# The Transient Characteristics of the Cavitation Evolution of the Shroud of High-Speed Pump-Jet Propellers under Different Operating Conditions

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## Abstract

**:**

_{s}= 1920 using FLUENT 2020R2 software. At the same time, the occurrence and development process of cavitation under 0.95 Q, 1.0 Q, and 1.05 Q conditions were analyzed (Q is the mass flow), the changes in gas volume fraction in the impeller channel were captured, the distribution characteristics of cavitation under different NPSH values were explored, and the change law of cavitation with time was determined. The results show that, when NPSH dropped to 95 m, the impeller cavitation first occurred under the 1.05 Q operating condition, and the impeller cavitation volume fraction was 0.0379525. When NPSH dropped to 85 m, the impeller cavitation occurred under the 1.0 Q operating condition, and the impeller cavitation volume fraction was 0.0185164. When NPSH dropped to 80 m, the impeller cavitation occurred under the condition of 0.95 Q, and the volume fraction of the impeller cavitation was 0.013541. The high-speed pump-jet propeller had better anti-cavitation ability with a small flow rate. The cavitation distribution law under the three operating conditions was similar; cavitation was first generated on the impeller inlet edge and near the shroud, and the vacuoles with large volumes were mostly concentrated on the impeller inlet side. As the NPSH gradually decreased, the entire flow channel was gradually occupied by vacuoles. As the flow decreased, the corresponding NPSH also decreased. When NPSH dropped to 50 m, the volume fraction of the impeller under all three operating conditions reached around 0.4. As the cavitation only occurred on the suction surface, the volume fraction of the cavitation on the suction surface exceeded 0.8, at which time the impeller had already undergone severe cavitation. Within a complete cycle, bubbles first appeared at the inlet edge of the impeller (measured near the shroud) and gradually spread toward the middle and rear of the impeller, ultimately covering the suction surface of the impeller. Under the design condition, the experimental results of the model pump were consistent with the numerical simulation results, and the error was only 2.68%, thus verifying the reliability of the numerical simulation. The research results provide a reference for the in-depth study of the cavitation performance of high-speed pump-jet propellers and provide a good theoretical basis and practical significance in the engineering field for the high-speed and miniaturization process of high-speed pump-jet propellers.

## 1. Introduction

_{s}= 1920) as the research object, and we conducted numerical simulation calculations on the pump-jet propeller at 0.95 Q, 1.0 Q, and 1.05 Q and verified the reliability of the numerical simulation through experiments. Furthermore, the changes in the impeller cavitation volume fraction under different NPSH allowances and different flow rates were recorded using numerical simulation. Through the numerical calculation of the pump-jet propeller under unsteady conditions, the distribution characteristics of cavitation on the impeller surface at different times under different flow conditions were obtained using post-treatment technology, and the change law of cavitation over time was explored. At the same time, the blade-to-blade surface of the impeller blade channel with a parameter span of 0.5 was selected to analyze the velocity nephogram of the impeller blade at different times under different operating conditions, so as to explore the relationship between impeller cavitation and the speed of the pump-jet propeller. The research methods and the results of this paper provide theoretical support and practical significance in the engineering field for the subsequent design and optimization of pump-jet propellers.

## 2. Calculation Model

#### Establishment of the Calculation Model

_{1}= 3; the number of diffuser blades, z = 5; and the design speed, n = 18,000 r/min. The calculation domain of the model includes four parts, namely the inlet extension section, the impeller, the diffuser, and the outlet extension section, in which the inlet extension section is 10 D and the outlet extension section is 5 D. This is because the longer the set length of the inlet section in the simulation, the smaller the outlet reflux, and the faster the convergence rate. D is the impeller diameter. The three-dimensional calculation model is shown in Figure 1.

## 3. Numerical Simulation and Boundary Conditions

#### 3.1. Turbulence Model

_{m}has a certain influence on the turbulent viscosity coefficient. The turbulent viscosity coefficient μ

_{t}is modified by modifying the density function ƒ(ρ

_{m}), which is determined as follows:

_{m}is the mixed phase density; α

_{v}is the gas-phase volume fraction; ρ

_{v}and ρ

_{l}are the density of gas and liquid phases, respectively; ${C}_{\mathsf{\mu}}$ is the viscosity coefficient, which is 1; k is the turbulent kinetic energy; and ω is the turbulent frequency. If the correction coefficient n is appropriate, the value can be effectively reduced, and the phenomenon of unsteady cavitation shedding in the impeller domain can be accurately simulated.

#### 3.2. Cavitation Model

^{+}) and the evaporation term (m

^{−}) are, respectively, expressed as follows:

_{v}is the saturated vapor pressure, and the value is 3169 Pa; R

_{b}is the cavity radius, and the value is 1 × 10

^{−6}m; α

_{n}is the volume fraction of the cavitation nucleon, and the value is 5 × 10

^{−4}; and ${C}_{p}$ and ${C}_{d}$ are the condensation coefficient and the evaporation coefficient, which are 0.01 and 50, respectively.

#### 3.3. Boundary Conditions

^{−4}. The interface between the rotating and stationary components was set to “transient frozen rotor interface” in the transient calculation. Two grid interfaces were generated before the inlet and after the outlet of the impeller to simulate the flow field with dynamic and stationary interference. The Rayleigh–Plesset bubble dynamic homogeneous flow model was used to simulate the occurrence and collapse of cavitation [29]. The specific numerical simulation was performed in three steps: Firstly, the simulation of the steady flow field inside the high-speed pump-jet propeller was carried out, and the reference pressure was set as a standard atmospheric pressure; cavitation was not considered in the steady calculation. Then, the cavitation simulation of the high-speed pump-jet propeller was carried out using the mixture flow model with the simulated steady flow field considered the initial condition. Finally, the cavitation simulation result was used as the initial value, and the instantaneous equation was discretized using the finite volume method, with every 1° rotation of the impeller considered a time step. In order to improve the convergence accuracy, the difference in the total pressure at the inlet and outlet of the high-speed pump-jet propeller was determined to monitor the state of the propeller. When the difference was less than 0.1%, the flow field was considered to be stable. On this basis, a periodic calculation was carried out, and the simulation results of the last cycle were obtained for analysis.

#### 3.4. Grid Division and Grid Independence Test

## 4. Experimental System and Experimental Method

#### 4.1. Experimental System

#### 4.2. Experimental Methods and Results

## 5. Calculation Results and Analysis

#### 5.1. Cavitation Experiment and Analysis

_{n}between the inlet and outlet with NPSH under different operating conditions. The total pressure difference between the inlet and outlet of the experimental pump was reduced by 3%, and the corresponding NPSH is NPSH

_{c}. As can be seen in Figure 4, with the gradual reduction in the flow rate, the NPSH

_{c}value of the pump-jet propeller became increasingly lower, and the critical points of cavitation under the three conditions were 78.27 m, 84.14 m, and 92.46 m, respectively. In the actual operation of the pump-jet propeller, the appropriate reduction in the flow rate is conducive to improving the cavitation performance of the pump-jet propeller. Under the design condition, the NPSH

_{c}of the high-speed pump-jet propeller was 84.14 m. Near the critical cavitation point, the head of the high-speed pump-jet propeller decreased slightly, and once the NPSH was less than the NPSH

_{c}, serious cavitation occurred in the high-speed pump-jet propeller, and the impeller’s functional force on the fluid decreased, and the total pressure difference between the inlet and outlet decreased rapidly. A comparison of the experimental data at 1.0 Q with the simulation data revealed that the NPSH

_{c}of the experiment was 86.4 m, slightly higher than the simulated value. This is caused by the loss of the experiment device, and the experimental results verify the accuracy of the numerical simulation and provide a reference for subsequent transient cavitation simulation.

#### 5.2. Cavity Change Characteristic Analysis

#### 5.2.1. Change in the Impeller Cavity Volume Fraction

#### 5.2.2. Cavitation Distribution of Impeller Blades

_{c}value, no vacuole was generated at this time, and the pump-jet propeller ran under stable conditions at this time. When the NPSH decreased to 100 m, the NPSH reached the NPSH

_{c}value, so cavitation occurred at the inlet of the impeller. When the NPSH continued to decrease until it reached 90 m, the cavitation started from the inlet edge and spread to the whole blade. When NPSH = 70 m, the cavitation area basically covered the whole blade. When the NPSH value continued to decrease, cavitation became more and more serious, and it eventually blocked the flow channel. Thus, the operation of the pump-jet propeller was affected.

#### 5.2.3. Characteristics of Cavitation Changes in Impeller Blades

## 6. Conclusions

_{c}to a certain extent and improve the anti-cavitation performance of high-speed pump-jet propellers.

## Author Contributions

## Funding

## Conflicts of Interest

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Scheme | Impeller Domain | Diffuser Domain | Internal Domain | Efficiency/% |
---|---|---|---|---|

1 | 659259 | 989440 | 476177 | 85.74 |

2 | 1091644 | 1836496 | 644494 | 86.32 |

3 | 2173485 | 2047547 | 909270 | 87.47 |

4 | 3077421 | 2951054 | 143765 | 88.15 |

5 | 5397257 | 3523181 | 3697778 | 88.17 |

NPSH (m) | Volume Fraction of Cavitation | ||
---|---|---|---|

0.95 Q | 1.0 Q | 1.05 Q | |

50 | 0.402632 | 0.402582 | 0.402554 |

60 | 0.335245 | 0.335237 | 0.335237 |

70 | 0.274699 | 0.27458 | 0.274566 |

80 | 0.013541 | 0.117368 | 0.203432 |

85 | 0 | 0.0185164 | 0.159795 |

90 | 0 | 0 | 0.11025 |

95 | 0 | 0 | 0.0379525 |

100 | 0 | 0 | 0 |

150 | 0 | 0 | 0 |

200 | 0 | 0 | 0 |

t | 1/6 T | 1/3 T | 1/2 T | 2/3 T | 5/6 T | T | |
---|---|---|---|---|---|---|---|

0.95 Q | |||||||

1.0 Q | |||||||

1.1 Q |

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## Share and Cite

**MDPI and ACS Style**

Gan, G.; Shi, W.; Yi, J.; Fu, Q.; Zhu, R.; Duan, Y.
The Transient Characteristics of the Cavitation Evolution of the Shroud of High-Speed Pump-Jet Propellers under Different Operating Conditions. *Water* **2023**, *15*, 3073.
https://doi.org/10.3390/w15173073

**AMA Style**

Gan G, Shi W, Yi J, Fu Q, Zhu R, Duan Y.
The Transient Characteristics of the Cavitation Evolution of the Shroud of High-Speed Pump-Jet Propellers under Different Operating Conditions. *Water*. 2023; 15(17):3073.
https://doi.org/10.3390/w15173073

**Chicago/Turabian Style**

Gan, Gongchang, Wenhao Shi, Jinbao Yi, Qiang Fu, Rongsheng Zhu, and Yuchen Duan.
2023. "The Transient Characteristics of the Cavitation Evolution of the Shroud of High-Speed Pump-Jet Propellers under Different Operating Conditions" *Water* 15, no. 17: 3073.
https://doi.org/10.3390/w15173073