Impact energy dissipation study in a simulated ship loading process

Powder Technology 354 (2019) 476–484

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Impact energy dissipation study in a simulated ship loading process 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 24 April 2019 Received in revised form 14 June 2019 Accepted 15 June 2019 Available online 19 June 2019 Keywords: GPU-DEM Ship loading Energy dissipation Degradation Particle breakage

a b s t r a c t Degradation of the iron ore during handling and transportation results predominantly from impact from drops, such as the ship loading process. The lump ore degradation is directly related to the particle energy dissipation during impacting with wall or particles. In this work, graphical processing units (GPU) and message passing interface (MPI)-based discrete element method (DEM) is developed for the large-scale iron ore ship loading process to analysis the particle impact and energy dissipation. The effect of particle properties such as size distribution and shape, belt speed and dropping height on energy dissipation are studied. The results illustrate that Young's modulus has little effect on the energy dissipation under the same loading condition. Degradation varies with particle size, with coarser particles suffering a greater energy dissipation than finer ones. Particles with a size distribution provide a significant cushion effect on particle degradation, as demonstrated by an obvious smaller value in energy dissipation. This is explained by the inter-particle contact during the dynamic loading process. Belt speed has negligible effect on impact energy dissipation within the range considered. Dropping height, as expected, is the most significant factors affecting the impact energy dissipation. When the dropping height reduces from 10 m to 5 m, the dissipated energy by particle-particle impacts reduces more than half. Vogel and Peukert [1] particle breakage model is used to study the individual particle breakage probability under specific material properties. For the same energy input, smaller particles have lower breakage probability, indicating that larger particles are easier to break than smaller ones. © 2019 Published by Elsevier B.V.

1. Introduction The unintentional and undesirable breakage of lump raw materials (such as coal, iron ore, blast furnace sinter and coke), referred as degradation, occurs during handling and transportation due to the drops at conveyor transfer points, stockpiling and reclaiming, and rail wagon/ship loading/unloading [2]. The breakage of lump into fines in these processes can represent a considerable loss in revenue. For example, the degraded products reduce the permeability and loss the productivity in the blast furnace, the degraded products also cause a large recycle load in sinter plant production [3,4]. The generated fines usually have to be removed in subsequent iron-making steps. Lump ore is the only traded iron ore product that can be introduced directly into the blast furnace. However, degradation of lump ores occurs in different sectors of the whole process at various degrees. It is affected by a number of factors, such as the drop height, number of drops, ore types and initial ore size distribution or fine content, and drop surface [2,5–7], in the handling ⁎ Corresponding author. E-mail address: [email protected] (J. Gan).

https://doi.org/10.1016/j.powtec.2019.06.029 0032-5910/© 2019 Published by Elsevier B.V.

and transportation processes. A number of experimental studies had been conducted to investigate ore degradation during handling. Generally, degradation during handling results predominantly from impact from drops [5]; and degradation is significantly reduced by using drop heights below about 1 to 3 m [2,5,7]. Degradation varies with particle size, with coarser particles suffering a greater degradation than finer ones; impact surface influences the level of degradation upon impact, and a cushioning effect occurs as the percentage of initial fines increases [2,5]. Ship loading is one of the key drops during iron ore handling and transportation processes where degradation occurs, as the drop height is as high as 30 m. To reduce the degradation degree in this process, knowledge of the microscopic impact energy dissipation and interparticle interaction of the granular materials in each processing sector is of significant importance. In this paper, graphical processing units (GPU)-based discrete element method (DEM), is applied to simulate the complex granular flow process, by virtue of its high computation efficiency and capability of generating micro-dynamic information, such as impact energy dissipation, which are difficult to be obtained by conventional experiments. The is based on our previous developed GPU-based

J. Gan et al. / Powder Technology 354 (2019) 476–484

DEM technology [8], which has the advantage of speedup ratio (single GPU to single CPU) of up to 75 and be able to handle billions of particles. It has the capabilities to deal with arbitrary wall geometries, moving wall boundaries and non-spherical particles, and has been successfully applied to hopper flow [9], screw conveyor [8], and rotating drums [10,11], and blast furnace top charging system [8]. In the present work, GPU-DEM is further extended to the ship loading process. The aim is to simulate the large-scale granular flow behaviour in this complicated process and to study the effects of drop height, belt speed, particle shape, and the cushion effect of different particle sizes (and size distribution) on energy dissipation. Furthermore, Vogel and Peukert [1] particle breakage model is also used to study the individual particle breakage probability under specific material properties. 2. GPU-DEM method description 2.1. Simulation method DEM model for spheres has been well established and documented [12], and its extension to non-spherical particles has also been established [13–15]. According to the DEM, a particle 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

mi

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

ð1Þ

and

Ii

kc   dωi X ¼ Mt;ij þ Mr;ij þ M n;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 the 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 the tangential force and causes particle i to rotate, and Mr,ij, commonly known as the rolling friction torque [16], is generated by asymmetric normal forces and slows down the relative rotation between particles. For non-spherical particles, an addition torque Mn,ij is added because the normal contact force doesn't necessarily pass through the particle centre. Moreover, particle may undergo multiple interactions, so the individual interaction forces and torques are summed over the kc particles interacting with particle i. The equations used to calculate the particle-particle interaction forces and torques are well documented elsewhere [8,14,17], and also given in this work in Table 1. The Vogel and Peukert [1] breakage probability of particles upon impacts is given as  S¼

  1− exp −f mat kdp ðEd −Emin Þ Ed NEmin 0 Ed ≤Emin

ð3Þ

where Ed is specific impact energy dissipation, Emin is the minimum specific energy required to break a particle, k is the number of impacts, dp is the feeding particle diameter, and fMat is a fitting material property parameter. While Emin is a size dependent material property, Vogel and

477

Table 1 Components of forces and torque acting on particle i. Forces and torques

Symbols Equations

Normal elastic force Normal damping force Tangential elastic force Tangential damping force Coulumb friction force Torque by normal force Torque by tangential force Rolling friction torque

fcn,ij

−4

fdn,ij

−cn ð8mij E

fct,ij

^t −μ s jf cn;ij jð1−ð1−δt =δt; max Þ3=2 Þδ

fdt,ij

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1=2 −ct ð6μ s mij j f cn;ij j 1−jVt j=δt; max =δt; max Þ vt;ij ðδt bδt; max Þ

ft,ij

^t −μ s jf cn;ij jδ

Mn,ij

Rij × (fcn, ij + fdn, ij)

Mt,ij

Rij × (fct, ij + fdt, ij)

Mr,ij

^ nt;ij μ r;ij Ri jf n;ij jω

 3

pffiffiffiffiffi E R δ3=2 n n pffiffiffiffiffiffiffiffiffiffi 1=2 R δn Þ vn;ij ðδt bδt; max Þ

ðδt ≥δt; max Þ

^t ^ t;ij ¼ ωt;ij =jωt;ij j, δ where, 1/mij = 1/mi + 1/mj, 1/R ∗ = 1/|Ri| + 1/|Rj|, E ∗ = E/2(1 − v2), ω ¼ δt =jδt j, δt, max = μs(2 − v)/2(1 − v) ⋅ δn, vij = vj − vi + ωj × Rj − ωi × Ri, vn, ij = (vij ⋅ n) ⋅ n,vt, ij = (vt, ij × n) × n. Note that tangential forces (fct,ij + fdt,ij) should be replaced by ft,ij when δt N δt,max.

Peukert [1] determined that the product dpEmin is a constant material property. The determination of the specific breakage rate parameter from Eq. (3) requires the impact energy distribution, which is obtained from DEM. The impact energy can be defined by several methods. The most common is the use of the collision energy Ecoll otherwise known  as the kinetic energy at impact given by Ecoll ¼ 1 2 mij v2n;ij , where mij is the reduced mass given as mij = 2mimj/(mi + mj), and vn,ij is the relative impact velocity. A second type of impact energy known as the impact energy dissipation Ed is commonly used in the modelling of impact milling leading to particle fracture [18,19]. This is the energy lost by the inelastic collision of two particles otherwise known as the deformation energy. Capece et al. [18] compared the collision energy and the dissipated energy for three impact scenarios and concluded that dissipation

Table 2 Simulation settings for particles. 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/hr Belt speed Vb, m/s Dropping height ΔH, m Belt width, m

Value 0.3–4.2 (default: 1.5) 3.0–40.0 4.3 × 103 Oblate, spherical (default), prolate 0.05–10.0 (default: 0.1) 0.29 0.3 0.1 0.6 0.6 10 Ep Ep 8000 3.5–5.1 (default: 4.8) 1.0–30.0 1.8

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simulation. In this work, for the ship loading process, we only consider the collision process of two particles.

Table 3 Particle size distribution. Size group, mm

Group mean size, mm

Lump weight fraction, wt%

+31.5–40.0 +25.0–31.5 +20.0–25.0 +14.0–20.0 +12.0–14.0 +9.5–12.5 +8.0–9.5 +6.3–8.0 +3.0–6.3

35.75 28.25 22.50 17.00 13.25 11.00 8.75 7.15 4.65

9.9 14.7 13.9 23.6 6.7 14.5 6.2 5.1 5.4

2.2. DEM implementation on GPU and MPI

energy (Ed) should be used in contrast to collision energy (Ecoll) to define the impact energy distribution. The dissipated energy is commonly calculated by integrating the normal damping force |fdn| and the tangential damping force |fdt| with respect to their overlaps over the entire contact period tcontact as shown in Eq. (4) Z Ed ¼

tcontact 0

ðjf dn jdδn þ jf dt jdδt Þ

ð4Þ

The total contact period includes the particle-particle collision time tc and contact duration time td which can be obtained from the

DEM has been applied to particle systems for many years, and has been implemented on GPU by a number of researchers [8,20–28]. In this work, based on the previous developed MPI-GPU-DEM technology for complex system [8], the GPU-based DEM code was run on MASSIVE M3 GPU cluster at Monash University with the advanced NVIDIA Tesla V100 GPUs. The studied domain is spatially divided into sub-domains, and the parallel processing is applied to each domain using a single GPU device. The data communications between different GPU devices are realized by using message passing interface (MPI) [29–33]. Each process or GPU only deals with the particles in its subdomain. 3. Simulation conditions The simulation begins with the random generation of particles into a feed hopper, after which the particles discharge into the belt conveyor and then drop into a rectangular box which is used to represent the ship. The belt conveyor has a fixed speed towards the ship (x direction in this work). When particles reach the belt conveyor, they are gradually accelerated to the belt speed due to the friction between belt and

Fig. 1. (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 size distribution (t=8.451 s).

J. Gan et al. / Powder Technology 354 (2019) 476–484

Particle - particle Particle - wall

0.1

Impact energy dissipation (J)

479

0.01

1E-3

0.1

1

10

Young's modulus of particles, Ep (GPa)

8

Ep=0.05GPa Ep=0.1GPa Ep=1GPa Ep=10GPa

7 6 5 4 3 2

Fig. 3. Particle velocity (left, unit: m/s) and energy dissipation (right, unit: J/kg) at impact surfaces for different particle sizes and size distribution (t = 8.451 s).

1 0

0

5

10

15

20

25

30

35

40

Particle size (mm)

(b) Fig. 2. (a) Energy dissipation by particle-particle and particle-wall collision for different Young's modulus of particles and (b) Energy dissipation by particle-particle collision for different particle sizes.

particles. The simulation setting and particle properties used in the simulation are listed in Table 2. These data are obtained from average shipment data from Rio Tinto, Australia to Baosteel, China in 2016. The particles have a wide size distribution from 3 to 40 mm, as given in Table 3. For the case of different particle sizes or size distribution, the total number of particles is different but with a fixed feed weight. The dissipation energy is calculated after all the particles are loaded into the ship bin. 4. Results and discussion 4.1. Effect of Young's modulus A Young's modulus of 107–108 Pa is usually used in DEM simulation, which is significantly smaller than the true values for iron ore. Although it is regarded to have no effect on either particle velocities or dissipation energy [34], it may of concern in this study. In order to confirm this for current cases, the energy dissipation of particle with different Young's modulus are compared. Fig. 1 shows the granular flow pattern, local energy dissipation and size distribution for Young's modulus of 100 MPa. It can be seen from Fig. 1(b) that energy mainly dissipates during the

impact with ship wall or particle surfaces, and large particles tend to be on the top of the particle stream and roll further on the granular surface than the fines. The dissipated energy during impact of particles with wall and particles for different Young's modulus of particles are plotted in Fig. 2(a). It can be seen that Young's modulus only has little effect on the total energy dissipation under the same loading condition. Due to the small 10

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

5

Impact energy dissipation (J)

Energy dissipation by particle-particle collision (J)

(a)

2 1 0.5

0.1

0.01

1E-3

5

10

15

20

25

30

35

40

Particle size (mm) Fig. 4. Particle velocity and energy dissipation for different particle sizes and size distribution (ΔH = 10.0 m).

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13.25 mm - 4.65 mm 13.25 mm - 8.75 mm 13.25 mm - 13.25 mm

1000

Contact Frequency, 1/s

Contact Frequency, 1/s

1000

35.75 mm - 4.65 mm 35.75 mm - 8.75 mm 35.75 mm - 13.25mm 35.75 mm - 22.50 mm 35.75 mm - 35.75mm

100

100

10

10 1

1 10-12 10-11 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100

10-12 10-11 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 102

Dissipation Energy, J

Dissipation Energy, J

(a)

100

6

35.75 mm - 4.65 mm, t=5.177s 35.75 mm - 4.65 mm, t=9.357s 35.75 mm - 4.65 mm, t=11.477s 35.75 mm - 8.75 mm, t=5.177s 35.75 mm - 8.75 mm, t=9.357s 35.75 mm - 8.75 mm, t=11.477s 35.75 mm - 22.5mm, t=5.177s 35.75 mm - 22.5 mm, t=9.357s 35.75 mm - 22.5 mm, t=11.477s 35.75 mm - 37.5 mm, t=5.177s 35.75 mm - 37.5 mm, t=9.357s 35.75 mm - 37.5 mm, t=11.477s

10

1

0.1 10-16

10-14

10-12

10-10 10-8 10-6 10-4 Dissipation Energy, J

10-2

100

(c)

Energy dissipation by particle-particle collision (J)

Contact Frequency, 1/s

1000

(b) t=3.018s t=5.021s t=7.002s t=9.055s t=11.047s t=13.099s

5 4 3 2 1 0 0

5

10

15 20 25 Particle size (mm)

30

35

40

(d)

Fig. 5. Contact frequency between different particle size pairs for (a) particle size of 35.75 mm impact with other sizes at t = 5.177 s, and (b) particle size of 13.25 mm impact with other sizes at t = 5.177 s, (c) at different time, and (d) energy dissipation by particle-particle collision for different particle sizes at different time.

amount of particles impacting with ship bottom wall, the energy dissipated by particle-wall interaction is much lower than that of particleparticle interaction. Although Young's modulus does not affect the total energy dissipation, as shown in Fig. 2(b), particles with different sizes in the feed size distribution have quite different energy dissipation. Larger particles have larger energy dissipation between particle-particle impacts, and for the same particle size energy dissipation decreases with the increase of Young's modulus. 4.2. Effect of particle size (distribution) As discussed above, particles shows quite different energy dissipation, which is consistent with the previous findings that degradation varies with particle size, with coarser particles suffering a greater degradation effect than finer ones [5]. Apart from particle size, impact surface also influences the level of degradation upon impact, and a cushioning effect occurs as the percentage of initial fines increases [2,5]. Sahoo and Roach [35] showed that the cushioning effect of fines on coal impact surface was least, compared to steel surface and conveyor surface. In the dynamic ship loading process, the impact surface depends on the granular flowing history such as particle segregation, and it is changing with time. Therefore, the energy dissipation Ed varies with impact surface and loading time. Fig. 3 shows the particle velocity and energy dissipation at impact surfaces for different particle sizes and size distribution. For

different particle sizes (or size distribution), particles have similar impact velocities but quite different energy dissipations. Large particles show greater E d than the smaller ones and particles with a size distribution. This is more intuitively shown in Fig. 4. The particle-particle energy dissipation for particles with a size distribution is as low as the mono-sized particles with size around 11 mm. The particle-wall energy dissipation for particles with a size distribution is even lower. Thus, consistent with previous findings, particles with a size distribution provide a significant cushion effect on particle degradation. The cushion effect of particles with a size distribution is mainly attribute to the dynamic inter-particle contacts between different sizes. By using DEM, the inter-particle contact information at different loading instants can be readily obtained. As shown in Fig. 5 (a) and (b), larger particles have much higher chances to contact with smaller particles which lead to a wider dissipation energy distribution, and smaller chances to contact coarser particles which has a narrower dissipation energy distribution. Interestingly, for the contact of 35.75 mm-sized particles, the curves generally have two peaks with one peak at around 0.003 J, which indicates that there may be two types of collision between 35.75 mm and other sized particles. One of the collision types with a lower energy might be caused by a second collision between the same particle size pairs (might be the same or different particle pair) which has dissipated some energy during their first collision.

J. Gan et al. / Powder Technology 354 (2019) 476–484

481

Particle-particle Particle-wall

0.07

Energy dissipation (J)

0.06 0.05 0.04 0.03 0.02 0.01 0.00

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

Aspect ratio

(a)

(b) Aspect ratio=0.50

(c) Aspect ratio=0.75

(d) Aspect ratio=1.00 Fig. 6. (a)Effect of particle shape on energy dissipation by particle-particle and particle-wall collision, and (b), (c)and (d)snapshot of dropping particles with different shapes (t = 5.4 s).

However, for the 13.25 mm-sized particles, there is only one peak at around 0.005 J on each distribution curve, indicating only one type of collision for this particle size. The much higher contact frequency and wider energy dissipation distribution give rise to a smaller average energy dissipation for coarse-fine collision particle pairs which leads to the cushion effect. Therefore, with a wider feed size distribution, the overall degree of degradation could reduce, however high content of fines is sometimes unwanted for the end user specifically for blast furnace where the fines reduce the permeability. From Fig. 5(a), with the degradation of coarse particles during impacts, more fines are generated, and meanwhile, the generated fines together with the fines in the feed could reduce the degradation in return. Again, with less fines generated, the cushioning effect weakens and degradation intensifies. Therefore, during the dynamic ship loading process,

from ship bottom to the top, particle degradation aggravates and weakens alternately. During the dynamic loading process, size-induced segregation could occur. With the time increase, as shown in Fig. 5(c), for coarse particles, the contact frequency increases for coarsecoarse collision particle pairs, and there is almost no change for coarse-fine particle pairs. According to Fig. 5(d), for a specific time, coarse particles have higher energy dissipation by particleparticle collision, consistent with Fig. 4, and it increases with time until the loading process becomes stable. 4.3. Particle shape Particle shape has a marked effect on a number of measures of particle breakage, since it directly influences the state of stresses inside

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the same equivalent diameter at each size group, and the feed particles have the same size distribution as spheres. According to Fig. 6(a), flat or elongate particles have higher particle-wall energy dissipation, but spherical particles have much higher particle-particle dissipation than near-spherical particles. Fig. 6 (b), (c) and (d) show that particles with different aspect ratios show quite different angles of repose, with oblate particles having larger angle of repose, which is consistent with previous findings for sandpiles of mono-sized ellipsoids [13]. Moreover, large particles segregated to the side for both spheres and ellipsoids. 4.4. Effect of belt speed Belt speed can affect the particle dropping velocity and dropping angle. Fig. 7 compares the energy dissipation for several belt speeds and the particle trajectory lines. It can be seen that, although higher belt speed moves particles further from the belt end with the particle trajectory lines shifting to the right, it has neglectable effect on impact energy dissipation within the range considered. Thus larger belt speeds are normally used to obtain higher feed rates. However, larger belt speed

0.007

0.006

0.005

0.004

0.003

0.002

0.001 3.4

3.6

3.8

4.0

4.2

4.4

4.6

4.8

5.0

5.2

Energy dissipation by particle-particle collision (J)

Energy dissipation by particle-wall collision (J)

the particle. The effects of shape on the energy dissipation for elongated particles had been reported [36–39]. For example, the total collisional dissipation rate, which is associated with both translational and rotational granular temperature change rates, increases linearly with the particle aspect ratio for frictionless mono-sized elongated cylinders [36]. For a range of particle elongations (1.5 b aspect ratio b 4.0), where the average energy transfer between the rotational and translational degrees of freedom results greater for spherocylinders than for homogeneous ellipsoids with the same aspect ratio [37]. In practice, iron ore particles are hardly spherical, thus, it is necessary to study the effect of particle shape on the energy dissipation during impacts. Particle shape also influences the progeny size distribution from single-particle breakage. It has been demonstrated that finer progeny results from breakage of flaky (lamellar) particles in the drop weight tester when compared to isometric (non-flaky) ones [40,41]. Although the real iron ore is irregular-shaped, in this paper, we still use regular mono-shaped ellipsoids to study the energy dissipation of near spherical particles with aspect ratio between 0.5 and 2.0. Fig. 6 shows the effect of particle shape on energy dissipation. It should be noted that, for each aspect ratio, particles still have

0.075

0.070

0.065

0.060

0.055

0.050 3.4

3.6

3.8

4.0

Belt speed (m/s)

(a)

4.4

4.6

4.8

5.0

5.2

(b) Sim., 3.5 m/s Sim., 4.0 m/s Sim., 4.5 m/s Sim., 4.8 m/s Sim., 5.1 m/s Theo., 3.5 m/s Theo., 4.0 m/s Theo., 4.5 m/s Theo., 4.8 m/s Theo., 5.1 m/s

0

-2

Height (m)

4.2

Belt speed (m/s)

-4

-6

-8

-10

0

1

2

3

4

5

6

7

Horizontal distance (m)

(c) Fig. 7. Effect of belt speed on energy dissipation by (a) particle-particle and (b) particle-wall collision, and (c) particle trajectory lines for different belt speeds.

Energy dissipation by particle-wall collision (J)

Energy dissipation by particle-particle collision (J)

J. Gan et al. / Powder Technology 354 (2019) 476–484

0.1

0.01

1E-3 0

5

10

15

20

25

30

Dropping height (m)

(a)

483

0.01

1E-3

0

5

10

15

20

25

30

Dropping height (m)

(b)

Fig. 8. Effect of dropping height on energy dissipation by (a) particle-particle and (b) particle-wall collision.

may give raise to other issues such as abrasion of lump ore (surface breakage), thus a safety belt speed range is chosen in practical operation.

4.5. Effect of dropping height The previous drop tests results suggested that the larger drops should be avoided and replaced by a number of smaller drops, which reduced the fines generated [4,7]. This effect can be achieved by installing series of rock ledges in a chute and thus creating a stepped chute. Sahoo et al. [42] showed that above 3 m critical heights replacing large drops with a number of smaller drops could reduce the fines generation. Fig. 8 plots theeffectof droppingheighton energy dissipation.As expected, dropping height is the most significant factor affecting the impact energy dissipation. For example, when the dropping height reduces from 10 m to 5 m, the dissipated energy by particle-particle impacts reduces more than half. However, in the ship loading process, the dropping height is determined by the ship cabin size, loading amount, water level, and loading operation mode, and so on. Therefore, properly and carefully control the ship loading operation mode may to some extent reduce the dropping height, and consequently reduce the iron ore degradation.

4.6. Particle breakage probability In order to study the individual particle breakage probability during the dropping processes, the Vogel and Peukert [1] breakage probability model is applied. Because the exported iron ore in this project is a mixture of a number of iron ore types, it is hard to obtain the material properties. Here we assume the material property parameters fmat = 0.169 kg/Jm and Emin = 249.8 J/kg for dp = 6 mm according to one type of Rio Tinto iron ore data from [43]. Fig. 9(a) shows the particle breakage probability as a function of the product dp(Ed − Emin) for different impact numbers. In this figure, each data point represents a particle, and some data are skipped for visualization purpose. According to the figure, a particle may undergo several impacts before it breaks up. For example, 3.8% of total number of particles have a tendency of breakage after only one impact, and 1.05% after 2 impacts, 0.39% after 3 impacts and 0.18% after 4 impacts. Fig. 9 (b) plotted the particle breakage probably as a function of energy dissipation for different particle size after one impact. For the same energy input, smaller particles have lower breakage probability, indicating that larger particles are easier to break than smaller ones.

Fig. 9. Particle breakage probability (a) as a function of the product dp(Ed − Emin) for different impact numbers (ΔH = 10.0 m, Vb = 4.8 m/s), and (b) as a function of energy dissipation for different particle size after one impact (ΔH = 10.0 m, Vb = 4.8 m/s).

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5. Conclusions In this work, a graphical processing units (GPU) and message passing interface (MPI)-based DEM is developed for the large-scale iron ore ship loading process. The GPU-MPI-DEM model is then applied to analysis the particle impact and energy dissipation in this process. The effect of particle dropping height, belt speed and particle shape on energy dissipation are investigated. The results illustrate that Young's modulus has negligible effect on the energy dissipation under the same loading condition. Degradation varies with particle size, with coarser particles suffering a greater energy dissipation than finer ones. Particles with a size distribution provide a significant cushion effect on particle degradation, as demonstrated by an obvious smaller value in energy dissipation. The cushion effect is explained by the interparticle contacts during the dynamic loading process. Belt speed also has very little effect on impact energy dissipation within the range considered. Dropping height, as expected, is the most significant factors affecting the impact energy dissipation. When the dropping height reduces from 10 m to 5 m, the dissipated energy by particle-particle impacts reduces more than half. Therefore, ship loading operation could be carefully designed and controlled to minimize the total dropping height in order to reduce lump ore degradation. Vogel and Peukert [1] particle breakage model is used to study the individual particle breakage probability under specific material properties. For the same energy input, smaller particles show lower breakage probability, confirming that larger particles are easier to break than smaller ones. Acknowledgment The authors are grateful to the ARC Hub for Computational Particle Technology (ARC IH140100035) for the financial support of this work, and the Monash MASSIVE for the support in computation. References [1] L. Vogel, W. Peukert, Breakage behaviour of different materials—construction of a mastercurve for the breakage probability, Powder Technol. 129 (2003) 101–110. [2] R. Sahoo, Degradation characteristics of steel making materials during handling, Powder Technol. 176 (2007) 77–87. [3] R. Sahoo, D. Roach, Quantification of the lump coal breakage during handling operation at the Gladstone port, Chem. Eng. Process. Process Intensif. 44 (2005) 797–804. [4] C.S. Teo, A.G. Waters, S.K. Nicol, Quantification of the breakage of lump materials during handling operations, Int. J. Miner. Process. 30 (1990) 159–184. [5] F. Fagerberg, N. Sandberg, Degradation of lump ores in transport, Proc. 2nd Int. Symp. On Transportation and Handling of Minerals, Rotterdam 1973, pp. 128–156. [6] L.M. Tavares, R.M. de Carvalho, Modeling ore degradation during handling using continuum damage mechanics, Int. J. Miner. Process. 112 (2012) 1–6. [7] T.E. Norgate, D.F. Tompsitt, R.J. Batterham, Computer simulation of the degradation of lump ores during transportation and handling, International Conference on Bulk Materials Storage, Handling and Transportation. Wollongong 1986, pp. 20–24. [8] J.Q. Gan, Z.Y. Zhou, A.B. Yu, A GPU-based DEM approach for modelling of particulate systems, Powder Technol. 301 (2016) 1172–1182. [9] T.F. Zhang, J.Q. Gan, D. Pinson, Z.Y. Zhou, Size-induced segregation of granular materials during filling a conical hopper, Powder Technol. 340 (2018) 331–343. [10] S. He, J. Gan, D. Pinson, Z. Zhou, Transverse mixing of ellipsoidal particles in a rotating drum, EPJ Web Conf. 140 (2017) 06018–06021. [11] S.Y. He, J.Q. Gan, D. Pinson, Z.Y. Zhou, Particle shape-induced radial segregation of binary mixtures in a rotating drum, Powder Technol. 341 (2019) 157–166. [12] H.P. Zhu, Z.Y. Zhou, R.Y. Yang, A.B. Yu, Discrete particle simulation of particulate systems: theoretical developments, Chem. Eng. Sci. 62 (2007) 3378–3396. [13] Z.Y. Zhou, R.P. Zou, D. Pinson, A.B. Yu, Angle of repose and stress distribution of sandpiles formed with ellipsoidal particles, Granul. Matter 16 (2014) 695–709.

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