## 4 Flow Velocity Analysis
### Velocity Analysis of Pipe Wall Flow Field  
When the rear jet strikes the pipe wall, the backflow from the front jet creates an interference, leading to varying velocities along the wall at the point of contact. This phenomenon contributes to a complex flow pattern in the vicinity. In analyzing the four different schemes, it is noted that the instantaneous wall velocities vary significantly: 1.22 m/s for the 25\({}^{\circ}\) scheme, 1.46 m/s for the 30\({}^{\circ}\) scheme, 2.52 m/s for the 35\({}^{\circ}\) scheme, and 2.53 m/s for the 40\({}^{\circ}\) scheme. Notably, the rear nozzle jet with a 25\({}^{\circ}\) axis angle has the longest distance to the wall, resulting in the lowest instantaneous velocity due to substantial kinetic energy loss. As the inclination angle increases, the jet distance shortens, yet the contact wall velocity fails to escalate. This phenomenon is primarily attributed to the intricate interaction between the front jet's backflow and the rear jet's entrainment. Consequently, the distance to the wall exerts a significant influence on the energy attenuation of the jet flow.  
An analysis of the simulation results for an aperture of 2 mm with varying post-spray hole inclination schemes has been conducted. The numerical relationship between velocity and displacement, measured 20 mm from the pipe wall, was examined, and a line chart (Figure 12) was generated for further analysis.  
Figure 11: (**a**), the yellow line represents the sampling position and the origin coordinates in the model; (**b**), the velocity and displacement of the fluid near the pipe wall in the flow field with a pore size of 3.5 mm and a rear inclination angle of 25\({}^{\circ}\)–40\({}^{\circ}\).  
From the diagram, it is evident that although the 40\({}^{\circ}\) inclination scheme exhibits the highest velocity at 20 mm from the pipe wall, this is solely an instantaneous value. This observation can be attributed to the large inclination angle, resulting in a shorter distance between the jet and the pipe wall, which subsequently leads to less kinetic energy loss, thereby producing the highest velocity. However, the velocity of the 40\({}^{\circ}\) inclination angle scheme at the front end of the pipeline is not the highest, as the liquid with substantial kinetic energy tends to diffuse along the pipe wall upon impact with the rear nozzle. Upon impacting the pipe wall, the jet of the 40\({}^{\circ}\) inclination angle scheme exhibits the shortest stroke, and the instantaneous kinetic energy imparted to the contact pipe wall is the highest, resulting in more diffuse jets, the increased diffusion of water towards the front end of the pipeline, caused by the impact of the front jet on the blocking surface, results in the water being subjected to impacts, vibrations, and vortex generation. Consequently, this hinders the timely flow of water at the front end of the pipeline into the outlet. A significant volume of water converges at the front end, which results in the attenuation of forward jet momentum and a subsequent decrease in velocity. The reflux water and vortex wrap around the gravel, impacting the jet nozzle, which exacerbates wear and ultimately reduces its service life. Upon observing the flow field images of the four schemes, it is apparent that the image of the 35\({}^{\circ}\) inclination scheme displays no pronounced mutations at the two peaks, exhibiting a gentler flow compared to the other three schemes. Hence, the flow field of the 35\({}^{\circ}\) inclination scheme is more stable, with the least occurrence of vortex and backflow phenomena.