# Parameter Optimization of Centrifugal Pump Splitter Blades with Artificial Fish Swarm Algorithm

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Method

#### 2.1. Research Model

#### 2.2. Turbulence Model and Boundary Conditions

#### 2.3. Mesh

#### 2.4. Flow Field Analysis

## 3. Orthogonal Test

#### 3.1. Experimental Design

#### 3.2. Data Analysis

## 4. Artificial Fish Swarm Algorithm Optimization

#### 4.1. Parameter Preparation

#### 4.2. Parameter Optimization

## 5. Experimental Verification

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Fluid domain view of centrifugal pump. (

**A**) Numerical model; (

**B**) Physical model: (

**a**) Inlet pipe; (

**b**) Impeller; (

**c**) Volute.

**Figure 3.**Wall ${y}^{+}$ distribution. (

**a**) Scatter distribution graph; (

**b**) Equivalent distribution map.

**Figure 10.**Flow channel distribution map. (

**a**) Comparison of pressure distribution; (

**b**) Comparison of velocity distribution.

**Figure 12.**Closed pump performance test bench. (

**1**) Front view; (

**2**) Side view; (

**3**) Part of instrument: (

**a**) Flowmeter; (

**b**) Control counter; (

**c**) Vacuum pump.

Parameters | Flow $\mathit{Q}\left({\mathbf{m}}^{3}/{\mathbf{h}}^{-1}\right)$ | Head $\mathit{H}\left(\mathbf{m}\right)$ | Speed $\mathit{n}\left(\mathbf{r}/\mathbf{m}\mathbf{i}\mathbf{n}\right)$ |
---|---|---|---|

value | 10 | 12.5 | 1440 |

Factor | A Thickness S $\left(\mathbf{m}\mathbf{m}\right)$ | B Diameter Di (Di/D2) | C Width Bi $\left(\mathbf{m}\mathbf{m}\right)$ | |
---|---|---|---|---|

Level | ||||

1 | 4.5 | 0.625 | 17 | |

2 | 6 | 0.65 | 19 | |

3 | 7.5 | 0.675 | 21 | |

4 | 9 | 0.7 | 23 |

SN | A (S) | B (Di) | C (Bi) | Head (m) | EFF (%) |
---|---|---|---|---|---|

1 | 6 | 0.65 | 23 | 14.25 | 64.95 |

2 | 6 | 0.625 | 19 | 15.21 | 62.50 |

3 | 9 | 0.625 | 23 | 13.52 | 60.03 |

4 | 7.5 | 0.65 | 17 | 15.35 | 63.20 |

5 | 7.5 | 0.625 | 21 | 13.56 | 63.87 |

6 | 4.5 | 0.675 | 23 | 15.17 | 61.96 |

7 | 4.5 | 0.625 | 17 | 14.98 | 57.36 |

8 | 4.5 | 0.7 | 19 | 14.35 | 61.80 |

9 | 7.5 | 0.7 | 23 | 13.88 | 62.23 |

10 | 4.5 | 0.65 | 21 | 15.02 | 63.60 |

11 | 9 | 0.65 | 19 | 14.36 | 61.96 |

12 | 9 | 0.7 | 21 | 13.31 | 62.79 |

13 | 6 | 0.7 | 17 | 14.04 | 60.40 |

14 | 7.5 | 0.675 | 19 | 14.69 | 66.30 |

15 | 9 | 0.675 | 17 | 14.96 | 62.15 |

16 | 6 | 0.675 | 21 | 14.35 | 64.97 |

Index | Factor | ||
---|---|---|---|

A | B | C | |

$\stackrel{-}{{K}_{1}}$ | 14.8825 | 14.165 | 14.85 |

$\stackrel{-}{{K}_{2}}$ | 14.45 | 14.775 | 14.625 |

$\stackrel{-}{{K}_{3}}$ | 14.35 | 14.7825 | 14.05 |

$\stackrel{-}{{K}_{4}}$ | 13.89 | 13.85 | 14.0475 |

$R$ | 0.9925 | 0.9325 | 0.8025 |

rank | 1 | 2 | 3 |

Index | Factor | ||
---|---|---|---|

A | B | C | |

$\stackrel{-}{{K}_{1}}$ | 61.18 | 60.94 | 60.7775 |

$\stackrel{-}{{K}_{2}}$ | 63.205 | 63.4275 | 63.14 |

$\stackrel{-}{{K}_{3}}$ | 63.9 | 63.845 | 63.8075 |

$\stackrel{-}{{K}_{4}}$ | 61.7325 | 61.805 | 62.2925 |

$R$ | 2.72 | 2.905 | 3.03 |

rank | 3 | 2 | 1 |

Parameter | Population Size | Maximum Iterations | Maximum Trials | Cognitive Distance | Degrees of Crowding |
---|---|---|---|---|---|

value | 50 | 200 | 150 | 0.5 | 0.518 |

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**MDPI and ACS Style**

Ke, Q.; Tang, L.; Luo, W.; Cao, J.
Parameter Optimization of Centrifugal Pump Splitter Blades with Artificial Fish Swarm Algorithm. *Water* **2023**, *15*, 1806.
https://doi.org/10.3390/w15101806

**AMA Style**

Ke Q, Tang L, Luo W, Cao J.
Parameter Optimization of Centrifugal Pump Splitter Blades with Artificial Fish Swarm Algorithm. *Water*. 2023; 15(10):1806.
https://doi.org/10.3390/w15101806

**Chicago/Turabian Style**

Ke, Qidi, Lingfeng Tang, Wenbin Luo, and Jingzhe Cao.
2023. "Parameter Optimization of Centrifugal Pump Splitter Blades with Artificial Fish Swarm Algorithm" *Water* 15, no. 10: 1806.
https://doi.org/10.3390/w15101806