# Numerical and Experimental Investigations of Flow Pattern and Anti-Vortex Measures of Forebay in a Multi-Unit Pumping Station

^{1}

^{2}

^{3}

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^{*}

## Abstract

**:**

## 1. Introduction

^{3}/s; the effective drainage area is about 9.13 million hm

^{2}, accounting for 42.9% of the total drainage area in China; the average annual drainage of large-scale drainage pumping stations is more than 40 billion m

^{3}, which protects the life and property safety of more than 200 cities and more than 150 million people in China [1,2].

## 2. Engineering Background

#### 2.1. Importance of Engineering

^{2}, including land area over 10,000 mu. The river basin is located in the humid monsoon climate zone in the north subtropical zone, with temperate and humid climate, abundant rainfall, moderate light, obviously monsoon climate, and the annual average rainfall of 1275 mm. As the area of the mountainous catchment in the Exi River basin is too large and the flood storage capacity of the river is small, there have been many major disasters in the history of the river basin. For example, the main city of the Fanchang County in the river basin and most of the county cities were flooded during the flood season of 1983 and 1999, and in 2016, the danger of exceeding the warning water level of 0.46 m occurred. Therefore, it is very necessary to strengthen the flood control and flood preparedness of the relevant flood control and drainage gate stations.

#### 2.2. Project Scale and Parameters

^{3}/s single unit design flow, 1250 kW auxiliary motor power, and 5000 kW total installed capacity. The characteristic water level is shown in Table 1.

## 3. Mathematical Formulation

#### 3.1. Mass Continuity Equation

_{x}is the fractional area open to flow in the X-direction and A

_{y}and A

_{z}are similar area fractions for flow in the Y- and Z-directions; R is set to unity; ξ is set to zero; R

_{SOR}is the mass source.

#### 3.2. Momentum Equations

_{x}, G

_{y}, G

_{z}) are body accelerations; (f

_{x}, f

_{y}, f

_{z}) are viscous accelerations; V

_{F}is the fractional volume open to flow; ρ is the fluid density.

_{w}= (u

_{w}, v

_{w}, w

_{w}) is the velocity of the source component.

_{s}= (u

_{s}, v

_{s}, w

_{s}) is the velocity of the fluid at the surface of the source relative to the source itself. It is computed in each control volume as

_{Q}is the fluid source density; dA is the area of the source surface in the cell; and n is the outward normal to the surface. When d = 0.0 in Equation (3), the source is of the stagnation pressure type. If d = 1.0, the source is of the static pressure type.

#### 3.3. Turbulence Transport Models

_{T}includes the convection and diffusion of the turbulent kinetic energy, the production of turbulent kinetic energy due to shearing and buoyancy effects, diffusion, and dissipation due to viscous losses within turbulent eddies. Buoyancy production only occurs if there is a non-uniform density in the flow and includes the effects of gravity and non-inertial accelerations. The transport equation is:

_{T}is the buoyancy production:

_{T}is the turbulent kinetic energy production:

_{x}is the fractional area open to flow in the X-direction, A

_{y}and A

_{z}are similar area fractions for flow in the Y- and Z-directions.

#### 3.4. VOF Fluid Interfaces and Free Surfaces

_{SOR}corresponds to the density source R

_{SOR}in Equation (1); F

_{SOR}is the time rate of change of the volume fraction of fluid associated with the mass source for fluid.

## 4. Physical Model Test and Numerical Simulation

#### 4.1. Model Test

#### 4.1.1. Similarity Criteria and Scales

#### 4.1.2. Velocity Measuring System

#### 4.2. Numerical Simulation

#### 4.2.1. 3D Modeling

^{3}/h, i.e., 0.0211 m

^{3}/s. The numerical simulation area is shown in Figure 4, and enlarged details of the forebay are shown on the right.

#### 4.2.2. Mesh Independence

#### 4.2.3. Convergence of Grid

_{s}= 1.25 was used as per the GCI method [20,22]. The calculation procedure was based on the literature [21,23]. Three grid plans, 767,646, 1,320,405, and 2,467,681, respectively, were simulated to verify the influence of grid density under the design operating water level under the original conditions.

#### 4.2.4. Arrangement of Measuring Points

#### 4.3. Rectification Plan

## 5. Results and Discussion

#### 5.1. Flow Pattern Comparison of the Model Test and Numerical Simulation

#### 5.1.1. Original Plan

#### 5.1.2. Extended Diversion Wall

#### 5.1.3. Rectifier Sill

#### 5.1.4. Rectifier Sill and Pier

#### 5.1.5. Rectifier Sill and Diversion Wall Opening

#### 5.2. Quantitative Analysis of Hydraulic Performance Parameters of the Forebay

^{2}; n is the total number of grid cells in the overflow section.

^{2}.

#### 5.3. The Best Plan

^{3}/s; ${S}_{E}$ is the flow area of section E, m

^{2}.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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Characteristic Water Level | Upper Reaches/m | Lower Reaches/m | Net Head/m |
---|---|---|---|

Minimum operating water level | 9.00 | 10.00 | 1.00 |

Design operating water level | 10.00 | 12.06 | 2.06 |

Maximum operating water level | 12.47 | 14.11 | 1.64 |

Flood control water level | 13.09 | 14.11 | 1.02 |

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

0.03 | 767,646 | 0.02100 | ||||

0.025 | 1,320,405 | 1.20 | 1 | 0.02115 | 0.00714 | 4.46519 |

0.02 | 2,467,681 | 1.25 | 1 | 0.02113 | 0.00094 | 0.47039 |

Plan Number | Plan Description | Action Description (Prototype in Parentheses) |
---|---|---|

1 | Original plan | No rectification measures |

2 | Diversion wall | The diversion wall is lengthened by 25 cm (7.5 m). The shape and arrangement of rectification measures are shown in Figure 8. |

3 | Diversion wall | The diversion wall is lengthened by 50 cm (15 m). The shape and arrangement of rectification measures are shown in Figure 9. |

4 | Rectifier sill | The bottom width of the sill is 5 cm (1.5 m), the top width is 2.5 cm (0.75 m), and the top elevation is 5 cm (1.5 m). The shape and arrangement of rectification measures are shown in Figure 10. |

5 | Rectifier sill and pier | The width of the rectifier pier bottom is 5 cm (1.5 m), top width is 2.5 cm (0.75 m), crest elevation is 5 cm (1.5 m), and length is 6.67 cm (2 m). The shape and arrangement of rectification measures are shown in Figure 11. |

6 | Rectifier sill and side opening of diversion wall | The side hole of the diversion wall is 20 × 20 cm (6 × 6 m). The shape and arrangement of rectification measures are shown in Figure 12. |

7 | Rectifier sill and side opening of diversion wall | The side hole of the diversion wall is 10 × 10 cm (3 × 3 m). The shape and arrangement of rectification measures are shown in Figure 13. |

Plan Number | Velocity Distribution Uniformity V_{u+} (%) | ||
---|---|---|---|

C | E | H | |

1 | 78.22 | 60.23 | 68.67 |

2 | 76.33 | 63.32 | 59.3 |

3 | 77.69 | 53.75 | 58.53 |

4 | 76.01 | 56.40 | 70.43 |

5 | 79.11 | 54.79 | 70.89 |

6 | 80.78 | 63.59 | 87.95 |

7 | 82.55 | 63.97 | 82.61 |

Plan Number | Vortex Area (m^{2}) | Area Ratio (%) | Reduction Rate (%) |
---|---|---|---|

1 | 0.284 | 13.590 | — |

2 | 0.099 | 4.742 | 65.107 |

3 | 0.358 | 17.113 | −25.923 |

4 | 0.004 | 0.167 | 98.769 |

5 | 0.004 | 0.177 | 98.699 |

6 | 0.039 | 1.883 | 86.141 |

7 | 0.022 | 1.033 | 92.402 |

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**MDPI and ACS Style**

Yang, F.; Zhang, Y.; Liu, C.; Wang, T.; Jiang, D.; Jin, Y.
Numerical and Experimental Investigations of Flow Pattern and Anti-Vortex Measures of Forebay in a Multi-Unit Pumping Station. *Water* **2021**, *13*, 935.
https://doi.org/10.3390/w13070935

**AMA Style**

Yang F, Zhang Y, Liu C, Wang T, Jiang D, Jin Y.
Numerical and Experimental Investigations of Flow Pattern and Anti-Vortex Measures of Forebay in a Multi-Unit Pumping Station. *Water*. 2021; 13(7):935.
https://doi.org/10.3390/w13070935

**Chicago/Turabian Style**

Yang, Fan, Yiqi Zhang, Chao Liu, Tieli Wang, Dongjin Jiang, and Yan Jin.
2021. "Numerical and Experimental Investigations of Flow Pattern and Anti-Vortex Measures of Forebay in a Multi-Unit Pumping Station" *Water* 13, no. 7: 935.
https://doi.org/10.3390/w13070935