Protection Layer in the Blast Furnace Hearth

Numerical Model to Simulate the Ti(C,N) Protection Layer in the Blast Furnace Hearth

Keisuke Matthew Komiyama

A thesis in fulfilment of the requirements for the degree of Doctor of Philosophy

Laboratory for Simulation and Modelling of Particulate Systems School of Materials Science and Engineering Faculty of Science

January 2014 ORIGINALITY STATEMENT

ORIGINALITY STATEMENT

‘I hereby declare that this submission in my own work and to the best of my knowledge it contains no materials previously published or written by another person, or substantial proportions of material which have been accepted for the award of any other degree or diploma at UNSW or any other educational institution, except where due acknowledgement is made in this thesis. Any contribution made to the research by others, with whom I have worked at UNSW or elsewhere, is explicitly acknowledged in the thesis. I also declare that the intellectual content of this thesis is the product of my own work, except to the extent that assistance from others in the projects design and conception or in style, presentation and linguistic expression is acknowledged.’

ABSTRACT

It is well understood that the erosion of the hearth refractories is by part a major limitation of the longevity of the blast furnace. Addition of titania via burdening or tuyere injection increases the titanium content in the molten pig iron and is believed to promote the so-called titanium-rich scaffold on the hearth surface, to protect the hearth from subsequent erosion. However, control of the titanium-rich scaffold is challenging as furnace operating condition makes it impossible to visualise and make direct measurements of the complex process. Aimed to elucidate the complex in–hearth transport phenomena during titania addition and to improve operational control, this thesis presents a series of numerical models to simulate the transport of titanium carbide particles in the blast furnace hearth during titania addition.

Firstly an improved three-dimensional Computational Fluid Dynamics (CFD) model is developed to simulate the flow and heat transfer phenomena in the hearth of BlueScope’s Port Kembla No. 5 Blast Furnace (PK5BF). Model improvements involve various rigorous CFD practices and better justified input parameters in turbulence modeling, buoyancy modeling, wall boundary conditions, material properties and modeling of the solidification of iron. The model is validated by comparing the calculated temperatures with the thermocouple data available, where agreements are established within  3 %. The flow distribution in the hearth is discussed for intact and eroded hearth profiles, for sitting and floating coke bed states. It is shown that natural convection affects the flow in several ways: for example, the formation of a) stagnant zones preventing hearth bottom from eroding or b) the downward jetting of molten liquid promoting side wall erosion, or c) at times, a vortex like peripheral flow, promoting the ‘elephant foot’ type erosion. A significant influence of coke bed permeability on the macroscopic flow pattern and the refractory temperature is observed.

Secondly a 2D two-phase multi-component model is used to simulate the complex transport phenomena associated with the formation and dissolution of solid particles in the hearth during titania addition via burdening. Based on the results gained,

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ABSTRACT

it is found that the isotherm of the equilibrium temperature of the incoming hot metal solution can be used as an excellent indicator to locate the extent of titanium compound particles. The particles can be managed by controlling the location of this isotherm. This can be conducted by either (a) altering the titanium dosage or (b) altering the hot metal pool temperature. The effects of these parameters on the solid holdup along the hearth linings are investigated. The equilibrium temperature isotherm concept may provide a better way to control titanium based particles for furnace operators during titania addition.

Finally, a 3D multi-component CFD model is developed to simulate the transport of titanium carbide particles in the blast furnace hearth. The model is an upgrade of the previous non-buoyant 2D model where it enables transient 3D simulations of flow, heat and mass transfers including phase change and natural convection through a valid simplified model framework. The effects of various key operational parameters are investigated during the practice of titania addition via burdening and tuyere injection. For the practice of titania injection, the following recommendations are made regarding the selection of titania injecting tuyere. To protect the side walls, titania injecting tuyere located upstream from the hot spot location, by an offset angle as proposed, should be selected. To protect the hearth bottom corner, titania injecting tuyere should be selected such that the hot spot location is between the active taphole and tuyere are around 60° apart. A light weighted and user friendly program that instantly presents graphical images of the TiC particle distribution along the bottom surface of the hearth of PK5BF of any operational conditionn set by the user is developed. The models developed in this work contribute comprehensive understanding of titanium behaviour in the hearth and provide reliable information for furnace operators during the practice of titania addition into the blast furnace.

ACKNOWLEDGEMENT

I would like to thank my supervisors Prof. Aibing Yu, Dr. Baoyu Guo, Dr. Habib Zughbi, and Dr. Paul Zulli for their continuous support and guidance throughout the preparation of this thesis. I would like to thank members of the Iron and Steelmaking research team from BlueScope Ltd. including Dr. Daniel Maldonado, Dr. XueFeng Dong, Dr. Mark Biasutti, Dr. Bryan Wright, Dr. David Pinson, Dr. Peter Austin, Dr. Sheng Chew, Dr. John Mathieson and Dr. Ian Bean for their valuable advice and suggestions through discussions.

I would like to thank my colleagues, especially the members of SIMPAS. Through discussions and exchange of ideas and knowledge, they have provided me encouragement, motivation and inspiration during my preparation of this thesis.

Finally, I would like to thank my friends and family for their continuous support and always been there for me in tough times.

LIST OF FIGURES

TABLE OF CONTENTS

CHAPTER 1 INTRODUCTION ...... 1

1.1 THE IRON MAKING BLAST FURNACE ...... 1

1.2 THE BLAST FURNACE HEARTH ...... 3

1.3 ADDITION OF TITANIA FOR PROTECTION OF THE HEARTH REFRACTORY ...... 4

1.4 NUMERICAL MODELLING OF THE HEARTH ...... 7

1.5 AIM OF THIS THESIS ...... 9

1.6 NAVIGATION OF THIS THESIS ...... 9

1.7 NOMENCLATURE ...... 12

CHAPTER 2 LITERATURE REVIEW ...... 15

2.1 INTRODUCTION ...... 15

2.2 FLOW AND HEAT TRANSFER OF HOT METAL IN THE HEARTH .... 15

2.2.1 Models Neglecting Natural Convection ...... 15

2.2.2 Models Considering Natural Convection ...... 26

2.3 DETERIORATION OF THE HEARTH REFRACTORY ...... 37

2.3.1 Wear Mechanism ...... 37

2.3.2 Models to Predict the Inner Hearth Profile ...... 39

2.4 TITANIUM CARBONITRIDE SCAFFOLD FORMATION IN THE HEARTH ...... 42

2.4.1 Discovery of Titanium Bear during Dissection Studies ...... 42

2.4.2 Mechanism of Ti(C,N) Protection Layer Formation ...... 45

2.4.3 Chemical Thermodynamic Studies Regarding the Formation of Ti(C,N) . 50

2.4.4 Plant Trials of Insertion of Titanium Bearing Materials into the Blast Furnace ...... 53

LIST OF FIGURES

2.4.5 Operational Adversities due to the Addition of Titanium Bearing Materials ...... 62

2.4.6 Models to Predict the Titanium Compound Distribution in the Blast Furnace Hearth ...... 63

CHAPTER 3 3D CFD MODEL TO PREDICT THE FLOW AND TEMPERATURE DISTRIBUTIONS IN A BLAST FURNACE HEARTH ...... 73

3.1 INTRODUCTION ...... 73

3.2 MODEL DESCRIPTION ...... 77

3.2.1 Geometry and Coke Bed State ...... 77

3.2.2 Mathematical Model ...... 79

3.2.3 Meshing ...... 84

3.2.4 Boundary Conditions ...... 85

3.2.5 Convergence Criteria ...... 86

3.3 RESULTS AND DISCUSSION ...... 87

3.3.1 Numerical Sensitivity and Model Validation ...... 87

3.3.2 General Flow Features ...... 93

3.3.3 The Effect of Natural Convection and its Impact on Hearth Erosion ...... 102

3.3.4 Effect of Coke Bed Permeability ...... 104

3.3.5 Effect on Refractory Temperature ...... 112

3.3.6 Further Comments on the Role of Natural Convection ...... 115

3.4 CONCLUSIONS ...... 117

CHAPTER 4 A METHOD TO MANAGE TITANIUM COMPOUNDS IN A BLAST FURNACE HEARTH DURING TITANIA ADDITION ...... 118

4.1 INTRODUCTION ...... 118

4.2 MODEL DESCRIPTION ...... 120

4.2.1 Governing Equations ...... 120

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LIST OF FIGURES

4.2.2 Constitutive Equations ...... 121

4.2.3 Geometry, Mesh, Boundary and Simulation Conditions ...... 123

4.3 RESULTS AND DISCUSSION ...... 125

4.3.1 Macroscopic Behaviour of Hot Metal Flow...... 125

4.3.2 Macroscopic Behaviour of the Particles ...... 128

4.3.3 Behaviour of Particles along a Streamline ...... 130

4.3.4 Effect of Inlet Titanium Mass Fraction ...... 134

4.3.5 Effect of Inlet Temperature ...... 138

4.4 CONCLUSION...... 142

CHAPTER 5 3D CFD MODEL TO SIMULATE THE TITANIUM COMPOUND BEHAVIOUR IN THE BLAST FURNACE HEARTH ...... 143

5.1 INTRODUCTION ...... 143

5.2 MODEL DESCRIPTION ...... 146

5.2.1 Physical Model ...... 146

5.2.2 Mathematical Model ...... 148

5.2.3 Numerical Model ...... 157

5.3 RESULTS AND DISCUSSION ...... 161

5.3.1 Model Validation ...... 161

5.3.2 General Flow Features ...... 162

5.3.3 Effect of Inlet Titanium Dosage on the Distribution of TiC Particles within the Hearth Volume ...... 172

5.3.4 Effect of Inlet Titanium Dosage on the Distribution of TiC Particles along the Inner Hearth Surface ...... 176

5.4 CONCLUSION...... 180

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LIST OF FIGURES

CHAPTER 6 TRANSIENT 3D CFD MODEL TO PREDICT THE DISTRIBUTION OF TITANIUM COMPOUNDS IN A BLAST FURNACE HEARTH DURING TITANIA INJECTION FROM TUYERE ...... 181

6.1 INTRODUCTION ...... 181

6.2 MODEL DESCRIPTION ...... 184

6.2.1 Physical Model ...... 184

6.2.2 Mathematical Model ...... 185

6.2.3 Numerical Modelling ...... 186

6.3 RESULTS AND DISCUSSION ...... 189

6.3.1 General Behaviour of TiC Particles ...... 189

6.3.2 Effect of Inlet Ti Concentration ...... 195

6.3.3 Effect of Injection Angle of Ti ...... 197

6.3.4 Analysis for Sidewall Protection ...... 202

6.3.5 PK5BF Titanium Injection Simulator for Hearth Bottom Protection ...... 205

6.4 CONCLUSIONS ...... 207

CHAPTER 7 SUMMARY AND FUTURE WORK ...... 209

7.1 SUMMARY OF THESIS ...... 209

7.1.1 STEP 1: Accurate Simulation of Hot Metal Flow and Heat Transfer in the Hearth ...... 209

7.1.2 STEP 2: Simulation of the Transport of Ti(C,N) Particles together with the Flow and Heat Transfer in the Hearth ...... 210

7.2 FUTURE WORK ...... 212

REFERENCES ...... 214

LIST OF PUBLICATIONS ...... 237

LIST OF FIGURES

FIGURE 1.1. Process in the steel production line (Cornish, 2008)...... 1

FIGURE 1.2. Schematic diagram of the iron making blast furnace (Dong et al., 2009)...... 2

FIGURE 1.3. Schematic diagram of the erosion profile of the blast furnace hearth in (i) pan shape and (ii) mushroom shape (or elephant foot shape) (Kurita and Ogawa, 1994)...... 4

FIGURE 1.4. Schematic diagram of the formation of titanium-rich scaffold during titania addition via tuyere injection (Okada et al., 1991)...... 5

FIGURE 1.5. Schematic illustration of the mechanism of titanium-rich scaffold formation during titania addition in the blast furnace (Bergsma and Fruehan, 2001)...... 6

FIGURE 1.6. 3D CFD model to simulate the flow and heat transfer of hot metal in the hearth of BlueScope’s PK5BF. (i) Plots of velocity vectors, streaklines and temperature contours of the hot metal (ii) Comparison between calculated and measured refractory temperatures. (Guo et al., 2008)...... 8

FIGURE 1.7. Numerical modelling of the hearth of BlueScope’s PK5BF during titania addition via tuyere injection. (i) Shows the distribution of titanium mass fraction and (ii) shows the distribution of solid Ti(C,N) particle distribution in the hearth (Guo et al., 2010)...... 9

FIGURE 1.8. Graphical outline of the CFD models developed through this thesis. (i) 3D CFD model to simulate the flow and heat transfer in the blast furnace hearth (Chapter 3). (ii) 2D two-phase multi-component CFD model to study the titanium particle formation and dissolution behaviour in the blast furnace hearth (Chapter 4). (iii) 3D CFD model to simulate the distribution of TiC particles during titania addition via burdening in the blast furnace

LIST OF FIGURES

hearth (Chapter 5). (iv) Titanium injection simulator for PK5BF (Chapter 6)...... 11

FIGURE 2.1. Experimental apparatus of the 3D cold water model simulating the flow of hot metal in the blast furnace hearth (Luomala et al., 2001)...... 16

FIGURE 2.2. Results of the 3D cold water model when (i) coke bed is sitting, (ii) coke bed is floating (flat base), (ii) coke bed is floating (convex base) (Peters et al., 1985)...... 17

FIGURE 2.3. Experimental apparatus of the 3D cold water model shown in (i) photograph and (ii) schematic diagram (Nnanna et al., 2004)...... 17

FIGURE 2.4. Experimental apparatus for 3D water model (Ohno et al., 1981)...... 18

FIGURE 2.5. Flow distribution of liquid in the experimental apparatus for (i) sitting and (ii) floating coke beds...... 18

FIGURE 2.6. (i) Apparatus of the physical water model experiment. (ii) Side and planar views of the flow pattern for a sitting coke bed without coke free gutter. (iii) Side and planar view of the flow pattern for a sitting coke bed with coke free gutter (Okada et al., 1991)...... 19

FIGURE 2.7. Comparison of calculated and measured refractory temperatures. Measurements are from China Steel Corporation’s No. 2 Blast Furnace (Huang et al., 2008)...... 20

FIGURE 2.8. For a floating coke bed state: (i) 3D velocity vector distribution along inner hearth surface and (ii) side view streaklines plot along the hearth symmetry plane (Huang et al., 2008)...... 20

FIGURE 2.9. Typical erosion profiles in a blast furnace hearth: (i) pan-shaped erosion and (ii) mushroom-shaped erosion (Kurita and Ogawa, 1994)...... 21

LIST OF FIGURES

sitting coke bed state with coke free gutter and (iv) peripheral inlet flow in sitting coke bed state with inhomogeneous porosity distribution (Kurita and Ogawa, 1994)...... 22

FIGURE 2.11. (i) Location of pad thermocouples embedded within the hearth refractories. (ii) Comparison between calculated and thermocouple temperatures (Tomita and Tanaka, 1994)...... 23

FIGURE 2.12. (i) Location of pad thermocouples embedded within the hearth refractories. (ii) Comparison between calculated and thermocouple temperatures (Tomita and Tanaka, 1994)...... 23

FIGURE 2.13. Planar and side views of streaklines and velocity contours for (i) sitting and (ii) floating coke bed states (Ohno et al., 1981)...... 25

FIGURE 2.14. Comparison between experimental and numerical models with respect to their travelling times for (i) sitting and (ii) floating coke bed states (Ohno et al., 1981)...... 25

FIGURE 2.15. (i) Experiment A flow visualisation at 60 min after ink inserted. (1) indicates the trajectory of the green ink and (2) indicates that of the blue ink. (ii) Experiment B flow visualisation after (1) 17 min 30 s after blue ink is inserted and (2) 3 min 30s after red ink is inserted...... 27

FIGURE 2.16. (i) Velocity vector plot, (ii) normalised effective viscosity (μeff / μ) contour plot and (iii) temperature contour plot (Yoshikawa and Szekely, 1981)...... 28

FIGURE 2.17. Velocity vectors and 1400°C isotherm in a fully sitting coke bed configuration. (Shibata et al., 1990) ...... 29

FIGURE 2.18. (i) 3D mesh of the CFD hearth model. (ii) Velocity vector plots along the hearth symmetry plane for a) sitting coke bed with gutter, b) coke bed with gutter floating above 0.325 m from the hearth bottom and c) coke bed with gutter floating above 0.9 m from the hearth bottom...... 30

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LIST OF FIGURES

FIGURE 2.19. Streamline with colouring based on residence time (Post et al., 2003)...... 31

FIGURE 2.20. Comparison between calculated and measured thermocouple temperatures for cases: (a) intact hearth, sitting coke bed, (b) intact hearth, floating coke bed, (c) eroded hearth, sitting coke bed, (d) eroded hearth, floating coke bed...... 32

FIGURE 2.21. Temperature profile and velocity vector of a fully sitting coke bed (Panjkovic et al., 2002)...... 33

FIGURE 2.22. Comparison between calculated and measured thermocouple temperatures for cases: (a) intact hearth and sitting coke bed, (b) intact hearth and floating coke bed, (c) eroded hearth and sitting coke bed, (d) eroded hearth and floating coke bed (Cheng et al., 2005)...... 34

FIGURE 2.23. Streamlines of hot metal for cases (i) with and (ii) without natural convection. Fully sitting bed with intact firebrick (Cheng et al., 2005)...... 35

FIGURE 2.24. Comparison between calculated and measured refractory temperatures for (i) sitting and (ii) floating coke bed states (Guo et al., 2008)...... 35

FIGURE 2.25. Velocity vectors, streamlines and temperature contours for cases (i) with natural convection and (ii) without natural convection, when the coke bed is sitting (Guo et al., 2008)...... 36

FIGURE 2.26. (i) Typical wear profile in the hearth of the blast furnace: 1. lost layer (eroded and dissolved); 2. protective layer (scab); 3. hot metal penetrated layer; 4. brittle zone; 5. slightly changed layer; 6. unchanged layer. (ii) Schematic diagram of wear mechanisms for the hearth refractory lining...... 39

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LIST OF FIGURES

comparison along the sidewall and bottom at a location between tapholes. (iii) Simulation of the 3D wear profile in the physical model (Kowalski et al., 1998)...... 40

FIGURE 2.28. (i) Carbon concentration contours along the hearth symmetry plane. (ii) Erosion velocity along the hearth side wall. Units are in cm/month (Preuer et al., 1992a)...... 41

FIGURE 2.29. (i) Erosion velocity for various stages of the tapping process. (ii) Erosion velocity for various cases investigating the effect of furnace productivity, inlet carbon concentration and coke bed permeability (Preuer et al., 1992a)...... 42

FIGURE 2.30. Location of titanium-rich scaffolds and their photographs found from the hearth of blown-out blast furnaces of (i) Kakogawa No. 1 Blast Furnace and (ii) Kobe No. 3 Blast Furnace (Narita et al., 1977)...... 44

FIGURE 2.31. (i) Single crystal of Ti(C,N) using optical micrograph. (ii) EPMA results showing titanium, carbon and nitrogen concentration profiles through Ti(C,N) crystal (Narita et al., 1976)...... 46

FIGURE 2.32. Optical micrographs of Ti(C,N) crystals with numbers representing mol%TiC in Ti(C,N) determined by EPMA at locations: (a) eroded portion of hearth wall, (b) in salamander, (c) On the surface and (d) in the joint of chamotte bottom brick (Narita et al., 1976)...... 47

FIGURE 2.33. (i) Confocal scanning laser microscope image of precipitates of Fe-

Csat-0.2mass%Ti at PN2=1atm. (ii) (a) SEM image and EDX element

mapping of: (b) Fe, (c) Ti, (d) N and (e) C on Fe-Csat0.2mass%Ti at

PN2=1atm and T=1775K ...... 48

FIGURE 2.34. Schematic illustration of the formation of Ti(C,N) protective layer along the damaged refractory linings of the blast furnace hearth (Figure reproduced from Bergsma and Fruehan (2001))...... 49

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LIST OF FIGURES

FIGURE 2.35. Change of apparent solidification temperature by Ti(C,N) formation (Bergsma and Fruehan, 2001)...... 50

FIGURE 2.36. (i) Ti(C,N) composition for various temperatures and nitrogen partial pressures. (ii) Minimum titanium concentration in hot metal required

for the formation of Ti(C,N) at a given nitrogen partial pressure (fTi = 0.023 at T = 1773 K). (iii) Minimum titania dosage required and the resulting titanium concentration in the hot metal to initiate Ti(C,N) as a function of

formation temperature (Hot metal – Slag equilibrium at 1500 °C, PN2 = 2.3 bar) (Bergsma and Fruehan, 2001)...... 52

FIGURE 2.37. Overall process during the addition of titanium bearing materials into the blast furnace via burdening and tuyere injection techniques (Kurunov et al. (2007) cited from Okada et al. (1991))...... 53

FIGURE 2.38. Comparison between the titanium concentration in the hot metal and the thermocouple temperature of the hearth lining walls in blast furnace No. 2 in Siderar plant (Kurunov et al. (2006), figure originally from Oscar and Eduardo (2005))...... 56

FIGURE 2.39. Schematic diagram of formation process of Ti bear in the hearth (Okada et al., 1991)...... 57

FIGURE 2.40. Equipment developed to inject Titania through tuyeres (Okada et al., 1991)...... 58

FIGURE 2.41. Schematic of the predicted path line of titanium content from the tuyere to the taphole that passes the worn regions of the lining (Okada et al., 1991)...... 58

FIGURE 2.42. Change in the temperature of the hearth walls in (i) BF no.3. and (ii) BF no.2 (Okada et al., 1991)...... 59

FIGURE 2.43. Schematic of ilmenite and rutilite structures. (I.F.Kurunov et al. (2007)) ...... 61

LIST OF FIGURES

FIGURE 2.44. Change in distribution coefficient [Ti]/(Ti) in relation to the temperature of the pig iron with the injection of rutilite AT (Kurunov et al., 2007)...... 61

FIGURE 2.45. Effect of rutilite AT tuyere injection (i) on TiO2 in the slag and (ii) on Ti concentration in the pig iron (Kurunov et al., 2007)...... 62

FIGURE 2.46. (i) Planar view of titanium mass fraction contours plot. (ii) Planar and side view of velocity vectors plot and temperature contours plot (Tomita and Tanaka, 1994)...... 65

FIGURE 2.47. TiC mass fraction contour plot along the inner hearth surface when

TiO2 is locally added from a position 135° and 180° (Lin et al., 2009)...... 66

FIGURE 2.48. Temperature contour plot along the inner hearth surface when TiO2 is locally added from a position 135° and 180° (Lin et al., 2009)...... 67

FIGURE 2.49.Temperature profile of the refectory at upper and outer thermocouple location (r = 5.2 m, z = 1.5 m) along the theta direction

contour plot for cases when no TiO2, TiO2 is locally added from a position 135° and 180° (Lin et al., 2009)...... 67

FIGURE 2.50. The framework of two-phase, multi-component model (Guo et al., 2010)...... 68

FIGURE 2.51. (i) Representation of solid forming and solid melting regions. (ii) Colour representation of Ti(C,N) particle concentration. (iii) Colour representation of Ti(C,N) particle size. Here, titanium concentration of 0.4 wt% is added throughout the hearth inlet (Guo et al., 2010)...... 69

FIGURE 2.52. Colour representation of: (i) titanium concentration and (ii) TiC particle concentration within the hearth during local addition of titania from a position far end of the taphole (Guo et al., 2010)...... 70

FIGURE 2.53. Colour representations of Ti and TiC particle concentrations in (i) fully intact, (ii) partly eroded and (iii) fully eroded hearth linings when

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LIST OF FIGURES

titanium inserted locally from a position opposite the taphole (Guo et al., 2011)...... 71

FIGURE 2.54. (i) Streaklines plot of the hot metal, (ii) temperature contours for the hot metal pool and refractories and colour representations of (iii) titanium concentration and (iv) TiC particle concentration within the blast furnace when the effect of natural convection is considered (Guo et al., 2011)...... 72

FIGURE 3.1. Geometry and thermocouple locations of Port Kembla No. 5 Blast Furnace (campaign: 1991-2009). Parenthesis shows the z and x coordinates. ... 78

FIGURE 3.2. Coke bed states for model validation for Cases A – D. Coke bed heights at hearth centre for intact and eroded hearths are 300 mm and 400 mm respectively...... 79

FIGURE 3.3. Meshing for the solid domain for an intact hearth...... 85

FIGURE 3.4. Meshing for the liquid domain for an intact hearth...... 85

FIGURE 3.5. Comparison of the calculated and measured temperatures for Cases A – D: × measured temperature, --- (dashed lines) calculated temperature

with γ = 0.35 and dh = 30 mm and — (solid lines) calculated temperature

with γ = 0.30 and dh = 12 mm...... 88

FIGURE 3.6. Effect of H-Energy RMS residual on temperature at centre thermocouple location for Case A. Note that the glitch in at T = 315°C is due to a divergence that was experienced during the solving process. The time step was reduced to allow the residual to return back to stable conditions...... 90

FIGURE 3.7. Mesh sensitivity on temperature at centre thermocouple location for Case B...... 92

FIGURE 3.8. Velocity u profile along hearth axis in Case B for mesh with various number of elements...... 92

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LIST OF FIGURES

FIGURE 3.9. Zoom up view of vector plots near upper steps under taphole for Case C...... 93

FIGURE 3.10. General flow and heat transfer features in ‘high permeability’ coke bed for Case A (left) and Case C (right). (a) Pool temperature contours, (b) streaklines and (c) velocity vectors...... 95

FIGURE 3.11. General flow and heat transfer features in ‘low permeability’ coke bed for Case A (left) and Case C (right). Side view: (a) refractory and (b) pool temperature contours, (c) streaklines and (d) velocity vectors; planar view: (e) streaklines and (f) velocity vectors at the taphole level...... 97

FIGURE 3.12. 3D streamlines in ‘low permeability’ coke bed for Cases A – D: yellow in Cases B and D shows the coke bed shape and grey in Case C shows the solidified region...... 98

FIGURE 3.13. General flow and heat transfer features in ‘high permeability’ coke bed for Case B (left) and Case D (right). (a) pool temperature contours, (b) streaklines and (c) velocity vectors...... 99

FIGURE 3.14. General flow and heat transfer features in ‘low permeability’ coke bed for Case B (left) and Case D (right). Side view: (a) refractory and (b) pool temperature contours, (c) streaklines and (d) velocity vectors; planar view: (e) streaklines and (f) velocity vectors in the coke free zones...... 101

FIGURE 3.15. Streaklines for Case A (left) and Case C (right) for permeabilities: -7 2 -8 2 (i) Kperm = 3.31×10 m (γ = 0.35, dh = 30 mm), (ii) Kperm = 9.11×10 m -8 2 (γ = 0.275, dh = 26 mm), (iii) Kperm = 4.70×10 m (γ = 0.425, dh = 10 -8 2 mm), (iv) Kperm = 1.80×10 m (γ = 0.30, dh = 12 mm), (v) Kperm = -9 2 8.01×10 m (γ = 0.275, dh = 10 mm). Grey regions indicate the solidified iron layer...... 106

FIGURE 3.16. Temperature contours for Case A (left) and Case C (right) for -7 2 permeabilities: (i) Kperm = 3.31×10 m (γ = 0.35, dh = 30 mm), (ii) Kperm -8 2 -8 2 = 9.11×10 m (γ = 0.275, dh = 26 mm), (iii) Kperm = 4.70×10 m (γ =

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LIST OF FIGURES

-8 2 0.425, dh = 10 mm), (iv) Kperm = 1.80×10 m (γ = 0.30, dh = 12 mm), -9 2 (v) Kperm = 8.01×10 m (γ = 0.275, dh = 10 mm)...... 107

FIGURE 3.17. Streaklines for Case B (left) and Case D (right) for permeabilities: -7 2 -7 2 (i) Kperm = 3.31×10 m (γ=0.35, dh=30 mm), (ii) Kperm = 1.21×10 m -8 2 (γ=0.275, dh=20 mm), (iii) Kperm = 4.70×10 m (γ=0.30, dh=18 mm), -8 2 (iv) Kperm = 1.80×10 m (γ=0.30, dh=12 mm)...... 109

FIGURE 3.18. Temperature contours for Case B (left) and Case D (right) for -7 2 permeabilities: (i) Kperm = 3.31×10 m (γ=0.35, dh=30 mm), (ii) Kperm = -7 2 -8 2 1.21×10 m (γ=0.275, dh=20 mm), (iii) Kperm = 4.70×10 m (γ=0.30, -8 2 dh=18 mm), (iv) Kperm = 1.80×10 m (γ=0.30, dh=12 mm)...... 110

FIGURE 3.19. Effect of deadman permeability on the maximum velocity within the coke free zone in intact and eroded hearth profiles...... 112

FIGURE 3.20. Effect of permeability on the normalized temperature of the refractory at the center thermocouple location for sitting coke bed state (Cases A and C)...... 114

FIGURE 3.21. Effect of permeability on the normalized temperature of the refractory at the center thermocouple location for floating coke bed state (Cases B and D)...... 115

FIGURE 4.1. Hypothesis of mechanism behind the formation of the Ti(C,N) protection layer in the blast furnace hearth (Bergsma and Fruehan, 2001)...... 119

FIGURE 4.2. Schematic diagram of a single TiC particle...... 122

FIGURE 4.3. Geometry of the eroded hearth of PK5BF (campaign: 1991-2009)...... 124

FIGURE 4.4. Meshing of the model...... 125

FIGURE 4.5. (a) Temperature contours for refractory and pool, (b) velocity vectors (c) streamlines, and contours of (d) titanium mass fraction, (e) solid holdup and (f) mean particle diameter of the pool...... 127

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LIST OF FIGURES

FIGURE 4.6. Solubility of Titanium in hot metal...... 129

FIGURE 4.7. Particle behaviour along a streamline. Arrow heads are placed on the hour. Coloured region represents: solidification (orange) and dissolution (blue)...... 130

FIGURE 4.8. Various parameters along time on a streamline for: (a) Temperature, (b) titanium mass fraction in the flow field, (c) equilibrium titanium mass fraction, (d) difference between the equilibrium and field titanium mass fractions, (e) solid holdup and (f) mean particle diameter...... 131

FIGURE 4.9. Effect of inlet Titanium on solid holdup distribution with equilibrium temperature isotherm (red line)...... 135

FIGURE 4.10. Solid holdup distribution along hearth bottom for various inlet Titanium mass fractoins...... 136

FIGURE 4.11. Average solid holdup and mean particle diameter along hearth bottom for various inlet Titanium mass fractions...... 137

FIGURE 4.12. Effect of average pool temperature on solid holdup distribution with equilibrium temperature isotherms...... 138

FIGURE 4.13. Solid holdup distribution along hearth bottom for various average pool temperatures...... 139

FIGURE 4.14. Average solid holdup and mean particle diameter along hearth bottom for various average pool temperatures...... 141

FIGURE 4.15. Behaviour of particles for cases (i) and (iv) including: temperature contours, a single streamline, solidification region (red) and dissolution region (blue)...... 141

FIGURE 5.1. Geometry with eroded inner hearth profile with (z, x) coordinates...... 147

FIGURE 5.2. Schematic of the coke bed at (a) sitting and (b) floating states...... 148

FIGURE 5.3. Schematic diagram of the “Variable Size Model”...... 155 xx

LIST OF FIGURES

FIGURE 5.4. Meshing of the (a) liquid domain and (b) solid domain for PK5BF. .... 158

FIGURE 5.5. Comparison between calculated and measured thermocouple temperatures for sitting (left) and floating (right) deadman states...... 162

FIGURE 5.6. (a) Temperature contour, (b) velocity vector and (c) streakline plots along the symmetry plane of the hearth for sitting (left) and floating (right) coke bed states...... 164

FIGURE 5.7. Planar view at taphole level of (a) velocity vector and (b) streakline plots for sitting (left) and floating (right) coke bed states...... 165

FIGURE 5.8. 3D view of (a) temperature distribution along inner hearth refractory surface and (b) streamlines plot for sitting (left) and floating (right) coke bed states...... 166

FIGURE 5.9. (a) Solid holdup, (b) mean particle diameter and (c) Ti mass fraction contour plots along the symmetry plane of the hearth for sitting (left) and floating (right) coke bed states...... 169

FIGURE 5.10. 3D view of (a) solid holdup and (b) mean particle diameter along the inner surface of the hearth refractory for sitting (left) and floating (right) coke bed states...... 171

FIGURE 5.11. Solid holdup contour plots along the hearth symmetry plane when

inlet titanium mass fraction set to (a) [Ti]in = 0.2 wt%, (b) [Ti]in = 0.4 wt%,

(c) [Ti]in = 0.8 wt%, (d) [Ti]in = 1.2 wt% and (e) [Ti]in = 2.0 wt% for a sitting coke bed state (left) and floating coke bed state (right). Red line indicates the equilibrium temperature isotherm for the corresponding titanium concentration...... 173

FIGURE 5.12. Solid holdup contour plots along the inner hearth surface when inlet

titanium mass fraction set to (a) [Ti]in = 0.2 wt%, (b) [Ti]in = 0.4 wt%, (c)

[Ti]in = 0.8 wt%, (d) [Ti]in = 1.2 wt% and (e) [Ti]in = 2.0 wt% for a sitting coke bed state (left) and floating coke bed state (right)...... 177

xxi

LIST OF FIGURES

FIGURE 5.13. (a) Surface average solid holdup, (b) surface average mean particle diameter and (c) area coated along the inner hearth surface for sitting (left) and floating (right) coke bed states...... 178

FIGURE 6.1. Location and area of titanium at the inlet for cases when titania injection from tuyere...... 187

FIGURE 6.2. Distribution of TiC concentration along hearth inner surface when injecting titanium with concentration of 2.0 wt% from 90° location. (i) t = 0 hr, (ii) t = 0.5 hr, (iii) t = 1.0 hr, (iv) t = 1.5 hr, (v) t = 2.0 hr, (vi) t = 2.5 hr, (vii) t = 3.0 hr and (viii) steady-state...... 190

FIGURE 6.3. (i) Area coated by TiC particles, (ii) maximum TiC concentration and (iii) maximum particle size along inner hearth surface with time for various inlet titanium concentrations during titania addition from burdening. . 191

FIGURE 6.4. Distribution of TiC concentration along hearth inner surface when injecting titanium with concentration of 2.0 wt% from 60° location. (i) t = 0 hr, (ii) t = 0.5 hr, (iii) t = 1.0 hr, (iv) t = 1.5 hr, (v) t = 2.0 hr, (vi) t = 2.5 hr, (vii) t = 3.0 hr and (viii) steady-state...... 193

FIGURE 6.5. (i) Area coated by TiC particles, (ii) maximum TiC concentration and (iii) maximum particle size along inner hearth surface along time for various inlet titanium concentrations when titania injection from 60° location...... 194

FIGURE 6.6. Distribution of TiC concentration along hearth inner surface at t = 3 hr when injecting titanium throughout the hearth inlet for various inlet titanium concentrations: (i) [Ti] = 0.2 wt%, (ii) [Ti] = 0.4 wt%, (iii) [Ti] = 0.8 wt%, (iv) [Ti] = 1.2 wt% and (v) [Ti] = 2.0 wt%...... 196

FIGURE 6.7. Distribution of TiC concentration along hearth inner surface at t = 3 hr when injecting titanium from 90° location for various inlet titanium concentrations: (i) [Ti] = 0.2 wt%, (ii) [Ti] = 0.4 wt%, (iii) [Ti] = 0.8 wt%, (iv) [Ti] = 1.2 wt% and (v) [Ti] = 2.0 wt%...... 197

xxii

LIST OF FIGURES

FIGURE 6.8. Distribution of TiC concentration along hearth inner surface when

[Ti]in = 2.0 wt% and t = 3 hr for various injection locations: (i) 30°, (ii) 60°, (iii) 90°, (iv) 120°, (v) 150°, (vi) 180° and (vii) all...... 199

FIGURE 6.9. Area of TiC particles coating along the inner hearth surface at t = 3.0 hr when titanium inserted from various locations of the hearth inlet...... 200

FIGURE 6.10. Maximum and average TiC mass fraction within the particle rich region along the inner hearth surface when titanium inserted from various locations of the hearth...... 201

FIGURE 6.11. Polar representation of average TiC mass fraction along hearth walls when Ti with mass fraction of 2.0 wt% is injected for a duration of t = 3.0 hr from various injection points...... 203

FIGURE 6.12. Average [TiC] distribution along hearth wall fixing 0° at location of tuyere injected. Taphole is located in the –ve direction. The taphole is

located in the –ve direction and titanium with [Ti]in = 2.0 wt% is inserted for a duration of t = 3.0 hr...... 204

FIGURE 6.13. Correlation between active tuyere location and location of hotspot. .. 204

FIGURE 6.14. Snapshot of PK5BF Titanium Injection Simulator...... 207

xxiii

LIST OF TABLES

TABLE 1.1. List of blast furnaces with long campaign life...... 3

TABLE 2.1 Specifications of Kobe Steel’s blast furnaces analysed by Narita et al. (1977)...... 43

TABLE 2.2. Locations of titanium-rich scaffolds found in Kakogawa No. 1 B.F. during dissection analysed by Narita et al. (1977)...... 44

TABLE 2.3. Chemical composition of the pig iron penetrated into the joint of chamotte bottom brick found from the hearth of Kakogawa No. 1 B.F. (wt%) (Narita et al., 1977)...... 45

TABLE 2.4. Chemical composition of the pig iron and salamander as tapped out found for Kakogawa No. 1 B.F. (wt%) (Narita et al., 1977)...... 45

TABLE 2.5. List of titanium bearing materials and their TiO2 concentration used for the addition of titanium in the form of burdening...... 54

TABLE 2.6. Technological program to mitigate the increase of temperature of the hearth linings (Kurunov et al. (2006), figure originally from Oscar and Eduardo (2005))...... 56

TABLE 2.7. Characteristics of titanium-bearing materials that are used for injection through tuyere (Okada et al., 1991)...... 59

TABLE 2.8. Effect of Titania injection on lining temperature (Okada et al., 1991). .... 60

TABLE 3.1. Material properties ...... 84

TABLE 5.1. Material Properties ...... 152

TABLE 5.2. Simulation Sequence ...... 160

xxiv

CHAPTER 1

CHAPTER 1 INTRODUCTION

1.1 THE IRON MAKING BLAST FURNACE Amongst all the iron making processes, the production of pig iron in the iron making blast furnace is the most widely used method. It is a preferred method of iron production due to its high production rate and high efficiency in heat utilization. Pig iron production rate of up to 12,000 ton of hot metal per day is possible in a modern high capacity furnace. Further, due to its counter-current heat exchange structure, it is possible to utilize heat to an extent of 85 – 90 % (Biswas, 1981). The iron making blast furnace is used in the primary processing stages of the steel production line (FIGURE 1.1).

FIGURE 1.1. Process in the steel production line (Cornish, 2008).

It is a large scale industrial reactor that converts iron oxide to usable pig iron using coke and coal as fuel. The mechanism behind the process of the iron production is described as follows (FIGURE 1.2). At the top of the furnace, iron oxide (generally in the form of 1

CHAPTER 1

ore, sinter and/or pellets) and coke are charged in alternate layers through a bell or bell- less top. The charged material gradually descends down the furnace passing the so- called lumpy, cohesive and dripping zones. In the mean time, hot gas is blast into the furnace from the tuyeres (along with pulverised coal which is injected through the tuyeres) where the coke and coal combusts in the raceway generating reducing gases. These reducing gases reduce the iron oxide to form liquefied pig iron and slag. It is the cohesive zone where the reduction occurs and hence the produced liquid iron and slag drips down from the cohesive zone through the dripping zone and gets accumulated in the hearth. The two liquids are then cast out from the taphole.

FIGURE 1.2. Schematic diagram of the iron making blast furnace (Dong et al., 2009).

Over the past few decades, there has been a trend in blast furnace technology to: (i) reduce coke consumption, (ii) increase furnace productivity and (iii) lengthen the campaign life (Kurunov et al., 2006). The latter trend is an essential part for the reduction of capital expenses and production costs. At current stage, the life of the furnace at most is about 20 years (TABLE 1.1) and relining the furnace costs about $372 million (cost for reline of Port Kembla No. 5 Blast Furnace (PK5BF) in 2009 (Hatch, 2014)).

CHAPTER 1

TABLE 1.1. List of blast furnaces with long campaign life. Campaign Campaign Company Blast Furnace Reference Life Number BlueScope Port Kembla No. 5 18 years 3 Hatch (2014) Kurunov et al. Onesteel Whyalla No. 2 23.4 years 3 (2006) Companhia Sederugica de Klein and Fujihara No. 1 21 years 1 Tubarao (2004) (CST)

It is well recognized that one of the main limitations of the campaign life is the wear of the hearth refractories (Panjkovic et al., 2002, Wright et al., 2003, Guo et al., 2008). For this reason, extensive research is conducted regarding the cause and mechanisms behind the wear of the hearth refractories, and based on the knowledge gained, various preventative measures are explored.

1.2 THE BLAST FURNACE HEARTH The hearth contains two immiscible liquids, slag and liquid iron, where the slag is layered on the top of the liquid iron due to its lower density. The removal of the liquids, through continuous casting, is conducted by drilling and opening the taphole, liquids casting (typically drainage for a duration of 3 hrs), and then closing the taphole by injecting clay into it. This procedure is repeated in another taphole either straight away, after a short duration for liquid accumulation or a short duration before the previous taphole is closed for more drainage.

The hearth is packed with coke particles forming a porous bed. The bed is continuously renewed as the carbon content of the submerged coke is dissolved into the liquid iron. Since the residence time of the submerged coke varies from one coke particle to another, the coke size can differ ranging from fines to about 50 mm (coke size as burdened). The smaller particles as well as other fines such as unburned coal and

CHAPTER 1

graphite precipitates may percolate through the bed (Nightingale et al., 2001). For these reasons, the bed is inhomogeneous in coke size and porosity (Guo et al., 2011).

The total weight of the burden material is balanced with the uplifting force at the raceway, solids pressure at walls and the buoyancy force of the submerged bed (Fukutake and Okabe, 1981). The last force is quite significant due to the large density difference between the coke and liquid iron. Therefore depending on the volume of the coke submerged, which is dependent on the porosity and the liquid level, the bed can either be sitting or floating (Nightingale et al., 2001).

The profile of the inner hearth refractory varies as the furnace ages. Starting initially from the original hearth design, the hearth lining refractory undergoes erosion or forms scaffolds where the hot face profile may change as the furnace ages. Generally towards the end of the campaign life of the blast furnace, the shape of the hearth lining profile is characterized as a pan-shaped or an elephant foot-shaped profile (FIGURE 1.3). The altered hearth volume and wall thickness will in turn change the heat transfer and flow of the hot metal.

FIGURE 1.3. Schematic diagram of the erosion profile of the blast furnace hearth in (i) pan shape and (ii) mushroom shape (or elephant foot shape) (Kurita and Ogawa, 1994).

1.3 ADDITION OF TITANIA FOR PROTECTION OF THE HEARTH REFRACTORY There are several measures that can be undertaken to decrease the wear of the hearth refractory linings. These include lowering the smelting rate, plugging of tuyere or 4

CHAPTER 1

improving the cooling efficiency of the hearth side walls and bottom (Kurunov et al., 2006). A measure that has gained popularity since 1960’s is the addition of titanium bearing materials into the furnace by means of forming scaffolds along the surface of the eroded hearth linings. This scaffold is rich in titanium and has a high melting point and it is believed to act as a protection agent to prevent the eroded hearth linings from further damage.

The titanium bearing materials can be added into the Blast Furnace in two methods: (i) burdening or (ii) tuyere injection. In the burdening method, titanium ore is charged from the top of the shaft generally along the periphery regions. On the other hand in the tuyere injection method, pulverised titania (generally rutile or illmenite (Okada et al., 1991)) is injected from one or more tuyeres via an injection lance (FIGURE 1.4). The selection of the tuyere for injection is made such that the titanium content can be delivered specifically to the eroded regions of the hearth lining.

FIGURE 1.4. Schematic diagram of the formation of titanium-rich scaffold during titania addition via tuyere injection (Okada et al., 1991).

The process of the titanium protection layer formation is hypothesised by Bergsma and Fruehan (2001) and can be described as follows (FIGURE 1.5).

1. Dissolution of titania in slag phase. 2. Reduction of titania in slag phase and dissolution of produced titanium into hot metal phase. 3. Transport of titanium to the damaged refractory linings. 5

CHAPTER 1

4. Formation of Ti(C,N) particles due to cooling. 5. Deposition of Ti(C,N) on the hearth walls and formation of scaffold.

FIGURE 1.5. Schematic illustration of the mechanism of titanium-rich scaffold formation during titania addition in the blast furnace (Bergsma and Fruehan, 2001).

In the last step, as the number of Ti(C,N) particles increases, the hot metal viscosity increases which stagnates the hot metal flow. Due to heat loss to the refractory this may reduce the local temperature below the iron solidus temperature where the Ti(C,N) protection layer is formed.

As such, controlling the protective layer involves altering the interactions between the flow, heat and mass transfers and chemical reactions. Since harsh operating conditions within the hearth make it practically impossible for direct measurement and visualisation, the titanium addition measure is practiced in almost black-box conditions. For this reason, CFD model plays an important role in understanding the transport phenomena in the hearth during titania addition and to gain better control of the measure.

CHAPTER 1

1.4 NUMERICAL MODELLING OF THE HEARTH In the previous section, the process of Ti(C,N) protection layer formation hypothesised by Bergsma and Fruehan (2001) is introduced. It can be understood that the process is extremely complex and therefore simulating the in-hearth transport phenomena becomes challenging, both in terms of model complexity and the availability of computer capability. In order to develop a comprehensive model to simulate the Ti(C,N) protection layer in the hearth in a feasible manner the following stepwise procedure is strategized.

STEP 1: Simulation of an accurate flow pattern and heat transfer in the hearth STEP 2: Simultaneous simulation of STEP 1 and the transport of Ti(C,N) particles in the hearth STEP 3: Simultaneous simulation of STEP1, STEP 2 and the prediction of the transport of Ti(C,N) protection layer in the hearth

As the step progresses, the complexity and the required computational resource significantly increases. At current stage, significant amount of studies on STEP 1 and several studies on STEP 2 is reported in literature. No studies are reported on STEP 3 due to its complexity, limited the computer performance and limited fundamental understanding of the physicochemical mechanism of Ti(C,N) protection layer formation.

For studies on STEP 1, one of the recent works was conducted by Guo et al. (2008). They have developed a 3D CFD model to predict the flow and heat transfer of the hearth of PK5BF (FIGURE 1.6(i)). The model features conjugate heat transfer, natural convection and turbulent flow through porous media where a modified k-ε turbulence model and thermal dispersion term is applied. However in their validation analysis, the calculated temperature under-predicts the measured temperature (FIGURE 1.6(ii)). Such under-prediction trend is experienced by most investigators who include natural convection in their models (Panjkovic et al., 2002, Cheng et al., 2005).

CHAPTER 1

For studies on STEP 2, one of the recent works was conducted by Guo et al. (2010). They developed an evolutional 2D two-phase multi-component model which distinctly follows the hypothesis of Bergsma and Fruehan (2001), to simulate the transport of Ti(C,N) particles in the hearth of Port Kembla No. 5 Blast Furnace (FIGURE 1.7(i-ii)). Although the effect of natural convection is neglected, the model considers the thermodynamics of key chemical reactions and the growth/shrinkage of Ti(C,N) particles.

CHAPTER 1

1.5 AIM OF THIS THESIS The aim of the research conducted in this thesis is broadly as follows. STEP 1: - To develop an improved 3D CFD model to accurately predict the flow and heat transfer in a blast furnace hearth. - To achieve good agreement between the calculated and measured thermocouple temperatures. - To gain better understanding of the physical nature of the coke bed in the hearth. STEP 2: - To develop 3D CFD model to predict the transport of TiC particles in a blast furnace hearth during titania addition via burdening and tuyere injection. - To better understand the transport phenomena regarding the formation and dissolution of the TiC particles in the hearth.

1.6 NAVIGATION OF THIS THESIS In this section, research work embodied in this thesis is outlined.

CHAPTER 1

Chapter 1 outlines the background of the formation of Ti(C,N) protection layer process via the measure of titania addition and introduces the research work conducted in this thesis, “Numerical Model to Simulate the Ti(C,N) Protection Layer in the Blast Furnace Hearth”.

Chapter 2 reviews the literature on the physical and numerical models of the hot metal flow, physical and numerical models of hearth refractory wear, and numerical models and mechanisms of Ti(C,N) protection layer formation of titania addition.

Chapter 3 details the development of the improved 3D CFD model to predict the flow and temperature distribution in the blast furnace hearth. The effect of coke bed permeability on the flow and temperature distribution in the hearth is investigated.

Chapter 4 presents a method to manage titanium compounds in a blast furnace hearth during titania addition. The titanium particle formation and dissolution behaviour is studied through parametric studies of key operational parameters using a 2D two– phase multi-component model.

Chapter 5 details the development of a steady-state 3D CFD model to simulate the titanium compound behaviour in the blast furnace hearth during titania addition via burdening. The effects of titanium dosage rate on the distribution of TiC particle concentration within the hearth volume and inner hearth surface for a sitting and floating coke bed state are investigated.

Chapter 6 details the development of a transient 3D CFD model to simulate the titanium compound behaviour in the blast furnace hearth during titania addition via tuyere injection. The effects of key operational parameters including titanium dosage rate and position of the tuyere for injection are investigated. Based on the simulation results, recommendations on the titania addition measures are provided and details of the titania injection simulator program are introduced.

CHAPTER 1

1.7 NOMENCLATURE

-1 Aαβ: Interfacial area density [m ] A: General activity [-]

Cμ: Turbulence model constant [-] c2: Turbulence model constants [-] cp: Specific heat of fluid [J/kg.K] 2 Deff C: Effective diffusion coefficient of a component [m /s] 2 Dm C: Molecular diffusion coefficient of a component [m /s] D: Diffusion coefficient [m2/s] 2 Dm: Molecular diffusivity [m /s] d: Solid TiC particle size [m] ds: Solid particle size [m] ds0: Seeding particle size [m] dp: Characteristic coke size [m] d: Coke size [m] dh: Harmonic mean coke size [m] F: Blending function [-] 3 Fd: Solid-liquid drag force [N/m ] 3 Fc: Interaction force between the phase and the coke bed [N/m ] fTi: Activity coefficient of Ti in hot metal [-] G: The mass flux [kg/m2] ΔG: Free energy of reaction [J/mol] g: Gravity [m/s2] H: Enthalpy [J] h: Henrian activity [-]

KN, KTiC:Equilibrium constants [-] k: Turbulence kinetic energy [m2/s2] -1 Kloss: Loss coefficient [m ] 2 Kperm: Permeability [m ] 2 Kperm,cr: Critical permeability [m ] 3 c: Mass transfer source of a component [kg/m .s] 3 C: Interphase mass transfer rate of total mass and of each component [kg/m .s] 12

CHAPTER 1

n: Particle number density [m-1] -1 ns: The particle number density of solid particle phase [m ] -1 ns0: Seeding particle number density [m ] nf: Number fraction of coke particles [-] p: Pressure [Pa] Pe: Peclet number [-]

PeD: Peclet number based on Darcian velocity [-] Pr: Prandtle number [-]

2 2 R : Resistance force [kg/m .s ] rc: Atomic radius [m] r: Radius [m] rhearth: Hearth radius [m] S: Strain rate constant [-] R: Universal gas constant [J/mol.K] R: Resistance force [N/m3] Re: Reynolds number [-] r: Phase volume fraction [-] rc: Radius of atom [m] S: Strain rate constant [-] 3 Sk: Source term for turbulence kinetic energy equation [kg/m.s ] 3 2 Sω: Source term for turbulence dissipation frequency equation [kg/m .s ] Sc: Schmidt number [-] Sh: Sherwood number [-] T: Temperature [K] * TTC : Normalized thermocouple temperature [K] U: Superficial velocity [m/s]

Us: Suspended solid superficial velocity [m/s] u: True velocity vector [m/s] u: Velocity [m/s]

u : Velocity vector [m/s]

u s : Superficial velocity vector [m/s] us: Superficial velocity [m/s]

CHAPTER 1

YC: Mass fraction of a component [-]

YTi: Ti mass fraction [-]

YTi’: Ti mass fraction at particle surface [-]

YTiC: TiC mass fraction [-] Y: Mass fraction of a component [-]

Greek Letters α: Turbulent model constant [-] β': Turbulence model constant [-] γ: Porosity of coke bed [-] δ: Unit tensor [-] ε: Packed bed porosity [-] ε: Turbulence eddy dissipation rate [m2/s3] ζ: Coke internal porosity [-] κ: Boltzmann’s constant (1.3807x10-23) [J/K] ρ: Density [kg/m3] μ: General viscosity of a phase or laminar viscosity of liquid [Pa.s]

μs: Solid shear viscosity [Pa.s]

μt: Turbulent viscosity [-] λ: Thermal conductivity [W/m.K]

λFe: Thermal conductivity of fluid [W/m.K]

λcoke: Thermal conductivity of coke particles [W/m.K]

λdis: Apparent thermal conductivity due to thermal dispersion [W/m.K]

λstg: Effective stagnant thermal conductivity [W/m.K]

μeff: Effective viscosity [Pa.s]

μL: Dynamic viscosity [Pa.s]

μT: Turbulent viscosity [Pa.s] ρ: Density of fluid [kg/m3] 3 ρref: Reference density of fluid [kg/m ]

σT: Turbulent Prandtl number [-] ϕ: Shape factor of coke particles [-] ω: Turbulence eddy frequency [s-1]

CHAPTER 2

CHAPTER 2 LITERATURE REVIEW

2.1 INTRODUCTION Extending the campaign life of the blast furnace is one of the trends in the current blast furnace technology. As mentioned in Chapter 1, failure of the of the hearth refractories, among others, is recognised as a limitation of a long furnace campaign. For this reason, significant amount of studies have been conducted regarding the hearth of the blast furnace. In this chapter, literatures regarding the studies to prevent hearth refractory wear by means of extending the furnace campaign are reviewed. First, the studies reported on the flow and heat transfer in the hearth are reviewed. Second, reports regarding the deterioration of the hearth refractory are reviewed. And finally, works conducted in the field of titanium carbonitride scaffold formation in the hearth are reviewed.

2.2 FLOW AND HEAT TRANSFER OF HOT METAL IN THE HEARTH Erosion and thermal stresses are some of the main factors that cause wear of the hearth linings. For this reason, the modelling of the flow and heat transfer in the hearth to better understand the in-hearth phenomena has been a hot topic in blast furnace technology. In this section, experimental and numerical studies regarding the flow and heat transfer in the hearth are reviewed. In literature, there has been a debate regarding the importance of natural convection where some claims its effect on the flow pattern is significant where others state that it has negligible effect. Here, experimental and numerical models that neglect the effect of natural convection are reviewed first, followed by those that do consider its effect.

2.2.1 Models Neglecting Natural Convection The section reviews studies conducted to model the flow and heat transfer of the blast furnace hearth when the natural convection is neglected. The physical model studies are reviewed first followed by the numerical model studies.

CHAPTER 2

2.2.1.1 Physical Models Luomala et al. (2001) conducted lab scale experiments to investigate the distribution of hot metal in the hearth. They used a 3D cold water apparatus and tracked the liquid by injecting NaCl solution at the inlet and measuring its electrical conductivity using 41 electric resistance sensors probed from the top (FIGURE 2.1). Various coke bed states (sitting, floating, impermeable core) were investigated. It was found that liquid entering the inlet near the taphole (45% of the inlet area) only passes through the packed bed whilst those entering from the rest of the inlet area pass the coke free zone before exiting.

FIGURE 2.1. Experimental apparatus of the 3D cold water model simulating the flow of hot metal in the blast furnace hearth (Luomala et al., 2001).

Peters et al. (1985) investigated the flow distribution in the hearth by using physical lab scale models. A kinetic model was used to measure the local flow rate and a flow-line model was used for visualization. They investigated the effects of various operational parameters such as coke bed configuration (sitting, floating with flat base, floating with concave base), liquid level, sump depth (i.e. distance from the hearth bottom to the taphole) and taphole length. In particular regarding the effect of shape of the floating coke bed, they found that for flat based coke bed, the greatest flow induced stress occurs at the hearth bottom center and for a convex based coke bed, it occurs along the lower hearth walls and hearth bottom periphery (FIGURE 2.2).

CHAPTER 2

FIGURE 2.2. Results of the 3D cold water model when (i) coke bed is sitting, (ii) coke bed is floating (flat base), (ii) coke bed is floating (convex base) (Peters et al., 1985).

Nnanna et al. (2004) built a 3D cold water model (1:10 scale of the hearth of ISPAT’s Inland Blast Furnace No. 7) to investigate the flow in the hearth (FIGURE 2.3). Dimensional analyses were conducted to determine the geometrical similarities between the model and the actual hearth. The water model is capable of looking at the effects of the coke bed configuration, the taphole depth and taphole diameters. The deadman configuration is structured with a porous central core of about 1/3 of hearth diameter (ε = 0.3) and the remaining peripheral region to be non porous (ε=0). The velocity of the liquid was measured by timing the displacement of dye. Average velocities were presented for porous and non porous, high and low taphole locations.

FIGURE 2.3. Experimental apparatus of the 3D cold water model shown in (i) photograph and (ii) schematic diagram (Nnanna et al., 2004).

CHAPTER 2

Ohno et al. (1981) from Nippon Steel Corporation (currently Nippon Steel and Sumitomo Metal Corporation (NSSMC)) conducted experimental modelling to predict the hot metal flow within the pool. They used 60 cm diameter and 40 cm high transparent plastic container to model the hearth and used ceramic balls with diameter 4 - 5 mm to model the coke particles (FIGURE 2.4). As shown in FIGURE 2.5(ii) they found that about 60 – 70% of the total liquid passes the coke free layer. Further, they conducted lab scale water model using ice to simulate the scaffold behaviour in the hearth. It was found that the scaffolds melt if the coke bed floats slightly, and the coke free layer thickness is maintained throughout the melting process.

FIGURE 2.4. Experimental apparatus for 3D water model (Ohno et al., 1981).

FIGURE 2.5. Flow distribution of liquid in the experimental apparatus for (i) sitting and (ii) floating coke beds.

CHAPTER 2

Okada et al. (1991) conducted water model experiments to understand the flow characteristics of liquid in porous media during tapping. The purpose of the experiment was to predict the transport of the titanium content in the hearth when titania is added via tuyere injection into the blast furnace. In the apparatus, a cylindrical tank with a single tap hole, packed with alumina particles filled with water was used (FIGURE 2.6(i)). Here, 2 cases were investigated. These are sitting coke bed with and without a coke free gutter. Coloured water was introduced from the water surface where the flow was visualised. In the sitting coke bed without a coke gutter, the liquid directly flow towards the outlet (FIGURE 2.6(ii)). On the other hand, in sitting coke bed with a coke gutter, the liquid first flow downwards along the side surface and into the gutter, then flow back into the coke near the taphole region and exit from the taphole (FIGURE 2.6 (iii)).

2.2.1.2 Numerical Models Huang et al. (2008) developed a 3D hearth model to simulate the flow and heat transfer in the hearth of China Steel Corporation’s (CSC) No. 2 Blast Furnace. The model uses constant material properties and disregards the influence of turbulence. In

CHAPTER 2

their model validation analysis, the calculated and measured (thermocouple temperatures from CSC No. 2 Blast Furnace) refractory temperatures were compared where they found good agreement (FIGURE 2.7). The effect of cooling water temperature was explored by altering the outer wall boundary temperature. The flow and temperature distributions were investigated for two different coke bed configurations, floating and sitting with coke-free gutter (FIGURE 2.8). They mentioned that a floating coke bed state causes deep pot-like erosion whereas the sitting coke bed state with coke-free gutter causes elephant foot type erosion.

FIGURE 2.7. Comparison of calculated and measured refractory temperatures. Measurements are from China Steel Corporation’s No. 2 Blast Furnace (Huang et al., 2008).

FIGURE 2.8. For a floating coke bed state: (i) 3D velocity vector distribution along inner hearth surface and (ii) side view streaklines plot along the hearth symmetry plane (Huang et al., 2008).

CHAPTER 2

Kurita and Ogawa (1994) from Sumitomo Metal Industries Ltd. (currently NSSMC) have developed a full 3D CFD model using crude number of mesh nodes. They investigated the flow and heat transfer of the liquid iron in the hearth and explained the cause of pan-shaped and mushroom-shaped erosion profile found in dissected hearths (FIGURE 2.9). For the characterisation of their coke bed, they used porosity of 0.5 and coke size of 20 mm as their base case. Five cases were conducted: (i) uniform dripping pattern in homogeneous coke bed, (ii) peripheral dripping pattern in homogenous coke bed, (iii) uniform dripping pattern but with variable temperature in homogenous coke bed, (iv) uniform dripping pattern with coke bed with coke free gutter and (v) uniform dripping pattern in coke bed with inhomogeneous porosity. The velocity vectors and temperature distributions for cases (i), (ii), (iv) and (v) are shown in FIGURE 2.10. They have concluded that a low temperature in the center and high temperature in the peripheral region leads to the “mushroom-shaped” erosion profile.

FIGURE 2.9. Typical erosion profiles in a blast furnace hearth: (i) pan-shaped erosion and (ii) mushroom-shaped erosion (Kurita and Ogawa, 1994).

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FIGURE 2.10. Velocity vector plot and temperature distributions along the hearth symmetry plane for (i) uniform inlet flow in sitting coke bed state, (ii) peripheral inlet flow in sitting coke bed state, (iii) uniform inlet flow in sitting coke bed state with coke free gutter and (iv) peripheral inlet flow in sitting coke bed state with inhomogeneous porosity distribution (Kurita and Ogawa, 1994).

Similar to Kurita and Ogawa (1994), Tomita and Tanaka (1994) from Nisshin Steel Co Ltd. have developed a 3D CFD model to predict the flow and temperature distributions of the hearth of Nisshin Steel’s Kure No.1 Blast Furnace (the hearth diameter is 9.4 m). They have also used crude number of mesh nodes ((r, θ, z) = (20×15×26)) and neglected the influence of turbulence. In their model, they used a temperature and titanium concentration dependant hot metal viscosity (expression not presented) and modelled the solidification of hot metal by stopping the flow at temperatures below 1150°C (Solidus temperature of pure iron). They have compared their calculated refractory temperatures to the measured thermocouple data embedded within hearth refractory of Kure No. 1 Blast Furnace and have verified good agreement (FIGURE 2.11). Their typical flow features are noticeably characterized by a solidified layer formed along the hearth bottom with thickness corresponding to almost half the 22

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pool depth. The effect of local addition of titanium on the hot metal flow and hot metal and refractory temperature was investigated. The review is detailed in Section 2.4.6.

FIGURE 2.11. (i) Location of pad thermocouples embedded within the hearth refractories. (ii) Comparison between calculated and thermocouple temperatures (Tomita and Tanaka, 1994).

FIGURE 2.12. (i) Location of pad thermocouples embedded within the hearth refractories. (ii) Comparison between calculated and thermocouple temperatures (Tomita and Tanaka, 1994).

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Elsaadawy and Lu (Elsaadawy and Lu (2005b), Elsaadawy and Lu (2005a)) developed a 2D CFD model to simulate hearth flow and drainage. No heat transfer was considered in the model. Discussions were presented in three areas: flow patterns, shear stresses and liquid tracking. Flow patterns and shear stresses were analysed with respect to various sump ratios (SR=metal depth/hearth diameter) and gap ratios (GR=thickness of coke free layer/hearth diameter). Liquid tracking (both slag and metal) was conducted using free surface transient calculations (VOF) and were analysed by monitoring the change in 7 separated volumes. In Elsaadawy and Lu (2006), their 2D model was extended to a full 3D CFD model to investigate the forced flow in the hearth at various coke bed configuration namely; sitting coke bed, partially sitting coke bed with coke free gutter, and floating coke bed with GR=0.2, 0.4, 0.6 and 0.9. No heat transfer was considered. Again, analyses were conducted based on shear stress along the hearth bottom and tap hole inlet. They found that the wall shear stress along the hearth bottom is low in a fully sitting coke bed, and increases significantly, then decreases gradually as the gap ratio increases.

Along with the water model experiment detailed in Section 2.2.1.1, Ohno et al. (1981) have conducted numerical studies to predict the hot metal flow within the hearth pool (refractory is excluded in the model). Here, only the continuity and conservation of momentum equations were solved. The flow pattern in a sitting and floating coke bed was investigated (FIGURE 2.13). They found that when the coke bed is floating, the velocity of the hot metal is about 20 times that when the coke bed is sitting. Further in their work, they have developed an approximate expression based on residual time and dripping location (FIGURE 2.14). Good agreement was met between the expression and residual times measured in two of their actual blast furnace hearths using radioactive isotopes. Based on these analyses, they found that the coke bed in the hearth floats and sinks in a period of several months.

CHAPTER 2

FIGURE 2.13. Planar and side views of streaklines and velocity contours for (i) sitting and (ii) floating coke bed states (Ohno et al., 1981).

FIGURE 2.14. Comparison between experimental and numerical models with respect to their travelling times for (i) sitting and (ii) floating coke bed states (Ohno et al., 1981).

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2.2.2 Models Considering Natural Convection The section reviews studies conducted to model the flow and heat transfer of the blast furnace hearth when the natural convection is considered. The physical model studies are reviewed first followed by the numerical model studies.

2.2.2.1 Physical Models One of the only investigators in literature, Preuer et al. (1992b), built a experimental 3D water model that considers the effect of natural convection, to study the flow behaviour in the blast furnace hearth. The apparatus was built using a half- cylinder shaped plexiglass tank (at 1:5 scale of the blast furnace hearth) where a piece of wood was placed at the center to model an impermeable zone. The effect of natural convection was modelled by placing the apparatus inside another cube-shaped tank which is filled with cold water at temperature of 16°C. Steady flow of heated water at temperature of 50°C was maintained in the half-cylinder tank to simulate the hot metal flow. Two experimental cases were reported. Experiment A: hearth core is impermeable and the remaining peripheral zone is porous free. Experiment B: hearth core is impermeable where the remaining peripheral zone is porous except for the bottom corner which is porous free (simulating a coke free gutter). In both experiments, they observed natural convection induced flow along a very thin layer along the wall with a maximum downward velocity of approximately 5 mm/s. This can be visualised in FIGURE 2.15(i). One of the remarkable flow features found in Experiment B within the coke free gutter, was the fact that the flow at the bottom region was flowing in the opposite direction to the main flow at the top region. This is caused by the effect of natural convection.

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2.2.2.2 Numerical Models One of the earliest investigators who performed numerical studies to predict the flow and temperature distributions in the blast furnace hearth was Yoshikawa and Szekely (1981). They conducted a 2D analysis to investigate the liquid iron distribution using a simple axi-symmetrical model. The computational field was set to be non porous and hence assumed that the coke bed was floating within the slag phase. They found strong recirculation flow near the side walls driven by thermally induced buoyancy force (FIGURE 2.16(i)). The flow pattern produces a strong downward current near the side walls with a velocity reaching up to 50 mm/s and impacts onto the bottom surface at the corner which may cause lining erosion. In their simulation, they found that the flow is turbulent. This can be seen in their normalised effective viscosity plot (FIGURE 2.16(ii)). The temperature field was found to be mostly isothermal except in the near wall region. Here, temperature significantly reduces causing the induction of natural convection.

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FIGURE 2.16. (i) Velocity vector plot, (ii) normalised effective viscosity (μeff / μ) contour plot and (iii) temperature contour plot (Yoshikawa and Szekely, 1981).

Through the use of a 3D numerical model, Shibata et al. (1990) investigated the effect of the coke bed structure, their porosity distribution and the taphole depth on the hot metal flow and heat transfer. The coke bed structure considered were namely; fully sitting bed, sitting bed with coke free gutter, floating bed with coke free layer, and floating bed with coke free gutter. The model used was a 3D laminar flow model with conjugate heat transfer, natural convection and temperature dependant viscosity. Also an empirical heat transfer coefficient was used to describe the transfer of heat between molten iron and refractory. The model was meshed using crude grid points. The hot metal was found to descend to the hearth bottom, and then flow towards the tap hole, where no sign of recirculation zones are observed FIGURE 2.17.

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FIGURE 2.17. Velocity vectors and 1400°C isotherm in a fully sitting coke bed configuration. (Shibata et al., 1990)

Kowalski et al. (1998) developed a 3D CFD model to attain information regarding the hot metal flow pattern in the hearth. The conservation equations of mass, momentum and energy were solved. They assumed symmetric conditions where 44,000 grid points were used (FIGURE 2.18). Temperature dependant material properties were incorporated. In particular in order to include the effect of natural convection, the following temperature dependant density was used.

[2.1]

The effect of coke bed height was investigated (FIGURE 2.18(i)). They found that the hot metal velocity is highest within the coke-free zone and near the taphole. Due to the low resistance force in the coke free zone, recirculating flow driven by natural convection was observed (FIGURE 2.18(i)).

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Post et al.(Post et al., 2003) developed a 2D CFD model to study the flow phenomena in the hearth. They emphasized the importance of natural convection and its significant effect on the flow and temperature distribution of the hot metal. A 2D model with simple geometry of the hot metal pool was used where the effect of turbulence was neglected. Since only the hot metal pool was modelled (i.e. the refractory domain was excluded), a heat flux was assigned to the sidewall and bottom as boundary conditions. As shown below, the hot metal viscosity is treated as a function of temperature and the density as a function of both temperature and carbon concentration.

[2.2]

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[2.3]

where αC is the coefficient of expansion, β is the coefficient of thermal expansion, YC is the mass fraction of carbon in hot metal, YC is the mass fraction of carbon in carbon saturated hot metal, Tm is the melting temperature of iron and ρo is the density at Tm.

It was found that a clear stratification occurs between the high velocity zone located at the upper half of the hearth and low velocity zone located at the lower half of the hearth (FIGURE 2.19). They reasoned that the stratification is caused by density differences due to temperature gradient across the hearth.

FIGURE 2.19. Streamline with colouring based on residence time (Post et al., 2003).

Panjkovic et al. (2002) developed a 3D hearth model to investigate the flow and heat transfer in the hearth of BlueScope’s PK5BF. In their hearth model, they modelled turbulence using an algebraic turbulence model. The viscosity and thermal conductivity of the hot metal were assumed to be constant and temperature dependent refractory thermal conductivity and hot metal density were used. The model validation analyses were conducted by comparing the calculated refractory temperatures to the measured thermocouple temperature retrieved from the hearth of PK5BF where reasonable 31

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agreements were met with some marginal under-prediction (FIGURE 2.20). The effects of various parameters were investigated including the coke bed state, lining profile and spatially variable boundary temperatures. Similarly to the findings of Post et al. (2003), the flow pattern was found to stratify in two zones: high velocity zone at the top region of the hearth and low velocity zone at the bottom region of the hearth (FIGURE 2.21).

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FIGURE 2.21. Temperature profile and velocity vector of a fully sitting coke bed (Panjkovic et al., 2002).

The effect of key parameters were investigated including parameters such as coke free gutter, height of coke free layer, refractory erosion, external boundary temperature, and embrittled layer. With respect to the base case (i.e. intact hearth and sitting deadman) it was found that by adding a coke free gutter and setting the coke free layer height to 250 mm, the calculated refractory temperature becomes closer to measurement. The effect of temperature of the external boundaries and the addition of an embrittled layer did not seem effect the flow and temperature distribution in the hot metal and hence the refractory temperatures.

Cheng et al. (2005) reproduced Panjkovic’s model to investigate the shear stress distribution along the hearth side wall (FIGURE 2.24). Compared to the model developed by Panjkovic et al. (2002) finer mesh was applied and a similar comparison between calculated and measured temperatures was achieved (FIGURE 2.22). They 33

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explicitly compared the difference in flow pattern for cases with and without the inclusion of natural convection. They pointed out the mixed (forced and natural) convective flow pattern causing recirculating flow features for the case with natural convection as opposed to the forced convective flow pattern in the case without natural convection (FIGURE 2.23).

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FIGURE 2.23. Streamlines of hot metal for cases (i) with and (ii) without natural convection. Fully sitting bed with intact firebrick (Cheng et al., 2005).

Most recently, Guo et al. (2008) developed a 3D CFD hearth model including natural convection, modified k-ε turbulence model and a modified thermal conductivity that considers thermal dispersion. They validated their model by comparing their calculated temperatures with measured thermocouple temperatures. The comparability were similar to what was obtained by Panjkovic et al. (2002) where calculated temperature still under-predicts measurements (FIGURE 2.24).

FIGURE 2.24. Comparison between calculated and measured refractory temperatures for (i) sitting and (ii) floating coke bed states (Guo et al., 2008).

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A comparison was made between buoyant and non-buoyant flow where significantly different flow and temperature distribution were observed (FIGURE 2.25). When natural convection is included, similar to that observed by Post et al. (2003) and Panjkovic et al. (2002), the flow field divides into high and low velocity zones located respectively in the upper and lower region of the hearth (FIGURE 2.25(i)). On the other hand when natural convection is neglected, the hot metal flows uniformly (with uniform velocity) from the inlet to the outlet throughout the hearth volume (FIGURE 2.25(ii)). Further, when natural convection is included in the model, “horizontal thermal layering” phenomenon occurs. This is when the temperature contour lines are horizontally layered along the hearth bottom region where the temperature decreases sharply towards the hearth bottom (FIGURE 2.25(ii)).

FIGURE 2.25. Velocity vectors, streamlines and temperature contours for cases (i) with natural convection and (ii) without natural convection, when the coke bed is sitting (Guo et al., 2008).

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2.3 DETERIORATION OF THE HEARTH REFRACTORY In order to prevent hearth wear and to take preventative actions, it is important to understand the causes that led to the hearth refractory wear. It is also important to quantify the timing to execute preventative actions or to judge the end of the campaign and these will depend on the state of the hearth refractories. In this section, studies conducted to elucidate the mechanisms of hearth refractory wear are reviewed. This is followed by a review of studies regarding the simulation of the hearth refractory lining thickness by use of hearth models.

2.3.1 Wear Mechanism Silva et al. (2005) conducted a set of experiments to investigate the cause of hearth refractory wear. The following subjects were experimented.

. oxidation resistance . thermal shock resistance . carbon monoxide deterioration . alkaline steam attack . alkaline attack by liquid phase . alkaline attack under temperature gradient . mechanical resistance deterioration with alkaline attack . hot metal dissolution through the effect of:  hot metal carbon saturation  liquid flow

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Based on the understanding gained in these experiments, they hypothesised that the eroded hearth refractories can be divided into 6 zones (FIGURE 2.26(i)). These are namely:

1. Lost layer (eroded and dissolved) 2. Protective layer (scab) 3. Hot metal penetrated layer 4. Brittle zone 5. Slightly changed layer 6. Unchanged layer

A comprehensive wear mechanism for the hearth refractory lining (resulting with the above mentioned zones) has been proposed (FIGURE 2.26(ii)). As hot metal penetrates into the pores of the hearth refractory and passes the 1150°C isotherm, it solidifies and shrinks allowing more space for further liquid to penetrate (FIGURE 2.26(ii)a). As the penetrated liquid dissolves excess carbon content (from carbon refractories) and precipitates as graphitic, it alters the heat transfer from hot to cold face. Also wear due to hot metal flow causes 1150°C isotherm to shift towards the cold side. This results the solidified iron to melt and expand, causing cracks in the local refractories (FIGURE 2.26(ii)b). The refractories at 800°C become thoroughly disintegrated and crumbly after alkali (potassium) and zinc attacks causing the local region to be brittle (FIGURE 2.26(ii)c). As oxygen penetrates the lining pores and adsorbs into the refractory pore surface, they react with the carbon content (at temperature above 500°C). The produced carbon monoxide desorbs from the refractory pore surface (FIGURE 2.26(ii)d).

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2.3.2 Models to Predict the Inner Hearth Profile In this section, hearth model studies conducted to simulate the hearth refractory profile are reviewed. Physical model studies are reviewed first followed by numerical model studies.

CHAPTER 2

2.3.2.1 Physical Models Kowalski et al. (1998) built a 3D physical model, 1:10 scale of the hearth of Thyssen Krupp Stahl’s blast furnace 1, to simulate its sidewall wear profile. In their apparatus, they installed erodible linings and measured its 3D profile using laser-optic technique. The model was set such that the unsaturated fluid feeds into the hearth inlet, then flows through the packed bed (consists a coke free gutter along the hearth bottom corner) and then drains out the taphole (tapping sequence computationally made consistent to that of blast furnace 1 before relining) (FIGURE 2.27(i)). The simulated sidewall wear profile was compared to the actual wear profile measured in BF1 after shutdown where good agreement was achieved (FIGURE 2.27(ii)). From their simulation, they presented a 3D side wall wear profile that was described to be a “mushroom-shape” (FIGURE 2.27(iii)).

FIGURE 2.27. (i) Apparatus of the 3D physical wear model of Thyssen Krupp Stahl’s BF1. (ii) Comparison between simulated wear profile and actual wear profile measured in BF1 after shutdown. The view shows the comparison along the sidewall and bottom at a location between tapholes. (iii) Simulation of the 3D wear profile in the physical model (Kowalski et al., 1998).

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2.3.2.2 Numerical Models Preuer et al. (1992a) (also summarised in Preuer and Winter (1993)) numerically investigated the cause of the mushroom erosion profile observed in their VoestAlpine blast furnace B. Based on experimental and numerical analyses on the liquid flow in their previous article (Preuer et al., 1992b), they extended their model to include carbon dissolution of coke and refractories in the hot metal. The conservation of carbon species were calculated based on the velocity field obtained in their previous model. Therefore they assumed that the presence of the carbon content does not influence the hot metal flow pattern. FIGURE 2.28(i) shows the carbon concentration contour plot. They found that the carbon content is high in the coke bed region due to its low local velocity. Based on the results gained in Preuer et al. (1992b), they calculated the erosion velocity along the hearth side walls (FIGURE 2.28(ii)) and conducted comparative studies for various operational parameters including the productivity, inlet carbon concentration and coke bed porosity (FIGURE 2.29).

FIGURE 2.28. (i) Carbon concentration contours along the hearth symmetry plane. (ii) Erosion velocity along the hearth side wall. Units are in cm/month (Preuer et al., 1992a).

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2.4 TITANIUM CARBONITRIDE SCAFFOLD FORMATION IN THE HEARTH As a measure to extend the blast furnace campaign life, the addition of titanium bearing materials into the furnace has become a common measure. The measure is understood that it may form a titanium carbonitride scaffold along the eroded regions of the hearth linings, preventing them from further eroding. The section reviews fundamental studies, reports on plant trials and model studies regarding the titanium carbonitride scaffold formation in the hearth during titania addition.

2.4.1 Discovery of Titanium Bear during Dissection Studies Dissection studies of the blast furnace provide valuable microscopic and macroscopic information of in-furnace conditions. Through these studies significant understanding of the in-furnace phenomena is gained. One of the discoveries found were the titanium-rich scaffolds forming along the eroded surface of the hearth linings which seems to protect the linings from further erosion. In this section, reports on

CHAPTER 2

dissection studies of blast furnaces are reviewed particularly regarding the titanium-rich scaffolds found in the hearth of the blast furnace.

Narita et al. (1977) reports on the titanium-rich scaffolds found in the hearths of Kobe Steel’s dissected blast furnaces. The hearths of the following blast furnaces were analysed (TABLE 2.1).

TABLE 2.1 Specifications of Kobe Steel’s blast furnaces analysed by Narita et al. (1977). Blast Furnace Volume [m3] Date of blow out Campaign life Kobe No. 3 B.F. 1850 September 1973 7 years Kakogawa No. 1 B.F. 2843 September 1974 4 years 1 month

FIGURE 2.30 shows the location of the titanium-rich scaffolds found in the hearths and the following points were reported.

For the hearth of Kakogawa No. 1 B.F.:

 Bottom chamotte bricks S4, S5 and S6 were all eroded.  Traces of titanium-rich scaffold were found within the hearth. Their location and colour are summarised in TABLE 2.2.  Pig iron had penetrated into the joint of the upper 1st layer of the chamotte brick. TABLE 2.3 summarises the chemical composition of the pig iron that

had penetrated in each S1, S2 and S3 chamotte bricks. TABLE 2.4 summarises the chemical composition of normal pig iron as casted. The titanium content in the penetrated pig iron was found to be high.

CHAPTER 2

TABLE 2.2. Locations of titanium-rich scaffolds found in Kakogawa No. 1 B.F. during dissection analysed by Narita et al. (1977). Legend Location Colour

T1 Eroded regions of the hearth wall Reddish brown

T2 In the salamander Reddish brown

T3 On the chamotte bottom bricks Yellowish orange

T4 In the joint of chamotte bricks Yellowish orange

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TABLE 2.3. Chemical composition of the pig iron penetrated into the joint of chamotte bottom brick found from the hearth of Kakogawa No. 1 B.F. (wt%) (Narita et al., 1977).

TABLE 2.4. Chemical composition of the pig iron and salamander as tapped out found for Kakogawa No. 1 B.F. (wt%) (Narita et al., 1977).

For the hearth of Kobe No. 3 B.F.:

 Carbon blocks C1, C2 and C3 were all eroded except in the region near the side wall.  About 1 m below the taphole level throughout the hearth wall periphery in a ring shape, the formation of titanium-rich scaffold was found. The cross- sectional area of the ring shape scaffold was 0.5 m2 and a large quantity of titanium compounds was contained in it (scaffold is indicated as “T” in FIGURE 2.30(ii)).

2.4.2 Mechanism of Ti(C,N) Protection Layer Formation

2.4.2.1 Morphological Studies of Ti(C,N) Scaffold Narita et al. (1977) investigated the samples obtained from the eroded portion of the hearth wall of Kobe No.3 blast furnace and observed that the Ti(C,N) crystal grew in faceted mode where it’s annual ring like cross-section consists of many layers (FIGURE 2.31(i)). The colour of the crystal varies from yellowish orange to purple and almost grey having similar colour sequence along with several other neighbouring crystals. An electron probe X-ray microanalysis (EPMA) which determines the relative chemical composition with respect to its colour appearance shows that the concentration

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of carbon and nitrogen change contrarily to each other and rich TiC content in the Ti(C,N) crystal is represented by bluish purple as opposed from yellowish orange colour representing richness in TiN (FIGURE 2.31).

FIGURE 2.31. (i) Single crystal of Ti(C,N) using optical micrograph. (ii) EPMA results showing titanium, carbon and nitrogen concentration profiles through Ti(C,N) crystal (Narita et al., 1976).

They also analysed samples taken from Kakogawa No.1 blast furnace and found that the composition and size of Ti(C,N) crystals in the hearth are related to temperature, nitrogen partial pressure and hot metal flow. Along the eroded hearth walls and in the joints of chamotte bottom bricks, the Ti(C,N) crystals with size of 500 µm were found. On the other hand, in the salamander and on the chamotte brick bottom surface only fine crystals (50 µm) were found (FIGURE 2.32). The reason for the range of size at different locations of the hearth can be explained by the flow characteristics of the local region.

In the local eroded portion of the hearth, Ti(C,N) crystals form due to the low temperature and/or the nitrogen partial pressure change. These titanium crystals remain in place without being carried away because the motion of hot metal is relatively small in the eroded regions compared to that in the bulk hearth.

Similar explanations were applied to the cause of large sized Ti(C,N) crystals in the joints of chamotte bottom bricks. The hot metal penetrated in the joints is mostly 46

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stagnant and hence crystals remain and grow. This crystal growth process is held over a long period of time. From sample analyses, the titanium content here was about 15% while titanium solubility in molten pig iron is less than 0.3% at nitrogen partial pressure of 1 atm and 1400°C. This indicates it is impossible to form a crystal of Ti(C,N) at a single time.

In contrast, there exist stronger current of hot metal in the salamander and along the chamotte brick surface. This prevents crystal growth and therefore the sizes of Ti(C,N) crystals are less than 50 µm at these regions.

Li and Fruehan (2001a) and Li and Fruehan (2001b) used confocal scanning laser microscope to find the precipitation temperature of TiC and Ti(C,N). In their analyses, two types of crystals were observed: one with rough surface and another with

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smooth surface (FIGURE 2.33(i)). The crystals with rough surfaces tend to aggregate but the bond is weak and can be broken by metal movement. On the other hand smooth surface crystals do not stick together when contact is made to one another. FIGURE 2.33(ii) shows the scanning electron microscope (SEM) and EDX element mapping image of the crystals formed. Since the carbon and nitrogen content of the crystals were higher than that of the surrounding molten iron, the crystal represents Ti(C,N). Both rough and smooth surfaces had identical composition.

FIGURE 2.33. (i) Confocal scanning laser microscope image of precipitates of Fe-Csat-

0.2mass%Ti at PN2=1atm. (ii) (a) SEM image and EDX element mapping of: (b) Fe, (c) Ti,

(d) N and (e) C on Fe-Csat0.2mass%Ti at PN2=1atm and T=1775K

2.4.2.2 Hypothetical Mechanisms of Ti(C,N) Protection Layer Formation Based on sample analyses of titanium rich scaffolds found in dissected blast furnaces such as those introduced in Section 2.4.1. Bergsma and Fruehan (2001) has developed a 2-part hypothesis regarding the mechanism of the formation of Ti(C,N) protection layer. The following are direct quotes extracted from Bergsma and Fruehan (2001).

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“Hypothesis Part 1 – A fraction of Ti-enriched HM will come close to the relatively cold hearth wall or will even pass a worn out area rapidly losing thermal energy. The solubility of Ti, C and N drops, resulting in a high driving force to form TiC and TiN. Homogeneous nucleation or growth on pre-existing nuclei (coke, graphites?) may occur if this sudden under cooling is sufficient” (Bergsma and Fruehan, 2001)

“Hypothesis Part 2 – How metal becomes increasingly viscous until it stops flowing due to an increase in the amount/volume of Ti(C,N) particles. From that point on, it can be regarded a solid having its own apparent solidus temperatures. An iron bear containing significant amounts of Ti(C,N) particles may be formed if this viscosity enhanced solidification takes place at the refractory wall of a blast furnace.” (Bergsma and Fruehan, 2001)

The first hypothesis proposed were summarised using the following schematic illustration (FIGURE 2.34). The mechanism of the formation of Ti(C,N) protective layer was described as follows.

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1. Dissolution of titania in slag phase. 2. Reduction of titania in slag phase and dissolution of produced titanium into hot metal phase. 3. Transport of titanium to the damaged refractory linings. 4. Formation of Ti(C,N) particles due to cooling. 5. Deposition of Ti(C,N) particles on the hearth walls and formation of scaffold.

The second hypothesis was based on the study conducted by Wen et al. (1996). The effect of titanium concentration on the viscosity of hot metal was investigated where they found that the apparent solidification temperature shifts when the titanium concentration exceeds a certain limit.

FIGURE 2.35. Change of apparent solidification temperature by Ti(C,N) formation (Bergsma and Fruehan, 2001).

2.4.3 Chemical Thermodynamic Studies Regarding the Formation of Ti(C,N) Bergsma and Fruehan (2001) investigated the thermodynamics of the Ti(C,N) formation to quantify the minimum amount of titania required to initiate the formation of Ti(C,N). Here, the results of their thermodynamic analyses are summarised. The relevant chemical reactions for Ti(C,N) formation are:

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[2.4]

[2.5]

where their reaction energies, equilibrium constants and derivations of other thermodynamic quantities are presented in their paper. Based on their thermodynamics model, they have calculated the composition of Ti(C,N) with respect to temperature and partial pressure of nitrogen (FIGURE 2.36(i)), and quantified the minimum titanium concentration required for the formation of Ti(C,N) (FIGURE 2.36(ii)). Moreover, by investigating the equilibrium relation between the Ti(C,N) formation in the hot metal phase and the TiOX reduction in the slag phase in blast furnace conditions, they calculated the minimum amount of titania required to initiate the formation of Ti(C,N) in the hot metal (FIGURE 2.36(iii)).

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FIGURE 2.36. (i) Ti(C,N) composition for various temperatures and nitrogen partial pressures. (ii) Minimum titanium concentration in hot metal required for the formation of

Ti(C,N) at a given nitrogen partial pressure (fTi = 0.023 at T = 1773 K). (iii) Minimum titania dosage required and the resulting titanium concentration in the hot metal to initiate Ti(C,N) as a function of formation temperature (Hot metal – Slag equilibrium at

1500 °C, PN2 = 2.3 bar) (Bergsma and Fruehan, 2001).

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2.4.4 Plant Trials of Insertion of Titanium Bearing Materials into the Blast Furnace As mentioned in Chapter 1, by means of forming a protection layer along the hearth side walls, there are two main techniques to add titanium bearing material into the Blast Furnace. These are (i) via burdening (charging from the top of the shaft) in the form of titanium rich lump ore or (ii) via tuyere injection in the form of pulverised titania. Each method has been conducted in practice having its own advantages and disadvantages. Okada et al. (1991) summarises the overall process for the two techniques from point of insertion of the titania bearing materials to the point of formation of the titanium rich scaffolding (FIGURE 2.37).

In this section, a review of plant trials for the addition of titanium bearing materials in the blast furnace is presented, first for the burdening technique followed by the tuyere injection technique. 53

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2.4.4.1 Titania Addition via Burdening Technique In this section, reports on plant trials of titania addition via burdening by means of forming a titanium rich protection layer along the hearth refractory lining is reviewed.

Kurunov et al. (2006) have summarised a variety of valuable reports (majority published in non-English language), on which are related to plant trials of burden addition of titania. According to their review, the addition of titania via burdening is done fairly often as a measure to protect the hearth linings where various forms of titanium containing materials are used. The types of materials that are burdened are summarised below in TABLE 2.5.

TABLE 2.5. List of titanium bearing materials and their TiO2 concentration used for the addition of titanium in the form of burdening.

Material TiO2 mass fraction [%] Titanium-bearing iron ores 15 - 40 Titanium-bearing blast furnace slags 5 – 9 Ferrotitanium 32 – 35 Pellets, sinter, briquettes 2 - 5

The materials are generally charged into the furnace from the shaft periphery as this ensures that titanium bearing materials will mitigate to the hearth wall to form the protective layer. Generally, the average consumption of titanium-bearing materials is about 10 kg/t of hot metal and is increased to 20 kg/t of hot metal if high temperature lining persists. Higher consumption rate is rare due to adverse effects mentioned in Section 2.4.5.

The practice of titania addition via burdening is conducted regularly by steel companies to reduce thermal loads on the hearth coolers and to reduce lining temperatures. These practices are briefly reviewed below.

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 Wuhan Iron and Steel Company (China) conducted plant trials in blast furnaces No. 2 (1433 m3 volume), No. 3 (1513 m3) and No. 4 (2516 m3). They were able to reduce the thermal loads by 10 – 15% when charging titanium bearing materials at a rate of 5 – 10 kg per ton of pig iron (Klein and Fujihara, 2004).  Onesteel (Australia) charged ilmenite ore in blast furnace No. 2 before it’s shut down (for repairs) during occasions when the temperature of the coolers in the hearth and bottom increases. A rate of 8.5 kg per ton of pig iron was charged where the hearth bottom refractory temperature was successfully reduced by 20% (van Laar and Tsalapatis, 2013).  Siderar (Argentina) periodically charged ilmenite ore into blast furnace No. 2, for a period starting from early 2003 to shut down (early 2005), at a rate of 5 – 10 kg per ton of pig iron. The titanium concentration in the pig iron remained at a level of 0.11%. At times when the hearth lining temperature further increased, the consumption of the ore was increased to 0.15 – 0.18% - with the exact amount charged depending on the titanium concentration of the pig iron. They found that ilmenite charging rate of 20 – 25 kg per ton of pig iron for over a 16 hr period before shut down resulted with the greatest effect (FIGURE 2.38). From these experiences, they have put together a technological program to mitigate rise in hearth refractory temperature (TABLE 2.6).  Although not detailed, charging of titanium bearing materials were practiced in other steelmaking companies including Mittal Steel, Corus, Salzgitter Flachstahl, Arselor and Severstal. Details can be found in (Spaleck et al., 2005, Pethke et al., 2005, Loginov et al., 2002, Takeda et al., 1999, Bobek et al., 2004).

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TABLE 2.6. Technological program to mitigate the increase of temperature of the hearth linings (Kurunov et al. (2006), figure originally from Oscar and Eduardo (2005)).

2.4.4.2 Titania Addition via Tuyere Injection Technique In this section, literature is reviewed regarding reports on plant trials of titania addition via tuyere injection by means of forming a titanium rich protection layer along the hearth refractory lining. Generally, the tuyere injection approach is recognised to be

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a more preferable technique compared to the burdening approach due to its flexibility in forming protective layers at a specific sector in the hearth. As reported by Okada et al. (1991), the process of titania addition via tuyere injection is shown in FIGURE 2.39. Compared to the burdening technique, the addition of titania via tuyere injection have the following advantages (Okada et al., 1991, Kurunov et al., 2007).

 The titanium-bearing materials (TiO2) can be delivered specifically to the severely worn lining that may be located at any sector of the hearth.  Slag viscosity is only adversely affected within a small region of the hearth.  Injection brings about quick and localised reduction of thermal loads and temperatures of the hearth refractory linings.  The burdening operation in the blast furnace does not have to be varied.  The protective crust with the same quality as the burdening technique can be achieved with less titania consumption.

FIGURE 2.39. Schematic diagram of formation process of Ti bear in the hearth (Okada et al., 1991).

One of the first attempts of injecting titania in the blast furnace through its tuyere is reported by Okada et al. (1991). This was conducted in Kobe steel’s Kakogawa Works No. 2 Blast Furnace in 1984. Prior to the injection, various fundamental experiments were conducted to understand the allowable limit of titania and titanium content in slag and molten iron such that viscosity of each liquid will be maintained low enough to prevent drainage problems. Titania injection system providing continuous titania injection in the tuyere was developed for tests to be conducted in the real blast furnace. In the system, the compressed air with pressure 5 kg/cm2 acting as a carrier gas 57

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suspends pulverized titania particles discharging from 0.6 m3 tank (FIGURE 2.40). This is injected in the lance (14.3 mm diameter) and ultimately blast into the blast furnace via the tuyere. The maximum rate of titania injection is 850 kg/hr.

FIGURE 2.40. Equipment developed to inject Titania through tuyeres (Okada et al., 1991).

Based on the results of the water model experiments (refer to Section 2.2.1.1), the pulverised titania was selected to be injected from two of the tuyeres, no.26 and no.28, so that source passes near the damaged wall before reaching the tap hole as shown in FIGURE 2.41.

FIGURE 2.41. Schematic of the predicted path line of titanium content from the tuyere to the taphole that passes the worn regions of the lining (Okada et al., 1991).

Positive results were obtained for both No. 3 and No. 2 blast furnaces after the injection. For both furnaces, severe rise in hearth wall temperature slowed down. For No. 2 blast furnace, the lining temperature decreased to the level before rising. Here, TiO2 injection was conducted with rutile powders (TiO2: 95.1%; particle size: 75 µm (95% or more)).

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FIGURE 2.42. Change in the temperature of the hearth walls in (i) BF no.3. and (ii) BF no.2 (Okada et al., 1991).

TABLE 2.7 shows the composition of the two particular materials for pulverised titania powder for the injection: rutile and ilmenite. Initially rutile was used however ilmenite has become a common media due to its availability and low cost.

TABLE 2.7. Characteristics of titanium-bearing materials that are used for injection through tuyere (Okada et al., 1991).

TABLE 2.8 summarises the results of the various plant trials of tuyere injection. It was concluded that upon suppressing the rise in wall temperature, the positions of the

TiO2 injection are important. For effective operation, angle between injected tuyeres and the damaged position of the hearth wall should be in the range of 40° to 90° and the

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angle between the injection tuyere and the active tap hole should be in the range of 80° to 160°.

TABLE 2.8. Effect of Titania injection on lining temperature (Okada et al., 1991).

A synthetic titania-containing material called rutilite AT and rutilite F was made by a German company Sachtleben Chemie in Duisburg. The two materials were obtained in the course of the production of titanium oxide and sulphuric acid. These titania-carriers attracted steel companies as a replacement of ilmenite due to its high reactivity. Ilmenite contains titanium dioxide in the form of FeO·TiO2 which takes additional energy to decompose this compound to retrieve the titania content. However, rutilite is composed of titania and different oxides of Fe which requires far less effort to retrieve the titania content and therefore is more suited in the given application

(FIGURE 2.43).The difference between the two synthetic materials is the TiO2 content. Rutilite AT contains 30% of titania content and is suggested to be used for preventive purposes in blast furnace where as rutilite contains 50% of titania content and used for urgent situations such as in severely worn lining having “hotspots” (Kurunov et al., 2007).

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FIGURE 2.43. Schematic of ilmenite and rutilite structures. (I.F.Kurunov et al. (2007))

Voest-Alpine Stahl Linz (VASL) have shifted their method to alleviate hearth lining in their blast furnace A (5900 t/day capacity), from charging of ilmenite ore through the top of the furnace to injecting rutilite through the tuyere. In one of their first attempts, they injected 50 tons each of rutilite AT and rutilite F and burdened 20 kg/ton of pig iron of ilmenite. As a result they were successful in reducing the temperature in the critical regions of the hearth lining by 100 °C. This shows that the high titanium content of the pig iron successfully drove the formation of Ti(C,N).

Following this, they performed commercial trials with blast furnace A. They compared the titanium content in the liquids (pig iron and slag) during a period when rutilite AT was injected (7kg per ton of pig over) and a period when ilmenite was burdened (10 kg per ton of pig). They found that the value of the distribution coefficient [Ti]/(Ti) increased from 0.25 to 0.35 at a finishing temperature of 1470 °C (FIGURE 2.44).

FIGURE 2.44. Change in distribution coefficient [Ti]/(Ti) in relation to the temperature of the pig iron with the injection of rutilite AT (Kurunov et al., 2007). 61

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They concluded that the mineralogical composition and the large specific surface area of the rutilite AT compared to the lump ilmenite increased the reduction of

TiO2 at the pig-iron/slag interface. They have presented FIGURE 2.45 to support the above conclusion which shows the changes in the amounts of Ti and TiO2 in the pig iron and slag, respectively, during the trial period of rutilite AT injection (Kurunov et al., 2007).

FIGURE 2.45. Effect of rutilite AT tuyere injection (i) on TiO2 in the slag and (ii) on Ti concentration in the pig iron (Kurunov et al., 2007).

2.4.5 Operational Adversities due to the Addition of Titanium Bearing Materials Although addition of titanium bearing material may protect the hearth from further erosion, excess amount of titanium addition will lead to adverse operational problems in the blast furnace. The following are a list of negative consequences:

 The existence of excess amount of high melting Ti(C,N) phase increases the viscosity of both pig iron and slag, and consequently lead to hearth drainage problems (Bergsma and Fruehan, 2001).  Risk of exceeding the limits of titanium content, standardised in pig iron for the Basic Oxygen Furnace process (downstream of the production line) which is about 0.3 wt% titanium (Kurunov et al., 2006). 62

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 Risk of exceeding the limits of titanium dioxide content standardised in the slag which is in the range of 1.5 – 2.5 wt% (Bergsma and Fruehan, 2001).  May cause excessive growth of the infusible layer on the hearth wall and bottom reducing the effective hearth volume. This may results with a decrease in the furnace production rate. Furthermore, it will disturb the internal flow distribution of liquids (Torrkulla et al., 2002).  The growth of the infusible layer in the notch will cause excessively slow flow of pig iron and slag from the tapping holes (Benesch et al., 1989).  More difficult reduction and desulphurization process in the liquid phases (Benesch et al., 1989).  Due to the injection of pulverised titania, the permeability of the packed coke in the dropping zone and in the hearth reduces. This may affect the flow of liquid through the bed and drainage site (Omori, 1987).  Difficulties in hot metal and slag separation after casting, breakage of tuyere, heaving phenomenon of the hearth and metal flowing from the cinder notch (Narita et al., 1977).

Therefore it is important to control the amount of titania to insert in the blast furnace, enough so that titanium bearing materials will form, but less than the amount where the of furnace operation is adversely effected.

2.4.6 Models to Predict the Titanium Compound Distribution in the Blast Furnace Hearth In Section 2.4.2.2, the stepwise mechanism involved in the formation of Ti(C,N) protective layer was described. The process involves: the transport of titanium content via the flow of hot metal (advection and diffusion of titanium); the formation (precipitation), growth and dissolution of Ti(C,N) particles (governed by thermodynamic based chemical reaction); and the transport of Ti(C,N) particles via the flow of hot metal. As it can be understood, the behaviour of the Ti(C,N) particles and hence the formation of the Ti(C,N) protection layer is strongly influenced by the flow, heat transfer and mass transfer of the hot metal solution within the hearth. Therefore with respect to modelling of Ti(C,N) particles and the protection layer, it is important to

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consider all the above mentioned transport phenomena. This is particularly the case for the tuyere injection approach as it requires the transport of titanium content from a selected tuyere to a specific damaged region of the hearth linings (FIGURE 2.39). This requires an accurate understanding of the hot metal flow pattern. In this section, numerical studies to investigate the transport of titanium species, Ti(C,N) particles and/or Ti(C,N) protection layer within the blast furnace hearth is reviewed.

In Section 2.2.1.2, Tomita and Tanaka (1994) conducted numerical studies using a 3D CFD model to investigate the flow and heat transfer behaviour in the blast furnace hearth. They extended their studies to numerically model the in-hearth phenomena during the practice of titania addition via tuyere injection, to see whether the hearth refractory linings would reduce. Additional to the mass, momentum and energy conservation equations required to model the flow and heat transfer of the hot metal (Section 2.2.1.2), the conservation of mass species, equation was solved for components including iron and titanium. The protection layer in their model was simulated by conducting the following two treatments. Firstly, the hot metal viscosity was modelled as a function of temperature and titanium concentration (the expression is not presented however it is presumed to be modelled so that the viscosity increases significantly at regions where temperature is low and titanium concentration is high, so that the flow slows down). Secondly, a solidification model was included (details are not provided however it is presume to program the flow to terminate at regions when the temperature of the particular cell is below 1150 °C and the switch its thermal conductivity from 35 to 20 W/mK (thermal conductivity of the hot metal above 1150 °C is 35 W/mK)). The effect of natural convection, chemical reactions and turbulence were neglected and the material properties were assumed constant except for the viscosity. They presented their results for two specific cases: when Ti (5 kg of Ti per ton of hot metal or [Ti] = 0.5 wt%) is injected from 90° and 180° (measured counter clockwise from the taphole when looking from above) (FIGURE 2.46(i)). In their results, when titanium is added, they found a shift in the temperature contours at regions with high titanium concentration causing the refractory temperature to be lower compared to the case when titanium is not added (FIGURE 2.46(ii)). The effect of bottom cooling water temperature was also investigated. They also briefed their ironsand injection trials in Kura No. 1 Blast Furnace (2 × 3.6 tonnes during 16th and 17th January 1991 and 1 × 7.3 tonnes during 19th 64

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January 1991) showing their success in decreasing the wall temperature according to their thermocouple history.

FIGURE 2.46. (i) Planar view of titanium mass fraction contours plot. (ii) Planar and side view of velocity vectors plot and temperature contours plot (Tomita and Tanaka, 1994).

Lin et al. (2009) and Lin et al. (2011) developed a 3D CFD model to investigate the flow, heat and mass transfer in the hearth when injecting titania. The geometry was based on BlueScope’s Port Kembla No. 5 Blast Furnace with an eroded fire brick layer. Both effects of turbulence and natural convection were neglected. The following expression for hot metal viscosity, μL, was used.

[2.6] where T is the temperature in Kelvin.

In their model, they considered the following non-reversible chemical reaction describing the formation of TiC species.

[2.7]

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[2.8]

where the reactions [2.7] and [2.8] are combined to express the following chemical reaction.

[2.9]

Here, titanium dioxide is inserted directly into the liquid iron phase, then undergoes reduction within the phase where the produced titanium reacts with the carbon to form titanium carbide. This process differs to that hypothesised by Bergsma and Fruehan (2001) where the reduction of titanium dioxide occurs in the slag phase where only the produced titanium enters the liquid iron phase. Nevertheless, they presented their results with respect to the TiC mass fraction distribution along the inner hearth surface for cases when titania is locally added from a position 90°, 135° and 180° (measured counter-clockwise from the active taphole looking from above) for a floating coke bed state with flat bottom and a sitting coke bed state with coke gutter and an impermeable zone at the hearth core (FIGURE 2.47 and FIGURE 2.48). They found that at regions where high TiC content exist, the temperature of the refractory located close by reduces (FIGURE 2.49).

FIGURE 2.47. TiC mass fraction contour plot along the inner hearth surface when TiO2 is locally added from a position 135° and 180° (Lin et al., 2009). 66

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FIGURE 2.48. Temperature contour plot along the inner hearth surface when TiO2 is locally added from a position 135° and 180° (Lin et al., 2009).

FIGURE 2.49.Temperature profile of the refectory at upper and outer thermocouple location (r = 5.2 m, z = 1.5 m) along the theta direction contour plot for cases when no

TiO2, TiO2 is locally added from a position 135° and 180° (Lin et al., 2009).

In a more recent work, Guo et al. (2010) developed a 2D two-phase multi- component model (modelled in a Eulerean-Eulerean approach) to study the Ti(C,N) particle formation and dissolution behaviour in the blast furnace hearth. In their model, they included the flow of fluid and dispersed solid particles through a packed bed, conjugated heat transfer, species transport and thermodynamic of key chemical reactions. They also considered the growth and shrinkage of particles however 67

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neglected the effect of natural convection. The model framework is shown below in FIGURE 2.50.

FIGURE 2.50. The framework of two-phase, multi-component model (Guo et al., 2010).

Generally in the model, two phases are considered; liquid and dispersed solid particle phase. The liquid phase consists of iron, titanium, nitrogen and carbon components and the dispersed solid particle phase consists of titanium carbide and titanium nitride components. The mass, momentum, energy and mass species conservation equations are solved for each phase. Added to this, the so-called “population balance” equation is also solved for the dispersed solid phase to model the growth and shrinkage of particles (i.e. change in diameter). Inter-phase transfers of momentum and mass were considered. In particular for the inter-phase mass transfer, its rate was modelled using the following formula.

[2.10]

where d is the particle size of the dispersed solid phase, ρ is the density of the fluid phase, Sh is the Sherwood number, Y’ and Y are the titanium mass fractions at the particle surface and far field of the continuum, respectively. With respect to Y’, chemical equilibrium is assumed where thermodynamic calculations were used to derive the term. The derivation can be found in Guo et al. (2010). Based on the model, when titanium is added throughout the inlet area, it was found that large Ti(C,N) particles are 68

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dynamically held up along the hearth bottom and corners of the steps (FIGURE 2.51(ii- iii)). They spatially presented the location where Ti(C,N) particles forms and grows and location where particles shrink and dissolve (FIGURE 2.51(i)).

A specific case where titanium is added locally at the inlet region opposite to the taphole was calculated. This simulates tuyere injection (FIGURE 2.510(i)). They found that the distribution of TiC particle is similar to the case when titanium is added throughout the hearth (compare FIGURE 2.51(ii) and FIGURE 2.52(ii)).

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Furthermore, through the use of the model the effect of key parameters was investigated. Parameters include initial seeding concentration, initial seeding particle size, nitrogen partial pressure and initial titanium concentration.

In other publications (Guo et al., 2011, Guo et al., 2009), further work was carried out regarding model studies to investigate the titanium behaviour in the blast furnace hearth. They investigated the effect of various inner hearth profile, namely fully intact, partly eroded and fully eroded hearth profiles. Here, titanium is inserted locally at the inlet from a position opposite the taphole. They found that in a fully intact hearth profile, the Ti(C,N) particles form in a small quantity along the bottom corner region of the hearth (although in small quantity). Particle formation increases significantly for a partly eroded hearth. However, the amount of particles did not increase further when the hearth is fully eroded.

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FIGURE 2.53. Colour representations of Ti and TiC particle concentrations in (i) fully intact, (ii) partly eroded and (iii) fully eroded hearth linings when titanium inserted locally from a position opposite the taphole (Guo et al., 2011).

They also simulated a case when natural convection is considered and when titanium is inserted locally at the inlet from a position opposite the taphole. In the buoyant flow field, the hot metal was found to flow mainly in the upper third region of the hearth (FIGURE 2.54(i)). The lower region of the hearth was found to be solidified as the temperature is below the solidus temperature at 1150 °C (FIGURE 2.54(ii)). The titanium content was found to be flushed out the taphole without reaching the hearth bottom surface (FIGURE 2.54(iii)) where the formation of Ti(C,N) particles is only found in a small region along the side wall below the point of titanium injection.

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CHAPTER 3

CHAPTER 3 3D CFD MODEL TO PREDICT THE FLOW AND TEMPERATURE DISTRIBUTIONS IN A BLAST FURNACE HEARTH

3.1 INTRODUCTION The iron making blast furnace remains the primary process for the production of pig iron. Over the past few decades, there has been a trend in blast furnace technology to: (i) reduce coke consumption, (ii) increase furnace productivity and (iii) lengthen the campaign life (Guo et al., 2011). The latter trend is an essential part for the reduction of capital expenses and production costs. It is well recognized that one of the main limitations of the campaign life is the wear of the hearth refractories (Panjkovic et al., 2002, Wright et al., 2003, Guo et al., 2008). Causes for such wear have been studied and various wear mechanisms have been proposed involving several factors including zinc and alkali attacks, thermal stresses, dissolution and erosion of hearth refractories. Refractory erosion has a particularly strong connection with the flow and heat transfer of liquid iron (Silva et al., 2005). Therefore in order to better understand the key mechanisms for hearth refractory wear, it is important to be able to predict the liquid iron flow and temperature distribution in the hearth.

The hearth contains two immiscible liquids, slag and liquid iron, where the slag is layered on the top of the liquid iron due to its lower density. The removal of the liquids, through continuous casting, is conducted by drilling and opening the taphole, liquids casting (typically drainage for a duration of 3 hrs), and then closing the taphole by injecting clay into it. This procedure is repeated in another taphole either straight away, after a short duration for liquid accumulation or a short duration before the previous taphole is closed for more drainage. During such a process, the liquid iron distributes within the hearth producing a certain flow pattern which may impact the erosion of the hearth linings. The hearth is packed with coke particles forming a porous bed. The bed is continuously renewed as the carbon content of the submerged coke is dissolved into the liquid iron. Since the residence time of the submerged coke varies 73

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from one coke particle to another, the coke size can differ ranging from fines to about 50 mm (coke size as burdened). The smaller particles as well as other fines such as unburned coal and graphite precipitates may percolate through the bed (Nightingale et al., 2001). For these reasons, the bed is inhomogeneous in coke size and porosity, and hence permeability, which influences the liquid flow (Guo et al., 2011). The total weight of the burden material is balanced with the uplifting force at the raceway, solids pressure at walls and the buoyancy force of the submerged bed (Fukutake and Okabe, 1981). The last force is quite significant due to the large density difference between the coke and liquid iron. Therefore depending on the volume of the coke submerged, which is dependent on the porosity and the liquid level, the bed can either be sitting or floating (Nightingale et al., 2001). The states of the bed affect the flow of liquid iron (Panjkovic et al., 2002, Guo et al., 2008, Preuer et al., 1992b). In a sitting bed, the liquid makes its way through the pores of the coke bed towards the taphole during drainage, whereas in a floating bed, the liquid may pass through the “coke free zone” at the bottom of the hearth before being drained out. Finally the hot face of the refractory, starting initially from the original hearth design, undergoes erosion or forms scaffolds where the hot face profile may change as the furnace ages. The altered hearth volume and wall thickness will in turn change the heat transfer and flow.

As mentioned above, the flow of liquid iron is influenced by various in-furnace factors. However, due to the elevated temperature and harsh operating conditions, direct measurement or visualization is very difficult to monitor the effects of these factors. For this reason, Computational Fluid Dynamics (CFD) modelling provides a useful exploratory tool where various ‘what if’ scenarios can be modelled to investigate in- furnace phenomena. Nevertheless, developing a CFD model enabling real time transient simulation of the momentum, heat and mass transfer of slag and liquid iron free surface flow, according to casting schedule, and refractory wear of the hearth is well beyond current computational capability. In fact, the simulation of liquid iron flow and heat transfer of the hearth during a single operational period is challenging as it involves complex geometry, conjugate heat transfer, porous media and natural convection. Further, there also exists a wide range of velocity and length scales. In current cases, for example, fluid velocities range from a fraction of a millimeter per second at quasi-

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stagnant regions to a few meters per second in the taphole. Length scales range from 11 m for the hearth inner diameter to 60 mm diameter at the taphole.

Over the past two decades, effort has been made by various investigators in simulating the flow and heat transfer in the hearth (Panjkovic et al., 2002, Wright et al., 2003, Guo et al., 2008, Preuer et al., 1992b, Yoshikawa and Szekely, 1981, Post et al., 2003, Ohno et al., 1981, Desai et al., 2006, Maldonado et al., 2006, Huang et al., 2008, Chang et al., 2009). The capability of hearth modelling has been improving, as high performance computation has become more readily available, allowing more accurate and realistic flow predictions. In one of the early works, Yoshikawa and Szekely (1981) conducted a 2D analysis to investigate the liquid iron distribution using a simple axi- symmetrical and a nonporous model. They found strong recirculation flow near the side walls driven by a thermally induced buoyancy force and estimated the erosion rate of the refractory. However this work was based on a rather specific case with a floating coke bed in the slag and closed taphole. Preuer et al. (1992b) performed a three- dimensional (3D) water-model experiment using warm water with appropriate cooling of the tank surface to visualize the natural convection behaviour. They have identified downward flow near the side walls forming a 1 mm boundary layer. On this basis, they simulated the hearth using a 3D symmetrical model with fine cells near side and bottom walls with moderate overall grid resolution. They pointed out a so-called ‘horizontally layered temperature distribution’ which causes distinct flow pattern in the coke gutter where liquid at the hearth bottom flows in the direction opposing the forced flow towards the taphole. In a 2D slot model with homogeneous coke bed, Post et al. (2003) specifically investigated the effect of buoyancy on liquid iron flow by using a temperature and carbon concentration dependent density. The liquid flow pattern indicated a clear stratification between ‘high speed zone’ at the top and a ‘low-speed zone’ at the bottom and also a ‘horizontally layered temperature distribution’ throughout the pool. Most of the abovementioned studies suggested that the liquid iron flow is significantly influenced by natural convection. Heat loss from the fluid to the cooler side refractories produces a large temperature gradient within the local region which induces a downward buoyancy force. However, in those models, the fluid boundaries are assumed with arbitrarily estimated temperature or heat flux, neglecting the heat transfer of the refractories. 75

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In recent years, as an approach to tackle the buoyancy induced flow, some investigators (Panjkovic et al., 2002, Wright et al., 2003, Guo et al., 2008, Maldonado et al., 2006) have developed comprehensive 3D CFD models that incorporate the flow and heat transfer of the liquid iron, conjugate heat transfer between the liquid iron and the refractory and conduction through refractories. The models were applied for the hearth of BlueScope Steel’s No.5 Blast Furnace. In particular, Panjkovic et al. (2002) included a simplified zero-equation turbulence model proposed by Takeda and Lockwood (1996) to model the turbulent flow through the packed coke bed in the hearth. They showed the validity of the model by comparing their calculated temperature to the PK5BF thermocouple data extracted at specific times throughout the campaign with characteristic inner hearth profiles and coke bed qualities. However, for all comparisons made, under-prediction was observed. They assumed the hot metal temperature of 1500°C which is likely to be too low. Turbulence modelling in the porous field was improved by Maldonado et al. (2006) where a modified k-ε model developed by Nakayama and Kuwahara (1999) was applied. A recent study conducted by Guo et al. (2008) further improved the PK5BF hearth model by doubling the number of grid points and organized them in such a way that relatively finer grids are used near the interfacial boundaries. They assumed the hot metal temperature to be 1550°C and also added a thermal dispersion term to consider the enhancement of the liquid iron conductivity caused by the presence of coke particles. The effects of coke bed height with heterogeneous porosity were investigated in an intact hearth. Despite the model improvements made, the hearth model still shows apparent under-prediction when comparing the calculated temperatures to the thermocouple data.

Numerical results produced by the majority of above mentioned investigators have commonly indicated that the liquid iron flow is strongly influenced by natural convection. Despite this observation, a number of investigators have neglected the natural convection in their models without sufficient justification(Ohno et al., 1981, Desai et al., 2006, Huang et al., 2008, Chang et al., 2009) and some even show good agreements with plant data, claiming the validity of their models (Ohno et al., 1981, Huang et al., 2008, Chang et al., 2009). Ohno et al. (1981) gave an expression correlating the residence time and the dripping location based on their lab scale 76

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experiment and corresponding numerical models. The laboratory scale model used cold water and hence the proposed expression is based on non-buoyant flow. However, they found good agreement between the expression and residence times measured using radioactive isotopes in the hearth of two of Nippon Steel’s Hirohata Works blast furnaces. Huang et al. (2008) and Chang et al. (2009) both neglected the natural convection and established good validity of their models shown by their good agreement between calculated temperature and measured thermocouple data of China Steel Corporation’s No. 2 Blast Furnace. Such outcomes imply that the natural convection can be removed from the model formulation, as far as the hearth refractory temperature is concerned, contradicting those claiming its significance as mentioned above. Such a disparity needs to be addressed.

In this study, further analysis of the PK5BF hearth is conducted in order to explicitly determine the roots of such contradictions by: (i) making further improvements to PK5BF hearth model, (ii) seek better agreements with thermocouple readings, (iii) investigating the effect of coke bed permeability, and (iv) based on the knowledge gained, establishing a realistic flow pattern in the hearth for various coke bed morphologies and erosion profiles.

3.2 MODEL DESCRIPTION The3D liquid iron flow and conjugate heat transfer for the liquid iron and solid refractory are modelled at steady-state using a commercial software, ANSYS CFX version 13.0. The details of the model are described below.

3.2.1 Geometry and Coke Bed State FIGURE 3.1 shows the initial profile of the hearth of Port Kembla No.5 Blast Furnace (1991-2009 campaign). A 3D geometry is created based on the figure where only one half of the hearth is modelled as the flow field is assumed symmetrical about the plane crossing the hearth and taphole axes.

Two different geometries, intact and eroded hearths are analysed. The intact hearth contains refractory elements, i.e. Carbon refractory (BC7S), ceramic cup and firebricks, 77

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whereas the eroded hearth represents a case where all firebrick and ceramic cup above z = 3m are eroded. The entrance of the taphole is presumed to have a trumpet shape. Thermocouple locations including the pad (bottom, middle and top layers) and the sides (outer and inner layers) are also presented in FIGURE 3.1.

FIGURE 3.1. Geometry and thermocouple locations of Port Kembla No. 5 Blast Furnace (campaign: 1991-2009). Parenthesis shows the z and x coordinates.

The coke bed may be recognized in various shapes. For each of the two geometries, two different coke bed shapes, sitting and floating, are analysed respectively. For the sitting coke bed state, the coke particles fill the entire volume of the hearth. On the other hand, for the floating coke bed state, a hemispherical shaped coke bed is floating 300 mm for the intact hearth profile and 400 mm for the eroded hearth profile. The total four cases analysed are listed below and schematic shown in FIGURE 3.2.

Case A: Intact hearth and sitting coke bed. Case B: Intact hearth and floating coke bed. Case C: Eroded hearth and sitting coke bed. Case D: Eroded hearth and floating coke bed. 78

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FIGURE 3.2. Coke bed states for model validation for Cases A – D. Coke bed heights at hearth centre for intact and eroded hearths are 300 mm and 400 mm respectively.

3.2.2 Mathematical Model

3.2.2.1 Governing equations A Reynolds Averaged Navier Stokes (RANS) equations approach is used to describe the turbulent porous flow field. The following are the steady-state continuity, momentum and energy conservation equations:

[3.1]

[3.3]

where [3.4]

[3.5]

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where γ is the porosity, ρ the density, ρref the reference density, u the velocity, μeff, μL and μT the effective, laminar and turbulence viscosities respectively, p is the pressure, k the turbulent kinetic energy, g the gravitational acceleration, R the resistance force, cp the specific heat, T the temperature, λstg and λdis the effective stagnant and dispersion thermal conductivities respectively and σT the turbulent Prandtl number. The second last term in Equation [3.3] is the buoyancy force due to thermal expansion and is calculated by the change in the liquid iron density within the flow field. Unlike the Boussinesq approach which assumes constant density throughout the flow field, this full buoyancy approach explicitly relates the fluid density to temperature, thus affecting the other terms of the governing equations (e.g. the advection terms) to a more or less extent (ANSYS, 2010).

3.2.2.2 Turbulence modelling The eddy viscosity approach is incorporated to close the RANS equations. Here, a k-ω Shear Stress Transport (SST) turbulence model is used where the turbulence viscosity, μT, is expressed as:

[3.6]

and is determined by solving the transport equations of the turbulence quantities i.e. turbulence kinetic energy, k, and turbulence eddy frequency, ω. The k-ω SST model has a functionality where it switches between a k-ε model in the freestream and k-ω model near the boundaries via a blending function, F. Compared to the k-ε model used by previous investigators (Guo et al., 2008, Maldonado et al., 2006), the k-ω model provides a more robust and accurate treatment at near-wall regions. However, it experiences a high sensitivity to the freestream conditions which is less likely when using the k-ε model (Menter, 1994). The k-ω SST model takes advantage of both k-ε and k-ω models (ANSYS, 2010, Menter, 1994). A study by (Guo et al., 2008) shows that the thermal buoyancy induced flow at near-wall regions has a significant impact on the global flow pattern of the hearth. Therefore, in order to model the hearth flow more realistically, particular attention to the prediction accuracy within the side wall

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boundary layers is necessary whilst maintaining good turbulence modelling performance within the main flow field. For this reason, the k-ω SST model is suited for such problems.

3.2.2.3 Treatment for coke particles Various treatments are implemented to account for the presence of coke particles in the hearth. The last term in Equation [3.3] represents the resistance force to the flow, based on the Ergun equation (Ergun, 1952), given by:

[3.7]

where and dh are the shape factor and harmonic mean size of coke particles. In particular, the shape factor of real coke particles is described by an empirical correlation (Ichida et al., 1991). This is a new feature compared to the previous model (Guo et al., 2008) where the shape factor and the coke size were lumped as a single effective particle size. The turbulence produced due to the presence of coke particles is modelled by additional source terms for k and ε equations according to Nakayama and Kuwahara (2008). By modifying the ε source term via the relation ε= β'ωk (ANSYS, 2010), the resulting k and ω source terms can be expressed as follows:

[3.8]

[3.9]

' where c2 and β are turbulence model constants with values 1.42 and 0.09 respectively. As the liquid iron flows through the pores of the coke bed, thermal dispersion caused by tortuous path which it follows. Empirical correlations for thermal dispersion are given by Yang and Nakayama (2010) for longitudinal and transverse directions in laminar and turbulent regimes. 81

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For longitudinal dispersion:

for laminar regime [3.10]

for turbulent regime [3.11]

For transverse thermal dispersion:

for laminar regime [3.12]

for turbulent regime [3.13]

The Ergun equation, the additional source term for the k and ε equations and the thermal dispersion are programmed to apply only where coke particles exist and are switched off in coke free zones.

3.2.2.4 Interfacial wall treatment Strong temperature and velocity gradients exist near the vicinity of the walls and it is important to model them with considerable accuracy for the reasons mentioned above. There are generally two methods to model the near-wall region, namely, the wall-function approach and the Low-Reynolds-Number approach. The wall function approach is commonly used in the k-ε model where empirical formulations are used to model the profiles of the variables within the boundary layer. The Low-Reynolds- Number approach used in the k-ω model resolves the variables within the spatially discretized boundary layer using a fine mesh (ANSYS, 2010). Here, an ‘automatic near- wall’ treatment is used, which is a fundamental idea of the k-ω SST turbulence model. It provides a smooth transition between the Low-Reynolds-Number and the wall function. For application of the wall function approach, a ‘scalable wall function’ technique is applied where the first off-wall node is placed outside the viscous sublayer (ANSYS,

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2010). This is an improvement over the ‘standard wall function’ technique used in the previous model (Guo et al., 2008) which may have a great sensitivity to the near-wall meshing as described by (Grotjans and Menter, 1998). For heat transfer, Kader’s law- of-the-wall function formulation (Kader, 1981) is used as opposed to the previous models (Panjkovic et al., 2002, Guo et al., 2008) using Jayatilleke’s formulation (Jayatilleke, 1969).

3.2.2.5 Material properties and solidification model Temperature dependent material properties are used for liquid iron and solid refractory phases. The effective stagnant thermal conductivity, λstg, of the saturated porous medium shown in Equation [3.5] is defined as:

[3.14]

The thermal conductivities of liquid iron and coke, λFe and λcoke, both temperature dependent, are listed in TABLE 3.1 (Jimbo and Cramb, 1993) have expressed the density of liquid Fe-C alloys as a function of carbon content and temperature, as shown in TABLE 3.1. In the present work, the carbon content of hot metal is assumed to be constant at 3.75 wt%. The laminar viscosity, L, depends on temperature (Gale and Totemeier, 2003). Below the solidus temperature of 1,150°C, the hot metal is considered as solidified and is modelled by applying a high viscosity so that the liquid iron stops flowing. Such effect is realized by the following expression for L.

[3.15]

This solidification model is introduced here for the first time. A summary of materials and coke bed properties are listed in TABLE 3.1.

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TABLE 3.1. Material properties Iron Carbon content [wt-%] 3.75 Density [kg/m3] (7100-73.2[C%])-(0.828-0.0874[C%])(T-1823) (Jimbo and Cramb, 1993) Laminar viscosity [Pa.s] (3.699x10-4)e41400/RT (Gale and Totemeier, 2003) Thermal conductivity [W/m.K] 0.0158T (Maldonado et al., 2006) Heat capacity [J/kg.K] 850 (Panjkovic et al., 2002) Production rate [t/d] 6912 (Guo et al., 2008) Liquid level from hearth bottom [m] 2.262 (Panjkovic et al., 2002) Refractories Heat capacity [J/kg.K] 1260 (Panjkovic et al., 2002) Thermal conductivity of BC7S [W/m.K] 12.0, T≤30°C (Panjkovic et al., 2002) 13.5, T=400°C 15.5, T≥1000°C Thermal conductivity of firebrick [W/m.K] 2.35 (Panjkovic et al., 2002) Thermal conductivity of ceramic cup [W/m.K] 2.20, T≤400°C (Panjkovic et al., 2002) Coke Bed Harmonic mean particle size [mm] 4 to 30

Shape factor [-] 0.39logdh+1.331 (Ichida et al., 1991) Bed porosity [-] 0.275 to 0.425 Coke internal porosity [-] 0.45 (Maldonado et al., 2006) Thermal conductivity [W/m.K] [0.973+(6.34x10-3)T] (1-ζ2/3) (Kasai et al., 1993)

3.2.3 Meshing The computational meshing for the intact and eroded geometries is generated using a total of 1,000,000 and 1,250,000 elements respectively. FIGURE 3.3 and FIGURE 3.4 shows the mesh for the solid and liquid domains for an intact hearth profile. The solid domain is meshed using tetrahedral elements and the liquid domain is meshed using hexahedral elements organized in a fully structured orientation. Since it is understood that the natural convection induced flow near the perimeter of the side walls influences the macroscopic flow, inflations with 2 mm first layer thickness (corresponding to y+ of 0.2 - 20) are added to all solid boundaries. The mismatched grids between the meshes for the liquid and solid domains are connected via the General Grid Interface (GGI) attachment method.

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FIGURE 3.3. Meshing for the solid domain for an intact hearth.

FIGURE 3.4. Meshing for the liquid domain for an intact hearth.

3.2.4 Boundary Conditions The top inlet boundary is set to a temperature of 1,550°C and a mass flow rate of 80 kg/s (corresponding to a productivity of 6,912 t/d). Inflow is set to occur only in the

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annular region , and none in the region in order to model a peripheral dripping pattern (Guo et al., 2008, Preuer et al., 1992b). The outlet is set as a constant pressure boundary. Temperatures for the bottom and side external boundaries correspond to the thermocouples layered along the bottom and side of the hearth (FIGURE 3.1). These values can be found in Panjkovic et al. (2002). Since there are no thermocouples in the bottom corner region of the hearth, the boundary temperature at this region must be estimated. The temperature in this region is determined by linear extrapolation from the outer bottom and lower side thermocouples to the bottom corner edge which is consistent with studies of Panjkovic et al. (2002). Thermocouple data are obtained from Panjkovic et al. (2002) for both intact and eroded hearth profiles, each in floating and sitting coke bed configurations. The top boundary for the solid domain is set as adiabatic.

3.2.5 Convergence Criteria Convergence of the simulations is judged from several perspectives. In terms of the residuals, the Root Mean Square (RMS) residuals for all equations are targeted below 1x10-6. Time steps are dynamically selected for each equation such that maximum residual reduction rates are attained without experiencing divergence. In particular, the enthalpy residual is the bottleneck i.e. slow residual reduction rate has been observed. The residual target is selected so that the temperature and flow pattern are no longer sensitive to the residual. Monitoring points are set throughout the domain including the centre-top pad thermocouple, centre of the hearth bottom, stagnant zones and other locations. Another criterion is that the variables at each point should reach a steady value. Once completed, the vector plots are checked and verified visually, particularly in regions with complex flow patterns (e.g. in the quasi-stagnant region near the steps below the taphole). Once all the above mentioned criteria are met, the solutions are judged as converged.

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3.3 RESULTS AND DISCUSSION

3.3.1 Numerical Sensitivity and Model Validation Validation of the model is conducted to assess the accuracy of the model with respect to the actual process and to see if the assumptions are reasonable. It is made with reference to three aspects including thermocouple comparisons, sensitivities to mesh and residuals and vector plot inspections.

3.3.1.1 Thermocouple comparisons As a process to check the validity of the model, the calculated temperatures are compared with measured thermocouple readings. Panjkovic et al. (2002) extracted the thermocouple temperatures for Cases A to D, each from specific times throughout the campaign. Using the current model, the calculated temperatures are compared to the thermocouple temperatures with respect to these four cases. For each case, comparisons are made with two different coke bed qualities namely, 'high' and 'low' permeabilities. FIGURE 3.5 shows the comparisons for Cases A to D, where the 'high' and 'low' permeabilities are shown as dotted and solid lines, and measured thermocouples are shown as ‘×’.

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FIGURE 3.5. Comparison of the calculated and measured temperatures for Cases A – D:

× measured temperature, --- (dashed lines) calculated temperature with γ = 0.35 and dh =

30 mm and — (solid lines) calculated temperature with γ = 0.30 and dh = 12 mm.

Firstly, the comparisons for the ‘high permeability’ coke bed are described. Here, the porosity and the harmonic mean coke size, is set to 0.35 and 30 mm respectively to characterize a high permeability coke bed. The quantities of these parameters are typical values used in previous studies (Panjkovic et al., 2002, Wright et al., 2003, Guo et al., 2008, Maldonado et al., 2006). As shown in FIGURE 3.5, it is apparent that the simulations under-predict the temperatures for all case. Based on center thermocouple temperature, the under-predictions for Cases A to D are respectively 8.5%, 4.1%, 15.3% and 11.6%. It is noticed that for each case, the under-predictions are inconsistent particularly between the intact (Cases A and B) and eroded (Cases C and D) hearth profiles, where the under-prediction for the latter is substantially larger.

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Secondly, for the comparisons in a ‘low permeability’ coke bed, a porosity of 0.3 and harmonic mean coke size of 12.0 mm is used. These values were selected through sensitivity studies as discussed in detail in Section 3.3.5. Unlike the ‘high permeability’ coke bed, excellent agreements are met between the calculated and measured temperatures for Cases A to D with an under-prediction of merely 2.1%, 2.7%, 0.06% and -1.9% respectively. The under-predictions are more consistent, where it varies only slightly between each case, compared to the cases of ‘high permeability’.

For the cases with an eroded hearth profile (Cases C and D) a large under- prediction is observed for the outer thermocouples (FIGURE 3.5). This may be explained by partial or full erosion of the bottom ceramic step (at 2.5 m < z < 3 m) with low thermal conductivity (FIGURE 3.1). Efforts have been made by previous investigators to predict the inner hearth profile of the PK5BF at a later stage of the campaign using a trial and error approach based on thermocouple comparisons (Wright et al., 2003, Maldonado et al., 2006). They established good agreement between calculated and thermocouple temperatures, including those at the outer thermocouples, when the bottom most ceramic step is partially eroded.

3.3.1.2 Residual sensitivity analysis In CFD modelling, it is crucial to verify that the results are insensitive to the residuals. As mentioned earlier, for the current problem, most difficulties were experienced in reducing the residual for the enthalpy equation and hence the sensitivity of enthalpy residual is investigated. FIGURE 3.6 shows the effect of the RMS residual for the enthalpy equation on the value of temperature at the central thermocouple location for Case A with a ‘low permeable’ coke bed. As an initial condition of this steady-state simulation, the liquid iron temperature throughout the hearth pool is set to 1,550°C.

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It can be seen, as residual reduces to 1x10-6, the temperature converges to 313°C. Similar converging behaviours are observed for other variables and other points monitored. Since the change in temperature is negligibly small at this residual level, it can be said that the model is no longer sensitive to the residuals once reduced below 1x10-6. It can be understood that such a low residual target is necessary because in such simulation problems, with respect to the high velocity found in the taphole of an order of a few meters per second, there exist quasi-stagnant regions within the hearth where velocity is merely fraction of a millimeter per second. Temperature is also affected for the subtle velocity changes in the quasi-stagnant region due to the strong coupling between the enthalpy and momentum equations. Therefore, the numerical solutions are sensitive to the residuals unless it is reduced to a substantially low value, for the current case as low as 1x10-6. This is the reason that the residual target is set to this value as part of the convergence criteria for the current problem. It should be noted that the calculated temperature will match the thermocouple temperature perfectly when the simulation is stopped at residual 1.36x10-4 (FIGURE 3.6). However, despite the good agreement, it is risky to claim for a validated model as the temperature along with other

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variables is still sensitive to the residual. For this reason, thermocouple comparisons should be conducted only if the temperature is no longer sensitive to residuals.

3.3.1.3 Mesh sensitivity analysis The number of elements to use in the mesh is selected so that it would roughly double that in the model used by Guo et al. (2008), for a feasible (accurate and robust) simulation. However, in order to be confident in the selection of the number of elements, mesh sensitivity studies are conducted for Case B by running the same simulation for mesh with 600,000, 1,000,000 and 2,000,000 elements. The temperature at the centre thermocouple location and the velocity profile at hearth centre are investigated. FIGURE 3.7 shows the sensitivity of the temperature at the centre thermocouple location to variations in the number of mesh elements. It can be seen that the temperature is barely sensitive to the mesh size within the range investigated where maximum temperature discrepancy is about 0.4 °C, a value that will provide negligible impact on the analysis of thermocouple comparisons. FIGURE 3.8 shows the velocity in the x-direction along the hearth axis from the inlet to the hearth bottom. It can be seen that within the coke free zone, as the number of elements increases, the velocity profile converges to that of mesh with 2,000,000 elements. Based on the mesh with 2,000,000 elements, |u|max for 600,000 elements and 1,000,000 elements differs by 20% and 6% respectively. Due to the low tolerance for the latter mesh compared to the finest mesh, the mesh with 1,000,000 elements is selected to be sufficient to conduct analysis for the current problem.

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FIGURE 3.7. Mesh sensitivity on temperature at centre thermocouple location for Case B.

FIGURE 3.8. Velocity u profile along hearth axis in Case B for mesh with various number of elements.

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3.3.1.4 Velocity vector plot inspections Finally, the velocity vectors for these simulations are inspected. FIGURE 3.9 is a snapshot of the vector plot for Case C, near the periphery of the top refractory step under the taphole. The figure shows that the vectors behaviour is physically plausible and appropriately describes complex flow features including mixed convection and the recirculation zone along a complicated geometry. Such observations visually demonstrate that the simulation result is numerically stable and the conservation laws hold.

FIGURE 3.9. Zoom up view of vector plots near upper steps under taphole for Case C.

3.3.2 General Flow Features The general flow features are described for Cases A to D. For each case, ‘high permeability’ (γ = 0.35 and dh = 30 mm) and ‘low permeability’ coke beds (γ = 0.30 and dh = 12 mm) are described. Here, the flow features of the sitting coke bed state (Cases A and C) will be described first, followed by the floating coke bed state (Cases B and D). With regard to the ‘high permeability’ coke bed, the flow features are compared to those predicted by Panjkovic et al. (2002) and Guo et al. (2008) who have also used γ = 0.35 and dh = 30 mm for their coke bed characterization. 93

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3.3.2.1 Flow in a sitting coke bed state FIGURE 3.10 shows the flow patterns in a sitting (Case A and C), ‘high permeable’ coke bed. Generally, the macroscopic flow pattern is described in two distinct zones, the bulk flow zone at the top and the quasi-stagnant zone at the bottom region of the hearth (FIGURE 3.10(b)). In the bulk flow zone, liquid iron flows from the inlet to the taphole in a uniform manner and the temperature is uniform close to the inlet temperature. On the other hand, in the quasi-stagnant zone, liquid iron is almost motionless (FIGURE 3.10(b)). The temperature contours in this layer are distributed horizontally close to each other, indicating a consistent and sharp temperature reduction from the top to the bottom of the zone (FIGURE 3.10(a)). The particular thermal distribution is known as “horizontally thermal layering” (Preuer et al., 1992b). Due to the extremely low velocity, as apparent from the almost constant temperature gradient along the vertical (vertical distance between contour lines are almost consistent), it can be understood that the heat transfer towards the bottom refractory is dominated by conduction. The macroscopic flow patterns are qualitatively similar to those predicted by previous investigators (Panjkovic et al., 2002, Guo et al., 2008) in spite of quantitative differences. In the flow pattern for Case A predicted by Guo et al. (Guo et al., 2008), the bulk flow zone is much thinner. This causes less mixing of liquid iron within the overall hearth leading to a much lower volume average temperature. This is partly due to the fact that they use a shape factor of 1, as opposed to 0.74 used in the current model (refer to shape factor in TABLE 3.1 when dh = 30 mm). This causes the bed permeability to be much higher (refer to Equation [3.17]), causing the bulk flow zone to be thinner. The relation between the permeability and the bulk flow zone thickness are detailed in Section 3.3.3. In the flow pattern for Case C predicted by Panjkovic et al. (2002), despite the fact that they also used a shape factor of 1 and their inlet temperature is set lower at 1500°C, their volume average temperature of the hearth is higher compared to the current model. The high eddy viscosity, predicted using their selected turbulence model (modified zero-equation turbulence model) may have caused such outcome. This results in a high effective viscosity (refer to Equation [3.3]), thereby the volume averaged value is approximately more than double that in the current model. Due to the high effective viscosity, a large amount of horizontal momentum in the bulk flow zone diffuses into 94

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the quasi-stagnant zone. As apparent from their velocity vectors plot (Panjkovic et al., 2002) the magnitude of the velocity vectors directing the taphole decreases slowly along the vertical from the bulk flow zone to the quasi-stagnant zone as opposed to the sudden change observed in FIGURE 3.10(c)-right. Therefore, the stronger liquid iron mixing causes the volume average temperature to be higher compared to the current case.

FIGURE 3.10. General flow and heat transfer features in ‘high permeability’ coke bed for Case A (left) and Case C (right). (a) Pool temperature contours, (b) streaklines and (c) velocity vectors.

In a ‘low permeability’ coke bed, the flow features are found to be quite different compared to the ‘high permeability’ coke bed. The flow patterns are shown in FIGURE 3.11 and FIGURE 3.12. Generally, the liquid iron enters the hearth and flows peripherally throughout the majority of the hearth. The average velocity is about 1.4 mm/s (FIGURE 3.11(c-f) and FIGURE 3.12(a) and (d)). In the region near the sidewall, a narrow downward-directed jet occurs due to natural convection (FIGURE 3.12(a) and (d)). Details of this phenomenon are shown in Section 3.3.3.1. The liquid iron is almost stagnant in the bottom corner region under the taphole where the velocity is about 0.1 mm/s. The size of this quasi-stagnant region is much greater in Case C spanning more than half the area of the hearth bottom compared to Case A where it is only slightly 95

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visible (FIGURE 3.11(d)). Due to the relatively good mixing of liquid, the majority of the liquid iron pool remains relatively uniform at a volume averaged temperature of 1,530°C for Case A and 1500°C for Case C. Within the pool, temperature gradient is observed mainly near the solid interface and in the quasi-stagnant region due to the convective heat transfer to the surrounding refractories (FIGURE 3.11(b)). For Case C, small regions at the bottom corner under the taphole the temperature are found with temperature below the iron solidus temperature (<1,150°C). Here, the liquid iron is solidified (FIGURE 3.11(d)-right and FIGURE 3.12(c)).

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FIGURE 3.12. 3D streamlines in ‘low permeability’ coke bed for Cases A – D: yellow in Cases B and D shows the coke bed shape and grey in Case C shows the solidified region.

3.3.2.2 Flow in a floating coke bed state The flow behaviour for a floating coke bed state (Cases B and D) is described, first in a ‘high permeability’ coke bed followed by the ‘low permeability’ coke bed. Generally, the flow features within the coke zone and the coke free zones are distinct for any coke bed permeability. FIGURE 3.13 and FIGURE 3.14 shows the general flow features in a ‘high’ and ‘low permeability’ coke bed respectively. A 3D streamline plot for the ‘low permeability’ coke bed is shown in FIGURE 3.12.

In a ‘high permeability’ coke bed, the flow behaviour in the coke zone and the coke free zone are quite distinct. In the coke zone, similar flow patterns are observed to

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the case in a sitting coke bed state, where the two zones, bulk flow zone and the quasi- stagnant zone exists (FIGURE 3.12(b-c)). For both Cases B and D, the thickness of the bulk flow zone is similar to the sitting coke bed state (Cases A and C). Again, the temperature is uniform, close to the inlet temperature in the bulk flow layer, whereas in the quasi-stagnant layer, “horizontal thermal layering” occurs (FIGURE 3.13(a)). For Case B, it can be seen that the liquid iron enters the coke free zone at the hearth side wall. Within the coke zone along the symmetry, the liquid iron flows in the direction away from the taphole at a high velocity (FIGURE 3.13(b)-left). On the other hand for Case D, it can be seen that the flow within the coke zone is totally isolated from the bulk flow occurring in the coke zone. Lack of fresh liquid in the coke free zone causes the temperature to be low. The temperature within the zone is nearly uniform, due to vertical recirculation driven by the buoyancy force induced near the side wall (FIGURE 3.13(b-c)-right). This recirculating zone occurs throughout the coke free zone in an axi- symmetric pattern about the hearth axis. A thin solidified iron layer is formed along the hearth bottom for Case D (FIGURE 3.13(b-c)-right). Unlike the solidified iron layer identified in the sitting coke bed state, no coke particles are expected within the layer.

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The flow pattern mentioned above has a strong resemblance with those predicted by Guo et al. (2008) and Panjkovic et al. (2002). The flow pattern for Case B predicted by (Guo et al., 2008) includes all features as predicted using the current model such as the separated bulk flow and the quasi-stagnant regions in the coke zone and the high velocity directing away from the taphole in the coke free zone. The axi-symmetric recirculating flow behaviour within the coke free zone is also apparent in the velocity vector plots for Case D as predicted by Panjkovic et al. (2002).

In a ‘low permeability’ coke bed, the flow is described as follows. Once the liquid enters the hearth, the majority directly flows into the coke free zone (FIGURE 3.14(c)). Since the liquid iron tends to travel in the route with the least resistance and the resistance force in the coke free zone is near zero, those that enter the hearth far away from the taphole would rather flow into the coke free zone first, travel within the coke free zone peripherally, re-enter the coke zone just under the taphole and flow towards the taphole. In this way, a smaller resistance force would be exerted on the liquid iron compared to that when the liquid flows towards the taphole via the coke zone. Within the coke free zone, two symmetrical sets of large scale recirculation zone span the whole diameter. FIGURE 3.14(e) and FIGURE 3.12(b) and (d) show one set of the recirculation zone. The velocity near the hearth corner is high and may reach up to a speed of 25 mm/s (Case D). Case B in a ‘high permeability’ coke bed also resembles such flow behaviour. Details of this flow features are shown in Section 3.3.3.1. Due to the high level of mixing maintained throughout the hearth volume (in both coke and the coke free zones), the heat transfer efficiency is high, resulting in a warm hearth. The temperature of the liquid iron is different before and after entering the coke free zone. The ‘S shaped’ temperature contours clearly distinguishes the freshly entered liquid iron to those with longer residence time as a result of being caught in the recirculation zone in the coke free zone (FIGURE 3.14(b)).

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101

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3.3.3 The Effect of Natural Convection and its Impact on Hearth Erosion The effect of natural convection on the liquid iron flow is significant (Panjkovic et al., 2002, Guo et al., 2008, Preuer et al., 1992b, Yoshikawa and Szekely, 1981, Post et al., 2003). This is particularly true in the regions near the refractory surface and may impact on the erosion behaviour in various ways. Generally, as a result of the induction of natural convection, two local flow features are observed. These are namely (i) downward jet near side walls and (ii) quasi-stagnant zone near hearth bottom. The mechanism of each of the flow features and their effect on erosion are described here.

3.3.3.1 Downward jet near side walls The downward jet occurs near the side walls throughout the hearth periphery. Due to heat transfer to the sidewall refractories, the local liquid iron temperature is low (FIGURE 3.11(b) and FIGURE 3.13(b)) and hence the density is high (refer to the expression for density in TABLE 3.1). As a result, the induced thermal buoyancy force generates the additional downward momentum, resulting in a downward jet. Due to the high velocity in the proximity of the side walls, the downward jet applies shear stress to the side refractories which may lead to erosion. Such flow feature occurs in both the coke zone and coke free zone, where the impact to the local refractories significantly varies leading to various erosion profiles.

Within the coke zone, as shown in FIGURE 3.12, the jet near the side wall occurs irrespectively to the hearth profile and the coke bed state and hence is expected to exist at all times throughout the campaign. This may be the main cause for sidewall erosion (except for the near-taphole region where the flow driven by pressure gradient at the taphole is the dominant cause of side wall erosion). The velocity of the jet seems to be strongly influenced by the coke bed permeability. In the ‘low permeability’ coke bed (γ = 0.30 and dh = 12 mm) the jet has a maximum velocity of about 2.5 mm/s (about 4.2 times the inlet velocity), on the other hand in a ‘high permeability’ coke bed (γ =

0.35 and dh = 26 mm), the maximum velocity is about 7.5 mm/s (about 14 times the inlet velocity). The erosion rate of the side wall refractory is expected to be greater in a ‘high permeability’ coke bed due to its greater jet velocity. The jet velocity does not

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seem to vary significantly between the coke bed states and the hearth profiles investigated (Cases A to D).

Within the coke free zone, the downward jet is substantially higher compared to the coke zone where the maximum velocity reaches 20 mm/s for Case B (32 times the inlet velocity) and 30 mm/s for Case D (48 times the inlet velocity). The jet velocity for the eroded hearth (Case D) is much greater than that in the intact hearth. This is because in the eroded hearth profile, the side wall is much thinner in the coke free zone resulting in a high temperature gradient. As a result, a greater thermal buoyancy force is induced along the non-porous side wall causing a much higher jet velocity. The downward jet causes the peripheral flow within the coke free zone to travel in a spiral motion as visualized in FIGURE 3.12(b) and (d). This acts as the main driving force to the large scale re-circulation zone found in the coke free zone (described in Section 3.3.2.2). Such flow pattern enhances the erosion of the refractory along the hearth bottom corner as it promotes high liquid iron velocity at a proximate location to both the vertical and horizontal refractory surfaces bounding the hearth bottom corner. Furthermore, the outer surface of the spiral flow has a donut shape and is geometrically similar to the profile of the inner surface of an “elephant foot” type erosion profile. Extended time period of such flow pattern may contribute to an “elephant foot” type hearth erosion.

3.3.3.2 Quasi-stagnant Zone Near Hearth Bottom Within the hearth at particular regions, the flow almost terminates and forms a quasi-stagnates zone. The quasi-stagnant zone is particularly more apparent in the sitting bed of ‘high permeability’ (Cases A and C) (FIGURE 3.10(c) and FIGURE 3.13(c)). Natural convection plays an important role for the cause of such phenomenon. As heat is transferred to the bottom refractory, the liquid iron near the hearth bottom has low temperature and hence high density. Due to natural convection, the heavy liquid is forced downwards by gravity and settles at the bottom of the hearth. Since the liquid iron is heavy and stagnant, it requires a large force to overcome its inertia and to start moving. Due to the infrequent mixing of liquid iron, further heat is transferred to the bottom refractory via conduction, which further lowers the local liquid temperature and raises its density and hence stagnates. Since the liquid iron has a high residence time in

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this zone, the carbon content is expected to be high close to its saturation limit. Therefore the quasi-stagnant zone may act as protection to the local hearth refractory from both convective and diffusive mass transfers.

3.3.3.3 Risks for models neglecting the natural convection As discussed above, the natural convection causes local flow patterns such that will affect the erosion behaviour of the surrounding refractories. When comparing the velocities near the bounding refractory surface predicted using models with and without natural convection, its magnitude may differ significantly. Guo et al. (2008) presents liquid iron flow patterns for Cases A and B when natural convection is not considered in the model. The porosity and coke size they used are identical to the current ‘high permeable’ coke bed ( = 0.35, dh = 30 mm). According to their velocity vectors plot, the sizes of the vectors near the side walls in the coke zone and those near the hearth bottom have similar sizes to the velocity vectors at the inlet. This contrasts to the current model (Cases A and B in ‘high permeable’ coke bed) where the jet at side wall has a velocity 14 times greater than the inlet velocity and the velocity near the hearth bottom is almost zero (FIGURE 3.15(i) and FIGURE 3.17(i)). These differences will significantly impact the carbon transfer rate between the refractory and the liquid iron. Therefore it is insufficient to refer to velocities obtained in the model without natural convection for investigations related to refractory erosion, e.g. simulations of inner hearth profiles, design for hearth refractories etc.

3.3.4 Effect of Coke Bed Permeability As in Section 3.3.2, the macroscopic flow pattern for a coke bed with high and a low permeability was found to be quite different. As in Section 3.3.1.1, the refractory temperatures at thermocouple location for the high and low permeability coke beds are also found to be quantitatively different. This indicates that there is a strong connection between the coke bed permeability, the flow pattern of the liquid iron and the heat transfer of the pool and refractories. In this section, the sensitivity to permeability is investigated to see its effect on flow and hence the refractory temperature.

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The permeability of the coke bed describes the ability of the liquid iron to flow through the pores among coke particles. Since the coke bed permeability is affected by various furnace operating conditions such as burden distribution (e.g. central coke charging), coke quality, coal injection rate, and so on, it is important to understand how it will affect the flow and heat transfer in the hearth. For this reason, the effect of the coke bed permeability on the flow and heat transfer is investigated.

Within the current numerical framework, the resistance force can be written in a general form, in terms of the permeability, Kperm as,

, [3.16]

where us is the superficial velocity and Kloss is the loss coefficient. By comparing this equation to the Ergun equation (Equation [3.7]) and through the relation us = u, the permeability used in the current model can be defined as,

. [3.17]

According to Ichida et al. (1991), shape factor, , for coke particles in a blast furnace is dependent on particle size (TABLE 3.1), thus the permeability depends only on the coke bed porosity and the mean coke size. The effect of permeability can be investigated by altering the coke bed porosity and the coke size. The effect of the coke bed permeability will be discussed in a sitting coke bed state (Cases A and C) first, followed by that in a floating coke bed state (Cases B and D).

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3.3.4.1 Effect in a sitting coke bed state FIGURE 3.15 and FIGURE 3.16 show streaklines and the temperature distribution of liquid iron for the intact and eroded hearth profiles for five selected cases (i) to (v), each with various pre-set coke bed permeability in descending order, from 2.3×10-7 to 8.0×10-9 m2 respectively. Here, the ‘high’ and ‘low permeability’ mentioned earlier corresponds to cases (i) and (iv) respectively.

FIGURE 3.15. Streaklines for Case A (left) and Case C (right) for permeabilities: -7 2 (i) Kperm = 3.31×10 m (γ = 0.35, dh = 30 mm), -8 2 (ii) Kperm = 9.11×10 m (γ = 0.275, dh = 26 mm), -8 2 (iii) Kperm = 4.70×10 m (γ = 0.425, dh = 10 mm), -8 2 (iv) Kperm = 1.80×10 m (γ = 0.30, dh = 12 mm), -9 2 (v) Kperm = 8.01×10 m (γ = 0.275, dh = 10 mm). Grey regions indicate the solidified iron layer.

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FIGURE 3.16. Temperature contours for Case A (left) and Case C (right) for permeabilities: -7 2 (i) Kperm = 3.31×10 m (γ = 0.35, dh = 30 mm), -8 2 (ii) Kperm = 9.11×10 m (γ = 0.275, dh = 26 mm), -8 2 (iii) Kperm = 4.70×10 m (γ = 0.425, dh = 10 mm), -8 2 (iv) Kperm = 1.80×10 m (γ = 0.30, dh = 12 mm), -9 2 (v) Kperm = 8.01×10 m (γ = 0.275, dh = 10 mm).

As shown, the coke bed permeability significantly affects the liquid iron flow pattern. For case (i), as mentioned earlier in Section 3.3.2.1, the macroscopic flow pattern is characterized with two distinct zones, namely the bulk flow zone at the top and quasi-stagnant zone at the bottom of the hearth (FIGURE 3.15(i)). As shown in FIGURE 3.15(i), the bulk flow zone has a thickness, where it occupies a certain volume of the pool. As the permeability decreases, the thickness of this bulk flow zone increases (FIGURE 3.15(i-v)) and the entire temperature contour lines shift downwards, resulting in a warmer hearth (FIGURE 3.16(i-v)). In particular for Case C cases (i-iii), this causes

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the solidified iron layer formed along the hearth bottom to decreases its thickness (FIGURE 3.15(i-iii)-right).

If the permeability is reduced, or in other words, the resistance force increases, the liquid iron is forced to flow in a longer route from the inlet to the taphole. Therefore, instead of liquid iron travelling directly towards the taphole resulting in a thin bulk flow zone as in case (i) (FIGURE 3.15(i)), this causes the liquid iron to flow further deeper into the hearth before reaching the taphole, causing the bulk flow zone to be much thicker as in case (iv) (FIGURE 3.15(iv)). Since this enhances the liquid iron mixing in the hearth, the volume-averaged hearth temperature increases.

Such trend is observed until the thickness of the bulk flow zone reaches the thickness of the coke zone (for sitting coke bed state this corresponds to the pool depth) or when the bulk flow zone saturates the coke zone. The permeability for this to occur is denoted here as the critical permeability and is found to be 4.7×10-8 and 1.1×10-8 m2 for Cases A and C respectively. It can be observed that reducing the permeability beyond the critical permeability does not further increase the volume-averaged hearth temperature. This is because the bulk flow layer saturates the hearth volume and the maximum degree of liquid iron mixing in the hearth is attained (FIGURE 3.15(iv-v) and FIGURE 3.16(iv-v)).

It is interesting to note that as the permeability increases, the velocity of the narrowing bulk flow layer increases (FIGURE 3.15). Since the liquid iron travels horizontally at a high velocity directly towards the taphole through the thin bulk flow layer, coke fines and small particles that have percolated up into the layer can be flushed out, resulting in a clean hearth. This means that once the coke bed permeability is improved, the cleaning process of the coke bed will become more efficient so that a high coke bed permeability can be maintained longer.

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3.3.4.2 Effect in a floating coke bed state FIGURE 3.17 and FIGURE 3.18 show the effect of coke bed permeability on the streaklines and temperature distribution respectively, each for Cases B and D. Four different pre-set coke bed permeabilities, cases (i) to (iv), are selected. The permeabilities are in a descending order, ranging from 3.3×10-7 down to 1.8×10-9 m2. The ‘high’ and ‘low permeability’ coke bed corresponds to cases (i) and (iv) respectively.

FIGURE 3.17. Streaklines for Case B (left) and Case D (right) for permeabilities: -7 2 (i) Kperm = 3.31×10 m (γ=0.35, dh=30 mm), -7 2 (ii) Kperm = 1.21×10 m (γ=0.275, dh=20 mm), -8 2 (iii) Kperm = 4.70×10 m (γ=0.30, dh=18 mm), -8 2 (iv) Kperm = 1.80×10 m (γ=0.30, dh=12 mm).

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FIGURE 3.18. Temperature contours for Case B (left) and Case D (right) for permeabilities: -7 2 (i) Kperm = 3.31×10 m (γ=0.35, dh=30 mm), -7 2 (ii) Kperm = 1.21×10 m (γ=0.275, dh=20 mm), -8 2 (iii) Kperm = 4.70×10 m (γ=0.30, dh=18 mm), -8 2 (iv) Kperm = 1.80×10 m (γ=0.30, dh=12 mm).

The effect of coke bed permeability for Case D is described first. Within the coke zone, similar observations are made as in Cases A and C. As the coke bed permeability decreases, the thickness of the bulk flow layer increases (FIGURE 3.17(i- -8 2 iii)-right). This continues until a critical permeability is reached (Kperm = 8×10 m ), where the bulk flow layer thickness increases until its extent reaches the coke free zone (FIGURE 3.17(iii)-right). At this point, part of the liquid iron in the bulk flow layer (particularly near the hearth periphery due to the hemispherical coke bed geometry), starts to short-circuit towards the taphole via the coke free zone where a large scale recirculation zone is formed. Since good liquid mixing occurs both in the coke zone and the coke free zone, further reducing the coke bed permeability does not necessarily increase the volume-averaged hearth temperature. For this reason, the temperature 110

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profiles do not change significantly when the permeability decreases below the critical permeability (FIGURE 3.18(iii-iv)-right).

For Case B, it can be seen that the bulk flow layer reaches the coke free zone for any permeability investigated (FIGURE 3.17-left). Due to the shallow pool depth, the bulk flow layer becomes easier to reach the coke free zone, even in a ‘high permeability’ coke bed (case (i)). This means that for Case B, the permeability range investigated (cases (i-iv)) is below the critical permeability. For this reason, the temperature distribution does not significantly change when further reducing the coke bed permeability (FIGURE 3.18-left).

As discussed in Section 3.3.3.1, one of the concerns in a floating coke bed state is the high liquid iron velocity at the refractory surface within the coke free zone which may subsequent to an ‘elephant foot’ type hearth erosion. For this reason, the effect of coke bed permeability on the velocity within the coke free zone is investigated. FIGURE 3.19 shows the maximum velocity within the coke free zone for various coke bed permeabilities for Cases B and D. For case D, the maximum velocity within the coke free zone is found to vary widely, depending on whether the deadman permeability -7 2 is above or below its critical value (Kperm,cr = 1×10 m ). When the permeability ranges below its critical value (KpermKperm cr), the maximum velocity is low at around 8 mm/s. For case B, although the permeability is always below its critical value, the maximum velocity in the coke free zone increases significantly from 17 to 42 mm/s as the permeability decreases. Therefore, in order to minimize the velocity near the refractories and reduce the erosion at the bottom corners of the hearth, it is desirable to maintain high coke bed permeability.

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FIGURE 3.19. Effect of deadman permeability on the maximum velocity within the coke free zone in intact and eroded hearth profiles.

3.3.5 Effect on Refractory Temperature The effect of coke bed permeability on refractory temperatures and hence the extent of agreement of the model’s results with measured values will be investigated in this section. FIGURE 3.20 and FIGURE 3.21 show the correlation between the normalized temperature to the coke bed permeability when the coke bed is sitting (Cases A and C) and floating (Cases B and D) respectively. Here, the normalized * temperature, TTC , is defined as the calculated temperature at the center thermocouple * location normalized by the center thermocouple temperature; where TTC >1 indicates * * over-prediction, TTC <1 indicates under-prediction and TTC =1 indicates a one to one agreement.

The effect of the permeability on the normalized temperature is observed to generally behave in a similar manner for all cases. As the permeability decreases, the normalized temperature increases until the critical permeability is reached. Then it remains unchanged when the permeability is further decreased. The overall trend is

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apparent for Cases A, C (FIGURE 3.20) and D (FIGURE 3.21). For Case B, only the latter trend is observed as the critical permeability is above the range investigated.

Such a trend can be explained in conjunction with the behaviour of the flow in the hearth. As discussed earlier, decreasing the permeability increases the bulk flow layer thickness and also the volume-averaged hearth temperature (Section 3.3.3.1). Here, the temperature of the hearth bottom surface (inner surface) increases as well. As a result of conductive heat transfer through the bottom refractory, now with a higher inner surface temperature, the temperature at the thermocouple location increases. Eventually the permeability reaches its critical value - when the bulk flow layer thickness reaches the coke layer thickness (for sitting coke bed state this corresponds to the hearth depth). Since maximum degree of mixing is attained at this point, reducing the coke bed permeability further does not increase the temperature at the thermocouple location.

Overall, for Cases A to D, the calculated temperatures agree better with thermocouple readings when the coke bed permeability is below its critical value. In particular, a coke bed permeability of 1.8×10-8 m2 (case (iv)) establishes best agreements between the calculated and thermocouple temperatures for all Cases A to D

(FIGURE 3.20 and FIGURE 3.21). Note that the porosity (γ = 0.30) and coke size (dh = 12 mm) for ‘low permeability’ coke bed in Sections 3.3.3.1 and 3.3.2 are selected based on this permeability via Equation [3.17]. From the current analysis, it may be stated that the macroscopic flow patterns within the actual hearth during the time corresponding to cases A to D should be similar to that described in FIGURE 3.11 and FIGURE 3.13 when the coke bed permeability is around 1.8×10-8 m2.

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FIGURE 3.20. Effect of permeability on the normalized temperature of the refractory at the center thermocouple location for sitting coke bed state (Cases A and C).

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FIGURE 3.21. Effect of permeability on the normalized temperature of the refractory at the center thermocouple location for floating coke bed state (Cases B and D).

3.3.6 Further Comments on the Role of Natural Convection An issue in the literature review has been raised in Section 3.1 that the models with natural convection under-predicts the temperature while those without natural convection gives good agreement. This issue is addressed in this section.

Firstly, the reason behind the under-prediction of the refractory temperature experienced by Guo et al. (2008) and Panjkovic et al. (2002) who both consider natural convection in their models is discussed through Case A. For Case A, for a model to attain a good agreement, the temperature at the center of the hearth bottom, Tbottom, must be 1427 °C. This is calculated using a simple 1D Fourier’s law of thermal conduction through the refractory along the hearth axis. The heat flux in the equation is determined from the temperature difference of the center thermocouples located at z = 0.3 m and 1.5 m (refer to FIGURE 3.1) and the thermal conductivity of the refractory (refer to TABLE 3.1). In order to attain this temperature, good liquid iron mixing within the pool 115

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is required. As discussed in Section 3.3.3.1, this is achieved when the coke bed -8 2 permeability is below its critical value (Kperm cr = 4.7×10 m ), such as cases (iii) to (v), where the bulk flow layer thickness reaches the pool depth limit (FIGURE 3.15(iii-v)). The hearth bottom temperatures for cases (iii) to (v) are 1435.9, 1436.3 and 1426.4 °C respectively which are close to the ideal value (FIGURE 3.16(iii-v)). On the other hand, Guo et al. (2008) and Panjkovic et al. (2002) used a coke bed permeability substantially -7 2 above its critical value of Kperm = 6.1×10 m , which limits the mixing of liquid iron in the hearth as the bulk flow layer is thin. The remaining liquid iron under the bulk flow layer is quasi-stagnant where “horizontal thermal layering” occurs. As a result, the hearth bottom temperature was predicted to be around 1100 and 1255 °C respectively, which substantially underestimates the theoretical value. This may be the main reason for their under-prediction.

Secondly, the reason behind the good agreement between the calculated and measured temperatures when the model neglects the natural convection is discussed. Generally, when natural convection is neglected from the model, liquid iron flows uniformly throughout the hearth volume from the inlet to the taphole. Liquid iron mixes well throughout and hence a high volume-averaged hearth temperature is maintained. Such flow pattern has a close resemblance with cases (iii-v) (i.e. with coke bed permeability Kperm < Kperm cr) and hence a similar temperature distribution in the refractory is expected. Therefore temperatures calculated using models neglecting natural convection has a good agreement with measured temperatures. Chang et al. (2009) and Huang et al. (2008) modelled the hearth of China Steel Corporation’s No.2 Blast Furnace without natural convection and the coke bed is in a floating state. Almost all liquid iron from the inlet flows immediately towards the coke free zone before being tapped out showing good liquid iron mixing throughout the hearth. The degree of mixing resembles that in Cases B and D-case (iv) where Kperm < Kperm cr. Therefore they have attained good agreement between calculated and measured refractory temperatures. It is emphasized that in spite the good agreement established, care should be taken when neglecting natural convection depending on the purpose of the simulation results due to causes mentioned in Section 3.3.3.3.

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3.4 CONCLUSIONS A 3D CFD model is developed to simulate liquid flow and heat transfer in the hearth of PK5BF, aimed at establishing a reliable and accurate numerical model of BF hearth. Compared to the previous work, significant improvements are made in terms of turbulence modelling, buoyancy modelling, temperature dependent material properties, wall boundary treatments and mesh resolution. A phase change model is also included to simulate the solidified iron layer. Coke bed properties such as particle size, shape factor and porosity are better justified. The model results are further verified through residuals and mesh sensitivities and vector plot inspections with convincing credibility. The model is validated by comparing the calculated temperatures with the thermocouple data available, where agreements are established within  3 %.

The flow and temperature distributions in the hearth are described for four distinct cases during the campaign, each characterized with a sitting or floating coke bed state in an intact or eroded hearth profile. Natural convection significantly influences the flow patterns which in turn effects the hearth erosion in two ways. Firstly, a downward-directed jet forms along the peripheral side walls. In the coke zone, this is expected to occur throughout the campaign and is the main cause of side wall erosions. In the coke free zone, this contributes to a vortex like peripheral flow with velocity reaching up to 48 times the inlet velocity and may lead to an ‘elephant foot’ type erosion profile. Secondly, it may cause the heavy liquid iron to remain stagnant at the hearth bottom, protecting the hearth bottom from erosion.

The effect of the coke bed permeability is investigated for each of the four cases. A strong link between the coke bed permeability, flow pattern and refractory temperature is found. Generally as the permeability decreases, the bulk flow becomes more prominent, thus increasing liquid mixing and leading to an increase in the refractory temperatures. Best agreements are established between the calculated and measured refractory temperature for all four cases when the coke bed permeability is 1.8×10-8 m2. Through this analysis, the dilemma in literature regarding the agreement of calculated temperatures to the measurements using models with and without natural convection is explained.

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CHAPTER 4 A METHOD TO MANAGE TITANIUM COMPOUNDS IN A BLAST FURNACE HEARTH DURING TITANIA ADDITION

4.1 INTRODUCTION A blast furnace (BF) remains the predominant industrial plant for the iron ore smelting process. Lengthening the furnace campaign life has always been considered important to reduce the cost for capital asset and production. In recent years, it is understood that the erosion of the hearth refractories is the main limitation of furnace campaign life (Silva et al., 2005). Furnace operators implement various measures to prevent such erosion, such as; to conduct continuous tapping with short period between alternate tap holes; closing local tuyeres; and minimizing the number and duration of the furnace stoppages; (Kurunov et al., 2007) however, these actions greatly affect the performance of the furnace. An effective measure widely used in practice is the addition of titanium bearing materials into the furnace by burdening or injection through tuyeres. A protection layer is formed along the worn out regions of the hearth linings due to the precipitation of solid titanium carbonitride.

The addition of titanium bearing material in BF for the protection of the hearth was first noticed in the mid 50’s through BF dissection studies(Eto, 1957, Hisada et al., 1964, Jomoto et al., 1965, Narita et al., 1977). Since iron ore contains some portion of titanium oxide, scaffolds containing high quantity of titanium were found along the hearth bottom, eroded portions of the side walls (Hisada et al., 1964) and in the joints of the chamotte bricks (Narita et al., 1977). X-ray diffraction scattering analysis shows that the titanium exist in the form of Ti(C,N) crystals, a solid solution containing TiN and TiC (Hisada et al., 1964), and it was understood that the scaffolds are solidified metal matrix with loose Ti(C,N) particles floating around (Bergsma and Fruehan, 2001).

Bergsma and Fruehan have proposed a hypothesis on the formation mechanism of the Ti(C,N) protection layer (FIGURE 4.1). The process is described as (a) added titanium oxide reaches the slag phase and reduces to titanium, (b) produced titanium 118

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enters the liquid iron, (c) titanium is transported to cooler regions of the hearth, (d) the formation of Ti(C,N) solid particles and (e) scaffold formation. Ti(C,N) solid particles are formed by nucleation on coke or graphite nuclei and are driven by the decrease in solubility of Ti, C and N in the liquid iron due to the reduction of the temperature. As more particles are formed and the particle density increases, the liquid iron becomes increasingly viscous to a point where it stops flowing. Such a state of iron is considered a solidified Ti(C,N) protection layer (Bergsma and Fruehan, 2001).

FIGURE 4.1. Hypothesis of mechanism behind the formation of the Ti(C,N) protection layer in the blast furnace hearth (Bergsma and Fruehan, 2001).

Successful formation of protection layer at the eroded regions of the hearth lining depends greatly on the flow and heat transfer of the liquid iron and hence furnace operating conditions. Further, the dosage of titania is required to be enough to form the protection layer but should be minimised as excess dosage causes adverse effect on the post processing of liquid iron. This parametric study is used to observe the solid particle formation behaviour at various operating conditions to provide useful information for blast furnace operators during titania additions in order to maximise the possibilities to form Ti(C,N) protection layer with minimum titania addition.

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4.2 MODEL DESCRIPTION In the present study, a two dimensional steady-state model based on ANSYS CFX software (version 13.0) is used to describe the formation and dissolution behaviour of the TiC particles in the blast furnace hearth during tapping. A general multiphase, multicomponent approach is used. Two phases, liquid and dispersed solid are considered where the liquid phase consists iron, titanium and carbon components and the solid phase consists Titanium carbide and Seed components. Complete details of the model are reported in Guo et al. (2010). A general outline of the model and some minor modification are described here.

4.2.1 Governing Equations Shown below is the steady-state conservation equations for mass, momentum, energy and mass species in general form for liquid and dispersed solid phases. Also shown is the so called population balance equation.

[4.1]

[4.2]

[4.3]

[4.4]

[4.5]

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An inhomogeneous model is used for the conservation equations of mass, momentum and mass species. A homogeneous model is used for the conservation of energy equation where the solid and dispersed phases share a common temperature field. and C are the interphase mass transfer rate for the total mass, and mass species respectively: Fd and Fc are the interphase drag force and the interaction force of the coke bed respectively. The population balance equation only applies to the dispersed solid phase, where ns is the particle number density and is related to the particle diameter of the dispersed solid, ds as:

[4.6]

4.2.2 Constitutive Equations Due to the abundance of carbon and nitrogen in the hot metal, the addition of titanium would produce solid titanium nitride and titanium carbide particles. However for the purpose of understanding the qualitative effects of key operational parameters on the solid particle behaviour, only the reaction related to the formation of titanium carbide is considered here. The effect of the inclusion of the reaction related to titanium nitride can be found in Guo et al. (2010). The chemical reaction related to the formation of titanium carbide is described as follows.

[4.7]

This reaction is reversible where the forward reaction represents a solidification reaction and backwards reaction represents a dissolution reaction. The rate of the reaction per unit volume is based on convective mass transfer from the surface of the spherical particle to the surrounding continuum and is given as (Guo et al., 2010):

[4.8]

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where Aαβ is the interfacial area density, ds is the particle diameter, ρ is the liquid density, DTi is the diffusion coefficient of titanium and Sh is the Sherwood number. The reaction rate is driven by the difference between Y’Ti and YTi which are the titanium mass fractions at the particle surface and the far field of the continuum, respectively. Chemical equilibrium is assumed for the quantification of the former and is determined by thermodynamic calculation of Equation [4.7] (Guo et al., 2010):

[4.9]

where KTiC is the equilibrium constant and fTi is the activity coefficient of titanium in liquid iron and is given by:

[4.10]

The relation between solidification and dissolution reaction rates is determined through stoichiometric relation of Equation [4.7] as:

[4.11]

A correlation between the particle diameter, d, and the flow field is derived as follows. FIGURE 4.2 shows a schematic diagram of a single TiC particle.

FIGURE 4.2. Schematic diagram of a single TiC particle.

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Here it is presumed that the TiC species grows onto the spherical seeds forming the TiC particle with a spherical shape. The dispersed solid phase consists of two species, TiC and Seed. Therefore within the dispersed solid phase, the following equation holds.

[4.12]

No particle size distribution is assumed to occur within any single unit volume. Under this assumption, with reference to FIGURE 4.2, the mass fraction of seeds, mfseed, can be described as:

[4.13]

where n is the number density. ρTiC and ρseed are the densities of TiC and seed and is assumed to be equivalent i.e. ρTiC = ρseed. This is because in this model, no buoyancy force due to density difference is assumed. From this, Equation [4.12] reduces to:

[4.14]

Which is rearranged to have the following correlation for particle diameter, d.

[4.15]

4.2.3 Geometry, Mesh, Boundary and Simulation Conditions A 2D slot model is used for the current study. The geometry used is shown in FIGURE 4.3, which models the hearth of BlueScope’s PK5BF for the campaign 1991 - 2009. Here, the inner profile of the hearth is such that all of the firebrick layer, the majority of the ceramic layers and part of the BC7S (small portion at the left and right 123

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bottom corners) are eroded (FIGURE 4.3). The taphole has a diameter of 60 mm and is inclined at 12.5°.

FIGURE 4.3. Geometry of the eroded hearth of PK5BF (campaign: 1991-2009).

FIGURE 4.4 shows the meshing of the model. The slot model is meshed so that it has a thickness of 0.1 m. The solid and liquid domains are meshed separately and are connected via the General Grid Interface (GGI) attachment method. The solid domain is meshed using triangular prisms in an unstructured orientation with 16,000 elements. On the other hand the liquid domain is meshed using rectangular prisms in a fully structured orientation with 52,000 elements. From numerical studies conducted by Guo et al. (2010), it was found that the dispersed particles form and accumulate mostly along the refractory surface resulting with a high solid holdup at these regions. Since in the current work, it is of interest to predict the distribution of the dispersed particles, finer meshes were used along all refractory surfaces by adding inflations using a first layer thickness of about 3 mm.

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FIGURE 4.4. Meshing of the model.

The boundary conditions used in the model for the base case are as follows. At the inlet: the titanium mass fraction of the hot metal is 0.4 wt%; the seed number density and diameter is 1x1010 m-3 and 10 μm respectively; the temperature is 1550 °C and the mass flow rate is 6912 t/day scaled via an area ratio between the slot model inlet area and the actual hearth inlet area. At the outlet, the relative pressure is 0 atm. The temperatures of the bottom and side external walls are 70 °C.

The convergence criteria are set as; RMS residuals for all equations to be below 1x10-5 and the volume fraction of the dispersed solid monitored at various solid rich locations to reach a steady value.

4.3 RESULTS AND DISCUSSION

4.3.1 Macroscopic Behaviour of Hot Metal Flow FIGURE 4.5(a-c) shows the temperature contours of the hearth and the velocity vectors, streamlines and temperature contours of the hot metal pool. In this two phase model, separate velocity fields are generated for each phase. Here, the velocity field for only the liquid phase is presented as the streamlines and the velocity vector plots are almost identical between the two phases. Generally, the hot metal flows uniformly with streamlines distributed relatively evenly throughout the pool from the inlet to the outlet with an average velocity of about 1 mm/s (FIGURE 4.5(c-d)). The hot metal at the bottom corner regions of the hearth is found to be quasi-stagnant (FIGURE 4.5(b)). Within the pool, temperature gradient is observed mainly near the eroded regions

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particularly at the corners. The temperature at the remaining majority of the pool volume remains uniform, close to inlet temperature, resulting with an average pool temperature of 1519°C (FIGURE 4.5(c)). Generally the temperature gradient in the refractory is high particularly in the ceramic cup layer (FIGURE 4.5(a)). The low thermal conductive ceramic cup prevents significant heat loss from the hot metal, as evident from the smaller high temperature gradient region above the layer in the pool compared to the corners where the material is totally eroded (FIGURE 4.5(c)).

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4.3.2 Macroscopic Behaviour of the Particles FIGURE 4.5(d-f) shows the contours of titanium mass fraction, solid holdup and the mean particle diameter. Colours of the solid holdup are represented in logarithmic scale and the rest is in linear scale. The solid holdup is the solid particles volume created per unit volume of hearth and is defined as:

[4.16]

where ε is the volume porosity of the packed coke bed, vfdispersed solid is the volume fraction of the dispersed solid phase and YTiC is the mass fraction of TiC within the dispersed solid phase.

As shown, a particle rich region is found near the bottom and side refractories where the solid particles distribute in a coating like manner covering the entire hearth bottom and the steps with varying thickness. No particles are found to exist outside this particle rich region. Within the region, the solid holdup increases rapidly towards the refractory surface. A particularly high solid holdup is found along the refractory surface of the hearth bottom and steps and at the corners, reaching a maximum of 1.3 wt% (FIGURE 4.5(e)). The distribution of the mean particle diameter follows that of the solid holdup where generally large particles are found in the particle rich region. The solid particles may grow to a maximum diameter of 78 μm at the left and right bottom corners. It can be seen particle diameter outside the particle rich region remains uniform at 10 μm (this corresponds to the particle diameter of the seeds) (FIGURE 4.5(f)). Here, no nucleation occurs on its nucleation site or seeds. The distribution of titanium mass fraction counteracts that of the solid holdup. The majority of the hearth volume has a titanium mass fraction equivalent to the inserted titanium mass fraction (0.4 wt%) and found to rapidly reduce near refractories at the bottom and side steps (FIGURE 4.5(d)). It can be seen that more titanium is being consumed as more TiC particles are formed and grown. When comparing FIGURE 4.5(d-f), the contours of the solid holdup, mean particle diameter, titanium mass fraction, both their distributions and shapes, are similar to that of the temperature. This indicates that the transport behaviour of the particles 128

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have a particularly close relation to the temperature field. In this steady-state system, the forced convection dominant flow provides good hot metal mixing and distributes the inserted titanium throughout the hearth. This results the titanium concentration of the majority of the hot metal above the particle rich region to be uniform at 0.4 wt% (FIGURE 4.5(d)). Based on thermodynamics calculation of Equation [4.7], the solubility of titanium can be described as a function of temperature (FIGURE 4.6). For a hot metal solution with titanium concentration of 0.4 wt%, the equilibrium temperature is calculated to be 1420°C. When plotting the isothermal line of this equilibrium temperature in the solid holdup distribution, it can be seen that it matches relatively well with the profile of the particle rich region. The isotherm clearly differentiates between the particle rich and no particle regions (FIGURE 4.5(e)). It can be seen that the contours of FIGURE 4.5(d–f) are closely packed to each to other starting at the isotherm downwards. As soon as the hot metal flow crosses this isotherm, the solid holdup, mean particle diameter and consumption of titanium, all increases rapidly. A slight deviation between the isotherm and particle rich region is observed downstream near the bottom corner. The titanium content in the hot metal passing this region is a result of events that occurred upstream where titanium may be consumed and/or produced at various rates during the chemical reaction (Equation [4.7]). This may have resulted the deviation.

FIGURE 4.6. Solubility of Titanium in hot metal.

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The above observations signifies that the particles in the hearth can be managed by controlling the location of the isotherm of the equilibrium temperature of the hot metal solution with titanium dosage as injected. The adjustment of the isotherm can be done in two ways by; (i) altering the injection dosage of titanium and (ii) altering the temperature environment of the hearth. The effect of these two parameters on the distribution of the titanium based particles are investigated in Sections 4.3.4 and 4.3.5 respectively.

4.3.3 Behaviour of Particles along a Streamline To further understand the particle formation behaviour, various parameters of an infinitesimal fluid packet travelling along a single streamline are monitored with time. The streamline is selected such that it passes through the particle rich region (FIGURE 4.7). FIGURE 4.8 shows the temperature, titanium concentration, solid holdup and mean particle diameter along the streamline. Regions with positive titanium carbide and titanium mass transfer rates (Equations [4.16] and [4.8]) are coloured to respectively specify the locations where particles undergo solidification and dissolution reactions (FIGURE 4.7).

FIGURE 4.7. Particle behaviour along a streamline. Arrow heads are placed on the hour. Coloured region represents: solidification (orange) and dissolution (blue).

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The following steps describes the particle behaviour as it flows along the streamline.

i. At t = 0, hot metal with 0.4 wt% Ti enters the hearth, then flows on following the streamline. Here, the high temperature hot metal is under-saturated in Ti

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where Ti mass fraction remains constant at 0.4 wt% (FIGURE 4.8(b)). No particles are formed.

ii. At t = 1.2 hr, hot metal flows to a point where temperature is 1420°C where particle formation occurs. This is the equilibrium temperature of hot metal solution containing 0.4 wt% Ti. This is the point where hot metal first contacts the orange region. iii. At t = 1.2 - 5.7 hr, the hot metal flows toward the cooler eroded region near the bottom left corner. As the temperature decreases, the solubility of Ti decreases. Therefore the process of solidification progresses leading to a growth of particles (FIGURE 4.8(f)) and hence an increase in solids holdup (FIGURE 4.8(e)). Here, Ti mass fraction is being consumed (forward reaction of Equation [7]) (FIGURE 4.8(b)), but at a slower rate than the decrease of Ti solubility

(FIGURE 4.8(c)). Therefore the [Ti] > [Ti]eqm and hence the section of the streamline is super-saturated (i.e. orange region in FIGURE 4.7). This continues until the temperature along the streamline reaches its minimum, at t = 5.7 hr. iv. At t = 5.7 - 10.5 hr, the hot metal flows along the hearth bottom region, left to right. The temperature increases from its minimum at t = 5.7 hr to a local maximum at t = 10.5 hr (FIGURE 4.8(a)). Following the temperature trend, the solubility limit also increases (FIGURE 4.8(c)). The particles undergo dissolution where particle size decreases causing the solids holdup to decrease to near zero at t = 10.5 hr (FIGURE 4.8(e)). Here, Ti mass fraction is produced (backward reaction of Equation [7]) at a faster rate (FIGURE 4.8(b)) than the

increase of Ti solubility (FIGURE 4.8(c)). Therefore the [Ti] < [Ti]eqm and hence the section of the streamline is sub-saturated (i.e. blue region in FIGURE 4.7).

v. The hot metal approaches and passes the eroded region at the bottom right corner of the hearth. Again, another cycle of particle growth and shrinkage is repeated, however this time, the process is rather complex as the velocity is high

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due to high pressure drop towards the taphole. As the hot metal approaches the eroded region, the temperature decreases rapidly (FIGURE 4.8(a)). Since the solubility of titanium also decreases (FIGURE 4.8(c)), the solidification reaction takes place where the particles grow and consume the titanium (FIGURE 4.8(b), (f)). However since the reaction rate is slower than the rate of decrease of solubility, the available titanium cannot be consumed in time causing the local region to be overly supersaturated (FIGURE 4.8(d)). The reverse is also true when the hot metal flows from the eroded region to the taphole where the temperature increases rapidly causing an extreme under-saturated region at the entrance of the taphole at t = 11.9 hr (FIGURE 4.8(d)). At t = 10.5 - 11.5 hr, the hot metal approaches and passes the eroded region at the bottom right corner of the hearth. Again, another cycle of particle growth and shrinkage is repeated, however this time, the process is rather complex as the velocity is high due to high pressure drop towards the taphole. As the hot metal approaches the eroded region, the temperature decreases rapidly (FIGURE 4.8(a)). Since the solubility of Ti also decreases (FIGURE 4.8(c)), the solidification reaction takes place where the particles grow and consume the Ti (FIGURE 4.8(b,f)). However since the reaction rate is slower than the rate of decrease of solubility, the available Ti cannot be consumed in time causing the local region to be overly supersaturated (FIGURE 4.8(d)). The reverse is also true at t = 11.5 - 11.9 hr, when the hot metal flows from the eroded region to the taphole where the temperature increases rapidly causing a significantly under-saturated region at the entrance of the taphole, at t = 11.9 hr (FIGURE 4.8(d)).

It is interesting to see at t = 11.5 hr, the solid holdup suddenly increases however the mean particle diameter remains constant (FIGURE 4.8(e)). Two compromising factors are identified that may have caused this phenomenon. (i) Since velocity increases at the corner region of the bottom step (FIGURE 4.5(b)), streamlines starts to converge to each other (FIGURE 4.5(c)) causing the solid holdup to increase. (ii) Now the volume fraction of the particles is high, the solid shear viscosity increases. Since the streamline passes close to the boundary, viscous friction causes the particle velocity to

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reduce. This causes the particle to dynamically be held up which increases the solid holdup further.

4.3.4 Effect of Inlet Titanium Mass Fraction FIGURE 4.9 shows the solid holdup distributions for various inlet titanium mass fractions ranging from 0.2 to 3.0 wt% corresponding to cases (i) to (vii) respectively. The colours of the contours are represented in logarithmic scale. It can be seen that as inlet titanium mass fraction increases, the solid holdup and the thickness of the particle rich layer increases throughout the hearth bottom as well as the side walls. As discussed in Section 4.3.2, the titanium concentration in the hot metal solution above the particle rich layer can be assumed to correspond to the titanium concentration at the inlet boundary. Also shown in FIGURE 4.9 is the isotherm of the equilibrium temperature of this hot metal solution for each of the cases determined according to FIGURE 4.6.

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FIGURE 4.9. Effect of inlet Titanium on solid holdup distribution with equilibrium temperature isotherm (red line).

As shown, each of the isotherms matches well with the profiles of the particle rich layer for cases (i) to (v). It can be seen that the isotherm shifts upwards, as the inlet titanium mass fraction increases. For case (i), the isotherm crosses the hearth bottom boundary. The equilibrium temperature isotherm is not shown for cases (vi) and (vii) because it is

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greater than the temperature at the inlet which is 1,550 °C. Here, particles are formed as soon as the titanium enters the hot metal pool. Since it is of interest to attain high concentration along the hearth refractory surface, the effect of titanium mass fraction is also investigated based on parameters of the particles along the bottom refractory surface. FIGURE 4.10 shows the solid holdup profile along the hearth bottom and FIGURE 4.11 shows the average values of the solid holdup and the mean particle diameter along the hearth bottom.

FIGURE 4.10. Solid holdup distribution along hearth bottom for various inlet Titanium mass fractoins.

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FIGURE 4.11. Average solid holdup and mean particle diameter along hearth bottom for various inlet Titanium mass fractions.

Generally, the solid holdup along the hearth bottom increases smoothly from the left to the right corner. As the inlet titanium mass fraction increases, the profile flattens (FIGURE 4.10) and the solid holdup increases in an almost linear manner (FIGURE 4.11). For case (i), it can be seen that there exists a region where almost no solid is held along the hearth bottom (FIGURE 4.10). Since the corresponding equilibrium isotherm crosses hearth bottom boundary (FIGURE 4.11), the region remains sub-saturated where no particles are formed. The small quantity of solid holdup (< 0.02 wt %) is due to the advection of particles from upstream. In such an event, the average solid holdup along the hearth bottom significantly reduces (FIGURE 4.11). Therefore for the purpose of protecting the hearth bottom, it is recommended to add sufficient amount of titanium such that the corresponding equilibrium temperature isotherm will completely lie within the hot metal pool. As inlet titanium mass fraction increases, the mean particle size along the hearth bottom increases. Since the particle rich layer thickens, the solidification region as shown in FIGURE 4.7 increases. This allows more time for particles to grow within its streamline.

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4.3.5 Effect of Inlet Temperature FIGURE 4.12 shows the distribution of the solid holdup for various average pool temperatures ranging from 1,445 to 1,593 °C. These are represented as cases (i) to (vii). The average temperature of the pool is altered by adjusting the inlet temperature. The inlet titanium mass fraction is fixed to 0.4 wt% and the corresponding equilibrium temperature isotherm (1420 °C) is also shown.

FIGURE 4.12. Effect of average pool temperature on solid holdup distribution with equilibrium temperature isotherms. 138

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Again for all case, the equilibrium temperature isotherm matches the profile of the particle rich layer, providing a good indicator where particle formation occurs and where the layer is expected in the hearth. It can be seen that as the pool temperature increases, the location of the equilibrium temperature isotherm shifts downward and the particle rich layer thickness reduces. Above an average pool temperature of 1,568 °C, the isotherm starts to cross the bottom boundary, causing a section along the hearth bottom surface to be sub-saturated. The particle rich layer becomes non-existent at this particular location.

FIGURE 4.13. Solid holdup distribution along hearth bottom for various average pool temperatures.

FIGURE 4.13 shows the distribution of solid holdup along the hearth bottom for cases (i) to (vii). As shown, the solid holdup near the left corner region along the hearth bottom is consistent at around 0.3 wt% for any case. However on the right corner region, the solid holdup increases, as the average pool temperature increases up to 1,519 °C, then decreases significantly when the temperature further increases. Such a trend can also be seen in terms of the average solid holdup along hearth bottom (FIGURE 4.14).

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As the average pool temperature increases, the average solid holdup along the hearth bottom increases until a certain temperature is reached, and then rapidly decreases when the pool temperature increases further. Here, the increasing and decreasing trends of the average solid holdup are due to different mechanisms. Firstly, the decreasing trend can be explained through the shifting of the equilibrium temperature isotherm as an effect of the pool temperature. As mentioned above, the equilibrium temperature isotherm crosses the bottom boundaries when the average temperature of the pool is high (FIGURE 4.12(vi) and (vii)). The hot metal at the portion of the hearth bottom, where the isotherm lies underneath the liquid-refractory boundary, is sub-saturated and hence no particle formation occurs here. Therefore the solid holdup along the hearth bottom reduces significantly at high average pool temperature. Secondly for the increasing trend, the mechanism is explained through FIGURE 4.15. The figure focuses on the chemical reaction behaviours for cases (i) and (iv) where the red coloured region shows the location where particles undergo solidification reaction, and the blue coloured region shows that where dissolution reaction undergoes. The figure also shows a close up of these distributions along the hearth bottom at the centre. A thin layer of red region is apparent along the hearth bottom. In most cases, a layer of blue region overlays on top of this thin red layer. And as the average pool temperature decreases, or as the equilibrium temperature isotherm shifts upward, another red layer appears on top of the blue layer and increases in thickness. Generally, a solidification reaction occurs when: (a) hot metal with fixed titanium concentration flows to a cooler and hence less soluble region and; (b) hot metal at a certain location with fixed temperature, increases in titanium concentration. The solidification reaction in the thin red layer along the hearth bottom is primarily caused by the latter. The excess titanium is produced from the dissolution reaction occurring in the overlaying blue region. When the equilibrium temperature isotherm is located at a low position like in case (iv), this excess titanium is only consumed by the red region along the hearth bottom. However, like in case (i), when the isotherm is located at a high position and the red layer is thick, more of the excess titanium is consumed in the over-laying red layer leaving less for the under- laying thin layer. Therefore, the solid holdup along the hearth bottom increases as the average pool temperature increases.

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FIGURE 4.14. Average solid holdup and mean particle diameter along hearth bottom for various average pool temperatures.

FIGURE 4.15. Behaviour of particles for cases (i) and (iv) including: temperature contours, a single streamline, solidification region (red) and dissolution region (blue).

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4.4 CONCLUSION A 2D multi-phase, multi-component model is used to simulate the behaviour of titanium in the blast furnace hearth during the addition of titanium bearing materials. The model considers flow, heat transfer, chemical species transport and phase change – formation and dissolution of titanium carbide. Inlet temperature and initial titanium concentration are considered for parametric study.

Main findings:  Various variables along a streamline passing through the particle rich layer located along the hearth linings are monitored. The change in stream-wise temperature determines the solid formation and dissolution reactions, causing the particle size and titanium mass fraction to change in an inversely proportional manner. Hot metal tends to become significantly super or under- saturated in high velocity regions.  The isotherm of the equilibrium temperature, of a hot metal solution with initial titanium concentration, is found to be an excellent indicator to locate particles in the hearth.  This isotherm can be adjusted to control the particles in the hearth by either altering the titanium dosage or the hot metal pool temperature. The effects of these two parameters on the solid holdup along the hearth lining were investigated.  The use of the equilibrium temperature isotherm concept may provide significant control of titanium based particles for furnace operators during the practice of titania addition.

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CHAPTER 5 3D CFD MODEL TO SIMULATE THE TITANIUM COMPOUND BEHAVIOUR IN THE BLAST FURNACE HEARTH

5.1 INTRODUCTION The addition of titanium-bearing materials via burdening or tuyere injection has become a common measure during the critical stages of the blast furnace campaign. Such measures may promote the formation of a titanium-rich, high melting point scaffold or so called Ti(C,N) protection layer, along the eroded regions of the hearth lining and as such, which is likely to protect it from subsequent erosion. The mechanism behind this process within the hearth is complex. Bergsma and Fruehan (2001) has hypothesized such a process as follows.

(i) titanium oxide dissolves in the slag phase, (ii) titanium oxide reduces and the produced titanium enters the hot metal pool, (iii) titanium is transported close to the hearth refractory lining, (iv) Ti(C,N) particles form due to cooling and (v) Ti(C,N) protection layer forms.

In step (v), as the number of Ti(C,N) particles increases, the hot metal viscosity increases which slows the local flow. Due to the reduced mixing of hot metal, more heat is lost to the refractory. This may reduce the local temperature below the iron solidus temperature so that the Ti(C,N) rich solid protection layer is formed. As such, the process of forming a protective layer is controlled by the interaction between the flow, heat transfer and chemical reactions.

The use of Computational Fluid Dynamics (CFD) plays an important role in understanding such complex transport phenomenon, particularly when direct measurements and visualization are restricted by harsh operating conditions within the

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hearth. There are a number of studies found in literature that investigates such phenomena in the hearth using CFD modelling techniques and are described below.

Lin et al. (2009) and Lin et al. (2011) have developed a 3D model to investigate the distribution of TiC within the hearth of PK5BF. The model is built within a single- phase multi-component framework with several components including Fe, TiO2, TiC and CO although the chemical reaction involved is inconsistent to that proposed by

Bergsma and Fruehan (2001). In their model, TiO2 is inserted into the liquid iron phase.

As explained above, TiO2 reduces within the slag phase and only the produced Ti enters the liquid iron phase (Bergsma and Fruehan, 2001). In their model, natural convection and turbulence are neglected. They have presented an expression for liquid viscosity as a function of temperature which values at 2.47 Pa s at T=1550 °C which seems to be substantially higher compared to other studies which is usually set to 0.00715 Pa s.

Tomita and Tanaka (1994) has also developed a 3D model to simulate the protective layer formed within the hearth during the injection of titania from the tuyere, using a single-phase multi-component model considering Fe and Ti components. The model does not consider natural convection, chemical reactions and turbulence and uses a crude mesh. In order to simulate the protective layer, the liquid iron is set to terminate at temperatures below 1150 °C. Also the hot metal viscosity was modelled as a function of temperature and [Ti] (although the expression not stated) such that a high value is assigned at high [Ti] and low temperature in order to significantly slow down the flow. Although their work shows the build-up of solidified layer within the hearth when titanium is added to the hearth, detailed morphology that has led to the Ti rich layer was not modelled.

Recently Guo et al. (2010) investigated the behaviour of the Ti(C,N) particles in the hearth by modelling the flow and heat transfer of fluid and the solid particles in two separate phases using a Eulerian-Eulerian approach. Based on Bergsma and Fruehan (2001)’s hypothesis, they have considered inter-phase mass transfer based on the thermodynamics of key chemical reactions to simulate the solidification and dissolution of the particles. They have also provided a detailed understanding regarding the particle behaviour and its close relation with the fluid flow and heat transfer. In Chapter 4, Guo 144

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et al. (2010)’s work was expanded to investigate further details of the titanium compound behaviour in the hearth during solidification and dissolution process. It was found that the chemical reaction governing the particle growth and shrinkage is more dominated by thermodynamic equilibrium rather than chemical kinetics in the low velocity field spanning the majority of the hearth space. However, in these works the effect of natural convection was neglected and was limited to a 2D framework.

As concluded in Chapter 3, the effect of natural convection is significant on the macroscopic hot metal flow pattern within the hearth. As it can be understood from the hypothesis given by Bergsma and Fruehan (2001), the distribution of titanium and Ti(C,N) particles are strongly influenced by the hot metal flow pattern. Therefore for the purpose of investigating the distribution of titanium, Ti(C,N) particles and/or Ti(C,N) protective layer, it is critical to consider the effect of natural convection in the hearth. All the models mentioned so far have neglected the effect of natural convection. After modifying the model developed by Guo et al. (2010), Guo et al. (2009) and Guo et al. (2011) have made preliminary efforts to investigate the Ti(C,N) particles within a buoyant flow environment within the 2D, two phase model framework developed previously. However, they have used a porosity of ε = 0.35 and coke size of dp = 30 mm to characterise the coke bed. As concluded in Chapter 3 Section 3.3.5, when assigning a high coke bed permeability (ε = 0.35, dp = 30 mm), less mixing occurs within the hearth resulting with a higher under-prediction when comparing the calculated temperatures to the thermocouple readings. It is more credible to investigate the Ti(C,N) particles within the hearth using a low coke bed permeability (e.g. ε = 0.35, dp = 9.5 mm) as this results in a better agreement with thermocouple readings.

In the present chapter, based on the understanding gained relating to titanium compound formation behaviour in the Chapter 4, the challenge is taken to integrate: (1) the titanium model framework consistent to Bergsma and Fruehan (2001)’s hypothesis, (2) a model in a 3D environment and (3) a model that simulates an appropriate flow environment i.e. considering the effect of natural convection and applying appropriate coke bed characteristics. The development of such a model is described and by using the model, the behaviour of the Ti compounds is investigated within the 3D buoyant

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environment simulating realistic conditions of the hearth of PK5BF. It is aimed to address the three factors desired by furnace operators during the practice of titania addition, i.e. practicality, accuracy and fast computation.

5.2 MODEL DESCRIPTION The model description of this 3D single-phase multi-component model is described. The main idea is to combine the model formulations of the 3D flow and heat transfer model in Chapter 3 and the 2D two-phase model with phase change and chemical reaction in Chapter 4, and further simplify the model with valid assumptions based on knowledge gained in Chapter 4 regarding the morphology of the TiC particle formation. The physical definition of the model is described first, followed by the mathematical formulation and finally the numerical formulation.

5.2.1 Physical Model The physical modelling, in particular the geometry of the hearth and the configuration of the coke bed are specified.

5.2.1.1 Geometry The geometry used in the model is based on the hearth of BlueScope’s PK5BF during the time period May 1995 to August 1996 after the dislocation and dissolution of the fire brick layer (refer to FIGURE 3.1). FIGURE 5.1 shows the geometry with an eroded hearth profile where all the fire brick is eroded and the ceramic cup at z > 3 m is eroded. Such a hearth profile is kept consistent with that of Cases 3 and 4 of Panjkovic et al. (2002) except for the following points. i. The location of the taphole is lowered by 430 mm. (The taphole location of Panjkovic et al. (2002) was mistakenly set to that of PK6BF.) Compared to PK5BF, PK6BF has an extra carbon layer with thickness 430 mm added under the taphole. The correct location of the taphole is obtained from the PK5BF hearth geometry shown in Guo et al. (2008). ii. The sump depth of the hearth is lowered by 278 mm. The sump depth in the current model is 2,722 mm as opposed to that of Panjkovic et al. (2002) where 3,000 mm was used.

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FIGURE 5.1. Geometry with eroded inner hearth profile with (z, x) coordinates.

5.2.1.2 Coke bed state Coke beds of two states, sitting and floating coke bed states are simulated. FIGURE 5.2 shows the schematic of these coke bed states. For the floating coke bed state, the hearth volume is divided between the coke zone and the coke free zone. The thickness of the coke free zone along the furnace axis (i.e. x = 0, y = 0) is set to be 800 mm compared to 400 mm used in Chapter 3. For the sitting coke bed state, the coke zone occupies the whole hearth volume.

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FIGURE 5.2. Schematic of the coke bed at (a) sitting and (b) floating states.

5.2.2 Mathematical Model The mathematical model frame work is described here.

5.2.2.1 Governing Equations The governing equations required to solve the turbulent flow field of the titanium-hot metal solution are listed. The equations are in 3D and are solved in steady- state. Unlike the 2-phase model used in Chapter 4, only a single phase is considered in this model. The following equations show the continuity, conservation of momentum, conservation of energy and conservation of mass species for iron (Fe), titanium (Ti), titanium carbide (TiC) and nucleation sites (Seed) components.

[5.1]

[5.2]

where [5.3]

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[5.4]

[5.5]

In the 2D 2-phase model used in Chapter 4, TiC and Seed components are solved as a dispersed solid phase and Fe and Ti components are solved as a liquid phase. In the current single-phase model, a mixture model is applied where all components are modelled within a single fluid phase. By applying such treatment, two assumptions are applied to the model. Firstly, the inter-phase drag force and the inter-phase heat transfer are neglected. (The latter is also neglected in the 2D 2-phase model as the energy equations is solved using a homogeneous model.) Secondly, the particle-coke interaction force is neglected. In Chapter 4, it was clarified using the 2D 2-phase model (note that this is an inhomogeneous model and Li et al. (2006)’s particle-coke interaction force is used), that the velocity of the solid particles and the hot metal were identical. The solid particles are completely entrained in the hot metal flow without slip velocity. This indicates that the two assumptions hold. As found in Chapter 4 the hot metal-particle system is dilute even at particle rich regions. (maximum solid holdup is 1.3 wt% when the inlet Ti mass fraction is 0.4 wt% (FIGURE 4.5). This also supports the fact that the two assumptions hold.

In the 2D 2-phase model used in chapter 4, including the population balance equation (Equation [4.5]), a total of ten governing equations are solved simultaneously. Note that

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a homogeneous model is used for the conservation of energy equation and the conservation of mass species equation is applied to one component for each phase as the other is treated as constraints. In the current model, all components are solved within a single fluid phase, and including the third dimension of the momentum equation, a total of 9 governing equations are solved (In this case three conservation of mass species equations for three of the components are counted whilst the remaining one is treated as the constraint). This means that despite the additional dimension considered, the turbulent flow field of the titanium-hot metal solution can be solved with one less governing equation.

5.2.2.2 Turbulence model The k-ω SST turbulence model was used to determine the eddy-viscosity that is expressed as,

[5.6]

where α is a turbulence constant and S is an invariant measure of the strain rate. This is determined by solving the transport equations of the turbulence quantities i.e. turbulence kinetic energy, k, and turbulence eddy frequency, ω. The suitability of such a model in the current hearth problem is discussed in Chapter 3 Section 3.2.2.2.

5.2.2.3 Treatment of Coke Particles Since this is a porous medium problem, various treatments are applied to each of the governing equations. The resistance force, R, shown in Equation [5.2], is described by the Ergun equation (Ergun, 1952) and is expressed as follows.

[5.7]

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where is the shape factor of the coke particles (refer to TABLE 3.1). For the turbulence field, Nakayama and Kuwahara (2008)’s turbulence source terms are added to each of the k and ω equations. Thermal dispersion is considered within the diffusion term in Equation [5.4] using Yang and Nakayama (2010)’s correlation. Gunn (1987)’s radial dispersion, Deff C, is applied to describe the dispersive diffusion of Ti in the hot metal (Equation [5.5]). Details of these treatments are discussed in Chapter 3 Section 3.2.2.3 and Chapter 4 Section 4.2. These treatments are only applied to the coke zone and are programmed to switch off within the coke free zone.

5.2.2.4 Material Properties The properties for all materials used in the current model are provided in

TABLE 5.2. In particular, the stagnant thermal conductivity, λstg, is the effective thermal conductivity calculated by volume-averaging the coke and the liquid iron thermal conductivities. The molecular diffusivity of Ti in the hot metal is estimated using Li-

Chang's formula (Kosaka and Minowa, 1968) as Dm Ti = κT/8μrc, where κ is the

Boltzmann constant and rc is the atomic radius of Ti. Whilst the TiC particles are dispersed solid particles, they are treated as a fluid in the current mixture model. The dispersed solid particle like behaviour is modelled by equating its molecular diffusivity in the hot metal to zero. Since the buoyancy force due to the change in density is neglected in this mode, the density of species is assumed to be equivalent to that of the liquid iron as in TABLE 3.1. A porosity of γ = 0.35 and a characteristic coke size of dp = 9.5 mm are used to characterize the coke bed. Modifications are made to the hot metal viscosity such that it increases to an arbitrarily large value when its temperature is close to the iron solidus temperature (1150°C). This will allow the hot metal flow to stagnate, simulating iron solidification, only at regions where the temperature is below 1150°C within the liquid domain (refer to Chapter 3 Section 3.2.2.5 for details).

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TABLE 5.1. Material Properties Hot Metal Carbon content [wt-%] 3.75 Density of hot metal mixture [kg/m3] (7100-73.2[C%])-(0.828-0.0874[C%])(T-1823) (Jimbo and Cramb, 1993) Laminar viscosity of hot metal mixture [Pa.s] (3.699x10-4)e41400/RT (Gale and Totemeier, 2003) Thermal conductivity of hot metal mixture [W/m.K] 0.0158T (Maldonado et al., 2006) Heat capacity of hot metal mixture [J/kg.K] 850 (Panjkovic et al., 2002) 2 Effective diffusion coefficient of Ti [m /s] udp/Pef + Dm/τ (Gunn et al. 1987) (-7/Re) where Pef = 40-29e (Guo et al., 2008) τ = 1.2

Dm=κT/8μrc (Kosake and Minowa, 1968) where κ=1.3807x10-23J/K (Boltzmann's constant)

rc is the radius of the atom 0 Diffusion coefficient of TiC, Seed [m2/s] 6912 (Guo et al., 2008) Production rate [t/d] 2.262 (Panjkovic et al., 2002) Liquid level from hearth bottom [m] Refractories Heat capacity [J/kg.K] 1260 (Panjkovic et al., 2002) Thermal conductivity of BC7S [W/m.K] 12.0, T≤30°C (Panjkovic et al., 2002) 13.5, T=400°C 15.5, T≥1000°C Thermal conductivity of firebrick [W/m.K] 2.35 (Panjkovic et al., 2002) Thermal conductivity of ceramic cup [W/m.K] 2.20, T≤400°C (Panjkovic et al., 2002) Coke Bed Coke bed state Sitting, Floating Coke free gutter height along hearth axis [mm] 800 (for floating coke bed state) Harmonic mean particle size [mm] 9.5

Shape factor [-] 0.39logdh+1.331 (Ichida et al., 1991) Bed porosity [-] 0.35 Coke internal porosity [-] 0.45 (Maldonado et al., 2006) Thermal conductivity [W/m.K] [0.973+(6.34x10-3)T] (1-ζ2/3) (Kasai et al., 1993)

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5.2.2.5 Inter-phase Mass Transfer Rate The last term in Equation [5.5] is the mass transfer rate between the liquid Ti and solid TiC particle. Presuming that the solid TiC particles are spherical and as the titanium solution (hot metal) convects around the solid sphere, the mass of Ti transfers through the surface boundary layer between the continuous and particle phases. The rate of mass transfer from the particles to the surroundings can be described as follows,

[5.8]

where Aαβ is the interfacial area density, ds is the TiC particle diameter, DTi is the diffusion coefficient of Ti in the hot metal pool and Sh is the Sherwood number. YTi’ and YTi are the Ti concentration at the particle surface and far away from the surface, respectively. The former is solution for conservation of mass species equation for Ti component. The latter is determined through thermodynamic calculations. Here, chemical equilibrium is assumed since the chemical reaction rate is high at high temperatures (Guo et al., 2010). The chemical reaction was considered according to Equation [5.9]. This is a reversible process where a forward reaction describes a solidification process and a backward reaction describes a dissolution process.

[5.9]

The corresponding free energy is,

[5.10]

Assuming that the hot metal is saturated with carbon, the equilibrium constant is reduced as follows, where YTi’ can be determined. A detail derivation is provided elsewhere (Guo et al., 2010).

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[5.11]

where aTiC(s) is the activity of TiC equated to 1 and fTi is the activity coefficient of Ti in liquid iron and is expressed as logfTi=6890/T-5.41. The mass transfer rate for TiC is calculated through the relation according to the stoichiometric relation of Equation [5.9].

5.2.2.6 Treatment of TiC Crystallization and Particle Growth As mentioned in Section 5.1, once the hot metal reaches the cooler regions of the hearth, the crystallization of Ti(C,N) occurs. Now within the hearth, the process of the crystallization either initiates through nucleation on coke particles, on hearth walls and/or on suspended fine debris (e.g. ash, coke fine, coal, slag etc). For the latter, the formed crystals themselves are suspended within the hot metal and crystal growth occurs as they are carried further towards a cooler region. This means that from a numerical perspective, in either nucleation process mentioned above, Ti(C,N) species are not to be inserted from the inlet, however are to be created somewhere at some time within the liquid domain where the formed Ti(C,N) particles may undergo growth or shrinkage, and to eventually form a spatial distribution of both Ti(C,N) concentration and Ti(C,N) particle size.

Similarly to Chapter 4 in the current work, only the nucleation on the suspended fines are considered. Under such assumptions, the above mentioned process is modelled by using a “variable size model” (Guo et al. (2011)). This is when inert seeds, acting as suspended nucleation sites, are injected from the inlet where the TiC crystal grows onto them as they are carried to the cooler regions of the hearth. The number of seeds inserted is specified as an inlet boundary condition. Since the inert seeds are not created or destroyed within the steady flow process, the number of seeds is conserved within the control volume. Further, since the TiC species only forms on the seeds, the number of formed particles is also conserved within the control volume. This means that in this model, the number of particles at any given time during the process is fixed. Such

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conditions can be described by the population balance equation. The steady-state form is expressed as,

[5.12]

where n is the particle number density per unit volume of hot metal.

In terms of the particle structure, it is presumed that the TiC species grows onto the spherical seeds forming the TiC particle with a spherical shape. In Chapter 4, this is modelled by introducing the correlation shown in Equation [4.6]. However the formula is based on a 2-phase model framework and must be modified to accommodate in the current single phase model framework. The expression of the particle size, d, with respect to the flow field in the current model framework is derived as follows.

The current single phase framework consists of four species, iron (Fe), titanium (Ti), titanium carbide (TiC) and seed. FIGURE 5.3 shows the schematic of these four components where one TiC particle is present.

FIGURE 5.3. Schematic diagram of the “Variable Size Model”.

Within this single phase model, we have the relation:

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[5.13]

Within the four components, the volume fraction of the particle can be expressed as:

Where n is the particle number density. Since , we have:

Now in order to eliminate n, the following relation can be made.

Here, it is assumed that there exists no buoyancy force due to density difference between the particles and hot metal and hence densities of all species are assumed equal.

Therefore vfc=mfc. Then the correlation between d and the flow field can be expressed as:

[5.14]

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5.2.3 Numerical Model The numerical model is described here starting with the meshing, boundary conditions, simulation strategy and convergence criteria.

5.2.3.1 Meshing FIGURE 5.4(a-b) shows the meshing of the 3D hearth geometry for the liquid and solid domains, respectively. Here, unlike the 2D slot model used in Chapter 4, and the 3D symmetrical model used in Chapter 3, the computational domain of the full 3D hearth is considered and meshed. Similar to the mesh for the model generated in Chapter 3, the liquid and solid domains are meshed separately and are connected together via the General Grid Interface (GGI) attachment method. The solid domain is meshed using unstructured tetrahedral elements and the liquid domain is meshed using a fully structured hexahedral elements. Fine inflations were added to all interfacial boundaries in the liquid domain with a first layer thickness of 2 mm (FIGURE 5.4(a)). A total of 3.5 million elements are used.

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FIGURE 5.4. Meshing of the (a) liquid domain and (b) solid domain for PK5BF.

5.2.3.2 Boundary Conditions For the inlet, the following boundary conditions are specified. . Temperature is 1550°C. . Productivity is 6912 t/d with a peripheral dripping pattern where hot metal enters

within the region .

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. Various Ti mass fractions are investigated ([Ti]in = 0.4 wt% for the base case), where the specified Ti mass fraction is applied throughout the whole inlet area. . TiC mass fraction is zero. 3 . Seed mass fraction is nπdo /6. 10 . Particle number density is 110 .

. Seed diameter, do, is 10 μm.

For the outlet Pressure is 1 atm.

For the external walls, the following boundary conditions were specified. . Temperature of bottom external wall corresponds to the temperature of the bottom thermocouple layer. . Temperature of the side external wall corresponds to the temperature of the side thermocouples. . Temperature of the bottom corner edge is 25 °C. . Temperature of the corner regions of the external wall is linearly interpolated from the temperature at the corner edge to the outer and lower thermocouple temperatures of the bottom and side of the thermocouple layers.

5.2.3.3 Simulation Strategy TABLE 5.2 shows the simulation sequence. The model is simulated in such a way that first, only the continuity, momentum and energy conservation equations are solved. The flow field is then validated against the measured thermocouple data. The obtained pressure, velocity, turbulence and temperature fields are fixed and within these fields, the conservation of mass species equations and the population balance equation are solved. The advantage of running the model in such a way is that the number of equations to solve simultaneously can be reduced and hence the simulation time can be reduced significantly.

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TABLE 5.2. Simulation Sequence Block A: Fluid Field Continuity equation (Equation [5.1]) Conservation of momentum equation: x (Equation [5.2]) Conservation of momentum equation: y (Equation [5.2]) Conservation of momentum equation: z (Equation [5.2]) Conservation of energy equation (Equation [5.4])

Block B: Mass Species Conservation of mass species equation: Ti (Equation [5.5]) Conservation of mass species equation: TiC (Equation [5.5]) Conservation of mass species equation: Seed (Equation [5.5]) Conservation of mass species equation: Fe (Equation [5.5]) Population balance equation (Equation [5.12])

The above simulation strategy brings about the assumption that the presence of TiC particles has no effect on the hot metal flow and its temperature. These assumptions are reasonable and can be applied to the model with little influence on the results, as the particles involved in the model is small (up to 100 μm) and the concentration of the particles is low (up to 1 wt%).

In order to compare the time taken to solve the current single-phase model framework to the two-phase model framework used in Chapter 4, the two-phase model framework was executed in the 3D field with natural convection. Using 8 CPUs run in parallel, due to the slow reduction of residual and numerical instabilities, the desired convergence criteria was not achieved after running the mode for more than 1 month. For the current model framework with corresponding conditions, as long as the flow field is solved, i.e. BLOCK A which is already solved in Chapter 3, the time taken to attain convergence is found to be about 1 day. Therefore, in a 3D environment with natural convection, the current model framework was found to be at least 30 times faster compared to the two-phase model framework.

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5.2.3.4 Convergence Criteria The convergence criteria are set so that (i) Root Mean Square (RMS) residuals for all equations fall below a level of 10-6, (ii) temperature at monitoring points set throughout the computational domain becomes insensitive to the residuals and (iii) the vector plots were inspected to clarify their validity.

5.3 RESULTS AND DISCUSSION Simulations are conducted using the model explained above. In this section, the simulation results are presented and are discussed. Three parts will be considered starting with the validation of the model followed by the description of the general flow features and finally the effect of inlet titanium mass fraction is discussed.

5.3.1 Model Validation As a measure to check the validity of the model, calculated temperatures were compared against measured thermocouple temperatures. These thermocouples are positioned within the carbon ceramics of the hearth in layers, namely, bottom, middle and top layers (FIGURE 5.1). The temperatures of the thermocouples are provided by Panjkovic et al. (2002) for their cases corresponding to the eroded hearth profile with sitting and floating coke bed states. FIGURE 5.5 shows the comparisons between the calculated and thermocouple temperatures for the three layers for sitting floating coke bed states. Note that the bottom layer corresponds to the external boundary of the model and its temperature corresponds to the bottom layer thermocouples. It can be seen that for both sitting and floating coke bed states, for the top and middle thermocouple layers, reasonably good agreement is met between the calculated and measured temperatures particularly towards the hearth center (x = 0, y = 0). In fact when comparing these temperatures to the calculated temperatures for Cases C and D for the 3D symmetrical model used in Chapter 3 (Section 3.3.1.1) as shown in FIGURE 3.5, the temperature profiles are identical. Here, the difference between the two is the fact that a full 3D model is used as opposed to the symmetrical 3D model used in Chapter 3. Also for the floating coke bed state, the height of the coke free layer is 400 mm higher at the furnace axis (x = 0, y = 0) compared to that used in Chapter 3. This indicates that the symmetry

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assumption used in the model for Chapter 3 is valid and the effect of height of the coke free layer on the refractory temperature is insignificant.

FIGURE 5.5. Comparison between calculated and measured thermocouple temperatures for sitting (left) and floating (right) deadman states.

5.3.2 General Flow Features The distribution of the flow, temperature and mass species are shown in this section. Results for BLOCK A (flow and temperature distributions) are described first followed by the results for BLOCK B (species distribution) for sitting and floating coke bed states.

5.3.2.1 BLOCK A: Distribution of flow and temperature FIGURE 5.6(a-c) shows the temperature contours, velocity vectors and streakline plots along the hearth symmetry, FIGURE 5.7(a-b) shows the planar view of the velocity vectors and streakline plots at the taphole level and FIGURE 5.8(a-b) shows a 3D view of the temperature along the inner hearth surface and the streamlines for both sitting and floating coke bed states. Generally in the current full 3D model for both 162

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sitting and floating coke bed states, all flow features identified in the symmetrical 3D model for Cases C and D (Chapter 3 Section 3.3.2) are observed (FIGURES 5.6 - 5.8). These include particular features formed as a result of the induction of natural convection such as: the downward jet along side walls (FIGURE 5.8(b)); the quasi- stagnant zone at the bottom corner region under the taphole in the sitting coke bed state (FIGURE 5.6(b-c)-left) and at the bottom core region of the coke zone in the floating coke bed state (FIGURE 5.6(b-c)-right); and the pair of symmetrical large scale recirculation zone in the floating coke bed state formed within the coke free zone which is driven by the downward jet near the non-porous side walls (FIGURE 5.8(b)-right). Since the flow patterns of the symmetrical and full 3D models are almost identical, the symmetry assumption used in chapter 3 is applicable for the current problem. In the current full 3D model, the macroscopic flow pattern can be visualized more clearly. Particularly for the case of the floating coke bed state, both pairs of the symmetrical large scale recirculation zone within the coke free zone are apparent (FIGURE 5.8(b)- right). Within the coke free zone, it can be seen that the flows along the wall travelling peripherally towards the taphole from either side collide at the region under the taphole and then consequently redirect away from the taphole along the hearth symmetry plane (FIGURE 5.8(b)-right). Such behaviour partly causes the symmetry for each pair of the recirculation zone.

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FIGURE 5.6. (a) Temperature contour, (b) velocity vector and (c) streakline plots along the symmetry plane of the hearth for sitting (left) and floating (right) coke bed states.

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FIGURE 5.7. Planar view at taphole level of (a) velocity vector and (b) streakline plots for sitting (left) and floating (right) coke bed states.

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FIGURE 5.8. 3D view of (a) temperature distribution along inner hearth refractory surface and (b) streamlines plot for sitting (left) and floating (right) coke bed states.

Although the flow and heat transfer within the hearth for this eroded geometry for sitting and floating coke beds are detailed in Chapter 3 Section 3.3.2, the following points are again emphasized as this plays an important part in the distribution of TiC particles which will be discussed in the following sections.  In a sitting coke bed state: The overall velocity within the hearth is low, particularly at the hearth bottom region where quasi-stagnant zone exists (FIGURE 5.6(b-c)-left). For this reason, the high temperature liquid iron entering the hearth mixes less frequently throughout the hearth volume. As a result, particularly at lower regions within the pool, conduction becomes more predominant compared to convection (i.e. Peclet number < 1), where heat transfers via conduction from the liquid iron to the surrounding refractories causing local liquid iron temperature to reduce (FIGURE 5.6(a)-left). Consequently, the volume average hearth temperature reduces to 1500.4 °C and the inner hearth surface temperature is substantially

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lower compared to the floating coke bed state (The average temperature of the hearth bottom is 1275.5 °C) (FIGURE 5.8(a)-left).  In a floating coke bed state: The liquid iron at the inlet flows directly into the coke free zone where the pair of symmetrical large scale recirculation zone exists (FIGURE 5.8(b)- right). As a result, the high temperature liquid iron entering the hearth mixes strongly throughout the hearth volume, where convection becomes more predominant than conduction (i.e. Peclet number > 1), causing the volume average hearth temperature to be high at 1532.9 °C (FIGURE 5.6(a)-right). This leads to a higher inner hearth surface temperature compared to the sitting coke bed state (the average temperature of the hearth bottom is 1504.4 °C) (FIGURE 5.8(a)-right).

5.3.2.2 BLOCK B: Distribution of particles and species The results for BLOCK B are presented first in the sitting coke bed state followed by the floating coke bed state. Here, similar to the previous chapter, the term solid holdup is used and is defined by:

[5.15]

where ε is the volume porosity and YTiC is the mass fraction of TiC. Note this solid holdup expression differs to [4.11] applied in the 2D two-phase multi-component model

(refer to Chapter 4) where the solid volume fraction vfdispersed solid is included. Within the terminology of current 3D single-phase multi-component model, YTiC is the mass fraction of TiC which is a component mixed with others within a common phase.

Therefore vfdispersed solid is disregarded. Nevertheless, Equations [4.11] and [5.15] both appropriately describes the solid holdup for their respective models i.e. 2D two-phase multi-component model (Chapter 4) and 3D single-phase multi-component model (Chapter 5) respectively.

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5.3.2.3 In a Sitting Coke Bed State FIGURE 5.9(a-c)-left shows the contour plots of the solid holdup, mean particle diameter and titanium mass fraction along the hearth symmetry in a sitting coke bed state. In the sitting coke bed state, it can be seen that the solid TiC particles are dynamically held up in the cooler regions of the hearth i.e. along the hearth bottom and in the corner region under the taphole, and the maximum solid holdup is found to be 0.18 % (FIGURE 5.9(a)-left). The mean particle diameter is larger also along the hearth bottom and in the corner region under that taphole with a maximum mean particle diameter of 99 μm (FIGURE 5.9(b)-left). The contour lines of the Ti mass fraction are distributed in an opposite manner to those of the Solid holdup. (The mass fraction is higher at the top (at the warm regions) and lower towards the bottom corner region under the taphole (cooler region)). Since under thermodynamic conditions the solubility of Ti in the hot metal reduces as the temperature reduces (FIGURE 4.6), the forward reaction of Equation [5.9] takes place as the hot metal flows towards the cooler regions of the hearth where Ti is consumed and TiC is produced. Therefore the Ti mass fraction is low and Solid holdup (or the TiC mass fraction) is high at the bottom corner under the taphole. The reverse is also true when the hot metal flows towards the warmer regions of the hearth, where the backwards reaction of Equation [5.9] takes place and TiC is consumed and Ti is produced.

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FIGURE 5.9. (a) Solid holdup, (b) mean particle diameter and (c) Ti mass fraction contour plots along the symmetry plane of the hearth for sitting (left) and floating (right) coke bed states.

The formation and dissolution behaviours of TiC particles can be understood when viewing the solid holdup contour plot (FIGURE 5.9(a)-left) together with the streamline and the temperature contour plots (FIGURE 5.6(a-c)-left and FIGURE 5.8(a- b)-left). Firstly, the hot metal entering the hearth from the hearth periphery is carried down along the side wall in the downward jet towards the bottom corner, then flows horizontally towards the taphole direction along the hearth bottom. As the hot metal approaches the region at the bottom corner under the taphole, the temperature decreases significantly (FIGURE 5.6(a)-left and FIGURE 5.8(a)-left). Here, the solubility of Ti in the hot metal decreases, where the mean particle size increases i.e. particle growth occurs (FIGURE 5.9(a-b)-left). Now passing the region at the bottom corner under the taphole, the hot metal redirects and flows upwards towards the taphole. Here, the temperature increases and hence the solubility of Ti in the hot metal also increases. As a consequence, the mean particle size decreases i.e. particle shrinkage occurs (FIGURE 5.9(b)-left), until complete dissolution by the time the taphole is reached.

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When comparing the distributions of solid holdup for the current 3D single- phase model (FIGURE 5.9(a)-left) to the 2D two-phase model used in the previous chapter (FIGURE 4.5(d)), it can be seen that particle rich layer along the hearth bottom is much thicker in the current model. This is despite the fact that in the 2D two-phase model, the thickness of the ceramic cup layer is 200 mm thinner and the bottom external boundary temperature is set substantially lower at constant 70 °C compared to the current 3D single-phase model as presented as “” in FIGURE 5.5. The reason is mainly due to the fact that natural convection is neglected in the 2D two-phase model. When natural convection is neglected, forced convection driven flow occurs throughout the hearth volume and over-predicts the degree of mixing occurring in the hearth where convection becomes more dominant form of heat transfer compared to conduction (i.e. Peclet number > 1 for the majority of the hearth volume). As a result, the volume average hearth temperature becomes high which reduces the solubility of Ti in the hot metal and hence causes the particle rich layer to be much thinner.

Since it is desirable to form the Ti(C,N) protective layer along the hearth surface, the solid holdup and the mean particle diameter along the hearth surface for the sitting coke bed state is presented in FIGURE 5.10-left. As shown, the solid particles are held up along the entire hearth bottom, entire surface of the bottom step (both horizontal and vertical surfaces) and partially on the second and third steps and the side walls near the taphole. It can be seen that the solid holdup and the mean particle size gradually increase towards the bottom corner region under the taphole (FIGURE 5.10(a- b)-left). The similarity of the contour lines distributions along the inner hearth surface of the solid holdup (FIGURE 5.10(a)-left) and the temperature (FIGURE 5.8(a)-left) shows that the solid TiC particle formation and its distribution strongly coupled to the temperature.

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FIGURE 5.10. 3D view of (a) solid holdup and (b) mean particle diameter along the inner surface of the hearth refractory for sitting (left) and floating (right) coke bed states.

5.3.2.4 In a Floating Coke Bed State FIGURE 5.9(a-c)-right shows the contour plots of the solid holdup, mean particle diameter and titanium mass fraction along the hearth symmetry and FIGURE 5.10(a-b)-right shows the contour plots of the solid holdup and mean particle diameter along the inner hearth surface for the floating coke bed state. In contrast to the case of sitting coke bed, there is almost no trace of TiC particles are found within the entire hearth volume when the coke bed is floating (FIGURE 5.9(a)-right). As shown, almost throughout the hearth volume the solid holdup is close to zero, the mean particle diameter is 10 μm and the titanium mass fraction remains at the value as inserted at 0.4 wt% (FIGURE 5.9(a-c)-right). Along the inner hearth surface, very limited traces of TiC particles exist on the upper step on either side of the taphole, with a maximum solid holdup of 0.011% and maximum mean particle diameter of 41 μm (FIGURE 5.10(a-b)- right). The reason for the absence of particles is that the flow in the coke free zone has significantly enhanced hearth mixing, maintaining the hearth temperature well above 171

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the 0.4 wt% Ti-Fe-C equilibrium temperature, so that solidification reaction is not possible. This has caused only titanium to exit the hearth where no solid TiC particles are formed within the hearth.

5.3.3 Effect of Inlet Titanium Dosage on the Distribution of TiC Particles within the Hearth Volume In Chapter 4 in Section 4.3.4, the effect of inlet titanium mass fraction was investigated in the 2D two-phase model. Here, this is repeated in the current 3D single- phase model. The following five cases, each with different inlet titanium mass fraction, are investigated for each of the sitting and floating coke bed states.

Case (a) [Ti]in = 0.2 wt%

Case (b) [Ti]in = 0.4 wt%

Case (c) [Ti]in = 0.8 wt%

Case (d) [Ti]in = 1.2 wt%

Case (e) [Ti]in = 2.0 wt%

FIGURE 5.11 shows the solid holdup contour plots along the hearth symmetry plane for various inlet titanium mass fractions for sitting and floating coke bed states. For convenience, the contour plots in FIGURE 5.9(a) are repeated here as FIGURE 5.11(b). The equilibrium temperature isotherms for each of the hot metal solution containing various titanium mass fractions are also presented. The relation between the equilibrium temperature and the mass fraction of titanium can be found in the Ti-Fe-C phase diagram shown in FIGURE 4.6. The effect of inlet titanium mass fraction will be discussed first in the sitting coke bed state followed by that in the floating coke bed state.

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FIGURE 5.11. Solid holdup contour plots along the hearth symmetry plane when inlet

titanium mass fraction set to (a) [Ti]in = 0.2 wt%, (b) [Ti]in = 0.4 wt%, (c) [Ti]in = 0.8 wt%,

(d) [Ti]in = 1.2 wt% and (e) [Ti]in = 2.0 wt% for a sitting coke bed state (left) and floating coke bed state (right). Red line indicates the equilibrium temperature isotherm for the corresponding titanium concentration.

5.3.3.1 In a Sitting Coke Bed State For the case when the coke bed is sitting, as shown in FIGURE 5.11(a-e)-left, it can be seen that as the inlet titanium mass fraction increases, the thickness of the particle rich layer increases. The maximum solid holdup also increases as the inlet

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titanium mass fraction increases. For any case considered, the solid holdup is at its highest at the bottom corner region under the taphole.

One of the conclusions in Chapter 4 was that the equilibrium temperature isotherm can be used as a good indicator to locate the TiC particles in the hearth. It was also mentioned that no TiC particles exist in the region above the isotherm because the titanium in the hot metal is sub-saturated and conversely, the particles are formed and distributed in the region below the isotherm because at this region, the titanium in the hot metal is either super-saturated or at equilibrium. Such conclusions can also be made in the current 3D single-phase model where it can be seen that the equilibrium temperature isotherms of the hot metal for each of the inlet titanium mass fractions investigated match almost perfectly to the profile of the contour of the particle rich layer (FIGURE 5.11). Here also, for any case investigated, the titanium in the hot metal in the region above the isotherm is sub-saturated and either super-saturated or at equilibrium in the region below the isotherm. Therefore TiC particles are only held up in the region below the isotherm. It can be seen that in the region below the isotherm, solid holdup increases rapidly in the immediate location below the isotherm and are more uniform towards the surface particularly at the bottom corner below the taphole. The equilibrium temperature isotherm is not present for the case with [Ti]in = 2.0 wt% because the corresponding equilibrium temperature is above 1550 °C (refer to FIGURE 4.6). This means that the hot metal in the whole hearth volume is either super-saturated or in equilibrium with titanium and hence particles are formed immediately once entering the hearth. In this case, large quantities of TiC particles are expected to be tapped out which may result with titanium rich scaffold within the taphole and may cause taphole blockage.

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5.3.3.2 In a Floating Coke bed State When the coke bed is floating, for cases (a) to (c), no particles are formed throughout the hearth volume (FIGURE 5.11). Solid holdup appears when the inlet titanium mass fraction reaches 1.2 wt% (case (d)) and increases as the inlet titanium mass fraction increases. For cases (c) and (d), it can be seen that a sudden jump in solid holdup is observed at the bottom surface of the coke bed where it increases rapidly from the coke zone to the coke free zone. Since the solid holdup is a function of the volume porosity (Equation [5.15]), and the volume porosity changes from 0.35 in the coke zone to one in the coke free zone, the solid holdup increases suddenly from the coke zone to the coke free zone. For case (e), the maximum solid holdup in the hearth volume of the floating coke bed is higher compared to that when the coke bed is sitting. This is the only case where the solid holdup is greater than the sitting coke bed state. The maximum solid holdup for case (e) when coke bed is floating is 1.5 wt% and is located in the coke free zone.

As mentioned above, the particle formation behaviour is influenced by the temperature field and the distribution of the particles can be determined by viewing the location of the equilibrium temperature isotherm of the respective cases. For cases (a) to (c), due to the rapid mixing of hot metal and hence the high volume average hearth temperature, the equilibrium temperature isotherm is shifted out of the pool to the refractory region. This indicates that the hot metal throughout the hearth volume is sub- saturated and hence no particles are formed. For case (d), the equilibrium temperature is much higher compared to cases (a) to (c) and hence its isotherm is located within the pool or even higher up to the coke zone. As a result the majority of titanium in the hot metal within the coke free zone is either super-saturated or in equilibrium. The TiC particles formed are carried throughout the zone via the large scale re-circulating flow. For case (e), since the equilibrium temperature is greater than the inlet hot metal temperature (1550 °C), the titanium in the entire hearth volume is either super-saturated or in equilibrium. TiC particles are formed immediately upon entry and exit the hearth via the taphole in its solid state.

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5.3.4 Effect of Inlet Titanium Dosage on the Distribution of TiC Particles along the Inner Hearth Surface FIGURE 5.12 shows the contour plots of the solid holdup along the inner hearth surface for the five cases, cases (a) to (e). Here, the contour plots in FIGURE 5.12(a-b) are repeated as case (b). FIGURE 5.13 shows the average solid holdup, average mean particle size and the area converge of the particles along the inner hearth surface. In particular, the latter is defined as the area along the inner hearth surface where solid holdup is greater than 0.05 wt%. The sitting coke bed state will be discussed first followed by the floating coke bed state.

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FIGURE 5.12. Solid holdup contour plots along the inner hearth surface when inlet titanium mass fraction set to (a) [Ti]in = 0.2 wt%, (b) [Ti]in = 0.4 wt%, (c) [Ti]in = 0.8 wt%,

(d) [Ti]in = 1.2 wt% and (e) [Ti]in = 2.0 wt% for a sitting coke bed state (left) and floating coke bed state (right).

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FIGURE 5.13.(a) Surface average solid holdup, (b) surface average mean particle diameter and (c) area coated along the inner hearth surface for sitting (left) and floating (right) coke bed states.

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5.3.4.1 In a Sitting Coke Bed State For the sitting coke bed state, it is observed qualitatively from the contour plots that as the inlet titanium mass fraction increases, the solid holdup along the inner hearth surface increases and the area of particle coverage also increases (FIGURE 5.13). It can be seen that for case (a), the TiC particles cover less than half of the hearth bottom surface with a maximum solid holdup of 0.08 wt% and on the other hand for case (e), the particles cover the entire inner hearth surface with a maximum solid holdup of 1.14 wt%. From a quantitative perspective as in FIGURE 5.13, it can be seen that the solid holdup and the mean particle size increase almost linearly with the inlet titanium mass fraction. In terms of the coverage area of the solid particles along the inner hearth surface, as the inlet titanium mass fraction increases, the coverage area increases rapidly then it slowly approaches its maximum at 168.65 m2 which is the total inner hearth surface area. In particular, when the inlet titanium mass fraction is around [Ti]in = 0.8 wt% (case (c)), the behaviour of the particles is quite desirable. Particles distribute in the majority of the inner hearth surface (almost 75%) whilst avoiding taphole clogging as no particles are observed in the taphole region. Furthermore, since the particles cover the surface of the bottom corner region, it may benefit in preventing the elephant foot type erosion.

5.3.4.2 In a Floating Coke bed State For the floating coke bed state, as expected from the view along symmetry plane in FIGURE 5.11, no TiC particles are found along the inner hearth surface for cases (a) to (c) (FIGURE 5.12(a-c)-right). For case (d), a small portion of TiC particles with solid holdup of around 0.2 wt% covers the surface of the side walls near the upper most step and at the hearth bottom (FIGURE 5.12(d)-right). For case (e), the TiC particles cover most of the entire hearth surface particularly within the coke free zone with a maximum solid holdup of 1.5 wt% (FIGURE 5.12(e)-right). The distribution of solid holdup along the hearth surface in the coke free zone is mostly uniform due to the enhanced mixing of liquid occurring within the zone as a result of the pair of the large scale recirculating flows. The surface average of solid holdup and mean particle diameter and also the area coverage of particles along the inner hearth surface increases as the inlet titanium mass fraction increase (FIGURE 5.13(a)-right). It is interesting to see that, unlike linear

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increase found in the sitting coke bed state, the surface averaged solid holdup increases almost exponentially with inlet titanium mass fraction (FIGURE 5.13(b)-right). A rapid increase is also observed for surface averaged particle diameter at around [Ti]in = 0.8 wt%. For the area coverage of the TiC particles, it increases rapidly at [Ti]in = 0.8 wt% then slowly approaches its maximum (inner hearth surface area) (FIGURE 5.13(c)- right).

5.4 CONCLUSION A full 3D single-phase CFD model is developed to investigate the Ti compound behaviour in the blast furnace hearth of PK5BF. The model considers hot metal flow with natural convection, conjugate heat transfer, species transfer, thermodynamics, variable particle size and key chemical reaction that follows the Bergsma and Fruehan (2001)’s hypothesis. Compared to the two-phase model framework as used in Chapter 4, several simplifications are implemented and it was achieved to reduce the calculation time by more than 30 times. The model agrees well with thermocouple readings. General flow features are described for the sitting and floating coke bed states. The equilibrium temperature isotherm of the titanium-hot metal solution matches well with the solid holdup profile. The effect of inlet titanium mass fraction is investigated. For a sitting coke bed, as the inlet titanium mass fraction increases, the particle rich layer thickness, its area coverage along the inner hearth surface, the solid holdup and the particle diameter all increase. For a floating coke bed, almost no particles are found for inlet titanium mass fraction at and below [Ti]in = 0.8 wt%. However the solid holdup, particle diameter and its area it covers along the inner hearth surface all increase with inlet titanium mass fraction above [Ti]in = 1.2 wt%.

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CHAPTER 6 TRANSIENT 3D CFD MODEL TO PREDICT THE DISTRIBUTION OF TITANIUM COMPOUNDS IN A BLAST FURNACE HEARTH DURING TITANIA INJECTION FROM TUYERE

6.1 INTRODUCTION The addition of titanium-bearing materials into the blast furnace during the critical stages of the furnace campaign is a common preventative measure conducted by integrated steel mills since 1960’s when titanium-rich scaffolds were discovered in dissected blast furnaces (Bergsma and Fruehan, 2001). It is understood that this may promote titanium-rich, high melting point scaffolds or so called Ti(C,N) protection layer, along the surface of the eroded hearth linings, preventing it from further erosion. There are generally two techniques to insert the titanium-bearing materials into the blast furnace: (i) addition of titania in the form of titanium containing ore/pellets/sinter/briquettes via burdening from the top of the blast furnace or (ii) addition in the form of pulverised titania via injection through the tuyeres. The latter is a preferred technique conducted in industry in recent years. This is because in the burdening approach, when titanium bearing materials is added in excess, the titanium oxide concentration within the slag increases causing its viscosity to increase (Kurunov et al., 2006). Further, the formation of solid deposits within the slag may lead to clogging of the taphole (Guo et al., 2010). These adversities cause difficulties in the liquid removal process and hence adversely affect the operation of the furnace. In comparison, the tuyere injection approach has the following advantages. (a) The Ti(C,N) protective layer can preferably be formed in any section of the hearth where the eroded lining exists, (b) the viscosity increase of the slag only occurs within a small section of the hearth, (c) the thermal loads on the hearth walls can be reduced quickly and (d) the consumption of titanium-bearing raw materials can be minimised (Kurunov et al., 2007).

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With respect to the tuyere injection approach, in order to effectively form a Ti(C,N) protection layer at the eroded regions of the hearth lining, the following points are necessary:

 To accurately predict the flow and temperature distribution of the hot metal in the hearth. By doing so, the specific trajectory that passes in the vicinity of the eroded region can be predicted, and by tracing it upstream, the appropriate tuyere can be selected for the injection of titania.

 Further understand the transport phenomena during the process from the point of injection at the tuyere to the point of formation of Ti(C,N) protection layer at the lining surface. By doing so, the most suitable local conditions for the formation of the Ti(C,N) protection layer can be better understood. This includes details such as Ti concentration and temperature as well as time required to form the Ti(C,N) particles. This information may be used as guidance to quantify the optimum operational conditions for titania injection such as the rate of injection and quantity (or duration) of titania injection.

 Since the injection is conducted during blast furnace operation, the operational condition must be accounted for. In particular, casting conditions such as the tapping duration and scheduling of the tapping cycle must be considered.

Along with increasing computer capability and as the use of high performing computers (HPC) is becoming readily available, CFD modelling is further recognized as a powerful tool, where it is becoming possible to simulate the complex in-hearth phenomenon. In literature, a number of investigators have made an effort to simulate the behaviour in the hearth during titania addition via tuyere injection (Lin et al. 2009, Lin et al. 2011, Tomita and Tanaka 1994, Guo et al. 2010). Details regarding the model framework of these studies have been made in the previous Chapter in Section 5.1. Here, the application of the model is briefly introduced.

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Lin et al. (2009) and Lin et al. (2011) have developed a 3D single-phase multi- component model to investigate the steady-state distribution of TiC along the inner hearth surface of PK5BF during tuyere injection when TiO2 with mass fraction of 0.3 wt% is inserted locally from 135° and 180° (angle measured counter-clockwise from the taphole when viewed from the top) at the hearth inlet. Their results show a reduction of refractory temperature at regions where high TiC concentration exists along the inner hearth surface. They presented limited information regarding the description of the model framework where it is difficult to understand the reason that has led to the decrease in refractory temperature.

Tomita and Tanaka (1994) has developed a 3D single-phase multi-component model without chemical reaction and investigated the effect of Ti addition on the flow and temperature distribution of the hot metal in the hearth of Nisshin Steel’s Kure No. 1 Blast Furnace. In their model, they have locally inserted titanium with mass fraction 0.5 wt% from the hearth inlet simulating an injection of titania from a tuyere positioned at 90° from the taphole. The hot metal viscosity is modelled as a function of temperature and Ti concentration. It was found that at titanium rich regions particularly near the hearth bottom, both the local hot metal velocity and temperature decreases. As a consequence, a decrease in refractory temperature was observed at the regions close to the titanium rich regions.

Guo et al. (2010) developed a 2D two-phase multi-component model which includes the thermodynamics of key chemical reactions. The model simulates the formation of Ti(C,N) particles as well as its growth and shrinkage. As a special case, they investigated the TiC particle distribution when titanium is locally added from either side of the inlet (i.e. 0° and 180° position). In their steady-state result, they have found that when the titanium is inserted locally at the inlet opposite to the taphole (i.e. 180° position), the TiC distribution behaves similarly to that when titanium is inserted throughout the inlet.

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The CFD models mentioned above simulate the in-hearth phenomena when titania is inserted locally via tuyere injection. Apart from the fact that these models neglect natural convection which is a factor known to significantly affect the in-hearth phenomena, it is simulated in steady-state. Such analyses are limited in providing information regarding the duration of injection. In this study, the 3D single-phase multi- component model developed in Chapter 5 is further modified such that the transient behaviour of TiC particles in the hearth can be simulated when tuyere injection of titania is conducted during a single tapping cycle.

6.2 MODEL DESCRIPTION The transient 3D single-phase multi-component model is described in this section.

6.2.1 Physical Model The physical modelling i.e. geometry and coke bed state is described.

6.2.1.1 Geometry Here, the full 3D hearth geometry used in the model in chapter 5 is used (refer to FIGURE 5.1). In the current study, the behaviour of the TiC particles in the hearth is investigated when titanium is inserted locally from the inlet simulating a tuyere injection method of titania addition. Unlike the burdening method of titania addition simulated in the previous chapter, in the tuyere injection method, non-symmetrical distribution of TiC particles is expected within the hearth and use of the full 3D geometry becomes meaningful.

6.2.1.2 Coke bed state It was concluded in Chapter 5 that almost no TiC particles are formed within the hearth during titanium insertion when the coke bed is floating. Therefore in the current study, only the sitting coke bed state is considered. The schematic of the sitting coke bed state is shown in FIGURE 5.2.

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6.2.2 Mathematical Model Generally, the model framework used in the current chapter is identical to that used in Chapter 5, except for the fact that a transient analysis is conducted instead of steady-state analysis conducted in Chapter 5. Therefore, only the governing equations of the model are described here. For details of the model description, refer to Section 5.2.2.

6.2.2.1 Governing equations The following equations show the continuity, conservation of momentum and conservation of energy equations in steady-state:

[6.1]

[6.2]

[6.3]

The transient conservation of mass species for iron (Fe), titanium (Ti), titanium carbide (TiC) and nucleation sites (Seed) components is shown as:

[6.4]

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where YC is the mass fraction of the component, DeffC is the effective diffusivity of the component and is the inter-phase mass transfer rate.

The transient population balance equation is shown as:

[6.5]

[6.6]

where rs is the solid volume fraction YTiC and YSeed are the mass fractions of TiC and seed species, n is the particle number density which is a function of particle size (refer to Section 5.2.2.6 for details) and Sn is the source term related to agglomeration and breakage of particles which assumed insignificant and is neglected in the current studies.

Details regarding the turbulence model, treatment of coke particles, material properties, constitutive models, treatment of crystallization of TiC particles and particle growth are detailed in Section 5.2.2.

6.2.3 Numerical Modelling Details regarding the numerical modelling including the meshing, boundary conditions, initial conditions and the simulation strategy are described.

6.2.3.1 Meshing and Boundary Conditions The mesh applied in the model described in Chapter 5 is used. Refer to Section 5.2.3.1 for details.

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The boundary conditions were kept consistent with the model used in Chapter 5 (refer to Section 5.2.3.2 for details) except for the inlet boundary condition for titanium mass fraction.

For the inlet boundary condition for titanium mass fraction, the settings are altered depending on the type of titania addition method considered, i.e. burdening or tuyere injection. When titania addition via burdening is considered, the titanium is inserted throughout the inlet as treated in chapter 5. When titania addition via tuyere injection is considered, the titanium is inserted locally from a particular location at the inlet. The titanium insertion points are attempted from either of 30°, 60°, 90°, 120°, 150° and 180° locations at the inlet area as shown in FIGURE 6.1. Here, the angle represents that between the direction of the active taphole and the insertion point along the X-Y plane looking from above. Titanium insertion from locations between 180-360° are not considered because the distribution of formed TiC particles are expected to be a mirror image of those inserted from 0-180°. The titanium insertion at the inlet is set to cover the area of a circle with radius of 0.8 m centred on the perimeter of the inlet at the injection angle (FIGURE 6.1).

FIGURE 6.1. Location and area of titanium at the inlet for cases when titania injection from tuyere. 187

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Herein the base case, [Ti]in is set to 2.0 wt%. This is set to a higher value than that set in the model used in Chapter 5 ([Ti]in = 0.4 wt%) where titania is added via burdening.

6.2.3.2 Simulation Strategy The simulation sequence described in the previous Chapter is also used in the current model (refer to TABLE 5.2). As mentioned in Section 5.2.3.3, the model is simulated in 2 blocks. Firstly, in Block 1, only the continuity, momentum and energy conservation equations were solved. The flow field is then validated against the measured thermocouple data. Then secondly, in Block 2, only the conservation of mass species equations and the population balance equation are solved, and are based on the pressure, velocity, turbulence and temperature fields attained in Block 1.

Here, the transient behaviour of the formed TiC particles is investigated. This is treated by simulating the model in hybrid (i.e. both steady-state and transient). Block 2 is simulated in transient whereas the Block 1 is simulated in steady-state. The transient simulation in Block 2 is conducted for the one tapping cycle i.e. from t = 0 hr to 3 hrs.

By applying this treatment, the simulation time can be decreased significantly however it brings about the following assumption. The transient change in TiC particle concentration and particle size during a single tapping cycle (t = 0-3 hr) is based on the steady-state flow and temperature environment. The flow and temperature fields during a single tapping cycle, particularly at the beginning, may be different from that at steady-state. However, since the solution for Block 1 is validated, where good agreement is confirmed between measured and calculated refractory temperatures as shown in Section 5.3.1, it is expected that such effect is insignificant in the current analysis.

6.2.3.3 Initial Conditions Since the transport of mass species and its population balance are analysed in transient (Block 2 simulation), their initial conditions must be specified. The following initial conditions are set in Block 2.  Velocities: u, v and w are the same as those in the solution of Block 1. 188

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 Pressure is the same as those in the solution of Block 1.  Liquid and solid temperatures (for hot metal and refractories) are the same as those in the solution of Block 1.  Turbulence kinetic energy and turbulence eddy frequency are the same as those in the solution of Block 1.  Titanium mass fraction is zero.  TiC particle mass fraction is zero.  Seed mass fraction is set identical to its inlet condition at nπd3/6.  Particle diameter is 10 μm.

6.3 RESULTS AND DISCUSSION Since it is of interest to form Ti(C,N) protection layer along the hearth surface, the results are mainly described in terms of TiC particle concentration distribution along the inner hearth surface.

6.3.1 General Behaviour of TiC Particles There are generally two methods to add titania into the blast furnace; through burdening in the form of lump ore that contains a large proportion of titanium; and through injecting through tuyeres in the form of pulverised titania. In either method, the titanium content enters the hot metal pool in the form of fully dissolved titanium molecules. Here, the transient behaviour of the TiC particles is described, first when titania is added via burdening and second when injected through the tuyeres.

6.3.1.1 Titania addition from burdening FIGURE 6.2 shows the contour plots of TiC mass fraction particles along the inner hearth surface from t = 0–3 hrs when titanium with a concentration of 2.0 wt% is added throughout the inlet to simulate titania addition via burdening. The contour plot for the steady-state case is also presented. Here, t = 0 hr represents the point where the titanium content enters the liquid iron phase in the hearth. As it can be seen, within t = 0.5 hr, formed particles coat the majority of the hearth side walls (FIGURE 6.2(ii)). By t = 1.0 hr, the majority of the surface of the bottom step becomes coated (FIGURE 189

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6.2(iii)). The hearth bottom gradually gets coated from the hearth periphery starting from the side opposite to the taphole (FIGURE 6.2(iv-vii)). At t = 3.0 hr or at the end of 1 tapping cycle, a large area of the hearth bottom still remains uncoated (FIGURE 6.2(vii)). As shown in the steady-state case, if liquid casting continues from the same taphole, it can be seen that the particles eventually coat the entire hearth bottom surface (FIGURE 6.2(viii)).

FIGURE 6.3 shows the coating area of TiC particles, the maximum TiC mass fraction and the maximum particle size along the inner hearth surface from t = 0-3 hr. It can be seen that the coating area of TiC particles increases significantly to about 80 m2 before t = 0.5 hr, then gradually increases to 127 m2 by t = 3 hrs. For both maximum TiC mass fraction and particle size, similar trends are observed. These values quickly increase reaching their maximum by t = 1 hr and remains unchanged afterwards.

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6.3.1.2 Titania addition from tuyere injection FIGURE 6.4 shows the contour plots of TiC mass fraction particles along the inner hearth surface from t = 0 to 3 hrs when titanium with concentration of 2.0 wt% is locally added from a position located 60° angle from the taphole. This simulates the case when pulverised titania is injected from a tuyere positioned 60° from the taphole. As shown, it can be seen that the particle rich region is formed locally along the inner hearth surface and spans from the near region of the injection point to the taphole region 191

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(FIGURE 6.4). The area covered increases with time. At t = 0.5 hr, the particles coat only on the side wall where the particle rich region slants towards the taphole, following the flow direction of the hot metal, as it descends (FIGURE 6.4(ii)). It can be understood that the formed particles are carried along the flow. At t = 1.0 hr, the particle rich region spreads on the surface of the bottom step (FIGURE 6.4(iii)). From t = 1.0 to 3.0 hr, the particle rich region spreads only slightly where no significant change in TiC mass fraction and the coverage area is observed (FIGURE 6.4(iii-vii)). The distribution of particles in the steady-state case differs significantly where it spreads largely along the hearth bottom surface near the taphole region (FIGURE 6.4(viii)). This is because after an extended period of time, the formed particles slowly flow into the recirculating zone located at the bottom corner region under the taphole, at a very low velocity (of quasi-stagnant). The flow feature can be seen in FIGURES 5.6(c)left and 5.8(b)left and details are shown in Section 5.3.2.1. After running the transient case for an extended period of time, it was found that it takes about 30 hrs for the TiC mass fraction to reach steady-state distribution. This is understandable because the hot metal within the recirculation zone is quasi-stagnant.

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FIGURE 6.5 shows the coating area of TiC particles, the maximum TiC mass fraction and the maximum particle size along the inner hearth surface from the point of insertion (t = 0) to t = 3 hr. Similarly to the case when titania is added via burdening, the coating area, maximum TiC mass fraction and the particle size increases significantly until t = 1.0 hr. The maximum TiC mass fraction and the maximum particle size reaches its steady-state value at t = 1.0 hr. At t = 1.0 – 3.0 hr, the coated area increases slightly, whereas the maximum TiC mass fraction and particle size remains unchanged. The area coated at t = 3.0hr is almost half that at steady-state. This is because no particles are formed within the quasi-stagnant zone at t = 3.0 hr.

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From these analyses, according to the current simulation results, it is understood that in either method of titania addition, formed TiC particles increases significantly in mass fraction and covered area on the inner hearth surface only for the first hour. Titania addition for a prolonged time (t = 1.0 – 3.0 hr) increases the coated area slightly, but will not necessarily increase the concentration of the particles along the inner hearth surface. It should be noted that in this model framework, only dynamic holdup of TiC particles are considered. Static holdup such as the deposition of particles on packed 194

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coke particles and hearth surfaces are neglected. The concentration of TiC particles along the hearth surface is expected to increase further when static holdup is considered in the model.

6.3.2 Effect of Inlet Ti Concentration The effect of inlet Ti concentration is investigated. FIGURES 6.6 and 6.7 show the contour plots of TiC mass fraction along the inner hearth surface at t = 3.0 hr for inlet Ti concentration ranging from [Ti]in = 0.2 – 2.0 wt% when titania is added via burdening and via tuyere injection from a tuyere positioned at 60° from the taphole, respectively.

Similar trends are observed for both cases. As the inlet Ti mass fraction increases, the coverage area as well as the TiC mass fraction increases (FIGURES 6.6 and 6.7). This can also be observed quantitatively in FIGURES 6.3(i-ii) and 6.5(i-ii). The reason for such result is as follows. As the inlet titanium mass fraction increases, the local titanium mass fraction of the hot metal increases. Since the solubility limit of titanium in hot metal increases as temperature increases (refer to FIGURE 4.6), and the temperature is higher in the upper region of the hearth and lower towards the hearth bottom, the titanium in hot metal reaches its solubility limit at a higher location of the hearth when the inlet titanium mass fraction increases. Therefore a larger volume in the hearth becomes supersaturated (or in equilibrium) causing more particles to form and grow leading to a higher TiC mass fraction and a greater coverage area along the inner hearth surface.

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6.3.3 Effect of Injection Angle of Ti One of the advantages of the model, particularly in the current full 3D framework, is that the distribution of particles in the hearth when titania is injected from various tuyeres can be studied. This is important because it is necessary to inject titania from the appropriate tuyere such that the protection layer will form exactly at the damaged lining. Here, the effect of titanium injection location is investigated.

FIGURE 6.8 shows the contour plots of the TiC particles at t = 3.0 hr when titanium with [Ti]in = 2.0 wt% is locally injected from various locations at the inlet. The locations investigated are 30°, 60°, 90°, 120°, 150° and 180°. These angles correspond to the angle between the taphole and the point of injection measured counter clockwise

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along the X-Y plane. The case when titania is added via burden is also shown for direct comparison.

As it can be seen, the distribution of TiC along the inner hearth surface varies depending on where the titanium is injected at the inlet. For 30° injection, the TiC particles only distribute in a small area along the hearth side wall near the inlet between the point of injection and the taphole (FIGURE 6.8(i)). For 60 - 180° injection, the TiC particle rich region forms along the sidewall and extends all the way to the hearth bottom (FIGURE 6.8(ii-vi)). The shape of the particle rich region depends on where the titanium is inserted. For 180° injection, the particle rich region spans straight downwards from the point of injection to the hearth bottom (FIGURE 6.8(vi)). For 120° injection, the particle rich region spans downwards such that it shifts slightly towards the taphole (FIGURE 6.8(iv)). For 60° injection, the particle rich region shifts significantly towards the taphole as it spans downwards, covering a large portion along the surface of the hearth corner (FIGURE 6.8(ii)). A trend is observed that, as the titanium is inserted at a position closer to the taphole, the particle rich region along the surface shifts more towards the taphole from the point of injection (FIGURE 6.8(i-vi)). It can be understood that the particles distribution along the inner hearth surface follows the direction of the flow close the refractory boundaries (refer 3D streamlines of the hot metal flow shown in FIGURE 5.8).

For the case when titanium is added throughout the inlet, the particle rich region covers the entire hearth sidewalls, most of bottom corner and partially the bottom surface (FIGURE 6.8(vii)). Through careful inspection of FIGURE 6.8(i-vii), it can be seen that the TiC mass fraction distribution of FIGURE 6.8(vii) in the first two quadrants of the hearth (0-180° measured from the taphole in a counter clockwise direction along the X-Y plane) is similar to the TiC mass fraction distributions of FIGURE 6.8(i) to (vi) integrated together. When comparing the TiC mass fraction at any point within the particle rich region along the inner hearth surface for any local injection from any angle, 30-180° (FIGURE 6.8(i-vi)), its magnitude is somewhat identical to that at the corresponding location for the case when titanium is added throughout the inlet (FIGURE 6.8(vii)). This signifies that it is not necessary to insert titanium throughout all the inlet area (which is what occurs during a burdening 198

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approach) and the addition of titanium only at the peripheral region of the hearth inlet is enough to achieve the TiC mass fraction distribution along the inner hearth surface shown in FIGURE 6.8(vii).

FIGURE 6.8. Distribution of TiC concentration along hearth inner surface when [Ti]in = 2.0 wt% and t = 3 hr for various injection locations: (i) 30°, (ii) 60°, (iii) 90°, (iv) 120°, (v) 150°, (vi) 180° and (vii) all.

FIGURE 6.9 quantitatively shows the coating area of TiC particles along the inner hearth surface when titanium is locally inserted from various positions in the hearth. Generally, for the case of local titanium insertion (simulating a tuyere injection method of titania addition), when inserting titanium from a 30° location, TiC particles cover the least area along the inner hearth surface with a coating area of 1.06 m2. On the other hand, when inserting form a 60° location, TiC particles cover the most area along the inner hearth surface with a coating area of 10.53 m2. For the rest, i.e. 90°, 120°, 150° and 180° insertion, the coating areas are similar with an average of 8.13 m2. Obviously,

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the coating area of TiC particles along the inner hearth surface is greater for the burdening method compared to tuyere injection method of titania addition. The coating area for the burdening method (titanium inserted throughout the inlet) is found to be 122.40 m2 which is more than 70% of the area of the inner hearth surface (168.65 m2).

FIGURE 6.9. Area of TiC particles coating along the inner hearth surface at t = 3.0 hr when titanium inserted from various locations of the hearth inlet.

FIGURE 6.10 shows the maximum and average TiC mass fraction within the particle rich region formed along the inner hearth surface for various titanium addition methods. Generally, titanium insertion from 30° location leads to the lowest and insertion throughout the inlet leads to the highest TiC mass fraction along the inner hearth surface. Apart from the 30° titanium insertion, no significant change in maximum TiC mass fraction along the inner hearth surface is found with value around 2.45 wt%. Here, the maximum TiC mass fraction occurs always at the hearth bottom corner where the temperature is the lowest (FIGURE 6.8). On the other hand, the average TiC mass fraction increases as the insertion point of titanium is located further away from the taphole.

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FIGURE 6.10. Maximum and average TiC mass fraction within the particle rich region along the inner hearth surface when titanium inserted from various locations of the hearth.

Based on the above analyses, the following points are raised. I. Titania addition via tuyere injection is more efficient than burdening. This is because less titania can be used in the tuyere injection method where the damaged regions along the hearth refractory surface can be specifically coated with equivalent TiC mass fraction as with the burdening method. II. Titania inserted from a tuyere located at 30° from the taphole results with the worst outcome. Inserted titanium simply flushes out the taphole without effectively transporting the formed TiC particles to the damaged linings. Such observations were also made by Guo et al. (2010) in their 2-D, two phase model. III. When injecting titania to protect hearth lining, the following recommendations are made.  When the hot spot is located at the side wall, the injection location should be shifted slightly towards the upstream direction of the location of the hot spot. The degree of shift should be increased as the hotspot is located closer to the active taphole. Quantification of the injection location with respect to the hotspot location is presented in the following section in Section 6.3.4.  When the hotspot is located along the bottom corner and extends through a large portion of the hearth periphery, such as in an elephant foot profile, it is recommended to select the active taphole and the titania injecting tuyere

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such that they are located 60° apart. This is because at 60°, the particle rich region along the inner hearth surface covers the hearth bottom corner the most (refer FIGURE 6.8(ii)). IV. Although in the current model framework, the maximum TiC mass fraction is reached in t = 1.0 hr (FIGURE 6.5(ii)), it is recommended to inject titania for an extended period of time (Kurunov et al., 2006). When the injection duration exceeds the duration of a single tapping cycle and the active taphole changes, the tuyere selected for the injection should also be altered according to point III depending on the angle between altered active taphole and the hotspot.

6.3.4 Analysis for Sidewall Protection Through the analysis in the previous section, the radial position of the particle rich region formed along the side wall was found to deviate from the radial position of the point where the titanium is injected. Here, the degree of deviation is investigated in order to provide guidance for the selection of the titania injecting tuyere.

FIGURE 6.11 shows the average mass fraction of TiC particles along the hearth side wall for cases when Ti is inserted from various injection points. It can be seen that TiC particles are distributed on the side walls near the injection point but are shifted slightly downstream towards the taphole. For example, when injected from 90° location from the taphole (refer blue line in FIGURE 6.11), the maximum TiC mass fraction along the side wall occurs at a location at around 85° from that taphole. For this case, 5° offset between the injection point and the location of the TiC particles along the side wall is observed. The degree of the shift differs depending on the location of the injection point, due to different local liquid flow environment.

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FIGURE 6.11. Polar representation of average TiC mass fraction along hearth walls when Ti with mass fraction of 2.0 wt% is injected for a duration of t = 3.0 hr from various injection points.

In order to see its dependencies clearly, the average mass fraction of TiC particles along side walls are plotted by fixing the injection point at 0° (this is shown in FIGURE 6.12 where circles show the center location of the distributed TiC particles for each injection location and represents the degree of offset). It can be seen that the TiC particles are distributed along the side wall at a location further downstream from the injection point as the injection point is positioned closer to the taphole. This means that when hotspots are identified in the hearth wall, the titania injecting tuyere should be selected by considering a certain offset from the hotspot location.

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FIGURE 6.12. Average [TiC] distribution along hearth wall fixing 0° at location of tuyere injected. Taphole is located in the –ve direction. The taphole is located in the –ve direction

and titanium with [Ti]in = 2.0 wt% is inserted for a duration of t = 3.0 hr.

Based on the location of circles (i.e. degree of offset) in FIGURE 6.12, the location of the hotspot is correlated with the location of the selected tuyere to inject titania shown in FIGURE 6.13. The correlation provides guidance to appropriately select the titania injecting tuyere such that formed TiC particles will pass the hotspot.

FIGURE 6.13. Correlation between active tuyere location and location of hotspot.

It should be noted that current analysis is based on a hot metal flow pattern in PK5BF (’91-’09 campaign) in an inner hearth profile during 1995 where all sacrificial bricks are eroded. Since the inner hearth profile in a severely eroded hearth (e.g. final

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years of the campaign) is considerably different from that during 1995, the flow pattern within the hearth may vary and may affect the degree of offset analysed above.

6.3.5 PK5BF Titanium Injection Simulator for Hearth Bottom Protection For actual practices of titania injection in the real blast furnace, operational and strategic preparation can be conducted to some extent. However quite often, actual practices may not run according to plan and in such case, operators must act accordingly and immediately based on the real time monitoring data. In such circumstances, a program that instantly outputs graphics and data regarding the TiC particles along the inner surface of the hearth corresponding to the current operational condition becomes useful. Here, a simple light weighted titania injection simulator program (30 MB) is developed such that it instantly outputs graphics and data gained from the results of 105 cases run in the current CFD model.

FIGURE 6.14 shows the snapshot of the program. The program is developed using Microsoft Visual Studio 2010. Generally, the program is a picture viewer and picture slideshow viewer. Within the program, the user inputs the desired operational conditions including the insertion location of titanium, inlet titanium mass fraction, coke bed state and duration of injection. Once the “simulate” button is clicked, the corresponding mass fraction distribution of TiC particles along the hearth bottom surface (z = 2.5 m) is graphically displayed. Here, the taphole is positioned on the right hand side and the legend is scaled linearly between zero and the maximum TiC mass fraction. At the same time, the coating area of the TiC particles along the hearth bottom surface, the maximum TiC mass fraction along the hearth bottom surface and the average TiC mass fraction within the coated area along the hearth bottom is displayed as data. Note that these are the coating area and TiC mass fraction along the hearth bottom surface and not the total inner hearth surface. The user can also select between a steady- state and a transient analysis. When a transient analysis is selected, the user can view the graphics and data corresponding to the desired injection duration time, from 0 to 3.0 hr, as still image, or as an animation. When the animation is played at 2 frames per second, each frame showing 0.5 hr intervals of the TiC mass fraction distribution along the hearth bottom surface. The specifications of the program are as follows.

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 Number of cases considered:  Total cases: 105 (315 images)  Steady-state cases: 70 (70 images)  Transient cases: 35 (245 images)  only for sitting coke bed state  User input options:  Titanium insertion angle: 30°, 60°, 90°, 120°, 150°, 180°, ALL  Inlet titanium mass fraction: 0.2 wt%, 0.4 wt%, 0.8 wt%, 1.2 wt%, 2.0 wt%  Coke bed state: sitting, floating  Analysis type: steady-state, transient  Injection duration: 0 hr, 0.5 hr, 1.0 hr, 1.5 hr, 2.0 hr, 2.5 hr, 3.0 hr  User navigation panel:  Display button, play button, pause button, fast forward button, rewind button  Output:  Graphical output: TiC mass fraction distribution along the bottom surface  Data output: Coated area, maximum TiC mass fraction, average TiC mass fraction within the coated area  Time tracker: 0 – 3.0 hrs

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FIGURE 6.14. Snapshot of PK5BF Titanium Injection Simulator.

For reference, the contour plots of TiC particle concentration along the inner hearth surface for all cases when the coke bed is sitting are presented in the Appendix section of this thesis. This consist 35 cases (35 images) for steady-state results and 35 cases (245 images) for transient results. The contour for TiC concentration when the coke bed is floating is not shown as no significant coating of TiC particles along the inner hearth surface is observed. For each titanium insertion location, plots of coated area, maximum TiC concentration and average TiC concentration along time within the range of 0 to 3 hr is also presented in the Appendix. A copy of the PK5BF Titanium Injection Simulator is available in a CD ROM in the back of this thesis.

6.4 CONCLUSIONS A 3D transient single-phase multi-component model is developed to simulate the TiC particle behaviour in the blast furnace hearth during titania addition via tuyere

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injection for a single tapping cycle. Analyses are conducted with respect to the distribution of TiC mass fraction along the inner hearth surface. The effect of titanium injection duration and key operational parameters is investigated for both burdening and tuyere injection methods. The following conclusions are made.  For both titania insertion methods, the area coated by TiC particles along the inner hearth surface rapidly increases in the first hour, followed by a gradual increase with time. The maximum TiC mass fraction and the maximum particle size increases rapidly reaching its steady-state value in the first hour then remains steady with time.  For both titania insertion methods, the maximum TiC mass fraction, the maximum particle size and the coated area along the inner hearth surface all increase with the inlet titanium mass fraction.  For the purpose of protecting the side wall, titania should be inserted from a tuyere positioned slightly upstream of the hot spot location. The correlation between locations of the hotspot and the injection point is quantified.  For the purpose of protecting the bottom corner of the hearth, titania should be inserted from a tuyere positioned around 60° from the active tuyere. A light weighted and user friendly program that instantly presents the TiC particle distribution along the bottom surface of the hearth of PK5BF of any operational condition set by the user is developed. Such studies and program will provide guidance to furnace operators during the practice of titania addition into the blast furnace.

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CHAPTER 7 SUMMARY AND FUTURE WORK

This chapter summarises the major conclusions of the research work conducted in this thesis. This is followed by a summary of recommended future research.

7.1 SUMMARY OF THESIS The major conclusions of this thesis are summarised as follows.

STEP 1: Accurate simulation of hot metal flow and heat transfer in the hearth (Chapter 3) STEP 2: Simulation of the transport of Ti(C,N) particles together with the flow and heat transfer in the hearth (Chapters 4, 5 and 6)

These are the first 2 steps of the 3-step procedure, as strategized in Section 1.4, for the purpose of developing of a comprehensive 3D hearth model that predicts the Ti(C,N) protection layer formation in the blast furnace hearth.

7.1.1 STEP 1: Accurate Simulation of Hot Metal Flow and Heat Transfer in the Hearth A 3D CFD model is developed to accurately predict hot metal flow and heat transfer in the hearth of PK5BF. Compared to the previous studies, significant improvements are made in terms of turbulence modelling, buoyancy modelling, temperature dependent material properties, wall boundary treatments, mesh resolution and coke bed properties. A phase change model is also included to simulate the solidified iron layer. The model is validated by comparing the calculated temperatures with the thermocouple data available, where agreements are established within  3 %.

The flow and temperature distributions in the hearth are described for various coke bed states and inner hearth profiles. It was found that natural convection significantly influences the flow pattern which in turn effects the hearth erosion in two 209

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ways. Firstly, a downward-directed jet forms along the peripheral side walls. In the coke zone, this is expected to occur throughout the campaign and may cause side wall erosion. In the coke free zone, this contributes to a vortex like peripheral flow with velocity reaching up to 48 times the inlet velocity and may lead to an ‘elephant foot’ type erosion profile. Secondly, it may cause the heavy liquid iron to remain stagnant at the hearth bottom, preventing erosion of the hearth bottom.

The effect of the coke bed permeability is investigated where a strong link between the coke bed permeability, flow pattern and refractory temperature is found. Generally as the permeability decreases, the bulk flow becomes more prominent. This increases liquid mixing and hence increases refractory temperature. Best agreements are established between the calculated and measured refractory temperatures when the coke bed permeability is 1.8×10-8 m2. Through this analysis, the dilemma in the literature regarding the agreement between the calculated and measured temperatures using models with and without natural convection is explained.

7.1.2 STEP 2: Simulation of the Transport of Ti(C,N) Particles together with the Flow and Heat Transfer in the Hearth A 2D two-phase, multi-component CFD model is used to study the complex transport phenomena associated with the formation and dissolution of solid particles in the blast furnace hearth during titania addition via burdening. The model considers non- buoyant flow, heat transfer, mass transfer and phase changing chemical reactions. The transport of TiC particles is studied by monitoring various parameters along a streamline passing through the particle rich layer located along the hearth linings. It is found that along a streamline, the TiC particle forms at the equilibrium temperature and grows as the stream-wise temperature decreases. The isotherm of the equilibrium temperature of hot metal solution after titanium insertion is found to be an excellent indicator to locate particles in the hearth. It is found that the particles in the hearth can be controlled by adjusting this isotherm by either (i) altering the titanium dosage or (ii) altering the hot metal pool temperature. The effects of these two parameters on the solid holdup along the hearth lining are investigated. The use of the equilibrium temperature

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isotherm concept may provide significant control of Ti(C,N) particles in the hearth during titania addition.

A 3D single-phase multi-component model is developed as an upgrade of the previous 2D two-phase multi-component model. The new model simulates the stead- state Ti compound behaviour in the 3D blast furnace hearth during titania addition via burdening. The model considers hot metal flow with natural convection, conjugate heat transfer, species transfer and thermodynamics of key chemical reactions. Various valid simplifications are implemented and as a result, the simulation time is reduced by more than 30 times compared to the two-phase model framework. The model agrees well with thermocouple readings. General flow features are described for the sitting and floating coke bed states. The equilibrium temperature isotherm of the titanium-hot metal solution matches well with the solid holdup profile. The effect of inlet titanium mass fraction is investigated. For a sitting coke bed, as the inlet titanium mass fraction increases, the particle rich layer thickness, its area coverage along the inner hearth surface, the solid holdup and the particle diameter all increase. For a floating coke bed, almost no particles are found for inlet titanium mass fraction at and below [Ti]in = 0.8 wt%; however the solid holdup, particle diameter and area the particles cover along the inner hearth surface all increase with inlet titanium mass fraction above [Ti]in = 1.2 wt%.

A transient 3D single-phase multi-component model is developed to simulate the TiC particle behaviour in the blast furnace hearth during titania addition via tuyere injection for a single tapping cycle. Analyses are conducted with respect to the distribution of TiC mass fraction along the inner hearth surface. The effects of key operational parameters are investigated for both burdening and tuyere injection methods. For the practice of titania injection, the following recommendations are made. To protect the side walls, titania injecting tuyere located upstream from the hot spot location, by an offset angle as proposed, should be selected. To protect the hearth bottom corner, titania injecting tuyere should be selected such that the hot spot location is between the active taphole and tuyere are around 60° apart. A simulator of the hearth during titania addition is developed. The simulator is a simple, user friendly program that instantly presents graphical images of the TiC particle distribution along the bottom 211

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surface of the hearth of PK5BF of any operational condition set by the user. Such studies will provide guidance to furnace operators during the practice of titania addition into the blast furnace.

7.2 FUTURE WORK The ultimate goal in this field of research is to gain precision control of the Ti(C,N) protection layer in the blast furnace hearth during titania addition practices through the use of numerical models. In the work presented in this thesis, progress has been made, however further studies is required to fulfil this goal. Based on the 3 step procedure mentioned in Chapter 1, the following aspects are recommended for future studies.

For STEP 2 procedure, i.e. simulation of the transports of Ti(C,N) particles, hot metal flow and heat transfer in the hearth, the following studies are recommended.  Development of a 3D model that considers both TiC and TiN particle formation reactions within the hearth during titania addition and to investigate the effects of key operational parameters such as initial carbon and nitrogen concentrations and titania dosage rate.  Development of a model that considers the deposition of TiC and TiN particles onto the packed coke and the hearth linings and to investigate the transport of Ti(C,N) particles in the hearth.

For STEP 3 procedure, i.e. simulation of the transports of Ti(C,N) protection layer, Ti(C,N) particles, hot metal flow and heat transfer in the hearth, the following studies are recommended.  Further experimental studies to elucidate the fundamental mechanism of the formation of Ti(C,N) protection layer in the blast furnace hearth. Quantification of material properties of Ti(C,N) containing hot metal at conditions expected in the hearth.  Development of a model that simulates the transport of Ti(C,N) protection layer in the blast furnace hearth and to investigate the effects of key operational parameters.

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The reviewer of this thesis has kindly recommended the following future studies.  The effect of the hot face profile of the eroded hearth, particularly for curved shaped surfaces (i.e. smoothed roundish shape) should be investigated. A step- like profile is used in the model where the flow and hence heat transfer behaviour may differ altering the distribution of the Ti(C,N) particles in the hearth during titania addition.  For STEP 3 procedure, the model should consider the transient dissolution process of refractories together with the process of formation of scaffolds. This would be one of the necessary ways to complete the study of blast furnace hearth protection from erosion.  For further work, the slag phase can also be considered in the model. During the

process of titania addition, the inclusion of TiO2 and TiO2 melts in the slag phase increases the slag viscosity and causes adversities to the operation of the

furnace. The study of TiO2 reduction kinetics and reduced Ti transportation process in the slag phase should also be implemented.  It would be ideal to support the simulation development with experimental validation.  Along with considering the TiN and TiC particle deposition onto the coke particles and hearth linings as mentioned above (page 212), the nucleation and particle growth mechanisms can also be further investigated to make possible improvements for the simulation of the nucleation process in the model.

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FIGURE A.1. Contour of TiC mass fraction along inner hearth surface for various inlet titanium mass fractions when titanium inserted from all throughout the inlet. Coke bed is sitting.

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FIGURE A.2. (i) Area coated by TiC particles, (ii) maximum TiC concentration and (iii) maximum particle size along inner hearth surface along time for various inlet titanium concentrations when titanium inserted from all throughout the inlet.

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FIGURE A.3. Contour of TiC mass fraction along inner hearth surface for various inlet titanium mass fractions when titanium inserted locally from 30° position. Coke bed is sitting.

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FIGURE A.4. (i) Area coated by TiC particles, (ii) maximum TiC concentration and (iii) maximum particle size along inner hearth surface along time for various inlet titanium concentrations when titanium inserted locally from 30° position.

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FIGURE A.5. Contour of TiC mass fraction along inner hearth surface for various inlet titanium mass fractions when titanium inserted locally from 60° position. Coke bed is sitting.

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FIGURE A.6. (i) Area coated by TiC particles, (ii) maximum TiC concentration and (iii) maximum particle size along inner hearth surface along time for various inlet titanium concentrations when titanium inserted locally from 60° position.

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FIGURE A.7. Contour of TiC mass fraction along inner hearth surface for various inlet titanium mass fractions when titanium inserted locally from 90° position. Coke bed is sitting.

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FIGURE A.8. (i) Area coated by TiC particles, (ii) maximum TiC concentration and (iii) maximum particle size along inner hearth surface along time for various inlet titanium concentrations when titanium inserted locally from 90° position.

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FIGURE A.9. Contour of TiC mass fraction along inner hearth surface for various inlet titanium mass fractions when titanium inserted locally from 120° position. Coke bed is sitting.

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FIGURE A.10. (i) Area coated by TiC particles, (ii) maximum TiC concentration and (iii) maximum particle size along inner hearth surface along time for various inlet titanium concentrations when titanium inserted locally from 120° position.

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FIGURE A.11. Contour of TiC mass fraction along inner hearth surface for various inlet titanium mass fractions when titanium inserted locally from 150° position. Coke bed is sitting.

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FIGURE A.12. (i) Area coated by TiC particles, (ii) maximum TiC concentration and (iii) maximum particle size along inner hearth surface along time for various inlet titanium concentrations when titanium inserted locally from 150° position.

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FIGURE A.13. Contour of TiC mass fraction along inner hearth surface for various inlet titanium mass fractions when titanium inserted locally from 180° position. Coke bed is sitting.

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FIGURE A.14. (i) Area coated by TiC particles, (ii) maximum TiC concentration and (iii) maximum particle size along inner hearth surface along time for various inlet titanium concentrations when titanium inserted locally from 180° position.

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FIGURE A.15. Contour of TiC mass fraction along inner hearth surface for various inlet titanium mass fractions and titanium insertion positions in steady-state. Coke bed is sitting.

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LIST OF PUBLICATIONS

JOURNAL PAPERS

KOMIYAMA, K. M., GUO B. Y., ZUGHBI H., ZULLI P. & YU A. B. (2014) A Numerical Model to Simulate the Flow and Heat Transfer in the Blast Furnace Hearth, Metallurgical and Materials Transactions B (accepted).

KOMIYAMA, K. M., GUO B. Y., ZUGHBI H., ZULLI P. & YU A. B. (2014) A Method to Manage Titanium Compounds in Blast Furnace Hearth during Titania Addition, Steel Research International (submitted).

KOMIYAMA, K. M., GUO B. Y., ZUGHBI H., ZULLI P. & YU A. B. (2014) A 3D CFD Model to Simulate the Titanium Compound Behaviour in the Blast Furnace Hearth (to be submitted).

KOMIYAMA, K. M., GUO B. Y., ZUGHBI H., ZULLI P. & YU A. B. (2014) A Transient 3D CFD Model to Predict the Distribution of Titanium Compounds in the Blast Furnace Hearth during Titania Injection from Tuyere (to be submitted).

CONFERENCE PAPERS

KOMIYAMA, K. M., GUO B. Y., ZUGHBI H., ZULLI P. & YU A. B. (2013) A 3D CFD Model to Simulate the Titanium Based Particle Formation and Dissolution in the Blast Furnace Hearth, 5th Baosteel Biennial Academic Conference, Shanghai, 4-6 June 2013.

KOMIYAMA, K. M., GUO B. Y., ZUGHBI H., ZULLI P. & YU A. B. (2012) CFD Model to Predict Flow and Temperature Distributions in a Blast Furnace Hearth 5th International Congress on the Science and Technology of Steel Making, Dresden 1-6 October 2012, paper number 1297.

KOMIYAMA, K. M., GUO B. Y., ZUGHBI H., ZULLI P. & YU A. B. (2011) Parametric Studies of Titanium Particle Formation in the Blast Furnace Hearth, Proceedings of CHEMECA 2011-Engineering a Better World, Sydney Hilton Hotel, NSW, Australia, 18-21 September 2011, paper number 2767. 237