use of the initial diameter of the cylindrical Si specimens for calculating the mass

transfer coefficients. The initial diameter underpredicts the mass transfer coefficient as the

dissolution progresses. As discussed in Section 3.3.2.3, as the radius of the specimen

decreases, the shrinkage rate increases, indicating a higher mass transfer coefficient.

On the other hand, the correlation may overpredict the experimental data because the

effect of gas agitation in Equation (5-8) is represented only by the magnitude of velocity

fluctuations, irrespective of the bulk velocity. As mentioned in Section 5.2.1, there are


143

studies that suggest that when predicting transport rate enhancement in a turbulent flow, that

the velocity fluctuations must be normalized by the liquid bulk velocity or its square root.

This reduction of dissolution enhancement at higher bulk velocities is observed

experimentally (Figure 5-4 and Figure 5-5), but is not incorporated in the correlation.


144

Table 5-2: Predicted mass transfer coefficients using the general combining law for Equation (5-6) and natural convection, and a comparison with experimental values (bulk velocity = 0, θ = 30°).

Bubble-induced velocities, cm s−1

(Average at steady state)

Re, based on initial specimen diameter

Mean transfer coefficient × 105, m s−1

Gas flow rate

(SLPM) V< > u< >

0dRe based

on V< > TRe based

on u< > Experimental

Predicted via

Equation (5-6)

Modified using combined convection correlation

Error (%) Combined convection correlation Experimental

100Experimental

−×=

0 – – – – 5.17 – – – 0.50 1.78 0.46 637 166 6.04 4.40 5.75 −5 1.00 1.90 0.81 680 290 6.48 5.35 6.26 −3

Table 5-3: Predicted mass transfer coefficients using the general combining law for Equation (5-8) and natural convection, and a comparison with experimental values (θ = 30°).

Bubble-induced velocities, cm s−1

(Average at steady state)

Re, based on initial specimen diameter Mean mass transfer coefficient × 105, m s−1

Gas flow rate

(SLPM)

Bulk velocity (cm s−1)

V< > u< > 0dRe based

on V< > TRe based

on u< > Experimental

Predicted via

Equation (5-8)

Modified using combined convection correlation

Error (%) Combined convection correlation Experimental

100Experimental

−×=

0.50 1.4 1.70 0.72 609 259 6.77 5.28 6.21 −8 0.50 3.5 3.43 0.76 1227 272 8.36 7.58 7.96 −5 1.00 3.5 3.46 0.91 1236 326 9.08 7.70 8.06 −11 0.50 7.0 6.91 0.96 2473 342 11.06 11.00 11.20 +2


145

5.5 Relationship Between Mass Transfer Coefficient and Energy Input into the Liquid in Single and Two-phase Flows

The effect of single-phase and two-phase flows on accelerating the dissolution rate of Si in

Al has been presented. We now briefly consider the implications for practical applications,

from an energy requirements point of view. The approach is to calculate the energy input to

the liquid for a certain degree of dissolution enhancement. Figure 5-11 shows normalized

mass transfer coefficient at the position of the Si specimen (θ = 30°, SPH = 40 K) vs. the

normalized time- and spatial-averaged liquid kinetic energy per unit mass of liquid

(calculated analytically for single-phase flow, and computed from the FLOW-3D results for

two-phase flow). The baseline is associated with the lowest single-phase flow velocity (bulk

velocity = 3.5 cm s−1).

To increase the dissolution rate, the required energy input into the liquid via gas injection

is less ( 1/3m lk K< > < >∼ ) than that required to increase the bulk flow velocity (

1/4m lk K< > < >∼ ). This may be surprising as in Figure 5-9 an increase in the bulk velocity

appears to be more effective at increasing the mass transfer coefficient. However, the results

suggest that the square root dependence (i.e. b 0.5l(U ) K< >∼ ) implies that increasing the

bulk velocity of a single-phase flow requires much more energy than is needed to induce

fluctuating velocities in a two-phase flow. (Deduction of a universal relationship between

energy input and the velocity fluctuations is not straightforward; however, the limited

simulation results suggest that at the position of the Si cylinder: 1.2lu K< > < >∼ .) This is a

significant practical implication, that dissolution can be enhanced by gas stirring with less

energy input to the liquid than is required by mechanical stirring.


146

Figure 5-11: Normalized mass transfer coefficient for single-phase and two-phase flows vs. normalized liquid kinetic energy per unit mass of liquid.

5.6 Summary

The dissolution of Si in Al in a gas-agitated liquid was examined. The effect of bath

temperature, bulk liquid velocity, gas flow rate and the lance position on dissolution was

quantified: gas agitation is relatively less effective at higher bath temperatures; gas injection

to agitate a bulk flow is more successful when forced convection is dominant; a higher gas

flow rate produces larger bubbles, which yield higher turbulence intensities resulting in a

higher dissolution rate; and gas agitation increased the dissolved fraction of Si specimens

both downstream and upstream of the lance.

At a given bulk velocity, the results offer quantitative guidance to enhance the dissolution

rate to a desired level, by increasing the bulk velocity or by blowing a prescribed amount of

gas. In this way, the effect of gas agitation on dissolution enhancement is expressed as an

equivalent increment to the bulk velocity.


147

The experimental results were compared to available mass transfer correlations

applicable to the rotating and non-rotating tank experiments. For the non-rotating tank, a

correlation developed for mass transfer from vertical cylinders in gas-agitated ladles

predicted the experimental results within 5%. For the rotating tank, the effect of free stream

turbulence was introduced into a correlation for heat and mass transfer from cylinders in

cross flow. The new correlation predicted the experimental results within 11%. The

discrepancies may be associated with the unknown incubation times in the two-phase flow,

an increase of the mass transfer coefficient with decreasing specimen size, and

overpredicting the effect of gas agitation at higher bulk velocities.

148

CHAPTER 6

SUMMARY, CONCLUSIONS AND FUTURE WORK

6.1 Summary

The dissolution of Si into Al is a bottleneck for the Al industries which produce Al–Si alloys

for cast parts. The slow dissolution results in material and energy losses, and reduces

productivity. Faster dissolution would yield economic savings and environmental benefits,

yet the effects of parameters that influence the dissolution rate have not been systematically

quantified.

By immersing more than 700 cylindrical Si specimens, this thesis represents a

comprehensive study of the dissolution rate of solid Si into molten Al under different fluid

flow conditions. The first series of experiments were conducted without gas agitation. The

dissolution of Si specimens with different impurity levels was examined both under natural

and forced convection conditions. In the next series of experiments, the Al bath was agitated

by introducing N2 bubbles into the liquid using top lance injection. The effects of bath

temperature, bulk liquid velocity, and gas flow rate on dissolution rate were related to each

other via deduced mass transfer coefficients.

CHAPTER 6. SUMMARY, CONCLUSIONS AND FUTURE WORK

149

To understand the localized mass transfer phenomena, the fluid dynamics of a

gas-agitated bath must be considered. A physical model (air–water system) was used to

provide insight into the bubble behavior (frequency, size, and trajectory), and the

gas-agitated free surface of the molten Al was video recorded. To estimate the velocity field,

the FLOW-3D software was used. The simulation results were validated by comparing with

the air–water results, and then simulations were run for some of the N2–Al experimental

cases.

The following are the conclusions drawn from the single-phase flow experiments, the

bubble characterization experiments, the simulations, and the two-phase flow experiments.

6.2 Conclusions

Single-phase flow experiments: The effects of solid Si impurities and Al bath temperature

and velocity on the dissolution rate of Si specimens were examined.

(1) Polycrystalline metallurgical grade Si (MGSi) with higher levels of impurities

dissolved more slowly than high purity polycrystalline MGSi, which showed a similar

dissolution rate to monocrystalline electronic grade Si (EGSi). The impurities were in the

form of inclusions composed of elements with lower diffusion coefficients in liquid Al

than that of Si in liquid Al. It is postulated that the inclusions obstruct the dissolution of

Si.

(2) For the high purity metallurgical grade Si, under natural convection, an increase in the

bath superheat from 40 to 80 K increases the mass transfer coefficient by 30%. Under

forced convection, increasing the bulk liquid velocity from 0 to 9.9 cm s−1 increases

the mass transfer coefficient by 100%.


150

(3) In the natural convection experiments, the value of GrmSc was in the turbulent

regime. For the high purity Si cylinders, the experimental data exhibited good

agreement with a dimensionless correlation for vertical cylinders:

1/3mSh (0.11 to 0.129)(Gr Sc)= , where 8 8

m,l5.5 10 Gr 7.4 10× < < × and 29 Sc 42< < .

(4) Under forced convection conditions (by rotating the liquid Al), the mass transfer rate

increased at higher liquid velocities, demonstrating that the dissolution process is

controlled by liquid phase diffusion (LPD). When the forced convection prevailed

over natural convection, the experimental data for high purity cylinders were fitted

with a dimensionless correlation for cylinders in cross flow [126]:

( )

4/55/81/2 1/3d d

1/42/3

0.62Re Sc ReSh 0.3 12820001 0.4 / Sc

⎡ ⎤⎛ ⎞= + +⎢ ⎥⎜ ⎟⎝ ⎠⎡ ⎤ ⎢ ⎥⎣ ⎦+⎣ ⎦

, where 0d510 < Re < 3800 and

29 Sc 42< < .

(5) At lower bulk velocities of the liquid (< 3 cm s−1), a combined effect of natural and

forced convection must be considered; this is important when the value of

( ) ( )4 2m,l dd l Gr Re⎡ ⎤

⎣ ⎦ is equal to or larger than unity. For this case, a new correlation

was presented based on the general combining law of Churchill and Usagi [131]:

( ) ( )1/44 4N F

m m mk k k⎡ ⎤= +⎢ ⎥⎣ ⎦.

Bubble characterization experiments: A series of bubble injection experiments in water and

in liquid Al were conducted to investigate the effect of gas flow rate and bulk velocity on

bubbling behavior.

(6) In water, using top lance injection, when air bubbles form they do not wet the lance.

Increasing the gas flow rate increases the bubble size and changes the formation

mechanism, from single bubbles, to the coalescence of bubble pairs during rise, to the


151

coalescence of bubbles at the lance exit. When bubble pairs form, the shape and size

of the trailing bubble is affected (i.e. the bubble is elongated and up to 45% smaller

by volume) by the leading one, especially in the third regime. Smaller wobbling

bubbles in water follow a zig-zag path, which changes to a rectilinear one with more

violent bubble interface deformation as the bubbles become larger.

(7) In liquid Al, using top lance injection, N2 bubbles form at a relatively constant

frequency (33-38 s−1),and so the bubble size increases with gas flow rate. The

estimated single bubble size was in the range of 1-2 cm, but it is postulated that the

bubbles may coalesce at the lance exit or during rise, especially at higher flow rates.

The bubbles wet the boron nitride coated lance, and so wick up the lance and reach

the free surface adjacent to it. The agitation of the liquid was noticeable due to the

rippling of the entire free surface.

(8) In liquid Al, increasing the liquid bulk velocity from 0 to 7 cm s−1, the estimated

bubble diameter decreases no more than 5%, and the bubbles still rise very near the

lance but on the downstream side. This is in contrast to air–water experiments where

the bubble diameter decreases more than 7% at a similar Re (based on lance

diameter), and the bubbles travel downstream of the lance by 4-7 lance diameters.

Fluid flow simulations: FLOW-3D software was used to examine top lance injection bubble

dynamics within water and molten Al, and to predict the 3D velocity field within a revolving

liquid metal tank.

(9) For the air–water system, the simulation and experimental results agree within the

respective standard deviations of bubble formation and rise time. For the N2–Al

system, FLOW-3D slightly overpredicts the bubble size (~8% by diameter); however,

the general bubble formation and rise behavior is predicted as expected.


152

(10) In the non-rotating tank, a recirculating flow is established around the lance due to

the rising bubbles. The region beneath the lance is nearly unaffected by the bubbles.

The largest induced velocities are observed near the lance and near the free surface.

(11) In the non-rotating tank, time and spatial averaging of velocities demonstrates that

liquid velocities decrease sharply near the lance, followed by a more gradual decrease

moving away from the two-phase region. Higher gas flow rates primarily increase the

turbulence intensities rather than the mean velocities. When the Si cylinder is outside

the two-phase region, FLOW-3D predicts that the rms velocity fluctuations increase

by 70%, but the mean velocity by less than 10%, when the gas flow rate is doubled.

(12) In the rotating tank, the bubble-induced flow causes an acceleration of the flow field

upstream of the lance, but induces velocities in the opposite direction of the bulk flow

downstream of the lane. As the bubbles rise just downstream of the lance, the vertical

velocities are highest in this region.

(13) In the rotating tank, time and spatial averaging of velocities reveals that gas injection

increases both mean velocity and turbulence intensity compared to the single-phase

flow. However, increasing the gas flow rate by a further factor of two, mainly affects

the rms velocity fluctuations (which increase by 20%), while the mean velocity

remains relatively unchanged. The bubble-induced motion and agitation are

significant both upstream and downstream of the lance, implying that the effect of gas

agitation is convected to the entire flow field.

Two-phase flow experiments: The effects of bath temperature, liquid bulk velocity, gas flow

rate, and the position of the lance on the dissolution rate of Si were examined:

(14) The effect of gas agitation on accelerating dissolution decreases with increasing bath

temperature, especially in the forced convection regime. This is because the mass


153

boundary layer thickness increases with increasing temperature: a thicker mass

boundary layer is less affected by gas agitation.

(15) Introducing bubbles to agitate the liquid yields a larger increase in the dissolution

rate under forced convection than under natural convection. This is because the bulk

velocity convects the effect of gas agitation throughout the domain. However, a

further increase in the bulk velocity yields a relatively smaller increase in the

dissolution rate.

(16) As the gas flow rate increases, the larger bubbles induce higher velocities, that

further decrease the mass transfer resistance adjacent to the solid Si, increasing the

dissolution rate. Increasing the gas flow rate from 0.25 SLPM to 1.00 SLPM

increases the mass transfer coefficient by 20-30%.

(17) When gas injection is combined with a bulk flow, gas agitation is effective both

upstream and downstream of the lance. This is in agreement with the simulation

results which reveal similar mean velocity and rms velocity fluctuations in upstream

and downstream positions.

(18) For high purity Si in the non-rotating tank, the experimental data is compared to a

dimensionless correlation for mass transfer from vertical solid cylinders in a gas

agitated liquid: ( ) ( ) ( )0.25 0.32 0.33d TSh 0.73 Re Re Sc= ; and the effect of natural

convection is included by applying a general combining law. At gas flow rates of 0.50

and 1.00 SLPM, the discrepancy between the predicted and experimental mass

transfer coefficients is −5% and −3%, respectively.

(19) For high purity Si in the rotating tank, a correlation for vertical cylinders in cross

flow is modified to take into account the turbulence in the bulk flow:


154

( )

4/55/81/2 1/30.066d dT1/42/3

0.62 Re Sc ReSh 0.3 1 Re2820001 0.4 / Sc

⎡ ⎤⎛ ⎞= + +⎢ ⎥⎜ ⎟⎝ ⎠⎡ ⎤ ⎢ ⎥⎣ ⎦+⎣ ⎦

. Combining this equation

with one for natural convection yields mass transfer coefficients within 11% of

experimental values.

6.3 Contributions

Owing to the difficulty of performing experiments at high temperatures, systematic

studies of transport rates in liquid metals, as a function of fluid flow conditions, are very

limited. By conducting a large number of dissolution experiments, corroborated with

physical and numerical modeling of the fluid flow, this thesis quantifies mass transfer rates

from a solid addition in a liquid metal under natural and forced convection conditions,

without and with high turbulence in the bulk flow. The turbulence was generated with top

lance injection method which, as suggested by the findings of this work, can be implemented

in alloying processes for enhancing the assimilation rates of metallic additions. Therefore, the

results of the current study have both theoretical and practical implications.

In the single-phase flow experiments the validity of an existing correlation for natural and

forced convection heat and mass transfer from vertical cylinders in a liquid metal system was

extended. Also, a correlation for mixed convection (at lower bulk velocities) was proposed,

for when the buoyancy force is normal to the direction of the bulk flow. In addition,

examining the effect of temperature and the bulk velocity of the liquid on the dissolution rate

yielded a quantitative guidance for correlating the effect of the two parameters on the

dissolution of Si in molten Al.

The numerical simulation of a gas-agitated ladle was validated with the results of

physical modeling in water, and measurements of bubble frequency in liquid Al. The

validated simulation tool, even though it did not fully resolve the flow, proved to be effective


155

for predicting bubble distribution and estimating the velocity field within the opaque liquid

metal, for the purpose of predicting mass transfer rates.

To the best of author’s knowledge, this is the first time the effect of gas injection

superimposed on a bulk liquid velocity was examined, in terms of the mass transfer rate from

a solid addition in a liquid metal. The results enabled us to present the effect of gas agitation

on the mass transfer rate as an equivalent increment to the bulk velocity. Finally, to extend

the application of the experimental results, an existing mass transfer correlation for a

gas-agitated liquid without an external bulk flow was used to fit the experimental data; with a

bulk velocity, a correlation for mass transfer from a vertical cylinder in cross flow was

modified to incorporate the effect of gas injection.

6.4 Recommendations for Future Work

The following are recommendations for improving and extending this work:

• The experimental study must be extended to analyze the recovery of Si and dross

formation under different operating conditions, to optimize the overall alloying

process.

• A major area of future research is to examine the correlations presented in this thesis

to other metallic systems. These correlations should also be tested for higher

velocities and degrees of agitation.

• In this thesis, the bubble-induced velocities were only approximated. The two-phase

flow could be resolved using LES or DNS, or reliable sensors for measuring

velocities in high temperature liquid metals should be developed.


156

• The analysis of the experimental results suggests that an increase in the liquid energy

by gas agitation yields a higher dissolution rate than by increasing the bulk velocity of

a single-phase flow. This finding must be developed further by identifying a

relationship between the energy input to a liquid and the induced velocity

fluctuations. More important, this laboratory observation must be confirmed at a plant

scale.

157

LIST OF REFERENCES

[1] JAS Green, Aluminum recycling and processing for energy conservation and sustainability, in: Green JAS (Ed.), ASM International, Materials Park, Ohio, 2007, pp. 135.

[2] DA Buckingham, PA Plunkert, EL Bray, Historical statistics for mineral and material commodities in the United States, US Geological Survey, 2013.

[3] R Lumely, Fundamentals of aluminium metallurgy: production, processing and applications, in: Lumley RN (Ed.), Woodhead Publishing Ltd, Cambridge, 2011.

[4] ME Schlesinger, Aluminum recycling, CRC/Taylor & Francis, Boca Raton, FL, 2007.

[5] D Doutre, Personal Communication, Novelis Global Technology Center, Kingston, Ontario, December 2013x.

[6] MJ Assael, K Kakosimos, RM Banish, J Brillo, I Egry, R Brooks, et al. Reference data for the density and viscosity of liquid aluminum and liquid iron, Journal of physical and chemical reference data. 35 (2006) 285-300.

[7] RK Endo, Y Fujihara, M Susa. Calculation of the density and heat capacity of silicon by molecular dynamics simulation, High Temperatures - High Pressures. 35-36 (2003) 505-511.

[8] T Bourgeois, A Chapdelaine, A Larouche, Optimal metal stirring with Alcan Jet Stirrer, in: MacEwwn S, Gilardeau J- (Eds.), Recent Metallurgical Advances in Light Metals Industries, The Metallurgical Society of CIM, Vancouver, BC, Canada, 1995, pp. 390-400.

[9] D Mazumdar, RIL Guthrie. Physical and mathematical modeling of gas stirred ladle systems, The Iron and Steel Institute of Japan. 35 (1995) 1-20.

[10] D Mazumdar, JW Evans. Macroscopic models for gas stirred ladles, The Iron and Steel Institute of Japan International. 44 (2004) 447-461.

[11] A Shafyei, The kinetics of dissolution of high melting point alloying elements in molten aluminum, Ph.D. Thesis, Department of Mining and Metallurgical Engineering, McGill University, Montreal, QC, Canada (1996).

[12] JR Welty, CE Wicks, RE Wilson, G Rorrer, Fundamentals of momentum, heat, and mass transfer, 5th ed., John Wiley & Sons, Inc., Chichester, 2008.

[13] G Baluais, M Brown, J Strydom. Silicon granules for aluminum alloys, Paper presented at the Light Metals: Proceedings of Sessions, TMS Annual Meeting (Warrendale, Pennsylvania). (2002) 817-819.

158

[14] DG Altenpohl, Aluminum: technology, applications, and environment: a profile of a modern metal: aluminum from within, 6th ed., The Aluminum Association, Washington, D.C., 1998.

[15] JE Gruzleski, MC Closset, The treatment of liquid aluminum-silicon alloys, American Foundrymen's Society, Des Plaines, III., 1990.

[16] DL Zalensas, Aluminum casting technology, in: Jorstad JL, Zalensas DL, Rasmussen WM, American Foundrymens Society. (Eds.), 2nd ed., American Foundrymen's Society, Des Plaines, III., 1993,.

[17] F Paray, Heat treatment and mechanical properties of aluminum-silicon modified alloys, Ph.D. Thesis, Department of Mining and Metallurgical Engineering, McGill University, Montreal, QC, Canada (1992).

[18] H Engstroem, LO Gullman. Multilayer clad aluminum material with improved brazing properties, Welding Journal (Miami, Fla). 67 (1988) 222-226.

[19] JL Murray, AJ McAlister, The Al-Si (Aluminum-Silicon) system, Bulletin of alloy phase diagrams, American Society for Metals, United States, National Bureau of Standards, Metals Park, Ohio, 1984, pp. 74-84.

[20] S Seetharaman, A McLean, R Guthrie, S Sridhar, Treatise on process metallurgy, Chapter VII, "Some applications of fundamental principles to metallurgical operations", Chapter editor. McLean, A. Elsevier, 2013.

[21] K Sun, SA Argyropoulos. The exothermicity and recovery of Al-Mn compacts into molten aluminum, Canadian Metallurgical Quarterly. 45 (2006) 223-232.

[22] D Mazumdar, JW Evans, Modeling of steelmaking processes, CRC Press, Taylor & Francis Group, Boca Raton, London, New york, 2009.

[23] JB Darby, DB Jugle, OJ Kleppa. The rate of solution of some transition elements in liquid aluminum, Transactions of the Metallurgical Society of AIME. 227 (1963) 179-185.

[24] MO Pekguleryuz, JE Gruzleski. Dissolution of non-reactive strontium containing master alloys in liquid aluminum and A356 melts, Canadian Metallurgical Quarterly. 28 (1989) 55-65.

[25] M Niinomi, Y Ueda, M Sano. Dissolution of ferrous alloys into molten aluminum, Transactions of the Japan Institute of Metals. 23 (1982) 780-787.

[26] M Kosaka, S Minowa. Mass transfer from the surface of stating steel cylinder into liquid Al or Zn, Tetsu-to-Hagane. 52 (1966) 539-542.

[27] PK Gairola, RK Tiwari, A Ghosh. Rates of dissolution of a vertical nickel cylinder in liquid aluminum under free convection, Metallurgical Transactions. 2 (1971) 2123-2126.

159

[28] VN Eremenko, YV Natanzon, VP Titov. Kinetics of chromium dissolution in aluminium at 700-900 °C, Russian Metallurgy. 6 (1980) 193-197.

[29] VN Eremenko, YV Natanzon, VP Titov. Kinetics of rhenium dissolution in molten aluminum, Russian Metallurgy. (1986) 52-55.

[30] VN Eremenko, YV Natanzon, VP Titov. Dissolution kinetics and diffusion coefficients of iron, cobalt, and nickel in molten aluminum, Soviet Materials Science. 14 (1979) 579-584.

[31] N Tunca, GW Delamore, RW Smith. Corrosion of Mo, Nb, Cr, and Y in molten aluminum, Metallurgical Transactions A. 21 A (1990) 2919-2928.

[32] VN Yeremenko, YV Natanzon, VI Dybkov. Interaction of the refractory metals with liquid aluminum, Journal of the Less-Common Metals. 50 (1976) 29-48.

[33] LN Shibanova, AA Vostryakov, BM Lepinskikh. Dissolution of iron and titanium in metal melts, Protection of Metals (English translation of Zaschita Metallov). 25 (1990) 519-521.

[34] VN Eremenko, YV Natanzon, VR Ryabov. Investigation of the kinetics of dissolution of solid metals in metal melts by the rotating disk method iron-aluminum system, Fiziko-Khimicheskaya Mekhanika Materialov. 4 (1968) 286-290.

[35] VI Dybkov. Interaction of iron-nickel alloys with liquid aluminium - Part I Dissolution kinetics, Journal of Materials Science. 28 (1993) 6371-6380.

[36] M Niinomi, Y Suzuki, Y Ueda. Dissolution of ferrous alloys into molten pure aluminum under forced flow, Transactions of the Japan Institute of Metals. 25 (1984) 429-439.

[37] VG Levich, Physicochemical hydrodynamics, Prentice-Hall, Englewood Cliffs, N.J., 1962.

[38] TF Kassner. Rate of solution of rotating tantalum disks in liquid tin, Journal of the Electrochemical Society. 114 (1967) 689-694.

[39] GS Ershov, AA Kasatkin, AA Golubev. Dissolution and diffusion of alloying elements in liquid aluminum, Izvestiya AN SSSR: Metally. (1979) 77-79.

[40] VI Lozovskiy, PF Politova. The diffusion of elements in liquid aluminum, Fiz. metallov i metalloved. 26 (1968) 381.

[41] M Lance, J Bataille. Turbulence in the liquid phase of a uniform bubbly air-water flow, Journal of Fluid Mechanics. 222 (1991) 95-118.

[42] TC Hsiao, T Lehner, B Kjellberg. Fluid flow on ladles - experimental results, Scandinavian Journal of Metallurgy. 9 (1980) 105-110.

160

[43] SM Pan, JD Chiang, WS Hwang. Simulation of large bubble/molten steel Interaction for gas-injected ladle, Journal of Materials Engineering and Performance. 8 (1999) 236-244.

[44] M Iguchi, T Chihara, N Takanashi, Y Ogawa, N Tokumitsu, Z Morita. X-ray fluoroscopic observation of bubble characteristics in a molten iron bath, The Iron and Steel Institute of Japan International. 35 (1995) 1354-1361.

[45] M Iguchi, T Nakatani, H Tokunaga. The shape of bubbles rising near the nozzle exit in molten metal baths, Metallurgical and Materials Transactions B: Process Metallurgy and Materials Processing Science. 28 (1997) 422-423.

[46] GA Irons, RIL Guthrie. Bubble formation at nozzles in pig iron, Metallurgical and Materials Transactions B. 9B (1978) 101-110.

[47] M Iguchi, H Takeuchi, Z Morita. Flow field in air-water vertical bubbling jets in a cylindrical vessel, The Iron and Steel Institute of Japan International. 31 (1991) 246-253.

[48] M Iguchi, K Nozawa, Z Morita. Bubble characteristics in the momentum region of air-water vertical bubbling jet, The Iron and Steel Institute of Japan International. 31 (1991) 952-959.

[49] YY Sheng, GA Irons. Measurements of the internal structure of gas-liquid plumes, Metallurgical Transactions B. 23B (1992) 779-788.

[50] Y Sahai, RIL Guthrie. Hydrodynamics of gas stirred melts: Part I. Gas/liquid coupling, Metallurgical Transactions B. 13 (1982) 193-202.

[51] Y Sahai, RIL Guthrie. Hydrodynamics of gas stirred melts: Part II. Axisymmetric flows, Metallurgical Transactions B. 13 (1982) 203-211.

[52] JH Grevet, J Szekely, N El-Kaddah. An experimental and theoretical study of gas bubble driven circulation systems, International Journal of Heat and Mass Transfer. 25 (1982) 487-497.

[53] RS Bernard, RS Maier, HT Falvey, A simple computational model for bubble plumes, Applied Mathematical Modeling. 24 (2000) 215-233.

[54] H Tsuge, M Mitsudani, Y Tezuka. The effect of nozzle shape on bubble formation from a downward nozzle, Chemical Engineering and Technology. 29 (2006) 1097-1101.

[55] T Goda, M Iguchi, Y Sasaki, H Kiuchi. Empirical equations for bubble formation frequency from downward-facing nozzle with and without rotating flow effects, Materials Transactions. 46 (2005) 2461-2466.

[56] A Gosset, P Rambaud, P Planquart, J- Buchlin, E Robert. Experimental characterization of bubbling in submerged lance injection, AIP Conference Proceedings. 1207 (2010) 205-210.

161

[57] Q Fu, D Xu, JW Evans. Chlorine fluxing for removal of magnesium from molten aluminum part I. Laboratory-scale measurements of reaction rates and bubble behavior, Metallurgical and Materials Transactions B: Process Metallurgy and Materials Processing Science. 29 (1998) 971-978.

[58] M Iguchi, T Uemura, H Yamaguchi, T Kuranaga, Z Morita. Fluid flow phenomena in a cylindrical bath agitated by top lance gas injection, The Iron and Steel Institute of Japan International. 34 (1994) 973-979.

[59] SV Gnyloskurenko, T Nakamura. Wettability effect on bubble formation at nozzles in liquid aluminum, Materials transactions. 44 (2003) 2298-2302.

[60] H Kogawa, T Shobu, M Futakawa, A Bucheeri, K Haga, T Naoe. Effect of wettability on bubble formation at gas nozzle under stagnant condition, Journal of Nuclear Materials. 377 (2008) 189-194.

[61] T Watanabe, M Iguchi. Water model experiments on the effect of an argon bubble on the meniscus near the immersion nozzle, The Iron and Steel Institute of Japan International. 49 (2009) 182-188.

[62] M Bertherat, T Odièvre, M Allibert, P Le Brun. A radioscopic technique to observe bubbles in liquid aluminum, Light Metals (Warrendale Pa). (2002) 861-867.

[63] AA Kulkarni, JB Joshi. Bubble formation and bubble rise velocity in gas-liquid systems: A review, Industrial and Engineering Chemistry Research. 44 (2005) 5873-5931.

[64] Z Liu, Y Zheng, L Jia, Q Zhang. Study of bubble induced flow structure using PIV, Chemical Engineering Science. 60 (2005) 3537-3552.

[65] JS Kim, SM Kim, HD Kim, HS Ji, KC Kim. Dynamic structures of bubble-driven liquid flows in a cylindrical tank, Experiments in Fluids. 53 (2012) 21-35.

[66] G Riboux, F Risso, D Legendre. Experimental characterization of the agitation generated by bubbles rising at high Reynolds number, Journal of Fluid Mechanics. 643 (2010) 509-539.

[67] JH Milgram. Mean flow in round bubble plumes, Journal of Fluid Mechanics. 133 (1983) 345-376.

[68] D Mazumdar, RIL Guthrie. Comparison of three mathematical modeling procedures for simulating fluid flow phenomena in bubble-stirred ladles, Metallurgical Transactions B. 25 (1994) 308-312.

[69] D Pfleger, S Becker. Modeling and simulation of the dynamic flow behaviour in a bubble column, Chemical Engineering Science. 56 (2001) 1737-1747.

162

[70] D Zhang, NG Deen, JAM Kuipers. Numerical simulation of the dynamic flow behavior in a bubble column: A study of closures for turbulence and interface forces, Chemical Engineering Science. 61 (2006) 7593-7608.

[71] J Lu, G Tryggvason. Numerical study of turbulent bubbly downflows in a vertical channel, Physics of Fluids. 18 (2006).

[72] J Lu, G Tryggvason. Dynamics of nearly spherical bubbles in a turbulent channel upflow, Journal of Fluid Mechanics. 732 (2013) 166-189.

[73] G Tryggvason, R Scardovelli, S Zaleski, Direct numerical simulations of gas-liquid multiphase flows, Cambridge University Press, Cambridge ; New York, 2011.

[74] SO Unverdi, G Tryggvason. A front-tracking method for viscous, incompressible, multifluid flows, Journal of Computational Physics. 100 (1992) 25-37.

[75] FH Harlow, JE Welch. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, Physics of Fluids. 8 (1965) 2182-2189.

[76] CW Hirt, BD Nichols. Volume of fluid (VOF) method for the dynamics of free boundaries, Journal of Computational Physics. 39 (1981) 201-225.

[77] S Osher, JA Sethian. Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics. 79 (1988) 12-49.

[78] Z Yujie, L Mingyan, X Yonggui, T Can. Three-dimensional volume of fluid simulations on bubble formation and dynamics in bubble columns, Chemical Engineering Science. 73 (2012) 55-78.

[79] M Nabavi, K Siddiqui, WA Chishty. 3-D simulations of the bubble formation from a submerged orifice in liquid cross-flow, Proceeding ASME Fluids Engineering Division Summer Conference, FEDSM. 1 (2009) 863-869.

[80] N Ashgriz, JY Poo. FLAIR: Flux line-segment model for advection and interface reconstruction, Journal of Computational Physics. 93 (1991) 449-468.

[81] H Schlichting, Boundary-layer theory, 7th ed., McGraw-Hill, New York, 1979.

[82] EW Comings, JT Clapp, JF Taylor. Air turbulence and transfer processes, flow normal to cylinders, Industrial and Engineering Chemistry Research. (1948) 1076-1082.

[83] A Kondjoyan, JD Daudin. Effects of free stream turbulence intensity on heat and mass transfers at the surface of a circular cylinder and an elliptical cylinder, axis ratio 4, International Journal of Heat and Mass Transfer. 38 (1995) 1735-1749.

[84] WJ Lavender, DCT Pei. The effect of fluid turbulence on the rate of heat transfer from spheres, International Journal of Heat and Mass Transfer. 10 (1967) 529-539.

163

[85] R Shinnar, JM Church. Statistical theories of turbulence in predicting particle size in agitated dispersions, Industrial and Engineering Chemistry. 52 (1960) 253-256.

[86] K Nakanishi, T Fujii, J Szekely. Possible relationship between energy dissipation and agitation in steel processing operations, Ironmaking Steelmaking. 2 (1975) 193-197.

[87] Y Sundberg. Mechanical stirring power in molten metal in ladles obtained by induction stirring and gas blowing, Scandinavian Journal of Metallurgy. 7 (1978) 81-87.

[88] JK Wright. Steel dissolution in quiescent and gas stirred Fe/C melts, Metallurgical Transactions B. 20 (1989) 363-374.

[89] RS Wright, Mass transfer modeling of DRI particle-slag heat transfer in the electric furnace, M.Sc. Thesis, Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, United States, (1979).

[90] CD Wilcox, Turbulence modeling for CFD, 3rd ed., DCW Industries, Inc., San Diego, CA, 2006.

[91] CS Mathpati, JB Joshi, Insight into theories of heat and mass transfer at the solid-fluid interface using direct numerical simulation and large eddy simulation, Industrial and Engineering Chemistry Research. 46 (2007) 8525-8557.

[92] TR Galloway, BH Sage. Thermal and material transport from spheres, International Journal of Heat and Mass Transfer. 10 (1967) 1195-1210.

[93] P Harriott. A random eddy modification of the penetration theory, Chemical Engineering Science. 17 (1962) 149-154.

[94] K Endoh, H Tsuruga, H Hirano, M Morihira. Effect of turbulence on heat and mass transfer, Heat transfer Japanese research. 1 (1972) 113-15.

[95] H Tennekes, JL Lumely, A first course in turbulence, MIT Press, Cambridge, Massachusetts, 1972.

[96] KK Kuo, Fundamentals of turbulent and multiphase combustion, Wiley, Hoboken, N.J., 2012.

[97] D Mazumdar, SK Kajani, A Ghosh. Mass transfer between solid and liquid in vessels agitated by bubble plume, Steel Research. 61 (1990) 339-346.

[98] J Szekely, T Lehner, CW Chang. Flow phenomena, mixing, and mass transfer in argon-stirred ladles, Ironmaking Steelmaking. 6 (1979) 285-293.

[99] S Taniguchi, M Ohmi, S Ishiura, S Yamauchi. A cold model study on the effect of gas injection upon the melting rate of solid sphere in a liquid bath, Transactions of the Iron and Steel Institute of Japan. 23 (1983) 565-570.

164

[100] S Whitaker. Forced convection heat transfer correlations for flow in pipes, past flat plates, single cylinders, single spheres, and for flow in packed beds and tube bundles, AICHE Journal. 18 (1972) 361-371.

[101] J Szekely, HH Grevet, N El-Kaddah. Melting rates in turbulent recirculating flow systems, International Journal of Heat and Mass Transfer. 27 (1984) 1116-1121.

[102] M Iguchi, J Tani, T Uemura, Z Morita. Flow phenomena and heat transfer around a sphere submerged in water jet and bubbling jet, The Iron and Steel Institute of Japan International. 29 (1989) 658-665.

[103] SA Argyropoulos, D Mazumdar, AC Mikrovas, D Doutre. Dimensionless correlations for forced convection in liquid metals, Part II: two phase flow, Metallurgical Transactions B. 32B (2001) 247-252.

[104] S Taniguchi, M Ohmi, S Ishiura. A hot model study on the effect of gas injection upon the melting rate of solid sphere in a liquid bath, Transactions of the Iron and Steel Institute of Japan. 23 (1983) 571-577.

[105] RL Steinberger, RE Treybal. Mass transfer from a solid soluble sphere to a flowing liquid stream, AICHE Journal. 6 (1960) 227-232.

[106] SA Argyropoulos, AC Mikrovas, DA Doutre. Dimensionless correlations for forced convection in liquid metals: Part I. single-phase flow, Metallurgical and Materials Transactions B. 32 (2001) 239-246.

[107] D Mazumdar, T Narayan, P Bansal. Mathematical modeling of mass transfer rates between solid and liquid in high-temperature gas-stirred melts, Applied Mathematical Modelling. 16 (1992) 255-262.

[108] Y Kim, RD Pehlke. Mass transfer during dissolution of a solid into liquid in the Iron-Carbon system, Metallurgical Transactions. 5 (1974) 2527-2532.

[109] N El-Kaddah, J Szekely, G Carlsson. Fluid flow and mass transfer in an inductively stirred four-ton melt of molten steel: A comparison of measurements and predictions, Metallurgical Transactions B. 15 (1984) 633-640.

[110] AK Singh, D Mazumdar. Mass transfer between solid and liquid in a gas-stirred vessel, Metallurgical and Materials Transactions B: Process Metallurgy and Materials Processing Science. 28 (1997) 95-102.

[111] IV Mateiko, MA Shevchenko, NV Kotova, VS Sudavtsova. The thermodynamic properties of Al-Si system melts, Russian Journal of Physical Chemistry A. 85 (2011) 164-170.

[112] B Melissari, The sphere melting technique: mathematical modeling, experimental measurements and applications, Ph.D. Thesis, Department of Materials Science and Engineering, University of Toronto, Toronto, ON, Canada (2004).

165

[113] HP Greenspan, LN Howard. On a time-dependent motion of a rotating fluid, Journal of Fluid Mechanics. 17 (1963) 385-404.

[114] W Zulehner, B Neuer, G Rau, Silicon, Ullmann's Encyclopedia of Industrial Chemistry, Wiley, 2005.

[115] PLT Brian, HB Hales. Effects of transpiration and changing diameter on heat and mass transfer to spheres, AIChE Journal. 15 (1969) 419-425.

[116] T Magnusson, L Arnberg. Density and solidification shrinkage of hypoeutectic aluminum-silicon alloys, Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science. 32 (2001) 2605-2613.

[117] DR Poirier, Transport phenomena in materials processing, Minerals, Warrendale, Pa., 1994.

[118] J Szekely, NJ Themelis, Rate phenomena in process metallurgy, Wiley-Interscience, New York Wiley-Interscience, 1971.

[119] M Kosaka, S Minowa. On rate of dissolution of carbon into molten Fe-C alloy, Tetsu-To-Hagane (Journal of the Iron and Steel Institute of Japan). 8 (1968) 392-400.

[120] M Kosaka, M Machida, Y Hirai. On the dissolution process of solid Al into molten Al-Si, Journal of the Japan Institute of Metals. 33 (1969) 465-470.

[121] SA Argyropoulos. Dissolution characteristics of ferroalloys in liquid steel, Iron and Steelmaker of ISS. (1984) 48-57.

[122] JC Anglezio, C Servant, F Dubrous. Characterization of Metallurgical Grade Silicon, Journal of Materials Research. 5 (1990) 1894-1899.

[123] YV Meteleva-Fischer, Y Yang, R Boom, B Kraaijveld, H Kuntzel. Microstructure of metallurgical grade silicon during alloying refining with calcium, Intermetallics. 25 (2012) 9-17.

[124] S Chang, C Elkins, JK Eaton, S Monismith. Local mass transfer measurements for corals and other complex geometries using gypsum dissolution, Experiments in Fluids. 54 (2013) 1-12.

[125] N Boškovic-Vragolovic, R Garic-Grulovic, R Pjanovic, Ž Grbavcic. Mass transfer and fluid flow visualization for single cylinder by the adsorption method, International Journal of Heat and Mass Transfer. 59 (2013) 155-160.

[126] SW Churchill, M Bernstein. A correlating equation for forced convection from gases and liquids to a circular cylinder in crossflow, Journal of Heat Transfer, Transactions ASME. 99 Ser C (1977) 300-306.

166

[127] GA Alenezi, MSE Abdo. Mass-transfer measurements around a single cylinder in cross flow at low Reynolds-numbers, Chemie Ingenieur Technik. 63 (1991) 381-384.

[128] LS Yao, FF Chen. A horizental flow past a partially heated, infinite vertical cylinder, Journal of Heat Transfer, Transactions ASME. 103 (1981) 546-551.

[129] N Joshi, S Sukhatme. Analysis of combined free and forced convection heat transfer from a horizontal circular cylinder to a transverse flow, Journal of Heat Transfer, Transactions ASME. 93 Ser C (1971) 441-448.

[130] TS Chen, A Mucoglu. Buoyancy effects on forced convection along a vertical cylinder, Journal of Heat Transfer, Transactions ASME. 97 Ser C (1975) 198-203.

[131] SW Churchill, R Usagi. A general expression for the correlation of rates of transfer and other phenomena, AICHE Journal. 18 (1972) 1121-1128.

[132] SW Churchill, Combined free and forced convection around immersed bodies, in: Hewitt GF (Ed.), Hemisphere Heat Exchanger Design Handbook, Hemisphere, Washington, D.C., 1990, pp. 2.5.9-1-2.5.9-7.

[133] J Li, G Brooks, N Provatas. Kinetics of scrap melting in liquid steel, Metallurgical and Materials Transactions B: Process Metallurgy and Materials Processing Science. 36 (2005) 293-302.

[134] T Miyahara, S Kaseno, T Takahashi. Studies on chains of bubbles rising through quiescent liquid, Canadian Journal of Chemical Engineering. 62 (1984) 186-193.

[135] R Clift, JR Grace, ME Weber, Bubbles, drops, and particles, Academic Press, New York, New York, 1978.

[136] T Mekayarajjananonth, S Winkler. Contact angle measurement on dental implant biomaterials. Journal of Oral Implantology. 25 (1999) 230-236.

[137] J- Liow. Quasi-equilibrium bubble formation during top-submerged gas injection, Chemical Engineering Science. 55 (2000) 4515-4524.

[138] D Gerlach, N Alleborn, V Buwa, F Durst. Numerical simulation of periodic bubble formation at a submerged orifice with constant gas flow rate, Chemical Engineering Science. 62 (2007) 2109-2125.

[139] MG Nicholas, DA Mortimer, LM Jones, RM Crispin. Some observations on the wetting and bonding of nitride ceramics, Journal of Materials Science. 25 (1990) 2679-2689.

[140] H Fujii, H Nakae, K Okada. Interfacial reaction wetting in the boron nitride/molten aluminum system, Acta Metallurgica Et Materialia. 41 (1993) 2963-2971.

[141] JL Xia, T Ahokainen, L Holappa. Study of flow characteristics in a ladle with top lance injection, Progress in Computational Fluid Dynamics. 1 (2001) 178-187.

167

[142] YY Sheng, Modeling and measurement of unconfined bubbly two-phase plume flow, Ph.D. Thesis, Department of Mining and Metallurgical Engineering, McMaster University, Hamilton, ON, Canada (1992).

[143] MP Schwarz, WJ Turner. Applicability of the standard k-ε turbulence model to gas-stirred baths, Applied Mathematical Modelling. 12 (1988) 273-279.

[144] D Mazumdar, RIL Guthrie. Hydrodynamic modeling of some gas injection procedures in ladle metallurgy operations, Metallurgical Transactions B. 16 (1985) 83-90.

[145] YY Sheng, GA Irons. Measurement and modeling of turbulence in the gas/liquid two-phase zone during gas injection, Metallurgical Transactions B. 24 (1993) 695-705.

[146] EP Dyban, EY Epick, LG Kozlova. Combined influence of turbulence intensity and longitudinal scale and air flow acceleration on heat transfer of circular cylinder, (1974) 310-314.

[147] VT Morgan, The overall convective heat transfer from smooth circular cylinders, Advances in Heat Transfer. 11 (1975) 199-264.

[148] P Bradshaw. The understanding and prediction of turbulent flow, The Aeronautical Journal. 76 (1972) 403-418.

[149] JG Sandoval-Robles, H Delmas, JP Couderc. Influence of turbulence on mass transfer between a liquid and a solid sphere, AICHE Journal. 27 (1981) 819-823.

168

APPENDIX A: CORRELATIONS FOR MATERIAL PROPERTIES

A.1 Diffusion Coefficient of Si into liquid Al

Using the rotating disk method, Ershov et al. [39] measured the diffusion coefficient of solid

Si into liquid Al in the temperature range 700-1000°C. The variation of diffusion coefficient

with temperature is described by an Arrhenius-type equation,

0QD D exp

RT⎛ ⎞= −⎜ ⎟⎝ ⎠

(A-1)

where D0 = 2.30 x 10−5 m2 s−1, Q = 61010 J mol−1, and R = 8.314 J mol−1 K−1. A linear

variation of −log D vs. 410 / RT is illustrated in Figure A-1.

Figure A-1: Diffusion coefficient of Si into Al as a function of temperature.

169

A.2 Density and Viscosity of Liquid Al

The density of liquid Al in the temperature range 660-917°C is given as [6],

Al 1 2 refc c (T T )ρ = − − (A-2)

where c1 = 2377.23 kg m−3, c2 = 0.311 kg m−3 K−1, and Tref = 933.47 K (melting point of Al).

The standard deviation of the correlation at the 95% confidence level is 0.0065.

The dynamic viscosity of liquid Al in the temperature range 660-997°C is given as [6],

0 210 1

alog ( ) aT

μ μ = − + (A-3)

where μ0 = 0.001 kg m−1 s−1, a1 = 0.7324, and a2 = 803.49 K. The standard deviation of the

correlation at the 95% confidence level is 0.137.

Using Equations (A-2) and (A-3), the kinematic viscosity of liquid Al ( / )ν = μ ρ is

plotted vs. temperature in Figure A-2.

Figure A-2: Kinematic viscosity of liquid Al as a function of temperature.

170

APPENDIX B: IMPROVING THE REPRODUCIBILITY OF Si DISSOLUTION

Significant anomalies in the data obtained from early dissolution experiments led to

inconclusive results. This required a thorough investigation, to improve the reproducibility of

the data. First, an X‐ray Photoelectron Spectroscopy (XPS) analysis was carried out to detect

surface impurities. Substantial amounts of impurities were identified on to the specimen

surfaces. The main elements were carbon and oxygen. The carbon was possibly deposited on

to the surface from the diamond drill used to make the Si cylinders. The oxygen was likely in

the form of SiO2 generated by Si oxidization in ambient air.

To further investigate the variability of the experimental results, 22 as‐drilled MGSi–I

specimens were immersed into 700°C liquid Al (SPH = 40 K) for 5 min. As seen in

Figure B-1, the dissolution of these samples varied significantly; both fully and partially

undissolved samples were retrieved after immersion. This suggested that there must be

dissolution barriers on the surface, possibly the impurities detected using the XPS analysis.

To confirm this, the impurities were mechanically removed by sand paper grinding

(removing 0.05-0.15 mm of the surface). This procedure was performed not more than 12

hours prior to the experiments, and then the ground specimens were kept in a desiccator to

minimize contact with air. Figure B-2 demonstrates that the scatter in the data is significantly

reduced following this preparation method. The ground specimens showed consistently

higher dissolved fractions compared to the as‐drilled ones. In addition, the grinding

eliminated the non‐uniform dissolution of specimens illustrated in Figure B-1.

171

Figure B-1: MGSi–I as‐drilled specimens after natural convection dissolution for 5 min in liquid Al at SPH = 40 K.

Figure B-2: Effect of sample surface preparation on the dissolved fraction of MGSi–I specimens immersed for 5 min in liquid Al under natural convection at SPH = 40 K.

Based on the above findings, all of the early data was discarded and the entire body of

experiments was repeated. Clearer conclusions on the effect of operating parameters were

obtained from the new results.

dissolution of si in molten al with gas injection · dissolution of si in molten al with gas...

Documents