# Numerical Investigation of Erosion Wear Characteristics of Hydraulic Spillway

^{1}

^{2}

^{*}

## Abstract

**:**

^{3}to 6 kg/m

^{3}, and the maximum erosion of the spillway increased from 2.58 × 10

^{−7}kg/m

^{2}to 1.53 × 10

^{−6}kg/m

^{2}. The erosion at the bottom of the spillway and gate leaf increases first and then decreases with the increase in sediment diameter and reaches the maximum value when the particle size is 0.002 mm. The erosion at the bottom of the spillway and the gate leaf increases with different growth trends as the flow velocity increases, when the flow velocity increases from 2 m/s to 9 m/s and the maximum erosion amount at the bottom of the spillway increases from 3.66 × 10

^{−7}kg/m

^{2}to 1.14 × 10

^{−6}kg/m

^{2}, and the maximum erosion of the gate leaf increased from 1.66 × 10

^{−8}kg/m

^{2}to 8.98 × 10

^{−6}kg/m

^{2}. The erosion amount at the bottom of the spillway increases with the increase in the gate opening between 0 and 3 m and tends to be stable when the gate opening is greater than 3 m. The maximum erosion position moves to the rear part of the spillway with the change in the gate opening. The change in the gate opening has no obvious effect on the erosion amount of the gate leaf but only changes the area of the gate erosion part. Thus, the erosion wear distribution of spillway under different work conditions is summarized, and the qualitative study between the erosion wear and the distribution of sediment diameter, sediment concentration, flow velocity and gate opening degree is made.

## 1. Introduction

## 2. Numerical Model

#### 2.1. Engineering Background

^{3}. More than 90% of the sediment is concentrated in the flood season, and the water level in the flood season is 6.5 m, so the flood season of the spillway is seriously eroded by sediment. According to the relevant literature [28,29,30], the particle size of sediment in the Yellow River Basin ranges from 0.008 to 0.034 mm, and the average density is 2.73 × 10

^{3}kg/m

^{3}. In the simulation calculation, the influence of particle shape on spillway erosion is not considered, and the sand particles are assumed to be homogeneous spheres.

#### 2.2. Numerical Model

#### 2.2.1. VOF Model Theory

_{aq}represents the mass source and ρ represents the density. The sum of each phase volume fraction is 1, which can be expressed as:

#### 2.2.2. DPM Model Theory

_{p}is the particle velocity, ρ is the fluid density, ρ

_{p}is the particle density, and F

_{y}is the force in the Y direction. C

_{D}is the drag coefficient, and Re

_{p}is the relative Reynolds number. d

_{p}is particle diameter, u is the fluid velocity and μ is the hydrodynamic viscosity; α

_{1}, α

_{2}and α

_{3}are constants. The Erosion model agreed to the Erosion/Accretion model.

_{p}is the number of particles, m

_{p}is the mass of particles, C(d

_{p}) is the particle diameter function, F (α) is the invasion angle function, u

_{p}is the velocity of particles relative to the wall, and b(v) is the relative velocity function. In general, the empirical constant is 2.41, and A

_{face}is the wall area of the calculation region.

#### 2.3. Mesh Partitioning and Boundary Conditions

## 3. Result and Analysis

#### 3.1. Spillway Erosion Analysis

^{3}, opening degree of the three radial leaves of the spillway were 2 m, and the water level before the radial leaf was 6.5 m. In the simulation process, the discrete phase is opened after the flow is stable, and the distribution of spillway erosion is observed after 20 s of particle flow erosion. The erosion amount of each part of the spillway obtained from simulation analysis is shown in Figure 3. As can be seen from Figure 3a, serious erosion at the bottom of the spillway is mainly distributed gate chamber section and the front part of the middle section of the spillway, while the erosion at the front section and the rear section of the spillway is very slight. Figure 3b shows the erosion situation of the spillway wall, and there is no obvious large-scale erosion phenomenon on the spillway wall. Figure 3c shows the erosion of the gate pier in the spillway, and there is no obvious erosion of the gate pier. Figure 3d shows the erosion of the gate leaf in the spillway, and the erosion is obvious and evenly distributed on the curved gate leaf.

#### 3.2. Effect of Erosion under Different Conditions

#### 3.2.1. Effect of Particle Size on Corrosion

^{3}, the water depth before setting the spillway is 6.5 m, the opening degree of the gate is 1 m, and the flow velocity is 5 m/s. The simulation process is that the multiphase flow model is opened after the water flow is stable, and the erosion cloud images of the bottom of the spillway and the gate leaf five seconds later are shown in Figure 6 and Figure 7. Obviously, when only sediment diameter changes, the position of maximum erosion at the bottom of the spillway remains unchanged, which is in front of the ground sill (the position of the ground sill is indicated in Figure 6), and the erosion position is mainly concentrated around the ground sill. With the increase in sediment diameter, the erosion of gate leaf tends to be evenly distributed.

#### 3.2.2. Effect of Sediment Concentration on Erosion

^{3}, 2 kg/m

^{3}, 3 kg/m

^{3}, 4 kg/m

^{3}, 5 kg/m

^{3}, 6 kg/m

^{3}were taken for simulation analysis. Sediment particle size is 0.025 mm, the water depth before the spillway is set at 6.5 m, the opening degree of the gate is 1 m, and the flow velocity is 5 m/s. The shapes of erosion cloud diagrams corresponding to different sediment concentrations are consistent, and the erosion conditions are basically the same as those in Figure 6e and Figure 7e, except that the amount of erosion varies with different sediment concentrations. The maximum value of erosion amount corresponding to different sediment concentrations is shown in Figure 10. The value of erosion amount shows an obvious linear relationship with the increase in sediment concentration, and this distribution rule is also obviously consistent with the conclusion of Hu [6].

#### 3.2.3. Effect of Flow Velocity on Erosion

^{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 sill, while the most obvious erosion area is also distributed around the ground sill. As the inlet flow velocity increases, the bottom 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.

_{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 α

_{1}, the gate leaf radian is ignored, and the impact angle is as follows:

_{2}at the bottom of the spillway is expressed as:

_{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, α

_{1}tends to be 90°, and α

_{2}tends to be 0°. The study of Xiong et al. [9] shows that the erosion amount will change with the change in erosion angle. Therefore, the complex relationship between the maximum erosion amount of the gate and the inlet velocity of the flow field is caused by the change in particle erosion velocity and impact angle.

#### 3.2.4. Effect of Gate Opening on Erosion

^{3}, the particle size of sediment is 0.025 mm, and the inlet velocity of the fluid domain is 5 m/s. The cloud diagram of spillway erosion results is shown in Figure 14. As the opening degree of the gate increases, the location where the maximum erosion occurs at the bottom of the spillway gradually moves backward, and the overall distribution of the erosion area has no obvious rule. The change in gate erosion with the opening is mainly reflected in that of the increase in the gate opening, the contact area between gate and water becomes smaller, and the corresponding erosion area becomes smaller.

## 4. Conclusions

- (1)
- The spillway erosion mainly occurs at the bottom of the spillway chamber and the middle section, and the most serious erosion wear occurs near the ground sill. Compared with the bottom of the spillway, the gate leaf wear is relatively slight, but due to the importance of the radial leaf in hydraulic construction, the erosion wear of the gate leaf should not be underestimated;
- (2)
- Under the same other conditions, the erosion amount increases first and then declines with the increase in sediment particle size, and the maximum erosion amount increases linearly with the increase in sediment concentration;
- (3)
- The maximum erosion of the spillway is positively correlated with the flow velocity. At the bottom of the spillway, the erosion increment decreases with the increase in the flow velocity. At the gate, the erosion increases exponentially with the increase in the flow velocity;
- (4)
- The opening of the radial leaf will affect the amount and location of sediment erosion on the spillway. When the gate opening degree is small (0~3 m when the water level is 6.5 m), the erosion at the bottom of the spillway reduces with the increase in the gate opening. When the opening reaches a certain range, the maximum erosion at the bottom of the spillway is usually stable. At the same time, with the increase in the opening, the highest erosion area at the bottom of the spillway changes gradually from the bottom sill of the gate to the rear section of the gate;
- (5)
- In this paper, a mechanism model of spillway erosion is built through numerical simulation, which can predict the erosion of the gate to a certain extent. Further research in this paper can be carried out by collecting information such as sediment diameter, sediment concentration, flow velocity and gate opening degree of the spillway at each working time. Then the erosion simulation model is used to simulate the erosion of the spillway so as to realize more economical and effective operation and maintenance of the spillway.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 5.**Finite element model of fluid domain in middle gate chamber and corresponding middle gate section.

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**MDPI and ACS Style**

Zhang, C.; Zhang, Y.; Zhao, H.; Wang, M.; Wang, T.
Numerical Investigation of Erosion Wear Characteristics of Hydraulic Spillway. *Appl. Sci.* **2021**, *11*, 8118.
https://doi.org/10.3390/app11178118

**AMA Style**

Zhang C, Zhang Y, Zhao H, Wang M, Wang T.
Numerical Investigation of Erosion Wear Characteristics of Hydraulic Spillway. *Applied Sciences*. 2021; 11(17):8118.
https://doi.org/10.3390/app11178118

**Chicago/Turabian Style**

Zhang, Cong, Yuqi Zhang, Huadong Zhao, Mao Wang, and Tongtong Wang.
2021. "Numerical Investigation of Erosion Wear Characteristics of Hydraulic Spillway" *Applied Sciences* 11, no. 17: 8118.
https://doi.org/10.3390/app11178118