## 4 Analysis of the Influence of Structural Parameters on the Erosion and Wear of Pipe Elbows
### The Impact of the Bending Angle on the Pipe Elbow Erosion Wear  
In the project, the bending angle of the elbow also affects the overall erosion wear rate of the elbow. The smaller the bend angle of the elbow, the stronger the constraint on small solid particles carried in the liquid phase, and the more violent the collision of the particles with the outer arch wall surface of the elbow. The effect of changing the bending angle at the inlet end on the erosion wear of pipe elbows is shown in the Figure 12.  
As shown in Figure 13, with the increase in the bending angle of the bend near the exit end of the bend, the maximum erosion location is from the side of the bias to the position of the central axis of the bend. When the bending angle is less than 90\({}^{\circ}\), both sections of the bend have more serious erosion areas. With the increase in the bending angle, the maximum erosion wear rate difference between the two sections of the bend increases. The inner wall of the bend with a smaller angle is subjected to an increased number of particle impacts, resulting in the existence of multiple erosion peaks in the bend.  
Figure 12: The effect of changing the bending angle at the inlet end on the erosion wear of pipe elbows.  
As can be seen in Figure 14a, at the inlet end of the bend angle of 45\({}^{\circ}\)-105\({}^{\circ}\), the overall maximum erosion wear rate of the bend changes gently. After exceeding 105\({}^{\circ}\), the maximum erosion wear rate of the bend increases. When changing the bending angle of the bend at the outlet end, the maximum erosion wear rate of the bend increases gradually with the increase in the bending angle.  
As illustrated in Figure 14b, when the bending angle of the inlet end of the bend increases from 45\({}^{\circ}\) to 90\({}^{\circ}\), the change in the erosion and wear rate there is gentle. When there is an increase from 75\({}^{\circ}\) to 135\({}^{\circ}\) at the inlet end of the bend, the erosion and wear rate change with the increase in the bending angle and decline. The erosion wear rate at the outlet end elbow is less affected by the change in the angle of the inlet end elbow [23]. Around a certain value, the erosion rate fluctuates up and down. However, when the inlet end elbow angle exceeds 105\({}^{\circ}\), the outlet end elbow erosion wear rate increases significantly. This is mainly because the increase in the bending angle of the inlet end bend results in a smoother flow of sand-carrying liquid. The sand particle incident angle decreases, and the degree of particle collision crushing is reduced, so that a large number of sand particles accumulate at the exit end of the bend, resulting in increased erosion and wear.  
Figure 14: Effect of the bending angle on erosion wear. (**a**) Comparison of the maximum erosion rate of a two-pipeline structure. (**b**) Changing the bending angle of the inlet end elbow. (**c**) Changing the bending angle of the outlet end elbow.  
Figure 13: The effect of changing the bending angle at the outlet end on the erosion wear of pipe elbows.  
As can be seen from Figure 14c, when the bend angle is located downstream of the liquid-phase flow and the bend angle of the exit bend is 75\({}^{\circ}\)\(\sim\)105\({}^{\circ}\), the change in the erosion and wear rate at the inlet end of the bend is small. After a bend angle of more than 105\({}^{\circ}\), the inlet end of the elbow erosion and wear increased.