*3.2. Simulation Conditions*

The apparatus of the Discharging Method in the simulation consists of a hopper, a baffle and a table, just like the components used in the experiments. In the Lifting Method, the apparatus is only a column barrel. The geometric models are both shown in Figure 1b. DEM parameters of pellet were chosen according to the results of previous work by the authors [29] and are presented in Table 2. In the simulations, we studied the effects of the DEM parameters on the angle of repose and porosity distribution. Furthermore, the effects of different drop heights of the Discharging Method, as well as the effects of lift speed and barrel size in the Lifting Method, on the angle of repose of the pile were also investigated.

**Table 2.** Physical and contact parameters used in DEM simulation, including pellet particle and walls.


In the table, p-p, p-w and p-g represent the coefficients for pellet-pellet, pellet-wall and pellet-plexiglass (breaker) interaction. Some parameter values were from the literature [17,18].

For the simulation of porosity, we used seven boxes (5 cm × 10 cm × 5 cm) placed along the diameter of the bottom of the pile to measure the bottom porosity distribution (BPD). In determining whether a particle belongs to the box, its central coordinates were used. The porosity of the bed in each box can be calculated by

$$P = \left(1 - \frac{nV\_p}{V}\right) \times 100\% \tag{4}$$

where *V* is the volume of the box and *Vp* is the volume of a single pellet, and *n* is the number of particles in the box.

#### **4. Results and Discussion**

#### *4.1. Simulation and Experimental Study of Angle of Repose*

#### 4.1.1. Angle of Repose by the Discharging Method

We first studied the influence of DEM parameters on the angle of repose of the pellet pile. As the effect of a physical parameter is studied, the other parameters were kept unchanged at the values reported in Table 2. From work reported in the literature [2], it is known that the angle of repose is sensitive mainly to the rolling and static friction coefficients between the particles. Vertical cross-sections of the pellet pile with different rolling and static friction coefficients are shown in Figure 3. It was observed that when the rolling and static friction coefficients increase from low (0.01) to high (0.99) values, the shape of the pile changed a lot, especially for the latter parameter. The results of contour extractions of the heap are shown in Figure 4. It is obvious that the height of the pile increases and then tends to be stable.

Figure 5 shows the angle of repose with different rolling and static friction coefficients, with error bars indicating the deviation of the angle of repose in different directions of the pile. The angle of repose shows a positive correlation with the friction coefficients. When the static and rolling friction coefficients change from 0.01 to 0.99, the angle of repose of the pellet pile changes about 8◦ and 20◦, respectively, which indicates that static friction coefficient has a stronger impact on the angle of repose. In general, high static friction is always accompanied by high rolling friction, and the latter depends on the physical properties on the particle surface. However, there is a decreasing trend when μ*<sup>r</sup>* > 0.6 or μ*<sup>s</sup>* > 0.8. A reason may be that the heap has reached the maximum stable angle at this point, and a further increase in the friction coefficient will cause the heap to collapse.

In addition to the effects of the DEM parameters on the angle of repose, the external conditions, such as the drop height cannot be ignored. Figure 6a shows the angle of repose for different drop heights for pellets with different static and rolling friction coefficients. It reveals that when the drop height increases, the angle of repose decreases and this trend will weaken when the friction coefficients increase. It was found that with an increase in the drop height, the bottom size of the heap decreased. Therefore, we define the normalized effective diameter (NED) to express the size, which is the diameter of the bottom circle of the heap where most particles gather, neglecting the particles scattered around the heap because there is an obvious boundary of the high-density particle area and the scattered particle area. Figure 6b shows that for particles with a large coefficient of static friction, the NED of the pile is small. In addition, the NED decreases sharply initially and then levels out when the drop height increases. The reason is that particles will have large kinetic energy when dropping from a high location, and when the particles collide with the packed bed, they more easily bounce and scatter around the heap.

**Figure 3.** Vertical cross-sections of the pellet pile simulated under different (**a**) rolling and (**b**) static friction (**b**) coefficients.

**Figure 4.** Extracted contours of the pellet pile for different (**a**) rolling and (**b**) static friction coefficients.

**Figure 5.** Relationship of the angle of repose of pellet piles and (**a**) rolling friction coefficient with μ*<sup>s</sup>* = 0.15, and (**b**) static friction coefficient with μ*<sup>r</sup>* = 0.12. Error bars indicate the deviation of the angle of repose in different directions of the pile.

**Figure 6.** (**a**) Angle of repose and (**b**) and normalized effective diameter of the heap (top view) with different coefficient of static and rolling friction for different drop heights in the Discharging Method. (The numbers in the two figures represent rolling and static friction coefficients, respectively) The inserted subfigure in (**b**) is a top view of the simulated pile.

#### 4.1.2. The angle of Repose by the Lifting Method

In the simulation of the Lifting Method, we designed four different cases (Table 3) to study the influence of the barrel size and lift speed on the angle of repose. Case 1 and Case 2 have the same coefficient of friction, but different barrel size. All the cases were considered with four different lifting velocities (0.005 m/s, 0.01 m/s, 0.02 m/s and 0.03 m/s). Figure 7 shows the angle of repose with different lifting velocities. The angle of repose tends to decrease when the lifting velocity increases, and this trend is weakened as the friction coefficient increases because a small lifting velocity makes it easier to keep the particles in their original positions. Through comparing Cases 1 and 2, it can be seen that the angle of repose will increase if the barrel size gets smaller. The dotted pink line and solid pink line in Figure 7 represent the angle of repose with different packing methods, but the same DEM parameters, which reveals that the angle of repose formed by the Lifting Method is larger than that determined by the Discharging Method.


**Table 3.** Different cases studied by the Lifting Method.

**Figure 7.** The angle of repose for different lifting velocities. Pink dotted and solid lines represent the angle of repose with different packing methods, but the same DEM parameters.

### 4.1.3. Simulated vs. Experimental Angles of Repose

The average of the experimentally determined angle of repose of the pellet pile is about 25◦. Comparing it with the simulated results in Figure 5, we found that when μ*<sup>r</sup>* = 0.12 and μ*<sup>s</sup>* = 0.15, the experimental and simulated results agree well. Thus, these two values can be used to study the BPD and average porosity of pellet piles. The profiles of the experimental and simulated heaps seen in Figure 8 as black and red lines illustrate the agreement. The figure also shows that the Lifting Method gives a higher heap and a larger angle of repose than the Discharging Method.

**Figure 8.** Profile of heap in simulation and experiment.
