The University of New South Wales Faculty of Science School of Materials Science and Engineering
Model Studies of Solid Flow and Size Segregation in Packed and Moving Beds
Thesis by Shimin Wu
Submitted in Partial Fulfillment of the Requirement of the Degree of
DOCTOR OF PHILOSOPHY In Materials Science and Engineering
July 2007 PLEASE TYPE THE UNIVERSITY OF NEW SOUTH WALES Thesis/Dissertation Sheet
Surname or Family name: Wu
First name: Shimin Other name/s:
Abbreviation for degree as given in the University calendar: PhD
School: Materials Science and Engineering Faculty: Science
Signature
The University recognises that there may be exceptional circumstances requiring restrictions on copying or conditions on use. Requests for restriction for a period of up to 2 years must be made in writing. Requests for a longer period of restriction may be considered in exceptional circumstances and require the approval of the Dean of Graduate Research.
FOR OFFICE USE ONLY Date of completion of requirements for Award:
THIS SHEET IS TO BE GLUED TO THE INSIDE FRONT COVER OF THE THESIS COPYRIGHT STATEMENT
'I hereby grant the University of New South Wales or its agents the right to archive and to make available my thesis or dissertation in whole or part in the University libraries in all forms of media, now or here after known, subject to the provisions of the Copyright Act 1968. I retain all proprietary rights, such as patent rights. I also retain the right to use in future works (such as articles or books) all or part of this thesis or dissertation. I also authorise University Microfilms to use the 350 word abstract of my thesis in Dissertation Abstract International (this is applicable to doctoral theses only). I have either used no substantial portions of copyright material in my thesis or I have obtained permission to use copyright material; where permission has not been granted I have applied/will apply for a partial restriction of the digital copy of my thesis or dissertation.'
Signed
Date cD V I ^
AUTHENTICITY STATEMENT
'I certify that the Library deposit digital copy is a direct equivalent of the final officially approved version of my thesis. No emendation of content has occurred and if there are any minor variations in formatting, they are the result of the conversion to digital format.'
Signed
Date CERTIFICATE OF ORIGINALITY
I hereby declare that this submission is my own work and that, to the best of my knowledge and belief, it contains no material which is previously published or written by any person nor material which to a substantial extent has been accepted for the award of any other degree or diploma of the university or other institute of higher learning, except where due acknowledgment is made in the text.
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.
Date ACKNOWLEDGMENTS
I would like to thank my supervisor Prof. Aibing Yu, my co-supervisors Dr. Haiping Zhu and Dr. Paul Zulli for their patience and helpful guidance in the undertaking of this project. I also thank Australia Research Council and BlueScope Steel for providing APAI Scholarship which made this research possible.
I would like to extend my thanks to all members in the Center for Simulation and Modelling of Particulate Systems for their help and useful discussion.
Finally I would like to thank my wife Xiaofeng Wen for her support and encouragement throughout these years.
Ill ABSTRACT
This work examines the fundamental behavior of granular materials in packed/moving beds under simplified blast furnace conditions. Such study has a significant impact on the development of new technology such as pulverized coal injection and the performance of blast furnace operation. The top part of a blast furnace covers ore and coke receiving hopper to shaft as a top down approach. The total process of burden distribution can be grossly subdivided into the following major parts: material flow through the charging device and free stream of material trajectory; surface profile and coke collapse; radial size segregation (radial distribution of void fraction); radial gas distribution; burden descent. Experiments have shown that a number of interesting phenomena appear in blast furnace operation. The most extensive phenomenon is the particle size segregation which happens in receiving hopper, central spout, burden formation process and deadman surface, and has been well developed. The most important phenomena in the raw materials discharging process are the coke collapse and gouging. The variation of coke collapse will significantly affect the blast furnace performance. The other phenomena include particle creep motion under surface flow, heap formation during coke/ore free flying and particle percolation during the descending process of burden materials. These phenomena involve rich granular dynamics which currently attract strong interest from a wide scientific and engineering community. However, previous work at this area, limited by the research techniques, is predominantly at large scales focusing on phenomenological descriptions, but rarely touching on the basic fundamentals governing these phenomena.
A novel discrete element simulation at an individual particle level can overcome these problems. For this purpose, this work conducts a systematic study of these important phenomena, including crater formation, coke collapse, creep motion and particle percolation, by use of the discrete element method (DEM). The experiments and simulations conducted in the impact of a particle stream onto a particle bed using a 2D slot model suggest that the discrete element method simulation can reproduce the experimental results well under comparative conditions. It is shown that as a result of impact by the falling particles, the particles in the top central region of the particle bed have relatively large velocities and contact forces. The velocities and forces propagate into the bed, and reach the bottom of the base layer quickly. They then continue to propagate leftwards and rightwards to create a crater. The crater size is shown to be affected by the discharging rate, discharging height and materials properties, and be related to the ratio of the input energy from the falling stream to the inertial energy from the original packing. Fundamental understanding of coke collapse based on three different configurations: batch charging, self loading and load impact has been investigated. It was found that collapse process involves weight from the top, particle motion and impact from the top. Collapse can be observed in batch charging top if there is density difference. Static load triggers the initial avalanche. Coke collapse is a kind of continuous avalanche due to top layer particles spreading. The other material properties such as particle size are not found significant to coke collapse. The creep motion of particles in a slot model has been studied based on the results generated by DEM. Experiments are carried out to validate the numerical model. The flow profiles of the surface granular flow and the creep motion of particles in the pile are studied. It is shown that the mean velocity of the surface flow exhibits a linear relationship with depth, while that of the creep motion in the pile decays exponentially with depth and the characteristic length of the decay is on the order of the particle size. The existence of the creep motion can be attributed to the variation of the porosity distribution of the pile. The granular flow on 'frozen' static pile is also investigated to understand the effect of the creep motion on the surface flow. Percolation happens due to both gravity and strain, the strain effect is more significant when the bed starts to move and in the case of larger particle size ratio. The particle percolation rate is increasing with the decreasing of friction coefficient, and is independent of descending velocity while the friction coefficient is smaller than 0.001. More and faster percolation happens near the wall with larger descending velocity. The percolation is definitely directional and vertical penetration occurs much more easily than radial penetration. Rotation is important to percolation. Additionally, this work demonstrates the value of discrete element simulation as a tool for complementing experimental observations. TABLE OF CONTENTS
TITLE PAGE I
CERTIFICATE OF ORIGINALITY II
ACKNOWLEDGMENTS Ill
ABSTRACT IV
TABLE OF CONTENTS VI
LIST OF FIGURES X
LIST OF TABLES XIV
NOMENCLATURE XV
CHAPTER 1 INTRODUCTION 1-17
CHAPTER 2 LITERATURE REVIEW 2-22
2.1 INTRODUCTION 2-23
2.2 BLAST FURNACE BURDEN DISTRIBUTION 2-24
2.2.1 Solid Flow Phenomena in Blast Furnace Top 2-25
2.2.2 Burden Distribution 2-26
2.2.3 Coke Gouging and Mixed Layer Energy 2-32
2.2.4 Coke Collapse Phenomenon 2-33
2.3 IMPACT DYNAMICS OF GRANULAR MATTER 2-37
2.4 GRANULAR SUFACE FLOW AND CREEP MOTION 2-40
2.5 PARTICLE SEGREGATION AND PERCOLATION 2-41
2.6 COMPUTER SIMULATION OF GRANULAR MATERIALS 2-45
VI 2.6.1 Classification of Simulation Methods 2-46
2.6.2 Discrete Element Method (DEM) 2-47
2.6.2.1 Governing equations 2-47
2.6.2.2 Contact forces between particles 2-49
2.6.2.3 Non-contact forces between particles 2-53
2.6.2.4 DEM application 2-55
CHAPTER 3 NUMERICAL INVESTIGATION OF CRATER PHONOMENON .3-56
3.1 INTRODUCTION 3-57
3.2 EXPERIMENTAL METHODS 3-58
3.2.1 Physical Modeling 3-58
3.2.2 Numerical Simulation 3-60
3.3 RESULTS AND DISCUSSION 3-62
3.3.1 Model Validity 3-62
3.3.2 Evolution of Velocity and Force Structure 3-65
3.3.3 Evolution of Energy 3-71
3.3.4 Effects of Geometry and Properties on Crater Size 3-74
3.4 CONCLUSIONS 3-77
CHAPTER 4 DEM STUDY OF COKE COLLAPSE 4-78
4.1 INTRODUCTION 4-79
4.2 METHODS 4-80
4.3 RESULTS AND DISCUSSION 4-83
4.3.1 Experimental Observation 4-83
4.3.2 Simulation Results 4-86
4.3.2.1 Model validation 4-86 VII 4.3.2.2 Batch charging 4-87
4.3.2.3 Self loading 4-91
4.3.2.4. Load impact 4-96
4.4 CONCLUSIONS 4-97
CHAPTER 5 CREEP MOTION OF SHEAR FLOW ON A GRANULAR PILE ....5-99
5.1 INTRODUCTION 5-100
5.2 SIMULATION CONDITION 5-102
5.3 RESULTS AND DISCUSSION 5-105
5.3.1 Flow Pattern and Comparison with Experiments 5-105
5.3.2 Translational Velocity Profile 5-107
5.3.3 Angular Velocity Profile 5-108
5.3.4 Effect of Mass Flow Rate 5-109
5.3.5 Porosity Distribution 5-111
5.3.6 Comparison with Frozen Base Layer Case 5-113
5.4 CONCLUSIONS 5-115
CHAPTER 6 INTER-PARTICLE PERCOLATION IN A MOVING BED 6-116
6.1 INTRODUCTION 6-117
6.2 SIMULTATION METHOD 6-120
6.2.1 Discrete Element Method 6-120
6.2.2 Simulation Conditions 6-121
6.3 RESULTS AND DISCUSSION 6-123
6.3.1 Percolation Characteristics 6-123
6.3.1.1 Velocity profile in the moving bed 6-123
6.3.1.2 Percolation pattern in the moving bed 6-125 VIII 6.3.1.3 Microscopic view of particle percolation 6-126
6.3.1.4 Percolation distribution in a moving bed 6-129
6.3.2 Effect of Operational Variables 6-131
6.3.2.1 Charging rate of percolating particles 6-131
6.3.2.2 Descending velocity of moving bed 6-133
6.3.2.3 Percolating particle number 6-134
6.3.3 Effect of Particle Properties 6-135
6.3.3.1 Particle size ratio 6-135
6.3.3.2 Friction coefficient 6-136
6.3.3.3 Density ratio 6-138
6.3.3.4 Percolation velocity with different size ratio 6-139
6.3.3.5 Particle rotation 6-139
6.4 CONCLUSIONS 6-140
CHAPTER 7 SUMMARY AND FUTURE WORK 7-142
REFERENCES 146
APPENDIX 162
PAPERS IN THE PROCESS OF PUBLICATION 162 LIST OF FIGURES
Figure 1. Charging equipment of blast furnace [24] 2-25
Figure 2. Effect of the installation of the stone box on the size variation 2-29
Figure 3. Comparison of the shape of burden deposit in the lower bunker 2-31
Figure 4. Burden profile after and before ore charging [43] 2-34
Figure 5. Schematic diagram for the collapse of coke bed [43] 2-36
Figure 6. Matrix -like graph for determination of safety factor [43] 2-36
Figure T.Experimental setup for the impact of granular material 2-38
Figure 8. Mechanisms of segregation [77] 2-43
Figure 9. Schematic illustration of the forces acting on particle i from contacting particle j
and non-contacting particle k (capillary force here) 2-48
Figure 10. Schematic representation of Cundall's model for the 2-49
Figure 11. Schematic diagram of the experimental set-up 3-59
Figure 12. Impact process of GB on WB (blue) when H=16d and D=4d: 3-63
Figure 13. Craters formed for different materials when H=16d and D=4d in physical (top)
and numerical (bottom) experiments: (1) pink WB on blue WB; (2) GB on blue WB;3-
64
Figure 14. Surface and subface profiles before and after GB impacting on 20d WB bed
when H=16d and D=4d (area in ABC is defined as the crater area) 3-64
Figure 15. The change of velocity field in the formation of a crater 3-66
Figure 16. Evolution of crater size in crater formation process (H=20d and D=5d) 3-67 Figure 17. Evolution of the normal contact forces in the formation of a crater when GB impacts on WB (H=20d and D=5d) 3-68 Figure 18. Stress distribution on the bottom wall at different times, 3-70 Figure 19. Energy dissipation in a cratering process (H=20d and D=5d): 3-73 Figure 20. Crater size as a function of: (a), orifice width; and (b), charging height 3-74 Figure 21. Correlation between dimensionless crater size Scrater (= [AjA^) • [dl jd^)) and
energy ratio Eratio (= {-m.v] + m^gH)!m^^gdj^), obtained by the DEM simulations....3- 76 Figure 22. Geometry of the model used for the case of batch charging (unitimm) 4-81 Figure 23. Collapse process of blue wooden ball base (GBIO top/WB14 base) 4-84 Figure 24. Collapse results under GB top with different particle size 4-85 Figure 25. Collapse results with different material top 4-85 Figure 26. Subsurface profile variation after collapse under different tops 4-85 Figure 27. Comparison of experiment and simulation results for batch charging case ....4-86 Figure 28. Packing bed collapse process (GB10/WB14) 4-87 Figure 29. Force network during collapse process(GB10AVB14) 4-88 Figure 30. Velocity evolvement during collapse process (GB10/WB14) 4-89 Figure 31. Profile evolvement during collapse process (GB 10/WB14) 4-90 Figure 32. Profiles after collapse under different top 4-91 Figure 33. Self loading process (5.215kg, 4d width) 4-92 Figure 34. Force network for loading process (5.215kg, 4d width) 4-94 Figure 35. Velocity vector in loading process (5.215kg, 4d width) 4-94 Figure 36. The load width effect comparison (5.215kg load) 4-95 Figure 37. The load weight effect comparison (4d width) 4-95
Figure 38. The velocity vector of load impact (3m/s,1.166kg.4d width) 4-96
Figure 39. Effect of the initial load velocity on collapse when the weight and width of the
load are 1.166kg and 4d respectively 4-97
Figure 40. Schematic diagram of experimental and simulation dimension 5-103
Figure 41. Schematic diagram of coordinate systems 5-104
Figure 42. Snapshots of a granular pile in a steady flow state 5-105
Figure 43. Flow pattern comparison between simulation and experiment 5-106
Figure 44. Translational velocity vector in the pile 5-107
Figure 45. Translational velocity distribution 5-108
Figure 46. Angular velocity variation 5-109
Figure 47. Mass flow effect on slope angle and thickness of flowing layer 5-110
Figure 48. Velocity near interface with different mass flow rate 5-110
Figure 49. Velocity distribution with different mass flow rate 5-111
Figure 50. Porosity distribution 5-112
Figure 51. Porosity change with time in marked regions 5-113
Figure 52. Particle configuration (blue color part frozen) 5-114
Figure 53. Velocity vector of flowing layer on fixed slope 5-114
Figure 54. Velocity comparison between quasi-static and fixed base layer 5-115
Figure 55. Schematic diagram of this slot model (d- packed bed particle diameter) 6-121
Figure 56. Particle configuration in a moving bed 6-122
Figure 57. Velocity field in the moving bed 6-124
Figure 58. Averaged translational and angular velocity profiles 6-124
Figure 59. Percolation pattern: (a), size ratio smaller than threshold; 6-125 XII Figure 60. Arching effect of percolating particle size 2mm 6-127
Figure 61. Microscopic view of particle percolation process 6-128
Figure 62. Average particle interaction force in the moving bed 6-129
Figure 63. Percolation in bed height 20d (descending velocity = O.lm/s particle size 3mm)
6-130
Figure 64. Percolation along different bed height 6-131
Figure 65. Percolating particle charge rate effect 6-132
Figure 66. Descending velocity effect 6-134
Figure 67. Percolating particle number effect 6-135
Figure 68. Particle size ratio effect 6-136
Figure 69. Friction effect on both static and moving bed (particle size 2mm) 6-137
Figure 70. Friction effect on a moving bed (particle size 3mm) 6-138
Figure 71. Percolation velocity with size ratio 6-139
Figure 72. Rotation effect on particle percolation 6-140 LIST OF TABLES
Table 1. General view about the solid flow in blast furnace 2-26
Table 2. Contact force and torque models 2-51
Table 3 List of a few typical non-contact forces 2-54
Table 4. Physical properties of the materials used in this work 3-60
Table 5. Components of forces and torque acting on particle i 3-61
Table 6. Parameters used in the DEM simulation 3-62
Table 7. Material properties of wooden balls, glass beads and steel balls 4-83
Table 8. Simulation conditions of self load 4-92
Table 9. Particle configuration of self load simulation 4-92
Table 10. Physical properties of materials used in experiments and simulation 5-104
Table 11.Physical properties of materials used in simulation 6-123
Table 12. Density ratio effect 6-138 NOMENCLATURE
c damping coefficient d particle diameter, m E Young's modulus, Pa Efr collision energy of ore, kgm^/s^
Ep potential energy of ore at falling position of ore, kgm^/s^ F safety factor F^ contact force, N
F^ damping force, N g acceleration due to gravity (vector, magnitude = 9.81), m/s2 G gravity (vector), N H^ vertical distance between falling position of ore and the burden surface at furnace centre at i-th turn, m / moment of inertia of particle, kgm2 m mass of particle, kg m. charged mass of ore at i-th turn, kg M rolling friction torque, Nm , «2 starting and finishing turn of the mixed layer formation, respectively N number of particles AP gas flow resistance, kg.m" R radius vector (from particle center to a contact point), m R magnitude of R, m R radius of arc representing slip surface, m Si p.q/N Ai time step, s t time, s T driving friction torque, Nm V velocity vector, m/s V. component of ore velocity in the direction of coke surface at i-th turn, m/s
W load on slip surface, kg.m'
Greek letters
p particle density, kg/m3 8 vector of the accumulated tangential displacement, m 5 magnitude of 6, m 6 angle of inclination of burden layer, deg 0 angle of internal friction of burden layer, deg
coefficient of rolling friction, m
Jd^ coefficient of sliding friction
V Poisson's ratio (0 angular velocity vector, rad/s 0) magnitude of angular velocity, m/s CO unit angular velocity
Subscripts
ij between particles i and j /, j corresponding to ith, jth particle max maximum n in normal direction t in tangential direction CHAPTER 1 INTRODUCTION 1-17
CHAPTER 1 INTRODUCTION
1-17 CHAPTER 1 INTRODUCTION 1-18
Granular materials consist of discrete, solid particles. They are often encountered in both natural and industrial settings such as sand, stones, soil, ores, grains, pharmaceuticals, and a variety of chemicals. Particulate systems are unique in that they can exhibit gas, liquid, and solid like properties. There are, however, important differences with each of these phases that make the behavior of granular materials even more unusual. A distinguishing feature between flows of granular materials and other solid-fluid mixtures is that in granular flows, the direct interaction of particles plays an important role in the flow mechanics. Thus, most of the energy dissipation and momentum transfer in granular flows occurs when particles are in contact with each other or with a boundary. Understanding how they behave can provide important design information.
Many industrial processes involve particulate materials, one of its typical applications is blast ftimace, granulate ore and coke are its continuous input. The blast ftimace is used to produce pig iron and which is a countercurrent parked-bed chemical reactor in which gases ascend and reduce descending iron oxide particles. Although the blast ftimace process has been studied by numerous researchers for many years, a variety of problems still remain unsolved concerning the rates and mechanisms for the phenomena occurring in the furnace. Understanding and modelling the solid flow and segregation in a blast ftimace has emerged to be a major research focus in recent years. It has a significant impact on the development of new technology such as pulverized coal injection (PCI) and the performance of blast ftimace operation. The top part of blast ftimace involves rich granular dynamic phenomena which currently attract strong interest ft^om a wide scientific and engineering community. Previous blast ftimace work in this area is experimental, laborious, and difficult to generate useftjl information that can be used reliably and generally. This project aims to tackle this problem by means of discrete element method (DEM) supported by necessary physical modelling. DEM has been proved to be a reliable and effective tool to handle phenomena involving granular materials [1-9].
The aim of this project is to develop and validate a particle scale model to describe the flow and segregation of particles of different properties in a blast ftimace and to generate micro- dynamic, ftindamental understanding that can be implemented into industrial application.
1-18 CHAPTER 1 INTRODUCTION IJ^
Chapter 2 reviews the previous work on blast furnace burden distribution, dynamics of particle impact, particle size segregation and discrete element method. Especially the details of DEM approach.
Chapter 3 presents an experimental and numerical study of the impact of a particle stream onto a particle bed using a 2D slot model. The numerical simulation is performed by means of the discrete element method (DEM). The results show that the DEM simulation can reproduce the experimental results well under comparative conditions. The dynamics in the formation of a crater is then analyzed in terms of velocity field, force structure, bottom stress distribution and energy exchange based on the DEM results. It is shown that as a result of impact by the falling particles, the particles in the top central region of the particle bed have relatively large velocities and contact forces. The velocities and forces propagate into the bed, and reach the bottom of the base layer quickly. They then continue to propagate leftwards and rightwards to create a crater. During the impact process, most of the energy from the falling particles is dissipated due to the inelastic collision and frictional contacts between particles, and only a small amount of the energy contributes to the formation of the crater. The crater size is shown to be affected by the discharging rate, discharging height and materials properties, and is related to the ratio of the input energy from the falling stream to the inertial energy from the original packing. hi chapter 4 the coke collapse phenomenon is investigated by the discrete element method. Coke collapse has been reported to play a significant role in controlling the burden distribution in ironmaking blast fiimace. In the past, a lot of experimental work has been done to predict the burden distribution based on the full scale or scaled blast furnace top. However, the governing mechanisms are not clearly understood. In this work, the discrete element method has been employed to develop such understanding based on three different configurations: batch charging, self loading and load impact. It is observed that collapse can be caused by continuous charging of particles and load impact. No obvious collapse has been observed in the case of self loading. The mechanisms to cause collapse for batch charging and load impact are different, which leads to the different final profiles of the base
1-19 CHAPTER 1 INTRODUCTION
bed for both cases. The effects of the material properties such as particle size and density on collapse have also been examined in details.
Chapter 5 presents a discrete element simulation on surface flow pattern on a pile under steady state, and demonstrates the existence of creep motion in the static layer which has been an assumption in some theoretical models for many years. We report here a full picture of motion inside the packing on grain level by tracking particle position, rotation and velocity, force network etc. without any assumptions, which is not achievable by theoretical analysis and experimental approaches. This numerical model has been validated by simply comparing the flow patterns with experimental results. The creep motion of particles in a slot model has been studied based on the results generated by DEM. The present findings include that the mean velocity of creep motion decays with depth, the velocity profile in the flowing layer is linear with its height, and there is no fixed boundary existing between the flowing and static layers. The slope angle of the flowing layer increases with the mass flow rate. In the rotating motion, most the particles rotate along the the axis vertical to the flow direction, the rotating motion along the other two axes is very small.
As shown in chapter 6, particle percolation is not only the mechanism of mixing but also a mechanism of separation. Inter-particle percolation occurs while particle mixtures are of very different size under the gravitational force or mobility owing to the influences of strain even they are similar in size. Numerical investigations of particle percolation in a quasi- static flow bed are described. The bed consists of two roughed parallel side walls and periodical boundary virtue walls in the front and rear. By considering the effect of bed descending velocity, particle size and density ratio between the percolating particles and the packing spheres, sliding coefficient of percolating particles, percolating particle number, the parking bed height and coefficient of restitution, it is found that the size effect is most significant and the density ratio effect is trivial. Percolation happens due to both gravity and strain, the strain effect is more significant when the bed starts to move and in the case of larger particle size ratio. The particle percolation rate is increasing with the decreasing of friction coefficient, and is independent with descending velocity if the friction coefficient is very small. More and faster percolation is happening near the wall with larger descending
1-20 CHAPTER 1 INTRODUCTION
velocity. The percolation is definitely directional in that vertical penetration occurs much more easily than radial penetration. Rotation is important for percolation.
Lastly, chapter 7 summarizes the current work and discusses future direction of this work in general.
1-21 CHAPTER 2 LITERATURE REVIEW 2-22
CHAPTER 2 LITERATURE REVIEW
2-22 CHAPTER 2 LITERATURE REVIEW ^
2.1 INTRODUCTION
Although granular materials are commonly found both in natural and industrial settings, it has not been fully understood how these materials behave. Particulate systems are unique in that they can exhibit gas, liquid, and solid like properties. Highly agitated systems of particles are often modeled in a manner similar to a rarefied gas [10-20]. An important difference, though, is that, unlike collisions between gas molecules, solid particle collisions are inelastic and dissipate energy. Granular materials also have liquid-like properties. For example, a granular material can flow as in an hourglass or an avalanche. Furthermore, when particles are poured into a large container, the assembly conforms, in a bulk sense, to the shape of the container. Unlike a liquid, though, a granular material can resist shear as in the slope of a sand pile [21]. This soUd-like behavior is limited only to compressive loads. When subjected to tensile loads, particles come apart. The reason granular materials can resist shear loads is due to the discrete size of the particles. In order for a densely packed assembly of particles to flow, it must first dilate, a phenomenon known as the Reynolds' Principle of Dilatancy [22]. The resulting normal strain due to an applied shear stress is a result of particles moving over one another as the assembly deforms. Another unusual result of the material granularity is that load transmission is typically anisotropic. Forces are transmitted along particle contacts and form long force chains [23]. Most of the knowledge of how to handle particulates is empirical; they have a number of constraining assumptions that limit their general application.
Many industrial processes involve particulate materials; one of its typical applications is blast furnace, which is a counter-current reactor of rising gas and descending liquid and solid. Although the blast furnace process has been studied by numerous researchers for many years, a variety of problems still remain unsolved concerning the rates and mechanisms for the phenomena occurring in the furnace. The major reason for this is that the blast furnace process includes many physical and chemical changes which occur simultaneously. A number of attempts have, however, been made to develop mathematical models for the better understanding of this complicated process. The models have also given a great deal of information on the internal situation of the blast furnace. This has
2-23 CHAPTER 2 LITERATURE REVIEW 2-24
proved useful for the improvement and the stabilization of the operation. It is therefore instructive for the fiiture advancement of a blast furnace model to review the models already proposed. Most of the previous work has focused on showing that these various behaviors exist. However, fundamental mechanisms of the phenomena are still lacking. The present work details experiments and simulations designed to provide some of this information.
This project aims to study the fundamentals govern the flow and segregation of particles in an iron making blast fiimace. It involves experimental study, numerical modelling, micro- dynamic analysis, and application. Discrete element method will be used to study the dynamic behavior of the formation process of the burden distribution at the blast furnace top. The experimental work aims to generate detailed and relevant data for verifying the developed discrete element method model and understanding the flow and segregation phenomena.
2.2 BLAST FURNACE BURDEN DISTRIBUTION
The blast furnace, used to produce pig iron, is a countercurrent parked-bed chemical reactor in which gases ascend and reduce descending iron oxide particles. Inputs to the blast are the load (layers of coke and ore) and hot blast. Outputs from the furnace are blast furnace gases, slag and pig iron. There are different kinds of physical, thermal and chemical processes inside the blast furnace, including combustion in front of blast tuyere; distribution of gas flow, temperature, and chemical composition; profile of blast furnace burden load; and position and shape of cohesive zone etc.
Among the blast furnace technologies that have been developed in recent years, radial gas distribution control by means of burden distribution control at the stock line is the most important for attaining better performance. The burden distribution is characterized by the structure of the layered bed of coke and ore. The structure is determined by the flow of burden materials at the time of charging. Although the flow of charged materials in the
2-24 CHAPTER 2 LITERATURE REVIEW 2-25
upper shaft is relatively uniform when the furnace runs normally, the burden descent rate varies radially across the furnace. This is mainly due to non-uniform combustion rate of coke at each tuyere and non-uniform flow resistance of the burden, particularly that in the cohesion zone, which gives rise to uneven gas flow.
2.2.1 Solid Flow Phenomena in Blast Furnace Top
Top of blast furnace consists of following components: receiving hopper; sealing device; flow control device; material distributing unit; stock line part of shaft. Fig.l shows two types of charging apparatus: bell and movable armor top and bell-less top. The layer thickness distribution is controlled by adjusting the trajectory of burden material by use of the moveable armor in the bell top, and by changing the titling angle of the distributing chute in the latter case. The bell-less top is widely in use for intensive burden distribution control, and bell types have been largely abandoned in large scale furnaces.
Receiving chute Sounding Upper sealing valve
Material f\o\N control gate
Lower sealir^ valve Feeder spout
(1): Position of armor Distribution chute
(a) Bell top with movable armor (b) Bell-less top
Figure 1. Charging equipment of blast furnace [24'
Receiving hopper receives the charging materials from the skip or from the belt conveyor. Sealing devices (upper seal and lower seal valves) help to isolate the inside furnace
2-25 CHAPTER 2 LITERATURE REVIEW 2-26
atmosphere from the outside ambience during the material charging process. Flow control device (e.g. common plunger valve in case of compact bell less top) controls the material flow rate in the charging process. The bell top or rotating chute distributes ore and coke 360° about the central axis for the furnace. The total process of burden distribution can be grossly subdivided into following major parts: Material flow through the charging device and free stream of material trajectory; Surface profile and coke collapse; Radial size segregation (radial distribution of void fraction); Radial gas distribution; Burden descent. The phenomena in the blast furnace operation are summarized in Table 1.
Table 1. General view about the solid flow in blast furnace
Phenomena Process Method Ref. Segregation 1).Receiving hopper (well developed) Analytic [25] 2).Central spout (well developed) Experimental [26] 2).Burden distribution Empirical 3).Deadman surface equation Collapse/gouging 1).Rotating chute Experimental [27] 2).Bell-top/armor [28] Piling Free flying (well developed) Experimental [21] DEM and alike Creep motion Under steady surface flow Experimental [29]
percolation 1).Packed bed (well developed) Experimental [30] 2).Radial distribution (well developed) [31] 3).Descending in shaft
Present knowledge about the flows of solids in the furnace is not as well developed. More work needs to be done to have a full understanding of the phenomena listed in the above table.
2.2.2 Burden Distribution
2-26 CHAPTER 2 LITERATURE REVIEW
In recent years, lots of efforts have been made to achieve the following benefits in blast furnace in order to improve its efficiency, including decreased fuel consumption; increased productivity; improved hot metal quality; stabilized operation. Generally speaking, the blast furnace process had its stormiest development phase during the past few decades, coupled with developments in plant engineering, the quality and supply of raw materials as well as comprehensive process monitoring and control equipment. It has been well known that the ratio of ore to coke layer thickness and particle size distribution in the radial direction are two key factors of burden distribution control in the blast furnace. The former has greatly improved the operational results of blast furnace through not only hardware development such as charging equipment and profile meter, but also software such as charging model. On the other hand, the latter has been relatively less investigated than the former [32], In the BF operation, the appropriate control of the burden distribution at the BF top is important to influence blast furnace performance, such as increase in the production, decrease of the fuel rate. Especially recently large efforts are made to increase the substitution of coke by coal in order to meet changing economical and environmental conditions. The proper distribution of burden materials improves bed permeability, air acceptance, and efficiency of gas utilization. Hence, the improved gas distribution results in better utilization of its thermal and chemical energy owing to improved gas-solid contact, and further results in better utilization of the sensible heat of the gases and increase in the extent of the indirect reduction, which significantly decreases the coke rate. Therefore for efficient operation of blast furnace equipped with a rotating chute distribution system, it is essential to optimize the distribution of the burden materials with particular reference to chute angle, ring number, and number of revolutions in the respective rings, correlating this with the above burden probe temperature (gas distribution profile) from the center to the wall of the furnace.
The blast furnace charge consists of materials of various sizes with different physical properties and it is difficult to distribute them at the top of the stock column in a manner such that the entire vertical and horizontal cross-section of the furnace could offer equal resistance to the gas flow. During charging, the materials tend to segregate along radial direction according to their nature, size and density. A non-uniform distribution of charge
2-27 CHAPTER 2 LITERATURE REVIEW
materials results in a non-uniform radial distribution of particle size, viodage, and hence permeability of the stock column. The resulting non-uniform radial distribution of the gas flow affects the charge descent rate and vice versa. As the stock line pattern has been found to persist during descent, much attention has been paid to obtaining an optimal burden distribution at the top. Based on model experiment as well as actual blast furnace data, the stock line cross-section can be divided into three zones (1). Peripheral; (2). Intermediate and (3). Central. According to Pandey et al [33], the intermediate zone consists of about 50% of total cross-sectional area, and 30-35% of total gas passes through this area. Each of the peripheral and central zones consists of about 25% of the area, and 65-70% of gas passes through them. Since the majority of gas passes though the central and peripheral zones, a uniform distribution in these zones is desirable. It is possible to attain this aim to a great extent by proper burden distribution at the top.
The important characteristic information such as mean size of burden components as well as the chute geometry together with angles of inclination that can be obtained through in depth burden distribution studies is summarized below: (1). Profile of individual burden layer and layer thickness; (2). Segregation behavior of burden materials; (3).Voidage and its distribution in the radial direction; (4). Ore/coke distribution in the radial direction and (5). Burden descent rate (furnace movement). Thus, for improved blast furnace performance with regard to productivity, fuel rate, and hot metal quality, the importance of in depth of burden distribution studies through physical and mathematical modeling is obvious. Kajiwara et al [34] investigated the burden distribution on the BF top by physical model and a mathematical model. They also employed a stone box in the upper part of the bunker to charge the size variation in the discharging process. They concluded that: (1). In the formation of the ore and coke layers, the mixed layer formation caused by the collapse of the coke layer during the ore charging plays the most important role; (2). The particle size distribution at the bell type BF is formed by the percolation of small particles in the flowing particle layer on the slope; (3). The particle size distribution at the bell-less type BF is dependent on the variation of the particle size during the discharging from the bunker. For the suppression of the size variation, the installation of a stone box in the upper part of the bunker is effective, and the result is shown in Fig 2; and (4). The dynamic behavior of
2-28 CHAPTER 2 LITERATURE REVIEW 2-29
the burden deposit on the slope can be quantitatively analyzed by the two-dimensional dynamic mathematical model with the consideration of the interaction between particles.
Stone box Key Condition - -o- - Without stone box 1.4 - 5 200 mm —•— With stone box xY m a» 1.2 .a
1.0 ss33 oc cr 0.8
0.6 0.2 0.4 0.6 0.8 1.0 Dimensionless discharging time (-} Figure 2. Effect of the installation of the stone box on the size variation during the discharging in the bell -less model experiment [27]
Earlier than these researchers, Narita et al.[35] studied the ore and coke distribution in BF on a full size bell charging model. It was found that the inclination of the ore and coke layers varied with charging sequence and dumping volume, it was clearly shown that the radial distribution of ore and coke depends on coke volume, ore to coke ratio in charging burdens, charging sequence and pellet content in burdens. By comparing the results of a full size model with those a one-tenth reduced model, it was found that the mixed layer of coke and ore was formed and the ore to coke ratio was decreased in the central part of the reduced model. It was reasoned that the ratio of particle weight of coke and ore should be taken as one of the scaling factors in the reduced model. In another paper, Narita et al [36] also studied the relationship of gas temperature distribution with the descending rate and layer thickness of burden in the throat of blast furnace and concluded that (1). The radial distribution of the gas temperature at the throat is closely related to the stability of furnace performance and the permeability in the furnace; (2). There exists the radial distribution of the burden descending rate, which changes the temperature distribution at the throat; (3). It is theoretically confirmed that the layer thickness could be varied by the change in the radial distribution of burden descent. The results obtained from the theoretical analysis are
2-29 CHAPTER 2 LITERATURE REVIEW
in good agreement with the operational results of the blast fiimace. Hockings et al [37] did trial tests on a full scale Paul Wurth test facility to validate the RABIT model with experimental data, the experimental work include: (1). Static angles of repose of raw materials; (2). Constants required for the algebraic function to describe the surface profile near the wall; (3). Radial size segregation; (4). Trajectory of materials falling from the rotating chute; and (5). The extent of coke collapse. They paid special attention on the coke collapse phenomena investigation on the factors: (1). The effect of discharge rate on the coke collapse volume; (2). Examination of ore/coke radial distribution and coke collapse volumes; (3). Confirmation of the number of the chute revolutions between initiation and completion of coke collapse; and (4). Estimation of the internal angle of friction for coke. Ichida et al [38] investigated influence of ore/coke distribution on descending and melting behavior of burden in blast furnace by using a three dimensional semicircular warm model of the blast furnace under conditions set as similar as possible to the physical phenomena in the furnace. It is confirmed that the ore/coke ratio largely influence the descending velocity of burden and gas flow. The following points obtained (I). In the case of the radially uniform ore/coke distribution, the descending velocity distribution in the shaft is nearly uniform in the radial direction, and an inverted V-shaped cohesive zone is formed; (2). In the case of the charging of ore closer to the fiimace centre, the dead man contracts, a W- shaped cohesive zone is formed and the temperature in the wall region increases; (3). In the case of the charging of ore further from the furnace centre, the dead man expands, an inverted U-shaped cohesive zone is formed and the temperature in the wall region decreases. It has been reported that even if the charging method is the same, the ore/coke distribution at the furnace top greatly varies depending on the radial distribution of burden descent velocity near the burden surface in the blast furnace by Ichida et al [39]. On the other hand, there was a report saying that the radial distribution of burden descent velocity near the burden surface in BP is correlated with the furnace internal condition. The development of reduced and real scale models that allow to see how the burden should behave inside blast furnace, are important part of studies. Jimenez et al [40] built a three dimensional cold model to test charging patterns and the effect of gas flow in burden distribution by digital image processing. Jung et al [32] investigated the improvement of gas flow through analyzing discharge behavior in the bunker used in blast furnace, both
2-30 CHAPTER 2 LITERATURE REVIEW 2-31
Stone box and central chute were employed in the bunker to change the radial size distribution of burden as shown in Fig.3
y centra! chute
a) before rebuilding b) after rebuilding Figure 3. Comparison of the shape of burden deposit in the lower bunker before and after attaching the central chute[32]
It was proved that rebuilding the interior structure of lower bunker could ftxndamentally modify the radial particle size distribution, which was strongly related to gas flow. Hattori et al [41] investigated the development of burden distribution simulation model for bell - less top in a large blast fiimace and its application, in their work, in order to establish the burden distribution simulation model, basic factors governing the burden distribution in the bell -less top for a large blast ftimace were examined through the 1/10 scale model experiment on the basis of the burden distribution model formerly developed for Fukuyama No.2 blast fiimace(1983 first bell -less). By incorporating these results and considering the particle size change during discharge, a burden distribution simulation model for Keihin No.l blast ftimace ( 1989, second bell-less, throat diameter Im) was newly constructed. As a result of application, a productivity of 1.9 t/d.m3 was achieved in only two weeks after blow-in. phenomena to be considered in constructing the burden distribution simulation model for the bell -less top are as follows: the falling behavior of materials from chute, the burden profile of layers after falling, the effect of gas flow, the effect of lower layer, the descent of burden, and particle size distribution in the radial direction. Among these factors, burden profile can be considered to be seriously affected by the throat diameter. In Keihin No.l blast furnace, the circumferential uniformity of burden distribution is ensured by the
2-31 CHAPTER 2 LITERATURE REVIEW 2-32
adoption of the vertical dual -hopper, the stone box was employed in the lower hopper, it is reported that, when the particle size segregation of raw materials occurs in the top bunker, the particles size on discharge from the bunker changes with time, and this cause the particle size segregation in the radial and the circumferential directions, thus result sing in changes in the gas flow distribution.
2.2.3 Coke Gouging and Mixed Layer Energy
Kajiwara et al [27] investigated the burden distribution in rotating chute charging by the use of a full scale experimental apparatus and simulation were developed on the basis of the experimental results. The discharging behavior of burden from the bunker was found to be primarily funnel flow and was quantitatively evaluated by the simulation model considering the distribution of particle velocity in the flow region above the discharging hole. It was found that sinter showed stronger tendency to funnel flow than coke. Furthermore sinter falls closer to the wall than coke at each chute angle. Noticeable formation of a mixed layer was observed in their full scale experiments, and the mixed layer is defined as layer which contains 25 to 75 vol% of coke. When ore is charge onto coke surface, part of coke near the falling position of ore is scooped out and is transported toward the centre to form large mixed layer in the central region. As a result, the actual O/C distribution in the radial direction differs from the one estimated from the profile measurement before and after the charging. It is worth to mention here the concept of "scoop out" is close to the concept "gouging" proposed by Austin [28]. They introduced the formation energy of mixed layer as:
Em =E^+E,= + (1)
where Ef^ total formation energy of mixed layer (kgm /s )
2-32 CHAPTER 2 LITERATURE REVIEW
Ef. collision energy of ore (kgm^/s^)
Ep potential energy of ore at falling position of ore (kgm^/s^) m. charged mass of ore at i-th ring (kg)
V. component of ore velocity in the direction of coke surface at i-th ring (m/s)
H^ vertical distance between falling position of ore and the burden surface at furnace
centre at i-th ring (m) «1, «2 starting and finishing turn of the mixed layer formation, respectively (-)
They also found that mass of ore effective to the mixed layer formation is expected to be limited up to the completion of covering of coke surface by ore.
2.2.4 Coke Collapse Phenomenon
When the sinter is dumped onto the inclined coke layer there is some coke slipping into the center and forms a mixed layer in the central region, this is what we called coke collapse [42]. Okuno et al [43] developed a mathematical model for predicting the burden distribution of blast furnaces, using a 1/3 scale charging equipment model with a rotating chute or bell-movable armor. The volume of the coke layer collapsed toward the furnace centre was quantified by using the theory of soil mechanics. The model was applied to Nippon steel's blast furnaces and helped to improve their operation. The burden distribution can not be easily grasped, because it varies with charging conditions ( such as charging mode, ore/coke ratio, stock level etc.) and charging equipment as well as furnace parameters such as gas flow distribution, coke layer collapse and burden descent speed distribution.
The mathematical model for predicting the burden distribution such as reported by Heynert et al [44], no models were available that quantitatively handle the furnace factors in general and the coke layer collapse in particular. Okuno et al clarified the effect of the coke layer collapse phenomena on burden distribution and on the basis of this finding, developed a
2-33 CHAPTER 2 LITERATURE REVIEW 2-34
mathematical model applicable to both bell-less and bell charged blast furnaces. They discussed the coke collapse phenomena in detail, when ore is charged in a layer on the inclined surface of the coke layer, the coke layer collapse phenomena was observed to occur extensively. It is a phenomenon in which the underlying coke layer partially collapses and rolls toward the centre under the load of ore when ore is locally piled as charged as shown in Fig. 4.
Figure 4. Burden profile after and before ore charging [43]
The ore layer thickness changed a little after the charging of coke and indicated that no ore layer collapse. A mixed layer is observed at the boundary between the collapsed coke layer and the ore layer. By using the soil mechanics (which is a discipline that applies the principles of engineering mechanics to soil to predict the mechanical behavior of soil), the angle of inclination 0 of coke layer can be expressed by the relation given below: tan 6 > tan ^ (2)
This relation means that the collapse of the coke layer does not occur when the angle of inclination 6 decrease to the angle of internal friction (j).
The collapse phenomena of coke layers was assumed to be that of shear failure occurring along a slip surface formed in the coke layer and the slip surface moving toward the ftimace
2-34 CHAPTER 2 LITERATURE REVIEW 2-35 centre at an angle corresponding to the angle of internal friction, as illustrated in Fig. 5. Accordingly, the collapse phenomenon was modelled by the slope stability theory of mechanics which will be discussed in the next section.
The profile of the slip surface is not a circular arc, strictly speaking, but is given as an arc or the combination of an arc and plane for the ease of calculation. To determine an arc, its origin and radius must be given. Although such an arc may be drawn in many ways, the arc of the slip surface when the coke layer collapses must satisfy the condition that the safety factor of the slope of the coke layer should show the smallest under a given load. The safety factor F is expressed by as the ratio of the shear strength of the failure plane to the shear force inducing sliding along the slope.
n
(3) 2 m. sine, i=l where F safety factor R radius of arc representing slip surface, m W load on slip surface, kg.m 6 angle of inclination of burden layer, deg (j) angle of internal friction of burden layer, deg AP gas flow resistance, kg.m"^
The safety factor is obtained by dividing the coke layer into n concentric slices in the radial direction and computing for the ith slice the sliding force that causes the resisting force that prevents the collapse. Matrix -like graph shown in Fig 6.
2-35 CHAPTER 2 LITERATURE REVIEW 2-36
A ^rt of ore
Portion of coke iay«r eoUapswi
Portion of coke l»r«T iJepoeitsd /
Wa2l C«at«r
Figure 5. Schematic diagram for the collapse of coke bed [43]
i 1 i 1j 4[ X >i
Line flrhich is dependent upon ang^ie of internal friction
Figure 6. Matrix -like graph for determination of safety factor [43 ^
The findings obtained were (1). The collapse of the coke layer by the charging of ore greatly changes the coke layer thickness from mid-radius region to the centre of the furnace. The scale of the collapse mainly varies with the charging mode selected. The amount of the collapsed coke ranges fi-om 4 to 16 wt% of the coke charge under usual charging conditions; (2), The moving pattern of coke as a result of the collapse remains the same, irrespective of the type of charging equipment employed and the charging conditions applied. The range of inclination of coke layer after collapse is independent of the charging conditions and is virtually equivalent to the angle of internal friction in the coke layer; (3), The collapse of
2-36 CHAPTER 2 LITERATURE REVIEW
the coke layer can be regarded as a phenomenon that a slip surface occurs in the coke layer under the load of ore deposited in the wall region and moves toward the furnace centre at an angle corresponding to the angle of internal friction. Therefore, this phenomenon can be mathematically handled be the slope stability theory of soil mechanics. Austin et al [28] investigated the coke collapse and gouging by using a 1/5.8 scale model, concluded that coke collapse - weight (potential energy) of sinter piling up on the coke may cause the coke terrace become unstable, eventually avalanching inwards. The coke layer collapsed when the minimum safety factor of coke layer is less than the critical safety factor. Coke gouging - Kinetic energy of the impacting sinter may form a crater on the coke surface, and either push or spray coke both radially inwards and outwards from the impact point.
Burden plays a key role in blast furnace performance, this is the reason why such a large number of studies concerning the influence of burden properties and burden distribution in the blast furnace have been performed in the past years, and are continuing. However, there are many unclear points about the distribution of burden materials such as mechanisms of coke collapse and coke gouging. Further simulation work regarding this part will be conducted in this project from microscopic view which would provide in depth understanding other than macroscopic view such as Okuno's model.
2.3 IMPACT DYNAMICS OF GRANULAR MATTER
The collision of particles is relevant to many areas of process engineering; lots of research works have been conducted to study the particle impact behavior. Collisions have been studied since the beginning of the century [45]and the rebound and energy loses can be modelled for most simple cases with few exceptions. Regarding dry collisions, Salman et al [46] presented the results of a comprehensive program of experiments in which particles are impacted under controlled conditions against solid targets. The overall aim of these experiments was to gain an understanding of the fragmentation process of particle products in a pneumatic conveying system. Ema et al [47] investigated tribo-charging of particles with particular attention to the effect of impact velocity. One of its findings was that
2-37 CHAPTER 2 LITERATURE REVIEW 2-38
translational energy loss normalized by initial translational energy had almost constant value when the impact angle is smaller than a certain critical angle. Beyond this critical angle, it decreased linearly to zero. This fact suggests that the contact mode changes from rolling to slipping at this critical angle.
Tanaka et al [48] investigated the dynamic response of two-dimensional granular matter subject to the impact of a spherical projectile experimentally and also numerically using DEM, the granular matter was modelled by a mono-disperse aggregation of nylon spheres arranged regularly and two-dimensionally in a rectangular container. The numerical simulations are compared with the experiments using high speed video camera for the impact velocity of about lOm/s. it is shown that the motion of each particle can be well simulated by discrete element modeling, also, the dynamic response of the particulate aggregation is elucidated in detail by inspecting the distribution of velocity vectors of individual particles, and very distinctive behaviors are found.
solenoid valve g
Figure T.Experimental setup for the impact of granular material
In order to clarify the dynamic behavior of granular matter experimentally, it is necessary to measure very accurately the movement of individual particles constituting the granular matter but the measurement is extraordinarily difficult because the duration of the impact is very short and displacements of individual particles are relatively small. Davies [49] found that when a coherent circular stream of small non-cohesive particles impacts onto a smooth inclined surface, it is dispersed as a thin sheet. The particles appear to move down the plate parallel to the plate surface on paths which straighten to run parallel to the longitudinal axis
2-38 CHAPTER 2 LITERATURE REVIEW
of the plate at the point remote from the impact point. Interest in post-impact behavior of a falling particle stream was prompted by its potential use in mixing devices and in removing oversize material from bulk flows. Thornton [50] found that collisions involve energy loss. When dealing with large systems of particles either analytical or numerical models have been used. It is essential that energy is dissipated in as natural a way as possible. Thornton et al illustrated the effect of oblique impact on the dissipation and redistribution of energy. A series of simulations were performed for different values of impact angle, from the corresponding force -displacement curve. However, their work clearly shows that, prior to rigid body sliding, energy is dissipated as a result of microslip. If the impact angle is greater than the angle of internal friction, rigid body sliding occurs from the start of the impact and continues until the decelerating relative tangential motion of the spheres and the accelerating particle spin induced by the tangential force combine to reduce the tangential force increment to Ai < //Ap. The energy is dissipated during the oblique impact of two perfectly elastic spheres is clearly demonstrated by the force -displacement curves. The evolution of the linear kinetic energy during an impact and the way in which the energy is converted into work were done by the contact forces. The effect of obliquity on the percentage loss in linear kinetic energy, the percentage gain in rotational kinetic energy and the percentage energy dissipated due to microslip and rigid body sliding. It can be seen that, as the angle of impact increases, the loss in linear kinetic energy and the gain in rotational kinetic energy increase until the impact angle is sufficiently large to produce rigid body sliding throughout the impact. Particle interactions within large systems of particles invariably involve oblique contact forces, following an oblique impact, the rebound angle, velocity and particle spin are all fiinctions of the total history of the impact duration. The energy dissipated and changes in both linear and rotational kinetic energy are significant and are complex functions of the angle of impact. Thornton et al [51] presented 3d simulation of agglomerate impact which result in rebound, fracture or shattering depending on the magnitude of the impact velocity specified. The study of oblique impact of agglomerate by Moreno et al [52] revealed that the normal component of the impact velocity is the dominate factor in controlling the breakage of contact, the size distribution of the fragments were affected by the impact angle, further work is needed to elucidate the cause of the difference.
2-39 CHAPTER 2 LITERATURE REVIEW
2.4 GRANULAR SUFACE FLOW AND CREEP MOTION
Many industrial processes like mining, iron-making, chemical and civil engineering involve the flowing of granular materials [18]. There are two different configurations for studying the free surface flows, one is the flow on a rough inclined plane [53, 54] , another is the flow on a pile [55-57]. Our focus in this work is restricted to the case of dry, cohesion-less granular media, and to situations where the granular flow is confined to a layer at the surface of a granular pile. The earliest models describing surface flows of granular materials have originated in the large amount of work devoted to the description of granular dynamics by the researchers in the filed of applied mechanics. Bagnold contributed his pioneered work on the fundamental laws at work inside these flows [58] , Savage and Hutter [59] developed a general model based on depth-averaged mass and momentum balance equations, which is restricted to the description of flows over fixed bottoms. Some recent models like the phenomenological 'BCRE' (Bouchaud-Cates-Ravi Prakash- Edwards) model and hydrodynamic model assume a sharp interface between a static phase and a rolling phase inside the granular packing, and exchanges of grains occur these two phase by dislodging immobile grains or trapping rolling grains. Capable of exchanging grains through collisions processes, forms the central hypothesis of the second generation of models [60, 61]. With a frozen bulk region below, many studies have been made under such assumption without convincing experimental evidence [61-64]. The more recent models integrate the particle exchange mechanisms into hydrodynamic description, initiated by Douady et al. [65]. Komatsu et al. [29] recently recognized that an important characteristic of solid flow is creep motion, where no such sharp frozen region exists and even the particles in the layer deep still exhibit very slow flow that can be detected everywhere in the packing .
Our understanding of the surface flows of granular remains fragmented and many elements lack to form a coherent and global picture, in particular, the creep motion. Another significant issue is to get a better understanding of the internal rheology of these surface flows: beyond the depth -average descriptions presented here, one would, for instance, to better understand why linear velocity profiles emerge in flows taking place at the surface of
2-40 CHAPTER 2 LITERATURE REVIEW 2-41
piles, and why non-linear profiles arise in the flows over fixed bottoms. We may mention here two arguments that have been proposed in the literature, the first is due to Komatsu et al. [29] who noticed that when a flow take place at the surface of a pile, the static phase in fact undergoes a slow creeping motion; these authors suggest that the suppression of these creeping motion when the flow occurs on a rigid bottom may be responsible for the change in nature of the velocity profile between these two types of experiments. The second is clusters of grains embedded within the flowing layer by Bonamy et al. [66]. Most of the emphasis has been on the theoretical side and several approaches, based on different physical assumptions have been proposed [67-69]. Quasi-two-dimensional experiments are becoming a common element in the toolkit of granular flow investigations. A question common to quasi-two-dimensional studies is the extent to which walls affect the results. To a first approximation the effect of walls may be quantified by the ration of particle diameter to the thickness of the container. The experiments reported here were conducted with different ratio such as Orpe et al. [70], Jain [71]and Komatsu et al. [29] . But they are all in the range 5-25 which is free of the wall effect.
2.5 PARTICLE SEGREGATION AND PERCOLATION hi the burden charging process, particles segregate due to coke/ore size and density difference, fiirthermore, when ore lands on coke, the coke surface might be gouged by the falling ore, or the weight of sinter might cause the coke to avalanche, this is a complex process inside the BF. Size segregation occurs due to the large size difference of coke or ore. It may affect the permeability and chemical reactions in the BF and leads to a low productivity and high energy consumption. However, size segregation in BF has not been quantitatively examined due to the lack of available quantitative information in physical experiments. In present work, DEM which can generate rich dynamic information at a particle scale is used to investigate the solid flow and size segregation in BF top zone.
Many researchers have done some work to find the segregation mechanisms in order to decrease segregation phenomena or eliminate it. When a non-cohesive material is
2-41 CHAPTER 2 LITERATURE REVIEW 2-42
discharged onto a free surface, it is found that differing particles become separated. Such effects can give rise to problems the BF charging process. Lots of researchers have studied the segregation phenomena. Brown [72] gave an early qualitative explanation of segregation and identified two types of segregation; the first was that occurring in a bed of material due to vibration, and the second that occurring at a free surface during flow down an inclined slope. For free surface segregation. Brown considered that the primary factor was the collisions between particles flowing onto the heap and those forming the free surface. Brown also considered the segregation of identically sized particles due to density difference. He believed that the greater momentum of the denser particles would cause these either to sink beneath the line of fall or to roll down the slope. Consequently, they would be concentrated partially beneath the point of feed and partly at the periphery. Williams [73, 74] gave an explanation for free surface segregation during heap pouring. He stated that materials roll down a sloping surface which contains holes of the same order of size as the diameter of the bigger particles, small particles will tend to sink through these holes preferentially. On the other hand, the larger particles that are unable to locate adequately sized holes will tend to roll to the bottom of the heap. Williams [26] stated that difference in particle size, density, shape and particle resilience could each, under certain circumstances, cause segregation but considered that 'all the available evidence' showed particle size difference to be far the most important. Harris and Hildon [75] considered size to be the most important factor controlling free surface segregation. The literature indeed suggests that both size and density are significant factors on causing free surface segregation but frequently the effect of density has been neglected, often studies on density are sketchy afterthought, the importance of both size and density will be demonstrated in this study. Darhun et al. [76] concluded that: (1). Free surface segregation occurs by avalanching, inter-particle percolation and particle migration; (2).The particle diameter ratio influences segregation. Smaller particles sink by percolation and are found close to the pouring point, whereas larger particles rise to the surface by particle migration and are found at the far end of the surface; and (3). The particle density ratio influences segregation, denser particles being found near the pouring point and less dense particles at the far end.
2-42 CHAPTER 2 LITERATURE REVIEW 2-43
Rhodes [77] has done extensive work on segregation and indicated that even if particles are originally mixed by some means, they will tend to unmix on handling ( moving, pouring, conveying, processing), although differences in size, density and shape of the constituent particles of a mixture may give rise to segregation, difference in particle size is by far the most important of these. Density difference is comparatively unimportant except in gas fluidisation where density difference is more important than size difference. Many industrial problems arise from segregation. Even if satisfactory mixing of constituent is achieved in a power mixing device, unless great care is taken, subsequent processing and handling of the mixture will result in demixing or segregation. Four mechanisms of segregation according to size was identified as shown in Fig.8: (1). Trajectory segregation, it means larger particles travel further than smaller ones (2).Percolation of fine particles, percolation of fine particles can occur whenever the mixture is disturbed, causing rearrangement of particles. This is happening in stirring, shaking, vibration or when pouring particles into a heap, charging or discharging storage hoppers. (3). Rise of coarse particles on vibration. If a mixture of particles of different sizes is vibrated the larger particles move upwards; (4).Elutriation segregation. When a powder containing an appreciable proportion of particles under 50 jjm is charged into a storage vessel or hopper, air is displaced upwards which entrains the fine particles. Mixtures of solid particles can separate or segregate while they are being handed. This often results in costly quality control problems due to the waste of raw materials, lost production, increased maintenance etc. Segregation problems occur in a wide range of industries handling materials as diverse as coal and pharmaceutical powders.
oPooco oou" o Oo o°oo O oo çp_ 'O
(a) Trajectory segregation (b) Segregation by percolation © Segregation by elutriation
Figure 8. Mechanisms of segregation [77]
2-43 CHAPTER 2 LITERATURE REVIEW 2-44
The penetration of the smaller particles into the interstices of larger ones is called particle percolation which will consequently cause the local variation in voidage of packed beds. Propster et al. [78] reported experimental results on the spatial dependence of the local void fraction for systems where particles of different size form horizontal layers in packed beds. The most important finding of this work is that the penetration of smaller particles into the interstices of the larger spheres occurs readily when the particle size ratio exceeds about two. With particular interest in particle mixing, Bridgwater et al. [79] examined the inter- particle percolation phenomenon which is one of the mixing mechanisms by physical experiments in which the percolating species are so small that penetration through any hole of the structure of large particles is possible . They concluded that inter-particle percolation is a process more closely analogous to molecular diffusion, the radial dispersion of very small spherical particles is in accord with a diffusion mechanism, the Peclet number has been used to describe the radial dispersion, and the diameter ratio of the percolating particles to the packing appears to be relatively unimportant. They also mentioned that a weak effect stemming from the density difference of equally sized particles is also believed to exist. Following this study, Bridgwater et al. investigated the rate of spontaneous inter- particle percolation [30]. It was found that the mean percolation velocity maybe determined by the coefficient of restitution and the diameter ratio of the percolating particles to the packing, the residence time distribution of percolating particles was shown to conform to a diffusive mechanism and the actual Peclet number was found to be virtually independent of the particle properties. With special attention to the geometry of the porous structure, Richard et al. investigated the inter-particle percolation of a fine particle through a packing of mono-size spheres by experimental and numerical approaches based on the geometry of the packing [80]. The percolating particle is charged in multiple points unlike Bridgwater's which was charged only in the center. By mapping the inter-particle space using the Voronoi tessellation of the packing whose edges describe the network of pores of the medium and deduce the possible paths of the falling sphere, the motion of the sphere can be easily simulated with a Monte-Carlo algorithm. They found that the radial diffusion of the falling bead increases linearly with the height of the packing and numerical results are in agreement with the experimental results. Unlike the single particle percolation study, Oger
2-44 CHAPTER 2 LITERATURE REVIEW
et al.[81] demonstrated the effects of particle number and packing bed height on the percolation process by employing experimental and DEM methods. They believed that collective behavior of particles plays an important role because the presence of many particles falling together induces many additional collisions and collective effects. Apart from the gravitation force, percolation also occurs in the shear zone between two layers of particles moving at different velocities, Scott et al. examined irregular particle movement in a failure zone by a horizontal shear box [82]. They concluded that the irregular movements of spherical particles in a simulated failure zone formed in the shear box could be approximately described by a diffusion equation. Further strain-induced inter-particle percolation study was carried out by Cooke et al. [83]. A reciprocating shear box was employed to study both lateral and axial diffusion during the process of percolation, found that the dimensionless lateral and axial diffusion coefficients are controlled mainly by the ratio of the diameter of the percolating particle to that of the bulk particles. Duffy et al. investigated the particle percolation in a vertical shear cell by considering variables particle size ratio, strain, strain rate and bed depth. It was found that the size ratio is most dominate, strain also had an effect, the percolation of fines through a bed of coarse particles was isotropic [84]. They also developed and validated a convective- diffusive segregation model to describe the percolation based on the experimental results [85].
2.6 COMPUTER SIMULATION OF GRANULAR MATERIALS
In the past years, many granular material studies were made by using conventional experiments, the resulting information has been helpful in developing a broad understanding of granular physics. However, the bulk behavior of a granular system depends on the collective interactions of individual particles, and hence particle scale analysis plays a critical role in elucidating the underlying mechanisms. Research at a particle scale has been recognized as a promising approach to probe the flow mechanisms of granular materials. Experimental techniques like PEPT is one of particle scale research technique which is able to measure a single particle trajectory, but it is difficult to obtain
2-45 CHAPTER 2 LITERATURE REVIEW 2-46
the micro-dynamic information such as inter-particle transient forces. Such information is key to elucidating the fundamentals governing the flow of particulate materials.
As computer processor speed increase and hard drive and memory costs decrease, computer simulations became an increasingly effective tool for studying granular materials. Simulations offer several important features for studying granular flows. Perhaps the most significant is that the state of the particulate system is known at all times in a simulation. Hence, the interior of a flow can be examined and measurements can be made that may be difficult to make in experiments. Furthermore, simulations can model environments that are not easily produced in experiments. For example, many simulations are performed with altered gravity environments or with frictionless particles. The insights that these simulations can provide are valuable for understanding how granular materials behave.
2.6.1 Classification of Simulation Methods
Most granular flow computer simulations refer to the fact that the simulation models the granular material as a system of individual particles. Computer simulations include Monte Carlo techniques, cellular automata, and discrete element method (DEM) [86].
Monte Carlo techniques are statistically based. A particle assembly state is chosen based on the energy of the configuration. For each new state, particles are given a random velocity or position within some distribution fiinction. The configuration which gives the lowest system energy is chosen as the new state. The movement of particles is limited by physical restraints which appear in the state energy. For example, two particles occupying the same position can be assigned to have a high energy making that particular configuration improbable. Simulations using the Monte Carlo technique have been performed by Rosato [87], Meakin [88] and Cahn et al [89].
The cellular automata method is a lattice-based, kinematic approach, where particles are constrained to move on discrete lattice points. At each time step, particles are allowed to 2-46 CHAPTER 2 LITERATURE REVIEW 2-47
move into neighboring empty lattice points with the constraint that only one particle may occupy a given lattice point at a time. The particle movement is also governed by a probability function which reflects the physics of the system [90-92]
Discrete element method is perhaps the most common simulation technique and was pioneered by Cundall and Strack [93]. Two types of particle dynamics methods are most common: one is hard-particle method, in which collisions are instantaneous and binary, and another is soft-particle methods, in which collisions are fmite and can occur between muhiple particles. Many flows, however, especially those occurring in a gravity field, have multiple, long duration particle contacts. Soft particle simulations are best suited for these situations, the forces acting on each particle in the system are determined.
2.6.2 Discrete Element Method (DEM)
2.6.2.1 Governing equations
A particle in a granular flow can have two types of motion: translational and rotational. During its movement, the particle may interact with its neighboring particles or walls and interact with its surrounding fluid, through which the momentum and energy are exchanged. Strictly speaking, this movement is affected not only by the forces and torques originated from its immediate neighboring particles and vicinal fluid but also the particles and fluids far away through the propagation of disturbance waves. The complexity of such a process has defied any attempt to model this problem analytically. In DEM approach, it is generally assumed that this problem can be solved by choosing a numerical time step less than a critical value so that during a single time step the disturbance cannot propagate from the particle and fluid farther than its immediate neighboring particles and vicinal fluid [93". Thus, at all times the resultant forces on a particle can be determined exclusively from its interaction with the contacting particles and vicinal fluid for coarse particle system. For a fine particle system, non-contact forces such as the van der Waals and electrostatic forces should also be included. Based on these considerations, Newton's second law of motion can be used to describe the motion of individual particles. The governing equations for the
2-47 CHAPTER 2 LITERATURE REVIEW 2-48 translational and rotational motion of particle i with mass /w,. and moment of inertia can be written as
g (4) k dio. L (5) ' dt , where Vi and ©i are the translational and angular velocities of particle i, respectively, F^ and Mij are the contact force and torque acting on particle i by particle j or walls, is the non-contact force acting on particle i by particle k or other sources, F/ is the particle-fluid interaction force on particle i, and F^ is the gravitational force. Fig. 9 schematically shows the forces and torques. Various models have been proposed to calculate these forces and torques, which will be discussed below. Once the forces and torques are known, Eqs. (1) and (2) can be readily solved numerically. Thus, the trajectories, velocities and the transient forces of all particles in a system considered can be determined.
Figure 9. Schematic illustration of the forces acting on particle i from contacting particle j and non-contacting particle k (capillary force here).
2-48 CHAPTER 2 LITERATURE REVIEW 2-49
2.6.2.2 Contact forces between particles
In general, the contact between two particles is not at a single point but on a finite area due to the deformation of the particles, which is equivalent to the contact of two rigid bodies allowed to overlap slightly in the DEM. The contact traction distribution over this area can be decomposed into a component in the contact plane (or tangential plane) and one normal to the plane, thus a contact force has two components: normal and tangential. The normal contact between two particles is modeled as a linear spring in parallel with a dashpot element as shown in Fig. 10, It is very difficult to accurately and generally describe the contact traction distribution over this area and then the total force and torque acting on a particle, as it is related to many geometrical and physical factors such as the shape, material properties and movement state of particles. Alternatively, to be computationally efficient and hence applicable to multi-particle systems, the DEM generally adopts simplified models or equations to determine the forces and torques resulting from the contact between particles.
Figure 10. Schematic representation of Cundall's model for the contact between two grains [2]
Various approaches have been proposed for this purpose. Generally, linear models are the most intuitive and simple models. The most common linear model is the so-called linear spring-dashpot model proposed by Cundall and Strack, where the spring is used for the 2-49 CHAPTER 2 LITERATURE REVIEW
elastic deformation while the dashpot accounts for the viscous dissipation. The linear spring model without inclusion of dashpot has also been used by, for example, Di Renzo and Di Maio[94]. More complex and theoretically sound model. Hertz- Mindlin and Deresiewicz model, has also been developed [95]. Hertz [96] proposed a theory to describe the elastic contact between two spheres in the normal direction. He considered that the relationship between the normal force and normal displacement was nonlinear. Mindlin and Deresiewicz proposed a general tangential force model. They demonstrated that the force- displacement relationship depends on the whole loading history and instantaneous rate of change of the normal and tangential force or displacement. A complete description of the theory of Mindlin and Deresiewicz can be seen in the recent work of Vu-Quoc and Zhang 97, 98]and Di Renzo and Di Maio[94]. Due to its complication, however, the complete Hertz-Mindlin and Deresiewicz model is time-consuming for DEM simulations of granular flows often involving a large number of particles, and is therefore not so popular in the application of DEM. Instead, various simplified models based on the Hertz's theory, Mindlin and Deresiewicz's theory or both have been developed for DEM modelling. For example, Walton and Braun [99] and Walton [100] used a semi-latched spring force- displacement model in the normal direction, and an approximation of the Mindlin and Deresiewicz contact theory for the cases of constant normal force in the tangential direction. Thornton and Yin[50]proposed a more complex model to simulate the tangential force. While adopting the Hertz's theory for the normal force, different from Walton and Braun's model, their model assumes that the incremental tangential force due to the incremental tangential displacement depends on the variation of the normal force. Both Walton and Braun's model and Thornton and Yin's model for tangential force are the direct simplifications of the Mindlin and Deresiewicz's theory. A more intuitive model was adopted by Langston et al. [101]. They used a direct force-displacement relation for the tangential force and the Hertz's theory for the normal force. Due to its simplicity and intuitiveness, the model has been extensively used to study the dynamic behavior of granular matter [102-105]. More recent advances on contact force incorporating the plastic deformation have also been made by Thornton and Yin [50]and Vu-Quoc and Zhang [97, 98]. However, they need more experimental validation. The above models are often used miscellaneously (Schäfer et al. [106]; Lätzel et al. [107]). Table 2 shows the equations for
2-50 CHAPTER 2 LITERATURE REVIEW 2-51
some commonly used force models for spherical particles, including the linear spring- dashpot model, the simplified Hertz-Mindlin and Deresiewicz model by Langston et al, and Walton and Braun's model.
The inter-particle forces act at the contact point between particles rather than the mass centre of the particle and they will generate a torque causing particles to rotate. Generally, the torque is contributed by two components of the tangential and normal traction distributions. Compared with the contribution of the tangential component, the determination of the contribution of the normal component, usually called as rolling friction torque, is very difficult and is still an active research area (Greenwood et al., [108]; Johnson [45]; Brillianton and Poschel [109]; Kondic [110]). The rolling friction torque is considered to be negligible in many DEM models. However, it has been shown that the torque plays a significant role in some cases such as the formations of shear band (Iwashita and Oda, 111]) and heaping (Zhou et al. [103]), and movement of a single particle on a plane (Zhou et al. [103]; Zhu and Yu [112]).
Table 2. Contact force and torque models
Force Normal force Tangential force References models Linear Cundall and
spring- where K^ and C„ are the where K^ and C, are the Strack[93] dashpot normal spring and tangential spring and Goldenberg and model damping coefficients. damping coefficients. Goldhirsch [113] Simplified Langston, et Hertz- V / al. [101, / 1 *E'^R S„ Mindlin and -cJsm '3„ r 102], V / 1—1— / • Deresiewicz Zhou et al, where E* and R* are the where C^ is the tangential model [103, 104],
2-51 CHAPTER 2 LITERATURE REVIEW 2-52
reduced modulus of damping coefficient, // is the Zhu and Yu elasticity and particle sliding friction coefficient, [105] radius respectively, /„^ is the elastic component
is the relative normal of normal interaction, is displacement at contact, the relative tangential C„ is the normal displacement, S^^ is the damping coefficient. maximum öf when the particles start to slide.
Walton and * \ 1/3 Walton and ft-ft Braun's (loading) ft +K 1- Braun[99], fn = Itfn-ft k2(S„-S„o),S„<0 V / model if öf in initial direction Walton [100] (unloading) 1/3 ft -ft where ki and ki are the 1- ASt
spring constants for the if in opposite direction loading and unloading. where kt^ denotes the initial 5no is the value of 5n tangential stiffness, ft* is where the unloading initially equal to 0 and set to curve intersects the the value ft whenever ¿^ abscissa under the given reverses its direction. circumstances, or the permanent plastic deformation.
Toque Rolling friction torque Torque from tangential References models forces
2-52 CHAPTER 2 LITERATURE REVIEW 2-53
Method 1 m^ = dt Iwashita and where kr is the rolling where R is the distance of the Oda [111] stiffness, Cr is the mass center of the sphere to viscosity coefficient, 0r contact plane. is the relative particle rotation. Method 2 Zhou et al.
where jir is the rolling [21, 103, fiiction coefficient, 114], is the rotational stif&iess, Zhu and Yu cOn is the component of 105 the relative angular velocity in contact plane.
As discussed above, linear and nonlinear contact force models have been developed for DEM simulations. Theoretically, the more complex nonlinear models simplified based on the Hertz and Mindlin-Deresiewicz theories should be more accurate than the linear model. However, in contrast, the numerical investigations conducted by Di Renzo and and Di Maio [94] showed that the simple linear model sometimes gives better results. This may be because theoretical models are often based on geometrically ideal particles, whereas there are no such perfect particles in practical applications. Selection of proper parameters also plays an important role in generating accurate results. Complicated models may also consume computational time with insignificant gain in DEM simulations. Moreover, as recently demonstrated by Zhu and Yu [112] most of the force models were developed focused on one or two aspects or based on simplified conditions, their combination in DEM simulation may lead to theoretical or conceptual problems. These issues should be considered in the fiirther development of force models.
2.6.2.3 Non-contact forces between particles
2-53 CHAPTER 2 LITERATURE REVIEW 2-54
When fine particles are involved and/or moisture exists, non-contact interparticle forces may affect the packing and flow behavior of particles significantly. In the past, the interparticle forces were often evaluated by some empirical indexes such as Hausner ratio, angle of repose and shear stress [115, 116]. These indexes may partially interpret the behavior of particles (see, for example, [116-119], but general quantitative application is still difficult. This difficulty can be overcome by DEM modeling because such forces can be directly considered. Often the non-contact forces involve a combination of three fundamental forces, i.e. van der Waals force, capillary force and electrostatic force, which can act concurrently or successively to different extents. Table 3 lists the forces, their origin and equations for their estimation.
Table 3 List of a few typical non-contact forces Force type Origin Formula References
F" =— P Van der Molecular dipole where A is Hamaker constant, h [120, 121] Waals force interaction is the surface gap between two particles.
Q' F' = 1- ìón^Qh Electrostatic Coulomb force where qo is the permittivity of [122] force vacuum, Q is particle charge, h is the separation distance
F' = -[IttjR sin p sin(/? + 0)
+ P] Surface tension where y is the liquid surface Liquid bridge (capillary pressure tension, (|) is the half-filling 123-125 force (static) and contact line angle, 0 is the contact angle, force) and Ap is the reduced hydrostatic pressure within the bridge.
2-54 CHAPTER 2 LITERATURE REVIEW
2.6.2.4 DEM application
DEM can predict fundamental properties of the particle assembly which are often difficult to measure experimentally such as stress and porosity. It is very effective in assisting microscopic understanding of the objects, process design and particle design. It has been used in areas such as in physics; molecular dynamics; civil engineering; soil mechanics; chemical engineering; fluidised bed; moving bed; granular drum; centrifugal mixer; mining; dragline mechanics etc. Tsuji [9] summarized that DEM can handle many processes such as hopper flow, fluidised bed, dense phase pneumatic conveying, particle mixing and segregation. Some of its applications include particle packing [126-129], hopper discharge [8, 102, 130-132], compression [133, 134], formation of a pile [21, 103, 104, 135-138], vibrated beds [5, 139], and flows in mixers of granular materials [3, 4, 6, 8, 140, 141], confined shear flows [142, 143], unconfined flows [144, 145], rotating drum [146-148] and mills [149-152]. It has been proved quite cost effective and reliable.
2-55 CHAPTER 3 NUMERICAL INVESTIGATION OF CRATER PHONOMENON 3-56
CHAPTER 3 NUMERICAL INVESTIGATION OF CRATER PHONOMENON
3-56 CHAPTER 3 NUMERICAL INVESTIGATION OF CRATER PHONOMENON 3-57
3.1 INTRODUCTION
Crater phenomena are very common in nature. For example, a meteorite from outer space falling on the earth will yield a big crater, and falling water stream and droplets will cause different sizes of craters on the water surface in a waterfall. The formation of these craters can be attributed to the rapid release of the kinetic energy from the moving meteorite or the falling water when impacting the earth or water surface. Similar phenomena have also extensively been reported in industries related to, for example, hopper flow, stockpiling process, and burden charging in a fluid bed reactor. In particular, in a blast furnace, the dropping ore stream usually creates a crater on the coke surface during the burden discharging process, and this phenomenon is called coke gouging [27, 153]. The impact process in such a particle system is very complicated. It often occurs in a short duration with relatively large impact forces, and involves many complicated physical characteristics such as stress waves propagating through the objects, local deformations produced in the vicinity of the contact area and dissipation of mechanical energy [50, 154].
The impact problem of particles under different conditions has extensively been investigated by means of various experimental and numerical techniques. In general, these studies can be classified into four aspects: the impact of two particles [50, 155, 156] , the impact of one particle on a fixed target [157, 158] , the impact of a particle stream on a plate [47, 49] , and the impact of one particle on a granular bed [159-163]. In particular, based on the theories of Hertz and Mindlin [164, 165], Thornton [50] investigated the impact of two single elastic spheres, and found that such collisions are relevant to energy dissipation and redistribution. Further, Zenit and Hunt [155] and Zhang et al. [156^ investigated the collision of two elastic spheres in liquids, which involves various liquid- related forces such as drag force. To describe the mechanics of particle collisions and the fi-agmentation process of particle products in a pneumatic conveying system, Li et al [157^ and Salman et al [158] studied the impact of a single particle on rigid targets. Moreover, the impact of a particle stream on an inclined plate has also been investigated by Davies et al [49] focused on the flow pattern and mass distribution, and Ema et al [47] with particular reference to the effect of impact velocity. Recently, the impact of a single particle on a
3-57 CHAPTER 3 NUMERICAL INVESTIGATION OF CRATER PHONOMENON 3-58
granular bed has been studied. Based on the experimental observations, different empirical equations have been formulated to relate the carter depth with impact energy and materials properties [160, 161, 163]. In addition, the dynamics of crater formation process also attracts research interest. For example, Tanaka et al [159] investigated the dynamic response of a two-dimensional granular bed subject to the impact of a spherical projectile both experimentally and numerically, and showed that the motion of each particle can be well simulated by discrete element method (DEM). Ciamarra et al [162] studied the penetration of a projectile into a two dimensional system, and revealed three distinct regimes of motion during the penetration process. These authors also found that the mean deceleration of the projectile is constant and proportional to the initial impact velocity. Moreover, Tsimring et al [154] analyzed the energy redistribution in the impact process.
In spite of the research efforts mentioned above, to date, the study of the impact of a solid flow onto a granular bed, which is as important as the other four impact problems, can not be found in the literature, probably except for a preliminary study by Grasselli and Herrmann [166] concerning the carter formation on a granular heap due to the impact of particles. This chapter presents a numerical study of this problem by means of DEM. The validity of the method is first verified by the good agreement between the simulated and measured flow patterns under comparable conditions. The formation mechanism of a crater is then analyzed in terms of the velocity, force structure and energy exchange. The effects of the orifice size and discharging height on crater size are investigated, and finally a correlation is formulated to describe the dependence of crater size on the geometrical and material properties.
3.2 EXPERIMENTAL METHODS
3.2.1 Physical Modeling
Physical experiments have been carried out using a two-dimensional slot model and spherical particles of different properties: blue and pink wooden balls (WB), glass beads
3-58 CHAPTER 3 NUMERICAL INVESTIGATION OF CRATER PHONOMENON 3-59
(GB) and steel balls (SB). The model contains a hopper for loading and unloading particles in its upper part, as schematically shown in Fig. 11.
20d < >
Top layer hopper
90d
D
Base layer surface
Figure 11. Schematic diagram of the experimental set-up
(d is the diameter of the blue wooden ball)
The hopper has an opening whose size is adjustable by controlling the width of the latch but typically four blue WB diameters. The height of the hopper can be adjusted. The whole model is made of wooden material except for the front wall which is made of Perspex for visualization. The model has a thickness of four blue wooden ball diameters. The relevant physical properties of the particles are shown in Table 3.
An experiment involves several steps. First, particles to be used to form a base layer or a packed bed are charged into the hopper. These particles pass through the orifice of the hopper, and settle down to form a packing under gravity in the lower part of the container. Slight adjustment, done manually, may be required in order to produce a flat surface. Secondly, the orifice of the hopper is closed, particles to be used to impact the particles in the base layer (which are referred to as impacting particles here) are charged in the hopper. Finally, the latch is pulled leftwards quickly so that these impacting particles fall down under gravity, hit the surface of the base layer, and produce a crater. Although the latch is
3-59 CHAPTER 3 NUMERICAL INVESTIGATION OF CRATER PHONOMENON 3-60 controlled manually, slightly different speeds of pulling the latch are tried and found to have insignificant effect on the results. The whole experimental process is recorded by a digital video camera. The variables examined in this work include the width of the orifice of the hopper D, discharging height H, and different base and impacting materials.
Table 4. Physical properties of the materials used in this work Variables GB WB (blue) WB (pink) SB shape Spherical spherical spherical spherical Number of particles in 20d system 1310 (top) 790 (top) 790 (top) 700 (top) (container width is 20d) 1310 (base) 790 (base) Number of particles in 40d system 1000 (top) 600 (top) 600 (top) 800 (top) (container width is 40d) 5000 (base) 3000 (base) Number of particles in 60d system 1000 (top) 9000 (base) (container width is 60d) Diameter (mm) 11.8 14 13.9 12.7 Density (kg/m^) 2450 583 573 7783
3.2.2 Numerical Simulation
DEM is used for the numerical simulation in this work [93]. The method employed has recently been used in the study of solid flows [167-172]. By this method, the motion of a particle in a considered system, which can undergo translational and rotational motions, is described by Newton's laws of motion. These equations are based on the forces and torques originated from its interaction with neighboring particles and wall, with the latter also treated as a particle with infinite size. Therefore, the translational motion of particle i can be described by ^ = +1 (/=;,,+F,,,) (1) at j=\ where m. and v^ are the mass and translational velocity of the particle, respectively. F^.. and F^ ¡j are the contact elastic force and contact damping force acting on particle i by particle j. Note that when particles at contact start to slide relatively, the tangential force 3-60 CHAPTER 3 NUMERICAL INVESTIGATION OF CRATER PHONOMENON 3-61
should be described by the dynamic friction, usually, given by the Coulomb friction model. Correspondingly, the rotational motion of the particle can be described by
(2)
where cOf is the angular velocity of the particle, I. is its moment of inertial, Ty is the torque stemming from the tangential contact forces, andM^^ is the rolling friction torques.
For the spherical particle used here, I. =jm.Rf and 7;.. = R. • The forces
and toques are calculated based on the non-linear models, as listed in table 5.
Table 5. Components of forces and torque acting on particle i
Forces and torques Symbol Equations s
Normal elastic force ^cn.ij
Normal damping force Tangential elastic force -M. Tangential damping force .max / ^i.max
Coulumb friction force ^UJ -Ms cn,ij Torque by tangential forces Rolling friction torque ß n^j (Dt^J Muj 1 1 1 _ k s: 2-V ^ Where -I- , E = 2(1-V) " R' R R O)t4j
= V. -y^-HOjXR. -0),XR,., y„,j = (V-n).n, V,= (V^ xn)xii. Note that tangential forces E should be replaced by F^, y when Ö, > •
The simulation conditions, including the geometrical and operational conditions, are the same as those used in the physical experiment in order to directly validate the simulation method. Then, in the further numerical experiments, period boundary conditions are
3-61 CHAPTER 3 NUMERICAL INVESTIGATION OF CRATER PHONOMENON 3-62
implemented to eliminate the influence of the front and rear walls. The properties of materials for the simulations are listed in Table 6. They are quoted from the studies of Nouchi et al. [170] and Zhou et al. [172].
Table 6. Parameters used in the DEM simulation
Variables GB WB (blue or pink) SB Sliding Friction of PP (-) 0.3 0.5 0.3 Sliding Friction ofPW(-) 0.3 0.3 0.3 Rolling Friction ofPP l%d l%d l%d Young's Modulus (P, W) (kg/ms) 1.0x10^ 1.0x10^ 1.0x10^ Poisson ration (P, W) (-) 0.3 0.3 0.3 Damping coefficient (P, W) (kg/s) 0.3 0.3 0.3 Time step (s) 5x10-^ 5x10-^ 5x10-^
3.3 RESULTS AND DISCUSSION
3.3.1 Model Validity
Fig. 12 shows the formation process of a crater observed in the physical and numerical experiments, where blue wooden balls are used to form the base layer, and glass beads are used as impacting particles. The discharging height is set to 16d whereas the orifice diameter is 4d (d is the diameter of the blue wooden balls). It can be observed that the impact processes for the physical and numerical experiments are similar. Glass beads fall under gravity when the orifice of the hopper is opened, collide with wooden balls in the central top of the base layer, push the wooden particles outwards to both sides to produce a crater. The crater size increases with the number of falling glass beads. The depth of the crater reaches its maximum quickly, but the width of the crater keeps increasing for a longer time.
3-62 CHAPTER 3 NUMERICAL INVESTIGATION OF CRATER PHONOMENON 3-63
Figure 12. Impact process of GB on WB (blue) when H=16d and D=4d:
top, experimental results; bottom, simulated results.
Fig. 13 shows the effect of material properties on the formation of a crater. For the cases considered, the results are quite different. When wooden balls are used as impacting particles, almost no crater is produced. However, when steel balls impact on glass beads, a big crater is produced. These phenomena indicate that the formation of crater depends on the impacting and base layer materials. For a given base layer, the larger the ratio of the densities of the impacting to base layer particles, the larger the crater size. However, the material properties of the base layer are also important. For example, when glass beads impact blue wooden balls (their density ratio is 4.20), a crater with an area of about 0.005m^ (the definition of crater area is shown in Fig. 14) is produced through the DEM simulation. However, when steel balls impact glass beads (their density ratio is 3.18), the area of the crater yielded is about 0.006ml This indicates that it is possible for a smaller density ratio to cause a bigger crater. Comparing Fig. 13(a) with Fig. 13(b) indicates that both the physical and numerical experiments produce similar results. The good agreement confirms the applicability of the DEM used in this work.
3-63 CHAPTER 3 NUMERICAL INVESTIGATION OF CRATER PHONOMENON 3-64
(1) (2) (3) (4) (5) Figure 13. Craters formed for different materials when H=16d and D=4d in physical (top)
and numerical (bottom) experiments: (1) pink WB on blue WB; (2) GB on blue WB;
(3) SB on blue WB; (4) blue WB on GB; (5) SB on GB.
25
20 -
15 — O) "(D
CO WB layer profile before GB impacting WB layer profile after GB impacting
5 10 15 20 Width of slot (d)
Figure 14. Surface and subsurface profiles before and after GB impacting on 20d WB bed when H=16d and D=4d (area in ABC is defined as the crater area).
3-64 CHAPTER 3 NUMERICAL INVESTIGATION OF CRATER PHONOMENON 3-65
3.3.2 Evolution of Velocity and Force Structure
In order to understand the fundamentals governing the formation of crater, we analyze the velocity field and force structure based on the DEM simulation results. Since the trajectories of and forces acting on individual particles are traced in a DEM simulation, information for such analysis can be readily established. We here focus on the case when glass beads are used as impacting particles whilst wooden balls are used as base layer material. The discharging height is set to 20d, and the diameter of the orifice 5d. To eliminate the effect of the front and rear walls, periodical boundary conditions are implemented in the simulation. The width and height of base layer may affect the size of crater. To examine this effect, we simulate two cases with: smaller base layer (both width and height are 40d), and larger base layer (both width and height are 60d). The result shows that the crater area and depth of the jdelded crater for both cases are almost identical, which indicates that the width and height of base layer have limited influence on the size of crater when they are larger than 40d. Therefore, both width and height are set to 40d in this work. On the other hand, as discussed below, the velocity and force propagation can reach a much longer distance, and the bed size would affect the propagation to some extent. Whether the bed size is important depends on the extent one would like to explore the details. To be clearer, in the following discussion, only particles in the base layer are shown in the figures about velocity field and force structure.
Fig. 15 shows the evolution of the velocity field. It can be seen that before the glass beads discharged from the hopper reach the base layer, the velocities of the wooden balls in the base layer are almost zero. At t = 0.21s, the glass beads come into contact with the base layer, which causes the wooden balls in the central region of the top of the base layer to have relatively large velocities. The velocities dominate in the vertical direction, propagate into the bed, and reach the bottom of the base layer at t = 0.22s. The branch vector connecting the mass centers of glass beads and wooden balls at contact may not be in vertical direction, which leads to that the wooden balls also move leftwards or rightwards.
3-65 CHAPTER 3 NUMERICAL INVESTIGATION OF CRATER PHONOMENON 3-66
» t = 0.20s t = 0.21s
rj-',- -y-'vV-'v' r.'H-' v'-
Figure 15. The change of velocity field in the formation of a crater when GB impacts on WB (H=20d and D=5d)
3-66 CHAPTER 3 NUMERICAL INVESTIGATION OF CRATER PHONOMENON 3-67
The wooden balls move in various directions, thus a crater forms and enlarges outwards as more glass beads impact on the base layer. For a big bed, the propagation of the velocity should become weaker with the distance from the crater and finally vanish when far enough. However, the size of the present bed is not big enough, so the effect of the bottom wall can be observed at t = 0.23s. The particle velocities propagate to the bottom wall, and reverse their directions, then propagate upwards. But the reverse velocities are very small when they reach the crater, and decrease with time. Therefore, they have a very limited effect on the downward expansion of the crater. The crater is filled with the glass beads falling onto the base layer. So, as the crater is getting larger, the glass beads discharged from the hopper are only able to contact with the glass beads falling earlier and occupying the crater. Such contacts should have less contribution to the evolution of the crater, because the velocities caused by the contacts are weaker when reaching the boundary of the crater. This is the reason why the increase of the crater size is slower after about t = 0.6s, as shown in Fig. 16. When all glass beads fall on the base layer at t = 0.76s shown in Fig. 15, some wooden balls at the two sides of the crater still move slowly. Finally, at t = 0.89s, a static crater is formed among wooden balls and filled with glass beads.
28 0.012
24 0.010
20 0.008 ^
Q. 16 CO 0) •D Qater depth(d) 0.006 cc O 12 Crater w idth(d) o1— lo Crater area(m2) lo ü 0.004 i— 8 ü
4 0.002
0 0.000 0.0 0.4 0.8 1.2 1.6 2.0
Elapse time (s)
Figure 16. Evolution of crater size in crater formation process (H=20d and D=5d)
3-67 CHAPTER 3 NUMERICAL INVESTIGATION OF CRATER PHONOMENON 3-68
t = 0.20s t = 0.21s
t = 0.22s t = 0.23s
t = 0.25s t = 0.28s
t = 0.76s t = 0.89s
Figure 17. Evolution of the normal contact forces in the formation of a crater when GB impacts on WB (H=20d and D=5d)
3-68 CHAPTER 3 NUMERICAL INVESTIGATION OF CRATER PHONOMENON 3-69
Force propagation is another key characteristic to understanding the dynamic behavior of particle flow [172]. Fig. 17 shows the snapshots of normal force network at different times corresponding to the velocity field, where the thickness of a line connecting the centers of two particles at contact stands for the magnitude of normal contact force. All the lines are drawn on the same scale, so the force networks at different times are comparable. It can be seen that before the glass beads reach the base layer surface at t = 0.2s, the normal contact forces are relatively small, distributing relatively uniformly at a given height, and increasing in magnitude with decreasing height. When the glass beads begin to collide with the base layer at t = 0.21s, the compact forces are large due to the relative large velocities between glass beads and wooden balls. The forces dominate in the vertical direction, propagate to the neighboring particles, reach the bottom at t=0.22s, and then cause larger contact forces between the particles and the bottom wall at t = 0.23s. The force propagation process is consistent with the evolution of the velocity field shown in Fig. 15. The forces resulting fi'om the contact between glass beads and wooden balls mainly propagate leftwards and rightwards after t = 0.23s. The forces push the wooden balls in the central area of the top of the base layer to move to form a crater. Larger contact forces under the crater can prevent the downward expansion of the crater. Therefore, the depth of the crater reaches its maximum quickly, whilst the area of the crater continues to increase mainly horizontally, as shown Fig. 16. When the final static crater is formed at 0.89s, large forces can be observed under the crater because wooden balls need to support the weight of glass beads in the crater.
The variation of the normal stress on the bottom wall has also been analyzed, as shown in Fig. 18. It can be observed that the stress in the middle of the bottom rises slightly when the velocity and force propagate to the bottom at t = 0.22s, and reaches its maximum quickly at t = 0.23s. The stress then has limited variation in the middle of the bottom, whilst it increases until its maximum is attained in the two sides of base layer. This stress distribution profile maintains until t = 0.46s. The stress then decreases on the whole bottom except adjacent to the side wall of the base layer due to the relaxation of the bed, and finally reaches a steady state when the impact process completes at t = 0.89s. The
3-69 CHAPTER 3 NUMERICAL INVESTIGATION OF CRATER PHONOMENON 3-70
magnitude of the stress at the final state is larger than the initial one at a given location, which is consistent with the force structure shown in Fig. 17.
3000
2500 -
2000 - wCO s 00 E 1500 CoQ
1000
500 10 15 20 25 30 35 40 Width (d)
Figure 18. Stress distribution on the bottom wall at different times,
obtained in one simulation.
Note that the bottom stress is usually very sensitive to the packing structure of particles in the base layer. When changing the way to form a packing, the initial bottom stress and hence the bottom stress distribution during the impact process vary. In Fig. 18, several peaks can be observed in the stress distribution profiles. It is unclear whether they are "robust" features or not. To test this, more simulations with identical parameters but different packed base layers should be conducted. We have conducted such numerical experiments five times but could not generate enough data to clarify this issue. Nonetheless, it is clear from Figs. 17 and 18 that the bottom stress distribution is associated with the evolution of the internal force structures.
3-70 CHAPTER 3 NUMERICAL INVESTIGATION OF CRATER PHONOMENON 3-71
To further understand the force propagation mechanism, a contrary case, blue wooden balls impacting glass beads, has been studied in detail. For brevity, the results are not shown here. The main finding is that the first contact between wooden balls and glass beads can still produce a relatively large force at the top of the base layer. But the force can not propagate farther. Consequently, the wooden balls are not able to create a clear crater on the glass beads surface.
3.3.3 Evolution of Energy
Energy exchange plays an important role in the impact process. Taking advantage of the DEM approach, the information about energy can be readily obtained, hi general, the total mechanical energy of a particle system consists of kinetic energy and potential energy. The kinetic energy contains two parts: transitional and rotational, whilst the potential energy also contains two parts: gravitational and elastic. In the impact process, the mechanical energy is partially dissipated due to three mechanisms corresponding to Newton's laws of motion given by Eqs. (1) and (2). One is the so called impact energy dissipation as a result of the relative velocity at contact point between particles and between particles and walls; the next one is the friction energy dissipation as a result of relative sliding between particles and between particles and walls; the last one is the rolling energy dissipation due to rolling fiiction arising from asymmetrical normal traction distribution on the contact area between particles. In the particle system studied in the present work, the rolling energy dissipation is comparatively very small. Therefore, we only consider the kinetic energy, potential energy (gravitational and elastic), impact energy dissipation and friction energy dissipation. Thus, the total energy of the system, including mechanical energy and dissipated energy, can be described as:
^ = (3) i i c c c where E^ ^ is the kinetic energy of particle /, E^^ . is the gravitational potential energy of the particle, E^^ ^ is the elastic potential energy due to contact c, and AE"^^ and AE^^ are
3-71 CHAPTER 3 NUMERICAL INVESTIGATION OF CRATER PHONOMENON 3-72
the impact energy dissipation and friction energy dissipation of the contact. They can be given as
y 1 2 1 T- 9 (4)
=m.gH, (5)
F - (6)
M^ = (7)
(8) where rrii, //, v/ and COi are the mass, moment of inertia, translational velocity and angular velocity of particle /, respectively. Ho is the distance to the base layer surface for impacting particles, and the distance to the middle height line of base layer for base layer particles, v^^ (0 and v^^ (t) are the relative normal and tangential velocities at contact c. (t) and fet,c (0 (fdn,c (0 and (t)) are the normal and tangential contact elastic (damping) forces. (t) is the friction described by the Coulomb friction model. From Eqs. (7) and (8), it can be seen that AE"^^ and AEy^^ are the total energies dissipated due to the damping force and sliding friction before time t, respectively. During the whole impact process, E should be constant.
Fig. 19 shows the variation of these energies during the impact process for the case considered in Figs. 14-17. As seen from Fig. 19(a), at the beginning, the gravitational potential energy of glass beads in the top layer (about 99.5%) is the main energy of the whole system (including top layer and base layer). The remainder energy (about 0.5%) is the elastic potential energy. During the impact process, some of the gravitational potential energy is transformed into the kinetic energy, but its share is relatively small. The kinetic energy reaches its maximum (almost 18% of the total initial energy) at about t=0.21, and
3-72 CHAPTER 3 NUMERICAL INVESTIGATION OF CRATER PHONOMENON 3-73
then decays to zero. This phenomenon is different from the case of a particle impacting on a granular bed, where the potential energy should be completely transformed into the kinetic energy when the particle comes into contact with the bed if we choose the bed surface as the zero height position of the potential energy. The peak of the kinetic energy corresponds to the instant when glass beads reach the base layer surface. Before the kinetic energy reaches its maximum, the total mechanical energy reduces slightly. The reduced energy is mainly dissipated by interaction between glass beads and between glass beads and walls in the hopper. In the whole impact process, most of the energy from the top layer is dissipated due to the interaction between glass beads: damping force (about 34.8%), and sliding friction (about 37.2%). Almost 23.5% of energy of the top layer is transferred into the base layer, as seen from Fig. 19(b).
1.00
0.80 g raw tali onal potential energy fritional energydissipatlon .9 0.60 c5
0) 0.40 frlctlonal energy dissipation c LU impact energydisssipatlon i mpact energ y dissi pation
0.20 kinetic energy elastic potential enernv elastic potential energy •g^rawtational potential energy kinetic energy ^ 0.00 0.4 0.8 1.2 1.6 0.4 0.8 1.2 1.6
Simulation time (s) Simulation time (s) (a) (b) Figure 19. Energy dissipation in a cratering process (H=20d and D=5d):
(a),energy for the top layer; and (b), energy for the base layer
In the base layer, the impact energy dissipation during the impact process is 13.5% of the total energy, much larger than the impact energy dissipation which is about 5.8%. The kinetic energy is very small, reaches a peak (about 2%) at about t = 0.35s, then decays to zero as the impact finishes. The gravitational potential energy increases from zero to about 1.95% when a steady crater is formed. The elastic potential energy increases from 0.5% to
3-73 CHAPTER 3 NUMERICAL INVESTIGATION OF CRATER PHONOMENON 3-74
2.7% as well. From Figs. 19 (a) and (b), it can be seen that most of the energy (about 91.3%) has been dissipated eventually, mainly by the interaction between glass beads or between glass beads and wooden balls (about 72%), only a small amount of the energy is contributed to the crater formation. Clearly, the impact problem of a solid flow onto a granular bed is very complicated.
3.3.4 Effects of Geometry and Properties on Crater Size
The orifice size and discharging height will affect the flow of impacting particles, and hence the size of crater including depth and area. To highlight this, different orifice sizes (D=3d, 4d, 5d, 6d) and discharging heights (H=10d, 20d, 30d, 40d) have been used in the present simulations. The slot width is 40d for all typical runs. Fig. 20(a) shows the effect of orifice size of hopper on crater size when the discharging height is 20d. It can be observed that a larger orifice size leads to a larger crater. However, different from the crater area, the crater depth varies little when the orifice size is larger than 5d. This is because with increasing the orifice width of the hopper, the impact area is getting larger, which results in a weaker impact intensity.
5 0.015 1.019 Crater depth Crater depth •o— Crater area 1.017 -•— Crater area 0.013 4 1.015^ CM 0.011' 1.013 ¿ £3 CO 03 Q. Q. 1.011 2 CD CD 0.007 1.007 ¿3 O O 1.005 1 0.005 1.003 LOOI 0 0.003 2 4 6 0 10 20 30 40 50 Orifice width (d) Charging height (d) (a) (b) Figure 20. Crater size as a function of: (a), orifice width; and (b), charging height 3-74 CHAPTER 3 NUMERICAL INVESTIGATION OF CRATER PHONOMENON 3-75 Fig. 20(b) shows the effect of discharging height on crater size when the orifice width is 5d. It can be seen that the crater depth and area increase, but the increase rate becomes lower with the increase of discharging height. The main reason is that with the increase of the crater depth, the contact forces between the particles beneath the crater increase, which causes higher resistance to the downward enlargement of the crater. Another reason may be that with the increase of the discharging height, the impact area will become wider, and hence the impact intensity is weaker. The initial energy of impacting particles, i.e., their initial potential energy, will be partially dissipated before they are discharged from the hopper. The dissipated energy has no contribution to the formation of crater. In order to describe more exactly the energy contributing to the crater formation, we define a concept, the input energy, given by (9) where m^ is the mass of particles in top layer, and v^ is the averaged velocity of particles at orifice. The input energy is the sum of the kinetic energy and potential energy of a particle at the orifice. Note that the rotational kinetic energy is relatively small, thus ignored in Eq. (9). The averaged velocity depends on the orifice size. The larger the orifice size, the higher the velocity. Detailed explanation about this relationship has been discussed in the earlier studies [167, 173]. Therefore, the first and second terms of Eq. (9) correspond to the orifice size and discharging height, respectively. On the other hand, the "strength" of base layer can be defined by its inertial energy given by m^gdj^, where m^, and d^ are the mass and diameter of base layer particle respectively. In theory, crater size should be proportional to the input energy from the top layer and inversely proportional to the inertial energy of the base layer. However, as discussed above, the crater size must also depend on the width of the orifice opening. A wider orifice opening can give a wider crater, although not deeper. Both the opening and crater sizes should be relative to particle sizes. Therefore, to be dimensionless, the crater size can be described as {A/Aj'{dl/df), where A is the crater area, ^^ is the area of the hopper orifice, and d^ is the diameter of top layer particle. With all these factors considered, after 3-75 CHAPTER 3 NUMERICAL INVESTIGATION OF CRATER PHONOMENON 3-76 some trial tests, we found the crater size can be related to the input energy from the top layer, inertial energy from the base layer, diameters of particles in the two layers and the width of the orifice, as shown in Fig. 21. The relationship can be fitted as -20.83/£, (10) where Staler ( = (A/Ag)-{dl /df) ) is the dimensionless crater size. Erath 2 (=(l/2m,v^ + m^gH)/nif^gdf^) is the ratio of the input energy from the top layer to the inertial energy from the base layer.). 4.0 ——^^^ g 3.0 0 — (U •5^5 2.oí5; Figure 21. Correlation between dimensionless crater size Scrater (= [AjA^)• [dl jd^]) and energy ratio Erath (= {-m.v] + m^gH Vm^gd^,), obtained by the DEM simulations. In Fig. 21, five different material pairs GB/WB, SB/GB, WB/WB, WB/GB and SBAVB have been considered. To form a visible crater, the energy ratio x should be greater than a certain value, i.e., the threshold energy ratio (about 2.0 from Fig. 21). A similar concept 3-76 CHAPTER 3 NUMERICAL INVESTIGATION OF CRATER PHONOMENON 3-77 was devised by Grasselli and Herrmann [166] who focused on the effect of impact height. As seen from Fig. 21, Eq. (10) describes this phenomenon reasonably. However, it should be noted that the relationship between crater and geometric/material properties is very complicated. It has been illustrated that even for a simpler case: a single particle impacting on a granular media, a general formulation to describe the crater size has not been obtained [160]. The equations proposed for this case [12, 13, 15] are not so comparable to Eq. (10) which predicts the crater size rather than the depth. We believe that more work is required to formulate a more general relationship for general application. 3.4 CONCLUSIONS An experimental and numerical study of the impact of a particle stream onto a particle bed has been conducted. The following conclusions have been obtained from this study: > DEM simulation can reproduce the experimental results very well, demonstrating the applicability of the DEM simulation in this work. > In the formation process of a crater, the depth of the crater reaches its maximum quickly, whilst the width of the crater keeps increasing for a longer time. The phenomena can be elucidated from the examination of the evolution of the velocity field and force structure of the base layer and the bottom normal stress. > During the impact process, most of the energy from the top layer has been dissipated eventually due to the inelastic collision and frictional contacts between impacting particles. Only a small amount of the energy is contributed to the crater formation. > The orifice size, discharging height, and top and base layer materials affect the size of crater. A larger orifice size or discharging height leads to a larger crater. For a given base layer, the larger the density ratio of the top to base layer particles, the larger the crater size. However, the effect is also dependent on base layer material. Based on these considerations, the crater size is shown to be related to the ratio of the input energy from the top layer to the inertial energy from the base layer. 3-77 CHAPTER 4 DEM STUDY OF COKE COLLAPSE 4-78 CHAPTER 4 DEM STUDY OF COKE COLLAPSE 4-78 CHAPTER 4 DEM STUDY OF COKE COLLAPSE 4.1 INTRODUCTION Burden distribution control has a significance influence on the operation of blast furnace, such as gas distribution, chemical reactions, the position and shape of the cohesive zone. The burden materials are charged into the furnace by using bells, or rotating chutes. Since the ore and coke are not fed into the furnace continuously but at discrete events by dumping the burden into the furnace in batches. The so-called coke layer collapse phenomenon can be observed in burden distribution process, where some coke are slipped into the center and form a mixed layer in the central region when sinter is dumped onto inclined coke layer. As a result, the actual 0/C distribution in the radial direction differs from that estimated from the profile measurement before and after the charging [27]. The collapse of coke layer results in the variation of the ore to coke layer thickness ratio and then consequently gas flow distribution. Coke collapse can not simply be ignored in maintaining a blast furnace smooth operation. Understanding the mechanism of coke collapse is significant in order to improve the controllability of the burden distribution. Previous studies on coke collapse are mainly experimental. Based on the full scale model experiments, Kajiwara et al. investigated the mixed later formation during the ore charging process [27]. They quantitatively formulized a relation to describe the extent of the mixed layer formation and the formation energy of mixed layer, the formation energy includes the potential and kinetic energy which the ore particles possessing effective to the mixed layer formation. With a 1/3 scale charging equipment model, Okuno et al. developed a mathematical model to predict the burden distributions, which is able to accurately predict the volume of coke layer collapse in terms of the theory of soil mechanics[43]. This model employed concepts like slip surface, inclination angle and safety factor. In theory, the collapse of the coke layer does not occur when the angle of inclination is less than the angle of internal friction. Practically the critical safety factor is used to predict the coke collapse, the coke layer collapsed when the minimum safety factor of coke layer is less than the critical safety factor. Based on the theory of soil mechanics, Luo et al. physically measured the critical safety factors of coke layer in different slope angle by adding a static load on 4-79 CHAPTER 4 DEM STUDY OF COKE COLLAPSE the top of the coke layer[174]. In order to get more particle scale information, 2D numerical simulation was carried out by Kajiwara et al. to study the solid flow behavior in relation to coke collapse in blast furnace [34]. Austin et al investigated the coke collapse on a 1/5 scale cold model[28], and found that coke collapse is because weight (potential energy) of sinter piling up on the coke may cause the coke terrace unstable and eventually avalanching inwards. Unlike the avalanche phenomena[62, 175-178], there are two different materials involve in the coke collapse process in which the density of one component is much larger than another one. However, there might be some links between these two. Although these studies have been very successful in individual application, the experimental results are normally not of general nature and thus experimental work must be repeated if the model is to be used for different plants and furnaces. So there is no a general model and understanding of coke collapse available so far. The mechanisms governing the particle behaviors during the collapse formation are not clearly understood. Fundamental understanding of coke collapse mechanism can greatly help to improve the controllability of burden distribution. This chapter presents a numerical study of the fundamentals governing coke collapse using a simplified slot model corresponding to blast furnace top and discrete element method (DEM). Three different top configurations, including batch charging (particles continuously charged on the top of a particle bed), self loading (static loading on a particle bed) and load impact (loading on a bed with an initial velocity), are considered. The effects of the material properties such as particle density, particle size, and weight and width of load are investigated. 4.2 METHODS Three cases are considered: batch charging, self loading and load impact. Physical experiments are based on batch charging top, which is similar to the real operation in the blast fiimace. The model geometry for batch charging is shown in Figure 22, consisting of two parts: a container and a hopper upon it. The container is used to form a base bed of particles, whilst the hopper is used to load particles discharged towards the base bed. A 4-80 CHAPTER 4 DEM STUDY OF COKE COLLAPSE 4-81 simulation for this case involves several steps. First, particles to be used to form a base bed are charged into the hopper. These particles pass through the orifice of the hopper, and settle down to form a pile under gravity in the container. Secondly, the orifice of the hopper is closed, particles to be used to impact the particles in the base bed (which are referred to as impacting particles here) are charged in the hopper. Finally, the orifice of the hopper is opened so that these impacting particles fall down under gravity, hit the surface of the base bed, and push the particles at the left side of the base bed towards the right side of the container. 168 600 Figure 22. Geometry of the model used for the case of batch charging (unit:mm). The models for the cases of self loading and load impact are similar. They have the containers for base bed with the same geometry as that for batch charging, but replace the hopper with a cubic rigid body with adjusted width. The load (rigid body) is initially put on the left top surface of the base bed, is allowed to move in the vertical direction without initial velocity (self loading) or with an initial velocity (load impact) in the simulations. Materials used include glass beads with diameter of 6, 8, or 10 mm (GB6, 8 or 10), wooden balls in blue and pink color with diameter of 14mm (BWB14, WB14), and steel bearing balls with diameter of 8 or 12 mm (SB8 or 12). Their densities are 2450, 583, 573, and 4-81 CHAPTER 4 DEM STUDY OF COKE COLLAPSE 4-82 7783kg/m^ respectively. For all simulations and experiments in this work, blue wooden balls are used to form the base bed. DEM is used for the numerical simulation in this work. By this method, the motion of a particle in a considered system, which can undergo translational and rotational motions, is described by Newton's laws of motion. These equations are based on the forces and torques originated from its interaction with neighboring particles and wall, with the latter also treated as a particle with infinite size. Therefore, the translational and rotational motions of particle i can be described by 0) where m. and /., v. and ^ are the mass, moment of inertial, translational velocity and angular velocity of the particle respectively, i.j and m^^. are the contact force and torque acting on particle i by particle j. The forces and toques are calculated based on the non- linear models [167, 179, 180]. The method and algorithm used to solve Eqs. (1) and (2) for the present particle system are the same as in the previous work [167]. The simulation conditions, including the geometrical and operational conditions, are the same as those used in the physical experiment in order to directly validate the simulation method. Then, in the further numerical experiments, period boundary conditions are implemented to eliminate the influence of the front and rear walls. The properties of materials for the simulations are listed in Table 5, which are quoted from the study of Wu et al. [179]. 4-82 CHAPTER 4 DEM STUDY OF COKE COLLAPSE 4-83 Table 7. Material properties of wooden balls, glass beads and steel balls Variables Glass beads Wooden ball Steel ball Particle diameter (mm) 10,8,6 14 (pink and blue) 8,12 Particle Density (kg/m^) 2450 583 /573 7885 Sliding Friction PP (-) 0.3 0.5 0.3 Sliding Friction PW (-) 0.3 0.3 0.3 Rolling Friction PP l%d l%d l%d Young's Modulus (kg/ms) 1.0x10^ 1.0x10^ 1.0x10^ Poisson ration (-) 0.3 0.3 0.3 Damping coefficient (kg/s) 0.3 0.3 0.3 4.3 RESULTS AND DISCUSSION 4.3.1 Experimental Observation Physical experiments have been carried out by using a batch charging method. The base layer consists of blue wooden particles for all the experiment, while a different top layer has been used for each experiment. The top layer particles include glass beads with different size, pink wooden balls and steel balls. Fig.23 shows the whole discharging process of glass beads on blue wooden balls. The top layer glass beads drop from the top hopper and land on the wooden ball surface, shortly some wooden balls on the left side are push to right along the slope until reaching the right side wall. During this collapse process, some glass beads and wooden balls mixed together in the right side. In blast furnace operation, it is called coke rearrangement and consequently 0/C distribution change. In the case of glass beads top, three different sizes including 6, 8 and 10 mm have been used. It was found that the final results of subsurface profiles of wooden ball layer are very close, but the repose angles of the top glass beads layer are different as shown in Fig.24. 4-83 CHAPTER 4 DEM STUDY OF COKE COLLAPSE 4-84 (a) (b) (c) 4 (d) (e) (f) Figure 23. Collapse process of blue wooden ball base (GBIO topAVB14 base) Fig.25 demonstrates the density effect on the base layer collapse, 10mm glass beads, steel ball and pink wooden balls are used as the top. Obviously the density is significant to the collapse results, which is the key point for coke collapse behavior. Fig. 26 shows the subsurface profile after discharge of top layer, by comparing Fig. 26(a) and Fig.26 (b) after the glass beads dumping, the results are very close, which means the particle size is not so important to the collapse results. As observed in the experiments the failure point is not the impacting point, but is a little bit right to the dumping point. Fig.26 (c) is the blue wooden balls dumping on the red wooden balls. It was found that after and before dumping, the base layer surface does not change much. Because their densities are same, so there is no obvious collapse happened. 4-84 CHAPTER 4 DEM STUDY OF COKE COLLAPSE 4-85 (a) 10mm GB top (b) 8mm GB top (c) 6mm GB top Figure 24. Collapse results under GB top with different particle size (a) 10mm GB top (b) steel ball top (c) pink wooden ball top Figure 25. Collapse results with different material top sbt width (d) slot width (d) slot width (d) (a) lOmmGB on WB (b) 6mmGB on WB (c) pink WB on blue WB Figure 26. Subsurface profile variation after collapse under different tops (Experimental results) 4-85 CHAPTER 4 DEM STUDY OF COKE COLLAPSE 4-86 4.3.2 Simulation Results 4.3.2.1 Model validation The simulation method is validated by comparing the simulated and measured results for the case of batch charging. The experiment conditions, including the geometrical and operational conditions, are the same as those used in the simulations. A 2-D slot model with real front and rear walls is applied. Glass beads with diameter of 10 mm and pink wooden balls with diameter of 14mm are used to push the blue wooden balls in the base bed respectively. For each experiment, the base bed with blue wooden balls is first formed, and glass beads or pink wooden balls are then charged into the hopper to form a top bed. Once all particles in the hopper completely settle down, the orifice of the hopper is opened, and then the particles in the hopper are discharged and drop towards the surface of the left side of the base bed. With the accumulation of the particles from top bed, wooden balls near the charging point are pushed towards the right side of the container. All the experimental processes are recorded by a digital video camera. The initial and final profiles of the base bed for the physical and numerical experiments are shown in Figure 27. It can be observed the profiles for both experiments are quite similar, which demonstrates the applicability of the numerical model in this work. To eliminate the influence of the front and rear walls, in the further numerical experiments, period boundary conditions are implemented. 10 20 30 10 20 30 40 Slot w idth (d) Slot w idth (d) (a) GB 10 top bed (b) WB14top bed Figure 27. Comparison of experiment and simulation results for batch charging case 4-86 CHAPTER 4 DEM STUDY OF COKE COLLAPSE 4-87 4.3.2.2 Batch charging In batch charging process, the particles from top layer are discharged from the hopper and land on the base layer surface gradually. A typical example is blast furnace burden discharging process. When particles from a packed bed are discharged on a slope of a granular bed the slope will collapse downwards, this phenomenon is called coke collapse, which is extensively existing in nature and industries [27, 43]. In this study, variables considered include particle density and particle size. Blue wooden balls are used to form the base layers. Glass beads (6mm, 8mm and 10mm), steel balls and pink wooden balls are used to form the top layers respectively. e £ ai 0.2 13 ai 0.5 0.6 ai 0.2 as a4 03 eie ai a2 as a4 o.s ae Slot width (m) Slot width (m) Slot width (m) t = O.Os t = 0.04s t = 0.12s ai a2 as .. a^ as ae a2 as 0.4 Slot width (m) Slot width (m) Slot width (m) t = 0.52s t= 1.32s t = 4.98s Figure 28. Packing bed collapse process (GB10AVB14) A typical run of 10mm glass beads top was chosen to demonstrate the micro-dynamic information including collapse process, force structure and velocity field. Fig.28 depicts the 4-87 CHAPTER 4 DEM STUDY OF COKE COLLAPSE 4-J base wooden layer collapse process under the impact of glass beads stream. The particle stream is discharged from left side to mimic the burden discharging behavior in blast furnace. It can be seen that at t = 0.04s, the glass beads stream reaches the surface of wooden ball layer, push the surface a little bit down, at t = 0.12s the glass beads stream penetrate further into the base layer and start to spread rightwards. This process keeps developing at t = 0.52s, glass beads steam penetrates more downwards and spreads more wooden balls rightwards. Some wooden particles have been relocated to right side near the right wall by the glass beads stream. t = 0.0s t = 0.04s t = 0.12s t = 0.52s t= 1.32s t = 4.98s Figure 29. Force network during collapse process(GB10AVB14) In order to understand the fundamentals governing the formation of collapse, we analyze the force structure and velocity field during a collapse process based on the DEM simulation results. Force propagation is a key characteristic to understanding the dynamic behavior of particle flow [167, 179]. We here focus on the case when 10mm glass beads are used as impacting particles whilst blue wooden balls are used as base layer material. Figure 29 shows the snapshots of normal force network at different times during the collapse process, where the thickness of a line connecting the centers of two particles at contact stands for the magnitude of normal contact force. All the lines are drawn on the same scale, so the force networks at different times are comparable. It can be seen that before the glass beads reach the base layer surface at t = 0.0s, the normal contact forces are relatively small, 4-88 CHAPTER 4 DEM STUDY OF COKE COLLAPSE 4-89 distributing relatively uniformly at a given distance to the inclined surface of the bed, and increasing in magnitude with increasing the distance. When the glass beads begin to collide with the base layer at t = 0.04s, the compact forces are large due to the relative large velocities between glass beads and wooden balls as shown in Fig. 30. The forces dominate in the vertical direction, propagate to the neighboring particles, reach the bottom at t=0.12s. The forces acting on the charging area push wooden balls at the top of the base layer to move rightwards, this also can be seen from the velocity field. The forces resulting from the contact between glass beads and wooden balls propagate rightwards after t = 0.52s. Correspondingly from the velocity field, more particles at top left size are being relocated down to the right corner. As observed from time t = 1.32s at velocity field, base layer particles stop moving to rightwards because of the covering by the top layer glass beads. When all glass beads are discharged at t= 4.98s, relatively large forces can be observed in the whole bed. 0.7 a3 a4 06 CIU6 ai a2 as a4 OB 0J6 Slot width (m) Slot width (m) Slot width (m) t = O.Os t = 0.04s t = 0.12s Ol 02 03 04 OS 06 ai a2 as a4 as 06 02 03 04 OS Slot width (m) Slot width (m) Slot width (m) t = 0.52s t= 1.32s t = 4.98s Figure 30. Velocity evolvement during collapse process (GB10AVB14) 4-89 CHAPTER 4 DEM STUDY OF COKE COLLAPSE 4-90 The profile evolvement during the collapse process is shown in Fig.31. The triangle line is the base layer surface before top layer discharging, in the early stage of the collapse from t= 0.0 to 0.3s, only the left side half profile changes, the right half keeps unvaried. After t = 0.3s, the left half profile changes a little and right half changes a lot. These lines clearly show the base layer particle relocation process. 10 20 30 40 Width ofslot(d) Figure 31. Profile evolvement during collapse process (GB10/WB14) To investigate the effect of the properties of particles in the top bed on the collapse, glass beads of 6 and 8mm diameters, steel balls of 8mm diameter and wooden balls of 14mm diameter have also been considered. The final profiles of all these cases are shown in Figure 32. It can be observed that wooden particles in the base layer are pushed away by the falling glass beads and steel balls from the impacting points, whilst the base layer just slightly changes for the case of pink wooden balls. Of all these cases, steel balls push the most wooden balls in the base bed to the right wall of the container. For glass beads with different diameters, the profiles are very close. These features indicate that the particle density ratio of top bed to base bed is one of the most important factors to cause collapse, and the effect of particle size is limited. 4-90 CHAPTER 4 DEM STUDY OF COKE COLLAPSE 4-91 0 10 20 30 40 Slot width (d) Figure 32. Profiles after collapse under different top 4.3.2.3 Self loading Self loading is a static load on the top of the base layer, which has been used to attempt to understand the mechanism of slope failure behavior [174]. In this work, a cubic rigid body is used as the load. The load is initially put on the left top surface of the base layer with a zero initial velocity. Its weight increases gradually to a certain value from zero in the simulations. In order to limit the load to move downwards, only the vertical components of the contact forces between the load and particles in the base layer are considered. The sliding friction between the load and the container wall is ignored. Assuming a cubic load with the same size as the slot model, its width can be adjusted as 4d, 6d, 8d and lOd. Every time the load is just put on the base layer left top surface except the impact study case where there is a gap between base layer top and the bottom of the load. The same base layer was used in both configurations. The loading rate is Ikg/s and the weight of load is selected as 1.166, 5.215, 10 and 16.52kg, in which 1.166, 5.215 and 16.52kg equal the weight of packing bed top of pink wooden ball, 10mm glass bead and steel ball respectively. The simulation condition and configuration are listed in Table 6 and Table 7. 4-91 CHAPTER 4 DEM STUDY OF COKE COLLAPSE 4-92 Table 8. Simulation conditions of self load Variables Run] Run2 Run3 Run4 Width of load (d) 4 6 8 10 Mass of load (kg) 1.166 5.215 16.52 10 Charging rate (kg/s) 1 1 1 1 Impact initial velocity(m/s) -9 -6 -3 -1 Impact height (m) 0.6 0.6 0.6 0.6 Table 9. Particle configuration of self load simulation Variables BW Top Top Top Top Top base wood gb6 gb8 gblO sb8 Diameter 14 14 6 8 10 8 Particle No. 2800 1390 19500 8000 3980 8000 Weight (kg) 2.35 1.166 5.616 5.425 5.215 16.52 ai a2 13 a-4 as ai a2 a3 m as Slot width (m) Slot width (m) Slot width (m) t = O.Os t = 0.04s t = 0.12s ai a2 aa a-4 ae ai a2 Q3 a< as Slot width (m) Slot width (m) Slot width (m) t = 0.52s t= 1.32s t = 4.98s Figure 33. Self loading process (5.215kg, 4d width) 4-92 CHAPTER 4 DEM STUDY OF COKE COLLAPSE A typical run of 5.215kg glass beads top is selected for further discussion, the driving force for load movement is the gravitational force. Figure 33 shows the loading process, where the weight of the load increases to 5.215kg from zero at a rate of Ikg/s. With the increase of the weight, the load moves downwards slowly under gravity. It can be seen that the particles under the load in the base layer are pushed rightwards at t= 0.52s. However, only few particles are finally pushed to the right wall of the container at t= 4.98s. And force network and velocity field for each corresponding snapshot are shown in Figs.34 and 35 respectively. As shown in Fig.33, in the beginning, the velocity and weight of load start from zero, with the increasing of the weight, the load goes down slowly under gravity, at t= 0.04s, the load starts to touch particles in the bottom. Under the force from load shown in Fig.34, few particles start to move downwards as in Fig.35. Further increasing the mass of the load as shown at t= 0.12s, the load almost stops move because the gravitational force is balanced by the force from the base layer particles. At t= 0.52s, the interaction force is very large due to the larger mass of the load, the base layer particles under the load was pushed to rightwards as shown in the velocity filed. At t= 1.32s, the interaction forces concentrate near the load and propagate mostly downwards, so just few particles in the top surface roll down rightwards along the slope. The force between load and particles is getting larger and larger, shortly the load stops to move once its mass reaches 5.215kg. The properties of the load may influence the load process. To highlight this, Figure 36 shows the final profiles of the base bed for different load widths. Four widths, 4, 6, 8 and lOd, are considered when the weight of the load is 5.215kg. It can be seen that a larger load width leads to a shorter distance the load moves downwards. It is because more particles act on the load with larger width, and hence there is more resistance to the movement of the load. Figure 37 shows the effect of the load weight on loading process. The weights are selected as 1.166, 5.215, 10 and 16.52kg, which equal the weights of the top bed with pink wooden balls, 10mm glass beads and 8mm steel balls in the case of batch charging respectively. It can be seen that the heavier the load, the farther the penetration of the load into the bed. However, the profile varies just little under different weights of load. 4-93 CHAPTER 4 DEM STUDY OF COKE COLLAPSE 4-94 t = O.Os t = 0.04s t = 0.12s t = 0.52s t= 1.32s t = 4.98s Figure 34. Force network for loading process (5.215kg, 4d width) a> X a2 as a4 as 0.1 a2 as a4 as Slot width (m) Slot width (m) Slot width (m) t = O.Os t = 0.04s t = 0.12s ai a2 as a^ as Slot width (m) Slot width (m) Slot width (m) t = 0.52s t= 1.32s t = 4.98s Figure 35. Velocity vector in loading process (5.215kg, 4d width) 4-94 CHAPTER 4 DEM STUDY OF COKE COLLAPSE 4-95 10 20 30 40 Slot width (d) Figure 36. The load width effect comparison (5.215kg load) 0 10 20 30 40 Slot width (d) Figure 37. The load weight effect comparison (4d width) 4-95 CHAPTER 4 DEM STUDY OF COKE COLLAPSE 4-96 4.3.2.4. Load impact If a load has an initial velocity, the result will be different, as shown Figure 38, where the velocity fields of the base layer at different times during the load impact process are shown. The initial load velocity is 3m/s and the height of the load from the top of the base bed is 0.6m. It can be observed that the early touching as shown at time 0.08s the particle near the load start to move straight down. At t= 0.1s the particles below the load keep moving down and particles in the right side of the load move rightwards under the impact with a relatively large velocity. When the load further hits the top of the left side of the base bed at t=0.12s, the particles below the load move downwards while those in the right side of the load move rightwards. Such an impact pushes the particles in the touching area to jump rightwards, and move along the surface of the bed to the right wall at t=0.48s. This is different from that in the cases of batch charging, where the particles in the charging area are continuously pushed to the right side of the base bed. •gs X Slot width (m) Slot width (m) Slot width (m) t = O.Os t = 0.08s t = 0.10s fs Slot width (m) Slot width (m) Slot width (m) t = 0.12s t = 0.21s t = 0.48s Figure 38. The velocity vector of load impact (3m/s,l .166kg.4d width) 4-96 CHAPTER 4 DEM STUDY OF COKE COLLAPSE 4-97 14 24 34 44 Slot width (d) Figure 39. Effect of the initial load velocity on collapse when the weight and width of the load are 1.166kg and 4d respectively. Figure 39 shows the effect of the initial load velocity on the collapse, where the initial velocities are 1, 3, 6 and 9m/s respectively, the initial height of the load is 0.6m, and the width is 4d. It can be seen that the larger the initial velocity, the more the particles near the left top of the base bed are pushed to the right wall. As expected, the final profiles are different from those in the case of batch charging as shown in Figure 32. 4.4 CONCLUSIONS Three different configurations: batch charging, self loading and load impact have been used to investigate the fundamentals governing coke collapse by means of DEM simulations. It is observed that collapse can be caused by continuous charging of particles and load impact. No obvious collapse has been observed in the case of self loading although the self loading can also lead to the failure of the base bed. For batch charging, the particles in the charging area of the base bed are continuously pushed to its right side in the case of batch charging. 4-97 CHAPTER 4 DEM STUDY OF COKE COLLAPSE 4-98 For load impact, the particles are impacted to jump rightwards and then move along the surface of the bed to the right wall in the case of load impact. The different processes for the two cases lead to the different final profiles of the base bed. The geometrical and physical properties of particles and load also affect the collapse. In particular, the particle density ratio of top bed to base bed is an important factor to cause collapse in the case of batch charge. The larger the initial load velocity, the more the particles are pushed to the right wall in the case of load impact. 4-98 CHAPTERS CREEP MOTION OF SHEAR FLOW ON A GRANULAR PILE 5-99 CHAPTER 5 CREEP MOTION OF SHEAR FLOW ON A GRANULAR PILE 5-99 CHAPTER 5 CREEP MOTION OF SHEAR FLOW ON A GRANULAR PILE 5-100 5.1 INTRODUCTION The surface flow of granular materials is a very important research topic as it is involved in many industrial processes such as those in mining, iron-making, chemical and civil engineering [18]. There are two different configurations for studying the free surface flows, one is the flow on a rough inclined plane [53, 54] , another is the flow on a pile [55-57]. Our focus in this work is restricted to the case of dry, cohesion-less granular media, and to situations where the granular flow is confined to a layer at the surface of a granular pile. The earliest models describing surface flows of granular materials have originated in the large amount of work devoted to the description of granular dynamics by the researchers in the field of applied mechanics. Bagnold contributed his pioneered work on the fundamental laws at work inside these flows [58] , Savage and Hutter [59] developed a general model based on depth-averaged mass and momentum balance equations, which is restricted to the description of flows over fixed bottoms. Some recent models like the phenomenological 'BCRE' model and hydrodynamic model assume a sharp interface between a static phase and a rolling phase inside the granular packing, and exchanges of grains occur these two phase by dislodging immobile grains or trapping rolling grains. Capable of exchanging grains through collisions processes, forms the central hypothesis of the second generation of models [60, 61]. With a frozen bulk region below, many studies have been made under such assumption without convincing experimental evidence [61-64]. The more recent models integrate the particle exchange mechanisms into hydrodynamic description, initialed by Douady et al. [65]. It has been recently recognized that an important characteristic of solid flow is creep motion by Komatsu et al. there is no such sharp frozen region exist and even the particles in the layer deep still exhibit very slow flow, such motion can be detected anywhere in the packing [29] . Our understanding of the surface flows of granular remains fragmented and many elements lack to form a coherent and global picture, in particular, the creep motion. Another significant issue is to get a better understanding of the internal rheology of these surface flows: beyond the depth -average descriptions presented here, one would, for instance, like to better understand why linear velocity profiles emerge in flows taking place at the surface 5-100 CHAPTER 5 CREEP MOTION OF SHEAR FLOW ON A GRANULAR PILE 5-101 of piles, and why non-linear profiles arise in the flows over fixed bottoms. We may mention here two arguments that have been proposed in the literature, the first is due to Komatsu et al. [29] who noticed that when a flow take place at the surface of a pile, the static phase in fact undergoes a slow creeping motion; these authors suggest that the suppression of these creeping motion when the flow occurs on a rigid bottom may be responsible for the change in nature of the velocity profile between these two types of experiments. The second is clusters of grains embedded within the flowing layer by Bonamy et al. [66]. Experimental and numerical approaches have been used in this work to investigate the underlying flow structure of the flow behavior by pouring particles continuously at one side in an open quasi-two-dimensional system. The study of granular material at the grain level has been possible with the development of experimental techniques like high speed camera, x-ray tomography etc. However, the experimental technique is still limited, such as in the creep motion analysis, the digitized streak line analysis is clumsy and also is not so accurate. In contrast, the DEM can undoubtedly play a role. It can capture the microscopic information such as positions and displacements etc, in steady flow state time averaging method could be used to eliminate the fluctuation of those local properties. Tracking the positions and orientations of individual particles allows us to obtain density distribution, velocity and particle rotation rate for the system. Most of the emphasis has been on the theoretical side and several approaches, based on different physical assumptions have been proposed. Quasi-two-dimensional experiments are becoming a common element in the toolkit of granular flow investigations. A question common to quasi-two-dimensional studies is the extent to which walls affect the results. To a first approximation the effect of walls may be quantified by the ration of particle diameter to the thickness of the container. The experiments reported here were conducted with different ratio such as Orpe et al. [70], Jain [71]and Komatsu et al. [29] . But they are all in the range 5-25. All results are qualitatively similar for different ratios. This chapter presents an attempt to deep the insight into an important free surface flow granular system by discrete element method. The results are found to be useful to understand the internal structure of solid flow. Lastly a 5-101 CHAPTER 5 CREEP MOTION OF SHEAR FLOW ON A GRANULAR PILE 5-102 Special case with the assumed static layer "frozen" numerically is investigated to further clarify that there is no such fixed layer at all. 5.2 SIMULATION CONDITION The current state of experimental technique does not allow us to measure the particle velocity and contact forces between the particles, limiting our knowledge of the microscopic features inside the flows. However, the discrete element method has been proved a powerful tool to study particulate flow problems without any experimental error or assumptions. To model the interaction of individual grains we use the so-called soft contact approaches. The grains are assumed to be non-cohesive, dry, inelastic spherical particles. Two grains interact via normal and tangential forces whenever they overlap. The system of equations describing the dynamic interaction of an assembly of spherical particles is solved by using an explicit time-stepping scheme; at each time step the change in the inter-particle forces is computed from the relative velocities at the particle contacts via the incremental force-displacement relation for each contact. After updating the inter- particle forces, the new out-of-balance force at each particle contact is determined and used to calculate the new translational and rotational particle accelerations from Newton's law of motion. Integration of the particle accelerations provides the particle velocities and thereby the particle displacements. The particle displacements give the new particle positions, after which, by using the updated velocities at the particle contacts, the procedure is repeated. The normal force versus the overlap contact law obeys the well-known Hertzian theory. A DEM slot model has been used to improve microscopic in depth understanding of creep motion. Simple experiments have been carried out to validate this model. Experiments are carried out in a quasi-two-dimensional bin with vertical, transparent Perspex walls with a gap of 56mm shown in Fig.40. A plastic funnel is used on the top of the hopper A to ensure a continuous flowing layer for each experimental run. The mass flow rate is controlled by changing the size of the hopper opening, and the vertical height of the exit can be adjusted. In order to reduce the impact of top layer, the top of the heap is very close to the stopper B by adjusting the height of right side short wall C. Particles are continuously fed into the left side of the hopper. A triangle shape pile with rapid flow on the surface 5-102 CHAPTER 5 CREEP MOTION OF SHEAR FLOW ON A GRANULAR PILE 5-103 slope is formed, pouring out of the system from the end of right side C. The existence of the short wall on end of right side ensures a granular pile under the flowing layer. In order to maintain a steady surface flow on the slope of pile, particles were continuously fed onto the pile from the left side by using a plastic funnel on the hopper A acting as a double hopper, in which the lower hopper was continuously filled with particles by the upper one. Once the right side outflux from the system is equal to the influx in left top, a steady state system is established. The supply of particles is cut off by the stopper B in the bottom of the hopper. 168 280 280 M 140 56 560 560 Figure 40. Schematic diagram of experimental and simulation dimension All the experimental processes have been recorded by a digital video camera, hi this experimental work, we do not focus on the experimental measurement of particle velocity in the pile, so only some simple experiments conducted to compare the flow pattern in particular to validate this numerical model. Mono-disperse particles were used including glass beads and some wooden balls. Two different layers can be identified by observation as shown in Fig. 43, there are flowing layer on the top of pile with a certain angle to the horizontal plane, and a slow motion layer underneath. Their properties are shown in Table 8. The DEM simulations are based on the same geometry as shown in Fig. 40. The periodical boundary condition is applied to this 56mm slot model to reduce the wall effect. The 5-103 CHAPTER 5 CREEP MOTION OF SHEAR FLOW ON A GRANULAR PILE 5-104 hopper A which is unlimited high to hold enough particles to maintain a steady state and the outlet right side wall of hopper reaches the bottom of the container, and then gradually opens upwards until a steady state established, this configuration guarantees a steady flow without any impact caused by the coming down particles. Table 10. Physical properties of materials used in experiments and simulation Variables Glass beadsl Glass beads2 Wooden ball Particle diameter (mm) 10 5 13.9 Particle Density (kg/m^) 2450 2450 573 Sliding Friction of PP (-) 0.3 0.3 0.5 Sliding Friction ofPW(-) 0.3 0.3 0.3 Rolling Friction ofPP l%d l%d l%d Young's Modulus (P, W) (kg/ms) 1.0x10^ 1.0x10^ 1.0x10^ Poisson ration (P, W) (-) 0.3 0.3 0.3 Damping coefficient (P, W) (kg/s) 0.3 0.3 0.3 In order to qualitatively study the internal flow structure of the heap under steady state, the new coordinate y'o'z' was employed as shown in Fig. 41, the y' axis is the surface of flowing layer. The layer depth h is measured perpendicularly to the surface, and starts from the surface all the way down to the deep region. The ho is the flowing layer depth. Figure 41. Schematic diagram of coordinate systems 5-104 CHAPTER 5 CREEP MOTION OF SHEAR FLOW ON A GRANULAR PILE 5-105 5.3 RESULTS AND DISCUSSION Many effects can influence the dynamics of the granular surface flows. They are very sensitive to various parameters such as flow rate, particle physical properties and wall roughness etc. However, the factors like gravity, energy dissipation, and trapping of grains between their neighbors are always present in any granular materials [57]. The effects of mass flow rate, geometry of container, particle size, density and particle sliding friction will be investigated in this work. The variables such as flow height h, flowing layer height ho and mean translational velocity etc are going to be used to characterize the flow behavior. 5.3.1 Flow Pattern and Comparison with Experiments When granular piles exhibiting steady surface flow, below the surface flow the slow motion of particles in such a deep region is creep motion which has been experimentally identified by Kamatsu et al.[29]. Fig. 42 demonstrates such a flow phenomenon, a snapshot in steady state is showing with different velocity scale which is getting smaller from (a) to (c). (a) (b) (c) Figure 42. Snapshots of a granular pile in a steady flow state Obviously we observed a flow with different flowing depth. These figures reveal that the height of flowing layer is changing other than fixed as assumed in some theoretical work. It 5-105 CHAPTER 5 CREEP MOTION OF SHEAR FLOW ON A GRANULAR PILE 5-106 is easy to identify a flowing layer on the top of the pile by going through (a) to (c). However, the existence of a static bottom was not observed in these figures. Apparent interface is not fixed by choosing different velocity scale, so the interface is moving with different velocity scale. By comparing the flow pattern of experiment and simulation results as shown in Fig.43 (a) and (b), the experimental result is comparable to this numerical model. Fig.43 (a) is the experimental result of pink wooden ball particles flowing on a blue wooden ball pile, and a flowing pink layer can be easily identified. This agreement provides a sound basis to justify the micro-dynamic analysis based on the DEM results discussed below. Micro-dynamic analysis is a particle scale analysis of not only the trajectories but also the transient forces of individual particles in a particulate system. DEM can produce other important dynamic information that is not possible to be produced by experimental methods. These variables can be treated as local average variables or variables directly associated with individual particles. Since the flow is macroscopically stable, their time dependence has been ignored for simplicity. However, to avoid fluctuation,[146, 167] in this work, the variables are averaged by time average method from the DEM generated data. ••••^mi (a) Experimental result (b) Simulation result Figure 43. Flow pattern comparison between simulation and experiment 5-106 CHAPTER 5 CREEP MOTION OF SHEAR FLOW ON A GRANULAR PILE 5-107 5.3.2 Translational Velocity Profile In steady state the mean velocity is approximately parallel to the surface like in Fig.44. in which a fast flowing layer can be identified by the velocity vector. Along the layer depth h, the velocity distribution is same in the pile except in the vicinity of left and right boundaries. The mean velocity is determined along the height of flowing layer which is vertical to the free surface. TVyz Im/s Figure 44. Translational velocity vector in the pile It has been found that the creep motion is driven by events occurring on a particle size scale by Komatsu et al, so the particle diameter is used to measure the depth of layer in this work. In the case of hopper opening size 4d (four wooden particle diameter wide), the particle translational velocity distribution along the whole layer depth is shown in Fig. 45 (a). It is obvious that the velocity profile is seen to bend at a certain depth. The bend means the existence of particle slow motion below the fast flowing layer. At such depth, there approximately exists a boundary at which the particle motion changes from rapid surface flow to slow creep motion. This boundary which is parallel to the surface lies just above the upper edge of the right side wall, which is determined by the height of the fixed wall existing downstream. The velocity distribution in the flowing layer is shown in Fig .45 (b), roughly it is a linear velocity distribution from this figure. 5-107 CHAPTER 5 CREEP MOTION OF SHEAR FLOW ON A GRANULAR PILE 5-108 10^ \ \ \ 10' r S B 4d \ \ 10° '^V Interface -N 10' r » cs \ - > s 10^ r \ . V N 10" - N N 10^ N 10^ . 1 1 1 1 10 -6 -4 (h-ho)/d (h-ho)/d (a) (b) Figure 45. Translational velocity distribution The velocity in flowing and quasi-static layer can be described by the following equations (l)and (2). (h n = e^V,, (h > ho) (2) From the case studied shown in Fig.45. parameters a and ¡5 are obtained, given by a^-lA\{}i-h,)ld\ (3) = (4) 5.3.3 Angular Velocity Profile Particle angular velocity distribution is shown in Fig. 46. AVx, AVy and AVz are the particle angular velocity along the x, y and z axis respectively. Figure (a) demonstrates that angular velocities in y and z direction are all very small, and a relatively stable large angular velocity presenting in x direction. The minus sign of angular velocity in x direction confirms particle's right side rotating down to the slot container bottom. Figure (b) shows the angular velocity distribution along the layer depth, it can be seen that the angular 5-108 CHAPTER 5 CREEP MOTION OF SHEAR FLOW ON A GRANULAR PILE 5-109 velocity in the layer deep region is very small and maintain a linear relationship in the flowing layer. 34 Time (s) (h-ho)/d (a) (b) Figure 46. Angular velocity variation 5.3.4 Effect of Mass Flow Rate As discussed previously, there is a slow motion even in the deep region in the steady state when maintain a continuous flow on a pile. But how the mass flow rate affects the particle flow in the pile, the following study is based on 4d, 6d, 8d and lOd hopper opening size which corresponding to the mass flow rate. Mass flow rate effect on the slope angle and flowing layer depth is shown in Fig. 47. The slope angle is not constant, but increases with mass flow rate. An increase in slope angle with flow rate was also reported by and Lemieux et al.[55] and Khakhar et al. [56]. Layer thickness increases with mass flow rate and is independent of particle size. 5-109 CHAPTER 5 CREEP MOTION OF SHEAR FLOW ON A GRANULAR PILE 5-110 P. 16 2 4 6 8 10 1 0 2 4 6 8 10 12 Hopper orifice (d) Hopper orifice (d) (a) Thickness of flowing layer (b) Slope angle variation Figure 47. Mass flow effect on slope angle and thickness of flowing layer Fig. 48 shows the velocity in the interface under different mass flow rate. This figure illustrates a very close velocity in the interface region which is independent of mass flow rate. 0 2 4 6 8 10 12 Hopper orifice (d) Figure 48. Velocity near interface with different mass flow rate Fig.49 shows the velocity distribution under four different mass flow rate, they are all demonstrating very similar distribution pattern even in different mass flow rate, a obvious common feature is a slow motion presenting under the interface region. 5-110 CHAPTER 5 CREEP MOTION OF SHEAR FLOW ON A GRANULAR PILE 5-111 -5 0 5 10 (h-ho)/d Figure 49. Velocity distribution with different mass flow rate 5.3.5 Porosity Distribution The flow structure of particles is examined in terms of porosity that has been widely used in the study of particle packing. A snapshot of porosity distribution in steady state is shown in Fig. 50, it was found that the bottom part, i.e. the static part, has a lower porosity while the top part, i.e. flowing layer, a higher porosity, the high porosity region must be from the unconfined movement of particles. In order to clarify the porosity variation, there are four 2x2 particle diameter regions are marked in this figure as A: flowing layer, B: interface region, C: lower part near interface and D: deep region. The porosity variations with time are plotted in Fig.51. In the flowing layer, the variation is very large, that means particle movement in a wide range. From A to D, the variation is getting small and small, especially in the deep region D, the porosity variation is very small, that provided the further evidence that more contacts in bottom static layer than in the flowing layer. 5-111 CHAPTER 5 CREEP MOTION OF SHEAR FLOW ON A GRANULAR PILE 5-112 Figure 50. Porosity distribution As we know, tlie porosity changes with time layer by layer, that means the voids variation exists in different region, that the reason why particles in the deep region even can experience slow motion. The translational velocity component perpendicular the flowing layer surface is very small and getting smaller along the layer depth, this velocity plus the voids variation gave a clue that exchange of particles exists inside the pile. This corresponding to BRCE model's grain exchange concept, in which different layers are able to exchange grains through an erosion or accretion mechanism, if slope angle is larger than neutral angle, gives erosion, less than neutral angle, gives accretion [181], the neutral angle of grains at which erosion of immobile grains balances accretion of the rolling grains. [64]. In such a low impact continuous flow, the friction is the major force for particles interaction. So void and shear force is the reason for creep motion. In the region of creep motion, particles are jammed tightly and sheared by the upper flow. For such particles to move, the existence of voids is essential. In our porosity distribution figure, it is observed that the porosity changes within the interface area with time. That means there is a void creation and ending process between two layers. In another word, shear causes plastic global deformation of the network formed by inter-particle connections and that such deformation occasionally creates voids. These observations, together with the realization that the characteristic length of the decay is on the order of the particle size, lead to a simple idea 5-112 CHAPTER 5 CREEP MOTION OF SHEAR FLOW ON A GRANULAR PILE 5-I13 that the exponential decay of the velocity profile can be understood on the basis of the void creation process. 1 0.9 Flowing layer Interface 0.8 Lower part near interface Deep region 0.7 30.6 ""w 0.5 E o Q. 0.4 0.3 0.2 0.1 I I 31 32 33 34 35 36 Time (s) Figure 51. Porosity change with time in marked regions 5.3.6 Comparison with Frozen Base Layer Case In order to further identify the creep motion under the surface flow, a special case with the so called static layer "frozen" numerically is investigated as show in Fig. 52. The blue frozen slope is similar to a rough inclined surface which is very often used to study the surface flows. No doubt the slope is static as indicated in Fig.53, the velocity is absolutely zero in this layer. Based on the velocity distribution of a free surface flow on a pile as shown in Fig. 48, the velocity profiles along the flowing layer height direction are plotted in Fig. 54 for both fixed and quasi-static base layer. Obviously the trends of velocity profiles are different, the velocity of surface flow on quasi-static layer is linear with the flowing layer height, and it is larger than the velocity of surface flow on the frozen layer which is not a linear relationship with the height especially in the top part of the flowing layer. The velocity profiles demonstrate that the particles under the flowing layer play a role and affect the behavior of the flowing layer. 5-113 CHAPTER 5 CREEP MOTION OF SHEAR FLOW ON A GRANULAR PILE 5-114 Figure 52. Particle configuration (blue color part frozen) TVyz Im/s Figure 53. Velocity vector of flowing layer on fixed slope 5-114 CHAPTER 5 CREEP MOTION OF SHEAR FLOW ON A GRANULAR PILE 5-115 0.9 0.8 -B quasi-static base layer 0.7 fixed base layer 0.6 CO 0.5 - >0.4 0.3 0.2 ;r 0.1 28 30 32 34 Flowing layer height (d) (from bottom to surface) Figure 54. Velocity comparison between quasi-static and fixed base layer 5.4 CONCLUSIONS Surface flow on a granular pile has been numerical studied using the discrete element method. Experiments have been carried out to validate the model. It has been obtained that the flow exhibits a linear velocity along the height of the flow layer. There is a slow creep motion in the pile. The creep motion can be observed anywhere in the pile, and varies with the distance from the base layer surface as an exponential manner. The variation of the porosity in different parts of the system has been examined to understand the existence of the creep motion. A case with the frozen base layer has also been considered to investigate the effect of the creep motion on the surface flow. It is found that the creep motion would lead to a larger flow velocity. The velocity of the surface flow for the non-frozen base bed is linear, whilst the velocity distribution for the frozen base bed is not linear. 5-115 CHAPTER 6 INTER-PARTICLE PERCOLATION IN A MOVING BED 6-116 CHAPTER 6 INTER-PARTICLE PERCOLATION IN A MOVING BED 6-116 CHAPTER 6 INTER-PARTICLE PERCOLATION IN A MOVING BED 6-117 6.1 INTRODUCTION There has been a growing interest in inter-particle percolation study due to its industrial significance. The penetration of the smaller particles into the interstices of larger ones is usually called particle percolation, which consequently causes the local variation in voidage of packed beds. Two different particle percolation mechanisms have been identified. One is the drainage of small particles through the interstices between large ones due to the influence of gravity; another is the interpénétration of close sized particles when subject to strain in failure zones. The gravity induced percolation is very similar to mechanism by which small particles penetrate to a screen in mechanical size separation, which can be associated with the sieve-like or filtering nature of the solid matrix. Investigation of the inter-particle percolation is of practical importance, for instance, quality control in pharmaceutical industry or in estimating the flow resistance of a moving bed such as blast furnace burden distribution. With a special reference to blast furnace top, alternating layers of coke and iron ore in general differ in size, density, shape and porosity. There are a wide range of particle sizes in blast furnace, coke size is in range 25mm to 80mm, and ore size is in range 6.3mm to 31.5mm. Understanding of particle percolation in coke/ore layers and coke ore mixed layers is critical to optimize the blast furnace operation. A great deal of work has been done on inter-particle percolation with consideration of gravity force and strain effect respectively. Most of the attention has been given to fine particle percolation under gravitational force. Propster et al. reported their experimental results on the spatial dependence of the local void fraction for systems where particles of different size form horizontal layers in packed beds [78]. The most important finding of their work is that the penetration of smaller particles into the interstices of the larger spheres occurs readily when the particle size ratio exceeds about 2.0. Also the larger the disparity in size of the particles from which the two layers are composed, the greater is the depth of the penetration, and the lower is the absolute value of the local minima in the void fraction especially in the interfacial region. When smaller particles are placed on a layer of larger particles, penetration will occur; in contrast, for the reverse case only a surface disturbance will take place. It has been realized that the gas flow through blast furnace is 6-117 CHAPTER 6 INTER-PARTICLE PERCOLATION IN A MOVING BED 6-118 generally non-uniform and is markedly affected by local variations in the porosity of the bed [78]. With particular interest in particle mixing, Bridgwater et al. examined the inter- particle percolation phenomenon which is one of the mixing mechanisms by physical experiments in which the percolating species are so small that penetration through any hole of the structure of large particles is possible [79]. They concluded that inter-particle percolation is a process more closely analogous to molecular diffusion, the radial dispersion of very small spherical particles is in accord with a diffusion mechanism, the Peclet number has been used to describe the radial dispersion, and the diameter ratio of the percolating particles to the packing appears to be relatively unimportant. They also mentioned that a weak effect stemming from the density difference of equally sized particles is also believed to exist. Following this study, Bridgwater et al. investigated the rate of spontaneous inter- particle percolation [30]. It was found that the mean percolation velocity may be related to the coefficient of restitution and the diameter ratio of the percolating particles to the packing, the residence time distribution of percolating particles was shown to conform to a diffusive mechanism and the actual Peclet number was found to be virtually independent of the particle properties. With special attention to the geometry of the porous structure, Richard et al. investigated the inter-particle percolation of a fine particle through a packing of mono-size spheres by experimental and numerical approaches based on the geometry of the packing [80]. The falling bead is charged in multiple points unlike Bridgwater's which was charged only in the center. By mapping the inter-particle space using the Voronoi tessellation of the packing whose edges describe the network of pores of the medium and deduce the possible paths of the falling sphere, the motion of the sphere can be easily simulated with a Monte-Cario algorithm. They found that the radial diffusion of the falling bead increases linearly with the height of the packing and numerical results are in agreement with the experimental results. Unlike the single particle percolation study, Oger et al.[81] demonstrated the effects of particle number and packing bed height on the percolation process by employing experimental and DEM methods. They believed that collective behavior of particles plays an important role because the presence of many particles falling together induces many additional collisions and collective effects. During the percolation process, energy is dissipated at the time of frictional and inelastic collisions which induce lateral and longitudinal dispersions. It has been shown by Samson [182] that, 6-118 CHAPTER 6 INTER-PARTICLE PERCOLATION IN A MOVING BED 6-119 for the case of a single particle falling down in a porous medium, the percolation velocity is also constant. In other words, a steady state is reached with a constant percolation velocity if the size of packing is large enough to avoid or minimize the influence of some transition regime in the beginning of the process. For different number of percolating particles, the mean transit time to the height of packing curves are not parallel which suggests that the percolation velocity depends on the number of percolating particles. Apart from the gravitation force, percolation also occurs in the shear zone between two layers of particles moving at different velocities. Scott et al. examined irregular particle movement in a failure zone by a horizontal shear box [82]. They concluded that the irregular movements of spherical particles in a simulated failure zone formed in the shear box could be approximately described by a diffusion equation. Further strain-induced inter-particle percolation study was carried out by Cooke et al. [83]. A reciprocating shear box was employed to study both lateral and axial diffusion during the process of percolation, found that the dimensionless lateral and axial diffusion coefficients are controlled mainly by the ratio of the diameter of the percolating particle to that of the bulk particles. Duffy et al. investigated the particle percolation in a vertical shear cell by considering variables such as particle size ratio, strain, strain rate and bed depth. It was found that the size ratio is most dominate, strain also had an effect, the percolation of fmes through a bed of coarse particles was isotropic [84]. They also developed and validated a convective- diffusive segregation model to describe the percolation based on the experimental results [85]. However, previous studies were mainly based on the static fixed packed bed with single particle central point charging, single particle multiple points charging or multi-particle charge in the central region. Less attention has been given to particle percolation in a moving bed. Due to the industrial importance, this study is undertaken in order to characterize the particle percolation in a moving packed bed which has a dynamic packing structure. The percolating layer consists of a number of particles. The bed is formed by layers of different particles, motivated by the relevance of this problem to a broad range of materials processing operations, where these effects may have a marked influence on 6-119 CHAPTER 6 INTER-PARTICLE PERCOLATION IN A MOVING BED 6-120 spatially distributed resistance to gas flow and hence on the performance of the processing unit such as blast furnace. This work aims at studying particle percolation in a moving bed under both gravity and shear force present. The effect of various properties on particle percolation will be considered, including bed descending velocity, particle size, density ratio between the percolating particles and the packing spheres, sliding coefficient of percolating particles, percolating particle number and parking bed height. 6.2 SIMULTATION METHOD 6.2.1 Discrete Element Method DEM is used for the numerical simulation in this work [93] . The method employed has recently been used in the study of solid flows [168-172]. By this method, the motion of a particle in a considered system, which can undergo translational and rotational motions, is described by Newton's laws of motion. These equations are based on the forces and torques originated from its interaction with neighboring particles and wall, with the latter also treated as a particle with infinite size. Therefore, the translational motion of particle i can be described by dv. k^ dt where m. and v. are the mass and translational velocity of the particle, respectively. F^ .j and F^ y are the contact elastic force and contact damping force acting on particle i by particle j. Note that when particles at contact start to slide relatively, the tangential force should be described by the dynamic friction, usually, given by the Coulomb fiiction model. Correspondingly, the rotational motion of the particle can be described by 6-120 CHAPTER 6 INTER-PARTICLE PERCOLATION IN A MOVING BED 6-121 where (o, is the angular velocity of the particle, I. is its moment of inertial, T.j is the torque stemming from the tangential contact forces, andM.. is the rolling friction torques. For the spherical particle used here, I. and T.j = R. .. . The forces and toques are calculated based on the non-linear models which have been extensively applied in our numerical studies of granular flows. 6.2.2 Simulation Conditions This numerical model has been validated by our previous study [179]. The bed consists of two roughed parallel side walls and periodical boundary virtue walls in the front and rear. The side walls are 40 packed bed particle diameters apart and the height of packed bed is 35 packed bed particle diameters. The packed bed is settled on a bottom plate as shown in Fig.55. Bottom plate Figure 55. Schematic diagram of this slot model (d- packed bed particle diameter) The roughed side walls are formed by fixing a single layer of particles as same size in the packed bed vertically on its surface with no contact in each other. Such treatment can 6-121 CHAPTER 6 INTER-PARTICLE PERCOLATION IN A MOVING BED 6-122 avoid the high void fraction near the walls. It has been known that the granular flow down a cylindrical container having rough wall exhibits a velocity profile characterized by a plug flow in the central and shear zones near the wall [180]. It has also been suggested that the mass density is almost constant in the central region and decreases with the radius in the region close to the wall. The decrease in density is due to the dilatancy that take place during shearing. In order to flow, the material has to dilate, so a sort of density wave that goes from the bottom plate to the top of the bin can be observed at the beginning of the simulation, and a steady state is finally attained [183]. A packed bed is built by randomly pouring mono-size spheres into a rectangular slot with 4 packed bed particle diameters width under gravity. The top percolating particles are generated 0.12m above the packed bed surface and settled on the packed bed under gravity. The basic particle configuration in this numerical model is shown in Fig.56. Figure 56. Particle configuration in a moving bed The bed starts to move downwards after all the percolating particles are in rest. The moving bed is controlled by descending a bottom plate at a preset velocity. Quasi-static vertical flow bed is maintained. For the case of spherical particles passing through a poured packed bed, it has been known that if size ratio < 0.1574, where size ratio equals the percolating particle diameter / the packed bed particle diameter, the small spheres may pass through any portion of the structure. This ratio is called percolation threshold [80]. Such a system 6-122 CHAPTER 6 INTER-PARTICLE PERCOLATION IN A MOVING BED 6-123 exhibits spontaneous inter-particle percolation. Cases with different size ratio and density ratio have been investigated in this study, especially the size ratio, which is in the range from 0.143 to 0.5. This range is designed to check the difference with size ratio lower and higher than threshold. The density ratio, which is density of percolating particle to packed bed particle, 1 and 4 are chosen to demonstrate its effect on the particle percolation. Table 11 lists the variables considered in this study Table 11 .Physical properties of materials used in simulation Variables Percolating particle(GB or WB) Packed bed(WB) Particle number 500,5000,10000,20000,30000 6400 Particle diameter (m) 0.002 - 0.007 0.014 Particle Density (kg/m^) 2450,583 583 Sliding coefficient (-) 0.001,0.1,0.3,0.5 0.5 Bed descending velocity(m/s) 0.05, 0.1,0.2, 0.3 Charging rate(particle/time step) 5,10,20,40 Time step (s) 5x10"^ 6.3 RESULTS AND DISCUSSION 6.3.1 Percolation Characteristics 6.3.1.1 Velocity profile in the moving bed It has been known that the granular flow down a cylindrical container having a rough wall exhibits a velocity profile characterized by a plug flow in the central zone and shear zone near the wall. The size of the shear zone was found to be between 5 and 15 particle diameters wide. The moving bed has been cut in half from center to show the velocity field in Fig.57. There are two zones have been identified as static and dynamic zones marked with a dashed vertical line. The particle motion in the central region is in the same direction, 6-123 CHAPTER 6 INTER-PARTICLE PERCOLATION IN A MOVING BED 6-124 but the direction of particle movement in the near wall region is random due to particle collisions with the roughed walls. »iSiiliffl . iiiii-- llil1 ill « Wall region Central region Figure 57. Velocity field in the moving bed The velocity profiles are plotted in Fig. 58 with the translational velocity profile in (a) and angular velocity profile in (b). From both very similar velocity profiles a shear zone approximately 6 particle diameters wide from the side wall and a plug flow in the middle of the container are clearly observed. Which are corresponding to the two zones identified from the velocity field shown in Fig. 57. -0.03 I -0.04 I -0.05 -0.06 0 3 6 9 12 15 18 21 24 27 30 33 36 39 0 3 6 9 12 15 18 21 24 27 30 33 36 39 Width(d) Width(d) (a) translational velocity (b) angular velocity Figure 58. Averaged translational and angular velocity profiles 6-124 CHAPTER 6 INTER-PARTICLE PERCOLATION IN A MOVING BED 6-125 6.3.1.2 Percolation pattern in the moving bed Size ratio threshold is an important indicator to identify the mechanisms of particle percolation. Two size ratios 0.143 and 0.36 are used to investigate the underlying mechanisms of particle percolation in a moving bed as shown in Fig.59 (a) and (b). Only percolating particles are displayed in both figures. The packed bed was formed by 14mm wooden balls, the glass beads 2mm and 5mm were used as the percolating particles, so the density ratio is 4 for both cases. L. L, (a) static bed move 0.16s move 1.29s move 2.05s m (b) f r 1 static bed movel.73s move 8.67s movelO.Ss Figure 59. Percolation pattern: (a), size ratio smaller than threshold; (b), size ratio greater threshold In case (a), the size ratio is 0.143, which is smaller than threshold. 30,000 particles were charged onto the packed bed. The first snapshot in Fig.59 (a) shows the state of the static bed right after all the percolating particles are settled. Most of the percolating particles have drained into the whole packed bed under gravity though pores in the bed. The penetration of particles is evenly distributed from left side wall to right side wall, but is not even along 6-125 CHAPTER 6 INTER-PARTICLE PERCOLATION IN A MOVING BED 6-126 the height of packed bed. The closer to the packed bed top, the more percolating particles get jammed as observed. The packed bed starts to descend at a velocity 0.05m/s once all the percolating particles are in rest. From the snapshot 0.16s to 2.05s the percolating particles near the left and right walls continue to penetrate deep into the bed. But noticeably the particles in the middle section still stay v^here they were. Those observations provide ftirther evidence of shear and plug zones in the moving bed, and consequently identified the fiirther particle percolation in the moving bed is caused by the shear force in the wall region, and more over, the gravity force is still in action to facilitate the percolation process once the pore generated by the shear force is larger than the size of percolating particles. In case (b), the size ratio is 0.36, which is larger than threshold. 5,000 percolating particles were charged onto the packed bed as shown in the first snapshot in Fig.59 (b). There is no particle penetration observed so far because the size of percolating particles is larger than the existing pores in the static bed. Similarly the packed bed starts to move after all the percolating particles are settled and in rest. Some percolating particles were found in the shear zones of the moving bed from the snapshots 1.73s to 10.8s. Clearly there is no particle percolation in the plug zone of the moving bed same as what have observed in case (a). But it is worthy to be noticed that particle percolating velocity in case (a) is much larger than case (b) because the double actions of shear and gravity force. 6.3.1.3 Microscopic view of particle percolation By taking advantage of the numerical approach, it is now possible for us to look at the internal packing structure evolvement during the particle percolating process. The jamming effect discussed above can be further identified by studying the pore structure of the packing bed. According to particle properties, the blocking phenomena are classified into three types. The first is a geometrical interlocking of coarse particles at an outlet of the container. It occurs predictably when the opening size is smaller than several times the particle diameter. It is caused by the friction between particles and /or a vessel wall[184]. The blockage of small particles in the percolation process is very similar to this mechanism as shown in Fig.60, which is part of the microscopic view of packing structure of the case 6-126 CHAPTER 6 INTER-PARTICLE PERCOLATION IN A MOVING BED 6-127 (a) in previous section. Some percolating particles formed particle arches as marked with blue dashed circles, consequently there are more particles are blocked till the pore is fully jammed. Particle jamming is governed directly by particle properties and self-weight of particles, and thus is closely related to the pore structure. The arching of particles can be broken by the interaction force of particles in the moving bed. And which results in further percolation of small particles into the packed bed. It is immediately evident that bed movement has a profound effect on the further particle percolation. Figure 60. Arching effect of percolating particle size 2mm Inter-particle percolation under moving bed is often encountered in practice. Microscopic information could provide considerable insights into the particle percolation processes. For example, it can provide information to answer how the particle undergoes a sequence of discrete jumps due to collisions with the packing during its downward fall. Snapshots in Fig. 61 demonstrate the process of how one single particle percolating into to the packed bed, where the size of percolating particle is 6mm and the size of the particles forming the pore is 14mm. Fig. 60 (a) is the example of a particle simply percolating through a large pore 6-127 CHAPTER 6 INTER-PARTICLE PERCOLATION IN A MOVING BED 6-128 under the gravitational force. Because the size of pore is larger than the size of percolating particle so it only took 0.005 second to reach the bottom of the pore under a free fall process. The particles consist of this pore has been marked with a number "1", this fast falling of blue particle can be proved by the velocity vector showing at timel3.89s. Fig. 60 (b) demonstrated the percolation process under shear force. Since the pore size is smaller than the percolating particle so the percolating blue particle can not simply pass through the pore formed by the four larger yellow particles as shown at time 12.63s. The small particle is located on the entry of a pore formed by its surrounding particles atl 2.65s, the pore is still too small to let the percolating particle pass through. However, the particle finally penetrated through the pore due the shear forces from bed movement at time 12.79s, but it took 0.15 second, which is much longer than a particle percolating through a big pore as shown in example (a). As this sample was taken from the shear zone in the moving bed, so the percolation is driven by the shear force from relative particle motion. (a) t= 13.86s t= 13.87s t= 13.90s t= 13.91s t= 12.63s t= 12.65s t= 12.77s t= 12.79s t= 12.80s Figure 61. Microscopic view of particle percolation process (a) gravitational force induced percolation,(b) shear force induced percolation The average particle interaction forces in the moving bed under different descending velocities were plotted in Fig.62. Particles percolate into the packed bed near the wall 6-128 CHAPTER 6 INTER-PARTICLE PERCOLATION IN A MOVING BED 6-129 region because of the shear forces, so the force information could help to improve our understanding to the particle percolation. The interaction force in this figure was the average of normal contact force between packed bed particles. The bed started to move at the time 18.5s, the total bed travel distance is 0.8m and then it stopped. As observed from Fig.62 the larger descending velocity the larger the interaction force generated in the bed. However, the percolation rate is not linear with the interaction force; the relationship is not clear yet, further work needs to be done to clarify the correlations between descending velocity and percolation rate. 2.00E-03 1.80E-03 1.60E-03 1.40E-03 n 1.20E-03 1.00E-03 8.00E-04 6.00E-04 4.00E-04 2.00E-04 O.OOE+00 14 19 24 29 34 39 Time (s) Figure 62. Average particle interaction force in the moving bed 6.3.1.4 Percolation distribution in a moving bed The percolation distribution of 3mm percolating particles inside the packed bed was examined to investigate the characteristics of percolation in a moving bed. The descending velocity is O.lm/s, the size ratio is 0.214, which is higher than the percolation threshold. The height of packed bed is 35d, in the following discussion 0 indicates the bottom of the bed and 35d is the top of the packed bed. The width of packed bed is 40d as discussed previously, 0 means the left side wall while 40d indicates right side wall. The evolution of 6-129 CHAPTER 6 INTER-PARTICLE PERCOLATION IN A MOVING BED 6-130 number of percolating particles inside the packed bed with time is shown in Fig. 63. The number of percolating particles is counted at the bed height 20d, this height is arbitrarily chosen. At time 15.5s there is no particles reached this section; at time 25.1s roughly 140 percolating particle penetrated into the packed bed height 20d and below; up to time 29.1s around 360 particles percolated into the bed below height 20d. As observed the percolating particle were only found in the regions from 0 to 5d and from 35d to 40d, which are corresponding to the velocity profile reported in the literature [185]. 100 200 300 400 500 Percolating particle number(-) Figure 63. Percolation in bed height 20d (descending velocity = O.lm/s particle size 3mm) More over, the particle percolation distributions at different bed heights have been investigated as shown in Fig.64. At the top part of the packed bed, such as heights 30d and 35d, some particles can be seen in the center part of the bed, this was caused by the large pores on the packed bed surface during the bed random forming process. However, those particles are just very small portion of total 5000 particles charged. The percolation distributions at height 20d and lOd are the real reflections of characteristics of percolation in the moving bed. As shown in Fig.64 no particles percolated into the center region of the packed bed, particles are only found in the zones near the left and right side walls. So for 6-130 CHAPTER 6 INTER-PARTICLE PERCOLATION IN A MOVING BED 6-131 case with size ratio higher than threshold percolation happens in the shear zones only due to the shear force caused by the movement of the packing bed. 0 100 200 300 400 500 Percolating particle number(-) Figure 64. Percolation along different bed height (descending velocity = 0.1 m/s, particle size 3mm) 6.3.2 Effect of Operational Variables 6.3.2.1 Charging rate of percolating particles The charging rate is defined as the number of particles generated in each time step on the top of the packed bed. To study the charging ratio effect only size ratios smaller than threshold have been considered. In this case the percolating particle diameter is 2mm, so the size ratio is 0.1429, which is smaller than threshold. Total 30,000 percolating particle were charged on a packed bed for each case studied. There are four different charge rates from 5 to 40 particles every time step (P/Timestep) as shown in Fig.65. All the data were 6-131 CHAPTER 6 INTER-PARTICLE PERCOLATION IN A MOVING BED 6-132 obtained when all percolating particles get rest in the packed bed. The effect of charging ratio is represented by the percolating particle hold up, which is defined as percentage of percolating particles blocked in the packed bed. The horizontal axis represents percolating particle hold up percentage in a certain height and vertical axis represents the packing bed height from height 3d to 35d in Fig.65. The bottom part of the bed from height 0 to 3d is shown in the inset. It can be seen that near the top part of the bed from 30d to35d, the larger the charge rate, the more particles accumulated. From the height 3d to30d, the numbers of percolating particles in each section of the bed are very close along the bed height. In other words, the patterns of particle percolation distribution in the middle sections are very similar. This phenomenon suggests that for a certain packing structure there are always major paths for the percolating particle to pass through and those passages are independent of the charging rate. Those paths like zigzag. The zigzag pattern of the displacements of particles resembles that of a random walk process. 35 r« 1 P 4 5 Particle holdup percentage (%) Figure 65. Percolating particle charge rate effect 6-132 CHAPTER 6 INTER-PARTICLE PERCOLATION IN A MOVING BED 6-133 The inset in Fig. 65 shows the percentage of particles penetrating into the bottom of bed. In the case of the smallest charge rate 5 P/Timestep, there are about 46% of percolating particles passing through the whole packed bed and reaching the bottom, and for the other three charge rates the percolating particle percentage is around 41%, which is less than the smaller charging rate. This indicates that the charging rate plays a role here. However, from the section of 3d to 30d, the smaller the charging rate, the more particles get through along the height of bed. This probably stems from blockage effect. For a certain charging rate on a packed bed, the top part of the packed bed just likes a sieve since it decides an upper size limit for the particle to go through. This explains the reason why in the middle part of this packed bed, the percolating particle hold up is less for larger charging rate. Moreover, there probably exists a critical value of the charging rate such as 5 P/Timestep in this case, any charging rates higher than this which could cause serious blockage and would have very close percolation percentage. This value could be determined by the packing structure and particle physical properties. 6.3.2.2 Descending velocity of moving bed To investigate the role of the descending velocity in the particle percolating process of a moving bed a case with percolating particle size 3mm is chosen to demonstrate the effect of descending velocity, the total particle number is 20,000. For size ratio smaller than the threshold, the effect of descending velocity is limited on the particle percolation, so only size ratio larger than the threshold is considered here. Under different velocities 0.05, 0.1, 0.2 and 0.3 m/s all the resuhs obtained are based on the total travel distance 0.8m other than the total bed descending time. The relationship between the percolating particles which still retain in the packed bed and the bed height has been plotted in Fig.66. The inset details the percolating particle percentage at the bed bottom. It is found that for the descending velocities 0.05m/s and O.lm/s the percolating percentage are 7% and 3.5% of the total particles have reached the bottom respectively, and for those higher descending velocities 0.2m/s and 0.3m/s, there is no percolating particles reach the bottom. This could be explained as that for the larger 6-133 CHAPTER 6 INTER-PARTICLE PERCOLATION IN A MOVING BED 6-134 descending velocities, the longer distance is for the percolating particles to travel to reach the bottom. Generally, for the velocity range considered as above, the effect is not significant based on the same travel distance. 359 10 20 Particle holdup percentage (%) Figure 66. Descending velocity effect 6.3.2.3 Percolating particle number Unlike previous studies where most of the spontaneous particle percolation focused on single particle percolating, in reality, there are always multiple particles working together. The collective behavior of multiple particles would play a role in the transport of large number of particles into a packed bed. Under the charging rate 10 P/Timestep the particle numbers of 500, 5,000, 10,000 and 20,000 are chosen for this study and percolating particle size is 2mm. As shown in Fig. 67 the inset shows the detailed percolating particle percentage. With smallest particle number 500 charged, 80% of the particles have simply passed through the packed bed to the bed bottom; For the large particle numbers 5000, 6-134 CHAPTER 6 INTER-PARTICLE PERCOLATION IN A MOVING BED 6-135 10,000 and 20,000, around 50% of top percolating particles were able to penetrated to the bottom and half of them get stacked inside the packed bed due to the arching effect, by which the passage ways have been blocked. It is evident that the presence of many particles falling together indices many additional collisions and collective effects. — 500 ^ 5000 e— 10000 ^ 20000 2 4 6 Particle holdup percentage (%) Figure 67. Percolating particle number effect 6.3.3 Effect of Particle Properties 6.3.3.1 Particle size ratio For the size ratio is smaller than the thresh hold, the particle is fine enough to drain through the packed bed for single one. The size ratio larger than the threshold was studied here to check the particle size ratio effect. The results of size ratio from 0.214 to 0.5 are shown in Fig.68. As derived from Bridgewater's equation, the percolation rate of size ratio larger 6-135 CHAPTER 6 INTER-PARTICLE PERCOLATION IN A MOVING BED 6-136 than threshold is related to the particle size ratio, the sliding friction coefficient plus the descending velocity in moving bed. As demonstrated in Fig.68 the impact of size ratio is quite different in static and moving bed. The void square line represents the static bed and the curve is very flat, even for the smaller size ratio, in which only less than 5% of percolating particles have penetrated through the packed bed. The solid square line represents the moving bed after being moving 10 seconds downwards. As observed once the bed starts to move the percolating particles start to penetrate into the packed bed. The smaller the size ratio, the higher the percolation percentage increased. Fig.68 suggests that the movement of bed has significant impact to the smaller percolating particles. 100 Static bed 80 Moving 10s CD O) c CD 60 O (D Q. 40 o ^ 20 Q. 0.1 0.2 0.3 0.4 0.5 0.6 Size ratio(-) Figure 68. Particle size ratio effect 6.3.3.2 Friction coefficient As discussed above the friction coefficient plays a role in the percolation process. Simulations have been done to investigate the friction coefficient effect on static and moving bed respectively. Firstly particles of diameter 2mm were used to represent percolation happening in the size ratio lower than threshold. All the results under friction 6-136 CHAPTER 6 INTER-PARTICLE PERCOLATION IN A MOVING BED 6-137 coefficient 0.001, 0.1, 0.3 and 0.5 are shown in Fig.69. There are two curves in this figure one is for static bed and another one is for moving bed. The percolation percentage trends in Fig.69 are similar in both beds. The percolation rate increases with the decreasing of friction coefficients. Once the bed starts to move, the percolation rate increases except the very small friction coefficient 0.001, in which all percolating particles drained to the bed bottom before the descending of bed. Obviously particles with smaller friction coefficient pass through the bed faster and movement of bed triggers the further particle percolation under shear force. 100 80 Static bed CD Moving 5s O) iS C CD 60 ££ CD Q. O) C 40 « ^o CD Q_ 20 0.1 0.2 0.3 0.4 0.5 0.6 Friction coefficient(-) Figure 69. Friction effect on both static and moving bed (particle size 2mm) In order to further examine effect of the friction coefficient on the size ratio larger than threshold the particles of diameter 3mm were used. Friction coefficients 0.05, 0.2 and 0.3, have been considered under the bed descending velocity 0.1 m/s as shown in Fig.70. It is clear that the smaller friction coefficient, the more particles percolating through the bed especially for the smaller friction coefficients such as 0.05. Even though the friction coefficient is significant in the percolating process, however, it is more affective in the case of size ratio smaller than threshold. 6-137 CHAPTER 6 INTER-PARTICLE PERCOLATION IN A MOVING BED 6-138 3 •D 0) jn 20 ^ a o O) if g 2 • 10 20 Particle holdup percentage (%) Figure 70. Friction effect on a moving bed (particle size 3mm) 6.3.3.3 Density ratio In industrial applications the density of percolating particle and the packed bed particle usually is different. Density ratio 1 and 4 have been used to investigate the density ratio effect under two different particle sizes 4mm and 6mm, which are corresponding to size ratios 0.2858 and 0.4286 as listed in Table 12. For the smaller size ratio 0.2858 under both density ratios the percolation percentage is very close; similarly for the larger size ratio the percolation percentage is still very close. Overall, the density ratio effect is limited on particle percolation in moving bed. Table 12. Density ratio effect Density ratio(-) Size ratio (-) Percolation percentage (%) 1 0.2858 31.04 1 0.4286 4.12 4 0.2858 33.26 4 0.4286 4.16 6-138 CHAPTER 6 INTER-PARTICLE PERCOLATION IN A MOVING BED 6-139 6.3.3.4 Percolation velocity with different size ratio As discussed previously particle percolation happens under both gravity and shear force in a moving bed. The size ratios lower and higher than threshold are used to understand the relationship between the size ratio and particle percolating velocity as shown in Fig. 71. The square marker line represents size ratio smaller than threshold and the triangle marker line is the size ratio greater than threshold. For the small size ratio 0.143 the percolation happens at both central and wall regions, but to the larger size ratio 0.214 percolation happens near the wall regions only. It is found that the closer to the side wall the larger the percolation velocity in the wall regions for all size ratios. The smaller size ratio, the larger the percolating velocity. Size ratio =0.214 Size ratio =0.143 0 0.1 0.2 0.3 0.4 Percolation velocity(m/s) Figure 71. Percolation velocity with size ratio 6.3.3.5 Particle rotation The gravitation force and the shear force have been identified as the underlying mechanisms for particle percolation in a moving bed. For size ratio smaller than the threshold the percolation is largely a free fall draining process, so effect of particle rotation 6-139 CHAPTER 6 INTER-PARTICLE PERCOLATION IN A MOVING BED 6-140 in the percolation process is limited. Here we focus on the size ratio higher than the threshold, in which the shear is the driving force for the particle percolation once the bed starts to move. In order to examine the particle rotation effect, the rotation of the particles in the moving bed has been frozen numerically. The results are shown in Fig. 72, which is the relationship between percolating percentage and particle size ratio. As can be seen from this figure the percolating percentage without particle rotation in the bed is lower than the particles under normal rotation with the entire size ratio higher than threshold, this is the evidence that the rotation of particles enhances the particle percolation. However, it is worthy to mention that the rotation of particles plays more significant role for size ratio larger than threshold as marked as a vertical dashed line in Fig. 72. This could be explained as the shear effect on percolation for larger size ratios. 0.2 0.3 Particle size ratio (-) Figure 72. Rotation effect on particle percolation 6.4 CONCLUSIONS In this work, particle percolation has been investigated in a moving packed bed by employing the discrete element method. There are two flow regions indentified in the 6-140 CHAPTER 6 INTER-PARTICLE PERCOLATION IN A MOVING BED 6-141 moving bed. The underlying percolating mechanisms in both regions have been identified through the microscopic information such as velocity filed, particle scale interaction force, internal pore structure, particle rotation etc. Moreover, the effects of well controlled parameters such as particle friction coefficients, particle charging rate, particle size ratio and density ratio have been thoroughly analyzed to understand the percolation process. The present results on the particle percolation in a moving bed lead to the following conclusions. • There are two flow zones identified in the moving bed through the analysis of the velocity profiles. Plug flow zone is in the middle and shear zones are next to the walls. • The percolation in the moving bed with size ratio smaller than threshold is happening in the whole bed cross from wall to central regions, and the percolation in the size ratio larger than threshold is only in the shear zones near the walls. • Particle percolation in a moving bed is caused by both shear and gravity force. Percolation velocity under gravity force is higher than that under shear force. • Size ratio, descending velocity, density ratio and friction coefficient play different roles in the percolation process. In particular, size ratio effect is most significant, whilst density ratio effect is limited. Friction coefficient of percolating particle is significant in smaller size ratio process. For large charging rate or large number of particles, arching effect presents. • For size ratio smaller than threshold, gravity induced percolation dominate. For size ratio larger than threshold, the effect of descending velocity is significant, shear induced percolation dominate. • Particle rotation plays an important role in particle percolation for size ratio larger than threshold. 6-141 CHAPTER 7 SUMMARY AND FUTURE WORK 7-142 CHAPTER 7 SUMMARY AND FUTURE WORK 7-142 CHAPTER 7 SUMMARY AND FUTURE WORK 7-143 The understanding of the dynamic behavior of solid flow is very important to improve the performance of blast furnace among different phases of blast fiimace process. The bulk behavior of a particle system depends on the collective interaction of individual particles. Microscopic study in terms of these interaction forces is therefore significant to understanding the mechanisms governing the dynamic behavior and producing results that can be generally used. In this work, a number of important phenomena identified in the blast furnace burden distribution, including crater formation (coke gouging), coke collapse, creep motion and particle percolation in moving bed, have been investigated by means of DEM simulations. It is shown that such DEM simulations can generate microdynamic information which is difficult to obtain experimentally but key to elucidating the fundamentals governing granular flow. The overall conclusion based on this study could be summarized as follows. Coke gouging is a kind of crater formation process seen in nature. Experimental and numerical study of the impact of a particle stream onto a particle bed has generated the following conclusions: DEM simulation can reproduce the experimental results very well. In the formation process of a crater, the depth of the crater reaches its maximum quickly, whilst the width of the crater keeps increasing for a longer time. During the impact process, most of the energy from the top layer has been dissipated eventually due to the inelastic collision and frictional contacts between impacting particles. Only a small amount of the energy is contributed to the crater formation. The orifice size, discharging height, and top and base layer materials affect the size of crater. A larger orifice size or discharging height leads to a larger crater. For a given base layer, the larger the density ratio of the top to base layer particles, the larger the crater size. However, the effect is also dependent on base layer material. Based on these considerations, the crater size is shown to be related to the ratio of the input energy from the top layer to the inertial energy from the base layer. Three different configurations: batch charging, self loading and load impact have been used to investigate the fundamentals governing coke collapse by means of DEM simulations. It is observed that collapse can be caused by continuous charging of particles and load impact. No obvious collapse has been observed in the case of self loading although the self loading 7-143 CHAPTER 7 SUMMARY AND FUTURE WORK 7-144 can also lead to the failure of the base bed. The mechanisms to cause collapse for batch charging and load impact are different. The particles in the charging area of the base bed are continuously pushed to its right side in the case of batch charging, whilst they are impacted to jump rightwards and then move along the surface of the bed to the right wall in the case of load impact, which leads to the different final profiles of the base bed for both cases. The geometrical and physical properties of particles and load also affect the collapse. In particular, the particle density ratio of top bed to base bed is an important factor to cause collapse in the case of batch charge. The larger the initial load velocity, the more the particles are pushed to the right wall in the case of load impact. Apparent frozen layer under the rapidly flowing layer is not stationary and slowly creep motion can be detected at an arbitrary depth. The mean velocity of creep motion decays exponentially with depth. The mean velocity was found to have a longer characteristic length for the rapid surface flow above the boundary than that for the creep motion, that is, the creep motion decays more rapidly as a function of the distance to pile surface than the surface flow. Increasing the flow rate can increase the thickness of the flowing layer, and slightly increase the slope angle. Creep motion is caused by the voids produced by the shear force. Velocity profile of the rapidly flowing layer is linear and is independent of flow rate. Particle percolation can be seen fi-om the whole blast furnace top to hearth. The following conclusions have been drawn through the study of particle percolation in a moving bed. Percolation happens due to both shear and gravity. Size ratio, descending velocity, density ratio and friction coefficient play different roles. In particular, size ratio effect is most significant, while density ratio effect is limited. Friction coefficient of percolating particle is significant in smaller size ratio process due to the local arching effect. For size ratio smaller than the threshold, gravity induced percolation dominate, otherwise the shear of particles due to the bed movement is significant. Particle percolate symmetrically, near the wall is faster. Percolation velocity under gravity is much greater than that under shear. For large charging rate or large number of particles, arching effect presents. Particle rotation plays an important role in particle percolation for large size ratio. 7-144 CHAPTER 7 SUMMARY AND FUTURE WORK 7-145 Future effort in the relevant area will be made to develop more robust models and efficient computer codes to investigate more complex cases, say, from mono-sized to multi-sized particles, simple spherical to complicated non-spherical particle system, small scale to large scale system, which are important to transfer the present phenomenon simulation to process simulation and hence meet real engineering needs. In addition, more phenomena involving in the blast furnace process will be studied. For example, surface flow segregation in the burden formation process will be investigated to form a more complete picture of solid flow phenomena at blast furnace top. 7-145 REFERENCES 146 REFERENCES REFERENCES 147 1. A. Thomason and G. Crest, Granular flow: fiiction and the dilatancy transition. Physical Review Letter, 1991. 67: p. 1751-1754. 2. J. A. Ferrez, Dynamic trigulations for efficient 3D simulation of granular materials. 2001, EPFL: Lausanne, Swiss. 3. D. V. Khakhar, J. J. McCarthy, T. Shibrot and J. M. Ottino, Transverse flow and mixing of granular materials in a rotating cylinder. Physics of Fluids, 1997. 9: p. 31-43. 4. P. W. Cleary, Dem Simualtion of industrial particle flows: case stuidioes of dragline excavators, mixing in tumblers and centrifugal mills. Powder Technology, 2000.109: p. 83-104. 5. S. Luding, E. Clement, A. Blumen, J. Rajchenbach and J. Duran, simulations of pattern formation in vibrated granular media. Europhysics Letters, 1996. 36: p. 247-252. 6. Y. Kaneko, T. Shiojima and M. Horio, Numerical analkysis of particle mixing characteristics in a single helical ribbon agitator using DEM simulation. Powder Technology, 2000.108: p. 55-64. 7. P. A. Langston, U. Tuzun and M. M. Heyes, discrete element simulation of interstitial air effects in axially symmetrical granular flow hoppers. Chemical Engineering Science, 1996. 51: p. 873-891. 8. G. H. Ristow, Dynamics of granular materials in a rotating drum. Europphysics Letters, 1996. 34: p. 263-268. 9. Y. Tsuji, T. Tanaka and T. Ishida, Lagrangian numerical simulation ofplug flow of cohesionless particles in a horizontal pipe. Powder Technology, 1992. 71: p. 239- 250. 10. G. D. R. Midi, On dense gmularflows, cond-mat/0312502, 2003. 11. C. H. Liu, S. R. Nagel, D. A. Schecter, S. N. Coppersmith, S. Majumdar, O. Narayan and T. A. Witten, Force fluctuation in bead packs. Science, 1995. 269: p. 513-515. 12. A. Aradian, E. Raphael and P. G. de Gennes, Thick surface flows of granular materials: Effect of the velocity profile on the avalanche amplitude. Physical Review E, 1999. 60: p. 2009-2019. REFERENCES 148 13. J. T. Jenkins and S. B. Savage, A theory for rapid flow of identical, smooth, nearly elastic spherical particles. J. Fluid Mech., 1983.130: p. 187-202. 14. A. Mehta and G. C. Barker, The dynamics of sand. Report on Progress in Physics, 1994. 57: p. 383-416. 15. D. Ertas, G. S. Grest, T.C. Halsey, D. Levine and L.E. Silbert, Gravity-driving dense granular flows, cond-mat/0005051, 2000. 16. D. M. Mueth, H. M. Jaeger and S. R. Nagel, Force distribution in a granular medium, cond-mat/9902282, 1999. 17. H. M. Jaeger and S. R. Nagel, Granular solids, liquids, and gases. Reviews of Modem Physics, 1996. 68: p. 1259-1273. 18. J. Rajchenbach, Granular flows. Advances in physics, 2000. 49: p. 229-256. 19. O. Pouliquen and F. Chevoir, Dense flows of dry granular material C.R.Physique, 2002. 3: p. 163-175. 20. S. Douady, B. Andreotti, A. Daerr and P. Clade, From a grain to avalaches: on the physics of granular surface flows. C.R.Physique, 2002. 3: p. 177-186. 21. Y. C. Zhou, B. H. Xu, A. B. Yu and P. Zulli, Numerical investigation of the angle of repose of monosized spheres. Physical Review E, 2001. 64: p. 021301. 22. O. Reynolds, On the dilatancy of media composed of rigid particles in contact. Phil. Mag., 1885.20. 23. H. M. Jaeger and S. R. Nagel, Physics of the granular state. Science, 1992. 255: p. 1523-1531. 24. Committee on Reaction within Blast Furnace, Joint Society on Iron and Basic Research and ISIJ, Blast furnace phenomena and modelling. 1987, London and New York: Elsewier Applied Science. 25. N. standish, studies of size segregation in filling and emptying a hopper, powder technology, 1985. 45: p. 43-56. 26. J. C. Williams, The Segregation of Particulate Materials. A Review. Powder Technology, 1976.15: p. 245-251. 27. Y. Kajiwara, T. Jimbo, T.Joko, Y. Aminaga and T. Inada, Investigation of bell-less charging based on full scale model experiements. Transactions ISIJ, 1984. 24: p. 799-807. REFERENCES 28. p. R. Austin, S. J. Chew, N. D. Giorgio and P. Zulli. Recent Blast furnace Burden Distribution Studies within BHP Steel, in 3rd International Conference on Science and Technology of Ironmaking Proceeding 16-20. 2003. 29. T. S. Komatsu, S. Inagaki and N. Nakagawa, Creep motion in a granular pile exihibiting steady surface flow. Physical Review Letters, 2001. 86: p. 1757-1760. 30. J. Bridgwater and N.D. Ingram, Rate of Spontaneous Inter-particle Percolation. TRANS.INSTN.CHEM.ENGRS, 1971. 49: p. 163-169. 31. J. Bridgwater and A.M. Scott, Statistical models of parking: application to gas absorption and solid mixing. TRANS.INSTN.CHEM.ENGRS, 1974. 52: p. 317-325. 32. S. K.Jung and W.S.Chung, Improvement of Gas Flow Through Analysing Discharge Behaviour in the Bunker Used in Blastfurnace. ISIJ International, 2001. 41. 33. B. D. Pandey and U. S.Yadav, Blast furnace performance as influenced by burden distribution. Ironmaking and steelmaking, 1999. 26: p. 187. 34. Y. Kajiwara, T. Inada and T. Tanaka, Two Dimesional Analysis on the formation Process of Burden Distribution at Blast Furnace top. Transactions ISIJ, 1988. 28: p. 916-925. 35. K. Narita, S. Inaba, I. Kobayashi, K. Okmoto, M. Shimizu, T. Yabata and S. Tamada, Study of Ore and Coke Distribution in Blast Furnace Carried Out on a Full Size Model. Transactions ISIJ, 1979.19. 36. K. Narita, S. Inaba, I. Kobayashi, K. Okmoto, M. Shimizu, K. Kuwano and K. Ikeda, Relationship of the Gas Temperature Distribution with the Descending Rate and Layer Thickness of Burden in the Throat of Blast Furnace. Transactions ISIJ, 1979.19: p. 659-666. 37. K. L. Hockings, J. M burgess, J. Monaghan, L. Jelenich, P. Zulli and F. Tanzil, Application of "RABIT" burden distribution model to BHP blast furnaces. Ironmaking conference proceedings, 1988: p. 289-296. 38 M. Ichida, K. Nishihara, K. Tamura, M. sugata and H. Ono, Influence of ore/coke distribution on descending and melting behaviour of burden in blastfurnace. ISIJ International, 1991. 31: p. 505-514. REFERENCES 39. M. Ichida, M. Takao, K. Kunitomo, S. Matsuzaki, T. Deno and K. Nishihara, Radial distribution of Burden Descent velocity near Burden surface In Blast furnace. ISIJ International, 1996. 36: p. 493-502. 40. J. Jimenez, J. Mochon, A. Formoso and J. S. Ayala, Burden Distribution Analysis by Digital Image Processing in a Scale Model of a Blast Furnace Shaft. ISIJ International, 2000. 40: p. 114-120. 41. M. Hattori, B. lino, A. Shimimura, H. Tsukiji and T.Ariyama, Development of burden distribution simulation model for bell -less top in a large blast furnace and its application. ISIJ International, 1993. 33. 42. Y. Kajiwara, T. Jimbo, T. Joko, Y. Aminaga and T. Inada, Investigation of bell-less charging based on full scale model experiements. Transactions ISIJ, 1984. 24: p. 799-807. 43. Y. Okuno, K. Kunimoto, S. Matsuzaki, M. Matsui and A. Suzawa. Development of a mathematical model for burden distribution in a blast furnace, in Proc. Ironmaking Conf 1985. 44. G. Heynert and J. Willems, StahlEisen, 1959. 79: p. 1545. 45. K. L. Johnson, Contact Mechanics, 1985: Cambridge University Press, Cambridge. 46. A. D. Salman, C. A. Biggs, J. Fu, I. Angyal, M. Szabo and M. J. Hounslow, An experimental investigation of particle fragmentation using single particle impact studies. Powder Technology, 2002. 128: p. 36-46. 47. A. Ema, D. Yasuda, K. I. Tanoue and H. Masuda, Tribo-charge and rebound characteristics of particles impact on inclined or rotating metal target. Powder Technology, 2003.135-136: p. 2-13. 48. K. Tanaka, M. Nishida, T. Kunimochi and T. Takagi, Discrete element simulation and experiment for dynamic response of two-dimensional granular matter to the impact of a spherical projectile. Powder Technology, 2002. 124: p. 160-173. 49. C. E. Davies, G. Weir and P. McGavin, The behavior of a dense stream of non- cohesive particles impacting on an inclined plate. Powder Technology, 1999. 106: p. 1-6. 50 C. Thornton and K. K. Yin, Impact of elastic spheres with and without adhesion. Powder Technology, 1991.65: p. 153-166. REFERENCES M 51. C. Thornton, M. T. Ciomocos and M. J. Adams, Numerical simulation of agglomerate impact breakage. Powder Technology, 1999. 105: p. 74-82. 52. R. Moreno, M. Ghadiri and S. J. Antony, Effect of the impact on the breakage of agglomerates: a numerical study using DEM. Powder Technology, 2003. 130: p. 132-137. 53. O. Pouliquen and N. Renaut, Onset of granular flows on an inclined rough surface: Dilatancy effects. J.Phys.II France, 1996. 6: p. 923-935. 54. L.E.Silbert, D.Ertas, G.S.Grest, T.C.Halsey, D.Levine and S.J.Plimpton, Granular flow down an inclined plane: Bagnold scaling and rheology. cond-mat/0105071, 2001. 55. P. A. Lemieux and D. J. Durian, From Avalanches to fluid flow: A continuous picture of grain dynamics down a heap. Physical Review Letters, 2000. 85: p. 4273- 4276. 56. D. V. Khakhar, A. V .Orpe, P. Andresen and J. M. Ottino, surface flow of granular materials:model and experiments in heap formation. J.Fluid Mech., 2001. 441: p. 255-264. 57. B. Andreotti and S. Douady, Selection of velocity proflle and flow depth in granular flows. Physical Review E, 2001. 63: p. 1-8. 58. R. A. Bagnold, Experiemtns on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear. Proc. R. Soc. Lond., 1954. A 255: p. 49-63. 59. S. B. Savage and K. Hutter, J. Fluid Mech., 1989. 199: p. 177. 60. M. E. Gates, J. P. Wittmer, J. P. Bouchaud and P. Claudin, Jamming, Force Chains, and Fragile Matter Physical Review Letters, 1998. 81: p. 1841-1844. 61. J. P. Bouchaud, M. E. Gates, J. R. Prakash and S. F. Edwards, A model for the sand pile surface. J.Phys.I France, 1994. 4: p. 1383-1410. 62. H. M. Jaeger and S. R. Nagel, Granular solids, liquids, and gases. Reviews of Modem Physics, 1996. 68: p. 1259-1273. 63. T. Boutreux, E. Raphael and P.-G. d. Gennes, Surface flows of granular mixtures:!. General principles and minimal model. J. Phys. I France, 1996. 6: p. 1295-1304. REFERENCES 152 64. A. Aradian, E. Raphael and P.-G. d. Geimes, Thick surface flows of granular materials: Effect of the velocity profile on the avalanche amplitude. Physical Review E, 1999. 60: p. 2009-2019. 65. S. Douady, B. Andreotti and A. Daerr, On granular surface flow equations. Eur. Phys.J. B, 1999.11: p. 131-142. 66. D. Bonamy, F. Daviaud, L. Laurent, M. bonetti and J.-P.Bouchaud, Multiscale Clustering in Granular Surface Flows. Physical Review Letters, 2002. 89: p. 034301-4. 67. P. A. Lemieux and D.J. Durian, From Avalanches to fluid flow: A continuous picture of grain dynamics down a heap. Physical Review Letters, 2000. 85: p. 4273- 4276. 68. T. Boutreux, E. Raphael and P.O. de Gennes, Surface flows of granular materials: A modified picture for thick avalanches. Physical Review E, 1998. 58: p. 4692-4700. 69. O. Pouliquen and N. Renaut, Onset of granular flows on an inclined rough surface: Dilatancy effects. J.Phys.II France, 1996. 6: p. 923-935. 70. A. V. Orpe and D. V. Khakhar, Scaling relations for granular flow in quasi-two- dimensional rotating cylinders. Physical Review E, 2001. 64: p. 031302. 71. N. Jain, J.M. Ottino and R.M. Lueptow, An Experimental Study of the Flowing Granular Layer in a Rotating Tumbler. Physics of Fluids, 2002.14: p. 572-582. 72. R. L.Brown, J.Inst.Fuel, 1939.13: p. 15. 73. J. C. Williams, Chemical Processing, April 1963: p. s6. 74. J. C.Williams, Fuel Soc. J., Univ.of Sheffield, 1963. 14: p. 29. 75. J. F. G.Harris and A. M. Hildon, Ind.Eng.Chem. Proc.Des., 1970: p. 363. 76. J. A. Drahun and J. Bridgwater, The Mechanisms of Free surface Segregation. Powder Technology, 1983. 36: p. 39-53. 77. M. ^odQS, Introduction of Particle Technology (book). 78. M. Propster and J. Szekely, The Porosity of Systems Consisting of Layers of Different Particles. Powder technology, 1977.17: p. 123-138. 79. J. Bridgwater, N.W. Sharpe and D.C. Stocker, Particle Mixing by Percolation. TRANS.INSTN.CHEM.ENGRS, 1969. 47: p. T114-Tl 19. REFERENCES 80. p. Richard, L. Oger, J. Lemaitre, L. Samson and N. N. Medvedev, Application of the Voronoi tessellation to study transport and segregation of grains inside 2D and 3D packings of spheres. Granular Matter, 1999. 1: p. 203-211. 81. L. Oger and F. Lomine. Particle percolation through a porous medium, in Powders & Grains. 2005: Taylor &Francis Group, London. 82. A. M. Scott and J. Bridgwater, Self diffusion of spherical particles in a simple shear apparatus, powder technology, 1976.14: p. 177-183. 83. M. H. Cooke, J. Bridgewater and A.M. Scott, Interparticle percolation: Lateral and axial diffusion coefficients. Powder Technology, 1978. 21: p. 183-193. 84. S. P. Duffy and V.M. Pun, Primary Segregation Shear Cell for Size-Segregation Analysis of Binary Mixtures. KONA (powder and particle), 2002. 20: p. 196-207. 85. S. P. Duffy and V.M. Puri, Development and Validation of a Constitutive Model for Size-Segregation during Percolation. KONA (powder and particle), 2003. 21: p. pl51-162. 86. C. S. Campbell, Powder Technology Handbook. Computer simulation of powder flows. 1996. 87. A. Rosato and F. Prinz, Monte Carlo simulation of particulate matter segregation. Powder Technology, 1986. 49: p. 59. 88. P. Meakin and R. Jullien, Simple models for two or three dimensional particle size segregation, physica A, 1992.180: p. 1-18. 89. D. Cahn and D. Fuerstenan, Simulation of diffusion mixing of particulate solids by Monte Carlo techniques, powder Technology, 1967. 1: p. 174-182. 90. C. Prado and Z. Olami, Inertia and break of self-organized criticality in sandpile cellular-automata models. Physical Review E. 45: p. 665-669. 91 G. Baxter and R. Behringer, Automata models for the flow of granular materials. physica D, 1991. 51: p. 465-471. 92 A Mehta and G. C. Barker, The dynamics of sand. Report on Progress in Physics, 1994. 57: p. 383-416. 93 P. A. Cundall and O. D. L. Strack, A discrete numerical model for granular assemblies. Geotechnique, 1979. 29: p. 47-65. references 15^ 94. A. Di Renzo and F.P.Di Maio, Comparison of contact-force models for the simulation of collisions in DEM-based granular flow codes. Chemical Engineering Science, 2004. 59: p. 525-541. 95. R. D. Mindlin and H. Deresiewicz, J. Appl. Mech., 1953. 20: p. 327. 96. H. Hertz, Über die Berührung fester elastischer Körper. Journal fur die reine und angewandte Mathematik, 1882. 92: p. 156-171. 97. L. Vu-Quoc and X.Zhang, An accurate and efficient tangential force-displacement model for elastic frictional contact in particle-flow simulations. Mechanics of Materials, 1999a. 31: p. 235-269. 98. L. Vu-Quoc and X.Zhang. An elastoplastic contact force-displacement model in the normal direction, displacement-driven version, in Proceedings of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences 455. 1999b. 99. O. R.Walton and R.L. Braun, Viscosity, granular-temperature, and stress calculations for shearing assemblies of inelastic, frictional disks. Journal of Rheology, 1986a. 30: p. 949-980. 100. O.R.Walton, Numerical simulation of inclined chute flows of monodisperse inelastic, frictional spheres. Mechanics of Materials, 1993. 16: p. 239-247. 101. P. A. Langston and U.Tuzun, continuous Potential Discrete Particle Simulations of Streess and Velocity Fields in Hoppers- Transition from Fluid to Granular flow. Chemical Engineering Science, 1994. 49: p. 1259-1275. 102. P. A. Langston, U. Tuzun and M. M. Heyes, discrete element simulation of granular flow in 2d and 3d hoppers-dependence of discharge rate and wall stress on particle interactions. Chemical Engineering Science, 1995. 50: p. 967-987. 103. Y. C. Zhou, W. D. Wright, R. Y. Yang, B. H.Xu and A. B.Yu, Rolling friction in the dynamic simulation of sandpile formation. Physica A, 1999. 269: p. 536-553. 104. Y. C. Zhou, Granular Dynamics with Special Reference to Piling and Mixing Process. 2002, UNSW: Sydney. 105. H. P. Zhu and A.B. Yu, Averaging method of granular materials, physical Review E, 2002. 66: p. 021302. 106 J. Schäfer, S. Dippel and D.E. Wolf, Force schemes in Simulations of Granular Materials. Journal de Physique I, 1996. 6: p. 5-20. REFERENCES 15^ 107. M. Látzel, S. Luding and H. J. Hermann, Macroscopic material properties from quasi-static, microscopic simulations of a two-dimensional shear-cell Granular Matter, 2000. 2: p. 123-135. 108. J. A.Greenwood, H. Minshall and D. Tabor. Hysteresis losses in rolling and sliding friction, in Proceedings of the Royal Society of London Series A-Mathematical and Physical Sciences. 1961. 109. N. V. Brillianton and T. Poschel, Rolling friction of a viscous sphere on a hard plane. Europhysics Letters, 1998. 42: p. 511. 110. L. Kondic, Dynamics of spherical particles on a surface, Collision-induced sliding and other effects. Physical Review E, 1999. 60: p. 751-770. 111. K. Iwashita and M. Oda, Rolling resistance at contacts in simulation of shear band development by DEM. Journal of Engineering Mechanics-ASCE, 1998. 124: p. 285- 292. 112. H. P. Zhu and A.B.Yu, A theoretical analysis of the force models in discrete element method. Powder Technology, 2006.161: p. 122-1290. 113. C. Goldenberg and I.Goldhirsch, Friction enhances elasticity in granular solids. Nattire, 2005. 435: p. 188-190. 114. Y. C. Zhou, A.B. Yu, R.L. Stewart and J. Bridgwater, Microdynamic analysis of the particle flow in a cylindrical bladed mixer. Chemical Engineering Science, 2004. 59: p. 1343- 1364. 115. H. H. Hausner, Ejfect of quench sintering on the grain structure of sintered metal. International Journal of Powder Metallurgy, 1972. 8: p. 159-161. 116. L. Svarovsky, Powder Testing Guide: Methods of Measuring the Physical Properties of Bulk Powders. 1987, London: Elsevier Applied Science. 117. D. Geldart and A.C.Y.Wong, Fluidization of Powders Showing Degrees of Cohesiveness.l. Bed Expansion. Chemical Engineering Science, 1984. 39: p. 1481- 1488. 118. D. Geldart and A.C.Y. Wong, Fluidization of Powders Showing Degrees of Cohesiveness.2. Experiments on Rates of De-Aeration. Chemical Engineering Science, 1985.40: p. 653-661. REFERENCES 119. A. B. Yu and J.S.Hall, Packing of fine powders subjected to tapping. Powder Technology, 1994: p. 247-256. 120. H. C.Hamaker, The london-van der waals attraction between spherical particle. Physica (Amsterdam), 1937. 4: p. 1058-1072. 121. J. N. Israelachvili, Intermolecular and surface forces. 1991, London: Academic Press. 122. H. Krupp, Particle adhesion theory and experiment. Advances in Colloid and Interface Science, 1967. 1: p. 111-239. 123. R. A. Fisher, On the capillary forces in an ideal soil, correction of formulate given by W.B. Haines. Journal of Agricultural Science, 1926.16: p. 492-505. 124. H. M. Princen, The effect of capillary liquid on the force of adhesion between spherical solid particles-comments. Journal of Colloid and Interface Science, 1968. 26: p. 249-253. 125. G. Lian, C. Thornton and M. J.Adams, A theoretical study of the liquid bridge forces between two rigid spherical bodie. Journal of Colloid and Interface Science, 1993.161: p. 138-147. 126. K. Z. Y. Yen and T. K. Chaki, A dynamic simulation of particle rearrangement in powder packings with realistic interactions. Journal of Applied Physics, 1992. 71: p. 3164-3173. 127. Z. P. Zhang, L.F.Liu, Y.D.Yuan and A.B.Yu, A simulation study of the effects of dynamic variables on the packing of spheres. Powder Technology, 2001. 116: p. 23- 32. 128. L. E. Silbert, D.Ertas, G.S.Grest, T.C.Halsey and D.Levine, Geometry of frictionless and frictional sphere packings. Physical Review E, 2002a. 65: p. 031304/1-6. 129 L. E. Silbert, G.S.Grest and J.W.Landry, Statistics of the contact network in frictional and frictionless granular packings. Physical Review E, 2002b. 66: p. 061303/1-9. 130 G. A. Kohring, S. Melin, H. Puhl, H. J. Tillemans and W. Vermohlen, Computer- simulations of critical nonstationary granular flow - through a hopper. Computer Methods in Applied Mechanics and Engineering, 1995.124: p. 273-281. REFERENCES \51_ 131. J. M. Rotter, J. M. F. G.Holst, J. Y. Ooi and A. M. Sanad, Silo pressure predictions using discrete-element and finite-element analyses. Philosophical Transactions of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences, 1998. 356: p. 2685-2712. 132. H. Sakaguchi, E. Ozaki and T. Igarashi, Pluging of the flow of granular materials during the discharge from a silo. International Journal of Modem Physics B, 1993. 7: p. 1949-1963. 133. L. F. Liu, Simulation of microstructural evolution during isostatic compaction of monosized spheres. Journal of Physics D-Applied Physics, 2003. 36: p. 1881-1889. 134. H. P. Zhang and H. A. Makse, Jamming transition in emulsions and granular materials. Physical Review E, 2005. 72: p. 011301. 135. S. Luding, Stress distribution in static two-dimensional granular model media in the absence of friction. Physical Review E, 1997. 55: p. 4720-4729. 136. J.Lee and H. J.Herrmann, Angle of repose and angle of marginal stability - molecular-dynamics of granular particles. Journal of Physics A-Mathematical and General, 1993. 26: p. 373-383. 137. K.Liffman, M.Nguyen, G.Metcalfe and P.Cleary, Forces in piles of granular material, an analytic and 3D DEM study. Granular Matter, 2001. 3: p. 165-176. 138. H. G.Matuttis, S.Luding and H. J.Herrmann, Discrete element simulations of dense packings and heaps made of spherical and non-spherical particles. Powder Technology, 2000. 109: p. 278-292. 139. J. Gallas, H. Herrmann and S. Sokotowski, convetion cells in vibrating granular media. Physical Review Letters, 1992. 69: p. 1371-1374. 140. B. H. Xu and A.B. Yu, Chemical Engineering Science, 1998. 53: p. 2646. 141. G. J. Weir, The fundamental modes of mixing of granular materials in slowly rotating cylinders. Waves in Random Media, 1999. 9: p. 463-476. 142. S. Masson and J. Martinez, Multiscale simulations of the mechanical behaviour of an ensiled granular material. Mechanics of Cohesive-Frictional Materials, 2000b. 5: p. 425-442. REFERENCES \5S 143. S. Lobo-Guerrero and L.E.Vallejo, Discrete element method evaluation of granular crushing under direct shear test conditions. Journal of Geotechnical and Geoenvironmental Engineering, 2005.131. 144. Z. Yi and C. S. Campbell, The interface between fluid-like and solid-like behavior in 2-dimensional granular flows. Journal of Fluid Mechanics, 1992. 237: p. 541-568. 145. M. Babic, Unsteady Couette granular flows. Physics of Fluids, 1997a. 9: p. 2486- 2505. 146. R.Y. Yang, R.P. Zou and A. B. Yu, Microdynamic analysis of particle flow in a hrozontal rotaingdrum. Powder Technology, 2003. 130: p. 138-146. 147. V. Buchholtz, T. Poschel and H.J. Tillemans, Simulation of rotating drum experiments using noncircularparticles, physica A, 1995. 216: p. 192-212. 148. N. Taberlet and V.^Qhdccá.Diffusion of a granular pulse in a rotating drum. Physical Review E, 2006. 73: p. 041301/1-6. 149. B. K. Mishra and R.K.Raiamani., Motion analvsis in tumbling mills by the discrete element method. KONA, Powder and Particle, 1990. 8: p. 92-98. 150. B. K. Mishra and R.K.Rajamani, The discrete element method for the simulation of ball mills. Applied Mathematical Modelling, 1992.16: p. 598-604. 151. T. Inoue and K. Okaya, Grinding mechanism of centrifugal mills - A simulation study based on the discrete element method. International Journal of Mineral Processing, 1996. 44: p. 425-435. 152. S. Agrawala, R. K. Rajamani, P. Songfack and B. K. Mishra, Mechanics of media motion in tumbling mills with 3D discrete element method. Minerals Engineering, 1997.10: p. 215-227. 153. P. R. Austin, S. J. Chew, N. D. Giorgio and P. Zulli, Recent Blast furnace Burden Distribution Studies within BHP Steel. 3rd International Conference on Science and Technology of Ironmaking Proceeding 16-20, June 2003: p. 598-604. 154. L. S. Tsimring and D. Volfson. Modeling of impact cratering in granular media, in Powders and Grains. 2005. Balkema, Rotterdam: Taylor & Francis Group. 155. R. Zenit and M. L. Hunt, Mechanics of immersed particle collisions. ASME J. Fluids Eng., 1999.121: p. 179-184. REFERENCES I59 156. J. Zhang, L. S. Fan, C. Zhu, R. Pfefer and D. Qi, Dynamic behavior of collision of elastic spheres in viscous fluids. Powder Technology, 1999.106: p. 98-109. 157. L.Y. Li, C. Thornton and C. Y. Wu, Impact behaviour of elastic spheres with a rigid wall Proc. Instn. Mech. Engrs., 1999. 214: p. 1107-1114. 158. A. D. Salman, C.A. Biggs, J. Fu, I. Angyal, M. Szabo and M.J. Hounslow, An experimental investigation of particle fragmentation using single particle impact studies. Powder Technology, 2002.128: p. 36-46. 159. K.Tanaka, M. Nishida, T. Kunimochi and T.Takagi, Discrete element simulation and experiment for dynamic response of two-dimensional granular matter to the impact of a spherical projectile. Powder Technology, 2002. 124: p. 160-173. 160. J. S. Uehara, M. A. Ambroso, R. P. Ojha and D. J. Durian, Low-Speed Impact Craters in Loose Granular Media. Phys. Rev. Lett., 2003. 90: p. 194301. 161. M. A. Ambroso, C. R. Santore, A. R. Abate and D. J. Durian, Penetration depth for shallow impact cratering. Phys. Rev. E., 2005. 71: p. 051305. 162. M. P. Ciamarra, A. H. Lara, A. T. Lee, D.l. Goldman, I. Vishik and H. L. Swinney, Dynamics of Drag and Force Distributions for Projectile Impact in a Granular Medium. Phys. Rev. Lett., 2004. 92: p. 194301. 163. A. M. Walsh, K. E. Holloway, P. Habdas and J. R. de Bmyn, Morphology and Scaling of Impact Craters in Granular Media. Phys. Rev. Lett., 2003. 91: p. 104301. 164. K.L. Johnson, Contact Mechanics. 1985: Cambridge University Press, Cambridge. 165. R.D. Mindlin and H. Deresiewicz, Spheres in Contact under Varying Oblique Forces. J.Appl. Mech. Trans.ASME, 1953. 20: p. 327. 166. Y. Grasselli and H. J. Herrmann, Crater formation on a three dimensional granular heap. Granular Matter, 2001. 3: p. 201-204. 167. H. P.Zhu and A. B. Yu, Steady-state granular flow in a three-dimensional cylindrical hopper with flat bottom: microscopic analysis. Journal of Physics D: Applied Physics, 2004. 37: p. 1-13. 168. C.Thomton, M.T. Ciomocos and M.J. Adams, Numerical simulation of agglomerate impact breakage. Powder Technology, 1999.105: p. 74-82. REFERENCES 160 169. P. A. Langston, U.Tuzun and M. M. Heyes, discrete element simulation of granular flow in 2d and 3d hoppers-dependence of discharge rate and wall stress on particle interactions. Chemical Engineering Science, 1995. 50: p. 967-987. 170. T. Nouchi, A.B. Yu and K. Takeda, Experimental and numerical investigation of the effect of buoyancy force on solid flow. Powder Technology, 2003. 134: p. 98- 107. 171. B. N. Asmar, P.A. Langston, A.J. Matchett and J. K. Walters, Validation tests on a distinct element model of vibrating cohesive particle systems. Computers and Chemical Engineering, 2002. 26: p. 785-802. 172. Y. C. Zhou, W. D. Wright, R.Y. Yang, B.H.Xu and A.B.Yu, Rolling friction in the dynamic simulation of sandpile formation. Physica A, 1999. 269: p. 536-553. 173. W. A. Beverloo, H.A. Leninger and J. Van de Velde, The flow of granular solids through orifices. Chem. Eng. Sci., 1961. 15: p. 260. 174. Z. Z. Luo, Application of Powder Mechanics on the Burden Distribution of A Bell - less Top Blast Furnace, in Chemical Engineering. 1988, Taiwan Institute of Technology: Taipei, p. 136. 175. G. C.Barker and A.Mehta, Two types of avalanche behavoir in model granular media. Physical A, 2000. 283: p. 328-336. 176. G. D .R.Midi, On dense grnularflows, cond-mat/0312502, 2003. 177. I. S. Aranson and L.S.Tsimring, Continuum description of avalanches in a grnular media. Physical Review E, 2001. 64: p. 1-4. 178. J. Rajchenbach, development of Grain Avalanches. Physical Review Letters, 2002. 89: p. 1-4. 179. S. M.Wu, H.P.Zhu, A.B. Yu and P. Zulli, Numerical Investigation of Crater Phenomena in a Particle Stream Impact onto a Granular Bed. Granular Matter, 2007. 9: p. 7-17. 180. H. P. Zhu and A. B.Yu, The effect of wall and rolling resistance on the couple stress of granular materials in vertical flow. Physica A, 2003. 325: p. 347-360. 181. T. Boutreux, E.Raphael and P.-G. d. Gennes, Surface flows of granular materials: A modified picture for thick avalanches. Physical Review E, 1998. 58: p. 4692-4700. REFERENCES 182. L. Samson, Analyse de l'écoulement d'un grain dans des systèmes désordonnés bi-et tridimensionnels. 1997, Université de Rennes 1. 183. R. Gutfraind and O. Pouliquen, Study of the origin of shear zones in quasi-static vertical chute flows by using discrete particle simulations. Mechanics of Materials, 1996. 24: p. 273-285. 184. K. Shinohara and J. Saitoh, ISIJ International, 1993. 33: p. 672-680. 185. O. Pouliquen and R. Gutfraind, stress fluctuations and shear zones in quasistatic granular chute flows. Physical Review E, 1996. 53: p. 552-561. APPENDIX 162 APPENDIX PAPERS IN THE PROCESS OF PUBLICATION APPENDIX 163 l.S.M.Wu, H.P.Zhu, A.B. Yu and P. Zulli, Numerical Investigation of Crater Phenomena in a Particle Stream Impact onto a Granular Bed Granular Matter, 2007. 9: p. 7-17 2. S.M.WU, H.P.Zhu, A.B. Yu and P. Zulli, Impact of Solid Flow on a Granular Bed. Fifth World Congress on Particle Technology, April 2006, Orlando, Florida, USA. 3. S.M.Wu, H.P.Zhu, A.B. Yu and P. Zulli, Numerical Study of Coke Collapse by Discrete Element Method, Discrete Element Methods 07, August 27-29, 2007, Brisbane, Australia. 4. C.K. Ho, S.M. Wu, H.P. Zhu, A.B. Yu and S.T. Tsai, Experimental and numerical investigations of gouge formation related to blast furnace burden distribution. Mineral Engineering, (in press). 5. S.M. Wu, H.P. Zhu, A.B. Yu, A. de Ryck and P. Zulli, DEM simulation of granular flows on a heap. Powder and Grains 09, (in press). 6. S.M.Wu, H.P.Zhu, A.B. Yu and P. ZuUi, Study of Coke Collapse Phenomenon by DEM (to be submitted) 7. S.M.Wu, H.P.Zhu, A.B. Yu and P. Zulli, Inter-particle percolation in a moving bed (to be submitted)