# Effect of Rotational Speed on Pressure Pulsation Characteristics of Variable-Speed Pump Turbine Unit in Turbine Mode

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Numerical Method and Setup

#### 2.1. Pump Turbine Model

#### 2.2. Grid Independence

#### 2.3. CFD Simulation Setup

#### 2.4. Operating Conditions and Monitoring Points

## 3. Results and Discussion

#### 3.1. Numerical Method Verification

#### 3.2. Flow Characteristics

#### 3.3. Pressure Pulsation Characteristics

_{n}is the rotational frequency, and f/f

_{n}is the ratio of frequency to rotational frequency. It can be seen that the dominant frequency in WKT1 is a low-frequency component.

_{n}= 18), and at N3 is the blade passage frequency (f/f

_{n}= 9, the number of blades is 9). The dominant low frequency is 0.86 f

_{n}.

_{n}= 18, the number of blades is 9) and at N3 is the blade passage frequency (f/f

_{n}= 9, the number of blades is 9). The essential frequency of PHCM3 at N1 is the multiplicative frequency of the blades (f/f

_{n}= 9, number of blades is 9) and under N2 and N3 the predominant frequency is the blade passing frequency (f/f

_{n}= 9, number of blades is 9). This is aroused by the dynamic and static interference of the runner and guide vane. With the increase in speed, the main frequency amplitude gradually increases. The higher the speed, the higher the main frequency amplitude. In the N1 and N2 models, the main frequency increases and then decreases, and in the N3 model it keeps decreasing. It can be found that there are more low-frequency components with larger pressure pulsation amplitude at each speed, which may be due to the operating condition of the turbine, where the movable guide vanes and runners create a large number of vortices and secondary currents are formed in the bladeless zone, resulting in more low-frequency components.

_{n}at N1, 0.83 f

_{n}at N2, and 0.8 f

_{n}at N3. In addition to this, in the high-frequency section there is mainly three times the blade overcurrent frequency.

_{n}, in N2 is 0.83 f

_{n}, and in N3 is 0.8 f

_{n}, and taking into account that these frequency components and the frequency of rotation are not a regular change, the cause of this aspect may be the inherent frequency of the pressure pulsation excited by the test bench piping system and its water body.

_{n}for the high-frequency component, and this pressure pulsation is mostly caused by the static and dynamic interference, and the pressure pulsation caused by the static and dynamic interference has the characteristics of isolated and clear spectral lines. As the speed increases, the flow field at the runner is gradually disturbed, making the pressure pulsation increase. The amplitude of pressure pulsation reduces gradually with spindling down.

#### 3.4. Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**Pressure distribution of N1~N3 at the runner inner surface. (

**a**) Pressure distribution of runner inner surface at N1; (

**b**) pressure distribution of runner inner surface at N2; (

**c**) pressure distribution of runner inner surface at N3.

**Figure 5.**Streamline in the flow passage of N1~N3. (

**a**) Streamline in the flow passage at N1; (

**b**) streamline in the flow passage at N2; (

**c**) streamline in the flow passage at N3.

**Figure 6.**Pressure pulsation and frequency spectra at monitoring point WKT1. (

**a**) WKT1 pressure pulsation; (

**b**) WKT1-frequency spectra.

**Figure 7.**Pressure pulsation and frequency spectra at monitoring points PHCM1~PHCM3. (

**a**) PHCM1 pressure pulsation; (

**b**) PHCM1 frequency spectra; (

**c**) PHCM2 pressure pulsation; (

**d**) PHCM2 frequency spectra; (

**e**) PHCM3 pressure pulsation; (

**f**) PHCM3 frequency spectra.

**Figure 8.**Pressure pulsation and frequency spectra at monitoring points PP1~PP2. (

**a**) PP1 pressure pulsation; (

**b**) PP1 frequency spectra; (

**c**) PP2 pressure pulsation; (

**d**) PP2 frequency spectra.

**Figure 9.**Pressure pulsation and frequency spectra at monitoring points PP3~PP4. (

**a**) PP3 pressure pulsation; (

**b**) PP3 frequency spectra; (

**c**) PP4 pressure pulsation; (

**d**) PP4 frequency spectra.

**Figure 10.**Pressure pulsation and frequency spectra at monitoring points RV1~RV2. (

**a**) RV1 pressure pulsation; (

**b**) RV1 frequency spectra; (

**c**) RV2 pressure pulsation; (

**d**) RV2 frequency spectra.

**Table 1.**The three speed models (the three speed models determined by the operating conditions of the prototype).

Model Number | Speed (m/s) |
---|---|

N1 | 398.57 |

N2 | 412.16 |

N3 | 428.6 |

Component | Element Type | Number of Elements |
---|---|---|

Spiral casing | Tetrahedra | 493,696 |

Stay vanes | Hexahedral | 579,660 |

Guide vanes | Hexahedral | 383,780 |

Runner | Hexahedral | 2,008,124 |

Gap | Hexahedral | 598,200 |

Pressure balance pipe | Hybrid | 72,236 |

Draft tube | Hexahedral | 372,265 |

Total | - | 4,389,241 |

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## Share and Cite

**MDPI and ACS Style**

Shang, L.; Cao, J.; Jia, X.; Yang, S.; Li, S.; Wang, L.; Wang, Z.; Liu, X. Effect of Rotational Speed on Pressure Pulsation Characteristics of Variable-Speed Pump Turbine Unit in Turbine Mode. *Water* **2023**, *15*, 609.
https://doi.org/10.3390/w15030609

**AMA Style**

Shang L, Cao J, Jia X, Yang S, Li S, Wang L, Wang Z, Liu X. Effect of Rotational Speed on Pressure Pulsation Characteristics of Variable-Speed Pump Turbine Unit in Turbine Mode. *Water*. 2023; 15(3):609.
https://doi.org/10.3390/w15030609

**Chicago/Turabian Style**

Shang, Linmin, Jingwei Cao, Xin Jia, Shengrui Yang, Sainan Li, Lei Wang, Zhengwei Wang, and Xiaobing Liu. 2023. "Effect of Rotational Speed on Pressure Pulsation Characteristics of Variable-Speed Pump Turbine Unit in Turbine Mode" *Water* 15, no. 3: 609.
https://doi.org/10.3390/w15030609