# Ballast Flow Characteristics of Discharging Pipeline in Shield Slurry System
## 3 Numerical Model Validation  
The ballast flow characteristics and the suspension velocity were computed and compared with the experimental data, which were acquired from the hydraulic lifting experiment platform, for verification of the ballast motion model. Table 5 list the parameters that were used for the numerical model.  
In the experiment, the ballast was pre-stacked on the top of the screen in the vertical pipeline, and by adjusting the working frequency of the pump, we observed a change in the slurry flow rate in the vertical pipeline, and the ballast motion state in the vertical pipeline was recorded by a high-speed camera (Phantom V310, Vision Research Inc., New Jersey, USA) during the flow rate from low to high. The test platform was composed of a pump, a flowmeter, a plexiglass tube, a blanking box, and a feeding machine. The length of the vertical lifting pipe section was 4 m, the plexiglass pipe in the observation section was 2 m, and the diameter of the pipe section was 200 mm. Figure 7 shows the specific structure.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Unit** \\ \hline \(L_{3}\) & 4 & m \\ \(D_{p}\) & 200 & mm \\ \(d_{b}\) & \(10,20,30,40\) & mm \\ \(\rho_{b}\) & 1860 & kg/m\({}^{3}\) \\ \(\rho_{f}\) & 980 & kg/m\({}^{3}\) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Data used for verification of numerical model and experiment.  
Figure 6: Computational flow chart of two-way coupling method (CFD–DEM) coupling procedure.  
The ballast group adopted spherical particles of uniform size with ballast density of 1860 kg/m\({}^{3}\), weight of the ballast group of 10 kg, and the conveying medium in the pipeline was water to facilitate observation and data acquisition. A high-speed camera was used to capture the motion state of the ballast group in the plexiglass pipe section under different flow conditions, as shown in Figure 8. We concluded that the motion state of the ballast group in the simulation model under different flow conditions is basically consistent with the observed results in the experiment. Taking a 20 mm ballast as an example, when the water flow rate in the vertical pipeline is 26 m\({}^{3}\)/h, the ballast accumulated above the screen is in a static state. When the flow rate increased to 51 m\({}^{3}\)/h, the ballast group changes from a static state to a slowly rising state, with the upper ballast in a free state and the lower ballast in a concentrated distribution. The ballast was distributed in the pipeline and entered the suspension state when the flow rate reached 74 m\({}^{3}\)/h. The suspension velocity was 0.65 m/s in the experiment. In the hydraulic lifting numerical model, when the flow rate was 80 m\({}^{3}\)/h, the ballast group was evenly distributed in the whole pipeline. At this time, the corresponding ballast velocity was 0.7 m/s.  
Similarly, the suspension velocities of ballast group with sizes of 10, 30, and 40 mm were obtained, as shown in Figure 9. The maximum difference between the experimental and simulation data was 8%. The simulation results are consistent with the experimental results.  
Figure 8: Comparison diagram between simulation and experiment on the motion state of ballast with size of 20 mm when \(Q=\) (**a**) 26, (**b**) 51, and (**c**) 74 m\({}^{3}\)/h.  
Figure 7: Schematic diagram of hydraulic lifting test bench for vertical pipe.