# Numerical Analysis of the Transient Behaviour of a Variable Speed Pump-Turbine during a Pumping Power Reduction Scenario

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Numerical Model

_{BEP}and 100% rpm.

^{−4}, v momentum 10

^{−4}, w momentum 3 × 10

^{−5}, and turbulence kinetic energy 10

^{−4}.

## 3. Results

#### 3.1. Validation of Numerical Model under Constant Flow Rate Conditions

#### 3.2. Numerical Analysis of the Pump-Turbine in a Power Reduction Scenario

_{ED}< −0.472), the wicket gate channels experience flow rate oscillation (Figure 5) and 11 channels with low flow rate are alternated by 11 channels with higher flow rate. This trend is due to the interaction with the return channel blades and it is consistent with the blockage effect due to the out of alignment of wicket gates with the return blades (Figure 3).

_{ED}< −0.450).

_{ED}< −0.435), the flow field evolves in a rotating partial stall moving from one group of adjacent wicket gate channels to the subsequent one according to the runner rotation direction as highlighted in Figure 5.

_{ED}< −0.465 (Figure 8 and Figure 9), the vortex core regions show many more effects. The vortex core regions almost block the stay vanes’ passages.

_{ED}= −0.45. The back flow volumes in the return vane channels become quite stable and the flow rate tend to remain quite constant in all the return channels (Figure 6) and the flow path does not change evidently.

## 4. Conclusions

- During the beginning of the power reduction process, the vortex, partially blocking the regular flow, moves from one channel to the subsequent one in the runner rotation direction with increasing intensity during the load rejection. Each steady channel alternates partial blocked flow according to the rotation frequency of the stall cell. The unsteady pattern in return channel strengthened, emphasizing its characteristic frequency with the rotational velocity decreasing, reaching a maximum and then disappearing. During this phase, the variation of force and torque on wicket gate pins is moderate.
- For lower rotational speed, the periodic flow oscillation inside the return channels disappeared. The flow field into the wicket gates channel start to manifest a full three-dimensional flow structure. The path analyses show that only the vortexes with intensity and structure changed stochastically. Hence, the fluctuations of pressure and torque for different monitoring points show relatively low variation.
- Close to the end of the power reduction process, serious fluctuations of both pressure and velocity could be observed, and the highest level occurs in the stay vanes showing a rotating stall. The parameters show serious fluctuations of torque and force on the guide vanes.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

B | Impeller or guide vane or return channel width | m |

${c}_{p}=\frac{\mathrm{p}-\overline{p}}{\mathsf{\rho}{\left(\mathsf{\omega}\frac{{\mathrm{D}}_{2}}{2}\right)}^{2}}$ | Pressure coefficient | - |

D | Diameter | m |

F | Force | N |

${\mathrm{F}}_{\text{ED}}=\frac{\mathrm{F}}{{\mathsf{\rho}\mathrm{D}}_{2}^{2}\text{gH}}$ | Force Factor | - |

g | Gravitational acceleration | m·s^{−2} |

Gxx | Power spectra | [] ^{2} |

H | Head | m |

n | Rotational speed of the impeller | rpm |

${\mathrm{n}}_{\text{ED}}=\frac{{\text{nD}}_{2}}{60\sqrt{\text{gH}}}$ | Speed factor | - |

n_{b} | Impeller number of blades | - |

n_{bR} | Return Vane number of blades | - |

n_{bW} | Wicket Guide number of blades | - |

Q | Flow rate | m^{3}·s^{−1} |

p | Pressure | Pa |

$\overline{\mathrm{p}}$ | Pressure averaged along the time | Pa |

${\mathrm{Q}}_{\text{ED}}=\frac{\mathrm{Q}}{{\mathrm{D}}_{2}^{2}\sqrt{\text{gH}}}$ | Discharge factor | - |

$\text{BPF}=\frac{{\mathrm{n}}_{\mathrm{b}}\mathrm{n}}{60}$ | Blade Passage Frequency | Hz |

$\text{St}=\frac{\mathrm{f}}{\text{BPF}}$ | Strouhal number | - |

${\mathrm{T}}_{\text{ED}}=\frac{\mathrm{T}}{{\mathsf{\rho}\mathrm{D}}_{2}^{3}\text{gH}}$ | Torque factor | - |

α | Angle | degree |

β | Angle | degree |

λ | Guide vanes’ azimuthally position | degree |

ω | Angular rotational velocity | rad·s^{−1} |

## Abbreviations

PHES | Pumped Hydro Energy Storage |

CFD | Computational Fluid Dynamics |

BEP | Best Efficiency Point |

BPF | Blade Passage Frequency |

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**Figure 2.**Meridional view of the numerical model. Regions filled in grey refer to the blades; region filled in black refers to the leakage system. 2: outlet impeller; 3: inlet wicket gate; 4: inlet return channel.

**Figure 3.**Detail of the coarse mesh of the numerical model: inlet duct, impeller, wicket gates and return channel.

**Figure 7.**Distribution of streamline and vortex core (Q-Criterion = 90,000 s

^{−2}) in stay vanes, for n

_{ED}= −0.480.

**Figure 8.**Distribution of streamline and vortex core (Q-Criterion = 90,000 s

^{−2}) in stay vanes, for n

_{ED}= −0.457.

**Figure 9.**Distribution of streamline and vortex core (Q-Criterion = 90,000 s

^{−2}) in stay vanes, for n

_{ED}= −0.439.

**Figure 10.**Detail and sketch of the tested configuration (λ = 8°) with the distribution of monitor points.

**Figure 11.**Power spectra density of the discharge factor Q

_{ED}acquired in the (

**a**) wicket gate and (

**b**) return channels.

**Figure 13.**Normalized power-spectra of pressure coefficient c

_{p}evaluated in the monitor point D06 (Figure 10) of two consecutive wicket gates: (

**a**) Wicket blade faced to the return vane; (

**b**) Wicket blade between two return vanes.

**Figure 14.**Normalized power-spectra of pressure coefficient c

_{p}evaluated in the monitor point D12 (Figure 10) of two consecutive wicket gates: (

**a**) Wicket blade faced to the return vane; (

**b**) Wicket blade between two return vanes.

**Figure 15.**Normalized power-spectra of pressure coefficient c

_{p}evaluated in the monitor point (

**a**) R11 and (

**b**) R19 (Figure 10) of a return channel.

**Figure 16.**Normalized power-spectra of torque coefficient T

_{ED}of two consecutive wicket gates: (

**a**) Wicket blade faced to the return vane; (

**b**) Wicket blade between two return vanes.

**Figure 17.**Normalized power-spectra of force coefficient on the pin of two consecutive wicket gates: (

**a**) Wicket blade faced to the return vane; (

**b**) Wicket blade between two return vanes.

Impeller Data | ||||

D_{2} (mm) | B_{2} (mm) | n_{b} | β_{2b} (°) | φ_{Des} |

400 | 40 | 7 | 26.5 | 0.125 |

Wicket Guide Data | ||||

D_{3} (mm) | B_{3} (mm) | n_{bW} | α_{3b} (°) | λ (°) |

410 | 40 | 22 | 10 ÷ 30 | −8 ÷ 8 |

Return Channel Vanes Data | ||||

D_{4} (mm) | B_{4} (mm) | n_{bR} | α_{4b} (°) | |

516 | 40 | 11 | 30 |

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**MDPI and ACS Style**

Pavesi, G.; Cavazzini, G.; Ardizzon, G.
Numerical Analysis of the Transient Behaviour of a Variable Speed Pump-Turbine during a Pumping Power Reduction Scenario. *Energies* **2016**, *9*, 534.
https://doi.org/10.3390/en9070534

**AMA Style**

Pavesi G, Cavazzini G, Ardizzon G.
Numerical Analysis of the Transient Behaviour of a Variable Speed Pump-Turbine during a Pumping Power Reduction Scenario. *Energies*. 2016; 9(7):534.
https://doi.org/10.3390/en9070534

**Chicago/Turabian Style**

Pavesi, Giorgio, Giovanna Cavazzini, and Guido Ardizzon.
2016. "Numerical Analysis of the Transient Behaviour of a Variable Speed Pump-Turbine during a Pumping Power Reduction Scenario" *Energies* 9, no. 7: 534.
https://doi.org/10.3390/en9070534