# Numerical Simulation and Engineering Application of a Dovetail-Shaped Bucket

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Model and Validation

#### 2.1. Numerical Model Setup

#### 2.2. Design of the Validation Experiments

#### 2.3. Boundary Condition Setting and Mesh Convergence Analysis

^{−3}, the calculation was considered to be convergent.

_{s}= 1.25. Taking working condition A as an example, the calculation results for the GCI are shown in Table 2.

#### 2.4. Comparison of Validation Results

## 3. Engineering Application and Case Analysis

#### 3.1. Introduction and Research Condition

^{3}, with an irrigation capacity of 4.15 million m

^{3}, thus making it a type IV small engineering project. The flood control standard of the dam is based on a 200-year flood event, while it is designed according to 30-year flood levels and the energy dissipation and anti-erosion design are based on the 20-year flood standard. The spillway energy dissipation structure consists of two sand wash bottom holes, three overflow gate holes, and a spillway. The gates are numbered from left to right as #1, #2, and #3, as shown in Figure 7.

_{1}= 13°, the right bank sidewall angle was taken to θ

_{2}= 6°, and the radius R = 10.2 m. The flow state of the nappe was controlled by changing the deflecting angle and the width of the dovetail slit. Figure 8 shows the shape of the dovetail slit, while the designed schemes are summarized in Table 4.

#### 3.2. Establishment of the Numerical Model

#### 3.3. Analysis of the Calculated Results

#### 3.3.1. Distribution of the Water Nappe Flow of Each Scheme

#### 3.3.2. Distribution of the Bottom Velocity under Different Working Conditions

#### 3.3.3. Distribution of the Bottom Pressure under Different Working Conditions

#### 3.3.4. Construction and Pitch of the Water Nappe

## 4. Summary

- Using the check flood level of 200-year flood conditions as the standard, after debugging, the angles of both sidewalls were set to θ
_{1}= 13° and θ_{2}= 6°. Based on this, the width of width B and the deflecting angle of dovetail slit θ_{3}were selected as variables. Four types of solutions were presented: B = 6 m and 8 m, and θ_{3}= 0° and −5°, and the water tongue hydraulic characteristics were analyzed. The results showed that the dovetail slit could effectively stretch the longitudinal length of the water nappe. As B increased, the flow rate increased, and the inner and outer edges of the water nappe and the throw distance decreased. When the opening width was smaller, the position of the water nappe entry was effectively distributed along a straight line. When the opening width increased, the position of the water nappe entry exhibited a curved distribution, and the direction of bending was opposite that of the river channel. - This study was based on the model of scheme II, and it analyzed the 30-year, 20-year, and 5-year flood design standard conditions under three different working conditions of the characteristics of the water nappe. The results showed that different working conditions resulted in different water flow patterns, but they all could be attributed to the main river channel. The differences arose mainly due to the different operation of the gate opening, which contributed to the large difference in the pattern of the water nappe. There was a slight difference between working condition 1 and working condition 2. However, in working condition 3, three surface holes were partially opened by 20%, and the flow discharge was small, resulting in the formation of three water nappe. In working condition 4, both the number 1 and number 3 surface holes were opened by 20%, and the water nappes on both sides entered the river channel after collision in the air.
- As a result of the different operation models in various working conditions, the range and size of the discharge flow, scouring of the downstream riverbed, and the area of negative pressure on the back surface of the overflow dam were all different.
- Different working conditions yielded different throw distances. The longitudinal stretching of the water nappe along the river course was suitable under working conditions 2 and 3, with lengths of 29.3 m and 20.6 m, respectively. Under working condition 4, two water streams did not pass through the notch of the anti-arc segment, and they were collected in the downstream channel after collision in the air without any obvious longitudinal stretching.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 12.**Flow patterns and the position of nappe entry into the downstream channel for each working condition.

Modeling Scheme | Working Condition A | Working Condition B | Working Condition C |
---|---|---|---|

Flow Rate (m^{3}/s) | 0.030 | 0.025 | 0.020 |

Flow Depth (m) | 0.143 | 0.127 | 0.109 |

Mesh Size D (m) | Total Grid (Millions) | $\mathit{r}({\mathit{D}}_{\mathit{k}}/{\mathit{D}}_{\mathit{k}+1})$ | Q (m^{3}/s) | Fractional Error $\left|\mathit{\epsilon}\right|=\left|\frac{{\mathit{Q}}_{\mathit{k}}-{\mathit{Q}}_{\mathit{k}+1}}{{\mathit{Q}}_{\mathit{k}+1}}\right|$ | $\mathit{G}\mathit{C}\mathit{I}=\frac{{\mathit{F}}_{\mathit{s}}\left|\mathit{\epsilon}\right|}{{\mathit{r}}^{\mathit{p}}-1}\times 100(\%)$ |
---|---|---|---|---|---|

0.018 | 5.04 | - | 2.997808 × 10^{−2} | - | - |

0.015 | 7.02 | 1.2 | 3.017997 × 10^{−2} | 0.006895 | 4.18 |

0.010 | 9.37 | 1.5 | 3.022485 × 10^{−2} | 0.001485 | 0.37 |

Working Condition | Inner Edge Jet Trajectory Length (m) | Relative Error (%) | Outer Edge Jet Trajectory Length (m) | Relative Error (%) | Water Nappe Highest Point (m) | Relative Error (%) | |||
---|---|---|---|---|---|---|---|---|---|

Experimental Value | Simulation Value | Experimental Value | Simulation Value | Experimental Value | Simulation Value | ||||

A | 0.37 | 0.37 | 0.00 | 2.17 | 2.14 | 1.38 | 0.52 | 0.48 | 7.69 |

B | 0.43 | 0.41 | 4.65 | 1.97 | 1.93 | 2.03 | 0.45 | 0.42 | 6.67 |

C | 0.47 | 0.46 | 2.13 | 1.78 | 1.77 | 0.56 | 0.43 | 0.39 | 9.30 |

Scheme | Left/Right Side-Wall Deflecting Angle | Width of Dovetail-Shaped Bucket (m) | Deflecting Angle of Dovetail Slit |
---|---|---|---|

I | θ_{1} = 13°, θ_{2} = 6° | 6 | θ_{3} = 0° |

II | θ_{1} = 13°, θ_{2} = 6° | 6 | θ_{3} = −5° |

III | θ_{1} = 13°, θ_{2} = 6° | 8 | θ_{3} = 0° |

IV | θ_{1} = 13°, θ_{2} = 6° | 8 | θ_{3} = −5° |

**Table 5.**Characteristics of the water level and discharge conditions used in the numerical simulations.

Working Condition | Flood Standard | Gate Opening (Numerical Simulation) | Maximum Reservoir Water Level (m) | Rated Flow Rate of Flood Discharge Building (m^{3}/s) | Tail Water Level (m) |
---|---|---|---|---|---|

1 | Check flood standard: once in 200 years | Three-hole full opening | 735.5 | 672 | 689.7 |

2 | Design flood standard: once in 30 years | Three-hole full opening | 734.8 | 506.2 | 688.6 |

3 | Energy dissipation and anti-impact design standard: once in 20 years | Three-hole opening 20% (e = 1.5 m) | 733.4 | 345.9 | 687.2 |

4 | Flood standard: once in 5 years | #1, #3 table opening 20% (e = 1.5 m) | 733.4 | 230.6 | 685.3 |

**Table 6.**Analysis of the water nappe features under different working conditions of the swallow-tailed bucket scheme II.

Modeling Scheme | Working Condition 2 | Working Condition 3 | Working Condition 4 |
---|---|---|---|

Inner edge jet trajectory length (m) | 32.8 | 41.7 | 56.4 |

Outer edge jet trajectory length (m) | 62.1 | 62.3 | 60.9 |

Longitudinal stretch length (m) | 29.3 | 20.6 | 4.5 |

Water nappe highest point (m) | 706.63 | 705.93 | 706.4 |

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**MDPI and ACS Style**

Li, G.; Li, X.; Ning, J.; Deng, Y.
Numerical Simulation and Engineering Application of a Dovetail-Shaped Bucket. *Water* **2019**, *11*, 242.
https://doi.org/10.3390/w11020242

**AMA Style**

Li G, Li X, Ning J, Deng Y.
Numerical Simulation and Engineering Application of a Dovetail-Shaped Bucket. *Water*. 2019; 11(2):242.
https://doi.org/10.3390/w11020242

**Chicago/Turabian Style**

Li, Guodong, Xingnan Li, Jian Ning, and Yabing Deng.
2019. "Numerical Simulation and Engineering Application of a Dovetail-Shaped Bucket" *Water* 11, no. 2: 242.
https://doi.org/10.3390/w11020242