# Improvement of the Flow Pattern of a Forebay with a Side-Intake Pumping Station by Diversion Piers Based on Orthogonal Test Method

^{1}

^{2}

^{*}

## Abstract

**:**

^{3}) groups to 9 groups, improving work efficiency. The results show that the diversion piers had a significant adjustment of uniformity of axial flow velocity and weighted average angle of flow velocity. After optimization of the forebay, the uniformity of axial flow velocity of intake of No.1 pump was 80.26% and the weighted average angle of flow velocity was 77.68°. The above values of the No.2 pump were 98.74% and 87.84°, respectively. The values of the No.4 pump were 93.41% and 77.28°. The results of numerical simulation, which was carried out to estimate the rectification effect under the operation combination of the No.1, No.3, and No.4 pumps, showed that the uniformity and the angle of the No.1 pump were 92.65% and 72.66°, respectively, the uniformity and the angle of No.3 pump were 94.54% and 85.14°, and the uniformity and the angle of the No.4 pump were 75.81% and 78.21°. This research proves that the orthogonal test method, in a reasonable and convenient way, can be applied in hydraulic optimization for a lateral intake pumping station.

## 1. Introduction

## 2. Study Area and Method

#### 2.1. Study Area

^{3}/s and the rated flow of the No.2 or No.3 pump is 5.4 m

^{3}/s. The inlet cross-section of every pump is 3.2 m high and 4.85 m wide. The water depth of the forebay before the slope is 4 m, the water depth of the forebay behind the slope is 5.4 m, and the bottom slope has a gradient of 1:8, as shown in Figure 2.

#### 2.2. Study Method

^{5}greater than 3 × 10

^{4}, which shows that the turbulence is fully developed. The SIMPLEC algorithm is adopted [27].

#### 2.2.1. Boundary Conditions

#### 2.2.2. Grid Independence Verification

_{f}, was used as an evaluation indicator for grid independence verification.

_{in}is the total pressure of the inlet; P

_{out}is the total pressure of the outlet; ρ is the density of water; and g is the gravity acceleration.

## 3. Typical Sections in Calculation Domain and Evaluation Indexes of Flow Pattern in Forebay

## 4. Design of Diversion Piers Based on Orthogonal Test Method

#### 4.1. Dimension Design of Diversion Piers

#### 4.2. Factors and Results Based on Orthogonal Test Method

#### 4.3. Analysis of Orthogonal Test Table of the Diversion Piers

#### 4.4. Analysis of Optimal Result

## 5. CFD Numerical Test Analysis of Pumps 1, 3, and 4

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

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**Figure 2.**The plane layout of the certain lateral intake pumping station (EL: m, OTH: mm:). (Scale 1:200).

**Figure 8.**Flow pattern for the optimal scheme of the diversion piers for operating pumps 1, 2, and 4.

**Figure 10.**Flow pattern for the optimal scheme of the diversion piers for operating pumps 1, 3, and 4.

Level | Factors | |||
---|---|---|---|---|

A | B (m) | C (m) | D | |

1 | 1.2 | 0.3 | 1 | 0.6 |

2 | 1.3 | 0.4 | 1.2 | 0.8 |

3 | 1.4 | 0.5 | 1.4 | 1 |

Test Number | Factors | Results of Test | ||||
---|---|---|---|---|---|---|

A | B | C | D | UAFV (%) | CWAAFV (°) | |

1 | 1 | 1 | 1 | 1 | 85.665 | 7.398 |

2 | 1 | 2 | 2 | 2 | 88.528 | 22.473 |

3 | 1 | 3 | 3 | 3 | 79.698 | 37.819 |

4 | 2 | 1 | 2 | 3 | 76.714 | 33.429 |

5 | 2 | 2 | 3 | 1 | 82.426 | 12.775 |

6 | 2 | 3 | 1 | 2 | 80.727 | 14.701 |

7 | 3 | 1 | 3 | 2 | 73.546 | 25.101 |

8 | 3 | 2 | 1 | 3 | 82.402 | 31.221 |

9 | 3 | 3 | 2 | 1 | 77.980 | 13.649 |

Range Analysis | UAFV | CWAAFV | ||||||
---|---|---|---|---|---|---|---|---|

A | B | C | D | A | B | C | D | |

K1 | 253.890 | 235.925 | 248.794 | 246.071 | 67.690 | 65.927 | 53.319 | 33.821 |

K2 | 239.867 | 253.356 | 243.222 | 242.801 | 60.904 | 66.469 | 69.551 | 62.274 |

K3 | 233.928 | 238.405 | 235.670 | 238.814 | 69.970 | 66.168 | 75.695 | 102.469 |

k1 | 84.630 | 78.642 | 82.931 | 82.024 | 22.563 | 21.976 | 17.773 | 11.274 |

k2 | 79.956 | 84.452 | 81.074 | 80.934 | 20.301 | 22.156 | 23.184 | 20.758 |

k3 | 77.976 | 79.468 | 78.557 | 79.605 | 23.323 | 22.056 | 25.232 | 34.156 |

R | 6.654 | 5.810 | 4.375 | 2.419 | 3.022 | 0.181 | 7.458 | 22.883 |

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**MDPI and ACS Style**

Zhang, C.; Yan, H.; Jamil, M.T.; Yu, Y. Improvement of the Flow Pattern of a Forebay with a Side-Intake Pumping Station by Diversion Piers Based on Orthogonal Test Method. *Water* **2022**, *14*, 2663.
https://doi.org/10.3390/w14172663

**AMA Style**

Zhang C, Yan H, Jamil MT, Yu Y. Improvement of the Flow Pattern of a Forebay with a Side-Intake Pumping Station by Diversion Piers Based on Orthogonal Test Method. *Water*. 2022; 14(17):2663.
https://doi.org/10.3390/w14172663

**Chicago/Turabian Style**

Zhang, Chen, Haodi Yan, Muhammad Tahir Jamil, and Yonghai Yu. 2022. "Improvement of the Flow Pattern of a Forebay with a Side-Intake Pumping Station by Diversion Piers Based on Orthogonal Test Method" *Water* 14, no. 17: 2663.
https://doi.org/10.3390/w14172663