## 3 Result and Analysis
### Effect of Erosion under Different Conditions
#### 3.2.3 Effect of Flow Velocity on Erosion  
Under the condition of other factors being the same, the influence of the inlet velocity of the spillway on erosion was analyzed. The inlet velocity of the fluid domain is 2 m/s, 3 m/s, 4 m/s, 5 m/s, 6 m/s, 7 m/s and 8 m/s, 9 m/s. The sediment concentration is 3.2 kg/m\({}^{3}\), the sediment particle size is 0.025 mm, the water depth before setting the spillway is 6.5 m, and the opening degree of the gate is 1 m. The cloud diagram of the bottom erosion of spillway corresponding to different flow velocities is shown in Figure 11. Under different inlet flow velocities, the maximum erosion area of the spillway remains unchanged and is always in front of the ground sil, while the most obvious erosion area is also distributed around the ground sil. As the inlet flow velocity increases, the bottom  
Figure 10: Relationship between erosion and sediment concentration. Figure 9: Cloud diagram of particle velocity distribution under different particle sizes. erosion area of the spillway becomes larger. When the speed is greater than 7 m/s, there are also noticeable erosion areas in the rear part of the middle section. The erosion amount distribution of different flow rates corresponding to the gate leaf part is basically the same, and the erosion amount cloud diagram is basically the same as that of Figure 7e. The maximum erosion amount corresponding to different inlet flow velocities is shown in Figure 12. In general, the erosion amount increases with the increase in flow velocity, but the growth trend is more complex. For the bottom of the spillway, the erosion increment decreases with the increase in the flow velocity. When the velocity is greater than 7 m/s, the erosion increment does not increase much and tends to be stable. For the gate, the erosion increases exponentially with the increase in flow velocity. Figure 11: Erosion cloud diagram of spillway bottom at different flow rates. Figure 12: Relationship between erosion amount and inlet velocity of flow field. The relationship between erosion and flow velocity at the bottom of the spillway and gate leaf is complicated. The relationship between erosion velocity and flow velocity is analyzed from particle energy and particle velocity vector. For particles, the kinetic energy equation is:  
\[e_{k}=\frac{1}{2}m_{p}v^{2} \tag{9}\]  
where, \(e_{k}\) is the kinetic energy of the particle, \(m_{p}\) is the mass of the particle, and \(v\) is the velocity value of the particle. When particles impact, their own kinetic energy will affect the erosion amount. However, the relationship between kinetic energy and velocity is a quadratic function, so the change rule of erosion amount and velocity cannot be explained from the perspective of kinetic energy alone. From the perspective of particle movement, the impact of sediment particles on the face plate and the bottom of the spillway is shown in Figure 13. For the impact angle of gate leaf \(\alpha_{1}\), the gate leaf radian is ignored, and the impact angle is as follows:  
\[\alpha_{1}=\arctan\frac{v_{y}}{v_{z}}=\frac{v_{0}+v^{\prime}}{gt} \tag{10}\]  
The impact angle \(\alpha_{2}\) at the bottom of the spillway is expressed as:  
\[\alpha_{2}=\arctan\frac{v_{z}}{v_{y}}=\arctan\frac{gt}{v_{0}+v^{\prime}} \tag{11}\]  
where, \(v_{0}\) represents the initial velocity of the sand inlet, \(v_{y}\) and \(v_{z}\) represent the velocity components of the sand in horizontal and vertical directions, respectively, represent the velocity increment caused by water carrying action, \(g\) is the acceleration of gravity, and T is the time value of the particle moving from the flow field inlet to the current position. As \(v_{0}\) increases, \(\alpha_{1}\) tends to be \(90^{\circ}\), and \(\alpha_{2}\) tends to be \(0^{\circ}\). The study of [PERSON] et al. [9] shows that the erosion amount will change with the change in erosion angle.