# Pressure Pulsation Characteristics of Agricultural Irrigation Pumps under Cavitation Conditions

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## Abstract

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## 1. Introduction

_{s}= 700. They utilized ANSYS CFX 19.2 software for numerical calculations to obtain the external characteristic curve. The analysis focused on investigating the impact of variations in inlet pressure and operating flow rate on the cavitation volume fraction of the submersible axial-flow pump. The findings highlighted that increasing the inlet pressure and adjusting the operating flow rate to the design value effectively mitigates cavitation. Bai et al. [22] investigated the hydraulic performance and anti-cavitation properties of the thrust plate-assisted impeller using experimental methods under different speeds, temperatures, and outlet conditions. The experimental results revealed that the speed variation pattern differs from that of traditional centrifugal pumps and is not applicable to the head produced by the thrust plate-assisted impeller. Gong et al. [23] employed a combination of experimental validation and numerical simulation to enhance the hydraulic performance of multi-stage submersible electric pumps. They quantified the relationship between the angle of the space guide vane leading to each flow surface using a linear equation and explored the influence of the equation’s slope variation on the separation flow within the guide vane and its impact on the guide vane performance. Their research outcomes provide a foundation and scientific support for investigating the impact of the guide vane’s outlet edge shape on the hydraulic performance of multi-stage submersible electric pumps. Kan et al. [24] utilized the immersed boundary method with large eddy simulation (IBM–LES) to examine the three-dimensional unsteady turbulent flow field of a specific mixed-flow pump operating under design conditions in cylindrical coordinates. The results contribute theoretical references and engineering applications for enhancing the stability of mixed-flow pump operation. Lang et al. [25] employed LIGHTHILL acoustic analogy theory and the FW–H equation in conjunction with computational fluid dynamics and computational acoustics to solve the internal hydrodynamic noise of a single-blade centrifugal pump. The investigation concluded that the distribution characteristics of pressure fluctuation directly impact the internal hydrodynamic noise of the single-blade centrifugal pump. Xu et al. [26] established a simulation model using the characteristic line method to study the hydraulic transition process. The model’s validity was confirmed by comparing it with actual load rejection test data. The simulation focused on the closing law of the guide vane during the hydraulic transition process.

## 2. Model Parameters

#### 2.1. Three-Dimensional Modeling

^{3}/h, head H = 20 m, rated speed n = 980 r/min, and specific speed size n

_{s}= 200. The impeller inlet diameter D

_{1}= 107 mm, impeller outer diameter D

_{2}= 415 mm, number of vanes Z = 6, vane outlet angle β

_{2}= 30°, volute base diameter D

_{3}= 425 mm, and volute inlet width b

_{3}= 220 mm. The hydraulic model of impeller and volute is shown in Figure 1. In this paper, Creo is used to model the main flow components of the centrifugal pump in point–line–plane 3D, respectively, as shown in Figure 2.

#### 2.2. Cavitation Model

_{ruc}is the volume fraction of nucleation position, taken as 5 × 10

^{−4}; R

_{B}is the radius of the vacuole, m, taken as 1 × 10

^{−6}; P is the flow field pressure, Pa; P

_{v}is the vaporization pressure, Pa; F

_{vap}is the empirical correction coefficient for the evaporation process, taken as 50; and F

_{cond}is the empirical correction coefficient for the condensation process, taken as 0.01.

## 3. Numerical Calculation

#### 3.1. Models and Meshes

#### 3.2. Boundary Condition

^{3}), and u is the impeller outlet circumferential velocity (m/s).

## 4. Experimental Verification

## 5. Pressure Pulsation Analysis of Pumps with Different Numbers of Vanes

#### 5.1. Time-Domain Characterization of Pressure Pulsations

^{3}/h working conditions, the trend of pressure change at the monitoring point in the blade working surface and backside monitoring area is more complicated; the regularity change is not obvious, but we can still see that the amplitude is cyclic, that six obvious troughs appear in the working surface and backside, and that the amplitude fluctuation of the working surface is bigger than the amplitude fluctuation of the backside. The difference between the test data and the numerical prediction becomes larger as the blade numbers vary. The pressure fluctuation at the outlet of the volute is relatively large, and for the three-bladed impeller, a total of 18 peaks and valleys appear at the outlet of the volute in six cycles, which is a periodic change.

^{3}/h, the pressure fluctuation at the monitoring point is larger than that of the three-bladed impeller in the monitoring area of the working surface and the back of the blades. The peaks and valleys of the waveforms show the same cyclic changes with the number of blades, and the values of the pressure coefficient of pulsation are basically the same, which indicates that the working surface of the six-bladed impeller and its back are more uniformly pressurized than those of the three-bladed impeller. It shows that the working surface and the back of the six-bladed impeller are more uniform than those of the three-bladed impeller. The amplitude fluctuation of the volute outlet is reduced compared with that of the three-bladed impeller, which indicates that the pressure fluctuation at the volute outlet of the six-bladed impeller is smaller, and the force is more uniform.

#### 5.2. Pressure Pulsation Frequency Domain Characterization

^{3}/h.

## 6. Analysis of Pump Pressure Pulsation under Cavitation Conditions

#### 6.1. Time-Domain Characterization of a Pump under Cavitation Conditions

^{3}/h working condition, the monitoring point pressure fluctuations in the blade working surface and the backside of the monitoring area appear to be undergoing cyclical change, and, compared to the six-bladed impeller, which showed no cavitation at the monitoring point, the overall trend of change is a slight increase in the pressure pulsation. It shows that when the cavitation number is 0.55, the cavitation has little effect on the pressure of the monitoring point of the six-bladed impeller, and the pressure pulsation of the monitoring point of the three-bladed impeller with the same cavitation number is more gentle and regular, which shows that under the working condition of 1000 m

^{3}/h, the pressure fluctuation of the working surface, the back surface, and the outlet of the volute of the six-bladed impeller is smaller than that of the three-bladed impeller.

#### 6.2. Frequency Domain Characterization of Pumps under Cavitation Conditions

## 7. Radial Force Analysis

^{3}/h. Many irregular fluctuations can be seen in the graph of the three-bladed impeller. From the perspective of the formula, it is speculated that they may be caused by the differences in the radial force on the impeller under the same instantaneous node.

## 8. Conclusions

- (1)
- Under the head and efficiency test, data were obtained through pump performance tests and the values were compared with the numerical simulation results. The results show that the data have small errors under the design conditions, indicating that the numerical simulation in this article has a certain level of reliability.
- (2)
- Under non-cavitating conditions, the pressure fluctuations at monitoring points on the working surface, back surface, and volute exit of impellers with different blade numbers show periodic variations and are related to the number of blades. The pressure fluctuation on the working surface is greater than that on the back surface. The pressure fluctuation of the six-bladed impeller is more uniform than that of the three-bladed impeller, and the internal flow is more stable. Under cavitation conditions, the pressure pulsation coefficients increase compared to the non-cavitating conditions, but the pressure fluctuations are affected by cavitation, which it’s uncertain. The pressure fluctuations at monitoring points on the three-bladed impeller are more complex and do not show obvious periodicity, while the overall trend of the six-bladed impeller changes less.
- (3)
- The frequency of pressure pulsation in the impeller is a multiple of its rotational frequency. Under non-cavitating conditions, the amplitude of the pressure pulsation on the working surface of the six-bladed impeller is larger than that of the three-bladed impeller at the same frequency. The pressure fluctuation at the volute exit is more complex, while the variations in other monitoring areas are not significant. Under cavitation conditions, the overall trend of the three-bladed and six-bladed impellers remains consistent with the non-cavitating conditions. The amplitude of the pressure pulsation at the same frequency on the three-bladed impeller is larger than that under non-cavitating conditions, while the increase in amplitude at monitoring points on the six-bladed impeller is slight.
- (4)
- By analyzing the unsteady characteristics of the radial force of centrifugal pumps with different impeller blade numbers during high-speed operation, it is found that, under constant flow rate conditions, the radial force on the impeller is significantly influenced by the number of blades, with the six-bladed impeller experiencing higher radial forces than the three-bladed impeller. Under cavitation conditions, the number of impeller blades and the distribution of radial forces are mutually influenced by the cavitation effect.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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Flow Parts | Impeller | Guide Vane | Inlet Section | Export Section |
---|---|---|---|---|

Grid number | 469,873 | 554,281 | 1,250,810 | 67,000 |

Flow (m^{3}/h) | Head (m) | ||
---|---|---|---|

CFD | Experimental | Relative Deviation (%) | |

800 | 17.30 | 16.90 | 2.36 |

1000 | 15.95 | 15.70 | 1.59 |

1100 | 15.10 | 14.50 | 4.13 |

1200 | 13.60 | 13.00 | 4.61 |

1300 | 11.63 | 11.30 | 2.92 |

1400 | 10.15 | 9.80 | 3.57 |

Flow (m^{3}/h) | Efficiency (m) | ||
---|---|---|---|

CFD | Experimental | Relative Deviation (%) | |

800 | 73.50 | 72.50 | 1.37 |

1000 | 77.10 | 76.00 | 1.44 |

1100 | 75.00 | 73.80 | 1.62 |

1200 | 73.80 | 72.30 | 2.07 |

1300 | 70.60 | 68.20 | 3.51 |

1400 | 67.80 | 64.90 | 4.46 |

Flow (m^{3}/h) | Head (m) | ||
---|---|---|---|

CFD | Experimental | Relative Deviation (%) | |

800 | 21.11 | 20.50 | 2.97 |

1000 | 19.60 | 19.40 | 1.03 |

1100 | 17.45 | 17.10 | 2.04 |

1200 | 16.50 | 16.45 | 0.30 |

1300 | 15.83 | 15.20 | 4.14 |

1400 | 12.50 | 12.00 | 4.16 |

Flow (m^{3}/h) | Efficiency (m) | ||
---|---|---|---|

CFD | Experimental | Relative Deviation (%) | |

800 | 74.50 | 72.98 | 2.08 |

1000 | 75.80 | 75.01 | 1.05 |

1100 | 74.04 | 72.93 | 1.52 |

1200 | 73.80 | 71.50 | 3.21 |

1300 | 72.60 | 71.15 | 2.03 |

1400 | 64.00 | 61.50 | 4.06 |

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**MDPI and ACS Style**

Yu, G.; Li, G.; Wang, C.
Pressure Pulsation Characteristics of Agricultural Irrigation Pumps under Cavitation Conditions. *Water* **2023**, *15*, 4250.
https://doi.org/10.3390/w15244250

**AMA Style**

Yu G, Li G, Wang C.
Pressure Pulsation Characteristics of Agricultural Irrigation Pumps under Cavitation Conditions. *Water*. 2023; 15(24):4250.
https://doi.org/10.3390/w15244250

**Chicago/Turabian Style**

Yu, Guisheng, Guohui Li, and Chuan Wang.
2023. "Pressure Pulsation Characteristics of Agricultural Irrigation Pumps under Cavitation Conditions" *Water* 15, no. 24: 4250.
https://doi.org/10.3390/w15244250