*4.2. Porosity Distribution of Pellet Pile*

### 4.2.1. Simulated vs. Experimental BPD

The BPD of the pile is used to specifically and quantitatively describe the pile porosity. Figure 9 shows the simulated and experimental BPD of the pellet pile measured by the containers. The simulated results include porosity distribution in containers and in-unit boxes. The coordinate 0.00 on the abscissa represents the center position of the pile, and ±0.15 represent the edges. The trends of the curves are seen to be the same in the experiments and simulations. The porosity distribution shows a V-shaped appearance, where the central value is lower than that at the edge. In fact, the experimental and simulated values measured by the containers are all larger than the real ones (without containers) because of the so-called wall effect. The difference of the simulated results (equal value of BPD) with containers and without containers can be used to quantify this effect. We found that the wall effect would result in an error of 3.3 percent points compared with direct measurement without a container. In Figure 9, the experimental porosities are a little larger than the simulated ones because a drainage method was used to measure the porosity in the experiments, and the operation loss of water leads to a larger porosity. In order to further study the distribution of the porosity, the coordination number (CN) was employed, where CN expresses the number of particles in contact with one particle. Figure 10, where different colors represent different values, indicates that CN increases from the edge to the center of the pile, because of the compact packing of particles in the center. These results coincide with the findings on the porosity distribution. The central position of the heap is formed by the vertical falling particles, which have greater kinetic energy, causing a more compact structure of the pile. After the formation of the initial heap, the pile with the continuous falling particles will collapse, and the edges form.

**Figure 9.** Comparisons of simulated (with and without containers) and experimental bottom porosity distribution (BPD) of the pellet pile.

**Figure 10.** Coordination number of a vertical cross-section of the simulated pellet pile.

#### 4.2.2. Effects of Rolling and Static Friction on BPD

Figure 11 shows the BPD of the heap when the rolling and static friction coefficients change, where the inserted graphs show the average value of BPD. When the static and rolling friction coefficient change from 0.01 to 0.99, the average porosities change by 7 and 3 percent points, respectively, which means that the static friction coefficient has a greater impact on porosity. This conclusion is also supported by findings reported in the literature [3,6,30–33].

**Figure 11.** BPD of the pellet pile and the inserted graph is the average porosity (the average value of seven points on a curve) with different (**a**) static and (**b**) rolling friction coefficients.

Figure 12 depicts the frequency distribution of CN for different static and rolling friction coefficients, showing a maximum value of the frequency at CN ≈ 4. Thus, most particles are in contact with four neighboring particles. The static friction coefficient affects the frequency distribution, but mainly for μ*<sup>s</sup>* < 0.6, and the rolling friction seems to have no effect. As seen in Figure 13, when the static friction coefficient increases, the CN of the heap decreases, but the decrease is small for μ*<sup>s</sup>* > 0.6. The reason may be that if the CN is small, the porosity is large. The average CN of the heap is only affected by the rolling friction when the coefficient is very small.

**Figure 12.** Frequency distribution of coordination number with different (**a**) static and (**b**) rolling friction coefficients.

**Figure 13.** The average coordination number of the whole heap for different static (μ*<sup>r</sup>* = 0.12) and rolling friction (μ*<sup>s</sup>* = 0.15) coefficients.
