## 4 Flow Velocity Analysis  
### Velocity Analysis of Front Nozzle  
In order to observe more clearly the flow field changes in water jet nozzles with different schemes within a slurry pipeline of 200 mm diameter, CFD post-processing was conducted on the Fluent simulation data. In the 2023 version of CFD processing software, the velocity-displacement relationship in the front jet region (indicated by the yellow line in the figure) is examined. The speed data collected along the yellow line are imported into Origin for further analysis and research. The resulting velocity-displacement relationship in this region is presented in Figure 11.  
Firstly, the aperture of the four schemes depicted in the Figure 11 is 3.5 mm, and the jet outlet velocity setting is uniform for all of them. The instantaneous space at the front jet outlet enlarges, leading to fluctuations in velocity, while the initial velocities among the four schemes remain relatively similar. However, the velocity subsequently undergoes a rapid decay, which is attributed to the presence of broken rocks within the space and the backflow that cannot be discharged in a timely manner, thus causing obstruction to the jet. On the other hand, the reason for this is that when water flows from a narrow space into a larger space, the kinetic energy of the water jet dissipates rapidly. As the four schemes approach the blocking surface, their velocities undergo rapid changes, which can be attributed to the velocity attenuation that occurs once again due to the wall backflow phenomenon. Through the analysis of the velocity changes in the diagram for the four schemes, it can be concluded that the velocity of the front jet impacting the wall, for schemes with rear jet axis angles of \(25^{\circ}\), \(30^{\circ}\), \(35^{\circ}\), and \(40^{\circ}\) and an aperture of 3.5 mm, are 5.71 m/s, 4.15 m/s, 8.07 m/s, and 7.72 m/s, respectively. For the scheme with the rear nozzle's inclination angle of \(35^{\circ}\), the front jet exhibits the maximum velocity on the blockage surface, suggesting that the vortex area in the region has minimal impact on jet obstruction and consequently has less influence on the outlet jet velocity. This can impact the blocking surface at a faster speed. Furthermore, the overall velocity variation in the scheme with a rear nozzle axis angle of \(35^{\circ}\) is smoother compared to the other three schemes, with the exception of a slightly  
Figure 10: Aperture 2 mm.  
smaller velocity fluctuation of 72 mm. The wall backflow phenomenon is also relatively minor in this case. In the 30\({}^{\circ}\) angle rear nozzle scheme, the front jet velocity decays rapidly due to the small angle between the jet axes of the rear nozzle and the water in front of the tube. This results in a weak entrainment effect, making it difficult to efficiently discharge the accumulated water outside the tube.  
In terms of the velocity change in the front jet, the overall velocity of the front jet in the scheme with a rear nozzle inclination angle of 35\({}^{\circ}\) is greater than that of the other three schemes, and the velocity it reaches when impacting the blockage surface is the highest, the velocity change curve is smoother, and the kinetic energy dissipation rate is lower, which makes it more conducive to the dredging work performed by the water jet nozzle.