## 4 Analysis of the Influence of Structural Parameters on the Erosion and Wear of Pipe Elbows
### The Impact of the Spatial Angle on Pipe Elbow Erosion Wear  
The pipeline structure of the connected section of the two bends can be rotated relative to each other. Changing the space angle between the two bends, the liquid phase fluid flows through the two sections of the bend [24]. The flow direction is different, resulting in different rates of erosion and wear. A cloud diagram of different angles of pipeline structure erosion wear is shown in Figure 15.  
An increase in the spatial angle of the two sections of the bend is shown in Figure 15. The maximum erosion location of the bend is changed from the lower end near the outlet end of the bend to the upper end near the inlet end of the bend. However, the maximum erosion wear rate at the first section of the bend does not change greatly. This is due to the two sections of the bend at a low angle and the convex wall of the bend being in the same party. The particles flow along the outer wall of the connecting straight pipe after flowing through the first section of the bend. When the spatial angle is greater than 30\({}^{\circ}\), the maximum erosion area of the lower bend is deflected to the side of the bend. In addition, there are multiple erosion peaks. When the connection angle exceeds 90\({}^{\circ}\), only a small portion of the particles flowing downstream along the wall of the straight pipe will accumulate at the second section of the bend [25]. This reduces the second bend erosion wear rate. As illustrated in Figure 16a, the maximum erosion wear rate decreases as the spatial angle between the two bends increases. Between 90\({}^{\circ}\) and 120\({}^{\circ}\), the maximum erosion rate changes less as the spatial angle between the two bends increases. As shown in Figure 16b, the maximum erosion wear rate at the inlet end of the bend floats up and down around a certain value as the spatial clamp angle increases, but the difference is small. Meanwhile, the maximum erosion wear rate at the exit end of the bend gradually decreases with the increase in the spatial angle [26]. When the spatial angle exceeds 120\({}^{\circ}\), the erosion wear rate tends to stabilize. Figure 15: The effect of changing the spatial angle on the erosion wear of space pipe elbows. Initial boundary conditions and meshing  
In the boundary condition setting, the inlet end is set to velocity inlet, the discrete phase of the inlet and outlet ends is set to escape and the wall condition is set to the default no-slip boundary. The discrete phase of the pipe wall is set as reflect, the gravitational acceleration is 9.8 m/s\({}^{2}\), the mass flow rate of the particles is 0.2 kg/s, the particle diameter is 0.00045 m and the impact angle function of the particles is defined in a segmented linear way. There is a certain amount of energy dissipation after the sand particles collide with the inner wall of the pipeline. This results in the particle velocity after collision being less than the initial velocity at the time of incidence. The energy dissipation before and after sand particle impact is defined using the wall recovery coefficient [27; 28; 29]. Numerical simulation results and analysis  
The numerical simulation method is used to calculate and analyse four common blind pass pipe types with different lengths and sizes using Fluent software. The erosion and wear results and the particle trajectories obtained are shown in Figure 16.  
As revealed in Figure 21, the number of particles entering the blind pass increases as the length and area of the T-shaped blind pass tube increases. The residence time of particles in the blind pass increases. The erosion wear rate at the pipe elbows as well as the maximum erosion wear rate decreases significantly, and the area of erosion wear is more uniform. The location of maximum erosion for a typical pipeline structure is at the lower end of the bend. In contrast, the maximum erosion location of the blind pass tube is at the junction of the blind pass tube and the elbow [30].