# Prediction for the Influence of Guide Vane Opening on the Radial Clearance Sediment Erosion of Runner in a Francis Turbine

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{3}and the maximum is 10.5 kg/m

^{3}. The sediment concentration in the Yellow River is higher. According to statistics, the average annual sediment concentration of the Sanmenxia reach of the Yellow River is 37.6 kg/m

^{3}. The high sediment concentration in rivers in China leads to sediment abrasion of 30~40% of hydropower stations [1,2].

^{3}/s, the rated head is 74 m, the guaranteed output is 13.8 MW, and the annual design power generation is 273.9 million kW·h. The high sediment concentration in Xinjiang makes the unit have serious sediment abrasion problem.

## 2. Mathematical and Geometrical Models

#### 2.1. Mathematical Model

#### 2.1.1. Governing Equations

_{t}is the source term. τ is the Reynolds stress defined as:

^{d}is the deviatoric Reynolds stress, k is the turbulent kinetic energy, δ is the Kronecker delta. Based on viscosity (ν

_{t}) assumptions, Equation (2) can be written as:

#### 2.1.2. Lagrangian Tracking of Particle Motion

_{p}is particle mass, u

_{p}is particle velocity, F

_{D}is resistance, F

_{B}is Basset force, F

_{G}is gravity, F

_{V}is virtual mass force, F

_{P}is pressure gradient force, and F

_{X}is the sum of other external forces considered.

_{s}is the slip velocity between particles and the liquid, C

_{D}is the drag coefficient related to Reynolds number, ρ

_{f}is the liquid density, ρ

_{p}is the particle density, D

_{p}is the particle diameter, and x

_{pi}is the spatial coordinate position of particles.

#### 2.1.3. Erosion Model

_{0}is the angle of maximum erosion, k

_{1}to k

_{4}, k

_{12,}and γ

_{0}are model constants and depend on the particle/wall material combination.

#### 2.2. Simulation Geometry Model

#### 2.2.1. Geometric Model Set Up

#### 2.2.2. Parameter Setting in Calculation Model

- (1)
- Boundary conditions

- (2)
- Calculation parameters

^{3}, the guide vane openings are 15°, 20°, and 30°; among these values, 20° of opening is the optimal opening (see Figure 5). The solution precision is set to 10

^{−5}. The interphase coupling between the fluid phase and the solid phase adopted the one-way coupling for the low particle concentration.

#### 2.3. Reliability Verification of Calculation Model

## 3. Result Analysis

#### 3.1. Flow Pattern of Turbine under Different Openings

#### 3.2. Sediment Distribution at Different Guide Vane Openings

#### 3.3. Sediment Erosion Distribution of Guide Vane and Runner Blade Wall

## 4. Conclusions

- (1)
- The increase in guide vane opening has an important effect on the particle motion in the runner. With the increase in guide vane opening, the velocity of sediment particles increases, and the impact velocity on the guide vane and runner wall increases. The particles have more energy to destroy the wall structure of the runner and blade. The smaller the opening, the higher the sediment concentration in the runner and guide vane channel. In the low-velocity region of the vortex return center, more particles are separated from the main flow into the vortex center of the channel and away from the runner wall. This is consistent with the flow change law in the runner and guide vane.
- (2)
- The opening of the guide vane affects the flow in the hydraulic turbine channel. When the opening of the guide vane is small, the velocity triangle of the water flow at the inlet of the blade head completely deviates from the design velocity triangle of the hydraulic turbine, the velocity loop of the water flow out of the guide vane cannot meet the velocity loop required by the runner blade, and the relative velocity angle of the water flow entering the runner is larger than the inlet angle of the runner blade, resulting in the water flow hitting the pressure surface of the runner blade at a large angle, and the flow phenomenon occurs at the head of the runner blade. The separated flow loses the restriction of the blade and forms a blade passage vortex in the runner.
- (3)
- The overall sediment erosion in the hydraulic turbine unit with the optimal opening is the smallest, and the erosion rate increases under a small opening and a large opening. The wear of the guide vane and the runner inlet head is mainly impact wear, and the sediment erosion on the outlet wall is mainly frictional wear. The sediment erosion in the unit channel is most serious under a large opening. The long-term wear of the runner inlet and guide vane outlet will cause the loss of local structure, increase the radial clearance of the runner, increase the clearance leakage, increase the vibration of the unit, and reduce the efficiency.

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 7.**Overall flow pattern of internal section of hydraulic turbine with different opening. (

**a**) 15° (

**b**) 20° (

**c**) 30°.

**Figure 12.**Volume fraction distribution of local solid phase in guide vane and runner passage: (

**a**) 15°, (

**b**) 20°, (

**c**) 30°.

**Figure 13.**Sediment erosion distribution of guide blade and runner blade under different openings: (

**a**) 15°, (

**b**) 20°, (

**c**) 30°.

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**MDPI and ACS Style**

Jin, Z.; Song, X.; Zhang, A.; Shao, F.; Wang, Z.
Prediction for the Influence of Guide Vane Opening on the Radial Clearance Sediment Erosion of Runner in a Francis Turbine. *Water* **2022**, *14*, 3268.
https://doi.org/10.3390/w14203268

**AMA Style**

Jin Z, Song X, Zhang A, Shao F, Wang Z.
Prediction for the Influence of Guide Vane Opening on the Radial Clearance Sediment Erosion of Runner in a Francis Turbine. *Water*. 2022; 14(20):3268.
https://doi.org/10.3390/w14203268

**Chicago/Turabian Style**

Jin, Zhiqiang, Xijie Song, Anfu Zhang, Feng Shao, and Zhengwei Wang.
2022. "Prediction for the Influence of Guide Vane Opening on the Radial Clearance Sediment Erosion of Runner in a Francis Turbine" *Water* 14, no. 20: 3268.
https://doi.org/10.3390/w14203268