## 4 Numerical Simulation
### Particle Flow Characteristics Under Different Gradations  
To evaluate the flowability of particles within the model under different particle size distributions, five monitoring surfaces were established inside the model prior to ore drawing. Nine monitoring points were arranged on each surface, as shown in Figure 22. During the draw process, real-time tracking of the particle height was performed at all 45 monitoring points. The particle height-versus-calculation step curves for different monitoring points within the model are presented in Figures 23-25. These curves illustrate the variation in monitoring point height with the calculation step. A particle's height is considered to be 0 when it descends continuously until it reaches the top plane of the drawbell opening. The cumulative calculation step count at which its height becomes 0 represents the number of steps required for it to move from its initial position to the drawbell opening. The ore extraction process demonstrates queuing behavior, requiring each ore unit to sequentially await clearance of the discharge outlet by preceding rocks before passing through. The computed step count directly equates to ore queuing duration, where fewer steps indicate  
Figure 21: Comparison of the relationships between the drawn height and the major axis/minor axis in the physical experiment and numerical simulation. (**a**) Major axis. (**b**) Minor axis. enhanced flow efficiency, while increased steps lead to longer release times for individual ore units. This cumulative step count can therefore serve as a quantitative indicator for evaluating particle flowability. Figure 23: Motion height-step curves of central monitoring points under different particle size distributions. (**a**) Gradient-I. (**b**) Gradient-II. (**c**) Gradient III. Figure 22: Layout of monitoring points. Figure 23 presents the height-versus-calculation step curves for the central monitoring point B2 in each layer. As the initial height of the monitoring point increases from layer 1 to layer 5, the calculation steps required to reach the top plane of the drawbell opening exhibit a continuous increase. However, comparing the numerical simulation results across different particle sizes reveals that Gradation I, possessing the smallest average particle size, also requires the fewest calculation steps for its central monitoring points B2 (layers 1-5) to reach the drawbell opening. Conversely, Gradation II ranks second, and Gradation III, owing to its largest average particle size, necessitates the highest number of calculation steps. The height-versus-calculation step curves for the left monitoring point B1 (shown in Figure 24) and the lower monitoring point C2 (shown in Figure 24) are similar to those presented in Figure 23. For particle Gradation I, the calculation steps required for each monitoring point to reach the bottom layer are fewer than those for corresponding points in the other two gradation models. Notably, in the monitoring curve of Figure 25, the time required for the B1 monitoring point in layer 1 to reach the bottom layer exceeds that of the B1 point in layer 2. The primary reason for this is that the layer 1 B1 point is situated outside the boundary of the extraction zone, where the flow velocity is lower than that of particles within the extraction zone. In particle size Gradation III (which has the largest  
Figure 24: Motion height-step curves of monitoring point B1 under different particle size distributions. (**a**) Gradient-I. (**b**) Gradient-II. (**c**) Gradient III. average particle size), the time required for its left monitoring point B2 to reach the bottom layer is longer than that for its monitoring points B2-3 in layer 3. The height-versus-calculation step curve for monitoring point C2 in Figure 23 is similar to those in Figures 23 and 24 mentioned above, with the exception that the height parameter of the layer 1 C2 point showed no significant change as ore drawing progressed.