# Study of Tip Clearance on Dynamic and Static Head of a Spiral Axial-Flow Blade Pump under Cavitation Conditions

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## Abstract

**:**

## 1. Introduction

## 2. Computational Model and Approach of Multiphase Pump

#### 2.1. Numerical Simulation Theory

- (1)
- Multiphase Flow Model

_{E}includes the efforts of all other volumetric heat sources.

- (2)
- Cavitation Model

_{v}is less than P:

_{v}:

_{B}means the bubble radius, 10

^{−6}m; α

_{nuc}stands for the volume fraction of the vapor nucleus position, 5 × 10

^{−4}; F

_{vap}and F

_{cond}mean the vapor evaporation and condensation parameters, and the values are 50 and 0.01.

- (3)
- Turbulence Model

_{1}stands for the blending role.

#### 2.2. Computational Model

#### 2.3. Mesh and Independent Verification

#### 2.4. Boundary Condition Settings

## 3. Experimental Rig and Numerical Validation

#### 3.1. Experimental Rig

#### 3.2. Numerical Verification

## 4. Results and Discussion

#### 4.1. Role of Cavitation Number in Head of the Pump under Different Tip Clearance Sizes

_{tc}= 0.5 mm, the pump head reaches 13.63 m without cavitation. The critical cavitation point is reached in the case of the cavitation number of 0.52, the stage of severe cavitation is reached in the case of the cavitation number of 0.29, and the fracture cavitation point is reached in the case of the cavitation number of 0.2.

_{tc}= 1.0 mm, the pump head without cavitation decreases with the cavitation number and reaches the critical cavitation point in the case of the cavitation number of 0.38, develops to the severe cavitation stage in case of the cavitation number of 0.36, and reaches the fracture cavitation point when the cavitation number is 0.31.

_{tc}= 1.5 mm, the pump head reaches 5.36 m without cavitation. The critical cavitation point is reached in the case of the cavitation number of 0.4, the stage of the severe cavitation develops in the case of the cavitation number of 0.37, and the fracture cavitation point is reached when the cavitation number is 0.19. The above data show that the tip clearance size and cavitation number have significant effects on the head of the SABP.

#### 4.2. The Influence of Different Size Clearance on the Absolute Speed

#### 4.3. Impact of Tip Clearance of Different Dimensions on Relative Velocity

#### 4.4. Impact of Tip Clearance with Different Sizes on Dynamic Head

#### 4.5. Effect of Tip Clearance on Static Head

## 5. Conclusions

- (1)
- It can be found that the tip clearance size exerts a significant impact on the absolute velocity of the middle and back of the impeller and the front of the diffuser. In the impeller, the absolute velocity generally decreases with the increasing tip clearance sizes in the front and back in the flow direction and grows with the increasing tip clearance sizes in the middle part. In the diffuser, the absolute velocity declines with the increasing tip clearance sizes in critical and severe cavitation stages. The absolute velocity under the 1.0 mm tip clearance in the fracture cavitation stage decreases significantly in the forward of the flow direction, making the absolute velocity under the 1.5 mm tip clearance condition exceed the absolute velocity distribution. The relative velocity has the greatest influence on the back of the impeller and in the flow direction of the front. In general, cavitation has little impact on the absolute and relative speed of the booster unit.
- (2)
- It can be found that the dynamic head in the impeller changes with the different tip clearance sizes. In the impeller, the bigger the tip clearance size, the quicker the dynamic head increases. In the middle and back part of the impeller, which is mainly affected by the tip clearance size, the dynamic head declines with the increasing tip clearance sizes. Tip clearance strongly affects the dynamic head of the middle and back section of the diffuser, and the dynamic head increases with the increasing tip clearance sizes. The static head is affected by the intensified cavitation, which makes the negative distribution of the front section in the impeller increase continuously, and declines with the increasing tip clearance sizes in most stages in the flow direction. In general, cavitation has little influence on the dynamic and static head of the booster unit.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 8.**Absolute velocity distribution in the impeller of the SABP with different tip clearance sizes.

**Figure 9.**Absolute velocity distribution in the diffuser of the SABP with different tip clearance sizes.

**Figure 10.**Relative velocity distribution in the impeller of the SABP with different tip clearance sizes.

**Figure 11.**Dynamic head distribution in the impeller of the SABP with different tip clearance sizes.

**Figure 12.**Dynamic head distribution in the diffuser of the SABP with different tip clearance sizes.

Parameters | Value | Unit |
---|---|---|

Flow rate Q | 100 | m^{3}/h |

Speed n | 3600 | rpm |

Impeller blades number | 3 | - |

Diffuser blades number | 11 | - |

Mesh Scheme | Mesh Number | Head/m |
---|---|---|

1 | 2,167,300 | 13.93 |

2 | 2,496,556 | 13.79 |

3 | 3,251,714 | 13.56 |

4 | 3,958,986 | 13.57 |

5 | 6,078,160 | 13.58 |

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**MDPI and ACS Style**

Wen, H.; Lv, W.; Shi, G.
Study of Tip Clearance on Dynamic and Static Head of a Spiral Axial-Flow Blade Pump under Cavitation Conditions. *Water* **2023**, *15*, 4304.
https://doi.org/10.3390/w15244304

**AMA Style**

Wen H, Lv W, Shi G.
Study of Tip Clearance on Dynamic and Static Head of a Spiral Axial-Flow Blade Pump under Cavitation Conditions. *Water*. 2023; 15(24):4304.
https://doi.org/10.3390/w15244304

**Chicago/Turabian Style**

Wen, Haigang, Wenjuan Lv, and Guangtai Shi.
2023. "Study of Tip Clearance on Dynamic and Static Head of a Spiral Axial-Flow Blade Pump under Cavitation Conditions" *Water* 15, no. 24: 4304.
https://doi.org/10.3390/w15244304