# Research on the Performance Characteristics and Unsteady Flow Mechanism of a Centrifugal Pump under Pitch Motion

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Centrifugal Pump Model

^{3}/h and the head as 16 m. The impeller rotation speed was set at 2900 r/min. The impeller’s three-dimensional shape was parameterized using fourth-order Bezier curves for the hub, shroud and blade characteristics. The volute with a circular cross section was designed using the Stepanoff method, ensuring a consistent absolute velocity along the circumferential direction under the rated operation conditions. Detailed geometric information on the model pump is listed in Table 1.

#### 2.2. Experimental Devices and Methods

^{T}, ρ, U

_{2}, Q, T, ω, R

_{2}and B

_{2}are the total pressure, water density, blade tip velocity, pump flow rate, torque, impeller angular velocity, impeller diameter and impeller outlet width, respectively. The subscripts 2, in and out indicate the impeller outlet and measuring locations at the pump inlet and pump outlet, respectively.

_{d}). Meanwhile, ψ presents a steadily sloping curve across the φ/φ

_{d}range, and the maximum ψ appears at the shut-off condition. The ψ curve and the η curve indicate that the model pump has good hydraulic performance.

#### 2.3. CFD Methodology

^{7}grid points was adopted on account of the ψ values at the pump’s rated flow rate.

## 3. Result and Discussion

#### 3.1. Pump Test Performances under Pitch Conditions

_{max}is the maximum pitch angle and k is the pitch period.

_{d}≤ 0.4, which causes unstable operating characteristics such as a sudden drop in pump outlet pressure or severe pump vibration and noise. The hump curve induces two flow-rate points under the same water pressure condition, which generates pulsating variations in pump flow rate and then produces some instability flows and flow excitation. Specifically, ψ experiences a small reduction at φ/φ

_{d}= 0 under the influence of pitch motion and decreases as the pitch period shortens. When model pump is in a static state, ψ reaches a maximum at φ/φ

_{d}= 0. However, the occurrence of maximum ψ shifts to a higher value of φ/φ

_{d}(φ/φ

_{d}= 0.2). Figure 6 indicates that the performance curves for ψ represent similar slopes at φ/φ

_{d}≥ 0.6, where ψ decreases as the pitch period reduces. The ψ curves for pitch motion conditions of 10 degrees, 15 degrees and 20 degrees show variations quite similar to those under pitch motion conditions of 5 degrees across the whole φ/φ

_{d}range, as shown in Figure 7, Figure 8 and Figure 9. Unsteady variation characteristics of pump performance including the hump curve and ψ reduction become more and more obvious as the pitch angle increases.

_{d}range as the maximum pitch angle increases. The ψ difference becomes more obvious as the pitch period shortens according to Figure 11 and Figure 12. Particularly, the ψ difference reaches a maximum at a pitch period of 5 s. Under the pump operating condition of φ

_{d}shown in Figure 13, the pitch motion causes a significant decrease in ψ compared to the static state. ψ reduces as the maximum pitch angle increases for the same pitch period. Meanwhile, ψ reduces as the pitch period shortens for the same pitch angle. ψ decreases by 6.3% to reach a minimum at a maximum pitch angle of 20 degrees and a pitch period of 5 s.

#### 3.2. Flow Characteristics under Pitch Motion

#### 3.3. Unsteady Pressure Characteristics

_{P}) is employed to evaluate the pressure distribution map in the pump.

^{T}, P, ρ and U

_{2}are the total pressure, static pressure, water density and blade tip velocity, respectively. The subscripts 2 and out indicate the impeller outlet and the measuring location at the pump outlet, respectively.

_{P}curves have similar slopes under the static state and under the influence of pitch motion, exhibited in Figure 21. The pressure magnitude gradually decreases as the pitch period shortens. Nevertheless, C

_{P}curves exhibit opposite slopes at the blade outlet between the static state and under the influence of pitch motion as shown in Figure 22. The pitch motion provides an additional force and varies the force characteristics and motion behaviors of fluid particles. The shape of the blade determines the law of pressure variation. Under the static state, the pressure development rate gradually increases along the blade passage and reaches a maximum at the outlet as shown in Figure 23a. Specially, the maximum pressure increase occurs in the middle section of the blade passage under the influence of pitch motion and the area with low pressure increase gradually increases; this phenomenon is most obvious under the minimum pitch period of 5 s as shown in Figure 23. The pressure gradient map indicates that the pitch motion makes the unsteady flow inside the impeller passage more turbulent.

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**Comparison between simulated and tested performance characteristics: (

**a**) static, (

**b**) pitch motion.

**Figure 6.**Comparison of performance curves for static state and different levels of pitch motion with three periods of 5 s, 10 s and 20 s under the maximum pitch angle of 5 degrees: (

**a**) ${\mathit{\phi}/\mathit{\phi}}_{\mathit{d}}\le 1.0$, (

**b**) ${\mathit{\phi}/\mathit{\phi}}_{\mathit{d}}\ge 1.0$.

**Figure 7.**Comparison of performance curves for static state and different levels of pitch motion with three periods of 5 s, 10 s and 20 s under the maximum pitch angle of 10 degrees: (

**a**) ${\mathit{\phi}/\mathit{\phi}}_{\mathit{d}}\le 1.0$, (

**b**) ${\mathit{\phi}/\mathit{\phi}}_{\mathit{d}}\ge 1.0$.

**Figure 8.**Comparison of performance curves for static state and different levels of pitch motion with three periods of 5 s, 10 s and 20 s under the maximum pitch angle of 15 degrees: (

**a**) ${\mathit{\phi}/\mathit{\phi}}_{\mathit{d}}\le 1.0$, (

**b**) ${\mathit{\phi}/\mathit{\phi}}_{\mathit{d}}\ge 1.0$.

**Figure 9.**Comparison of performance curves for static state and different levels of pitch motion with three periods of 5 s, 10 s and 20 s under the maximum pitch angle of 20 degrees: (

**a**) ${\mathit{\phi}/\mathit{\phi}}_{\mathit{d}}\le 1.0$, (

**b**) ${\mathit{\phi}/\mathit{\phi}}_{\mathit{d}}\ge 1.0$.

**Figure 10.**Comparison of performance curves for static state and different levels of pitch motion with maximum pitch angles of 5 degrees, 10 degrees, 15 degrees and 20 degrees for a pitch period of 20 s: (

**a**) ${\mathit{\phi}/\mathit{\phi}}_{\mathit{d}}\le 1.0$, (

**b**) ${\mathit{\phi}/\mathit{\phi}}_{\mathit{d}}\ge 1.0$.

**Figure 11.**Comparison of performance curves for static state and different levels of pitch motion with maximum pitch angles of 5 degrees, 10 degrees, 15 degrees and 20 degrees for a pitch period of 10 s: (

**a**) ${\mathit{\phi}/\mathit{\phi}}_{\mathit{d}}\le 1.0$, (

**b**) ${\mathit{\phi}/\mathit{\phi}}_{\mathit{d}}\ge 1.0$.

**Figure 12.**Comparison of performance curves for static state and different levels of pitch motion with maximum pitch angles of 5 degrees, 10 degrees, 15 degrees and 20 degrees for a pitch period of 5 s: (

**a**) ${\mathit{\phi}/\mathit{\phi}}_{\mathit{d}}\le 1.0$, (

**b**) ${\mathit{\phi}/\mathit{\phi}}_{\mathit{d}}\ge 1.0$.

**Figure 14.**Velocity distributions along the normalized meridional locations for blade passage inlet.

**Figure 15.**Velocity distributions along the normalized meridional locations for blade passage outlet.

**Figure 16.**Flow structures under different pitch motion periods: (

**a**) static, (

**b**) 20 s, (

**c**) 10 s, (

**d**) 5 s.

**Figure 17.**Unsteady flows under different pitch motion periods: (

**a**) static, (

**b**) 20 s, (

**c**) 10 s, (

**d**) 5 s.

**Figure 18.**RVS distributions under different pitch periods: (

**a**) static, (

**b**) 20 s, (

**c**) 10 s, (

**d**) 5 s.

**Figure 19.**CORF distributions under different pitch periods: (

**a**) static, (

**b**) 20 s, (

**c**) 10 s, (

**d**) 5 s.

**Figure 20.**VISD distributions under different pitch periods: (

**a**) static, (

**b**) 20 s, (

**c**) 10 s, (

**d**) 5 s.

**Figure 21.**Pressure distributions along the normalized meridional locations for blade passage inlet.

**Figure 22.**Pressure distributions along the normalized meridional locations for blade passage outlet.

**Figure 23.**Pressure gradients under different pitch periods: (

**a**) static, (

**b**) 20 s, (

**c**) 10 s, (

**d**) 5 s.

impeller inlet diameter/m | 0.04 |

impeller outlet diameter/m | 0.16 |

blade outlet width/m | 0.006 |

blade number | 5 |

blade wrap angle/° | 120 |

blade inlet angle/° | 22 |

blade outlet angle/° | 24 |

volute base circle diameter/m | 0.162 |

volute outlet diameter/m | 0.032 |

Parameters | Values | |
---|---|---|

Number of elements | N_{1}/N_{2}/N_{3} | 9.4 × 10^{6}/1.2 × 10^{7}/2.1 × 10^{7} |

Computed head coefficients (ψ) corresponding to N_{1}, N_{2} and N_{3} | ψ_{1}/ψ_{2}/ψ_{3} | 0.565/0.561/0.559 |

Apparent order | p | 1.32 |

Grid convergence index corresponding to N_{1}, N_{2} and N_{3} | GCI_{1}/GCI_{2}/GCI_{3} | 3.08%/2.12%/1.93% |

Level 1 | Level 2 | Level 3 | Level 4 | |
---|---|---|---|---|

θ_{max}/degree | 5 | 10 | 15 | 20 |

k/second | 5 | 10 | 20 |

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## Share and Cite

**MDPI and ACS Style**

Yuan, Y.; Gong, W.; Wang, G.; Wang, J.
Research on the Performance Characteristics and Unsteady Flow Mechanism of a Centrifugal Pump under Pitch Motion. *Water* **2023**, *15*, 3706.
https://doi.org/10.3390/w15203706

**AMA Style**

Yuan Y, Gong W, Wang G, Wang J.
Research on the Performance Characteristics and Unsteady Flow Mechanism of a Centrifugal Pump under Pitch Motion. *Water*. 2023; 15(20):3706.
https://doi.org/10.3390/w15203706

**Chicago/Turabian Style**

Yuan, Ye, Weihong Gong, Guojun Wang, and Jun Wang.
2023. "Research on the Performance Characteristics and Unsteady Flow Mechanism of a Centrifugal Pump under Pitch Motion" *Water* 15, no. 20: 3706.
https://doi.org/10.3390/w15203706