Application of GPU-DEM simulation on large-scale granular handling and processing in ironmaking related industries

PTEC-14603; No of Pages 16 Powder Technology xxx (2019) xxx

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Powder Technology journal homepage: www.elsevier.com/locate/powtec

Application of GPU-DEM simulation on large-scale granular handling and processing in ironmaking related industries Jieqing Gan a,⁎, Tim Evans b, Aibing Yu a,c a b c

Laboratory for Simulation and Modelling of Particulate Systems, Department of Chemical Engineering, Monash University, Clayton, VIC 3800, Australia Rio Tinto Iron Ore Group, Australia Monash University - Southeast University Joint Research Institute, Suzhou Industrial Park, 210008, China

a r t i c l e

i n f o

Article history: Received 12 June 2019 Received in revised form 14 August 2019 Accepted 16 August 2019 Available online xxxx Keywords: GPU- DEM Large-scale Granular handling and processing Ironmaking industry

a b s t r a c t Graphics processing unit (GPU)-based DEM combined with message passing interface (MPI) has been applied to large-scale handling and processing systems, including granular conveying, reclaiming, screening, ship loading, grab and screw unloading, and blast furnace top charging systems. The issues in terms of particle flow behaviour, particle-wall interaction/wall stress, particle energy dissipation, size segregation, and process efficiency, etc., are discussed. The results showed that for a belt conveying chute, wear became more severe at higher flow rates. In the reclaiming process, there was an increase in the digging resistance on the buckets with increasing bucket rotation speed. For the screening process, lower vibrating frequency lead to a higher screening efficiency, but also higher wall stresses. In a ship loading process, particle streams with a wide size distribution provided a significant cushioning effect on particle degradation, and when the dropping height reduces, the dissipated energy by particleparticle impacts greatly reduced. For a grab unloader, particle velocities became smaller with an increase in grab close time with tangential stresses only slightly reduced within the close time range considered. An increase of rotational speed of the bottom blades of a screw unloader indicated a higher unloading efficiency. A full blast furnace top charging process model was also developed. Size segregation was observed at different stages of the charging process. This paper demonstrated that GPU-based DEM can be successfully applied to the whole granular process chain of ironmaking related industries at different scales and provide guidelines for the key issues in different processes. © 2019 Elsevier B.V. All rights reserved.

1. Introduction Between the mine and end user, lump material is subject to a number of mechanical actions including [1]: 1) at the mine site - crushing and screening, conveying, stockpiling and rail wagon loading; and 2) at the port - rail wagon unloading, conveying, screening, stockpiling, reclaiming and ship loading. At the end user, for example, the blast furnace, lump material is still subject to a series of handling processes such as conveying, screening and blast furnace top charging. The flow behaviour of particulate materials plays a critical role in these processes. For example, in a belt conveying system, packing on the belt and blocking at the transfer points could occur if the particle flow is not smooth. Wear and degradation are common problems existing in material handling caused by normal and tangential stresses between granular material and equipment wall. Getting insight into the granular flow fundamentals such as interparticle/particle-wall interactions and energy dissipation helps to provide guidelines to some process bottleneck ⁎ Corresponding author. E-mail address: [email protected] (J. Gan).

problems. Moreover, small reductions in energy consumption or increases in output represent significant financial benefits for plant owners [2]. Discrete element method (DEM) is a numerical modelling technique which is ideal for solving engineering problems which exhibit discontinuous behaviour as the motion and interaction of each individual discrete particle or cluster of particles are explicitly modelled [3]. Although it is a computationally intensive technique where simulation times are governed by contact detection algorithms, contact models, the size and number of particles, the size of the simulation domain and computational resources (i.e. parallel processing and memory), DEM has proven to be an optimal design tool and has increasingly played significant role in material handling equipment [4]. This approach has been successfully used in processes such as conveyor transfer chutes [5–8], grinding, size segregation in hopper flow [9], burden distribution [10,11], horizontal [12], inclined [13] and vertical screw conveyor [14]. Some of the key problems in these processes have been investigated. For example, Xie et al. [7] investigated the effects of particle size, feed rate, belt speed and chute structure on

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J. Gan et al. / Powder Technology xxx (2019) xxx Table 2 Particle properties and operation condition settings in DEM simulations of belt conveying chutes.

Fig. 1. Flowchart of DEM implementation on CPU and GPU.

Table 1 Specification of different GPU graphic processors. Model name

Tesla K20 m

Tesla K80

Tesla P100

Tesla V100

Memory clock, GHz Maximum bandwidth, GB/s Peak performance of double precision, TFlops

2.6 208 1.170

5 480 2.91

715 732.2 4.763

876 897.0 7.066

Parameters

Value

Particle diameters, mm Particle density, kg/m3 Belt width, mm Belt speed, m/s Flow rate, ton/h

15–30 5170 450 5.0 700–1500

the granular velocity distributions and the impact force on the pipes and belts for conveyor transfer chutes. Very few DEM studies had been done on the excavating or reclaiming processes. For the process of excavator bucket filling [15], the flow patterns of material entering the bucket, drag force acting on bucket due to material interaction, energy requirements and the bucket fill rates were studied. Yang et al. [16] used the commercial software EDEM to simulate the reclaiming process of the bucket wheel mechanism under different rotational speeds. By contrast, a number of DEM studies had been conducted for the screening processes. For example, Dong et al. [17] used DEM to simulate the particle flow in typical multi-deck banana screens and study the effects of vibration conditions and geometry of the screen on the sieving processes. Cleary et al. [18] used DEM to simulate a full industrial scale double deck banana screen for a range of accelerations. The nature of the particle flow through this complex machine was explored for a range of peak accelerations. Later, Jahani et al. [19] investigated the screening performance of an industrial double-deck banana screen using the DEM solver ‘LIGGGHTS’. Effects of design parameters and operational parameters are examined. Recently, Ahad et al. [20] studied the effects of various design and operating variables on the efficiency of screening in industrial vibrating screens using DEM. Also, very limited DEM studies could be found for the loading and unloading processes. Mei [21] studied the vertical conveying mechanism and the variation law of conveyor design parameters and performance parameters for a screw unloading system. Many studies had also been conducted from small scale to large scale for the burden distribution in blast furnace top charging systems. For example, Liu et al. [11] studied the effects of particle shape, chute angle and friction coefficients on burden distribution. Wu et al. [22] established a three dimensional model to investigate the effects

Speed-up ratio to a single CPU

1200

Elapsed time per step [s]

1

0.1

0.01

1000 800 600 400 200 0

1E-3

CPU

K20m

K80

GPU graphic processor

(a)

P100

V100

K20m

K80

P100

V100

GPU graphic processor

(b)

Fig. 2. (a) The elapsed time per second with CPU and GPU, and (b) speedup ratio of different GPU graphic processors to a single CPU for the homogenous case of packing in a rectangular box with 300,000 spheres.

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Fig. 3. Snapshot of a belt conveying process at flow rate = 1000 ton/h and t = 11.06 s: coloured by (a) particle velocity Vp, (b) particle diameter dp, and (c) particle-wall force/gravity |Fpw|/|mg|.

of various variables on particle size segregation in and out of the hopper, as well as on the discharging sequence. Zhang et al. [23] used DEM to analyse the flow and segregation of particles in a charging process from the weighing hopper to the top layer of a blast furnace. Mio et al. [24] developed a particle flow simulator for a full blast furnace charging process using DEM. These above-mentioned processes are all featured with large scale, complicated wall geometries, and complex moving wall boundaries. However, most of the studies focused on the particle flow behaviour, and less attention was paid to inter-particle and particle-wall interactions and energy dissipation which are closely related to process continuity and smoothness of operation, equipment wear and energy consumption. On the other hand, despite the increasing application of DEM in granular flow in different processes, further development of

DEM technology is required to enhance its applicability to real-world industrial problems. One particular area of importance involves the simulation of large-scale geometrically complex systems. In recent years, Graphics Processing Units (GPUs) - based DEM has been increasingly applied in various scientific and industrial fields [25–34]. The overall speedup ratio of GPU parallel codes to its serial CPU counterparts are reported to be from several times to tens of times depending on the force models [35] and friction models [26,28,36]. The combined GPU and message passing interface (MPI) technology [26,37,38] was also developed to achieve a higher speedup ratio for a larger number of particles. In this work, GPU-based DEM combined with MPI was applied to study granular flow in different granular handling and processing systems related to the ironmaking industry. These processes include

Fig. 4. Particle-wall force/gravity |Fpw|/|mg| at different flow rates and t = 11.06 s: (a) 700 ton/h, (b) 1000 ton/h and (c) 1500 ton/h.

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0.08 particle-particle, 700 ton/hr particle-particle, 1000 ton/hr particle-particle, 1500 ton/hr

Impact energy dissipation (J)

0.07

2. Simulation methods and conditions

particle-wall, 700 ton/hr particle-wall, 1000 ton/hr particle-wall, 1500 ton/hr

2.1. DEM governing equations

0.06

According to the DEM, a particle in a particle system can have two types of motion: translational and rotational, which are determined by Newton's second law of motion. The governing equations for the translational and rotational motion of particle i with radius Ri, mass mi, and moment of inertia Ii can be written as

0.05 0.04 0.03

mi

0.02

kc   dVi X ¼ f c;ij þ f d;ij þ mi g dt j¼1

ð1Þ

0.01 0.00

and 0

2

4

6

8

10

12

Time (s) Fig. 5. Impact energy dissipation by particle-particle and particle-wall collision at different flow rates.

Table 3 Material properties of particle and geometry [16]. Items

Parameters

Value

Iron ore particles

Density, kg/m3 Young's modulus, Pa Size, mm Weight fraction, % Particle number, million Uniform rotational speed, rpm Uniform translational speed, m/s Bucket wheel diameter, mm Volume of bucket V, m3 Number of bucket z

3380 107 15, 20, 25, 30 10, 40, 40, 10 1.15 4, 5, 8 0.0147 9000 1.23 9

Operation conditions Geometry

granular conveying, reclaiming, screening, ship loading and unloading, and blast furnace top charging systems. The particle flow pattern, particle velocity, inter-particle forces, particle-wall forces and energy dissipation were studied to understand the common and key problems in each of the process. The aim of this work was to demonstrate the application of GPU-based DEM at different scales in the process chain of the ironmaking industry, therefore the detailed studies on the effects of key variables on each process will not be the focus of this work.

Ii

kc   dωi X ¼ Mt;ij þ Mr;ij dt j¼1

ð2Þ

where vi and ωi are the translational and angular velocities of the particle, respectively, and kc is the number of particles in interaction with the particle. The forces involved are: the gravitational force mig, and interparticle forces between particles, which include elastic force fc,ij, and viscous damping force fd,ij. These interparticle forces can be resolved into normal and tangential components at a contact point. The torque acting on particle i by particle j includes two components: Mt,ij which is generated by tangential force and causes particle i to rotate, and Mr,ij commonly known as the rolling friction torque, is generated by asymmetric normal forces and slows down the relative rotation between particles. A particle may undergo multiple interactions, so the individual interaction forces and torques are summed over the kc particles interacting with particle i. The accuracy of DEM depends heavily on the force models. As mentioned earlier, in GPU-based DEM simulation, a few researchers used simplified force models (e.g. the force model provided by NVIDIA SDK [35], without consideration of particle rotational and tangential components of the contact force, or use of non-incremental friction model [26,28,36]) to obtain much higher speedup ratios and significantly save GPU global memories (e.g., the memories to store some important particle information such as the tangential displacement δt and tangential elastic force fct,ij) for the current time step t and the previous time step t-Δt. In this work, the practical force model (compared to the simplified force models) is used for higher simulation accuracy.

Fig. 6. (a) Mesh and snapshot of a bucket wheel stacker reclaiming process: (b) digging, (c) lifting, and (d) discharging (coloured by particle velocity, unit: m/s).

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Fig. 7. Particle velocity (left, unit: m/s), normal (middle) and tangential stress (right) (unit: N/m2) on the buckets during digging at (a) t = 0.664 s and (b) t = 1.106 s.

Fig. 8. Effect of rotation speed on the normal (top) and tangential (bottom) wall stress (unit: N/m2) on the buckets at the beginning of digging when the rotation angle θr = 19.908°: (a) 4 rpm, (b) 5 rpm, and (c) 8 rpm.

Fig. 9. Double deck banana screen used in the DEM model and the parameters for the decks.

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Table 4 Parameters used for the DEM simulation of the industry banana screen. Parameters

Value

Screen length, m Screen width, m Vibration frequency, rmp Vibration frequency, Hz Vibration amplitude, mm Density, kg/m3 Posion ratio Young's modulus, Pa Sliding friction coefficient Rolling friction coefficient, dp Feed rate, ton/h Particle size dp, mm Particle size distribution, %

6.1 2.4 1000 16.67 14 1400 0.45 5 × 106 0.4 0.1 1000 (default)-3000 170, 120, 85, 65, 54.5, 45.5, 38.5, 31.5, 25, 30, 16.5 5.0, 5.0, 10.0, 10.0, 10.0, 10.0, 10.0, 10.0, 10.0, 10.0, 10.0

2.2. DEM implementation on GPU and MPI DEM has been applied to particle systems for many years, and its implementation on CPU has been well documented [39–41]. Generally, there are four key steps for DEM: particle grid partitioning and sorting, neighbour list generation, force calculation, and particle information updating. When DEM is implemented on GPU, the framework, as shown in Fig. 1, is similar to the conventional sequential algorithm on the CPU, but the four major steps of DEM are exerted on the GPU device. From our previous study [42], for homogenous (packing in a rectangular box with 300,000 spheres) and heterogeneous system cases (screw conveyor with 100,000 spheres), the speed up ratio (single GPU (NVIDIA Tesla K20m) to a single CPU) could reach as high as 75 and 30, respectively. The GPU-based DEM code in this work was run on MASSIVE M3 GPU clusters at Monash University with advanced NVIDIA Tesla K80, P100 and V100 GPUs. Table 1 compares the specification of different GPU

graphic processors. Fig. 2 compares the elapsed time per second for packing in a rectangular box with 300,000 spheres with the CPU and different GPU graphic processors. It can be seen from Fig. 2(a) that the elapsed time per second can be greatly reduced with more advanced GPU graphic processors such as P100 and V100. According to Fig. 2(b), the simulation can be further sped up several times compared to the previous NVIDIA Tesla K20 m GPU graphic processor, and with the advanced Tesla V100 GPU, the current homogenous packing process can be totally sped up by more than 1000 times. However, it should be noted that for the heterogeneous systems, the speed-up ratio could be somewhat less. In this work, most of the cases were run on V100 GPUs. For some cases, due to the limitation of global memory on a single GPU, multi-GPUs were applied, where the studied domain was spatially divided into sub-domains and a single GPU device was applied to each sub-domain. The data communications between different GPU devices were realized by using message passing interface (MPI) [43–47]. Each process or GPU only deals with particles in its sub-domains. Take the one-dimensional domain division as an example. Firstly, particles are partitioned into the sub-domain grids, and the particle indices are sorted according to their grid indices within the sub-domain. Then, if the particles are in the boundary cells or outside of sub-domain i, their information (position, velocity, neighbour list history, etc.) should be sent to or received from neighbour sub-domain i + 1 (for right boundary) or sub-domain i-1 (for left boundary) by MPI. After data communication, the neighbour list can be generated, and forces are calculated for the inner particles in each sub-domain. Lastly, when the forces are added to particles, particle properties, such as positions and velocities, need to be updated. 2.3. Simulation conditions In the present work, GPU-basedDEM has been applied to different handling and processing systems at different scales, including granular conveying, reclaiming, screening, ship loading and unloading, and blast furnace top charging systems. The DEM

Fig. 10. Snapshot of a screening process: coloured by particle size dp (m): ((a) t = 2.633 s, (b) t = 6.582 s and (c) t = 10.531 s).

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Fig. 11. Snapshot of screening processes with different vibrating frequencies ((a) 500 rpm, (b) 1000 rpm, and (c) 2000 rpm) (t = 10.531 s) and (d) the separation efficiency.

simulation conditions including particle properties, the system geometry and the operation conditions, are given in the corresponding sub-Sections in Section 3. In this work, unless otherwise specified, the geometry wall is assumed to have the same property as the particles in the system. 3. Application and discussion 3.1. Conveying Belt conveyor systems are widely used for loading and redirecting bulk materials of both coarse grain material (such as cereals, mineral ore and coal) and fine powders (as used in the chemical and pharmaceutical industries). Particle properties, operation conditions (such as feed rate, belt speed) and system geometry (such as impact chute structure), affect the granular flow. Among which, optimal conveyor chute design ensures efficient transport without spillage and blockages, with minimum chute and belt wear, and it is also driven by the trend towards higher conveying speeds. In our previous work, GPU-DEM has been applied to the screw conveyors with a speed-up ratio (single GPU to single CPU) being larger than 30 [42]. In this work, we extended it to the belt conveying chute system. To demonstrate the different aspects of the operation of highspeed conveying, a two-belt system with a width of 450 mm and speed of 5.0 m/s was simulated using GPU-DEM. The particle properties and operation condition settings in DEM simulations are listed in Table 2. Fig. 3 shows snapshots of a belt conveying process. The first transfer point was where an oncoming belt conveyor drops the material

with an impact plate to change the direction onto a following conveyor. At the second transfer point the direction of the material flow was changed by approximately 90° using another impact plate. In this type of chute the cross-section must be correctly designed, otherwise blockages such as plugging occur and the flow of the material is obstructed [5]. Fig. 3(a) shows particles had a smooth flow without blockages, and due to the impact with the curved impact plates, particle flow directions changed and the velocities reduced because of the energy dissipation after the impact. From Fig. 3(b), after particles were loaded into the upper belt, segregation occurred when particles were moving forward, with smaller particles accumulating at the bottom of the belt. However, particles became remixed during the transfer from the upper belt to the lower belt. From Fig. 3(c), it is clear that the particle-wall forces were much higher than other places in the rock box, thus proper design of the impact plates in the transferring point plays an important role in providing a smooth granular flow and minimal impact. Fig. 4 compares the particle-wall interaction forces at different flow rates. When the flow rate increased from 700 to 1500 ton/ h, the force ratio |Fpw|/|mg| increased, indicating the wear problem became more severe at higher flow rates. This is consistent with the findings of Xie et al. [7]. Moreover, there was some spillage off the edge of the lower belt when the flow rate was 1500 ton/h, indicating the maximum flow capacity was under 1500 ton/h with the current design. During the conveying process, particle energy was dissipated due to abrasion with the belt and impact with the rock box and lower belt surface. Compared with energy dissipation by abrasion, impact energy dissipation is more conspicuous. Fig. 5 compares

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Fig. 12. Wall stress (N/m2) of the screen with different vibration frequencies (left: 500 rpm, middle: 1000 rpm, right: 2000 rpm).

the energy dissipation by particle-particle and particle-wall collisions at different flow rates. The dissipated energy was calculated by integrating the normal damping force |fdn | and the tangential damping force |f dt| with respect to their overlaps over the entire contact period tc as Ed = ∫tc 0 (| fdn |dδn+| f dt |dδt ). It can be seen that the energy dissipated by particle-particle collisions was higher than the particle-wall collisions due to the limited wall surface for particles to contact. When the flow rate increased, the energy

dissipations by particle-particle and particle-wall collisions both increased. 3.2. Reclaiming Bucket wheel reclaimers, as the world's universal large continuous complete equipment to process bulk materials, are widely used in large open-pit mine storage yards and large port terminals in mining

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Fig. 13. Snapshot of screening processes with different flowrates ((a) 1000 ton/h, (b) 2000 ton/h, and (c) 3000 ton/h) (t = 10.531 s) and (d) the separation efficiency.

and metallurgy industries. The reclaiming process of the bucket wheel system was simulated using GPU-based DEM in this work. The DEM parameter settings are according to Yang et al. [16] and given in Table 3. Particles were first loaded into the middle of a material bin, and then the reclaimer started to rotate and translate at given speed. A pseudo wall was used in the material bin to block the dry and non-cohesive particles collapse into the

Table 5 Simulation settings for particles in the ship loading system. Parameters Particle properties: Particle number, million Particle size range dp, mm Particle density ρp, kg/m3 Particle shape, [−] Young's modulus Ep, GPa Poisson's ratio ν, [−] Friction coefficient μs, [−] Rolling friction coefficient μr, dp Normal damping coefficient cn, [−] Tangential damping coefficient ct, [−] Wall material properties: Ship Young's modulus Es Belt conveyor Young's modulus Es,b Operation conditions: Feed rate, ton/h Belt speed Vbelt, m/s Dropping height ΔH, m Belt width, m

Value 0.3–4.2 3–40 4.3 × 103 Spherical 0.1 0.29 0.3 0.1 0.6 0.6 10 Ep Ep 8000 4.8 10–30 1.8

left of the bin. For wet or cohesive particles, the wall could be removed. Fig. 6(a) shows the mesh of the reclaiming system and the typical reclaiming processes, including digging, lifting and discharging. It can be seen that after one bucket passed through the particle pile, the surface was almost clean with only a few dynamic particles rolling down to the left side of the pile (Fig. 6(b)). These particles were then excavated by the following bucket (Fig. 6(c)), and finally the particles in the first bucket were discharged to the conveyor (Fig. 6(d)) whilst the wheel moves forward slowly (towards outside of the screen) and the whole particle pile was gradually cleaned. During digging process, particles exert normal and tangential forces on the bucket wall, and the tangential forces cause the main digging resistance. The normal and tangential stresses on the bucket at different stages of digging are shown in Fig. 7. At the beginning of digging (Fig. 7(a), rotation angle θr = 19.908°), the particles were loaded into the bucket with low velocities between 1 and 2 m/s. The normal stresses were low and mainly located around the tip of the bucket, while the tangential stress was quite high, and located close to the left end of the bucket. With the rotation of the bucket (Fig. 7(b)), more particles were loaded into the bucket at velocities of 2 and 3.5 m/s. The normal stress is mainly located at the edge of bucket near the bottom, while the tangential stress is mainly at the bottom (left end) of the bucket. Fig. 8 compares the normal and tangential wall stress at different rotation speeds. Obviously, with the increase of rotation speed, both the normal and tangential stress increased, especially the latter, indicating an increase of digging resistance and wear problem in the red colour area of the bucket.

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Fig. 14. (a) Flow pattern (Hdrop = 10 m, Ep = 100 MPa, Ew = 10 Ep coloured by particle diameter (m), Vbelt = 4.8 m/s), and (b) local energy dissipation and particle size distribution.

3.3. Screening Banana screens are often used for high capacity separation of iron ore, coal and aggregates into different size fractions. They consist of one or more curved decks that are fitted with screen panels with arrays of square or rectangular holes. The screen structure is vibrated at high frequency to generate peak accelerations which separates particles flowing over each screen according to their size. In the past decades, DEM has been applied into the screening processes at different scales [17–19,48]. It was used to test a range of strategies for optimization of

screen operating conditions, panel selection and wear minimization with a view to increasing capacity and availability [18]. However, most of these studies were conducted at lab scale, only a few applied it to industrial scale [18,19]. In this work, the screening process of an industry banana double deck screen, as shown in Fig. 9, was simulated using GPU-based DEM. The DEM parameter settings are according to refs [18, 19] and given in Table 4. It should be noted that for this polydispersed particle system with large particle size ratio, the hierarchical grids [49–51] were applied for the DEM neighbour list generation and contact detection. Two hierarchies were used with the size ratio of coarse grids to fine grids setting to 3.0. Feed particles were loaded into the top deck from a material bin

10

Impact energy dissipation (J)

2

Energy dissipation by collision (J)

particle-particle particle-wall particle-particle, size distribution particle-wall, size distribution

5

1 0.5

0.1

0.01

particle-particle particle-wall 0.1

0.01

1E-3 1E-3

5

10

15

20

25

30

35

40

Particle size (mm) Fig. 15. Energy dissipation for different particle sizes and size distribution (ΔH = 10.0 m).

0

5

10

15

20

25

30

Dropping height (m) Fig. 16. Energy dissipation at different dropping heights.

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J. Gan et al. / Powder Technology xxx (2019) xxx Table 6 Parameters used for the DEM simulation of the grab unloader (0.7 scale of the grab unloader geometry in ref [57]). Parameters

Value

Grab width (m) Grab volume (m3) Dead grab weight (t) Particle density (kg/m3) Young's modulus (Pa) Size, mm Fraction, % Grab open time (s) Grab lift up speed (m/s)

1.889 6.7 21.6 3380.0 107 15, 20, 25, 30 10, 40, 40, 10 1.50, 2.64(default), 4.0 2.667

11

with a fixed feed rate. The top and bottom screen decks were vibrated linearly at 45° to the vertical direction. Fig. 10 shows the dynamic screening process. For wide particles size distributions with feeding into the top deck and vibration of the deck, the particles gradually flow down to the lower panels or pass through the holes into the bottom deck. The undersized particles of the bottom deck pass through the holes and go into the undersize chute. Finally, all the products are conveyed and collected through the three conveyors. Fig. 11 compares the flow pattern of particles at different vibrating frequencies. Clearly, at higher vibrating frequency, particles were bouncing higher on the decks, especially the top deck where particles have more space to bounce. Thus, particles have less time to pass through the holes to go into the lower deck or undersize chute. As a

Fig. 17. Snapshots of the grabbing and lifting process (coloured by particle velocity, m/s).

Fig. 18. Normal (top) and tangential (bottom) wall stress (N/m2) on the left grab (start to lift at t = 2.654 s).

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Fig. 19. Effect of grab close time on (top) particle velocity and (bottom) tangential wall stress (N/m2).

result, from the end of the right panels and also Fig. 11(d), a lower screening efficiency was obtained. Fig. 11(d) also shows that when the vibrating frequency increased from 500 rpm to 1000 rpm, there was only a slight decrease in the screening efficiency, but when it increased from 1000 rpm to 2000 rpm, the screening efficiency dropped greatly. This is consistent with Jahani et al. [19]. Although 500 rpm can obtain a higher separation efficiency, the stresses and wear problem on the screen clothes need to be considered. Fig. 12 compares the normal and tangential stresses on the top and bottom decks. Note that the wall stresses have the maximum value at the tip of the top panel because of the impact of the feed materials. For the normal and tangential stresses of both the top and bottom decks, and from the left to the right panels, the stresses gradually increased because the weight of particles increased. With a vibrating frequency Table 7 Settings for the screw unloading system in DEM.

Material bin Screw

Particle

Operation condition

Parameters

Value

Width×depth, mm Height, mm Vertical pitch, mm Horizontal pitch, mm Vertical casing diameter, mm Horizontal casing diameter, mm Blade Radius, mm Thickness, mm Horizontal screw length, m Vertical screw length, m Particle diameter dp, mm Density ρp, kg/m3 Young's modulus, Pa Rolling friction coefficient, dp Vertical rotational speed, rpm Horizontal rotational speed, rpm Bottom blades rotational speed, rpm Angle between horizontal and vertical screws Screws and tube translation velocity, m/s Particle number

1800*900 500 750 750 820 1180 400 10 3.0 8.0 5 1023.0 1 × 107 0.05 300 100 40 90 0.12 3,000,000

increase from 500 to 1000 rpm, the normal and tangential stresses on both top and bottom decks reduced significantly, and when the vibrating frequency further increased from 1000 to 2000 rpm, the stresses on both top and bottom decks also reduced but less obviously. Therefore, in order to keep a high screening efficiency and low screen wall stresses, the vibrating frequency of 1000 rpm is a better option. In the previous work of Cleary et al. [18] and Jahani et al. [19], the system flow rate was fixed to 1000 ton/h. With GPU-DEM, larger screening systems can be simulated. Fig. 13 compares the flow pattern for different flowrates and the separation efficiency. It can be seen that with the increase of flowrate, particles tended to pack on the screen decks, which hinders the particles to pass through the holes, and as a result, both the top and bottom decks showed significant decreases in separation efficiency. Therefore, a proper flowrate should be chosen in practice in order to get a balance between separation efficiency and processing capacity per unit time.

3.4. Loading and unloading 3.4.1. Ship loading After screening, the high-grade iron ore product is loaded into the ship cargo to be exported. During the ship loading processes, the particle dropping height could vary from 10 to 30 m, which may cause severe degradation. In this work, GPU-DEM was applied to the ship loading process to study the effect of key variables on iron ore degradation. The simulation began with the random generation of particles into a feed hopper, and then the particles were discharged into a belt conveyor and then dropped into a rectangular box which represented the ship. The simulation settings and particle properties used in the simulation are listed in Table 5, which were obtained from average shipment data from Rio Tinto, Australia to Baosteel, China in 2016. The particles had a wide size distribution from 3 to 40 mm. Therefore, in this polydispersed particle system with large particle size ratio, the hierarchical grids [49–51] was also applied for the DEM neighbour list generation and contact detection.

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Fig. 20. (a) Screw unloader geometry and (b-e) snapshots of the screw unloading processes (coloured by particle velocity, m/s).

Fig. 14 shows the granular flow pattern, local energy dissipation and size distribution for different Young's modulus of particles. It can be seen from Fig. 11(b) that energy mainly dissipated during the impact with ship wall or particle surfaces, and large particles tended to be on the top of the particle stream and roll further on the granular surface than the fines. A number of factors can affect the energy dissipation, as was demonstrated in our previous work [52]. Fig. 15 shows the energy dissipation at impact surfaces for different particle sizes and size distribution. The particle-particle energy dissipation for particles with a size distribution was as low as the mono-sized particles with size around 11 mm. The particle-wall energy dissipation for particles with a size distribution was even lower. Thus, consistent with previous findings [1,53], particles with a size distribution provided a significant cushioning effect on particle degradation. It has been suggested that larger drops should be avoided and replaced by a number of smaller drops, which reduced the fines generated [54,55]. Sahoo et al. [56] showed that above 3 m critical heights, replacing large drops with a number of smaller drops could reduce the fines

generation. Fig. 16 plots the effect of dropping height on energy dissipation. As expected, dropping height significantly affects the impact energy dissipation. For example, when the dropping height reduced from 10 m to 5 m, the dissipated energy by particle-particle impacts reduced by more than half. 3.4.2. Ship unloading After the bulk materials reaches the cargo terminal, they need to be unloaded and transported to customers. Ship unloading equipment can

25

Mass flowrate (kg/s)

20

15

rmp=30 rmp=40 rmp=50

10

5

0

6

7

8

9

10

11

12

Time (s) Fig. 21. Effect of rotational speed of bottom blades on the mass flowrate.

Fig. 22. Snapshot of granular flow in blast furnace top charging system (a) Bell-less type and (b) two-bell type (Particle number N = 300~1000 K for each batch).

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Fig. 23. Blast furnace top (a) mesh, (b) one-dimensional domain division into 8 sub-domains and (c) snapshots of the full model of the particle flow for the bell-less type charging process of a blast furnace the charging behaviour.

be simply classified into continuous and discontinuous types according to the operational continuity. Grab ship unloaders, as a typical type of discontinuous ship unloaders, are normally used for handling materials like coal, iron ore and bauxite. A clamshell bucket is cycled in and out of the ship's hold, suspended from a traversing trolley, and raised and lowered by a winch. It typically incorporates a hopper that provides a metered material flow to the pier conveyor and traverses the ship on pier-mounted rails to access each hold. In this work, the grabbing and lifting process were simulated by GPU-DEM. The simulation settings are given in Table 6, which is at 0.7 times scale of an industry grab unloader [57]. Fig. 17 shows the snapshots of the grabbing and lifting process. At the beginning of the process, the particle pile had a flat surface. When the grabs started to grab particles, the particles near the grab wall and in between the two grabs had small velocities caused by the rotation of the grabs (Fig. 17(a)). When t = 2.654 s, the grabs were closed and just started to lift. Due to the sudden lift of the grabs, particles near the grab bottom walls had an obvious increase in velocity (Fig. 17(b)). The sudden movement of the grab also caused some particles within the grab to move, so the particle surface curve changed (Fig. 17(c)). When particles were lifted up, particles have stable velocities close to the lift speed (Fig. 17(d)). The normal and tangential stress variation with time is shown in Fig. 18. At the beginning of grabbing, due to the slow and gradual progress of grabbing, the tangential stress was actually smaller than the normal stress, and both stresses were concentrated at the tips of the grabs

Table 8 Settings for the blast furnace top charging system in DEM.

Particles

Operation conditions

Parameters

Value

Particle type Particle diameter dp, mm Density ρp, kg/m3 Feed rate, ton/s Young's modulus, Pa Rolling friction coefficient, dp Coke shift angle, ° Coke shift rounds Ore Shift angle, ° Ore shift rounds Bottom chute rotational speed, rpm Gates opening time, s DCD gates opening time, s

Coke 25–80 833 13.499 1 × 107 0.1 42.6 39.6 2 3 42.6 39.6 1 2 8 0.5 0.5

Pellet 10–40 2966 58.38 1 × 107 0.05 36.1 32.1 2 2 36.1 32.1 2 2

Sinter 13 2966 29.125 1 × 107 0.5 27.6 12.0 1 1 27.6 1

(Fig. 18(a)). When the grabs started to lift, both normal and tangential stresses greatly increased, with the tangential stress being much larger than the normal stress. The tangential stress accumulated mostly in the area of the grab bottom, while the normal stress also spread to the front and rear wall of the grabs (Fig. 18(b)). During the lifting process (Fig. 18(c) and (d)), the tangential stress remained far larger than the normal stress, and distributed mainly close to the bottom tip of the grab. Fig. 19 shows the effect of grab close time on the particle flow and tangential stress. With an increase in grab close time, particle velocities became smaller, and the tangential stress only slightly reduced. Therefore, shorter grab close time can be used to obtain higher grabbing efficiency, while keeping a moderate tangential grabbing resistance. Another typical type of ship under is the continuous ship unloader. The applications of continuous screw ship unloader show that it has the advantages of higher efficiency, strong adaption to materials and ships, a returning branch, light structures, dexterity of action, a closed transport system reducing pollution, occupying a large share in the continuous ship unloader market, and it is an excellent type of continuous bulk unloading machine. In this work, GPU- DEM was also applied to studying the performance of a screw unloading system for coal particles. Settings for the screw unloading system in DEM is given in Table 7. Fig. 20 shows the screw loading system and particle velocities of coal unloading at different times. After filling the material bin, particles were loaded into the vertical tube through the bottom rotating tube, then transported by the vertical screw to the horizontal screw. Meanwhile, the whole screw loading system (tubes and screws) translates in the y direction at a specific speed. With rotation and translation of the loading system, particles were continuous unloading from the stockpile and a pit appeared after the screw passed by. Fig. 21 shows the effect of rotational speed of bottom blades on the mass flowrate.

Table 9 Feed size and rate settings for the blast furnace top charging system in DEM. Coke

Sinter

Pellet

Size, mm

Feed rate, ton/s

Size, mm

Feed rate, ton /s

Size, mm

Feed rate, ton /s

80 70 50 33 25

0.655 2.056 1.9 6.938 1.95

40 32 20 13 10

8.383 16.152 15.726 13.391 4.728

13

29.125

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Fig. 24. Size segregation occurs in (a) charging into top material bin, (b) discharging from top material bin to hopper (material gate open, DCD gate closed), (c) discharging from top material bin into hopper (material gate open, DCD gate open), and (d) discharging from hopper into blast furnace.

Clearly, with an increase of rotational speed, the mass flowrate increased, indicating a higher unloading efficiency.

3.5. Blast furnace top charging After the bulk materials reach the end user, they still need to go through a series of handling steps. For example, in the blast furnace feeding system, iron ore goes though processes such as conveying and screening, and finally reaches the top of blast furnace to be charged into the furnace. Ore and coke particles are stacked alternately in layers. Optimizing the burden distribution is one of the most important factors for efficient operation, because gas permeability strongly affects the reactivity of particles. In practice, the burden is usually charged with that large particles in the center in order to guarantee the central gas flow, and small particles at the periphery in order to prevent the hot gases from burning the furnace wall [22]. Thus, particle size segregation during charging into and discharging from the top hopper directly affects the burden distribution in the blast furnace. Although many researchers had studied this aspect [11,22–24], only a few studied the particle segregation history during delivering in the full blast furnace top charging system. In this work, GPU-DEM was applied to a blast furnace top charging system at different scales. Fig. 22 shows a bell-less and two-bell type blast furnace top charging process with rotating chute in an ironmaking blast furnace. Particles (coke or ore) were randomly generated with a small initial velocity in the top bin, and then the particles flowed through a rotating chute (clockwise, chute rotating speed = 7.5 rpm) before falling into the blast furnace (the bottom bin). Here, only ¼ of the bin was used in these two cases using a single GPU. It can be observed from the burden distribution results that for both cases, after three batches of discharging (already removed the effect of flat geometry bottom), the burden distribution almost remained stable. Therefore, GPU-based DEM can be successfully applied to the complex granular flow systems such as blast furnace top charging systems, which is helpful in optimizing these systems. A full model of the particle flow for the bell-less type charging process of the blast furnace was also simulated, as shown in Fig. 23. The simulation settings are given in Tables 8 and 9. To realize large-scale simulation without the limitation of GPU global memory, the whole mesh domain was divided into 8 sub-domains in one-dimensional (see Fig. 23(a) and (b)), and each CPU process deals with a subdomain. The data communication between neighbouring sub-domains was realized by MPI. As demonstrated in Fig. 23(c), the particles were discharged from the top chute into material bins and then to the discharge funnel (hopper) and to the blast furnace through the rotating chute in this simulation. The discharge rate of particles into the blast furnace was automatically controlled by the DCD gate located above the rotating chute.

In this process, particle segregation by size occurs not only spatially but also temporally, as shown in Fig. 24. When charging into top material bin (Fig. 24(a)), most large particles accumulated at the outer side, while small particles accumulated at the hopper bottom and the inner side to the vertical axis of symmetry. During discharging into the hopper (Fig. 24(b) and (c)), large particles tended to flow at the top of the particle stream and roll far away from the material bin. When the DCD gate was open, particles discharged into the blast furnace through the rotating chute. In this process, as indicated in Fig. 24(c) and (d), more and more large particles accumulated at the top of material bin and at the top of the hopper on the opposite side of the material bin. 4. Conclusion GPU-basedDEM combined with MPI has been applied to large-scale handling and processing systems, including granular conveying, excavating and reclaiming, screening, ship loading and unloading, and blast furnace top charging systems. Particle flow behaviour, particlewall interaction/wall stress, particle energy dissipation, size segregation, and process efficiency, etc., are discussed. The findings are summarized below: • For a belt conveying chute, the wear problem became more severe at higher flow rates. • In the reclaiming process, with an increase in bucket rotation speed, there was an obvious increase in the digging resistance on the buckets. • For the screening process, a lower vibrating frequency lead to higher screening efficiency, but also high wall stresses. • For a ship loading process, a wide particle size distribution provided a significant cushioning effect on particle degradation, and when the dropping height reduced, the dissipated energy by particle-particle impacts greatly reduced. • For a grab unloader, with an increase in the grab close time, particle velocities became smaller, and the tangential stress only slightly reduced within the close time range considered. • An increase of rotational speed of the bottom blades of a screw unloader indicated a higher unloading efficiency. • A full blast furnace top charging process model was also developed. Size segregation was observed at different stages of the charging process. In this work, only some key variables or problems are discussed, and in the future, more detailed studies need to be conducted for a more comprehensive understanding of these processes. Moreover, in this work, GPU-DEM was not applied to the processes involving particle breakage such as crushing, grindings and milling processes, and should be a focus of future work. However, the current GPU-DEM methodology has already shown to be able to simulate various representative

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