Numerical and Experimental Studies of Granular Dynamics in Isamill

NUMERICAL AND EXPERIMENTAL STUDIES OF GRANULAR DYNAMICS IN ISAMILL

CHANDANA .T. JAYASUNDARA

A thesis submitted in fulfillment of the requirements for the degree of Doctor of Philosophy

Centre for Computer Simulation and Modelling of Particulate Systems School of Materials Science and Engineering Faculty of Science The University of New South Wales

June 2007 Certificate of Originality I hereby declare this submission is my own work and to the best of my knowledge it contains no materials previously published or written by another person, nor materials which to a substantial extent has accepted for the award of any other degree or diploma at UNSW or any other institute, except where due acknowledgment is made in the 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 project's design and conception or in style, presentation and linguistic expression is acknowledged.

(Signed) ………………………………….…………………………...... …..

ii To my wife and parents

iii ACKNOWLEDGMENT

I would like to express my sincere gratitude to my supervisor, Prof. Aibing Yu, for giving me the opportunity to carry out this research project. Without his invaluable guidance and boundless knowledge given to me over the whole course of the project, this work would have not been possible. I also wish to thank my co-supervisor Dr. Runyu Yang, for his helpful comments and guidance throughout the whole course. I also wish to thank my industrial supervisor Mr. Daniel Curry for his helpful comments and support towards this project. I also have to thank the Australian Research Council (ARC) and Xstrata Technology for the financial support for this project. Thanks also to my friends and colleagues in the “Centre for Simulation and Modelling of Particulate Systems” for providing me with much help in my study. I am also grateful to the staff in the School of Materials Science and Engineering in UNSW for their various helps during the course of my study. Last but not least, I owe endless thank to my wife Shirmila Jayasundara and my parents for their love, patient and support which has always been a source of inspiration in my work. Without their supporting comments and care over the last three years, this work would have not been successful.

iv ABSTRACT

IsaMill is a stirred type mill used in mineral industry for fine and ultra-fine grinding. The difficulty in obtaining the internal flow information in the mill by experimental techniques has prevented the development of the fundamental understanding of the flow and generating general methods for reliable scale-up and optimized design and control parameters. This difficulty can be effectively overcome by numerical simulation based on discrete element method (DEM). In this work a DEM model was developed to study particle flow in a simplified IsaMill. The DEM model was validated by comparing the simulated results of the flow pattern, mixing pattern and power draw with those measured from a same scale lab mill. Spatial distributions of microdynamic variables related to flow and force structure such as local porosity, particle interaction forces, collision velocity and collision frequency have been analyzed. Among the materials properties of particles, it is shown that by decreasing particle/particle sliding friction coefficient, the particle flow becomes more vigorous which is useful to grinding performance. Restitution coefficient does not affect the particle flow significantly. A too low or too high particle density could decrease grinding efficiency. Although grinding medium size affects the flow, its selection may depend on the particle size of the products. Among the operational variables considered, the results show that fill volume and mill speed proved to be important factors in IsaMil process. Increase of fill volume or mill speed increases the interaction between particles and agitating discs which results in a more vigorous motion of the particles. Among the mill properties, particle/stirrer sliding friction plays a major role in energy transfer from stirrer to particles. Although there exists a minimum collision energy as particle/stirrer sliding friction increases, large particle/stirrer sliding friction may improve grinding performance as it has both large collision frequency and collision energy. However, that improvement is only up to a critical particle/disc sliding friction beyond which only input energy increases with little improvement on collision frequency and collision energy. Reducing the distance between stirrers or increasing the size of disc holes improves high energy transfer from discs to particles, leading to high collision frequency and collision energy. Among the different stirrer types, the energy transfer is more effective when disc holes are present. Pin stirrer shows increased collision energy and collision frequency which also result in a high power draw.

v Using the DEM results, a wear model has been developed to predict the wear pattern of the discs. This model can be used to predict the evolution of the disc wear with the time. It is shown that energy transfer from discs to particles are increased when discs are worn out. An attempt has also been made to analyze the microdynamic properties of the mill for different sizes. It is shown that specific power consumption and impact energy are correlated regardless of the mill size and mill speed.

vi Table of Contents Page Number Title Page ...... i

Certification of Originality ...... ii

Acknowledgement ...... iv

Abstract ...... v

Table of Contents ...... vii

List of Tables ...... x

List of Figures ...... xi

Chapter 1 Introduction...... 1

Chapter 2 Literature Review ...... 5 2.1 Introduction ...... 6 2.2 Grinding theory and experimental results ...... 7 2.2.1 Fundamentals of comminution ...... 7 2.2.2 Coarse grinding ...... 12 2.2.3 Fine and ultra-fine grinding ...... 15 2.2.4 Experimental results of fine grinding ...... 20 2.3 Numerical techniques ...... 27 2.3.1 Population balance method ...... 27 2.3.2 Computational Fluid Dynamics (CFD) ...... 31 2.3.3 Discrete Element Method ...... 36 2.5 Summary and Proposed Research...... 47

Chapter 3 Discrete particle simulation of particle flow in the IsaMill ...... 49 3.1 Introduction ...... 50 3.2 Simulation method and conditions ...... 51 3.3 Macroscopic observation and model validation ...... 55 3.4 Microdynamic analysis ...... 58 3.4.1 Motion of individual particles ...... 59 3.4.2 Velocity Field ...... 61

vii 3.4.3 Flow structure ...... 64 3.4.4 Force structure ...... 67 3.5 Collision frequency and collision energy ...... 73 3.6 Other useful correlations ...... 76 3.7 Conclusions ...... 80

Chapter 4 Effect of grinding media properties, operational control parameters

and mill properties ...... 81 4.1 Introduction ...... 82 4.2 Simulation method and conditions ...... 82 4.3 Results and discussion ...... 84 4.3.1 Grinding media properties...... 85 4.3.1.1 Particle-particle sliding friction coefficient ...... 85 4.3.1.2 Particle-particle restitution coefficient ...... 89 4.3.1.3 Particle density ...... 93 4.3.1.4 Particle size ...... 97 4.3.2 Operational control parameters ...... 102 4.3.2.1 Effect of mill loading ...... 102 4.3.2.2 Effect of mill speed ...... 109 4.3.2.3 Power model ...... 116 4.3 Conclusions ...... 118

Chapter 5 Effect of mill properties ...... 121 5.1 Introduction ...... 122 5.2 Simulation method and conditions ...... 122 5.3 Results and discussion ...... 123 5.3.1 Particle-disc sliding friction coefficient ...... 124 5.3.2 Distance between stirres ...... 129 5.3.3 Disc hole size ...... 133 5.4 Conclusions ...... 142

Chapter 6 Prediction of disc wear of the IsaMill with aid of Discrete Element Modelling ……………………….…………………………………….....144

viii 6.1 Introduction ...... 145 6.2 Simulation method and conditions ...... 146 6.3 Results and Discussion ...... 146 6.3.1 Wear model ...... 146 6.3.2 Wear prediction for different stirrer geometries ...... 148 6.3.3 Prediction of disc life span...... 151 6.3.4 Effect of disc wear on grinding performance ...... 154 6.4 Conclusions ...... 157

Chapter 7 Microdynamic analysis of IsaMill of different scales ...... 159 7.1 Introduction ...... 160 7.2 Simulation method and conditions ...... 162 7.3 Background ...... 162 7.4 Results and Discussion ...... 163 7.4.1 Validity of the numerical resutls ...... 163 7.4.2 Velocity and porosity ...... 165 7.4.3 Energy intensity...... 167 7.4.4 Collisoion frequency and collision energy ...... 167 7.4.5 Specific power and energy intensity ...... 170 7.4 Conclusions ...... 171

Chapter 8 Conclusions and Further Study ...... 173

Bibliography ...... 177

Appendix ...... 193

ix List of Tables

LIST OF TABLES

CHAPTER 3. DISCRETE PARTICLE SIMULATION OF PARTICLE FLOW IN THE ISAMILL Table 3.1. Physical parameters of the simulation.

CHAPTER 4. EFFECT OF GRINDING MEDIA PROPERTIES and OPERATIONAL CONTROL PARAMETERS Table 4.1. Physical parameters used in the present simulation. Table 4.2. Factorial design for J and N. Table 4.3. Regression coefficients.

CHAPTER 5. EFFECT OF MILL PROPERTIES Table 5.1. Physical parameters used in the present simulation.

CHAPTER 6. PREDICTION OF DISC WEAR OF THE ISAMILL WITH AID OF DISCRETE ELEMENT MODELLING Table 6.1. Physical parameters of the simulation.

CHAPTER 7. MICRODYNAMIC ANALYSIS OF ISAMILL OF DIFFERENT SCALES

Table 7.1. Physical parameters used of the simulation. Table 7.2 Power draw for different mill scales at constant rotational speed and at constant tip speed.

x LIST OF FIGURES

CHAPTER 2. LITERATURE REVIEW Figure 2.1 Strain of a crystal lattice resulting from tensile or compressive stresses. Figure 2.2 Fracture by crushing. Figure 2.3 The Davis Circle (Redrawn after Davis, 1919). Figure 2.4 Idealised charge motion (Redrawn after Hogg and Fuersttenau, 1972). Figure 2.5 Different Stirrer designs used by the industry for stirred mills. Figure 2.6 Vertical stirred mill:` (a) Sala Agitated mill; (b) Svedala VertiMill. Figure 2.7 Netzsch horizontal stirred mill. Figure 2.8 Schematic illustration of the IsaMill. Figure 2.9 CRFS and HMPR media performance. Figure 2.10 Different stress energy regions in the grinding chamber (After Stender et al, 2001, 2004).

Figure 2.11 Radial-axial fluid velocities (Theuerkauf and Schwedes, 1999). Figure 2.12 Product fineness as function of stress intensity and specific energy input for comminution of limestone (After Becker et al, 2001).

Figure 2.13 Effect of grinding bead wear on relation between specific energy and product fineness for the comminution of fused corundum.

Figure 2.14 Effect of hardness of grinding beads, hardness of product particles and shape of product particles on grinding bead wear.

Figure 2.15 Comparison of specific energy consumption for IsaMill at McArthur river and laboratory mill.

Figure 2.16 Grinding phenomenon in a ball mill as interpreted in terms of collision energy and frequency.

Figure 2.17 Rd = 60, Rs = 21, Rc = 75, Dd = 43, Wd = 9, Lm= 380; all dimensions in mm Fig.2.17 Stirred ball mill.

Figure 2.18 Power characteristics of the stirred ball mill.

Figure 2.19 Radial and axial velocities.

11 Figure 2.20 Agglomeration of particles in a rotating drum: (a) initial state; (b) intermediate state after one and quarter of revolutions. Figure 2.21 Dynamic angle of repose as a function of rotation speed.

Figure 2.22 Time-averaged spatial distribution of (from left to right): porosity, coordination number, (snapshot) force network, total force (mg), collision velocity (m/s), and collision frequency (1/s) in a cylindrical rotating drum for granulation when rotation speed is 20 rpm.

Figure 2.23 Comparison of charge motion in a 90-cm diameter mill.

Figure 2.24 Comparisons of power draw for ball mills of different diameters. Figure 2.25 Wear distribution calculate by the DEM model and the predicted liner shape after 5000 hours of operation for J = 80%.

Figure 2.26 Impact energy spectra obtained from the DEM modeling.

Figure 2.27 Predicted and measured product size distribution: 90.0 cm mill, 20% ball load, 18 rpm, 5.08 cm balls.

CHAPTER 3. DISCRETE PARTICLE SIMULATION OF PARTICLE FLOW IN THE ISAMILL

Figure 3.1 Schematic illustration of the forces acting on particle i from contacting particle j and non-contacting particle k.

Figure 3.2 Geometry of the model Isamill and different cross sections: (a) axial direction; and (b) radial direction. All dimensions are in mm.

Figure 3.3 The lab mill for model validation: (a) mill body; (b) inlet; (c) motor; and (d) stand.

Figure 3.4 End view of experimental (top) and numerical (bottom) particle distributions for different solid loadings and rotation speeds: (a) : = 300rpm and J = 40%; (b) : =300rpm and J = 60%; (c) : = 800rpm and J = 60%; and (d) : = 1000rpm and J = 80%.

12 Figure 3.5 Axial view of experimental (top) and numerical (bottom) particle distributions for different solid loadings and rotation speeds: (a) : = 300rpm and J = 40%; (b) : = 300rpm and J = 60%; (c) : = 800rpm and J = 60%; (d) : = 1000rpm and J = 80%.

Figure 3.6 Experimental (top) and numerical (bottom) mixing patterns when rotation speed is 100 rpm: (a) t = 0 and (b) t = 10 s for the initial top/bottom layered arrangement; and (c) t = 60 s, for the initial side- by-side arrangement.

Figure 3.7 Comparison of power draw between the physical and numerical experiments at different rotation speeds and mill loadings.

Figure 3.8 Trajectories of two representative particles Pe (ƕ) and Pm (u) at (a) radial plane; and (b) axial plane when : =1000rpm and J = 80%.

Figure 3.9 The evolution of some typical microdynamic results: r – radial

position; z – axial position; Vr – radial velocity; Vt – tangential

velocity; Fn(p) – total normal force; of particles Pe and Pm with time when : =1000rpm and J = 80%.

Figure 3.10 Variation of power draw in log scale (a) mill speed and (b) fill volume.

Figure 3.11 Spatial distribution of particle velocities in the axial direction (a); and the radial direction (b) when : = 1000 rpm and J = 80%.

Figure 3.12 Mixing behaviour in region B when : = 100 rpm and J = 60% at different times: (a) t = 1s; and (b) t = 10s.

Figure 3.13 Particle distribution in different cross regions when : = 1000 rpm and J = 80%: (a) section XX ' [-5mm

Figure 3.14 Spatial distribution of porosity when : = 1000 rpm and J = 80%: (a) region A; (b) region B: (c) axial direction; and (d) radial direction.

13 Figure 3.15 The spatial distributions of the force Fn(p) on particle in radial (a) (only for region B), and axial (b) directions when : = 1000 rpm and J = 80%.

Figure 3.16 The spatial distributions of the instantaneous and maximum forces per contact and the total forces on a particle in the axial (a) and radial (b) directions when : = 1000 rpm and J = 80%.

Figure 3.17 The correlation between the mean force and particle velocity when : = 1000 rpm and J = 80%.

Figure 3.18 The correlation between normal and tangential forces: (a) Fn and Ft; (b)

Fn(p) and Ft(p); and (c) Fn(max) and Ft(max). The points are the numerical results obtained when : = 1000 rpm and J = 80%, and the lines are the best fits.

Figure. 3.19 The spatial distributions of the collision energy (Ce) and the collision

frequency (Cf) in the axial (a) and radial (b) directions when : = 1000 rpm and J = 80%.

Figure. 3.20 The correlation between collision frequency and collision energy when : = 1000 rpm and J = 80%.

Figure. 3.21 The relationship between the collision energy and the maximum force. The cross and the dotted line are the numerical results and the solid line is the theoretical results from Eq. (5) when : = 1000 rpm and J = 80%.

Figure. 3.22 Collision energy and collision frequency as a function of: (a), local porosity; and (b) local velocity when : = 1000 rpm and J = 80%.

CHAPTER 4. EFFECT OF GRINDING MEDIA PROPERTIES AND OPERATIONAL CONTROL PARAMETERS

Figure 4.1 Schematic illustration of the model IsaMill: (a) sectional front elevation; and (b) sectional end elevation (all dimensions in mm).

14 Figure 4.2 Spatial distribution of velocities for different particle/particle sliding

friction coefficients: (a) Ps, pp = 0.01; and (b) Ps, pp = 1.0.

Figure 4.3 Spatial distribution of porosity for different particle/particle sliding

friction coefficients: (a), Ps, pp = 0.01; and (b) Ps, pp = 1.0.

Figure 4.4 Distribution (a) and mean value (b) of the collision frequency for different particle/particle sliding friction coefficients.

Figure 4.5 Distribution (a) and mean value (b) of the collision energy for different particle/particle sliding friction coefficients.

Figure 4.6 Power draw as a function of particle/particle sliding friction coefficient.

Figure 4.7 Spatial distribution of velocities for different particle restitution coefficients: (a) 0.38; and (b) 0.88.

Figure 4.8 Spatial distribution of porosity for different particle restitution coefficients: (a) 0.38; and (b) 0.88.

Figure 4.9 Distribution (a) and mean value (b) of the collision frequency for different restitution coefficients.

Figure 4.10 Distribution (a) and mean value (b) of the collision energy for different restitution coefficients.

Figure 4.11 Power draw as a function of restitution coefficient.

Figure 4.12 Spatial distribution of velocities for different particle density: (a) U = 1000 kgm-3; and (b) U = 3500 kgm-3.

Figure 4.13 Spatial distribution of porosity for different particle density: (a) U = 1000 kgm-3; and (b) U = 3500 kgm-3.

Figure 4.14 Distribution (a) and mean value (b) of the collision frequency for different particle density.

15 Figure 4.15 Distribution (a) and mean value (b) of the collision energy for different particle densities.

Figure 4.16 Power draw as a function of particle density.

Figure 4.17 Spatial distribution of velocities for different particle sizes:dp = 2mm; and (b) dp = 4mm %.

Figure 4.18 Spatial distribution of porosity for different particle sizes: (a) dp = 2mm; and (b) dp = 4mm.

Figure 4.19 Spatial distribution of velocity and porosity for different particle sizes in enlarged upper region of sectional elevation at XX ': (a) dp = 2mm; and (b) dp = 4mm.

Figure 4.20 Distribution (a) and mean value (b) of the collision frequency for different particle sizes.

Figure 4.21 Distribution (a) and mean value (b) of the collision energy for different particle sizes.

Figure 4.22 Power draw as a function of particle size.

Figure 4.23 End view of experimental (top) and numerical (bottom) particle distributions for different solid loadings: (a) : = 300rpm and J = 40% and (b) : =300rpm and J = 80%. Figure 4.24 Axial view of experimental (top) and numerical (bottom) particle distributions for different solid loadings: (a) : = 300rpm and J = 40% and (b) : = 300rpm and J = 80%. Figure 4.25 Comparison of power consumption between the physical and numerical experiments at different mill loadings. Figure 4.26 Spatial distribution of velocities in redial direction (top) and sectional elevation at section XX ' (bottom) for different fill volume at ȍ = 1000rpm : (a) J = 40%; and (b) J = 80%. Figure 4.27 Probability distribution (a) and mean value of the collision frequency (b) for different J.

16 Figure 4.28 Probability distribution (a) and mean value (b) of the collision energy for different J. Figure 4.29 End view of experimental (top) and numerical (bottom) particle distributions for different solid loadings: (a) : = 300rpm and J = 60% and (b) : =800rpm and J = 60%. Figure 4.30 Axial view of experimental (top) and numerical (bottom) particle distributions for different solid loadings: (a) : = 300rpm and J = 60% and (b) : = 300rpm and J = 60%. Figure 4.31 Comparison of power consumption between the physical and numerical experiments at different mill speeds when J = 80%. Figure 4.32 Spatial distribution of velocities in redial direction (top) and sectional elevation at section XX ' (bottom) for different mill speeds at J = 80%: (a) ȍ = 500rpm; and (b) ȍ = 1000rpm. Figure 4.33 Probability distribution (a) and mean value of the collision frequency (b) for different ȍ. Figure 4.34 Probability distribution (a) and mean value (b) of the collision energy for different ȍ. Figure 4.35 Variation of power draw in log scale (a) mill speed and (b) fill volume.

CHAPTER 5. EFFECT OF MILL PROPERTIES Figure 5.1 Different stirrer geometries of 0H, 3H, 5H and pin (from left to right). All dimensions in mm. Figure 5.2 Spatial distribution porosity and velocity vectors for different

particle/stirrer sliding friction coefficients: (a) Ps, pd = 0.1; and (b) Ps, pd = 2.0. Figure 5.3 (a) Probability distribution; and (b) the mean value of the collision

frequency for different Ps,pd. Figure 5.4 (a) Probability distribution; and (b) mean value of the collision energy

for different Ps, pd.

Figure 5.5 Power draw of IsaMill as a function of Ps, pd.

17 Figure 5.6 Variations of (a) mean collision frequency; (b) mean collision energy

and (c) power draw for different Ps,pw. Figure 5.7 Spatial distribution of velocity and porosity for different disc distances:

(a) ld = 17mm; and (b) ld = 30mm. Figure 5.8 Spatial distribution of velocities at section XX ' for different stirrer

distance: (a) ld = 17mm; and (b) ld = 30mm. Figure 5.9 Probability distribution (a) and the mean value (b) of the collision

frequency for different ld. Figure 5.10 Probability distribution (a) and the mean value (b) of the collision

energy for different ld.

Figure 5.11 Variation of power consumption with ld. Figure 5.12 Spatial distribution porosity and velocity vectors for disc holes of

different sizes: (a) dh = 12mm; and (b) dh = 2mm. Figure 5.13 Probability distribution (a) and the mean value (b) of the collision

frequency for different dh. Figure 5.14 Probability distribution (a) and the mean value (b) of the collision

energy for different dh.

Figure 5.15 Power draw as a function of disc hole size dh. Figure 5.16 Particle flow for different stirrer geometries: (a) 0H; (b) 3H; (c) 5H; and (d) pin. Figure 5.17 Spatial distribution of velocity and porosity for different stirrer geometries when : =1000rpm and J = 80%: (a) 0H; (b) 3H; (c) 5H; and (d) pin.

Figure 5.18 Spatial distribution of velocities at section XX ' for (a) 5H stirrer; and (b) pin stirrer. Figure 5.19 Probability distribution (a) and the mean value (b) of the collision frequency for different stirrers. Figure 5.20 Probability distribution (a) and the mean value (b) of the collision energy for different stirrers. Figure 5.21 Power draw as a function of stirrers.

18 CHAPTER 6. PREDICTION OF DISC WEAR IN THE ISAMILL WITH THE AID OF DISCRETE ELEMENT MODELLING Figure 6.1 A schematic drawing of pin on disc tribometer. Figure 6.2 Spatial distribution of wear rate for different disc geometries:(a) 0H ; (b) 3H; (c) 5H and (d) PIN, 1 wear unit = 10-6 cm3/Sec. Figure 6.3 Wear pattern of discs of industrial IsaMill after 3000 hrs of operation (courtesy of Xstrata Technology, Australia). Figure 6.4 Representation of worn area of the hole; all dimensions in mm. Figure 6.5 Wear rate variation with time. Figure 6.6 Predicted geometry of the progressively worn discs: (a) new disc; (b) moderately worn disc (after 4 months); (c) worn disc (after 8 months); (d) well worn disc (after 12 months). Figure 6.7 Spatial distribution of porosity and velocity for:(a) new disc and (b) well worn disc. Figure 6.8 Variation of mean values of (a) collision energy and (b) collision frequency with time. Figure 6.9 Power draw variation with disc wear.

CHAPTER 7. MICRODYNAMIC ANALYSIS OF ISAMILL OF DIFFERENT SCALES Figure 7.1 Variation of specific energy consumption and product size Figure 7.2 Geometry of the model Isamill: (a) sectional front elevation; (b) sectional end elevation; All dimensions in mm. Figure 7.3 Correlation between power draw and: (a) tip speed at constant rotational speed; (b) volume at constant tip seed.

Figure 7.4 Spatial distribution of velocity and porosity (a) 1X; (b) 2.5X when ȍ = 1000rpm, J = 80%.

Figure 7.5 Normalized velocity distribution for different mill scales at = 1000 rpm: (a) by mean velocity; (b) by median velocity. Figure 7.6 Variation of average velocity for different mill scales.

19 Figure 7.7 Normalized energy intensity distributions for different mill scales at = 1000 rpm: (a) normalized by mean velocity; (b) normalized by median velocity. Figure 7.8 Variation of (a) collision frequency; and (b) collision energy; for different scales at constant rotational speed. Figure 7.9 Collision energy and collision frequency as a function of: (a), local porosity; and (b) local velocity when : = 1000 rpm and J = 80%. Figure 7.10 Power draw variation for different mill sizes at different rotational speed. Figure 7.11 Correlation between specific power consumption and impact energy.

20 CHAPTER 1

INTRODUCTION 1.0 INTRODUCTION

Grinding is the single largest energy consumption process in the mineral industry. Traditional grinding in tumbling mills (e.g. ball mills) is a low-efficiency (1-2%, typically) process and can account for up to 40% of the direct operating cost of a mineral processing plant (Joe, 1979; Wills, 1992). Furthermore, many of the base and precious metal deposits discovered are now fine-grained and complex, and there is a need for grinding them to very fine sizes to permit sufficient mineral liberation, for example, 80% of particles (P80) should be below 20 or even 10 microns. Grinding to such fine sizes economically is beyond the capability of conventional grinding technologies. IsaMill is a high-speed stirred mill developed by Mount Isa Mines (Xstrata) in Australia for economically grinding minerals to fine and ultra-fine size at an industrial-scale (Gao and Forssberg, 1995). It consists of a horizontally mounted shell and rotating grinding discs mounted on a shaft which is coupled to a motor and gearbox. The grinding discs agitate the media and ore particles in a slurry that is continuously fed into the feed port. The product separator (dynamic, centripetal classifier) keeps the grinding media inside the mill allowing only the product to exit. Simple control strategies based on power draw enable the IsaMill to produce a constant target product size. Comparing with the conventional grinding mills such as ball mill and tower mill, IsaMill can significantly reduce total comminution circuit energy cost (Curry and

Clermont, 2005) and reduce the size of mineral particles to as fine as P80 passing 7Pm (Gao and Forssberg, 1995). However IsaMill is still a new technology and most relations established between the quality of the final products and operating parameters of the mill are empirical, and are inadequate to comprehensively understand the grinding process. As a result, its optimum control and scale-up need to rely on empirical methods, experience and trial and error testing, rather than detailed scientific principles. There is a need for research into the grinding process to be predicted and modelled based on knowledge of the characteristics of the mill and the properties of the grinding materials.

This thesis presents a numerical investigation of the flow of grinding media in a simplified IsaMill, aiming to examine the feasibility of using DEM simulation to predict particle flow in a high speed stirred mill. The proposed DEM model is firstly validated with a 1:1 scale experimental setup which allows qualitative and quantitative comparison of flow and mixing patterns and power consumption. Then, the flow of particles will be analysed in terms of velocity, force and power draw. The effect of some variables related to key material properties and operational conditions are also investigated.

Chapter 2 reviews and discusses some previous work, mainly focus on fundamentals of mineral grinding, different types of mills and their applications to the mineral industry, previous research work on ball mills and stirred mills.

Chapter 3 presents the DEM model development and validation with 1:1 scale experimental setup which allows qualitative and quantitative comparison of flow and mixing patterns and power consumption. Then, the flow of particles will be analysed in terms of velocity, porosity, force and power draw. The correlations between microdynamic variables are also established.

Chapter 4 extends the analysis to investigate the effect of material properties, and operational variables on the particle flow of the IsaMill. Among these properties the most significant properties are identified. The results are compared with those reported in the literature and the reason for the differences observed is discussed.

Chapter 5 discusses the effect of mill properties on the particle flow of the IsaMill. Among the mill properties mill geometry and different stirrer types have been used. The results are compared and the reason for the differences observed is discussed. Chapter 6 discusses the development of wear model which can be used to predict the disc wear pattern. The results are analysed spatially to predict the wear pattern in different types of discs. It is shown that the wear model can be used to predict the disc life span depending on the materials properties.

Chapter 7 discusses scale-up issues of the IsaMill. Numerical results are compared with the results reported by the industry. Microdynamic properties relating particle flow is discussed for different scales of the mill. Finally, a new scaling relation has been proposed in terms of specific power consumption and impact energy.

Chapter 8 concludes this thesis work and discusses some future work.

It should be noted that though there is a logical sequence throughout the thesis, each chapter is based on the paper or papers already published or submitted for publication. CHAPTER 2

LITERATURE REVIEW 2.1 Introduction In the mineral industry, grinding is performed in rotating cylindrical vessels known as tumbling mills. Nowadays many of the base and precious metal deposits discovered have been fine-grained, therefore there is a need for them to grind to very fine sizes (< 10μm). Grinding to such fine sizes economically is beyond the capability of traditional ball mills. Therefore, the emerging technology for fine grinding is stirred milling. The fundamentals of fine grinding were established by Klaus Schonert in the 1980s and the fundamentals of stirred milling where developed in the 1980s and 1990s by Steier, Schwedes, Stehr, Kwade and others. This work led to the development of a new generation of stirred mills capable of grinding finer and finer. The IsaMill is a stirred type mill developed by Mt Isa Mines (currently known as Xstrata Technology, Australia) and Netszch- Feinmahltechnik (German) in 1990s for fine and ultrafine grinding. IsaMills are installed in more than two-thirds of the world’s ultra fine grinding metal ferous applications and quickly demonstrated its ability for very power efficient grinding to less than 10 microns. Despite gaining increasingly industrial importance, Isamill is still a new technology and its optimum control and scale up have to rely on empirical method, experience and trial and error tests, rather than the detailed scientific principles. Stirred milling development work in the mining industry up until now has been limited to that related to simply adopting the technology and making it work in high throughput, low value product conditions: larger mill sizes, low cost grinding media, wear protection, etc. Only limited work on the fundamentals has been undertaken and there remain many important issues of stirred milling operation which are not well understood by the industry. Computer simulations, based on discrete element method (DEM) provide direct and meaningful microscopic observations of granular dynamics of the IsaMill process which is impossible to obtain by experimental methods. DEM simulations have been applied to many particulate systems (Yu et al, 2003) including milling ball milling (Mishra and R.J. Rajamani, 1992; Mishra and Rajamani, 1994; Cleary, 1998, 2001; Rajamani and Mishra 1996; Cleary and Hoyer 2000). DEM allows isolating individual particles so that the microdynamic properties at particle scale can be generated. This review mainly focuses on fundamentals of mineral grinding, different types of mills and their applications to the mineral industry, previous research work on different types of mills, numerical techniques used in minerals industry particularly applied to ball mills, stirred mills, and rotating drums. 2.2 Grinding theory and experimental results Liberation of the valuable minerals from the gangue is accomplished by comminution, which involves crushing and, if necessary, grinding, to such a particle size that the product is a mixture of relatively clean particles of mineral and gangue. As it is this process which achieves liberation of values from gangue, it is also the process which is essential to efficient separation of the minerals, and it is often said to be the key to good mineral processing. In order to produce clean concentrates with little contamination with gangue minerals, it is necessary to grind the ore finely enough to liberate the associated metals. Fine grinding, however, increases energy costs. Grinding therefore becomes a compromise between clean (high-grade concentrates), operating costs and losses of fine minerals.

2.2.1 Fundamentals of comminution Comminution is the process of size reduction of the ore until the clean particles of minerals can be separated. Most minerals are crystalline materials in which the atoms are regularly arranged in three dimensional arrays. In the crystalline lattice of minerals, these interatomic bonds are effective only over small distances, and can be broken if extended by a tensile stress. Such stresses may be generated by tensile or compressive loading. The distribution of stress depends upon the mechanical properties of the individual minerals, but more importantly, upon the presence of cracks or flaws in the matrix, which act as sites for stress concentration (Fig.2.1). Fig.2.1 Strain of a crystal lattice resulting from tensile or compressive stresses.

It has been shown that the increase in stress at such a site is proportional to the square root of the crack length perpendicular to the stress direction (Inglis, 1913). Further increment of stress level at the crack tip is sufficient to break the atomic bond at that point causing the fracture. Breakage is achieved mainly by crushing, impact, and attrition, and all three modes of fracture (compressive, tensile, and shear) can be discerned depending on the rock mechanics and the type of loading. When an irregular particle is broken by compression, or crushing, the products fall into two distinct size ranges – coarse particles resulting from the induced tensile failure, and fines from compressive failure near the points of loading, or by shear at projections (Fig.2.2). Fig.2.2 Fracture by crushing.

In impact breaking, due to the rapid loading, a particle experience a higher average stress while undergoing strain that is necessary to achieve simple fracture, and tends to break apart rapidly, mainly by tensile failure. The products are often very similar in size and shape. Attrition (shear failure) produces much fine material which may occur mainly in practice due to particle-particle interaction (inter-particle comminution). All theoretical approaches and experimental results which help to describe qualitatively or quantitavely the event of stressing and breaking particles can be subsumed with the expression “physical fundamentals of comminution”. The oldest theory is that of Von Rittinger (1867), which states that the energy consumed in the size reduction is proportional to the area of new surface produced. The surface area of a known weight of particles of uniform diameter is inversely proportional to the diameter, hence Rittinger’s law equates to

§ 11 · KE ¨ ¸ (2.1) © DD 12 ¹

where E is the energy input, D1 is the initial particles size, D2 is the final particle size, and K is a constant. The second theory is that of Kick (1885). He stated that the work required is proportional to the reduction in volume of the particles concerned. Where f is the diameter of the fed particles and p is the diameter of the product particles, thus reduction ratio R is given by

R f (2.2) p and the energy required for comminution is proportional to

Rlog (2.3) log 2 Later some researchers started to investigate the breakage of single particles and measure strength, breakage energy, fragment size distribution and newly created surface. The first paper on this matter was published by Carey and Bosanquet in 1933. They compressed cubes and irregularly shaped particles of coal, gypsum and other materials, the specimen size ranges between 2 and 5mm. This was followed by publications of Hönig (1936), Andersen (1937), Fahrenwald et al (1937), Gaudin and Hukki (1944), Axelson and Piret (1950). In 1952 Bond developed an equation which is based on the theory that the work input is proportional to the new crack tip length produced in particle breakage, and equals the work represented by the product minus that represented by the feed. In particles of similar shape, the surface area of unit volume of material is inversely proportional to the diameter. The crack length in unit volume is considered to be proportional to one side of that area and therefore inversely proportional to the square root of the diameter. For practical calculations the size in microns which 80% passes is selected as the criterion of particle size. The diameter in microns which 80% of the product passes is designated as P, the size which 80% of the feed passes is designated as F, and the work input in kilowatt hours per ton is W. Bond’s third equation is W 1010 W W i i (2.4) P F where Wi is the work index. The work index is the comminution parameter which expresses the resistance of the material to crushing and grinding; numerically it is the kilowatt hours per ton required to reduce the material from theoretically infinite feed size to 80% passing 100μm. Carey and Stairmand (1953) introduced the ideas of fracture physics into field. Rumpf and Schönert (1962) developed a classical model for predicting the static tensile strength of granules. Considering a granule under the action of applied loads, he pointed out that fracture of the granule is mainly caused by the tensile stress generated within the assembly. The theoretical tensile strength of a granule is suggested to be the summation of all the inter-particle bond strengths across the fracture surface. The implicit assumption in this analysis is that all the inter-particle bonds across the fracture surface ruptured simultaneously during the fracture process. This leads to the derivation of the following expression for theoretical granule tensile strength, ıt , in its general form 1 H F)( V .11 (2.5) t H D 2 where İ and D are the intra-granular void fraction and constituent particle diameter, respectively. However, there are a number of deficiencies in the model of Rumpf. The model assumption that all the inter-particle contacts in the fracture plane fail suddenly is contested by Kendall (1988). They argue that simultaneous failures do not usually occur in practice, where the real failure mode is by cracking due to contacting primary particles in a granule separating sequentially. According to Kendall (1988), fracture of granule is a consequence of crack nucleation at flaws leading to subsequent crack propagation through the granular structure. Thus, the failure mechanism in this case is a sequential separation of interparticle bonds in contrast to the crack tip provides the driving force to create new surfaces. Kendall (1988) applied these concepts to derive the following expression of fracture strength of granules, ıf

// 61654 / 21 f .615 c **IV )Dc( (2.6) where ĭ is the solid fraction of the granular assembly, īc is the fracture surface energy, ī is the equilibrium surface energy, D is the constituent particle diameter, and c is the flaw size in the assembly. Grinding is the last stage in the process of comminution. In this stage the particles are reduced in size by a combination of impact and abrasion, either dry or in suspension in water. Depending on the size of product particles grinding can be divided into coarse grinding and fine grinding. Coarse grinding refers to particle at mm scale where as fine grinding refers to particle at μm scale.

2.2.2 Coarse grinding In the coarse grinding process, crushing is the first mechanical stage in which the main objective is to liberate the valuable minerals from the gangue. It is generally a dry operation and is usually performed in two or three stages. Lumps of run-of-mine ore can be as large as 1.5m across and these are reduced in the primary crushing stage to 10-20 cm in heavy-duty machines. It is performed in rotating cylindrical vessels known as tumbling mills. These contain a charge of loose crushing bodies – the grinding medium – which is free to move inside the mill, thus comminuting the ore particles. The grinding medium may be steel or rods, or balls, hard rock, or, in some cases the ore itself. In the grinding process, particles between 5 and 250 mm are reduced in size to between 10 and 300μm. Greater than 100μm can be considered as coarse grinding and less than 100μm can be considered as fine grinding. Low-speed tumbling mills and roller mills belongs to this category. Work on charge motion dates back to 1919 by Davis who developed a physical and mathematical description of the ball charge motion, although it may be argued that this is based on the earlier work of White (1905). According to Davis, particles move in a locked manner in a circular path until a point is reached where the centrifugal and gravitational forces balance. At this point particles commence free fall in a parabolic path until they impact the mill shell and start their circular path once more. The point of projection of a particle from the body of the charge, under the condition of no interference from other particles in the charge or any sticking effects, was given by a circle, know as the ‘Davis Circle’, of radius g/2Ȧ2 whose center was vertically above the center of rotation of the mill at a distance of 2Ȧg . The Davis circle idea is presented in Fig.2.3. Fig.2.3 The Davis Circle (Redrawn after Davis, 1919).

More intense studies on this aspect were initiated in 1970’s. Most of this work was related to the prediction of the mill power draw. Hogg and Fuerstenau (1972) considered the widely accepted theory of materials in horizontal rotary kilns and developed an idealized charge motion as shown in Fig.2.4. They assumed that this shape remains constant with changes to mill speed and load. Fig.2.4 Idealised charge motion (Redrawn after Hogg and Fuersttenau, 1972).

Based on the motion of the charge in a ball mill, researchers took different approaches to develop a relationship between the power requirement with the mill dimensions and operating parameters of tumbling mills. The correlation of power input with mill dimensions, speed, and load has been brought about by three principal methods: torque formulae, dimensional analysis, and analysis of the ball charge dynamics. In this method, the charge profile is considered as a single mass, and the torque necessary to maintain the offset in the center of gravity is calculated as follows:

gb sinrMT D (2.7) where T is the torque, Mb is the mass of the balls, rg is the distance from the mill center to the center of gravity of the load, and Į is the angle of repose. The power draft, P, is given by 2STNP (2.8) where N is the rotational speed of the mill in revolutions per second. This idea has been exploited by, among others, Hogg and Fuerstenau (1972); they considered an infinitesimal mass in the charge and derived an algebraic equation for potential energy required to lift this mass to the top side of the ball load. Then this energy is integrated over the entire ball mass to compute the total energy supplied from which the mill power is deduced. Their power draft formulae are given by: 6273 UI . 352 sinsinLD.P DT (2.9) where ȡ is solid volume fraction in slurry, ĳ is fraction of critical mill speed, L is mill length, D is mill diameter, and ș is toe angle. Guerrero and Arbiter (1960) considered the circumferential mass flow rate of the charge to find the energy consumption and hence power: 6273 U .52 )J(fLD.P (2.10) where J is fractional mill filling. A commonly used design equation for ball mills was developed by Bond, who incorporated certain empirical results into his power equation: 26212 U .32 210193701 109 I )( )/.)(J.(JLD.P (2.11)

With the advancement of computing capabilities numerical techniques become more popular of describing the charge motion of tumbling mills. These techniques are discussed in detail at later chapters.

2.2.3 Fine and ultra-fine grinding

Many of the base and precious metal deposits discovered recently have been fine- grained and complex, therefore there is a need to grind to very fine sizes. For some ores, adequate liberation of values is obtained only after grinding to an 80% passing size (P80) below 20 μm. It is now widely understood that grinding to such fine sizes economically is beyond the capability of traditional ball mills, so mining companies are being forced to examine alternative machines to obtain a cost effective ultra-fine grinding solution for their ores. Fine grinding is usually the sub sieve particle size and more appropriately sub 10 microns. The measure of the fineness of grind is often taken as a percentage of material passing 75 microns and if this percentage is high then one would conclude that the grind is fine. However, the standard sieving arrangement allows to go as low as 25 microns and this is still in the fine grinding range. Special cloths can be used to screen down to 10 microns and below this size cyclosizers would be the best method to obtain fractions. Cyclosizing depends on density so the particle sizes in the different fractions are highly dependent on the ore density. .

Stirred milling is an emerging technology for ultra-fine grinding. Differences between commercially available stirred mills are evident in terms of stirrer design, mill orientation (vertical or horizontal), available power intensity and in the means of separating balls (or beads) from the slurry. Stirrer designs by various manufacturers are shown in Fig.2.5 (after Heinrich and Kreitner, 1981). Of the vertical stirred mills, two designs have found application in mineral processing; mills with a spiral stirrer design (Fig.2.6a) and mills with pin stirrers (Fig.2.6b). Among the horizontal stirred mills most commonly used one is mill with rotating discs (Fig.2.7).

Fig.2.5 Different Stirrer designs used by the industry for stirred mills. (a) (b) Fig.2.6 Vertical stirred mill: (a) Sala Agitated mill; (b) Svedala VertiMill.

Fig.2.7 Netzsch horizontal stirred mill.

Stirred media mills are used successfully for fine and ultrafine grinding of several products. Basically the stirred media mill consists of a stirrer placed in the centre of a fixed grinding cylinder. The so-called grinding chamber is filled with grinding media (normally spherical glass, steel or ceramic beads) and a suspension containing the product particles. The filling rate of the grinding media (bulk volume related to the net volume of the grinding chamber) normally varies between 0.7 and 0.85. By stirring the product-fluid-grinding media mixture a characteristic flow pattern and a grinding effect is generated in the grinding chamber. The respective kind of flow determines the spatial distribution of zones with high comminution intensity as well as the predominant types of comminution mechanisms and their composition. The designed power intensity for horizontal stirred mills is an order of magnitude higher than that of vertical ones. Furthermore, as the power intensity is increased so is the ability to grind effectively to finer sizes. Apart from power intensity, a major difference between vertical and horizontal stirred mills is in the way that the grinding media and ground product are separated. In general, vertical stirred mills rely on a settlement zone at the top to separate the media from the slurry product. To prevent the media from overflowing, the highest stirrer tip speed is limited to about 3 m/s and the smallest media size is about 3 mm. These two limitations of vertical mills appear to confine the finest economical top product size to about 10 μm. Compared with horizontal stirred mills, however, the vertical stirred mills have the advantage of a simpler design in that there is no need for a mechanical seal on the stirrer shaft. The horizontal stirred mills use a closed milling chamber. Milled product is separated from the media mechanically through a screen or a ring gap at the discharging end. A certain pressure is maintained in the milling chamber to keep the mill charge suspended and to retain the necessary residence time for achieving the required product. Since the media and product are separated mechanically, the stirrer tip speed can be as high as the mechanical design of the mill allows (normally up to 15 m/s) and the media size can be as small as 0.5 mm. The high stirrer speed and small media size have improved the efficiency of grinding to very fine sizes enormously. As the power intensity is increased, so the engineering complexity required to deal with that energy is increased and the more difficult it becomes to build large mills. In mineral processing this limitation becomes a difficulty when there is a need to treat large flows. It is possible to treat quite large flows in a tower mill circuit, but production of a very fine product becomes difficult and depends heavily on maintaining accurate classification. IsaMill The IsaMill is a stirred type mill developed by Mt Isa Mines Limited (Australia) and Netszch- Feinmahltechnik (Germany) in 1990s. It is in fact a large version of the Netszch horizontal stirred mill which was being used for various ultrafine grinding applications in various chemical processing industries. The IsaMill is available in three models (named according to net grinding volume in liters): • M1000 (375 kW) • M3000 (1,120 kW) • M10000 (2,600 kW) IsaMills are installed in more than two-thirds of the world’s ultra fine grinding metalliferous applications and quickly demonstrated its ability for very power efficient grinding to less than 10 microns (Gao et al, 2001). The most distinctive feature of the IsaMill is its media separation system that enables slurry to exit the mill but prevents the grinding media from leaving the mill (Enderle et al, 1997). Fig.2.8 shows the schematic diagram of the IsaMill.

Fig.2.8 Schematic illustration of the IsaMill.

One of the major issues for IsaMil is the medium selection. The cost of traditional medium for stirred mills such as silica-alumina-zirconia (SAZ) bead are comparatively high. Thus alternatively low cost medium must be sought, preferably local and dispensable. Further study discovered that there were two waste materials that could be used as the medium for the IsaMill (Gao et al, 1996). They are the copper reverberatory furnace slag (CRFS) and the heavy medium plant rejects (HMPR). After extensive trials in laboratories and in full scale plant operations, these local waste materials were successfully used as the IsaMill grinding medium for producing products with 80% passing 10 microns or finer. Fig.2.9 shows CRFS and HMPR medium performance obtained using 1.5 liter laboratory mill. P80, microns P80, microns Fig.2.9 CRFS and HMPR media performance (Gao et al, 2001).

2.2.4 Experimental results of fine grinding For development and refinement of any technology, an understanding of its fundamental processes is required. The fundamentals of fine grinding were established by Klaus Schonert in the 1980s and the fundamentals of stirred milling where developed in the 1980s and 1990s by Steier, Schwedes, Stehr, Kwade and others. This work led to the development of a new generation of stirred mills capable of grinding finer and finer. The active grinding volume in a stirred mill is shown in Fig.2.10. Grinding is a consequence of the velocity gradient between the grinding media and the particles in the slurry which generate stress events. The different gray shades in Fig.2.10 indicates the different stress energies (dark zones=high stress energies) present within the volume of a stirred mill. The distinct stress energy regions in the mill are as follows: V1 – Media tangential velocity drops from a high velocity at the disc surface to about 50% of the tip speed over an axial distance of 2.5 mm, independent of disc size and disc spacing, but dependent on grinding media size. V2 – Media tangential velocity drops from almost tip speed to almost zero. V3 – Small stress energies are acting within about 60% of the mill volume. V4 – The grinding media and particles are interacting with almost the same velocity thus resulting in negligible stress energies. This region comprises about 25% of the mill volume. Fig.2.10 Different stress energy region in the grinding chamber (After Stender et al, 2001, 2004).

The mechanisms of motion of the stirred product-bead fluid mixture in the grinding chamber are very complex. According to Molls and Hornle (1972) they are affected by forty-four parameters and can only he calculated by means of an appropriate (from the mathematical point of view) realizable limitation of the problem. Therefore, different approaches are available for stirrer type mills to understand the fundamentals of the complex grinding process. Most commonly used entity is the specific energy of the mill. As the investigations of Schwedes, Welt and Stehr (1992, 1993) have shown, the specific energy input (net energy input into the grinding chamber related to the mass or the volume of the product) is the main parameter which determines the comminution result. The specific energy describes the influence of mill size, circumferential speed of the stirrer, solids concentration of the suspension and density of the beads on the comminution result for a wide range. Thus, the respective value of the specific energy characterizes the efficiency of comminution without knowing the predominant combination mechanisms which are mainly dependent on the motion of grinding beads and suspension. In 1999, Theuerkauf and Schweded were explored the operation of both horizontal mills with disc stirrers and vertical pin mills. Media velocities were measured using a light- sheet technique (Fig. 2.11). When comparing the mixing achieved by disc and pin type stirrers, it was found that the flow field resulting from the pin stirrer was more mixed. The pin type stirrers exhibited higher and more fluctuating circumferential fluid velocities than the disc stirrers. It was therefore confirmed that to achieve intense mixing, a stirrer with pins should be used.

Fig.2.11 Radial-axial fluid velocities (Theuerkauf and Schwedes, 1999).

Numerous studies conducted in the last ten years have shown that stirrer speed and grinding media density and size have a significant influence on comminution results. Work published by Kwade and Schwedes (1996, 1999) indicates that in high speed stirred mills the effect of mill tip speed, media size and density can be evaluated simultaneously using the grinding media “stress intensity” approach:

3 2 SIm = mm UU v)(D t (2.12)

where: SIm = stress intensity of the grinding media (Nm)

Dm = grinding media size (m) 3 U m = grinding media density (kg/m ) U = slurry density (kg/m3)

vt = stirrer tip speed (m/s) For different specific energy inputs, different relationships exist between the stress intensity and product fineness. In Fig.2.12, the curves for six different specific energies were presented. Each curve has a different optimum value of stress intensity. With increasing specific energy and therefore increasing product fineness, the optimum stress intensity decreases because with decreasing particle size, less stress energy and smaller forces of pressure are required to break a product particle.

Fig.2.12 Product fineness as function of stress intensity and specific energy input for comminution of limestone (After Becker et al, 2001).

In 1993, Gao et al have conducted series of laboratory experiments to identify the most important parameters of stirred mill that can affect the grinding performance. Four important parameters of the Drais stirred ball mill, i.e., the bead density, slurry density, mill speed, and the effect of dispersant were selected for investigation. The experimental work was based on a factorial design and 27 milling tests were conducted. It is found that the bead density has an optimum value of 3.7 g/cc in this investigation. A lower slurry density and a smaller amount of dispersant appear to be better conditions. The mill speed should be as high as possible within the speed limit tested in this work for the best process efficiency. A mathematical model has also been developed by Varinot et al(1999), based on the experimental results, for the influence of the operating parameters stirrer speed, solids concentration, bead diameter on the particle size distribution of the product. This model treats grinding kinetics separately from the flow through the mill and shows that associations of mills in series can decrease the spread of the product size distribution. A mathematical model of continuous grinding was obtained by combining batch grinding kinetics and solids residence time distribution. The flow model proposed for the mill used in this study suggests that this can be done either by multiplying the number of identical mills associated in series or by multiplying the number of passages through the same mill. Experiments performed with the same overall residence time in the mill but with different numbers of passages through the grinding chamber showed that the median diameter and the spread of the distribution are actually decreased when the number of passages is increased even changing the ‘‘shape’’ of the distribution which becomes more narrow. This method is therefore a very simple and a low-cost way of controlling the particle size distribution of the product both in terms of median diameter and spread with no additional equipment. M. Becker et al (1999) carried out an experimental investigations on the comminution of fused corundum and silicon carbide and showed that the comminution behavior as well as the wear behavior is affected by the size of the primary particles of which the grinding beads consist. The energy input into the grinding chamber is not only used for the comminution of the product particles but also for the comminution of the wear particles. If the size of the primary particles of the grinding beads is relatively small (<1.5 μm) the grinding bead wear essentially depends on the hardness of the beads as well as on the hardness and the shape of the product particles. Therefore, to minimize the specific energy requirement and the contamination of the product, grinding beads which are composed of small primary particles (< 1.5 μm) and have a high hardness as well, should be used. Fig.2.13 Effect of grinding bead wear on relation between specific energy and product fineness for the comminution of fused corundum (Becker et al, 1999).

Fig.2.14 Effect of hardness of grinding beads, hardness of product particles and shape of product particles on grinding bead wear (Becker et al, 1999).

Another approach of stirred media grinding was reported in 2005 by Eskin et al, particularly for nano grinding. A model was proposed to describe the media dynamics based on the transformation of the kinetic energy of turbulence into the kinetic energy of the milling bead fluctuations. The dynamics of the milling media in a turbulent flow was considered. The mean velocity of the milling beads was calculated on the assumption that the power spent on stirring is transferred into the energy of turbulent eddies. The energy spent on stirring dissipates as a result of media–liquid viscous friction, lubrication, and by inelastic collisions of the beads with each other. The maximum force at which the milling beads can compress particles between them was calculated by the Hertzian theory of elastic impact. The frequency of compressions for a single particle was evaluated by probabilistic analysis. A criterion of milling efficiency, based on calculating the energy spent on the plastic particle deformation, was proposed. In this simplified analysis, the circulation streams between discs were neglected only considering rotating flow where velocities were assumed to be linearly distributed along the radius. This one-dimensional analysis may be useful for specific grinding conditions such as nano size particles which fails to establish a solid foundation for general stirred milling technique due to some of the rough assumptions.

Scale-up A typical scale-up procedure for designing large industrial-scale mills consists of several steps (Herbst et al, 1980). First, laboratory experiments in smaller size mills are conducted under identical operating conditions to obtain the breakage properties of a particular ore. Then, these properties are scaled to larger mills using suitable mathematical models. In the end, the mill dimensions are computed from the feed and the estimated product size distributions. For Isamill process, currently there are no available rigorous methods to determine how this process should be scale-up. The most commonly used method to scale up from lab tests is to look at the specific energy consumption. Essentially, the power consumption on the mill and the mass flow rate need to be recorded. The typical values recorded are the kilowatt input and the mass flow rate in tons per hour. By dividing the kilowatt input by the mass flow rate, the specific energy input is given in kilowatt-hours per ton, the specific energy consumption. A slightly more accurate method is to use a totaling kilowatt-hour meter. The mass of the entire batch processed through the mill is known, even in a ‘continuous’ process. By dividing the total kilowatt hours used by the mass of product processed, kilowatt hours per ton can be determined. It is reported that the energy versus product P80 relations of the two mills fell on the same a straight line on a log-log scale (Gao et al, 1996). Fig. 2. Variation of specific energy consumption and product size

In addition, two most commonly used empirical methods involve matching power ratio to the tip speed velocity at constant rotational speed and power ratio to the volume ratio at constant tip speed.

3 P1 § v1 · at constant rotational speed v ¨ ¸ (1) P2 © v2 ¹

2 3 P1 § V1 · at constant tip speed; ¨ ¸ (2) P2 ©V2 ¹ where P is the power consumption, V is the mill volume, and v is the tip speed. Validity of these relations is verified by the industry and now it is standard practice to use this relations for actual scale-up of IsaMill. However, scaling of microdynamic properties which are useful to identify the grinding performance of the IsaMill process has not been studies up until now. Therefore, there is a need for research in this direction.

2.3 Numerical techniques 2.3.1 Population balance method

Population Balances is a widely used tool in engineering, with applications including crystallisation, pharmaceutical manufacture, pollutant formation in flames and growth of microbial and cell populations (Ramkrishna, 2000). Wherever the interaction of a large number of particles (eg. gas-phase nano-particles, liquid droplets in liquid-liquid dispersions or solid powder agglomerates) is studied, solution of the population balance equation is necessary to determine the properties of the resulting product and its dependence on processes such as coalescence, breakage and surface growth.

Populations balance methods for well-mixed batch milling process was introduced by Epstein (1947), and developed further by several researchers (Whiten, 1974; Herbst and Fuerstenau,1968, 1973; Austin and Shah, 1983).

w )t,x(m f ³ dy)t,y(m)t,y(S)y,x(b)t,x(m)t,x(S (2.13) wt x

with 0 ini )x(m),x(m where t, m, S, and b represent time, mass density distribution function, specific breakage rate function, and normalized breakage distribution function, respectively. Let us consider a sufficiently small time interval ǻt during which only a single breakage of some particles of size x occurs. Then, the product S(x,t)ǻt defines the fraction of particles of size x selected for breakage, also known as the selection function. The normalized breakage distribution function, b(x,y), describes the fraction of progeny particles in size range x + įx formed directly when unit mass of particles of size y is broken ( y t x ). In view of these definitions, the first term in Eq. (2.13) represents the death rate of particles of size x due to breakage of particles of size x, while the second term describes the birth rate of particles of size x due to breakage of all larger particles of size y t x . The size parameter x is usually taken as a linear dimension such as an equivalent sphere diameter. One can also choose particle volume as the size parameter, which makes the particle change mechanisms more apparent for physical interpretation (Scarlett, 2002). The traditional linear population balance theory has been subjected to some criticism by many researchers (Austin, 1971; Rajamani, 1995; Verma, 1995; Gupta, 1986; Yildirim, 1999; Meloy 1992) and various concepts and theories have been proposed for the breakage and selection functions. The traditional population balance model for batch milling process is a linear integro-differential equation which is known as linear time- invariant (LTINV) model if the specific breakage rate does not vary with time, otherwise it will be referred to as the linear time-varying (LTVAR) model. The LTVAR model was introduced to explain some of the experimentally observed deviations from the predictions of the LTINV model (Austin 1981). Regardless of the time-dependence and the functional forms of selection and brakeage functions, the linearity has been the fundamental assumption in the traditional population balance method for milling processes (Austin, 1971; Bilgili, 2003). Simpler analytical solutions were obtained assuming special functional forms for S and b (Gaudin, 1962; Harris, 1968). As the experimental data for batch milling is invariably in discrete form, the following size- discrete form of Eq. 2.14 is usually preferred over the size-continuous form (Prasher, 1987; Austin, 1971; Sedlatschek, 1953):

i1 i )t(dm ii ¦ jjij )t(m)t(Sb)t(m)t(S , (2.14) dt j 1

jiN ttt 1 with i 0 m)(m ini,i

where i and j are the size-class indices running up to N; and mi, Si, and bij represent the size-discrete counterparts of the continuous functions defined above. The convention is such that size class 1 contains the largest particles (the coarse), whereas size class N, also called the sink, contains the smallest particles. Due to mass conservation, SN must be equal to zero. Eq. 2.14 is the most widely used form of the PBM for batch milling processes. Previously, several researchers have proposed the concept of energy-based breakage rate and breakage distribution functions and have attempted to derive these functions from the collision patterns inside a mill (Narayanan, 1987; Cho, 1987; Hofler and Herbst, 1990; King and Bourgeois, 1993; Morrell and Man, 1997). Some of these models did not have adequate information about impact patterns in the mill, and in other cases, the models were too complex and required a considerable amount of parameter estimation. In order to reduce the difficulties encountered in the previous efforts, a simple and direct model is formulated by Amalan Datta et al (2002) that requires minimal parameter estimation. This work was based on collision energy. During the tumbling action in a ball mill, it is assumed that each collision nips a certain amount of material of a particular size class and breaks some material in that class. The broken material is redistributed in the lower sizes, and this distribution depends on the energy of that collision. The breakage due to the tumbling action, as shown in Fig.2.16, is assumed to be equivalent to subjecting individual layers of particles to a series of impacts of various energy levels at an identical rate. Fig.2.16 Grinding phenomenon in a ball mill as interpreted in terms of collision energy and frequency (Datta et al, 2002).

It is assumed that collisions of energy ek are generated in the tumbling charge at a rate of Ȝk collisions per second and that each collision of energy ek nips mj,k grams of particles in size interval j. The breakage function based on the energy, bij,k, is defined as the fraction of that mj,k grams of broken particle from size j that reports to a smaller size i. For all size classes of particles and all collisions associated with various levels of energy, a population balance equation for a batch grinding mill can be written as: N N i1 i )t(dM i )t(M j )t(M ¦O m k,ik ¦¦O bm k,ijk,jk (2.15) dt k 1 H k 1 j 1 H

The term Mi(t)/H in Eq. (2.15) represents the instantaneous mass fraction of size class i in the mill. The model equation incorporates three input terms: the impact energy spectra, broken mass in the particle bed at a given impact energy, and the energy-based breakage function. The first one is obtained from the Discrete Element Modelling simulation of ball charge motion, and the other two are experimentally determined from drop-ball tests. Some of the draw backs of this method are: z Breakage of particles due to abrasion is negligible. Impact is the only mode of energy transfer from the grinding media to the particles. In other words, shearing of particles during ball-to-ball or ball-to-wall collision is absent. z There is no progressive damage leading to breakage due to low-energy impacts, i.e., breakage due to repeated collisions at low energy is not accounted for in the model. z The linearity assumption is also implied here, i.e., the broken-mass and breakage functions remain the same as the size distribution changes in the mill.

2.3.2 Computational Fluid Dynamics (CFD) Modern CFD techniques emerged between the late 1960s and early 1970s when fluid flow investigations were largely experiment based and only very simple fluid flow problems could be accurately numerically solved. With the rapid development of modern computational techniques and numerical solution methodologies over the last few decades, CFD has now been widely used in various industrial applications for investigating a vast range of industrial and environmental problems. The constituent equations for fluid flows are well established and they are basically in the form of a coupled set of partial differential equations, known as the Navier–Stokes equations (Blecher, 1967), Different ways of numerically solving these equations give rise to different CFD techniques in which various forms of these equations may be employed. In the framework of the finite difference/volume technique, the most fundamental solution method is referred to as the Direct Numerical Simulation (DNS). In the DNS method, the transient form of the Navier–Stokes equations is solved numerically by means of spectral and pseudospectral techniques. The fundamental parameters required to describe a fluid flow are the pressure and the velocity of the fluid flow. If the flow is assumed to be incompressible and Newtonian, then these parameters are solely governed by the constitutional Navier–Stokes equations which are based on the basic physical principles of conservation of mass and momentum. For an incompressible and turbulent fluid flow, the Reynolds-averaged form of the Navier–Stokes equations may be written in a Cartesian coordinate system as follows (Hinze, 1975): Navier–Stokes equation

wu i wu i wp w ª § wu i wu j ·º wW ij UU u j P¨ ¸ Ug i (2.16) j ji « ¨ j i ¸» j wt wx w wxx ¬ © wx w ¹¼ wxx Continuity equation wu i 0 (2.17) wx i

where xi represents the components of the Cartesian coordinate system (i = 1, 2, 3); t represents the time; ui, p, ȡ and μ are the mean fluid velocity components, pressure, density and molecular viscosity, respectively; and gi represents the gravitational acceleration. The first term on the left side of equation (2.16) represents the rate of change of momentum per unit volume with respect to time, the second term represents the change of momentum resulting from advective motion. On the right side of the equation, the first term is the force resulting from the pressure differences in the fluid flow, the second term combines the viscous shear forces resulting from the motion of the fluid and the third term is the force produced by the turbulent fluctuations of the fluid particles. This third term is a result of the Reynolds-averaging of the original Navier–Stokes equations, known as the Reynolds stress tensor and defined as

(2.18) and, in practice, it represents the effects of the turbulence on the fluid flow.

Blecher et all (1996) developed a numerical method based on laminar stirred, homogeneous Newtonian fluid (in the absence of beads). The flow pattern of the stirred Newtonian fluid was calculated using a simulation program (finite volume procedure). Furthermore, the distribution of the specific energy in the grinding chamber was calculated directly from the flow pattern previously determined. Finally, the motion of individual spherical beads exposed to the flow pattern of the stirred fluid was investigated. Steady-state stirring of the Newtonian fluid and discontinuous processing was provided in all investigations. Fig.2.17 shows the schematic diagram of a stirred mill and the calculation domain considered by Blecher.

Fig. 2.17 Rd = 60, Rs = 21, Rc = 75, Dd = 43, Wd = 9, Lm= 380; all dimensions in mm Fig.2.17 Stirred ball mill (Blecher 1996).

Fig.2.18 shows one of the experimental results of Weit (1987) characterizing the entire power consumption of the mill represented in Fig.2.17 in terms of the Newton Ne and the Reynolds Re number which is defined as: P Ne 23 (2.19) RV dd U RV U and Re dd (2.20) K The results were obtained in discontinuous stirring experiments using homogeneous Newtonian fluids carried out in the absence of beads. It was shown that the power values obtained from the power number correspond well to the experimental results. Depending on the Reynolds number three different ranges of power input was defined which can be approximated using correlations known from stirring technology. Range I can be approximated by the power input of a cylindrical agitator of radius R operating in laminar state. The two other ranges were approximated by power inputs of disc stirrers operating in laminar (range II) or turbulent (range III) states. For three ranges, three completely different flow patterns in the grinding chamber with different energy distributions can be expected. The results represented in the Fig. 2.18 confirm this assumption for the laminar ranges I and II except the turbulent range III. Turbulent range has not been investigated yet.

Fig.2.18 Power characteristics of the stirred ball mill (Weit, 1987).

Study from Blecher et all (1996) reported that near of the shaft (Fig.2.19) the fluid is rotating like a solid body. Thus for an identical radius the tangential velocity of the fluid corresponds to the velocity of the rotating disc. With increasing radial distance to the shaft a velocity profile develops with decreasing values in positive z-direction. The highest velocity gradient was located at the disc surface. Another profile with a similar course was found above the non-dimensional outer disc radius at r = 1.05. Due to the no-slip condition at the disc surface maximum speed values of u = 1 m/s occur at the outer radius of the disc. The shape of the velocity profile shown in Fig.2.19 is characteristic for all investigated Reynolds numbers. By increasing the Reynolds number significant qualitative modifications of the flow profile just occur in the vicinity of the disc, where the gradients in axial direction become higher. Figure 2.19 shows a characteristic result of the velocity distribution in the calculation domain for range I (here: Re = 10). Velocity vectors which were composed of the radial and axial velocity components (secondary velocities) were represented. This figure proved that a cyclic flow exists in the r-z plane. The cyclic flow is caused by the fluid driven outwards by the rotating disk (centrifugal effect). After driven outwards the fluid is diverted at the chamber wall. In order to satisfy the continuity equation the fluid has to flow back to the direction of the shaft from where it is driven outwards again. The order of magnitude of the secondary velocities is very low (see the scale at the right hand side of Fig. 4). Compared to those of the tangential velocity they are located in the per mill range. This is a typical result for calculations carried out in range I of power input. In the vicinity of the outer disk radius and on the symmetry line between two disks the velocity reaches maximum values of about 8%0 of the circumferential speed of the agitator disk. Therefore, compared to the tangential velocities the secondary velocities are negligibly small. Thus they do not contribute much to the specific energy consumption which is considerably responsible for the product fineness that can be achieved. Above mentioned techniques are particularly applied for laminar flow of the mill. Since stirred mill operate at high speeds, it was evident that the high turbulent regions are created within the mill.

Fig.2.19 Radial and axial velocities (Blecher et al, 1996).

2.3.3 Discrete Element Method (DEM) In the recent research, numerical modelling based on Discrete Element Method (DEM) (Cundall and Stack, 1979) has been extensively used in the study of particle flow for various systems (Yu, 2003). The DEM refers to a numerical scheme that allows finite rotations and displacements of discrete bodies which interact with their nearest neighbor through local contact laws, where loss of contacts and formation of new contacts between bodies take place as the calculation cycle progresses. Cundall and Strack (1979) originated the DEM concept and applied it to model the behavior of soil particles under dynamic loading conditions. Subsequently, this technique has been adapted as an alternative to the continuum mechanics approach in modeling a variety of physical systems (Cleary, 2001; Kano and Saito, 1998; Langston et al., 1995; Mishra, 2003; Yang et al., 2003a; Zhou et al., 2003). In a system of N particles interacting via forces, each particle can possess two types of motion, namely, translational motion and rotation motion, which can be described by Newton’s second law of motion, given by

m Fr iii (2.18)

I ș Tiii (2.19) where ri, Ti, mi and Ii are, respectively, Cartesian coordinates, angular position, mass and moment of inertial of particle i. Fi and Ti represent the total forces and total torques acting on the particle. It is an essential part of DEM simulation to correctly evaluate the contact forces between the particles in collision by employing accurate and efficient force-displacement models. A detailed specification of forces will be presented in chapter 3. Solving two systems of 3N second-order differential equations, particle trajectories can be computed. In DEM, the ordinary differential equations such as Eqs. (2.18) and (2.19) are integrated numerically using a step-by-step integration procedure. Assume that the particle positions, velocities, and other dynamic information are known at time tn. The task is to compute the forces and moments that act on each particle at tn, then to compute the new position and velocity etc. of each particle at later time tn+Gt to a sufficient degree of accuracy. The process is repeated until the unbalanced forces and momentums approach equilibrium or until the process is stopped. Among the many integration algorithms most widely used algorithms are the Verlet algorithm, which is a direct solution of the differential equations, and the Gear predictor-corrector algorithm (Allen, 1987). The choice of the time step Gt is more crucial in DEM simulation. (Allen, 1987). In order to have least number of time steps, Gt has to be as large as possible. However, if the time step is too large the simulation becomes inaccurate and can even become unstable. Therefore, it has to be sufficiently small such that any disturbance does not propagate further than that particle’s immediate neighbors within one time-step. Several possible criteria have been developed to establish a trial step (Thompson and Grest 1991). Ultimately, the only sure test is to discover empirically if the simulation is stable and leads to consistent results with small variations near to a particular value of the time step. Various types of contact relations are available to describe the interaction between particles. These models include contact between smooth, spherical, non-spherical, cylindrical, and non-cylindrical elastic particles with friction and surface adhesion. The simplest contact model is the linear contact law in which the spring stiffness is a constant. This type of contact model has been used extensively by many investigators to analyze tumbling mill problems (Cleary, 1998; Hoyer, 1999; Inoue and Okaya, 1996; Mishra and R.J. Rajamani, 1992). An improvement over the linear law can be made by considering the Hertz theory to obtain the force deformation relation. This approach has been extended to the cases where colliding bodies tend to deform. Here, the Hertz theory is employed to obtain the force deformation relation for the contact. Unlike the linear contact model, according to the Hertzian contact law the normal stiffness kn varies with the amount of overlap. Here again one can assume a very small amount of overlap to evaluate the stiffness from the Hertzian model and use the value as a constant in DEM models. DEM enjoys a wide range of application; indeed, in recent years, there has been a rapid advancement in the understanding of tumbling mills through computer simulation using the discrete element method. It has thus far been able to qualitatively capture the behavior of the charge in ball, semi-autogenous, planetary, and many other types of tumbling mills (Cleary, 2001; Mishra, 2003; Radziszewski, 1999; Rajamani et al., 2000b; Venugopal and Rajamani, 2001). Quantitatively, it also allows accurate predictions of individual particle trajectories, distribution of contact forces and energies between collisions, wear, and most importantly, power draw. In the forthcoming sections, application of DEM in milling industry, particularly for tumbling mills and horizontal rotating drum has been discussed. Application of DEM in rotating drum Particle flow in a partially filled rotating drum which is similar to ball mill is an another area which DEM can assists with. DEM has been applied to this area since 90’s and make a significant contribution in better understanding of particle dynamics. To validate the numerical model, extensive comparison has been made between simulated results and measured ones (Yang et al, 2003). More detailed, quantitative comparison was also carried out, such as mixing pattern (Yamane et al., 1998), angle of repose (Yamane et al., 1998; Yang et al., 2003), and velocity field (Yamane et al., 1998, 2003). Mishra et al used DEM to analyse the wet granulation process in the rotating drum. In this work the (Mishra et al, 2002) agglomeration process was modeled by the DEM that incorporates rigorous contact models for particle–particle interaction in the presence of adhesion. The model was developed to study the agglomeration problem in two- dimensions only. Using this model it was possible to predict the steady-state size distribution of the agglomerate mass for a very hypothetical and simplified system. Nevertheless, the preliminary simulation results clearly illustrate the dynamic nature of the process. In particular it was determined that due to the very nature of the agglomeration process in a rotating drum the largest size of the agglomerate attainable is finite for a given set of operating conditions.

Fig.2.20 Agglomeration of particles in a rotating drum: (a) initial state; (b) intermediate state after one and quarter of revolutions (Mishra et al, 2002).

Yang et al (2003), have analysed the flow structue in terms of porosity and coordination number, and force structure such as particle interaction forces, relative collision velocity and collision frequency. Numerical results were compared against the PEPT measurements and reported that both resutls shows dynamic angle of repose increases linearly with the speed of rotation. Such linear relationships have also been found in the work of Yamane et al (1998). Fig.2.21 Dynamic angle of repose as a function of rotation speed (Yang, 2003).

Fig.2.22 Time-averaged spatial distribution of (from left to right): porosity, coordination number, (snapshot) force network, total force (mg), collision velocity (m/s), and collision frequency (1/s) in a cylindrical rotating drum for granulation when rotation speed is 20 rpm (Yang, 2003).

A computational study (Finnei, 2005) using three-dimensional DEM simulations has been performed of mixing in horizontal rotary kilns. Separate descriptions have been formulated for mixing in longitudinal and transverse directions. The transverse mixing is vigorous, while the longitudinal mixing is slow. DEM simulations have been performed for various values of the primary operating conditions, i.e., the rotational speed and the filling degree. The results of the simulations showed that longitudinal mixing can be described by a one-dimensional diffusion equation. The dependence of the corresponding diffusion coefficient on the operating conditions has been determined. The diffusion coefficient D* is proportional to the rotational speed ȍ, while its dependence on filling degree J is weak. Mixing in the transverse plane has been characterised by an “entropy”-like mixing index M(n). The simulations show that the evolution with number of revolutions of this mixing index is exponential. From this exponential evolution, a transverse mixing speed S has been defined. The dependence of this mixing speed on the operating conditions has been determined from the simulations. It has been shown that, at identical number of revolutions, the speed of mixing in the transverse plane decreases with increasing rotational speed ȍ and filling degree J. A comparison of the transverse mixing speed S in two-dimensional and three-dimensional DEM simulations showed that this mixing speed is higher in the two dimensional case. Furthermore, it was shown that the transitions between flow regimes occur at different values of Froude number Fr. Therefore, he proposed that caution should be exercised when using two-dimensional simulations to quantity (three-dimensional) transverse mixing. Another DEM approach was reported by M. Kwapinska et all (2005) to simulate the transverse mixing of free flowing particles in horizontal rotating drums. Calculations were carried out for different drum diameters, drum loadings, rotational frequencies, and particle sizes. Though simple models for inter-particle interactions have been implemented, the agreement with respective experimental data from literature was good. The results have been presented and discussed in terms of mixing times and mixing numbers that means numbers of revolutions necessary for uniform mixing of the solids. This enables comparison with penetration models, as typically applied to thermal processes. Such models were found to provide only a very coarse description of mechanical mixing, and significantly underestimate its intensity. It, therefore, appears reasonable to replace them with DEM approaches for modelling of thermal processes in the future.

DEM for ball mill simulation Early work of DEM on ball mills was developed by Mishra and R.J. Rajamani (1992, 1994) followed by Cleary (1998). Similarly SAG mills were modelled by Rajamani and Mishra (1996) and subsequently by Cleary (2001). Experimental validation has been performed for a centrifugal mill (Cleary and Hoyer 2000) and charge motion predicted in a HICOM mill by Cleary and Sawley (1999). Currently, there are several concerted research efforts directed towards understanding charge dynamics in tumbling mills; notably among them are: Mishra and Rajamani (1990, 1992), Inoue and Okaya (1996), Powell and Nurick (1996), Kano et al. (1997), Zhang and Whiten (1996, 1998), Cleary (1998), Radziszewski (1999), Rajamani et al. (1999, 2000), Van Nierop et al. (2001), Bwalya et al. (2001). Fig.2.23 shows the comparison, where the similarity between the experimental and predicted charge profile is evident. Here they compare typical experimental data obtained from a 90-cm diameter and 15- cm-long batch mill fitted with eight 4 x 4-cm lifters with DEM simulation results. Extensive validation of experimental data can be found in Venugopal and Rajamani (2001) and Dong and Moys. A more rigorous validation would be to predict the velocity, acceleration, and force on a ball. These quantities are difficult to measure but Agrawala et al. (1997) have attempted to do so, albeit with limited success.

Fig.2.23 Comparison of charge motion in a 90-cm diameter mill (Mishra, 1992). The computational demands and lack of sound experimental verification have limited the value of these techniques in the mining industry. To fill this vital gap linking computational results to rigorous experimental data, Powell and Nurick (1996) described the use of diagnostic X-rays for the study of particle motion in an experimental mill. The work described herein is based on an extension and refinement of the technique developed by Powell. The procedure was extended to include automated 3D reconstruction of the particles motion from a sequence of X-ray images taken simultaneously front two different orientations (Govender et al., 2000). It is reported that this method provide highly accurate experimental results which can be compared with the numerical results.

The power draft and grinding efficiency of tumbling mills depend solely on the motion of the grinding charge and the ensuing ball collisions that utilize the input power to cause particle breakage. Empirical correlations sprang up to calculate the mill power draft from design and operating parameters (Bond, 1961; Hogg and Fuerstenau, 1972; Guerrero and Arbiter, 1960; Harris et al., 1985; Moys, 1993). Nevertheless, all the correlations were based on the torque-arm principle where the charge is considered as a single mass. The torque-arm approach to determine power had many shortcomings. Several factors such as shifts in the center of gravity and mill-operating conditions such as mill-speed, ball load, etc., were not incorporated. Keeping that in mind, the next important modification was proposed by Fuerstenau et al. (1990). They incorporated the cascading and cataracting portion of charge separately in their model. Powell and Nurick (1996) also considered the ball mass that are in free flight in his model. Recently, Morrell (1992) and Morrell and Man (1997) developed models that are similar to many of the earlier works on this subject but have much wider applicability and accuracy. Despite these improvements over the years with regard to power prediction, one wonders why even today different manufacturers provide widely differing power estimates for identical mills. The reason lies in a lack of detailed information about the mill charge motion, thereby precluding an accurate steady state prediction of power draw. The discrete element method on the other hand allows the balls to cascade, interpenetrate between layers while cascading, and also cataract (Datta et al., 1999; Cleary, 1998). The balls can bounce off the mill shell and lifters, and moreover, balls of different sizes can collide with each other at oblique angles. To illustrate the accuracy of power draw prediction, a DEM-based computer program, Millsoft (1999), was used. It was originally developed to understand the motion of the charge in ball mills under various operating and design conditions. It has been extensively used for predicting power draft of ball mills over a wide range of diameters. Fig.2.24 shows the predictive capability of the DEM model (Datta et al., 1999) where the power draw comparison is made for different diameter mills in the range of 0.25–4.8 m. The best-fit straight lines in log-scale have a slope of 2.5 and 2.3 for laboratory- and industrial-scale mills, respectively, which are close to the Bond exponent of 2.5. Such predictions verify that the total energy loss summed over all the individual collisions is an accurate indication of power integrated over a specified time.

Fig.2.24 Comparisons of power draw for ball mills of different diameters (Datta et al, 1999).

Liner and lifter wear is extremely important in milling operations. The replacement costs of the liner and the cost of production lost during re-lining are both significant. Minimising these costs is important to improving plant performance. Being able to predict the liner wear is a first step in using DEM simulations to design mill liners that assist in this goal. Wear predictions was modeled from the DEM collisional data collected in the object bins using the Finnie model (Clearly, 1998). This uses particle impact speeds and material hardnesses to estimate the wear produced by each impact. The wear information is collected around the entire mill. Since the lifters and liner spacing in between are symmetric for the mill we are modelling, we can average the wear for each bin of the first lifter with the matching bins on the other 22 lifters. Fig.2.25 shows the typical wear pattern obtained for a mill lifter. Fig.2.25 Wear distribution calculate by the DEM model and the predicted liner shape after 5000 hours of operation for J = 80% (Clearly, 1998).

DEM simulations cannot be run for long enough to actually simulate lifter evolution, but most of the effect can be achieved by using the binned wear rate data and spatially smoothing it with adjacent bins. In this case we smooth each bin with the eight bins to either side. Significant development remains to be done on wear prediction. The Finnie model is the simplest of those available. Replacing this with more sophisticated models would be expected to improve the predictions. The inclusion of the abrasiveness of the charge is also important. Finally, detailed validation against good well defined wear experiments is very important. Other issues that are relevant here are (a) how does liner wear affects the mill power and mill capacity, and (b) how does liner design and operating conditions affect media and liner wear. All these issues can be addressed by DEM simulation of mills with worn out lifters and with the different set of parameters to induce different extent of wear. An extensive research is underway to use DEM predict wear of liners and lifters in SAG mills. Recently, Radziszewski (2002) used DEM to compute the impact energy associated with the collisions inside the mill to estimate wear. This is a step in the right direction that has lot of potential. Most popular model for particle breakage in grinding process is based on the Population balance model. However, there have been arguments and counter arguments about the validity of the population balance model in predicting particle size distribution in the context of grinding (Herbst, 1997). Microscale modeling such as DEM modeling potentially offers an alternative to population balance. In the milling context, microscale modeling involves combining the data relating to single-particle breakage and impact energy to compute the particle size distribution. In simple terms, single-particle breakage data are obtained by dropping a ball of a given size from various heights onto a bed of monosize particles resting on an anvil (Narayanan, 1987; Cho, 1987; Hofler and Herbst, 1990; King and Bourgeois, 1993; Morrell and Man, 1997; Datta and Rajamani, 2002). The impact energy spectra can be obtained through DEM simulations. The model involves combining these two specific pieces of information in a framework that predicts size distribution similar to population balance models. A conceptually simple modeling approach was originally introduced by Rajamani et al. (1993) and followed later by Mishra and Rajamani (1994) and most recently by Datta and Rajamani (2002). It works within the premise that milling involves impacts of various energies. Grinding occurs when these impacts are imparted to particles that are positioned for breakage. Thus, given the impact energy spectra and the corresponding breakage behavior of particles it is possible to make a direct calculation of the resulting size distribution. Fig.2.26 shows the typical impact energy distribution obtained from the DEM simulation.

Fig.2.26 Impact energy spectra obtained from the DEM modeling (Datta, 2002).

Combining impact energy spectrum with the single particle breakage data (Datta and Rajamani, 2002) the size distribution of the particles were obtained. The result of this simulation was claimed to be comparable with the experimental data carried out under identical conditions. Fig.2.27 shows that the predictions and the experimental result within the limits of experimental error. Thus, the DEM combined with the single- particle breakage approach allows the detailed physics of the process to be incorporated in the modeling of the breakage process, which eliminates a lot of inherent empiricism in earlier approaches. Nevertheless, microscale modeling has a long way to go before its range of applicability is increased.

Fig.2.27 Predicted and measured product size distribution: 90.0 cm mill, 20% ball load, 18 rpm, 5.08 cm balls.

2.4 Summary and Proposed Research Stirred type mills are becoming popular in the mineral industry for fine and ultrafine grinding. Despite gaining increasingly industrial importance, study of the grinding of stirred type mills are very limited. Therefore, there is a need for research into the grinding process to be predicted and modeled based on knowledge of the characteristics of the mill and the properties of the grinding materials. Although the dynamics of milling media has been previously studied to some extent, some studies were limited to dilute flows. Computations have been carried out for laminar flow and some studies later for turbulent flow. Multiple trajectories of separate milling beads were computed and measured in some case without grinding media. Thus, until now, no comprehensive theory of the stirred media milling has been developed at a particle scale to understand the microdynamic properties of the mill. With the recent advancement of the computing facilities, numerical modelling based on DEM has been extensively used in the study of particle flow for various systems. In recent years, there has been a rapid advancement in the understanding of tumbling mills through computer simulation using the discrete element method. It has thus far been able to qualitatively capture the behavior of the charge in ball, semi-autogenous, planetary, and many other types of tumbling mills. Quantitatively, it also allows accurate predictions of individual particle trajectories, distribution of contact forces and energies between collisions, wear, and most importantly, power draw. In short, it appears DEM has great potential to extend its range of applicability beyond tumbling mills to more complicated and sophisticated mills that are used in the industry for ultrafine grinding. The objective of this research is to develop a numerical model based on discrete element method to simulate the grinding media of the IsaMill process, investigate the microdynamic properties and establish the relationship between microscopic and macroscopic properties. This will be accomplished by the following steps:

z Developing and validating DEM model to simulate the grinding media of the IsaMill; z Investigating particle properties on grinding performance and power draw; z Investigating operational conditions on grinding performance and power draw; z Investigating mill properties and mill geometry; z Developing wear model in order to predict the disc wear; and z Studying scaling relations and developing scale up laws for IsaMill process. CHAPTER 3

DISCRETE PARTICLE SIMULATION OF PARTICLE FLOW IN THE ISAMILL 3.1 Introduction

IsaMill is a high-speed stirred mill developed by Mount Isa Mines (Xstrata) in Australia for economically grinding minerals to fine and ultra-fine size at an industrial-scale (Gao and Forssberg, 1995). It consists of a horizontally mounted shell and rotating grinding discs mounted on a shaft which is coupled to a motor and gearbox and rotates with disc tip speeds of 10 to 23 ms-1. The grinding discs agitate the media and ore particles in a slurry that is continuously fed into the feed port. The product separator (dynamic, centripetal classifier) keeps the grinding media inside the mill allowing only the product to exit. Simple control strategies based on power draw enable the IsaMill to produce a constant target product size. Comparing with the conventional grinding mills such as ball mill and tower mill, IsaMill can significantly reduce total comminution circuit energy cost (Curry and Clermont, 2005) and reduce the size of mineral particles to as fine as P80 passing 7Pm (Gao and Forssberg, 1995). However IsaMill is still a new technology and most relations established between the quality of the final products and operating parameters of the mill are empirical, and are inadequate to comprehensively understand the grinding process. As a result, its optimum control and scale-up need to rely on empirical methods, experience and trial and error testing, rather than detailed scientific principles. There is a need for research into the grinding process to be predicted and modelled based on knowledge of the characteristics of the mill and the properties of the grinding materials.

The bulk behavior of media particle flow depends on the collected outcome of the interactions between particles and between particle and mill. As a result, a better understanding of the flow at the individual particle scale would greatly facilitate the design and scale-up of IsaMill. However, it is a very difficult, if not impossible, task using experimental techniques to obtain microdynamic information such as voidage, force and velocity distributions within the mill. On the other hand, simulation based on the discrete element method (DEM) (Cundall and Stack, 1979) has been extensively used in the study of particle packing and flow for various systems and has been demonstrated as an effective way to link microscopic information with macroscopic behavior of particle flow (Yang et al., 2004). However, despite the usefulness, DEM simulation studies have not been applied widely to the high speed stirred mill system like IsaMill. This chapter presents a numerical investigation of the flow of grinding media in a simplified IsaMill, aiming to examine the feasibility of using DEM simulation to predict particle flow in a high speed stirred mill. The proposed DEM model is firstly validated with a 1:1 scale experimental setup which allows qualitative and quantitative comparison of flow and mixing patterns and power consumption. Then, the flow of particles will be analysed in terms of velocity, force and power draw.

3.2 Simulation method and conditions

The numerical model is developed based on the theory of Discrete element method (DEM) modelling. DEM was first developed by Cundall et al. for rock mechanic problem and later applied to granular materials (Cundall and Stack, 1979). The general algorithm of DEM is based on the finite difference formulation of the equation of motion and can be described as follows (Allen and Tildesley, 1987; Cundall and Stack, 1979). In a system of N particles interacting via forces, each particle can possess two types of motion, namely, translational motion and rotation motion, which can be described by Newton’s second law of motion, given by

dv i n s mi ¦ ij ij mi gFF (3.1) td j and

dȦ I i s R FFR n ˆ i ¦ iji u P ijir Ȧi (3.2) td j where vi, Zi and Ii are, respectively, the transitional and angular velocities, and moment of inertia of the particle. Ri is a vector running from the centre of the particle to the contact point with its magnitude equal to particle radius Ri. The first part of the right

s side in Eq. (3.1) is the torque due to the tangential force Fij , the second part is the rolling friction torque arising from the elastic hysteresis loss or viscous dissipation, and

Pr is the coefficient of rolling friction (Brilliantov et al., 1996; Tabor, 1955). This frictional resistance has been demonstrated to play a critical role in achieving physically or numerically stable sandpile, viz the unconfined packing of particles although it is still unclear which model can best decribe rolling friction (Zhou et al., 1999). Fig.3.1 Schematic illustration of the forces acting on particle i from contacting particle j and non-contacting particle k.

The normal contact force consists of two components: an elastic, conservative component due to the deformation or overlap [n and a viscous, dissipative component due to the dissipation of energy in the solid particle linked to normal impact velocity. Using the nonlinear Hertz model, the normal force acting on particle i, due to the collision with particle j is given by (Brilliantov et al., 1996; Johnson, 1985):

3 n ª2 º 2 Fij nn RERE [J[ nnv ˆˆ ijijijn (3.3) ¬«3 ¼» where parameter E =)Y 1/( V~2 , Y and V~ are the Young modulus and the Poisson ratio,

nˆ ij is a unit vector running from the centre of particle j to the centre of particle i, and

RRRRR jiji )( . The normal damping constant, Jn, can be treated as a material property directly linked to the normal coefficient of restitution. (Schwager and Poschel 1998; Zhang et al. 2001). The relative motion between particles i and j in the contact surface (perpendicular to the normal direction) leads to a tangential force. This force opposes the motion of the interacting particles in the tangential direction and is given by (Mindlin and Deresiewicz 1953; Langston et al. 1995): 3 ª 2 º § ,min [[ max,ss · Fs sgn P[ n « ¨11F ¸ » (3.4) ij ijss « ¨ [ ¸ » ¬ © max,s ¹ ¼ where Ps is the sliding friction coefficient, [s is the total tangential displacement of 2( V~) particles during contact, and P[ [ (Langston et al., 1995). Eq. (3.4) s max, 1(2 V~) n suggests when two particles start touching each other, a virtual spring is activated in the tangential direction; and if |[s| > [s,max, then gross sliding is deemed to have started, the virtual spring is detached and the frictional force reduces to the Coulomb law of friction.

s s The torque on particle i due to the tangential force is ij u FRT iji , where Ri is a vector running from the centre of the particle to the contact point with its magnitude equal to particle radius Ri.

The mill used in this work consists of three parts (Fig.3.2): a fixed chamber with inner diameter of 120 mm and length of 147 mm, a rotating shaft of diameter of 25 mm, and three discs each of which is 100 mm in diameter and 9 mm in thickness and is 30 mm apart from each other. Each disc has five holes of 18mm in diameter. The mill is divided into different sections/regions along the axial and radial directions for data analysis. Note that the mill used in practice has more discs, but that only generates more regions in which the flow patterns are similar to that in region B. Using fewer discs can reduce the number of particles and speed up the simulation.

(a) (b)

Fig.3.2 Geometry of the model Isamill and different cross sections: (a) axial direction; and (b) radial direction. All dimensions are in mm. Two types of simulations with different boundary conditions were used in this work. In the first type of simulation, the mill has a chamber with two side walls and three discs inside. This would be mainly for model validation by comparing with a 1:1 scale experiment. In the second type of simulations, only one disc was considered in the mill but the periodic boundary conditions applied along the axial direction. This set up corresponds to the region B in Fig.3.2a, and allows large scale simulations with a small number of particles.

A simulation starts with a packing process in which the shaft and discs are at rest and all particles are fed into the mill to form a stable packed bed. Then the shaft and discs start to rotate at a given speed to agitate the particles. In reality, the grinding media mixed with fine slurry are continuously fed into the mill from one end and the fines exit from the other end. However, the present simulation focused on the flow of grinding media (i.e. glass beads) which are sealed in the mill. Therefore, the effect of slurry flow is not considered in this work. A lab mill with the same dimensions was also set up, as detailed in Fig.3.3, to validate the numerical model.

c b

a d

Fig.3.3 The lab mill for model validation: (a) mill body; (b) inlet; (c) motor; and (d) stand.

Table 3.1 lists the values of the physical parameters used in the simulation. It is assumed that the mill has the same material properties as the particles. In this work, the rotating speed (:) and the solid loading (J) of the mill are varied to consider their effects on particle flow. Table 3.1. Physical parameters of the simulation.

Parameter Value

Number of particles 44000 Particle diameter (mm)3 Particle density U (kgm-3) 2.5u103 Young’s modulus Y (Nm-2) 1.0u107 Poisson ratioV~ 0.29

Sliding friction coefficient Ps 0.2

Rolling friction coefficient Pr 0.01 Restitution coefficient e 0.68

3.3 Macroscopic observation and model validation Fig.3.4 and Fig.3.5 show the representative flows from simulations and experiments for different solid loadings and rotation speeds. It can be seen that the overall flow patterns obtained from experiments and simulations are comparable. At low solid loading and low rotation speed (Figs.3.4a and 3.5a), most of particles stay at the bottom of the mill with slow movement, and only a small number of particles are agitated by the rotating disc to the upper half of the mill. Increasing either the solid loading or the rotation speed (Figs. 3.4b, c and 3.5b, c) can agitate the particles more vigorously due to higher chance of collisions between particles and between particles and disc. All cases show that particles near discs obtain larger kinetic energy, move up to the top half of the mill, and then cascade down along the free surface to the bottom half of the mill. (a) (b) (c) (d)

Fig.3.4 End view of experimental (top) and numerical (bottom) particle distributions for different solid loadings and rotation speeds: (a) : = 300rpm and J = 40%; (b) : =300rpm and J = 60%; (c) : = 800rpm and J = 60%; and (d) : = 1000rpm and J = 80%.

(a) (b) (c) (d) Fig.3.5 Axial view of experimental (top) and numerical (bottom) particle distributions for different solid loadings and rotation speeds: (a) : = 300rpm and J = 40%; (b) : = 300rpm and J = 60%; (c) : = 800rpm and J = 60%; and (d) : = 1000rpm and J = 80%;

More detailed comparison can be obtained from the mixing behaviour of the particles in the mill, as shown in Fig.3.6. In the radial mixing, particles of two different colours (light and dark) are initially separated into two vertical layers (Fig.3.6a), then the mill rotates at 100rpm and the particles are gradually mixing together. Fig.3.6b shows the mix pattern after 10 seconds. Both simulation and experiment show that the particles near discs move more vigorously than those near the end wall, mainly because of the strong agitation from discs and the weak influence from the end wall. This causes a much faster mixing process in the central part of mill and therefore more dark particles are found mixed with light particles in the centre. For the axial mixing, particles are initially separated along the axial direction. As particle movement in the axial direction occurs only due to the random inter-particle collisions, axial mixing is much slower than radial mixing. Fig.3.6c shows that, even after 60 seconds, the dispersion of particles in the axial direction is still very limited.

(a) (b) (c) Fig.3.6 Experimental (top) and numerical (bottom) mixing patterns when rotation speed is 100 rpm: (a) t = 0 and (b) t = 10 s for the initial top/bottom layered arrangement; and (c) t = 60 s, for the initial side-by-side arrangement.

Power draw is an important factor for mill design and process optimization. It can be obtained in the experiments by measuring voltage and current across the DC motor. In the simulations, power draw is the product of rotation speed and total torque acting on the discs and shaft. At a particular time, each contact between a particle with the rotating shaft or discs produces a torque on the mill which is the product of the contact force and distance between the contact point and centre line of the drum. The individual torques are summed to give the total torque which, multiplied by the angular mill velocity, gives the power draw of the mill at that particular time. Due to impulsive nature of the interactions between particles and discs, fluctuation occurs in power draw. Averaging the power draw over a certain time gives a relatively invariant value.

Fig.3.7 shows that the power draw increases with rotation speed and mill loading. The overall results from simulation and experiments are quite comparable, and the discrepancy at high rotation speeds can be attributed to the mechanical and other energy losses (e.g. sound and heat) which are not considered in the simulation. Nevertheless, the good agreement between the numerical and physical results in Figs. 3.4-3.7 confirms the validity of the proposed model.

100 J = 80% Physical 80 Numerical

J = 60% 40 Power /(W)

20 J = 40%

0 400 600 800 1000 1200 Speed /(rpm)

Fig.3.7 Comparison of power draw between the physical and numerical experiments at different rotation speeds and mill loadings.

3.4 Microdynamic analysis

Microdynamic analysis at the particle scale can be made based on information such as the trajectories of and the transient forces on individual particles(Yang et al., 2003a; Zhou et al., 2003), which can be readily generated from DEM simulation. To establish a general understanding about the particle flow in IsaMill, the analysis in this section will focus on the spatial distributions of the microdynamic variables related to flow and forces at the macroscopically stable state which is a dynamical equilibrium state of particles at a microscopic level(Yang et al., 2006). Different operational and flow conditions give different flow properties but similar general trends. For convenience, therefore, all analyses below, unless otherwise specified, are based on a single case with rotation speed of 1000rpm and filling level of 80%.

3.4.1. Motion of individual particles

Fig.3.8 gives the trajectories of two selected particles in radial and axial planes from regions A (Pe) and B (Pm). Fig.3.9 shows some microdynamic information of the two particles including their radial and axial positions r and z, radial and tangential velocities Vr and Vt, and total normal forces Fn(p) on them. The total normal force on a particle is the sum of instantaneous contact forces given by Fn(p) = Ȉ Fn,ij . Particle Pm is initially in the upper part of the mill and close to the disc. It then enters into a region where velocity field features with a cyclic flow pattern. In this region, due to the dominant axial velocity Vz, the particle is drawn to the symmetrical plane of the two discs (Fig.3.8b). At this stage, radial distance also changes as a result of high radial velocity Vr. Once the particle enters into the centerline of the two discs, it has limited axial movement due to the interaction with surrounding particles. In this region the radial and tangential velocities Vr and Vt are relatively low. At this stage, the particle has a relatively strong interaction with other particles showing a large fluctuation in forces. So its trajectory is largely governed by the contact force between particles. Since the particle mainly follows a circular trajectory, it tends to move towards the mill shaft (Fig.3.8a), where its interaction with other particles is limited as seen from the evolution of the normal contact force (Fig.3.9).

The same analysis can be applied to particle Pe. The particle is originally between disc and end wall. It then gradually moves towards the disc with relative low radial and tangential velocities. Once it touches the disc a large contact force with the disc is generated at t | 4.0 s, Pe bounces back to the end wall, followed by a slow movement along the chamber of the mill (Fig.3.8a). At this stage, its radial and axial movements are very limited, so the radial and axial positions are almost constant and the radial velocity is almost zero (Fig.3.9). It moves along the mill chamber but with a very small tangential velocity Vt. Its slow movement can also be reflected from the very small force acting on the particle.

Figures 3.8 and 3.9 clearly demonstrate that information at the particle scale can be obtained from the present DEM simulation. Consideration of all the particles in the system, facilitated by a proper temporal and/or spatial average technique, can establish the flow, structure and force fields in Isamill as discussed below.

60 40

40 20 20

0 Y /(mm) Y 0 Y /(mm)

-20 -20

-40 -40

-60 -60 0 20 40 60 80 100 120 140 -60 -40 -20 0 20 40 60 X /(mm) Z /(mm)

(a) (b)

Fig.3.8 Trajectories of two representative particles Pe (ƕ) and Pm (u) at (a) radial plane; and (b) axial plane when : =1000rpm and J = 80%.

60 P 40 m P e

r /(mm) 20

0 P 60 m 40 P e z /(mm) 20 0 e

m P 0.62 1.2 e 0 0.6 P m /(m/s),P /(m/s),P -0.62 r r 0 V V -0.6 -1.25 2.03 P 2.5 e

m e 1.35 1.25 0.67 0 /(m/s),P /(m/s),P t t V

V P 0 m -1.25

P 0.15 e P 0.55 e

m m 0.1 0.27 /(N),P

/(N),P 0 0.05 n(p) F n(p)

F -0.27 0 00.511.52 Time /(s) Fig.3.9 The evolution of some typical microdynamic results: r – radial

position; z – axial position; Vr – radial velocity; Vt – tangential velocity; Fn(p)

– total normal force; of particles Pe and Pm with time when : =1000rpm and J = 80%.

3.4.2 Velocity Field Fig.3.10 shows the spatial distributions of the particle velocities in the radial and axial directions. The distribution is obtained by dividing the mill into a number of cells of 3 particle diameters in size and calculating average velocity for particles whose centres are in a cell. This calculation is carried out at different times, and the results are then averaged to obtain the so-called time average value. In the radial direction, it shows that particles in region B have direct contact with discs and therefore obtain high velocities (Fig.3.10b), whereas the particles in region A have low velocities (Fig.3.10a). The velocity profile in the radial section indicates that particles rotate from the lower region (at about 4 o’clock position) to the upper region (at around 11 o’clock). The particles in the upper region obtain high velocities and then accelerate towards the mill drum where they collide with the upper section of the drum.

Fig.3.10c shows that, in the axial direction, the velocities point towards the discs at lower radius, indicating particles are drawn into disc holes at the lower radius side and then ejected back into the bulk of particles from the upper radius of the disc, causing circulating flow. This observation agrees with the previous study of Blecher and Schwedes (1996). Such back flow recirculation has also been observed in the grinding experiments by Heitzmann et al. (1996). Using coloured tracer fluid, they found the flow moving through the mill as a block in succession and a return flow between stirrers, indicating that the flow could be considered as a series of perfect mixing stages with a flow recycle between them. By incorporating this phenomenon into their model, they have successfully predicted the product size distribution in continuous grinding process. Note that the geometry and flow conditions used in the two studies (Blecher et all, 1996; Berthiaux, 1996) are not exactly the same as those in Isamill. Focused on the flow of particles, the present study indicates that the circular flow is caused by the particles driven outwards by the centrifugal effect generated by the rotating discs. Then, particles are diverted at the chamber wall. In order to satisfy the continuity condition, particles have to flow back to the shaft from where it is driven outward. Since the axial flow is restricted, the order of the magnitude of axial velocity component is very low compared to the angular velocity component.

1m/s 1m/s

(a) (b)

Upper region 1m/s 1m/s

(c) (d) Fig.3.10 Spatial distribution of velocities when : =1000rpm and J = 80%: (a) region A; (b) region B; (c) sectional elevation at section XX’ (please refer to Fig.3.1b); and (d) enlarged upper region of sectional elevation.

Fig.3.11 shows the spatial distributions of the radial, tangential and axial velocities in the axial and radial directions. In the axial direction, the mill is divided into thin slices and the average velocity for each of them is then calculated. A similar treatment is applied to the radial direction, where the mill is divided into annular regions having same thickness. All the velocities are normalized by the disc tip velocity ( SrZ 602 , where r is disc radius). The vertical dotted lines represent the disc positions in Fig.3.11a and the centre of disc hole in Fig.3.11b. It is clear that the tangential velocity Vt is dominant, followed by the axial velocity Vz and radial velocity Vr. Fig.3.11a shows that the velocities are symmetrical along the axial direction with the peak values near the discs. On the other hand, the velocities show peak value near the outer edges of the holes in the radial direction (Fig.3.11b). Due to the particle redistribution through the disc holes, the axial velocity also shows a high value near disc holes.

0.15

v 0.12 t

0.09 d v a v/v 0.06 v r 0.03

0 0 20 40 60 80 100 120 140 Z/(mm)

(a)

0.15

v t 0.1 v a d v/v

0.05 v r

0 10 20 30 40 50 60 r /(mm) (b) Fig.3.11 Spatial distribution of particle velocities in the axial direction (a); and the radial direction (b) when : = 1000 rpm and J = 80%. 3.4.3 Flow structure The flow structure is quite complicated in IsaMill and the inner flow structure can be quite different from that observed on the surface. Fig.3.12 shows the inner mixing behaviour in region B at different times. Unlike the particles close to mill drum (region A), mixing of particles is rather significant because particles driven by the discs can move more vigorously.

(a) (b) Fig.3.12 Mixing behaviour in region B when : = 100 rpm and J = 60% at different times: (a) t = 1s; and (b) t = 10s.

Fig.3.13 shows the distribution of particles in sectional axial and radial directions. It can be seen from Fig.3.13a that particles may be carried to the upper part by discs from the lower part of the mill. Since the particles in region B have higher velocities than in region A, they move outward and create voids in the middle section. On the other hand, particles in region A (close to the end wall) are tightly packed and their participation in mixing with other particles is limited.

(a) (b) (c) Fig.3.13 Particle distribution in different cross regions when : = 1000 rpm and J = 80%: (a) section XX ' [-5mm

Porosity İ can be used to quantify the flow structure of particles (Yang et al., 2003; Zhou et al., 2003). The so called local porosity is used in this work, which is achieved by dividing the calculation domain into a series of spherical cells having 3 particle diameters and porosity is calculated for each cell. Results at different times are collected and averaged to obtain the time average value. Fig.3.14 shows the spatial distributions of porosity in regions A and B. Fig.3.14a shows low porosity throughout the mill section (region A) where particles are distributed rather uniformly. In the upper part, high porosity is evident because of the small number of particles. On the other hand, non-uniformity is obvious in Fig.3.14(b): the bottom part, i.e. the rotating solid bed, has a lower porosity while the top part has a higher porosity where particle velocity is high (Fig.3.10a). The high porosity region forms due to the unconfined movement of particles.

The axial and radial distributions of porosity are obtained by applying the similar treatment used for velocity. Peak values can be seen in the axial distribution (Fig.3.14c) and their positions are close to discs, whereas minimum porosities occur between discs or between disc and end wall, indicating particles are relatively densely packed between discs. In the radial direction (Fig.3.14d), region B shows a high porosity due to the voids between discs.

0.76

0.71

0.66

0.61

0.56

0.50

0.45

0.40

0.35

0.30

(a) (b) 0.9 0.85 0.8 0.75 0.7

Porosity 0.65 0.6 0.55 0.5 0 50 100 150 z/(mm)

(c)

0.75

0.7 region B

0.65

0.6 Porosity 0.55 region A 0.5

0.45 10 20 30 40 50 60 r/(mm)

(d) Fig.3.14 Spatial distribution of porosity when : = 1000 rpm and J = 80%: (a) region A; (b) region B: (c) axial direction; and (d) radial direction.

3.4.4 Force structure

Various grinding mechanisms have been identified in the stirred mills, including attrition, abrasion and impact (Bemrose et al, 1997; Conti et al, 1980; Schornet et al 1989). These mechanisms are directly related to the contact forces on particles (Yang et al, 2003; Kwade, 1996,1999). It is therefore important to quantify the forces between particles and between particles and wall. In this work the magnitudes of three forces are analyzed: the instantaneous normal and tangential forces at a contact (Fn and Ft), the maximum forces at a contact (Fn(max) and Ft(max)) and the total contact forces on a particle

(Fn(p) and Ft(p)). The instantaneous force at a contact is calculated by considering the contact force at a given time according to Eqs. (3) and (4). By tracing the contact history, the maximum force in a collision can be determined. The total forces on a particle are the sum of the instantaneous contact forces between the particle and others, given by

pn )( ¦ FF ,ijn and pt )( ¦ FF ,ijt .

Fig.3.15 shows the time-averaged spatial distribution of F pn )( along the radial and axial directions. From Fig.3.15a, it is evident that the large contact forces exist near the chamber wall as particles centrifuge towards the mill drum. Relatively large forces can also be found between 12 and 2 o’clock positions where particles with high velocities impinge on the wall. In the axial direction (Fig.3.15b), the force distribution is symmetric due to the symmetric geometry and limited axial dispersion. Upper region close to discs and lower bottom region show large forces. Particularly, relatively large forces are observed in the upper region where particle velocities are high. -3 2.94 x10 N

2.45

1.96

1.47

0.98

0.49

0.00

(a) (b)

Fig.3.15 The spatial distributions of the force Fn(p) on particle in radial (a) (only for region B), and axial (b) directions when : = 1000 rpm and J = 80%.

Fig.3.16 gives the quantitative description of the spatial distribution of the three forces along the radial and axial directions. Fig.3.16a shows that the distributions in the axial direction are quite similar, although the magnitudes are different. They are all symmetrical along the centre disc with 3 maxima at the disc positions and the minima between discs. In the radial direction (Fig.3.16b), the forces have the largest value at the position slightly outside the disc holes. These characteristics are quite comparable to the distributions of particle velocities. The high velocity gradient near the discs means the particles moving with different velocities. Therefore, two particles with high speed collision usually generate a large force.

However, it should be pointed out that the contact force between particles depends on their relative velocity. Particles with high velocities may not generate large contact force if their relative velocity is small. Consequently, contact forces do not necessarily correlate with particle velocities and such a correlation, if exists, should be very much system-dependant. For the system considered, as shown in Fig.3.17, generally the mean normal force increases to a maximum and then decreases with the mean particle velocity . Note that the so called mean is obtained by the following method. The mill is divided into a number of cells of 3 particles diameter in size and then average normal force and average particle velocity are obtained for each cell. 0.03 0.1

F n(max) 0.075 0.02 F n(p) /(N) / (N) 0.05 n(p) n(max) ,F n F

F 0.01 0.025 F n 0 0 0 50 100 150 Z/(mm)

(a)

0.0035 0.02 F t(max) 0.0028 F 0.015 t(p) 0.0021 / (N) 0.01 / (N) t(p) ,F t

0.0014 t(max) F F F t 0.005 0.0007

0 0 0 50 100 150 Z/(mm)

(b)

0.1 - - - - region A F 0.08 n(max) ___ region B

0.06

0.04 F Normal forceNormal / (N) n(p) F 0.02 n

0 10 20 30 40 50 60 r /(mm)

0.01

F t(p) Tangential forceTangential /(N) 0.005 F t

0 10 20 30 40 50 60 r /(mm)

(d) Fig.3.16 The spatial distributions of the instantaneous and maximum forces per contact and the total forces on a particle in the axial (a), (b) and radial (c), (d) directions when : = 1000 rpm and J = 80%.

0.02

0.016

0.012 > /(N)

n(p) 0.008

0.004

0 0 0.5 1 1.5 2 2.5 /(m/s)

Fig.3.17 The correlation between the mean force and particle velocity when : = 1000 rpm and J = 80%.

Fig.3.18 shows the correlations between the normal and tangential forces. As expected, a linear relation can be observed for each of the three types of forces considered.

Fig.3.18a shows that Ft/Fn relation can be described with Ft = 0.098 Fn. Note that the ratio of Ft/Fn is approximately half of the sliding friction coefficient. This is expected as the tangential forces at a particular time ranges from [0, P]Fn for all contacts and the mean value should be Ps/2. A similar correlation has also be found previously (Radjai et al., 1996). Because Fn(p) and Ft(p) are only the sum of Fn and Ft, so their relation should be same as that of Fn and Ft, as shown in Fig. 17b. On the other hand, the Ft(max) -Fn(max) relation can be fitted with Ft(max) = 0.19 Fn(max). The ratio of Ft(max)/Fn(max) is very close to the sliding friction coefficient (Ps=0.2), indicating that all contacts at the maximum force state are sliding, fully mobilized contacts.

0.01

0.008

0.006 / (N) t F 0.004

0.002

0 0 0.02 0.04 0.06 0.08 0.1 0.12 F /(N) n

(a)

0.005

0.004

0.003 / (N) t(p)

F 0.002

0.001

0 0 0.01 0.02 0.03 0.04 0.05 F /(N) n(p)

(b) 0.15

0.1 / (N) t(max) F 0.05

0 0 0.2 0.4 0.6 0.8 F /(N) n(max)

(d)

Fig.3.18 The correlation between normal and tangential forces: (a) Fn and Ft;

(b) Fn(p) and Ft(p); and (c) Fn(max) and Ft(max). The points are the numerical results obtained when : = 1000 rpm and J = 80%, and the lines are the best fits.

3.5 Collision frequency and collision energy The effectiveness of particle-particle interactions in a size reduction or enlargement process depends on two aspects: collision energy Ce and collision frequency Cf (Yang et al, 2003; Bemrose et al, 1997; Rajamani et al 2000). Collision energy per contact is 2 usually referred to as the kinetic energy given by ½ mvij , where vij is the relative velocity of two particles (vij = |vi – vj|). Collision frequency is defined as the number of collisions per particle per second. These two factors are difficult to quantify in physical experiments. But in this numerical work, they can readily be determined because the motion of a particle and its interactions with others are traced. In order to obtain the collision frequency, the mill is again divided into cells of equal size. Within a period of time, the number of collisions in each cell was recorded and then divided by the time to obtain the collision frequency. Here, to be different from the enduring contact, two particles are considered to have a collision when they come at least from a critical gap to contact(Yang et al., 2003a). This critical gap was set to 5% of particle diameter after some trial test in this work.

Fig.3.19 shows the distributions of collision energy and collision frequency along the axial and radial directions. Both distributions are symmetrical in the axial direction. However, the distributions have opposite characteristics in the mill except for the regions close to the end walls: the peak position in the distribution of collision energy corresponds to the valley position of collision frequency or vice versa. At the disc positions, particles move very fast with a large velocity gradient, their collisions usually lead to large collision energy. But there are fewer particles in that region so particles can move a relatively long distance before colliding with other particles, leading to a low collision frequency. On the other hand, particles between discs are relatively densely packed and they undergo a rapid series of collisions with their neighbours leading to high collision frequency.

350 10 C C e f 280 8 J)

210 6 -6 /(s) f C / (10

140 4 e C

70 2

0 0 0 50 100 150 z/(mm)

(a) 250 60

region A C 200 f region B 40

150 J)

C -6 e / (s) f C

100 / (10 e

20 C

0 0 10 20 30 40 50 60 r/ (mm)

(b)

Fig.3.19 The spatial distributions of the collision energy (Ce) and the

collision frequency (Cf) in the axial (a) and radial (b) directions when : = 1000 rpm and J = 80%.

In the radial direction, the collision frequency and the collision energy in region B are always greater than in region A. Peak values occur close to disc holes where particles obtain high velocities due to the lifting action of the holes. Compared with the normal contact forces shown in Fig.3.16, collision energy shows a similar characteristic except for the region near mill drum (wall). Unlike particles in the middle section, contact forces near the mill drum is governed by centrifugal forces due to the radial dispersion. As a result, characteristics of collision energy and contact forces near wall are different from other regions.

High collision frequency is not necessarily always corresponding to high collision energy, as shown in Fig.3.20. This figure is obtained by the following method. The mill is firstly divided into a number of cells of 3 particle diameters in size. When the system is in steady state, average collision frequency and collision energy are calculated for each cell. This calculation is carried out for different times. The results are finally averaged to obtain time average values. Time-average collision energy is sampled into intervals and the corresponding collision frequency is obtained. It is found that high collision energy with low collision frequency corresponds to region close to discs and low collision energy with high collision frequency corresponds to region between disc and close to mill drum. Therefore, the correlation between Ce and Cf is very much system dependant.

350

300

250

200 /(Hz) f

C 150

100

0 0 20406080 C /(10-6 J) e

Fig.3.20 The correlation between collision frequency and collision energy when : = 1000 rpm and J = 80%.

3.6 Other useful correlations

Various concepts have been proposed in the literature to characterize the milling performance. For example, the concepts of stress intensity and stress number were used to describe the performance of stirred media mills (Kwade, 1996,1999). While the stress intensity is associated with the contact forces, the stress number is with the collision frequency. The analysis is based on rather rough assumptions without any validation. Another approach is the energy method which is represented by the impact and abrasion energies(Cleary, 2001; Rajamani et al., 2000). As our work considers both force and energy, it would be worthwhile to examine the correlations between these variables.

Fig.3.21 shows the correlation between Fn(max) and Ce, indicating the maximum force increases with the collision energy. In principle, the collision energy equals the kinetic energy before the collision which is totally converted to the strain energy at the maximum overlap with maximum force. Their relation can be obtained by the integration of Eq. (3.3) through the contact history, given by:

5/3 n(max) 1 e KCKF 2 (3.5)

5/2 where K1 and K2 are parameters relating to particle properties: 1 REK 1542 and

3/1 K 2 22 J n 3 EvRE dij , where Ed is the energy loss due to the damping effect. From the numerical results, it can be seen that K2 is negligible, so Eq.(3.5) can be simplified

5/3 to n(max) 1CKF e (3.6)

The fitting value from the simulation results of K1 0283.0 is comparable with the theoretical value ofK1 023.0 .

Fig.3.21 shows a reasonably good agreement between theoretical and numerical results, particularly for low Ce. For high Ce, the theoreticalFn(max) is higher than the numerical one. This is because, to derive Eq. (3.5), we assume that the total collision energy converts into normal strain energy without considering the tangential strain energy. Nonetheless, the above equation confirms that as expected, force and energy are directly linked, although they are used by some investigators in different ways.

0.5

0.4

0.3 /(N)

n(max) 0.2 F

0.1

0 0 102030405060 C /(10-6 J) e

Fig.3.21 The relationship between the collision energy and the maximum force. The cross and the dotted line are the numerical results and the solid line is the theoretical results from Eq. (5) when : = 1000 rpm and J = 80%. With advance of experimental techniques, it is now possible to image the dynamic internal characteristics of particle flow in three dimensions. For example, with the x-ray tomography technique, the local voidage and velocity of particle flow can be obtained(Williams et al., 1995). On the other hand, collision energy and collision frequency are two important, but immeasurable in a physical experiment, parameters to assessing the performance of a grinding process. So it would be worthwhile to examine if the two parameters can be linked with the measurable parameters such as the local porosity H and local velocity v. The results for the IsaMill considered are shown in

Fig.3.22. In Fig.3.22a, local C f and Ce are plotted as a function of local porosity İ. The collision frequency C f has a peak at H | 5.0 . This is understandable as for a dilute system a particle may have to travel a relatively long distance before a collision. For a dense system, particles are closely packed and can keep in contact without collision. So there should be an optimum porosity for a maximum collision frequency. On the contrast, the collision energy increases steadily with İ. This corresponds to the fact that particles in a dilute system are not so confined by their neighbours and hence generate large relative velocities for collisions (Fig.3.22).

25 600 C f 20 C e 400

J) 15 -6 /(Hz) f /(10 e 10 C C 200

0 0 0.42 0.56 0.7 0.84 0.98 H (a) 25 400

20 300

J) 15 -6 200 /(Hz) f /(10 C

e 10 C C f 100 5 C e 0 0 00.511.52 v /(m/s) (b) Fig.3.22 Collision energy and collision frequency as a function of: (a), local porosity; and (b) local velocity when : = 1000 rpm and J = 80%.

Fig.3.22b plots the local C f and Ce against the local velocity v. It can be seen that C f increases sharply to a peak at v = 0.3m/s, decreases gradually until v = 1.0m/s and then fluctuates with further increase of v. A similar trend is observed in the Ce - v relation which shows Ce has a rapid increase before reaching a saturated value at v = 1.0m/s. Fig.3.22b indicates that increasing particle velocity increases the collision frequency and collision energy. This is understandable because increasing particle velocity means the more vigorous motion and hence more vigorous interactions of particles in a system. However, there exists a limit beyond which the velocity has little effect on collision frequency and collision energy. This is because the interactions among particles depend on their relative motion. For example, a large local particle velocity may simply means that particles are moving fast, like a block of objects of fixed relative position, without any collisions between particles. As the particle velocities are related to the rotational speed of discs, and collision frequency and collision energy are related to the grinding performance, the results suggest that the grinding performance only increases with the mill rotational speed until a certain value, beyond which increasing speed only consumes more power and has little effect on the grinding performance. This has been indeed observed in industry (Gao and Forssberg, 1992). 3.7 Conclusions A DEM model has been developed and validated in simulating the particle flow in a simplified IsaMill. The experimental and numerical results are compared qualitatively or quantitatively in terms of flow pattern, mixing behaviour and power draw. Spatial distributions of microdynamic variables related to flow structure and force structure in different regions of the mill are analysed. The main findings can be summarized as: x Discs play a critical role in agitating particles in the mill. Particles near discs move more vigorously than those close to side walls. In the radial direction, high velocity can be seen in the vicinity of the discs with the tangential velocity as the most dominant component, followed by the radial velocity. In the axial direction, circular flow can be observed between discs. x Particles do not distribute uniformly in the mill. Flow pattern and the spatial distribution of porosity indicate that there are fewer particles in the region near discs and particles are more densely packed near the end wall and between discs. x The contact forces between particles can be analysed differently although they are linked. It appears that for the grinding operation, the maximum contact force is more representative. Force variation along the radial direction gives the peak values near disc holes. The tangential force has a linear relation with the normal force. x Collision energy and frequency are two important parameters for characterizing grinding performance. The distributions of collision energy and collision frequency indicate that high collision frequency is not necessarily corresponding to high collision energy. For the Isamill considered, high collision frequency occurs in the region between discs, and high collision energy occurs near discs. x The collision energy between particles is closely related to the contact force. The relationship between the maximum force and collision energy can also be derived from the basic contact force equations. CHAPTER 4

EFFECT OF GRINDING MEDIA PROPERTIES AND OPERATIONAL CONTROL PARAMETERS 4.1 Introduction

In the previous section numerical model was developed to analyse particle motion of the IsaMill process and then microdynamic properties relating to flow and force structures were analysed. The flow in IsaMill is also affected by the particle properties and operational conditions. Therefore, in this section we will investigate the effect of particle properties and operational conditions on the grinding performance of the IsaMill. The results were analysed in terms of velocity distribution, porosity distribution, collision frequency, collision energy and power draw.

Depending on the particle material properties such as particle/particle sliding friction, particle restitution coefficient, particle density and particle size grinding performance may be different. For example alloy steel balls, due to their high relative density and hardness, are particularly suitable for crushing and mixing heavy, hard materials. The forged steel balls, on the other hand, are used to reduce particle size and fine dispersion of highly viscous fluids (Peukert, 2004). The dispersity is characterized by the particle size distribution, particle shape and morphology, and their interfacial properties which are related to sliding friction coefficient, mass density and restitution coefficient (Rumpf, 1973). However, quantification of the effects of some material variables by physical experiments is difficult. Therefore, we use the numerical model to investigate the grinding performance of the IsaMill. In addition to the particle material properties, operational conditions such as fill volume and mill speed also have a strong influence on particle flow (Gao and Forssberg, 1992a). In this work we investigate the effect of fill volume and mill speed on the grinding performance. Finally, attempt has been made to identify the effect of mill properties such as particle-disc sliding friction coefficient, particle-wall sliding friction coefficient, distance between discs, disc hole size and different stirrer geometries on the grinding performance.

4.2 Simulation method and condition

Numerical method used in this work was described in section 3.2. The model Isamill used in this work consists of a fixed chamber, a rotating shaft and three stirrers, as shown in Fig.4.1. Initially the shaft and discs were at rest and all particles were fed into the mill to form a stable packed bed. Then the shaft and discs started to rotate at a given speed to agitate the particles. To investigate the effect of grinding media properties, simulations were carried out with the same rotation speed of 1000rpm and the solid loading of 80%. To investigate the effect of operational variables, simulations were carried out for different mill loading J and different speeds ȍ. Table 4.1 lists the base values and their varying ranges of the parameters used in the simulation. The effect of a parameter is examined while the others are fixed at their base values.

(a) (b)

Fig.4.1 Schematic illustration of the model IsaMill: (a) sectional front elevation; and (b) sectional end elevation (all dimensions in mm).

Table 4.1 Physical parameters used in the present simulation.

Parameter Base Value Varying range

Number of particles 44000 - -3 Particle density , U (kgm ) 2500 1000 - 6000 -2 Young’s modulus, Y (Nm ) 1.0u107 - ~ Poisson ratio, V 0.29 -

Particle/particle sliding friction coefficient, Ps,pp 0.2 0.01 – 1.0

Particle/mill sliding friction coefficient, Ps, pm 0.2 -

Rolling friction coefficient, Pr 0.01 - Restitution coefficient, e 0.68 0.38 – 0.88

Particle diameter, dp (mm) 3 2 – 4 Mill loading, J (%) 80 40,60,80 Mill speed, ȍ (rpm) 1000 500 - 1200 4.3 Results and discussion The particle flow is analysed in terms of flow velocity, local porosity, collision energy, collision frequency and power draw, which have been demonstrated to be useful to assess the performance of IsaMill (Jayasundara et al., 2006). A simulation starts from a packing process in which the shaft and discs are at rest and all particles are fed into the mill to form a stable packed bed. Then the shaft and stirrers start to rotate at a given speed to agitate the particles. In the simulation, abundant macroscopic and microscopic data can be obtained. It is always a challenge, however, to make best use of such information. Various concepts have been proposed to characterize the flow pattern and mill performance, e.g. the stress intensity (Kwade, 1996) and energy method (Cleary, 2001; Rajamani et al., 2000). Since our previous work has demonstrated that collision energy can be related to the contact force (Jayasundara et al., 2006), the present work quantify the particle/particle and particle/mill interactions in terms of collision energy and collision frequency. Collision energy is defined as the kinetic energy at a collision,

2 & & which is given by ½vm iji , where m is the mass of particle and vij vv ji )( is the relative velocity between two particles. Collision frequency is defined as the number of collisions per particle per second. While the two factors are difficult to measure in physical experiment, they can be readily determined in the simulation. In the following sections, we will investigate the effect of mill properties and stirrer geometry on the particle flow in terms of flow velocity, local porosity, collision energy, collision frequency and power draw. The distributions of flow velocity and porosity were obtained by dividing the mill into a series of cells of 3d in size and calculating the time average values for particle whose centers are located in the cell. All the analysis will be based on the particle flow in the central region of IsaMill shown in Fig.4.1(a), unless otherwise specified.

4.3.1 Grinding media properties 4.3.1.1 Particle-particle sliding friction

Fig.4.2 shows the flow velocity fields for different particle-particle sliding friction coefficient Ps,pp. For all the Ps,pp considered particles start to accelerate at 11 o’clock and collide with high velocity with the upper part of the drum. However, increasing Ps,pp from 0.01 to 1.0 greatly reduces the velocity gradient in radial direction. This is because, as sliding friction between particles increases, the energy transfer among particles becomes more efficient so the flow is strongly stratified, forming a moving bed around the chamber wall. This can also been seen from Fig. 4.3 which shows more homogeneous porosity distribution around the chamber wall for larger sliding friction coefficient. Note the high porosity at the upper part of mill for low sliding friction coefficient is due to the unconfined particle movement. As the grinding in IsaMill is mainly caused by the shear between layers of the particles, the reduced velocity gradient will indeed decrease the grinding performance which is also reflected from the collision energy and collision frequency, as will be discussed below.

1m/s 1m/s

(a) (b)

Fig.4.2 Spatial distribution of velocities for different particle/particle

sliding friction coefficients: (a) Ps, pp = 0.01; and (b) Ps, pp = 1.0. 0.8

0.7

0.6

0.5

0.4

(a) (b)

Fig. 4.3 Spatial distribution of porosity for different particle/particle

sliding friction coefficients: (a), Ps, pp = 0.01; and (b) Ps, pp = 1.0.

Figs. 4.4 and 4.5 show the distribution and the mean value of collision frequency Cf and collision energy Ce for different Ps,pp. While the collision frequency for low Ps,pp has a wide distribution with a flat region from 300~500 Hz, the distribution becomes narrower with a sharp peak at less than 200 Hz as Ps,pp increases. This leads to a sharp decrease in the mean collision frequency when Ps,pp increases to 0.4. However, beyond this point the mean collision frequency is almost unchanged with only a slight increase.

As mentioned above, the increase in Ps,pp reduce the velocity gradient at radial direction so the particles move at similar speed and behaviour like a solid bed. This reduces the chance of particles to collide with others. However when Ps,pp reaches to a critical point

(0.4 for the system considered), further increase of Ps,pp does not have effect on the collision frequency.

On the other hand, the mean collision energy has a peak value at around 0.2, as shown in Fig. 4.5b. Increasing Ps,pp from 0.01 to 0.2 can see 30% increase in the collision energy. When comparing with 50% decrease in the collision frequency as shown in Fig. 4.4b, it is not very clear how the sliding friction will affect the grinding efficiency.

However, after Ps,pp = 0.2, increasing Ps,pp decreases both the collision frequency and energy, which will reduce the grinding performance. These results are in accordance with those reported by Xstrata Technology with the development of new grinding media called Keramax MT1 (Curry and Clermont, 2005). Fig.4.6 shows the variation of power draw with Ps,pp, indicating the sliding friction coefficient between particles has a negligible effect on the power draw. Note that, it was observed in our previous study of a single disc mill, the increase of both particle/particle and particle/mill sliding friction leads to an increase in power draw (Yang et al., 2006). So the present results indicate that the increase in power draw is mainly caused by the increasing particle/disc sliding friction.

0.003

0.01 0.2 0.002 1.0

0.001 Probability density

0 0 200 400 600 800 C /(Hz) f

(a)

400

> /(Hz) 300 f

200

0 0.2 0.4 0.6 0.8 1 P s,pp

(b) Fig.4.4 Distribution (a) and mean value (b) of the collision frequency for different particle/particle sliding friction coefficients. 1

0.01 0.1 0.2 1.0 0.01

0.001 Probability density 0.0001

10 -5 0 50 100 150 200 C /(10 -6 J) e

(a)

5 J) -6 4 /(10 e C

3 0 0.2 0.4 0.6 0.8 1 P s,pp

(b) Fig.4.5 Distribution (a) and mean value (b) of the collision energy for different particle/particle sliding friction coefficients. 250

200 Power /(W)Power 150

100 0 0.2 0.4 0.6 0.8 1 P s,pp

Fig.4.6 Power draw as a function of particle/particle sliding friction coefficient.

4.3.1.2 Particle-particle restitution coefficient

Figs. 4.7 and 4.8 indicate that the restitution coefficient has negligible effect on the velocity and porosity distributions. On the other hand, Figs.4.9 and 4.10 show both collision energy and collision frequency increases with the restitution coefficient. A larger restitution coefficient means less energy dissipated when particles collide, so particles move more vigorously leading to more collisions. Therefore the collision frequency has a broader distribution and a larger mean (Fig.4.9). The same explanation is applicable to the collision energy (Fig.4.10): less energy loss results in larger collision energy. The input power remains constant as the restitution coefficient increases, as shown in Fig.4.11. For a large restitution coefficient, energy loss due to the dissipative collision becomes small, leading to high collision energy while maintaining a constant input power. Therefore, grinding media with high restitution coefficient can give better grinding performance than those with low restitution coefficient. Since materials with high hardness values tend to have high restitution coefficient, one may argue that grinding media with high hardness should be more effective than those with low hardness. This has been indeed observed in practice (Curry and Clermont, 2005). 1m/s 1m/s

(a) (b)

Fig.4.7 Spatial distribution of velocities for different particle restitution coefficients: (a) 0.38; and (b) 0.88.

0.8

0.7

0.6

0.5

0.4

(a) (b)

Fig.4.8 Spatial distribution of porosity for different particle restitution coefficients: (a) 0.38; and (b) 0.88. 0.006

0.38 0.56 0.004 0.88

0.002 Probability density Probability

0 0 100 200 300 400 500 600 700 C (Hz) f /

(a)

250

225

> /(Hz) 200 f

175

150 0.3 0.4 0.5 0.6 0.7 0.8 0.9 e

(b) Fig.4.9 Distribution (a) and mean value (b) of the collision frequency for different restitution coefficients. 100

10-1 0.38 0.56 -2 0.88 10

10-3

10-4 Probability density Probability 10-5

10-6 0 50 100 150 200 250 300 350 C /(10-6 J) e

(a)

6 J) -6 5 /(10 e C

4 0.3 0.4 0.5 0.6 0.7 0.8 0.9 e

(b) Fig.4.10 Distribution (a) and mean value (b) of the collision energy for different restitution coefficients. 250

200

Power /(W) 150

100 0.3 0.4 0.5 0.6 0.7 0.8 0.9 e Fig.4.11 Power draw as a function of restitution coefficient.

4.3.1.3 Particle density In this work we tested several types of grinding particles with different densities. Figures 4.12 and 4.13 show the spatial distributions of the flow velocity and porosity for different particle density U, which suggests that U has almost no significant effect, consistent with that reported elsewhere (Jayasundara et al., 2006). However, Figs.4.14 and 4.15 show increases in both collision frequency and collision energy as particle density increases. It is understandable as the collision energy is directly proportional to the particle density and the higher collision energy is expected for heavier particle. In conventional ball grinding, heavier grinding medium is always the first choice as long as it is practical. However, the results in Fig. 4.14 show that, for IsaMill, the medium density has an optimum value at U | 3000 kg/m-3 which gives the highest collision frequency. These results are in accordance with the results reported by Gao (1993) with the Drais stirrer mill which is similar to IsaMill and has the similar dimensions with our numerical model (Gao and Forssberg, 1992). In their work maximum energy utilisation was obtained at 3700 kg/m-3 which is close to the ȡ obtained here. Major part of the energy requirement for stirred milling involves stirring and lifting of the grinding media, energy required for lifting the media is directly associated with the particle density. Therefore, increase of U leads to increase in power consumption, as shown in Fig.4.16. 1m/s 1m/s

(a) (b)

Fig 4.12 Spatial distribution of velocities for different particle density: (a) U = 1000 kgm-3; and (b) U = 3500 kgm-3.

0.8

0.7

0.6

0.5

0.4

(a) (b)

Fig.4.13 Spatial distribution of porosity for different particle density:

(a) U = 1000 kgm-3; and (b) U = 3500 kgm-3. 0.005

1000 0.004 3000 6000 0.003

0.002 Probability density 0.001

0 0 200 400 600 800 C /(Hz) f

(a)

230

220 /(Hz) f C 210

200 1000 2000 3000 4000 5000 6000

U /(kg/m3)

(b) Fig.4.14 Distribution (a) and mean value (b) of the collision frequency for different particle density. 1

0.1 1000 3000 0.01 6000

0.001

0.0001 Probability density

10-5

10-6 0 20 40 60 80 100 120 140 C /(10-6 J) e

(a)

8 J) -6 6 /(10 e

C 4

0 1000 2000 3000 4000 5000 6000

U(kg/m3)

(b) Fig.4.15 Distribution (a) and mean value (b) of the collision energy for different particle densities. 240

210

180

Power /(W) 150

120

1000 2000 3000 4000 5000 6000 U /(kgm-3)

Fig.4.16 Power draw as a function of particle density.

4.3.1.4 Particle size The size of the grinding medium is one of the most significant factors which affect the mill performance (Wolfgang, 2004). To understand the effect of medium size, we have varied the particle size from 2 to 4 mm. Figs. 4.17 and 4.18 show that, while 2mm particle flow has quite inhomogeneous distribution of velocity and porosity in the radial direction, the flow of 4mm particles shows quite uniform distributions. 2mm particles in the mill obtain high velocities at 11 o’clock and then accelerate to collide with the upper part of the drum, leading to high porosity between 11 and 2 o’clock. On the other hand, 4 mm particles give a reduced velocity gradient along the radial direction. Particles with high velocities tend to move towards the mill chamber, creating a large void in the middle near the shaft (Fig.4.18b). The velocity and porosity distributions in the axial direction reveal interesting differences for the two sized particles, as shown in Fig. 4.19. 2mm particles have a small circulating flow, caused by the centrifugal effect generated by the rotating discs. In order to satisfy the continuity condition, particles have to flow back to the shaft from where it is driven outward again. In the vicinity of the discs, particles obtain high velocity while regions near the shaft show low velocity profile. When particle size is increased to 4mm, circulatory flow in the axial direction diminishes (Fig.4.19b) due to the same effect, but less distinct velocity profile. High porosity regions are evident in between discs and low porosity regions develop close to end wall. 1m/s 1m/s

(a) (b)

Fig.4.17 Spatial distribution of velocities for different particle sizes:

(a) dp = 2mm; and (b) dp = 4mm %.

0.8

0.7

0.6

0.5

0.4

(a) (b)

Fig.4.18 Spatial distribution of porosity for different particle sizes:

(a) dp = 2mm; and (b) dp = 4mm. 0.8

0.7

0.6

0.5

0.4

(a) (b)

Fig.4.19 Spatial distribution of velocity and porosity for different particle sizes in enlarged upper region of sectional elevation at XX ':

(a) dp = 2mm; and (b) dp = 4mm.

Figs.4.20 and 4.21 show the collision frequency and collision energy for different particle sizes, indicating both the collision frequency and the collision energy increase with increasing particle size. The number of particles decreases about 8 times (from 117000 to 14400) to keep a same 80% solid loading when particle size increases from 2mm to 4mm. The 50% increase in the collision frequency means that the total number of collision for 2mm particles is still 5 times that of 4mm particles. On the other hand, the collision energy has 5 times increase when particle size increases from 2mm to 4mm. The decreased number of collision and increased collision energy form two competitive mechanisms when assessing grinding performance. It suggests there may exist an optimum grinding medium size which has a good balance of the collision number and energy. This optimum size may vary with milling systems and depend on the size of the product. For a stirred mill, the most efficient grinding was obtained with 1.7-1.2 mm media (Jankovic, 2003). The decrease of the power draw with particle size (Fig.4.22) is attributed to the reduced number of collisions between particles. As energy is dissipated for each collision, less collision between particles requires less input energy to maintain the flow dynamics. 0.006

2mm 3mm 0.004 4mm

0.002 Probability density Probability

0 0 200 400 600 800 C /(Hz) f

(a)

300

250 > /(Hz) f

150 12345 d /(mm) p

(b) Fig.4.20 Distribution (a) and mean value (b) of the collision frequency for different particle sizes. 100 2mm 3mm 4mm 10-2

-4

Probability density Probability 10

10-6 0 100 200 300 400 500 C /(10-6 J) e

(a)

10 J) -6 > /(10 e 5

0 12345 d /(mm) p

(b) Fig.4.21 Distribution (a) and mean value (b) of the collision energy for different particle sizes. 450

300 Power /(W) 150

0 12345 d /(mm) p

Fig.4.22 Power draw as a function of particle size. 4.3.2 Operational control parameters

4.3.2.1. Effect of mill loading

The effect of mill loading proved to be significant in stirred type mills (Gao and Forssberg, 1992b). For horizontal stirred mills, 90% of the net mill volume is considered to be the maximum in order to avoid excessive media wear and heat generation (Weller and Gao, 1996). In IsaMill grinding, majority of operations carried out with high fill volume. Therefore, it would be worthwhile to investigate the effect of fill volume on the grinding performance. In this work we consider three levels of fill volumes: 40%, 60% and 80%. Figures 4.23 and 4.24 show the representative flows from simulations and experiments for 40% and 80% solid loadings at 300rpm. It can be seen that the overall flow patterns obtained from experiments and simulations are qualitatively comparable. At low solid loading (Figs. 4.23a and 4.24a), most of particles stay at the bottom of the mill with slow movement, and only a small number of particles are agitated by the rotating disc to the upper half of the mill. Increasing the solid loading to 80% (Figs. 4.23b, c and 4.24b, c) can agitate the particles more vigorously due to higher chance of collisions between particles and between particles and disc. Both simulation and experiment show that the particles near discs move more vigorously than those near the end wall, mainly because of the strong agitation from discs and the weak influence from the end wall. This causes a much faster mixing process in the central part of the mill. As particle movement in the axial direction occurs only due to the random inter-particle collisions, axial mixing is much slower than radial mixing and hence dispersion of particles in the axial direction is still very limited. (a) (b)

Fig.4.23 End view of experimental (top) and numerical (bottom) particle distributions for different solid loadings: (a) : = 300rpm and J = 40% and (b) : =300rpm and J = 80%.

(a) (b) Fig.4.24 Axial view of experimental (top) and numerical (bottom) particle distributions for different solid loadings: (a) : = 300rpm and J = 40% and (b) : = 300rpm and J = 80%.

Fig.4.25 shows experimental and numerical power consumption obtained for different mill loading at : = 1200rpm. Experimental power consumption was calculated by measuring voltage and current across the DC motor. Power losses at no load are deducted from the gross power in order to obtain the power consumed by the particles. However, when mill is loaded with particles, mechanical and other energy losses (e.g. sound and heat) are not considered in the simulation. In the simulation, every particle collision with the discs and shaft produces torque on the mill. For each time step these individual torques are summed to give the instantaneous torque on the driving shaft. The product of the total mill torque with the angular mill speed gives the instantaneous power consumption required to maintain the mill moving at the specified speed against the applied torque. Due to impulsive nature of the interactions between particle and discs, fluctuation occurs in the instantaneous power consumption. Averaging the power over a certain time gives a relatively invariant measure of the power draw. According to the Fig.4.25, the overall results from simulation and experiments are quite comparable and the quantitative discrepancy could be attributed to the above mentioned energy losses which are not considered in the simulation. In order to improve the quantitative power draw it is very important to ascertain the effect of various modelling assumptions (Cleary, 1998). However, DEM results are quite close enough to predict the power draw for different operational conditions. For low mill loading (J = 40%), both experimental and numerical power draw is less than that of high mill loading. For low mill loading it is expected to have low power consumption, since less number of particles interactions. With increasing mill load, power draw increases rapidly.

100

Experimental 75 Numerical

Power draw /(W) draw Power 25

0 30 40 50 60 70 80 90 J /(%)

Fig.4.25 Comparison of power consumption between the physical and numerical experiments at different mill loadings.

Fig.4.26 shows the spatial distributions of the particle velocities in the radial and axial directions for 40%, and 80% mill loading. The distribution is obtained by dividing the mill into a number of cells of 3 particle diameters in size and calculating average velocity for particles whose centers are in a cell. This calculation is carried out at different times, and the results are then averaged to obtain the so-called time average value. In the radial direction, 40% loading shows a disoriented velocity profile in the upper region which is caused by few particles. As a result of majority of particles stay in lower region, not much interactions can be seen in the upper region (Fig.4.26a). In contrast, 80% loading shows rather oriented velocity profile. With 80% loading majority of particles close to discs have direct contact with discs and therefore obtain high velocities and kinetic energy (Fig.4.26b). The velocity profile in the radial section indicates that particles rotate from the lower region (at about 4 o’clock position) to the upper region (at around 11 o’clock). The particles in the upper region obtain high velocities and then accelerate towards the mill drum where they collide with the upper section of the drum.

In axial direction, 40% loading shows that in the lower region velocities point towards the disc at the lower radius. In the upper region, however, velocity shows irregular profile caused by few number of particles. As a result, circulatory flow filed would not be possible with low fill levels. On the other hand with 80% loading, the velocities point towards the discs at lower radius, indicating particles are drawn into disc holes at the lower radius side and then ejected back into the bulk of particles from the upper radius of the disc. The particles reaching the centerline of the hole may subsequently exit to either side, resulting in the redistribution of particles along the length of the mill. According to the velocity profile in the upper part, circulating flow exists in the r-z plane. The circular flow is caused by the particles driven outwards by the centrifugal effect generated by the rotating discs.

0.25 m/s 1m/s 0.2 m/s 0.2 m/s

(a) (b)

Fig.4.26 Spatial distribution of velocities in redial direction (top) and sectional elevation at section XX ' (bottom) for different fill volume at ȍ = 1000rpm : (a) J = 40%; and (b) J = 80%.

Fig.4.27 shows the distributions and the mean values of collision frequency for different fill levels. With low fill level, the distribution become narrow leading to low frequency as a result of less interactions with neighbour particles. As fill level increases, the distribution becomes wider and flatter, promoting larger collision frequency. When fill level is high, as a result of high number of particles, particles are relatively densely packed and they undergo rapid series of collisions with their neighbours leading to high collision frequency. Fig.4.28 shows the distribution and the mean value of collision energy for different fill levels. When fill level is decreased, the distribution shifts to right promoting high Ce. It is interesting to note that, however, when fill level is increased, Ce increases to a maximum at 60% and then drops down at 80%. This would results in a reduction of the mill performance above 60% of fill level. Note that, at 80% fill level Cf increases to a maximum whereas Ce is decreased. This verifies the fact that high Cf is not necessarily gives high Ce which was reported in our previous work

(Jayasundara et al., 2006a). Although, Ce decreases when fill level is increased, power consumption increases as a result of kinetic energy Ek increment (Fig.4.28b). Since, Ce is associated with energy dissipation and Ek with energy transfer, at high fill level (>60%) energy transfer mechanism is dominant. Reduction in mill performance at high fill level can be attributed to the fact that when particle obtain high velocities they can form aggregates which can cling to the mill wall. Once the aggregates are attached to the mill drum, they are essentially restrict the interaction with the other particles. Thus, a significant amount of particles may undergo a collisions having low collision energy. Similar results were reported in the literature (Fuerstenau et al., 1985; Mankosa et al., 1989). However, it is suggested that horizontal stirred mill need to be operated with the maximum load of media. (Gao et al., 2001) Qualitatively this result makes sense, because increase of media volume increase the interaction of the media with all stirring discs. As the current numerical model does not take into consideration the viscous effect of the slurry, results obtained for 80% fill level could contradict with some results reported in the literature (Mingzhao et al., 2006). Therefore, further research is needed by considering mixture of particle and fluid.

0.01

0.008 40 60 0.006 80

0.004 Probability density Probability 0.002

0 0 200 400 600 C (Hz) f (a) 250

200 /(Hz) f C 150

100 40 60 80 J /(%) (b)

Fig.4.27 Probability distribution (a) and mean value of the collision frequency (b) for different J.

100

10-2 60 80

10-4 Probability density Probability

10-6 0 100 200 300 400 C /(10-6 J) e (a) 10 J) -9 5 /(10

6 e K

J) 0 -6 40 60 80 J /(%) /(10 e C

40 60 80 J /(%) (b) Fig.4.28 Probability distribution (a) and mean value (b) of the collision energy for different J.

4.3.2.2 Effect of mill speed

The mill speed is believed to be one of the most important factors in ultra-fine grinding (Gao and Forssberg, 1992a). It was reported, however, in some conditions the speed appears to influence the process to a very small degree, such as when using a heavy bead and at a very high slurry density. In order to quantify the effect of mill speed on the grinding performance, we consider different mill speeds with constant fill volume. Figures 4.29 and 4.30 show the representative flows from simulations and experiments for 300rpm and 800rpm at 60% solid loading. It can be seen that the overall flow patterns obtained from experiments and simulations are qualitatively comparable. At low mill speed (Figs. 4.29a and 4.30a), most of particles stay at the bottom of the mill and only a small number of particles are agitated by the rotating disc to the upper half of the mill. Increasing the mill speed up to 800rpm (Figs. 4.29b and 4.30b) can agitate the particles more vigorously due to higher energy transfer from disc to particles. Particularly at high speeds, particle fluidised in the upper region of the mill leading to more vigorous interactions among them.. (a) (b)

Fig.4.29 End view of experimental (top) and numerical (bottom) particle distributions for different solid loadings: (a) : = 300rpm and J = 60% and (b) : =800rpm and J = 60%. (a) (b)

Fig.4.30 Axial view of experimental (top) and numerical (bottom) particle distributions for different solid loadings: (a) : = 300rpm and J = 60% and (b) : = 300rpm and J = 60%.

Fig.4.31 shows experimental and numerical power consumption obtained for different mill speeds at J = 80%. It is obvious that increasing mill speed cause power draw to be increased as a results of high number of particle interaction with the agitating discs. The overall results from simulation and experiments are comparable. Power draw characteristics are in accordance with results reported in the literature (Gao and Forssberg, 1992a).

80 Experimental Numerical

40 Power draw /(W)

400 600 800 1000 1200 Speed /(rpm)

Fig.4.31 Comparison of power consumption between the physical and numerical experiments at different mill speeds when J = 80%. Fig.4.32 shows the spatial distributions of the particle velocities in the radial and axial directions for mill speed of 500rpm and 1200rpm when J = 80%. In the radial direction, both speeds show similar velocity profile except the magnitude. The velocity profile in the radial direction indicates that particles rotate from the lower region to the upper region. In upper region (at around 1 o’ clock) particles obtain high velocity due to the fluidized nature of the bulk of particles. From the particle distribution (Fig.4.30), it was observed that for both systems, the majority of particles follow similar trajectories with different velocities. As a result, even though mill speeds are different, similar velocity profile can be observed with different magnitudes. In the axial direction, both mill speeds show that velocities point towards the disc at the lower radius indicating particles are drawn into disc holes at the lower radius side and then ejected back into the bulk of particles from the upper radius of the disc. In the upper region, particles show circulatory velocity profile in r-z plane. Intensity of the circulatory velocity profile is proportional to the mill speed. Thus, one would expect a more vigorous motion of the particles as mill speed is increased which could result in a increase of the grinding performance.

0.4 m/s 1m/s 0.1 m/s 0.2 m/s

(a) (b)

Fig.4.32 Spatial distribution of velocities in redial direction (top) and sectional elevation at section XX ' (bottom) for different mill speeds at J = 80%: (a) ȍ = 500rpm; and (b) ȍ = 1000rpm.

Fig.4.33 shows the distributions and the mean values of collision frequency for different mill speeds. With low mill speeds, the distribution shifted to left leading to low frequency. With low mill speeds due to less number of fluidised particles, interactions between particles are restricted causing low collision frequency. As mill speed increases, the distribution shifts to right, promoting high collision frequency. When mill speed is high, as a result of high number of fluidised particles, particles undergo rapid series of collisions with their neighbours leading to high collision frequency. Variation of Cf with mill speed is comparable with hydrodynamic analysis in stirred mills reported in the literature (Eskin et al., 2005). Fig.4.34 shows the distribution and the mean value of collision energy for different mill speeds. When speed is decreased, the distribution shifted to left promoting low Ce whereas high mill speeds correspond to high Ce. This would results in an increase of the mill performance when mill speed is increased. These results are in accordance with the results reported by Jankovic (2003). However, for coarser media this effect could be stronger and for finer media the effect could be small (Jankovic, 2003). 0.006

500 800 0.004 1200

0.002 Probability density

0 0 200 400 600 800 1000 C /(Hz) f

(a) 250

230

210 /(Hz) f C

190

170 500 700 900 1100 Speed /(rpm)

(b) Fig.4.33 Probability distribution (a) and mean value of the collision frequency (b) for different ȍ. 500 10-1 800 1200

10-3 Probability density

10-5 0 100 200 300 400 500 Ce /(10-6 J) (a)

J) 4 -6 /(10 e 3 C

1 500 700 900 1100 Speed /(rpm) (b) Fig.4.34 Probability distribution (a) and mean value (b) of the collision energy for different ȍ. 4.3.2.3 Power model

Power draw is a very important quantity in grinding process, for optimization and design of mills (Cleary, 1998). Since DEM results are comparable with experimental results, it is worthwhile to examine the correlation between power draw and the operational variables which can be used for power predictions. From the above DEM results it is evident that the mill power draw is strongly effected by the above two operating parameters. Clearly both factors caused the power draw substantially, and the change is probably non-linear. The non-linear relations can be transformed into linear relations by selecting a suitable transformation model. Among the available linear transformations, it became evident that the simplest is to use logarithmic transformation. Plotting the same data on log scale appears to have close linear relation with the power draw (Fig.4.35). The fact that the relationship is linear means that the relationship between power draw and each one of the independent variables can be described by a straight line which can be analyzed by multiple regression analysis(Harnett and Murphy, 1975). Thus, the generalized form of the linear regression model can be written to test for linear and quadratic effects of the two operating variables as:

2 2 log P = Į + ȕ1log (N) + ȕ2log(J) + ȕ3log(N) + ȕ4log(J) + ȕ5log(N).log(J) (4.1)

where P is power draw (W); N, mill speed (rpm); Į, regression constant and ȕi is the regression coefficient for each term. Table 4.2 shows the factorial design for testing two factors at three levels of J and eight levels of N giving total of 24 degrees of freedom. Table 4.3 gives the regression analysis for the fit of Eq. 4.1.

2 2 J=40% N = 500rpm J=60% N = 800rpm 1.5 J=80% 1.5 N = 1200rpm

1 1 log(P) log(P)

0.5 0.5

0 0 2.6 2.7 2.8 2.9 3 3.1 1.5 1.6 1.7 1.8 1.9 2 log(N) log(J) (a) (b) Fig.4.35 Variation of power draw in log scale (a) mill speed and (b) fill volume. Table 4.2. Factorial design for J and N. Numerical Predicted J /(%) N /(rpm) power power /(W) /(W) 40 500 1.6 2.1 40 600 2.2 3.0 40 700 3.7 3.9 40 800 5.0 5.0 40 900 6.6 6.2 40 1000 8.4 7.4 40 1100 10.4 8.8 40 1200 12.6 10.3 60 500 8.5 6.6 60 600 10.5 9.1 60 700 12.5 12.0 60 800 15.0 15.2 60 900 18.0 18.8 60 1000 22.0 22.8 60 1100 26.5 27.0 60 1200 30.0 31.6 80 500 16.0 14.5 80 600 20.0 20.1 80 700 25.0 26.5 80 800 32.0 33.7 80 900 40.0 41.6 80 1000 49.0 50.2 80 1100 59.0 59.6 80 1200 70.0 69.7

Table 4.3. Regression coefficients. Source Regression coefficient log(N) 8.277 log(J) 16.211 log(N)2 -0.193 log(J)2 -1.319 log(N).log(J) -3.029 Constant -30.212

This model gives a standard error Se of 0.042. Since 95% data fall within 2Se, 95% data predictions appears to be accurate only within a factor of 10 r 042.0*2 which means that maximum potential error in estimating power will be aboutr .102.1 However, traditional approach to modelling unit processes is to look for a simple power law incorporating only the linear effects of the tested variables, and to judge the effectiveness of the model solely on the basis of the square of the correlation coefficient, R (Gao et al., 1996). Also from the regression coefficients, it can be seen that non-linear effects of N and J are not significant as much as linear effects. Therefore, the above model can be simplified without considering the non-linear terms from Eq. 4.1. Thus, a simplified multiple linear regression line may be rewritten as:

log P = Į + ȕ1log (N) + ȕ2log(J) (4.2) From the regression analysis, equation (4.2) can be solved and given by: log P = -8.922 + 2.754log (N) + 1.794log(J) (4.3) which can be rewritten as: P = 1.1967*10-9 ( J )2.754 ( N )1.794 (4.4)

The values of the regression coefficient in Eq. 4.4 are dependent on the units of measurements used in the independent variables, so if units are changed coefficient should changed accordingly. Eq. 4.4 provides an accurate fit with correlation coefficient 2 R = 0.96 to the 24 data set. It has a residual standard error Se of 0.0649. Hence data predictions appears to be accurate only within a factor of 10 r 0649.0*2 which means that maximum potential error in estimating power will be about r .348.1 With compared to the previous model (Eq. 4.1), change of potential error in simplified model is insignificant. Thus, empirical equation for power draw can be developed with the results obtained with the transparent model. A similar approach can be extended for the real mills when the slurry flow is introduce in the simulation which would be the future work.

Conclusions

DEM simulations have applied to investigate the effect of grinding medium properties and operational variables of the particle flow in a simplified IsaMill. Their effects on particle flow and grinding performance are examined in terms of flow velocity, porosity, collision energy, collision frequency and power draw. The results can be summarized as: x Increasing particle/particle sliding friction will greatly decrease the velocity gradient in the radial direction. Power draw is not sensitive to the friction. When the sliding friction coefficient is smaller than a critical value, increasing the sliding friction coefficient decreases the collision frequency and increases the collision energy. When the friction coefficient is higher than the critical value, increasing the sliding friction coefficient decreases both the collision frequency and the collision energy, and hence the grinding performance. x Particle/particle restitution coefficient has little effect on the velocity and porosity distributions, and power draw as well. But a high restitution coefficient can result in a high collision frequency and collision energy, which is beneficial to grinding. x Particle density does not evidently affect the velocity and porosity distributions. However, heavier particles have high number of collisions and collision energy, and need a high power input. For an IsaMill process, there may exist an optimum particle density for maximum process efficiency. x Smaller particles have a larger number of collisions for given operational conditions (e.g. constant solid loading), although the number of collision for each particle is lower. Larger particles have larger collision energy. The two competitive mechanisms indicates there may exist an optimum particle size for better grinding. But this optimum size is also dependent on the size of the ground products. The power draw decreases with the increase of particle size. x When fill level is decreased, majority of particle stay at the bottom of the mill with slow movement, and only a small number of particles are agitated by the rotating disc. Increasing the solid loading results in a more vigorous motion of the particles. x Increase in fill volume causes circulatory flow field in the upper region which would increase the mixing of the bulk volume. Circulatory flow field diminishes with decreasing fill volume. x Collision frequency increases with increasing fill volume whereas collision energy gives maximum at 60% fill volume. Further increase in fill volume leads to decrease in collision energy which could result in a reduction in grinding performance. x Although, increase of mill speed causes particle to be moved more vigorously, velocity profiles are similar for different mill speeds. x Both collision frequency and collision energy increase with increasing mill speed which could result in a increase of grinding performance. x A power model has been developed in terms of operational variables for predicting power draw. x In the current simulation, as we do not consider the viscous effect from the fluid phase, further research is needed by considering both particle and fluid. However, predictions obtained from this work is useful for comparison of different operating conditions in IsaMill provided that fluid phase is not present. CHAPTER 5

EFFECT OF MILL PROPERTIES 5.1 Introduction

In the previous section effect of particle material properties and operational conditions on the flow and force structure have been investigated. Apart from the particle properties and operational conditions, the properties and geometry of the mill also have influence on particle flow. Therefore, in this section we will investigate the effect of mill properties and mill geometry on the grinding performance of the IsaMill. The results were analysed in terms of velocity distribution, porosity distribution, collision frequency, collision energy and power draw. Mill properties and mill geometries such as particle-disc sliding friction coefficient, particle-wall sliding friction coefficient, distance between discs, disc hole size and different stirrer geometries were analysed.

5.2 Simulation method and condition

Numerical method and simulation conditions are similar to previous chapter. To investigate the mill properties, different types of stirrers were used as shown in Fig.5.1, namely disc without holes (0H), disc with three holes (3H), disc with five holes (5H) and pin type stirrer. In simulation, the mill material properties, the gap between stirrers and the stirrer shape were varied to examine their effects on the flow. Table 5.1 lists the base values and their varying ranges of the parameters used in the simulation. The effect of a parameter is examined while the others are fixed at their base values.

Fig.5.1 Different stirrer geometries of 0H, 3H, 5H and pin (from left to right). All dimensions in mm. Table 5.1 Physical parameters used in the present simulation.

Parameter Base Value Varying range

Number of particles 44000 - -3 Particle density , U (kgm ) 2500 1000 - 6000 -2 Young’s modulus, Y (Nm ) 1.0u107 - ~ Poisson ratio, V 0.29 -

Particle/particle sliding friction coefficient, Ps,pp 0.2 -

Particle/mill sliding friction coefficient, Ps, pm 0.2 -

Rolling friction coefficient, Pr 0.01 - Restitution coefficient, e 0.68 -

Particle diameter, dp (mm)3- Mill loading, J (%) 80 - Mill speed, ȍ (rpm) 1000 -

Distance between discs, ld mm)( 30 17, 22.2, 30

Disc hole diameter, d h mm)( 18 12 - 24 Stirrer 5H 0H, 3H, 5H, Pin

5.3 Results and discussion The particle flow is analysed in terms of flow velocity, local porosity, collision energy, collision frequency and power draw, which have been demonstrated to be useful to assess the performance of IsaMill (Jayasundara et al., 2006). A simulation starts from a packing process in which the shaft and discs are at rest and all particles are fed into the mill to form a stable packed bed. Then the shaft and stirrers start to rotate at a given speed to agitate the particles. Since our previous work has demonstrated that collision energy can be related to the contact force (Jayasundara et al., 2006), the present work quantify the particle/particle and particle/mill interactions in terms of collision energy and collision frequency. Collision energy is defined as the kinetic energy at a collision,

5.3.1 Particle-disc sliding friction coefficient

In IsaMill, stirrers are coated with rubber liners whose coefficient of friction can be expected to be greater than one (Savkoor, 1965), which contributes high sliding friction between particles and stirrers. As a result, the stirrer sliding friction was changed so that the particle/stirrer sliding friction coefficient Ps,pd varies from 0.1 to 2.0. Fig.5.2 shows the spatial distributions of the flow velocity and porosity for different Ps,pd. With small

Ps, pd of 0.1, particles rotate from the lower region (about 4 o’clock position) to the upper region (around 11 o’clock). Those particles in the upper region obtain high velocities and then accelerate towards the mill drum where they collide with the upper part of the drum. This leaves the flow having a low porosity at the bottom part and high porosity at the upper part. The region of high porosity is caused by the unconfined movement of particles. With large Ps, pd of 2.0 and therefore more efficient energy transfer from stirrer to particles, particles are more densely packed and form a solid centrifuged layer around the entire perimeter of the mill, creating a large void in the centre. The particle flow also becomes faster but the velocity gradient is reduced along the radial direction. 0.86 0.81

0.76 0.71

0.66 0.60

0.55 0.50

0.45 0.40

(a) (b)

Fig.5.2 Spatial distribution porosity and velocity vectors for different

particle/stirrer sliding friction coefficients: (a) Ps, pd = 0.1; and (b) Ps, pd = 2.0.

Fig.5.3 shows the distributions and the mean values of collision frequency for different

Ps,pd. With Ps,pd = 0.1, the distribution in Fig.5.3(a) shows a strong peak at low frequency of around 100Hz. As Ps,pd increases, the distribution becomes wider and flatter. The distribution of collision frequency shows two peaks at low and high frequencies, respectively. Our previous work indicated that the collision frequency of particles between discs is lower than those near discs (Jayasundara et al., 2006), so the first peak corresponds to the collisions between the discs and the second peak corresponds to the collisions close to the discs. Note although that the collision frequency increase with the sliding friction as shown in Fig.5.3(b), where there is a turning point at Ps,pd = 1.0 beyond which the increase become slow. 0.004

0.1 0.003 0.5 1.0 2.0 0.002

Probability density 0.001

0 0 500 1000 1500 C /(Hz) f

(a)

500

400

> /(Hz) 300 f

200

100 00.511.52 P s,pd

(b) Fig.5.3 (a) Probability distribution; and (b) the mean value of

the collision frequency for different Ps,pd.

Fig.5.4 shows the distribution and the mean value of collision energy for different Ps, pd.

As Ps,pd increases from 0.1 to 0.5, the distribution become sharper with a stronger peak -6 at 4u10 J. Further increases in Ps,pd to 2.0 causes the distribution to become flat again with a long tail at large collision energy. This decrease-increase change can also be observed in the mean collision energy variation with Ps,pd, which shows a minimum at

P , pds | 7.0 in Fig.5.4(b). This suggests that stirrers with either very small (Ps,pd < 0.3) or very large (Ps,pd > 1.0) friction should increases the collision energy. However, as stirrers with larger friction have larger collision frequency comparing with those with smaller friction as shown in Fig.5.3(b). This means that particles in IsaMill with rougher stirrers can have more and stronger collisions with particles or mill which will be beneficial to the grinding process. This also explains the use of rubber liners in the industry, which has high friction coefficient. However, as can be observed in both Figures 5.3 (b) and

5.4(b), there exist a turning point at Ps,pd = 1.0. Beyond this point, increasing particle/disc sliding friction does not significantly effect on either collision energy or collision frequency. But the power draw still increase with sliding friction as shown in Fig.5.5, because more input energy is required to overcome the friction between particles and stirrers. Therefore, a very high particle/stirrer friction may consume high energy without significant improvement in grinding.

0.2

0.1 0.15 0.5 2.0 0.1

Probability density 0.05

0 0 5 10 15 20 C /(10-6 J) e

(a) 6 3 J) -9 2 /(10 K

5 E 1 J)

-6 0 012 P 4 s,pd > /(10 e

2 00.511.52 P s,pd

(b)

Fig.5.4 (a) Probability distribution; and (b) mean value of the

collision energy for different Ps, pd.

500

400

300

200 Power /(W)

100

0 00.511.52 P s,pd

Fig.5.5 Power draw of IsaMill as a function of Ps, pd.

In the present work, we have also varied the sliding friction between particles and shell of the mill Ps,pw while keeping particle/stirrer friction unchanged. The simulation results show that varying Ps,pw has negligible effect on the flow velocity and porosity distribution (not shown here). Although the collision frequency, collision energy and power draw increase with Ps,pw, that increase is very minimal as shown in Fig.5.6. This suggests that the effect of the friction of mill shell is not as significant as that of stirrers. 168

166

164

> /(Hz) 162 f

158

156 0 0.5 1 1.5 2 P s,pw

(a)

4.9 J) -6 4.8 > /(10 e 4.7

4.6

4.5 00.511.52 P s,pw

(b) 42

40 Power /(W)

38 00.511.522.5 P s,pw

collision energy and (c) power draw for different Ps,pw.

5.3.2 Distance between stirrers

Distance between discs is another important parameter in IsaMill design. In this work we have changed the distance between discs by varying the number of discs while keeping the length of the mill unchanged. Note the number of particles was changed correspondingly to keep the constant loading of 80%, so increasing the disc number (decreasing the distance) means reducing the number of particles in IsaMill. Fig.5.7 indicates that, by increasing the disc distance to 30mm, more particles stay in the centre of mill. This is because when distance increases, the ratio of the particles near disc to the total number of particles is reduced. The energy transferred from discs can not be propagated effectively to the particles away from discs, therefore the particles do not obtain enough kinetic energy to move along the mill. For smaller disc distance, particles can obtain higher kinetic energy which in turn increases the centrifugal force. As a result, particles tend to move towards the mill drum, creating empty space in the middle. Also, if the flow is viewed from the axial direction as shown in Fig.5.8, the stirrer distance has major influence on flow circulation between the stirrer discs. The particle flow with disc distance of 17mm does not show detectable recirculation between the discs, while the flow with disc distance of 30mm reveals a circulating flow between the stirrers (Fig.5.8(b)). These results are comparable with the results reported by CFD methods by other investigators (Theuerkauf et al., 1999). 0.86

0.81

0.76

0.71 0.66

0.60

0.55

0.50 0.45

0.40

(a) (b)

Fig.5.7 Spatial distribution of velocity and porosity for different

disc distances: (a) ld = 17mm; and (b) ld = 30mm.

1m/s 1m/s

(a) (b)

Fig.5.8 Spatial distribution of velocities at section XX ' for different

stirrer distance: (a) ld = 17mm; and (b) ld = 30mm.

Figures 5.9 and 5.10 show the variation of the collision frequency and collision energy with the stirrer distances. Generally speaking, increasing the stirrer distance leads to the decrease in both collision frequency and collision energy. This is because, by reducing the number of stirrer in the mill to increase the stirrer distance, the energy input from the motor is reduced, as shown in Fig.5.11. Furthermore, more space is occupied by particles because of this. This means that the energy intensity, defined as the total energy input divided by the volume occupied by the particles, decreases with increasing stirrer distance. With lower energy intensity, particles do not have enough kinetic energy to move along the stirrer and tend to stay at the bottom of the mill. This leads to smaller collision frequency and collision energy.

0.006

0.004 22.2 17

0.002 Probability density

0 0 250 500 750 1000 C /(Hz) f

(a)

300

280

260 > /(Hz) f

220

200 15 20 25 30 35 l d /(mm)

(b) Fig.5.9 Probability distribution (a) and the mean value (b)

of the collision frequency for different ld. 10-1 30 22.2

10-3 17

-5

Probability density 10

10-7 0 30 60 90 120 150 C /(10-6 J) e

(a)

1.8

J) 1.6 -6 > /(10 e

1.2 15 20 25 30 35 l d /(mm)

(b)

Fig.5.10 Probability distribution (a) and the mean value (b) of

the collision energy for different ld. 80

50 Power /(W)

30 15 20 25 30 35 l d /(mm)

Fig.5.11 Variation of power consumption with ld.

5.3.3 Disc hole size

In stirred mills, energy is transferred from stirrers to particles mainly in two ways: through particles/stirrer friction and through normal impact between particles and disc holes. The effect of particle/stirrer friction has been discussed earlier, here we quantify the effect of the size of disc holes on particle flow. The diameter of holes dh was varied from 12mm to 24mm, and Fig.5.12 shows the spatial velocity and porosity distribution for different sized holes. The characteristics of the two distributions are very similar but the small holes result in lower velocity. Porosity distribution also indicates that, with small hole, more particles are in the bottom part of the mill. By increasing dh, more localized high porosity regions are evident in the mill centre. This is because the energy transferred from discs hole to particles is the primary way as the holes act as lifters for the particles. With large holes, more particles are captured by the rotating holes, and therefore gain more energy. 0.86

0.81

0.76 0.71

0.66 0.60

0.55

0.50

0.45

0.40

(a) (b)

Fig.5.12 Spatial distribution porosity and velocity vectors for disc holes

of different sizes: (a) dh = 12mm; and (b) dh = 2mm.

Figures 5.13 and 5.14 show the variations of the collision frequency and collision energy with the hole diameter. With large hole, the distribution of collision frequency shifts to right, leading to a large collision frequency. In the mean time, the collision energy also increases with hole size, but more slowly. Fig.5.15 shows the power draw increases almost linearly with dh. Obviously, with large dh, more particles are captured and lifted, therefore more power is required to maintain the momentum of particles.

0.004

12 0.003 18 24 0.002

Probability density 0.001

0 0 200 400 600 800 C /(Hz) f

(a) 220

200

180 > /(Hz) f

140

120 10 15 20 25 d h /(mm)

(b)

Fig.5.13 Probability distribution (a) and the mean value (b) of

the collision frequency for different dh.

12 0.1 18 24 0.01

Probability density 0.001

0.0001 0 50 100 150 C /(10-6 J) e

(a) 8

6 J) -6

4 > /(10 e

0 10 15 20 25 d h /(mm)

(b)

Fig.5.14 Probability distribution (a) and the mean value (b) of

the collision energy for different dh.

40 Power /(W)

20 10 15 20 25 d h /(mm)

Fig.5.15 Power draw as a function of disc hole size dh.

4.3.3.4 Disc geometry

In stirred mills, energy transfer takes place primarily through the stirrer. It has been observed that stirrers of different types can be used for different process for power consumption and product size control (Kwade, 1999). Here we have proposed four types of stirrers, namely, disc without holes (0H), three holes (3H), five holes (5H) and pin type stirrer (PIN). Figures 5.16 and 6.17 show the flow pattern, velocity field and porosity distribution for these stirrers. For 0H stirrer, quite low velocity profile can be observed and particles stay in the bottom part of the mill because of the lack of normal impact to the particles from hole. With only agitation is from friction between particles and stirrers, thus far less energy transferred to the particles. For 3H and 5H stirrers, energy transfer to particles is more effective when holes are present. The velocity profile shows a maximum near disc holes with velocity for 5H being slightly larger. No significant difference is observed, however, between 3H and 5H stirrers in terms of flow pattern and porosity distribution. In the case of pin stirrer, the normal impact from the stirrers to particles is far greater than that from disc holes, so the particles have high kinetic energy and centrifuge towards the mill drum and leave an empty space in the middle. The velocity profile in the radial direction is quite uniform and its magnitude is considerably larger comparing with other three types of stirrers.

(a) (b)

Fig.5.16 Particle flow for different stirrer geometries: (a) 0H; (b) 3H; (c) 5H; and (d) pin. 0.86

0.81

0.76

0.71 (a) (b) 0.66 0.60

0.55

0.50 0.45

0.40

(c) (d) Fig.5.17 Spatial distribution of velocity and porosity for different stirrer geometries when : =1000rpm and J = 80%: (a) 0H; (b) 3H; (c) 5H; and (d) pin.

By comparing the axial velocity distribution for 5H and pin stirrer, Fig.5.18 shows that, for 5H disc, the axial velocities point towards the discs at lower radius, indicating particles are drawn into disc holes at the lower radius side and then ejected back into the bulk of particles from the upper radius of the disc. The particles reaching the centerline of the hole may subsequently exit to either side, resulting in the redistribution of particles along the length of the mill. According to the velocity profile in the upper part, circulating flow exists in the r-z plane. The circular flow is caused by the particles driven outwards by the centrifugal effect generated by the rotating discs. On the other hand, flow field for pin stirrer (Fig.5.18b) is different significantly. At the lower region velocities point towards the disc whereas at the upper region more mixed flow field can be visible. Unlike the flow field observed for 5H disc, circulatory flow field in r-z plane is disappeared as a result of particle centrifuged towards the mill drum. However, particles obtain high velocities due direct contact with the pin surface. (a) (b)

Fig.5.18 Spatial distribution of velocities at section XX ' for (a) 5H stirrer; and (b) pin stirrer.

Figures 5.19 and 5.20 show the collision frequency and collision energy for different stirrers. 0H stirrer has the lowest collision frequency and collision energy and pin stirrer has the highest. 3H and 5H stirrers have very similar frequency and energy, although the frequency distributions are slightly different. Fig.5.21 shows variation of power for different stirrer geometries. Clearly, the power draw increase with the number of holes, and there is a significant increase when pin stirrer is used. The change corresponds to that in collision energy. That is, the more rigorous the motion of particles, the more input energy is required. This consideration applies to all the variables considered in this work.

0.005 0H 0.004 3H 5H 0.003 pin 0.002 Probability density 0.001

0 0 500 1000 1500 2000 C /(Hz) f

(a) 500

400

300 > /(Hz) f

100

0 0H 3H 5H pin Stirrer Type

(b) Fig.5.19 Probability distribution (a) and the mean value (b) of the collision frequency for different stirrers.

103 0H 3H 5H pin 10-1 Probability density

10-5 10-5 0.001 0.1 10 1000 C /(10-6 J) e (a) 10

8 J) -6 6 > /(10 e 4

0 0H 3H 5H pin Stirrer Type

(b)

Fig.5.20 Probability distribution (a) and the mean value (b) of the collision energy for different stirrers.

350

280

210

140 Power /(W)

0 0H 3H 5H pin Stirrer Type

Fig.5.21 Power draw as a function of stirrers.

Conclusions

DEM simulations have applied to investigate the effect of mill properties and geometry on the particle flow in a simplified IsaMill. Their effects on particle flow and grinding performance are examined in terms of flow velocity, porosity, collision energy, collision frequency and power draw. The results can be summarized as: y Increasing particle/stirrer sliding friction can increase the collision frequency but there exists a minimal in the plot of the collision energy as a function of the sliding friction. By considering both collision frequency and collision energy, increasing particle/stirrer sliding friction can improve grinding performance. However, that improvement is only up to a critical particle/disc sliding friction. Beyond that point, increasing particle/disc sliding friction may consume high input energy without significant benefit to grinding process. y Compared to particle/stirrer sliding friction, particle/shell sliding friction does not affect the particle dynamics significantly. y Reducing the distance between stirrers increases the power draw as well as the energy intensity of the mill, and therefore increases the collision frequency and collision energy which is beneficial to the grinding process. y Size of the disc holes plays a key role in energy transfer from discs to particles. With larger holes, collision energy and collision frequency can be increased significantly. Also more particles are captured and lifted with larger holes, and therefore more input power is needed. y Among the different stirrers proposed, 0H stirrer has lowest energy transfer because of lacking the impact between hole and particles. When holes are present, energy transfer is more effective. Pin stirrer shows the highest energy transfer, leading to high collision frequency, high collision energy and high power draw. CHAPTER 6

PREDICTION OF DISC WEAR OF THE ISAMILL WITH AID OF DISCRETE ELEMENT MODELLING 6.1 Introduction

The use of stirred media mills in minerals processing has been increasing since last 15 years due to the fact that conventional grinding mills are incapable for fine grinding. The IsaMill is a high-speed stirred mill developed by Mount Isa Mines (Australia) and Netszch-Feinmahltechink (Germany) for fine and ultra fine grinding in 1990s (Gao et al., 2001). So far, the IsaMill technology has been used in several projects with outstanding success in delivering product as fine as 7Pm with very high power efficiency (Gao et al., 2001; Johnson et al., 1998). Despite gaining increasing industrial importance, Isamill is a new technology and its fundamental understanding of the grinding process is not yet matured. Several studies, both theoretical and experimental, have been conducted on different aspects of this subject (Blecher et al., 1996; Gao et al., 2001; Kwade, 1999; Lane, 1999; Zheng et al., 1995). However, those techniques are inadequate of analysing the microdynamic properties in IsMill process. In order to develop a comprehensive method we have recently developed a DEM model in simulating a simplified IsaMill (Jayasundara et al., 2006a; Yang et al., 2006) and this method have been widely used by other researchers to study different milling processes (Cleary, 2001; Hoyer, 1999; Kano and Saito, 1998; Langton et al., 1995; Mishra, 2003; Yang et al., 2003). The microdynamic properties relating to flow structure such as porosity, and force structure such as particle interaction forces, collision velocity and collision frequency has been analysed with focus on the spatial distribution of these properties (Jayasundara et al., 2006). The effects of particle materials properties and mill properties have also been investigated (Jayasundara et al., 2006; Jayasundara et al., 2006).

Apart from the microdynamic analysis of the mill, material wear in the mill components are an important issue. The replacement costs of the disks and the cost of production lost are significant. Minimising these costs is important to improving plant performance. And also due to wear the geometry of the stirrers will change, and hence the mill performance will also change and some times suffer. So being able to design disks that maintain grinding performance for longer is also a very important area that DEM modelling can assist with. In stirred type mill it is understandable that erosion may be caused due fluid flow and erosion by solid particles. Since slurry flow inside the mill is not considered in this work, erosion by fluid is out of scope of this work. We only consider the wear caused by grinding media. Attempt has been made to develop a wear model which can be used to predict the disk life span. Also the results are analysed spatially to predict the wear pattern in different types of disks.

6.2 Simulation method and condition

Numerical method used in this work was described in section 3.2. The model Isamill used in this work consists of a fixed chamber, a rotating shaft and three stirrers, as shown in Fig.3.1a. A simulation starts from a packing process in which the shaft and discs are at rest and all particles are fed into the mill to form a stable packed bed. Then the shaft and stirrers start to rotate at a given speed to agitate the particles. Simulations were repeated with worn disc holes in order to analyse the wear rate. Table 6.1 lists the parameters and their values used in the simulation.

Table 6.1 Physical parameters of the simulation Parameter Base Value Particle density , U (kgm-3) 2.5u103 Young’s modulus, Y (Nm-2) 1.0u107 Poisson ratio, V~ 0.29

Sliding friction coefficient, Ps 0.2

Rolling friction coefficient, Pr 0.01 Restitution coefficient, e 0.68 Mill loading, J (%) 80 Mill speed, ȍ (rpm) 1000

6.3 Results and discussion

6.3.1 Wear model In many particulate systems a surface is attacked by solid particles entrained in a flow stream and causes material wear on the surface. This type of wear is generally described as erosion (Finnie, 1960). Numerous workers have dealt with erosion wear (Bitter, 1963; Finnie, 1960; Podra and Andersson, 1997; Rabinowicz and Dunn, 1961; Tilly, 1969; Winter and Hutching.Im, 1974); this phenomena is very complex and, the parameters are often misapprehended (Magnee, 1995). What can be stated is that the damage observed for a given material necessarily results from a determined collection of stress occurrences which is proportional to the energy dissipation at the contact point. This theory has been well accepted and has been used extensively in the past (Bitter, 1963; Finnie, 1960; Magnee, 1995; Rabinowicz and Dunn, 1961). Generally wear occur in two methods: (i) wear due to impact and (ii) wear due to abrasion. Wear due to impact is proportional to the kinetic energy of each collision with the inclusion of a strong angular dependence (Finnie, 1960). Wear due to abrasion is proportional the shear work which is the energy dissipation by sliding (Rabinowicz and Dunn, 1961). Thus, from the Finnei wear model

2 2 wear due to impact1 v MVW sin32(sin DD ) D d 5.18 q (6.1)

22 or 1 v MVW cos D D 5.18 qt (6.2) where; M – particle mass, V – impact velocity, Į – angle of attack

Abrasive wear is associated with the energy dissipation where particle slide over the surface. The relationship between wear and energy can be described by the following equation (Rabinowicz and Dunn, 1961).

wear due to abrasion 2 v tGxFW (6.3)

where; Ft – shear force, įx – sliding distance

Also wear is inversely proportional to the material hardness (Podra and Andersson, 1997) Therefore total wear can be written as, K W = WW (6.4) H 21 where K – non dimensional material constant, H – material hardness

Eq. 6.4 is comparable with the wear model developed for Winkler surface model (Podra and Andersson, 1997). For a given material, K can be determined by a friction test which is performed using a CSEM pin-on-disc tribometer (Chaiwan et al., 2002). Testing configuration is shown in Fig.6.1.Wear rates can be measured on the pin by interrupting the test at various sliding distances and determining the area of the worn flat end of the hemispherical pin under a microscope. From the change in area of the worn flat, the volume of material removed per unit sliding distance can be calculated. Thus, for a given material wear volume and the corresponding sliding friction coefficient can be found.

Fig.6.1 A schematic drawing of pin on disc tribometer (Chaiwan et al. 2002).

Now, the Eq. 6.4 can be rearranged as;

W2 W = K (since impact wear is not present, W1 = 0). H GxF W = K t H

P nGxF W = K , where μ – friction coefficient, Fn – normal force H From the literature we have obtained the wear data for tool steel which has hardness of 1128 MPa. Wear data in the above equation are given as W = 2.5 cm3,

μ = 0.5, Fn = 9.12 N, įx = 26917 km (Archard, 1953). Now non dimensional value of K for tool steel can be found as 0.0229 which is being used in this work.

6.3.2 Wear prediction for different stirrer geometries

One of the major contributions of DEM is that it allows isolating individual collisions so that the precise location of each impact is known accurately. The impact damage is measured by considering the collision energy and shear energy which is the energy dissipated by sliding. Wear data is collected on a high resolution mesh that covers the middle disc. The contribution of every particle collision with the disc is accumulated in the triangle elements in which the collisions occur. In this section attempt has been made to analyse the spatial wear distribution for different stirrer geometries. Figure 6.2 shows wear distribution for four different stirrer types: disc without holes (0H), disc with three holes (3H), disc with five holes (5H) and pin type stirrer. Colour represents the volume of material being removed per unit time due to wear caused by particle interactions with the discs. For 0H disc, quite low velocity profile can be observed and particles stay in the bottom part of the mill because of the lack of normal impact to the particles from hole (Jayasundara et al., 2006). With only agitation is from friction between particles and stirrers, thus far less energy transferred to the particles. It is evident that majority of particles are in contact with the side faces of the disc. As a result, 0H disc shows a rather uniform wear distribution caused by abrasion between particles and disc. Outer face shows the highest wear rate where as side faces show progressively reduced wear rate towards the center. Due to the high velocity gradient between outer face and the mill drum, abrasion ware is more dominant in the outer face.

Figures 6.2b and c show wear distribution for 3H and 5H discs. Wear distributions are more or less the same for both discs. As the disc rotates in clockwise, it is evident that most of the wear takes place on the lifting side of the disc holes and outer edges. In particular, the wear is substantially higher across the entire outer face of the disc and lifting side of the hole. From our previous work (Jayasundara et al., 2006) it was observed that the particle velocity between disc outer face and the mill drum is restricted by the friction cause by the mill drum. As a result, particles in this region show a very low velocity compared to disc tip speed such that there is a high relative velocity between particles and disc outer face. This suggests that abrasive wear is likely to dominate the disc outer face with less impact damage. Unlike the disc outer face, disc holes act as lifters to the particles, so a constant interaction between particles and hole surface cause material removal from the holes. This damage is produced by the particles smashing into the hole edges which are in the vicinity of the disc. As a result, impact damage is more likely to dominate near the holes than abrasive damage. Infact, simulation results are comparable with the results reported by the industry. Fig 6.3 shows wear pattern of the industrial IsaMill at 3000 hours. Clearly highest wear can be seen at the outer face and the lifting side of the holes which are comparable with the simulation results.

Figure 6.2d shows the wear distribution for pin stirrer. From the particle disc interaction it is evident that the majority of the energy transfer take place from the direct contact of the leading faces (Jayasundara et al., 2006). As the pin rotate clockwise, leading face of the pin smash in to the particles. This will lead to high impact damage rather than abrasive wear. Thus asymmetric wearing of the pins is likely to result from impacts with the front half of each pin producing a flattened of the leading edges.

21 17 13 8 4 0

(a) (b) (c)

68 51 34

17 0

(d)

Fig.6.2 Spatial distribution of wear rate for different disc geometries: (a) 0H ; (b) 3H; (c) 5H and (d) PIN, 1 wear unit = 10-6 cm3/Sec.

Fig.6.3 Wear pattern of discs of industrial IsaMill after 3000 hrs of operation (courtesy of Xstrata Technology, Australia). 6.3.3 Prediction of disc life span The cost of liner and media wear in grinding compares well with the cost of electrical energy consumed. The economic of mill liner is even more important in high capacity mills because of the high expense of shut down time for relining and replacement of discs. Therefore, predicting disc life span would be much of interest for the mineral industry. DEM simulations cannot be run for long enough to actually simulate the wear evolution, but most of the effect can be achieved by using progressively worn disc geometries. Sacrificial discs can be used to analyse the effect of disc wear on the particle flow. Although, disc outer face shows high wear rate (Fig.6.6), it is evident that compared to disc holes, change of geometry of outer face does not affect the flow of particles significantly (Jayasundara et al., 2006; Jayasundara et al., 2006). Therefore, at this stage we do not consider the change of disc outer face, focus is given to effect of change of hole shape on the particle flow. Following section describe the method of designing worn holes. When the system is in steady state, considering a new disc, wear rate per unit time was calculated from the simulation. Assuming that the worn volume is spread over the thickness of the disc, effective worn area which is shown in Fig.6.4 can be calculated. For example, with the aid of the above parameters, newly installed disc shows an average wear rate of 1.81*10-4 mm3/Sec. At this rate total worn volume after 4 months would be 1.88 cm3. This volume is divided by the number of holes and thickness of the disc in order to find out the corresponding worn area per hole which is given by 42 mm3. Then the holes are redesigned to accommodate the total worn volume. With the new hole shape, again the simulation is repeated to find out the total worn volume. This procedure is carried out for a series of simulations in order to find out the total worn volume with the time which is shown in Fig.6.5. It is evident that as the holes are progressively worn out, the wear rate increases with time. When holes are worn out, more particles are captured which results in a increased energy transfer from discs to particles. As a result, particles obtain high kinetic energy that leads to high energy dissipation at the collision point and ultimately leads to increase in material wear. Fig.6.6 shows the predicted hole geometry of the progressively worn disc. It is evident that as the disc wear increases, hole geometry turns into an elongated shape. Indeed, this observation is comparable with the results reported by the industry. Further wearing of the disc may leads to a structural failure of the disc due to the reduced gap between hole face and the disc outer face. At this stage disc life span would be expired and need to be replaced. Note that the as the wear rate increases with time, the elongated length shown in Fig.6.6 also increases. Results obtained from the simulation for tool steel discs (Vickers hardness of 1128 MPa) indicate that after 12 months, total elongated length | 10mml which is about ½ of the original hole diameter. When elongated length becomes ½ of the hole diameter, one would argue that discs are fully worn and need to be replaced. These are quite plausible predictions of the disc life span. Higher rotation rates and different grinding media would change the wear rates that would change the disc life span.

Fig.6.4 Representation of worn area of the hole; all dimensions in mm. 0.34

/Sec) 0.32 2 mm -3 0.3

0.28 WearRate /(10 WearRate

0.26 2 4 6 8 10 12 14 16 18 Time /(Month) Fig.6.5 Wear rate variation with time.

17 13 (a) (b) 8 4 0

Fig.6.6 Predicted geometry of the progressively worn discs: (a) new disc; (b) moderately worn disc (after 4 months); (c) worn disc (after 8 months); (d) well worn disc (after 12 months). 6.3.4 Effect of disc wear on grinding performance In the following section, we will investigate the effect of disc wear on the particle flow. The particle flow will be analysed in terms of flow velocity, collision energy, collision frequency and power draw. All the analysis will be based on the particle flow in the central region of Isamill as shown in Fig.3.1a. Although various concepts have been proposed in the literature to characterize the mill performance (Kwade, 1996) (Cleary, 2001; Rajamani et al., 2000), according to our previous work it was observed that collision energy has a comparable correlation with the

5/3 maximum contact force which is given by Fn(max) = K1 Ce , where K1 = material constant, Fn(max) = maximum contact force per contact, Ce = collision energy per contact (Jayasundara et al., 2006a). Therefore, in this work effectiveness of particle-particle interactions in a size reduction is quantified by considering collision energy and collision frequency. Collision energy is defined as kinetic

2 energy which is given by ½vm iji , where mi is the mass of a particle and

vij vv ji )( is the relative collision velocity between two particles. Collision frequency is defined as the number of collisions per particle per second.

Figure 6.7 shows the spatial distributions of the particle velocities and local porosity in the radial direction for a new disc and a well worn disc. The distribution is obtained by dividing the mill into a number of cells of 3 particle diameters in size and calculating average velocity for particles whose centers are in a cell. This calculation is carried out at different times, and the results are then averaged to obtain the so-called time average value. The characteristics of the two distributions are similar but well worn disc shows comparatively high velocity. Both distributions show particle rotate from the lower region (about 4 o’clock position) to the upper region (around 11 o’ clock position). Those particles in the upper region obtain high velocities and then accelerate towards the mill drum where they collide with the upper part of the drum. This leaves the flow having a low porosity at the bottom part and high porosity at the upper part. When holes are worn out, more localised high porosity regions are evident in the mill center. This is because with large holes, more particles are captured by the rotating discs, and hence obtain high kinetic energy. Particle with high kinetic energy move towards the mill drum creating more voids in the middle section. 0.8

0.7

0.6

0.5

0.4

(a) (b)

Fig.6.7 Spatial distribution of porosity and velocity for: (a) new disc and (b) well worn disc.

Figures 6.8 and 6.9 show the variation of the collision energy, collision frequency and power draw with the time. It can be seen that rapid increase in Ce, Cf and power draw as the disc worn out. From the velocity distribution it was observed that increase in hole size leads to increase in particle velocity which has an positive effect on Ce, and Cf. This is understandable because increasing particle velocity means the more vigorous motion and hence more vigorous interactions of particles in the system. However, there could be a saturation point where the velocity has little effect on collision frequency and collision energy (Jayasundara et al., 2006). This is because the interactions among particles depend on their relative motion. For example, a large local particle velocity may simply means that particles are moving fast, like a block of objects of fixed relative position, without any collisions between particles. However, the so called saturation point is cannot be seen in this analysis. As the collision energy and collision frequency are related to the grinding performance, the results suggest that the grinding performance could be increased as disc worn out. At the same time, power draw also increases exponentially which may have an adverse effect on the energy efficiency. Obviously when the holes are worn out, as a result of increase in hole size, more particles are captured and lifted. Therefore, more power is required to maintain the momentum of particles. 5.6

5.2 J) -6 4.8 /(10 e C

4.4

4 048121620 Time /(Month) (a)

255

245 /(Hz) f C 235

225 2 6 10 14 18 Time /(Month) (b)

Fig.6.8 Variation of mean values of (a) collision energy and (b) collision frequency with time. 16

13 Power /(W)

11 2 6 10 14 18 Time /(Month) Fig.6.9 Power draw variation with disc wear.

6.4 Conclusions

Prediction of disc wear is one of the very important area that DEM modelling can assist with. Attempt has been made to develop a wear model which can be used to predict the disc life span of the IsaMill. It was shown that wear caused by particle striking on a disc can be represented by the energy dissipation of the collision. A non dimensional wear constant for any given material can be determined by a friction test which was performed using a CSEM pin-on-disc Tribometer. Among the different stirrers being used, 0H disc shows the highest wear rate on the outer face of the disc due to the high velocity gradient between outer face and the mill drum. Disc side faces show progressively reduced wear rate towards the center. 3H and 5H discs show more or less the same wear patterns in the vicinity of the holes and the outer face. It is evident that most of the wear take place on the lifting side of the disc holes and outer edges. In particular, the wear is substantially higher across the entire outer face of the disc and lifting side of the hole. This damage is produced by the particles smashing into the hole edges which are in the vicinity of the disc. As a result, impact damage is more likely to dominant near the holes than abrasive damage. For the pin type stirrer it is evident that the majority of the energy transfer take place from the direct contact of the leading faces. Consequently, leading face of the pin smash in to the particles. This will lead to high impact damage rather than abrasive wear. Disc life span can be determined by using sacrificial discs. It is evident that as the disc wear increases, hole geometry turns into an elongated shape. Shape evolution of the holes was captured by multiple overlapping holes. Results obtained from the simulation for tool steel discs (Vickers hardness of 1128 MPa) indicate that after 12 months, total elongated length was about ½ of the original hole diameter. When elongated length becomes ½ of the hole diameter, one may say that discs are fully worn and need to be replaced. Indeed, these are quite plausible predictions of the disc life span and higher rotation rates and different grinding media would change the wear rates that would change the disc life span. Effect of the disc wear on the grinding performance was discussed in terms of collision frequency and collision energy. It is evident that collision frequency and collision energy increase as the disc worn out which may increase the grinding performance. But, at the same time power draw also increases exponentially which may have an adverse effect on the energy efficiency. CHAPTER 7

MICRODYNAMIC ANALYSIS OF ISAMILL OF DIFFERENT SCALES 7.1 Introduction IsaMill is a high-speed stirred mill developed by Mount Isa Mines (Xstrata) in Australia for fine and ultra fine grinding at an industrial scale which is more energy-efficient than conventional grinding technologies such as ball mill and tower mill (Gao et al., 2001; Johnson et al., 1998). However, the IsaMill process is still not mature and the majority of results are reported by experimental methods which cannot be used to explain the grinding mechanism. This limitation can be effectively overcome by the numerical model based on the discrete element method (DEM) (Cundall et al., 1979), which describe the motion of particles individually. The method has been used to study different milling processes (Cleary, 2001; Hoyer, 1999; Kano et al.,1998). Recently, we have developed a DEM model in simulating a simplified IsaMill (Yang et al., 2006; Jayasundara et al., 2006). The microdynamic properties relating to flow structure such as porosity, and force structure such as particle interaction forces, collision velocity and collision frequency has been analyzed with focus on the spatial distribution of these properties. The effects of particle materials properties and mill properties have also been investigated (Jayasundara et al., 2006). Due to the increased throughput of the IsaMill, now it is standard practice to use large scale mills in the industry. When the mill size is increased, predicting of power consumption and throughput is beneficial to the industry in mill designing. A typical procedure for designing large industrial-scale mills consists of several steps (Herbst et al., 1980). First, laboratory experiments in a smaller size mill are conducted the same operational conditions and using the same grinding medium to obtain the breakage properties of a particular ore. Then, these properties are scaled to larger mills using suitable mathematical models. Finally the mill dimensions are computed from the feed and the estimated product size distributions. For Isamill process, currently there are no rigorous methods to determine how this process should be scaled-up. The common method to scale up from lab tests is to examine the specific energy consumption. In this method the power consumption (KW) of the mill and the mass flow rate (ton / hr) need to be recorded. Then the specific energy input is given by kilowatt-hours per ton. A slightly more accurate method is to use a totaling kilowatt-hour meter. The mass of the entire batch processed through the mill is known, even in a ‘continuous’ process. By dividing the total kilowatt hours used by the mass of product processed, kilowatt hours per ton can be determined. It is reported that the energy versus product P80 relations of the two mills fell on the same a straight line on a log-log scale.

Fig. 7.1 Variation of specific energy consumption and product size.

In addition, two most commonly used empirical methods involve matching power ratio to the tip speed velocity at constant rotational speed and power ratio to the volume ratio at constant tip speed.

2 3 P1 § V1 · at constant tip speed; ¨ ¸ (7.2) P2 ©V2 ¹ where P is the power consumption, V is the mill volume, and v is the tip speed. Validity of these relations are verified by the industry and now it is standard practice to use this relations for actual scale-up of IsaMill. However, carrying out experiments in large scale mills are time consuming and expensive. Therefore, development of alternative methods such as numerical techniques are becoming more popular. Scaling of microdynamic properties which are useful to identify the grinding performance of the IsaMill process has not been studies up until now. In this paper, the scale-up method for the IsaMill was studied using DEM. Firstly, we compare the numerical results with the results reported by the industry. Then we study the scaling relations of microdynamic properties and propose a new set of scaling criteria which represent the grinding performance. 7.2 Simulation method and conditions

Numerical method used in this work was described in section 3.2. The model Isamill used in this work consists of a fixed chamber, a rotating shaft and a single disc with periodic boundary conditions, as shown in 7.2a. A simulation starts from a packing process in which the shaft and disc are at rest and all particles are fed into the mill to form a stable packed bed. Then the shaft and stirrers start to rotate at a given speed to agitate the particles. Simulations were carried out for different mill sizes with the same loading J and different speeds ȍ. Table 7.1 lists the base values and their varying ranges of the parameters used in the simulation. Mills of different sizes of diameter 120mm (1X), 180mm (1.5X), 240mm (2X) and 300mm (2.5X) have been tested. For all the simulations a single disc with periodic boundary condition has been considered to reduce the number of particles. In the following sections, we will investigate the effect mill size on the particle flow.

(a) (b)

Fig. 7.2 Geometry of the model Isamill: (a) sectional front elevation; (b) sectional end elevation; All dimensions in mm. Table 7.1. Physical parameters of the simulation

Parameter Value Particle density , U (kgm-3) 2.5u103 Young’s modulus, Y (Nm-2) 1.0u107 Poisson ratio, V~ 0.29

Sliding friction coefficient, Ps 0.2

Rolling friction coefficient, Pr 0.01 Restitution coefficient, e 0.68 Mill loading, J (%) 80 Mill rotation speed, ȍ (rpm) 1000 Particle size, (mm) 3

7.4 Results and discussion

The particle flow will be analysed for flow structure in terms of porosity and flow velocity and grinding performance will be analysed in terms of collision energy Ce, collision frequency Cf [18] and energy intensity Ei. Collision energy is defined as kinetic

2 energy which is given by ½vm iji , where mi is the mass of a particle and vij vv ji )( is the relative collision velocity between two particles. Collision frequency is defined as the number of collisions per particle per second. Impact energy is defined as collision energy per collision of a ball against other balls or the mill wall within a second.

Product of average collision frequency C f and the average collision energyCe gives the impact energy Ei.

C.CE fei (W) (7.5)

Despite the difficulty in quantifying these variables in physical experiments, they can readily be determined by DEM simulation because the motion of a particle and its stochastic interactions with other particles are traced.

7.4.1 Validating the numerical results We have carried out series of simulations at constant rotational speed and at constant tip speed for different mill scales. Table 7.2 gives power draw obtained for different mill sizes at the same rotational speed and same tip speed. At constant rotational speed, the 3 § v1 · results show that power ratio is proportional to ¨ ¸ which is the same as described by © v2 ¹ Eq. 7.1. At constant tip speed results show that power ratio is proportional to

2 3 § V1 · ¨ ¸ which is the same as Eq. 7.2. Thus, numerical results are in accordance with the ©V2 ¹ results reported by the industry which confirms the validity of the numerical results. Therefore, these set of equations can be treated as performance equations which describe how the process should be scaled up.

Table 7.2 Power draw for different mill scales at constant rotational speed and at constant tip speed.

Mill Power draw at Power draw at Scale diameter constant mill constant tip /(mm) speed /(W) speed / (W) 1X 120 13.8 13.8 1.5X 180 66.9 39.2 2X 240 224.1 87.4 2.5X 300 586.4 162.5

0.4 0.6

0.3 0.4 2 2 /P /p 1 1 0.2 P p

0.2 0.1

0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 (v /v )3 (V /V )2/3 1 2 1 2 (a) (b) Fig. 7.3 Correlation between power draw and: (a) tip speed at constant rotational speed; (b) volume at constant tip seed. 7.4.2 Velocity and porosity

Microdynamic analysis at a particle scale can be made based on information such as the trajectories of and the transient forces on individual particles (Yang et al., 2003; Zhou et al., 2003), which can be readily generated from DEM simulation. To understand the particle flow in IsaMill at different scales, the analysis in this section will focus on the spatial and statistical distributions of the microdynamic variables related to flow and forces such as velocity (v), porosity (İ), collision energy (Ce), collision frequency (Cf) and energy intensity (Ei) at the macroscopically stable state which is a dynamical equilibrium state of particles at a microscopic level (Jayasundara et al., 2006).

Figure 7.4 shows the spatial distributions of the particle velocities and porosity in the radial direction for 1X, and 2.5X at constant rotational speed. The distributions of flow velocity and porosity were obtained by dividing the mill into a series of cells of 3 particle diameters in size and calculating the time average values for particle whose centers are located in the cell. This calculation is carried out at different times, and the results are then averaged to obtain the so-called time average value.

Fig 7.4a shows a uniform velocity distribution whereas Fig 7.4b shows relatively high velocity particularly around 1 o’clock position where porosity is high. When the mill size is increased (Fig.7.4b) high porosity can be seen only around 1 o’clock position. Majority of particles in the lower region of the mill are densely packed and interactions between particles are limited.

(a) (b)

Fig. 7.4 Spatial distribution of velocity and porosity (a) 1X; (b) 2.5X when ȍ = 1000rpm, J = 80%. Figure 7.5 shows particle velocity distribution normalized by mean velocity and median velocity vm. According to Fig. 7.5a when mill size is increased, distribution become flatter and towards the tail, probability density slightly increased promoting high average velocity. This is understandable because when mill size is increased particle obtain high angular velocity due to the increase of disc diameter and hence increase the average particle velocity. However, normalized median velocity distributions lies on the same curve regardless of the mill size (Fig. 7.5b). Therefore, although average particle velocity increases with mill size, normalized statistical distributions are the same. Only difference is the increase of average velocity (Fig. 7.6).

2 1 1X 1X 0.8 1.5X 1.5X 2X 2X 0.6 1 2.5X 2.5X 0.4 Probability density Probability density Probability 0.2

0 0 01230123456 v / v v / m

(a) (b)

Fig. 7.5 Normalized velocity distribution for different mill scales at = 1000 rpm: (a) by mean velocity; (b) by median velocity.

0.9

0.8

0.7

0.6

Mean velcoityMean / (m/s) 0.5

0.4 0.511.522.53 Scale

Fig. 7.6 Variation of average velocity for different mill scales. 7.4.3 Energy intensity

Combination of collision energy and collision frequency defines the energy intensity Ei.

Therefore, it would be worthwhile to examine the statistical distribution of Ei for different mill size. Fig. 7.7 shows energy intensity distributions normalized by mean and median energy intensity values. None of the curves shows similarity among different mill sizes.

1X 1.2 1X 1.5X 1.5X 2 2X 2X 0.8 2.5X 2.5X

1 Probability density Probability density 0.4

0 0 0123012345 E / E / E i i i i(m)

(a) (b)

Fig. 7.7 Normalized energy intensity distributions for different mill scales at = 1000 rpm: (a) normalized by mean velocity; (b) normalized by median velocity.

7.4.4 Collision frequency and collision energy

In this section focus is given to average Cf and Ce. Figure 7.8 shows average Cf and Ce variation for different mill scales. It can be seen that at constant rotational speed, increase of mill size leads to decrease in collision frequency (Fig 7.8a). This phenomena can be explained by the correlation between porosity and Cf which was obtained in our previous work (Jayasundara et al., 2006). Note that the highest Cf was obtained when 0.45 < İ < 0.7 (Fig 7.9a). For 1X mill 40% of the porosity data lies in this range, i.e. 0.45 < İ < 0.7 whereas for 2.5X mill it is 24%. Therefore, porosity of the 1X mill shows 40% of the mill volume is in the state of high frequency region whereas 2.5X mill shows 24% mill volume in the high frequency region. As a result, in 1X mill higher percentage of particles obtain high collision frequency which leads to high average collision frequency whereas in 2.5X mill majority of particles obtain low collision frequency and hence leads to low average collision frequency. According to the correlation between particle velocity and collision energy which is shown in Fig 7.9b, high velocity promote high collision energy. Therefore, at constant rotational speed when mill size is increased, collision energy can be increased. Figure 7.10 shows the power draw variation with mill size. Obviously when mill size is increased power draw also increases as a result of lifting and stirring of large number of particles.

220

500rpm 210 800rpm 1000rpm 200

/(Hz) 190 f C 180

170

160 0.5 1 1.5 2 2.5 3 Scale (a)

25 500rpm 800rpm 20 1000rpm J) -6 15 /(10 e C 10

0 0.511.522.53 Scale (b) Fig. 7.8 Variation of (a) collision frequency; and (b) collision energy; for different scales at constant rotational speed. 600

480

360 /(Hz) f

C 240

120

0 0.42 0.56 0.7 0.84 0.98 H (a)

J) 15 -6 /(10

e 10 C

0 00.511.52 v /(m/s) (b)

Fig. 7.9 Collision energy and collision frequency as a function of: (a), local porosity; and (b) local velocity when : = 1000 rpm and J = 80%. 600

500 500rpm 800rpm 400 1000rpm

300

Power /(W) Power 200

100

0 0.511.522.53 Scale

Fig. 7.10 Power draw variation for different mill sizes at different rotational speed.

7.4.5 Specific power and energy intensity From Fig. 7.1 it was observed that the specific energy consumption and product particle size distribution has a linear relation in log-log scale. Specific energy consumption which is defined as kilowatt-hours per ton is a measure of power consumption per unit volume of the product. Since we do not consider the product particles in the simulation we define specific energy as power consumption divided by the total mill volume. Next step is to relate the particle size distribution to the numerical results. It was shown that the energy intensity and the grinding rate has a strong relation and can be used as a measure of describing the grinding performance (Kano et al., 1998; Mio et al., 2004). High energy intensity means high throughput, in other words more fine product particles. Therefore, it is reasonable to argue that Ei and particle size distribution has a strong correlation. Now we plot Ei vs specific power consumption in log-log scale. Figure 7.11 shows specific power consumption and impact energy for different mill speeds and different tip speed velocities for different mill scales. All the data lies on a straight line which describe the correlation between specific power consumption and impact energy index. The slope of the line is determined as 0.45. Thus, it would be

.450 concluded that specific power consumption is proportional to Ei . This would be important for predicting product particle size distribution provided that correlation between energy intensity and particle size distribution is known, which would be the future work.

105 ) -3

104 ȍ = 1000rpm ȍ = 800rpm ȍ = 500rpm v = 5.23m/s

Specific power / (Wm / power Specific v = 4.18m/s v = 2.61m/s 103 101 102 103 104 E / (W) i

Fig. 7.11 Correlation between specific power consumption and impact energy.

7.5 Conclusions

In this work, the scale-up of the IsaMill has been investigated by DEM simulation. The numerical results are compared with the results reported by the industry in order to validate the numerical results. Secondly, microdynamic analysis has been carried out in order to understand the particle flow in IsaMill for different mill sizes. Finally, a new scale-up relation has been established in terms of specific power consumption and impact energy. The results can be summarized as:

x At constant mill speeds power ratio is proportional to the cube of the tip speed ratio and at constant tip speed power ratio is proportional to the Ҁ of the mill volume ratio.

x Although average particle velocity increases with mill size, its normalized statistical distributions with respect to median, are the same.

x At constant mill speed, when mill size is increased particle obtain high velocity. As a result collision energy increases with increasing mill size. However, according to the porosity distribution it was observed that when mill size is increased motion of majority particles are restricted which result in a low collision frequency. x For both constant mill speed and constant tip speed velocity, when mill size is increased power consumption increases due to stirring and lifting of large number of particles. x It was observed that specific power consumption and impact energy shows a linear

.450 relation in log-log scale. Thus specific power consumption is proportional to Ei . CHAPTER 8

CONCLUSIONS AND FURTHER STUDY Research towards the fine grinding, particularly applied to stirred type mills are limited and fundamental are largely depend on laborious experimental techniques. This thesis presents a numerical method which is based on discrete element method (DEM) to investigate the microdynamic properties of particle flow in a stirred type mill known as IsaMill. Notably, the technique can generate information which is not possible to obtain by the conventional experimental techniques. The following conclusions can be obtained from the study. x Discs play a critical role in agitating particles in the mill. Particles near discs move more vigorously than those close to side walls. Due to the uneven distribution of particles, flow pattern and the spatial distribution of porosity indicate that there are fewer particles in the region near discs and particles are more densely packed near the end wall and between discs. x Among the different contact forces between particles, the maximum contact force is more representative and it is closely related to the collision energy which can be treated as an important parameter for describing the grinding performance. x Effect of the grinding media properties on the grinding performance have been analysed. Among the grinding material properties, particle/particle sliding friction is an important factor to be considered. When the sliding friction coefficient is smaller than a critical value, increasing the sliding friction coefficient decreases the collision frequency and increases the collision energy. When the friction coefficient is higher than the critical value, increasing the sliding friction coefficient decreases both the collision frequency and the collision energy, and hence the grinding performance. Therefore grinding media with low sliding friction coefficient are preferable for effective grinding. Although particle/particle restitution coefficient has little effect on the velocity and porosity distributions, a high restitution coefficient can result in a high collision frequency and collision energy, which is beneficial to grinding. For an IsaMill process, there may exist an optimum particle density for maximum process efficiency. Smaller particles have a larger number of collisions for given operational conditions (e.g. constant solid loading), although the number of collision for each particle is lower. Depending on the media size, effectiveness of the grinding may be different and there may exist an optimum particle size for better grinding. But this optimum size is also dependent on the size of the ground products. x Two operational variables such as fill level and mill speed are two significant factors to be considered. Increase in fill level and mill speed always give high throughput. Mill efficiency, however, will be the same due to increase in power draw. y Among the mill properties considered, particle/disc sliding friction coefficient plays and significant role in energy transfer from disc to particles. Increasing particle/stirrer sliding friction can increase the collision frequency but there exists a minimum in the collision energy as a function of the sliding friction. By considering both collision frequency and collision energy, increasing particle/stirrer sliding friction can improve grinding performance. However, that improvement is only up to a critical particle/disc sliding friction. Beyond that point, increasing particle/disc sliding friction may consume high input energy without significant benefit to grinding process. Compared to particle/stirrer sliding friction, particle/shell sliding friction does not affect the particle dynamics significantly. Reducing the distance between stirrers increases the power draw as well as the energy intensity of the mill, and therefore increases the collision frequency and collision energy which is beneficial to the grinding process. Size of the disc holes plays a key role in energy transfer from discs to particles. With larger holes, collision energy and collision frequency can be increased significantly. Also more particles are captured and lifted with larger holes, and therefore more input power is needed. Among the different stirrers proposed, disc with holes show effective energy transfer and hence increase the grinding performance. Pin stirrer shows the highest energy transfer, leading to high collision frequency, high collision energy and high power draw. y Prediction of disc wear is one of the important area that DEM modelling can assist with. Attempt has been made to develop a wear model which can be used to predict the disc wear pattern. Results can be used to predict the life span of the disc. It is shown that as the disc is worn out more energy can be transferred from discs to particles which result in an increase in grinding performance. y The scale-up method of the IsaMill process has been investigated using DEM results. It was confirmed that the numerical results are in accordance with the results reported by the industry. Microdynamic analysis for mill sizes are useful to describe the particle flow and grinding performance of the mill. A new scale-up relation has been established which describe the grinding performance. Finally, it should be pointed out that the present work, as a first step to develop a comprehensive DEM based model, is limited to the flow of grinding media in Isamill. In reality, Isamill process is much more complicated, involving grinding media of different sizes, flow of slurry (mixture of water and fine particulate products) and complicated separating geometry. There is a need to extend the present work by including more variables in order to generate results that can be used directly in industry. The UNSW- Xstrata team is now working in this direction and hopefully more results will be reported in the future. BIBLIOGRAPHY

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List of publications

Journal Papers

1. Jayasundara, C.T., Yang, R.Y., Yu, A.B. and Curry, D., Discrete particle simulation of particle flow in IsaMill. Ind. Eng. Chem. Res., 2006. 45: p. 6349-6359. 2. Yang, R.Y., Jayasundara, C.T., Yu, A.B. and Curry, D., DEM Simulation of the Flow of Grinding Medium in IsaMill. Miner. Eng., 2006. 19: p. 984-994. 3. Jayasundara, C.T., Yang, R.Y., Yu, A.B. and Curry, D. Discrete particle simulation of particle flow in IsaMill - Effect of grinding medium properties. Chem.Eng.J., 2007, CEJ 5219 1-10 (in press). 4. Jayasundara C.T., Yang R.Y., Yu A.B. and Curry D., “Discrete particle simulation of particle flow in IsaMill – Effect of operational variables”, (to be submitted). 5. Jayasundara C.T., Yang R.Y., Yu A.B. and Curry D., “Discrete particle simulation of particle flow in IsaMill – Effect of mill properties”, (to be submitted). 6. Jayasundara C.T., Yang R.Y., Yu A.B. and Curry D., “Prediction of disc wear of the IsaMill with aid of Discrete Element Modelling”, (to be submitted). 7. Jayasundara C.T., Yang R.Y., Yu A.B. and Curry D., “Microdynamic analysis of IsaMill of different scales”, (to be submitted).

Refereed conference papers

1. Jayasundara, C.T., Yang, R.Y., Yu, A.B. and Curry, D. Discrete particle simulation of particle flow in IsaMill - Effect of mill properties. in Comminution 06. 2006. Perth, Australia. 2. Jayasundara, C.T., Yang, R.Y., Yu, A.B. and Curry, D. Discrete particle simulation of particle flow in IsaMill - Effect of grinding medium properties. in Process Intensification and Process Innovation (PI)2. 2006. Christchurch, New Zealand. 3. Jayasundara, C.T., Yang, R.Y., Yu, A.B. and Curry, D. Granular dynamic simulation of IsaMill. Canberra International Physics Summer School on Granular Materials. Dec 2006. Canberra, Australia. 4. Jayasundara C.T., Yang R.Y., Yu A.B. and Curry D., “Discrete particle simulation of particle flow in IsaMill – Effect of operational variables”, DEM 07. Aug. 2007. Brisbane, Australia.