# Evaluation of the Influence of Upstream Flow on the Energy Characteristics of a Giant Kaplan Turbine

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## Abstract

**:**

## 1. Introduction

## 2. Research Method

#### 2.1. Governing Equation

#### 2.2. Calculation Model and Boundary Conditions

#### 2.3. Mesh Division

## 3. Results and Analysis

#### 3.1. Impact of Upstream Reservoir Flow on Unit Flow

#### 3.2. Impact of Upstream Reservoir Flow on Unit Efficiency

#### 3.3. Impact of Upstream Reservoir Flow on Unit Output

## 4. Conclusions

- Due to the influence of the layout position of the left bank unit, there is a significant deviation of streamlines near the inlet of Unit 1, which is significantly different from the normal flow at the inlet of Unit 1 under ideal conditions. As a result, the flow rate of Unit 1 under the same water level conditions is significantly lower than that of Unit 2 and Unit 3.
- Based on the relationship curve between unit efficiency and unit flow, the estimated efficiency values of the three units on the left bank under different water level conditions are obtained through interpolation. It can be found that due to the uneven distribution of flow in the upstream reservoir area, the efficiency of Unit 1 is significantly lower than the design value under the same water level and inflow conditions, especially when the efficiency drops by more than 5% under low water level conditions.
- Comparing the output of three units on the left bank under different water level conditions, it is found that the decrease in output of Unit 1 compared to the design value is greater than 3%, and even reaches 20% under low water level conditions. This is consistent with the phenomenon observed during actual operation on site.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CFD | Computational Fluid Dynamics |

VOF | Volume of Fluid |

## References

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**Figure 3.**Local calculation domain of free surface flow in upstream reservoir. (

**a**) Cross Section. (

**b**) Fluid distribution.

**Figure 5.**Mesh division. (

**a**) Meshes of the overall model. (

**b**) Meshes near the inlet section of the unit.

**Figure 8.**Unit flow of three units on the left bank under different water level conditions. (

**a**) ${H}_{up}$ = 61 m. (

**b**) ${H}_{up}$ = 55.67 m. (

**c**) ${H}_{up}$ = 50.33 m. (

**d**) ${H}_{up}$ = 45 m.

**Figure 9.**Relationship between unit efficiency and unit flow under different water level conditions. (

**a**) ${H}_{up}$ = 61 m. (

**b**) ${H}_{up}$ = 55.67 m. (

**c**) ${H}_{up}$ = 50.33 m. (

**d**) ${H}_{up}$ = 45 m.

**Figure 10.**Estimated efficiency values of three units on the left bank under different water level conditions. (

**a**) ${H}_{up}$ = 61 m. (

**b**) ${H}_{up}$ = 55.67 m. (

**c**) ${H}_{up}$ = 50.33 m. (

**d**) ${H}_{up}$ = 45 m.

**Figure 11.**Difference between the estimated and designed efficiency values of the three units on the left bank under different water level conditions. (

**a**) ${H}_{up}$ = 61 m. (

**b**) ${H}_{up}$ = 55.67 m. (

**c**) ${H}_{up}$ = 50.33 m. (

**d**) ${H}_{up}$ = 45 m.

**Figure 12.**Estimated output values of three units on the left bank under different water level conditions. (

**a**) ${H}_{up}$ = 61 m. (

**b**) ${H}_{up}$ = 55.67 m. (

**c**) ${H}_{up}$ = 50.33 m. (

**d**) ${H}_{up}$ = 45 m.

**Figure 13.**Relative difference between estimated output values and design values of three units on the left bank under different water level conditions. (

**a**) ${H}_{up}$ = 61 m. (

**b**) ${H}_{up}$ = 55.67 m. (

**c**) ${H}_{up}$ = 50.33 m. (

**d**) ${H}_{up}$ = 45 m.

Upstream Water Level ${\mathit{H}}_{\mathit{up}}$ (m) | Condition | Unit Working Head H (m) | Ideal Unit Specific Discharge ${\mathit{Q}}_{11}$ (m${}^{3}$) |
---|---|---|---|

61 | 1 | 37.79 | 585.34 |

2 | 805.12 | ||

3 | 1023.56 | ||

55.67 | 4 | 31 | 660.17 |

5 | 903.43 | ||

6 | 1147.51 | ||

50.33 | 7 | 23.41 | 763.38 |

8 | 1054.91 | ||

9 | 1335.78 | ||

45 | 10 | 10.07 | 1033.45 |

11 | 1624.93 | ||

12 | 2053.18 |

Upstream Water Level ${\mathit{H}}_{\mathit{up}}$ (m) | a | b | c | d | e |
---|---|---|---|---|---|

37.79 | - | 4.424 × ${10}^{-10}$ | −1.196 × ${10}^{-6}$ | 1.072 × ${10}^{-6}$ | 0.6111 |

31 | −7.733 × ${10}^{-13}$ | 3.117 × ${10}^{-9}$ | −4.686 × ${10}^{-6}$ | 3.126 × ${10}^{-3}$ | 0.1496 |

23.41 | −1.525 × ${10}^{-13}$ | 8.127 × ${10}^{-10}$ | −1.67 × ${10}^{-6}$ | 1.567 × ${10}^{-3}$ | 0.3568 |

10.07 | - | 2.765 × ${10}^{-10}$ | −1.263 × ${10}^{-6}$ | 2.143 × ${10}^{-3}$ | −0.659 |

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**MDPI and ACS Style**

Luo, H.; Liu, C.; Luo, H.; Zhou, L.; Wang, Z.
Evaluation of the Influence of Upstream Flow on the Energy Characteristics of a Giant Kaplan Turbine. *Water* **2023**, *15*, 3920.
https://doi.org/10.3390/w15223920

**AMA Style**

Luo H, Liu C, Luo H, Zhou L, Wang Z.
Evaluation of the Influence of Upstream Flow on the Energy Characteristics of a Giant Kaplan Turbine. *Water*. 2023; 15(22):3920.
https://doi.org/10.3390/w15223920

**Chicago/Turabian Style**

Luo, Hongyun, Chengming Liu, Haiqiang Luo, Lingjiu Zhou, and Zhengwei Wang.
2023. "Evaluation of the Influence of Upstream Flow on the Energy Characteristics of a Giant Kaplan Turbine" *Water* 15, no. 22: 3920.
https://doi.org/10.3390/w15223920