# Numerical Study on the Influence of Combined Rectification Facilities on the Flow in the Forebay of Pumping Station

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## Abstract

**:**

## 1. Introduction

## 2. Research Object

^{3}/s. The forebay of the pumping station is 38.38 m long and is diverted by two steel pipes with a diameter of 2.6 m. The slope of the pool bottom is 0.049, the divergence angle of the forebay is 39.02°, and the inlet pool is 15 m long and 39.2 m wide. The center distance between two adjacent pumps is 8.5 m, and the design water level is 19.5 m. The diameter of the trumpet tube is D = 2.6 m, the suspended height is 0.4 D, and the rear wall distance is 0.08 D. From top to bottom, these are units 1–5. The 3D model of the pumping station is shown in Figure 1.

## 3. Numerical Simulation

#### 3.1. Turbulence Model

^{−4}.

#### 3.2. Calculation Region and Grid

#### 3.3. Boundary Condition

^{3}/s. The outlet is set at the outlet of the water-absorbing horn tube, and the static pressure outlet is set to 0 atm.

## 4. Simulation Analysis of Forebay Flow in Original Scheme

- (1)
- The diffusion angle of the forebay is too large, close to the critical value of the pumping station design specification [24] (the forebay diffusion angle of the forward water pumping station is <40°).
- (2)
- The forebay of the pumping station uses pressurized steel pipes to divert water, which causes high-speed water jets to form and impact the pier, thereby forming reverse water flow. This occurrence causes large-scale backflow, vortexing, and other undesirable flow patterns in the forebay.

## 5. Analysis of Influence of Rectification Facilities on Forebay Flow

#### 5.1. Rectification Facilities and Operating Conditions

#### 5.2. Analysis of the Influence of Rectification Facilities on Forebay Flow

#### 5.2.1. Comparative Analysis of Forebay Flow under Different Operating Conditions

#### 5.2.2. Comparative Analysis of Unit Flow Distribution

_{i}of the suction horn tube corresponding to the operating unit to the design flow rate of a single pump Q = 3.75 m

^{3}/s (i represents the number of operating unit) and expressed as follows:

#### 5.2.3. Comparative Analysis of Flow Velocity Distribution Uniformity and Average Drift Angle

_{a}and the cross-sectional average drift angle θ [25] and uses them as indicators to evaluate the actual effect of the rectification device.

_{a}is to 100% and the average drift angle θ is closer to 0°, the more uniform is the axial flow velocity distribution of the water pump impeller inlet section. Thus, the inflow conditions of the water flow introduced into the pump unit improve, and the safe and stable pump operation and the operating efficiency of the pump device are also enhanced. The expression is as follows:

_{a}is the uniformity of flow velocity distribution; θ is the average drift angle; m is the number of units; ${\overline{u}}_{a}$ is the average axial velocity of the horn tube inlet; ${u}_{ai}$ is the axial velocity of each unit in section i; ${u}_{ti}$ is the lateral velocity of the ith calculation unit, and ${u}_{ti}=\sqrt{{u}_{wi}{}^{2}+{u}_{ri}{}^{2}}$ (${u}_{wi}$ and ${u}_{ri}$ are the tangential and radial velocities of the ith calculation unit, respectively).

## 6. Conclusions

- In the original scheme, the forebay of the research object has large-scale backflow, vortex, and other adverse flow structures when the units are turned on and running under the design working conditions. When multiple units run in parallel, uneven flow distribution occurs and the pumps have poor water inlet conditions, and this situation becomes more and more serious as the position moves down.
- The bottom sill is set in the forebay and causes the following benefits: Improves the centering of the mainstream, facilitates the diffusion of water flow on the plane, reduces the range of the forebay recirculation zone, and improves the uniformity of flow velocity distribution at the entrance of the suction horn pipe and the flow distribution uniformity of each operating unit. However, there are still backflow and vortices on both sides of the front pool, which need to be further improved.
- The combined facility of “bottom sill + diversion pier” is added to the forebay. The bottom sill diverts the central water beam from the water diversion pipe to spread to both sides of the forebay. The diversion pier then performs secondary rectification on the diverted forebay flow, which effectively improves the centering of the mainstream.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 5.**Streamlines of horizontal sections of forebay and pump sump: (

**a**) Surface layer; (

**b**) middle layer; (

**c**) bottom layer.

**Figure 9.**Velocity vector diagram of horizontal section (z = 13.5 m) of forebay and pump sump under different operating conditions: (

**a**) Condition 1; (

**b**) condition 2; (

**c**) condition 3; (

**d**) condition 4; (

**e**) condition 5; (

**f**) condition 6; (

**g**) condition 7; (

**h**) condition 8; (

**i**) condition 9.

**Figure 10.**Vorticity diagram of horizontal section of front pool and inlet pool under different operating conditions: (

**a**) Condition 1; (

**b**) condition 2; (

**c**) condition 3; (

**d**) condition 4; (

**e**) condition 5; (

**f**) condition 6; (

**g**) condition 7; (

**h**) condition 8; (

**i**) condition 9.

**Figure 12.**Flow distribution coefficient of operating units before and after rectification: (

**a**) 3 units running in parallel; (

**b**) 4 units running in parallel; (

**c**) 5 units running in parallel.

Water Diversion Pipe + Forebay | Inlet Pool | Suction Trumpet | Total |
---|---|---|---|

Number of grids (10,000) | 165.14 | 34.48 | 249.55 |

Program Number | Rectification Measures | Scheme Description |
---|---|---|

Scheme 1 | Bottom sill | Located at 10 m in front of the forebay, across the bottom, width × height: 1 × 1.5 m |

Scheme 2 | Bottom sill + diversion pier | Data The diversion pier is located 7 m behind the bottom sill, and the distance between the heads of the two diversion piers is 8.7 m. The length × width × height: 10 × 1 × 5 m, and the included angle with the center line of the forebay is 18° |

Operating Conditions | Rectification Measures | Flow m^{3}/s | Boot Group Number |
---|---|---|---|

1 | Original design scheme | 11.25 | 1#, 3#, 5# |

2 | 15 | 1#, 2#, 4#, 5# | |

3 | 18.75 | 1#, 2#, 3#, 4#, 5# | |

4 | Scheme 1 | 11.25 | 1#, 3#, 5# |

5 | 15 | 1#, 2#, 4#, 5# | |

6 | 18.75 | 1#, 2#, 3#, 4#, 5# | |

7 | Scheme 2 | 11.25 | 1#, 3#, 5# |

8 | 15 | 1#, 2#, 4#, 5# | |

9 | 18.75 | 1#, 2#, 3#, 4#, 5# |

**Table 4.**The uniformity and average drift angle of the inlet flow velocity distribution of the suction horn in various operating conditions.

Original Scheme | Bottom Sill | “Bottom Sill + Diversion Pier” | ||
---|---|---|---|---|

Three units run in parallel | Velocity distribution uniformity V_{a} | 73.58% | 76.20% | 77.38% |

Mean drift angle θ | 18.21° | 16.89° | 15.42° | |

Four units run in parallel | Velocity distribution uniformity V_{a} | 73.37% | 74.85% | 78.88% |

Mean drift angle θ | 22.87° | 19.88° | 14.43° | |

Five units run in parallel | Velocity distribution uniformity V_{a} | 70.52% | 75.62% | 77.98% |

Mean drift angle θ | 21.09° | 20.33° | 15.30° |

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**MDPI and ACS Style**

Zheng, X.; Zhang, P.; Zhang, W.; Yu, Y.; Zhao, Y.
Numerical Study on the Influence of Combined Rectification Facilities on the Flow in the Forebay of Pumping Station. *Water* **2023**, *15*, 3847.
https://doi.org/10.3390/w15213847

**AMA Style**

Zheng X, Zhang P, Zhang W, Yu Y, Zhao Y.
Numerical Study on the Influence of Combined Rectification Facilities on the Flow in the Forebay of Pumping Station. *Water*. 2023; 15(21):3847.
https://doi.org/10.3390/w15213847

**Chicago/Turabian Style**

Zheng, Xiaobo, Pengli Zhang, Wenjing Zhang, Yue Yu, and Yaping Zhao.
2023. "Numerical Study on the Influence of Combined Rectification Facilities on the Flow in the Forebay of Pumping Station" *Water* 15, no. 21: 3847.
https://doi.org/10.3390/w15213847