# Analysis of the Flow Energy Loss and Q-H Stability in Reversible Pump Turbine as Pump with Different Guide Vane Opening Angles

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## Abstract

**:**

## 1. Introduction

## 2. Research Objective

_{r}= 9. Both the guide vane blade number Z

_{g}and stay vane blade number Z

_{s}are 22. The runner diameter (diameter at high pressure side) D

_{1}is 554 mm. The design head H

_{d}is 52.9 m, the maximum head H

_{max}is 58.0 m and the minimum head H

_{min}is 50.8 m. The rated rotational speed n

_{d}is 1100 rpm. The specific speed n

_{q}can be calculated by:

_{q}is approximately 34.6.

Parameter | Symbol | Value |
---|---|---|

Runner blade number | Z_{r} | 9 |

Guide vane blade number | Z_{g} | 22 |

Stay vane blade number | Z_{s} | 22 |

Runner diameter | D_{1} | 554 [mm] |

Design head | H_{d} | 52.9 [m] |

Maximum head | H_{max} | 58.0 [m] |

Minimum head | H_{min} | 50.8 [m] |

Rated rotational speed | n_{d} | 1100 [rpm] |

Specific speed | n_{q} | 34.6 |

## 3. Methodology

#### 3.1. Governing Equations

_{ij}—Kroneker delta, μ—dynamic viscosity, S

_{ij}—mean rate of strain tensor, h

_{sta}—static enthalpy, h

_{tot}—total enthalpy, λ

_{t}—thermal conductivity.

_{1}—the blending function. σ

_{k}, σ

_{ω}—constants of turbulence model. l

_{k}

_{-ω}—the turbulence scale. It can be expressed as:

_{k}—the model constant.

_{pro}with 4 main sub-terms. ${S}_{\overline{pc}}$ and ${S}_{pc{}^{\prime}}$ are the sub-term of entropy production caused by loss term, ${S}_{\overline{pd}}$ and ${S}_{pd{}^{\prime}}$ are the sub-term of entropy production caused by dissipation term. They can be calculated by:

#### 3.2. Computational Fluid Dynamics Setup

^{−5}.

#### 3.3. Model Test

_{s}and the pressure difference p

_{sd}between inlet and outlet were measured. The calculation formula is as follows:

## 4. Comparison of Energy Performance

_{BEP}) of each guide vane opening angle. The operation of the prototype pump turbine will follow this curve in order to have a higher efficiency. The head values H of these best efficiency points (Q

_{BEP}) were recorded as the Q-H envelop curve. For each Q-H curve, its BEP point matches with the Q-η envelop curve and Q-H envelop curve. Generally, as shown by the Q-H envelop curve, H increases with a decrease in Q. The Q-η envelop curve has a peak (best efficiency point) as indicated in Figure 4. The global best efficiency point is under α = 14 degrees.

_{STA}. If the flow rate continually decreases, H will rise again, the valley point is defined as the head valley point and the flow rate is denoted as Q

_{VAL}. The values of Q

_{STA}and Q

_{VAL}are shown in Figure 5a,b. Both Q

_{STA}and Q

_{VAL}decrease with a decrease in α. This means that the unstable flow rate of the guide vane decreases synchronously with the decrease in the guide vane opening angle. A detailed analysis of the best efficiency η

_{BEP}and flow rate of best efficiency points Q

_{BEP}is shown in Figure 5c,d. The value of η

_{BEP}increases within α = 10~14 degrees and decreases within α = 14~18 degrees. The value of Q

_{BEP}generally increases from α = 10 degrees to α = 18 degrees, with an exception at α = 16 degrees. This means that the optimal matching opening angle of the guide vane increases synchronously with the increase in the flow rate. Therefore, the optimal matching and undesirable matching of the guide vane and impeller need further analyses.

## 5. Analysis of Internal Flow

#### 5.1. Large Guide Vane Opening Angle (18 Degrees)

_{BEP}is approximately 0.415 m

^{3}/s and Q

_{VAL}is approximately 0.339 m

^{3}/s. Through the analysis of the flow energy loss proportion inside the volute, stay vane, guide vane, runner and draft tube as shown in Figure 6b, it is found that, when the flow rate is at the Q

_{BEP}point, the loss proportion of the guide vane is approximately 40.8%. The loss proportion inside the runner is close to that inside the guide vane. The loss proportion of the stay vane and volute is relatively small. The loss in the draft tube is less than 1%, which is very small. When the flow rate decreased to Q

_{VAL}, the loss proportion of guide vane increased significantly to 53.9%, which was higher than the sum of other components. It can be seen from the S

_{pro}contour and v vectors at the Q

_{BEP}point that there is only a small amount of guide vane passages with an obvious loss increase, and that the intensity is not high. This is related to the local secondary flow structures. At the Q

_{VAL}point, there are approximately seven channels of the guide vane with significant loss. The local intensity is very high, which is also related to the secondary flow in the guide vane channels, and it causes the flow blockage in the downstream components.

#### 5.2. Medium-Large Guide Vane Opening Angle (16 Degrees)

_{BEP}is approximately 0.339 m

^{3}/s and Q

_{VAL}is approximately 0.327 m

^{3}/s. As shown in Figure 7b, it is found that, when the flow rate is at the Q

_{BEP}point, the loss proportion of the guide vane is approximately 51.8%, which is the largest. The loss proportion inside the runner is the second largest. The loss proportion of the stay vane and volute is smaller. The loss in the draft tube is also less than 1%, which is very small. When the flow rate decreased to Q

_{VAL}, the loss proportion of the guide vane became 52.2%, which was almost unchanged. It can be seen from the S

_{pro}contour and v vectors at the Q

_{BEP}point and Q

_{VAL}point that secondary flow structures are found in guide vane channels. Flow blockage in the downstream components can be also observed. Based on the comparison between the Q

_{BEP}point and Q

_{VAL}point, the intensity of the flow energy loss at the Q

_{VAL}point is much stronger. This is why head H drops suddenly.

#### 5.3. Medium Guide Vane Opening Angle (14 Degrees)

_{BEP}is approximately 0.363 m

^{3}/s and Q

_{VAL}is approximately 0.267 m

^{3}/s. As shown in Figure 8b, it is found that when the flow rate is at the Q

_{BEP}point, the loss proportion of the guide vane is approximately 36.9%. The loss proportion inside the runner is close to that inside the guide vane. The loss proportion of the stay vane and volute is smaller than that in the runner and guide vane. The loss in the draft tube is still much smaller. When the flow rate decreased to Q

_{VAL}, the loss proportion of the guide vane increased significantly to 69.7%, which was higher than the sum of other components. The proportion of loss in the runner becomes lower. It can be seen from the S

_{pro}contour and v vectors at the Q

_{BEP}point that only few guide vane passages have a relatively strong energy loss and that the intensity is not that high. At the Q

_{VAL}point, there are approximately eight channels of the guide vane with a significant flow energy loss with very high intensity. The sudden increase in S

_{pro}also indicates the mismatching of the guide vane and runner incoming flow. The bad flow regime will cause flow blockage in the stay vane and volute.

#### 5.4. Medium-Small Guide Vane Opening Angle (12 Degrees)

_{BEP}is approximately 0.315 m

^{3}/s and Q

_{VAL}is approximately 0.219 m

^{3}/s. As shown in Figure 9b, it is found that, when the flow rate is at the Q

_{BEP}point, the loss proportion of the guide vane is approximately 47.5%, which is the largest. The loss proportion inside the runner, stay vane and volute is similar. The loss in the draft tube is still less than 1%. When the flow rate decreased to Q

_{VAL}, the loss proportion of the guide vane increased significantly to 65.6%, which was higher than the sum of other components. The proportion of loss in the volute becomes obviously lower. It can be seen from the S

_{pro}contour and v vectors at the Q

_{BEP}point that the loss is relatively low and the flow regime is smooth in all of the guide vane channels. At the Q

_{VAL}point, some guide vane channels have a high flow energy loss with a high intensity. This is related to the secondary flow in the guide vane, and the downstream components are influenced.

#### 5.5. Small Guide Vane Opening Angle (10 Degrees)

_{BEP}is approximately 0.243 m

^{3}/s and Q

_{VAL}is approximately 0.183 m

^{3}/s. As shown in Figure 10b, it is found that, when the flow rate is at the Q

_{BEP}point, the loss proportion of the guide vane is approximately 54.8%, which is the largest. The loss proportion inside the runner and stay vane is similar and lower than that in the guide vane. The loss in the volute is much lower. The loss in the draft tube is less than 1%, which is very low. When the flow rate decreased to Q

_{VAL}, the loss proportion of the guide vane increased significantly to 70.5%, which was higher than the sum of other components and completely dominant. The proportion of loss in the stay vane and volute becomes obviously lower. It can be seen from the S

_{pro}contour and v vectors at Q

_{BEP}point that the loss is relatively low and the flow regime is smooth in all of the guide vane channels. At the Q

_{VAL}point, the flow regime in the guide vane becomes bad and causes an increase in the flow energy loss.

## 6. Discussion

_{BEP}and Q

_{VAL}. The most important change from the Q

_{BEP}point to Q

_{VAL}point is the decrease in the flow rate.

_{m}can be calculated by [32]:

_{m}is analyzed.

_{BEP}, which represents a good flow condition, the absolute flow angle between the runner and guide vane, defined as α

_{icf}, will be almost equal to the guide vane installation angle α

_{gv}. When the flow rate Q decreases, v

_{m}will become smaller. Because the direction of w is almost unchanged, α

_{icf}will be smaller, as indicated. The absolute difference Δα between α

_{gv}and α

_{icf}can be defined as:

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Fluid domain and grid. (

**a**) Grid independence check; (

**b**) the schematic map of the final grid.

**Figure 3.**Test rig and apparatus. (

**a**) The schematic map of the test rig and apparatus; (

**b**) the on-site view of the test rig.

**Figure 5.**Variation in typical conditions of different attack angles α. (

**a**) Q

_{STA}. (

**b**) Q

_{VAL}. (

**c**) η

_{BEP}. (

**d**) Q

_{BEP}.

**Figure 6.**Performance curve and flow pattern at 18° attack angle. (

**a**) Q-H and Q-η curve; (

**b**) proportion of flow energy loss; (

**c**) VAL S

_{pro}; (

**d**) VAL v; (

**e**) BEP S

_{pro}; (

**f**) BEP v; VAL: local valley of Q-H curve; BEP: best efficiency point.

**Figure 7.**Performance curve and flow pattern at 16° attack angle. (

**a**) Q-H and Q-η curve; (

**b**) proportion of flow energy loss; (

**c**) VAL S

_{pro}; (

**d**) VAL v; (

**e**) BEP S

_{pro}; (

**f**) BEP v; VAL: local valley of Q-H curve; BEP: best efficiency point.

**Figure 8.**Performance curve and flow pattern at 14° attack angle. (

**a**) Q-H and Q-η curve; (

**b**) proportion of flow energy loss; (

**c**) VAL S

_{pro}; (

**d**) VAL v; (

**e**) BEP S

_{pro}; (

**f**) BEP v; VAL: local valley of Q-H curve; BEP: best efficiency point.

**Figure 9.**Performance curve and flow pattern at 12° attack angle. (

**a**) Q-H and Q-η curve; (

**b**) proportion of flow energy loss; (

**c**) VAL S

_{pro}; (

**d**) VAL v; (

**e**) BEP S

_{pro}; (

**f**) BEP v; VAL: local valley of Q-H curve; BEP: best efficiency point.

**Figure 10.**Performance curve and flow pattern at 10° attack angle. (

**a**) Q-H and Q-η curve; (

**b**) proportion of flow energy loss; (

**c**) VAL S

_{pro}; (

**d**) VAL v; (

**e**) BEP S

_{pro}; (

**f**) BEP v; VAL: local valley of Q-H curve; BEP: best efficiency point.

Component | Grid Number |
---|---|

Draft tube | 388,445 |

Runner (including clearance) | 3,368,717 |

Guide vane | 1,462,120 |

Stay vane | 2,669,804 |

Volute | 1,779,870 |

Total | 9,668,956 |

Quantity | Apparatus | Type | Uncertainty |
---|---|---|---|

Flow rate | Electromagnetic flowmeter | Rosemount 8705TSE | ±0.1% |

Rotation speed | Rotary encoder | E6B2-CWZ1X | ±0.02% |

Head | Differential pressure sensor | SHAE 1151HP6E | ±0.1% |

Torque | Load sensor | GWT MP47/22C3 | ±0.015% |

Tail-water pressure | Absolute pressure sensor | Rosemount 1151AP | ±0.1% |

Guide vane angle | Angular displacement sensor | BGJ 60 | ±0.10° |

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## Share and Cite

**MDPI and ACS Style**

Yan, W.; Zhu, D.; Tao, R.; Wang, Z.
Analysis of the Flow Energy Loss and *Q-H* Stability in Reversible Pump Turbine as Pump with Different Guide Vane Opening Angles. *Water* **2022**, *14*, 2526.
https://doi.org/10.3390/w14162526

**AMA Style**

Yan W, Zhu D, Tao R, Wang Z.
Analysis of the Flow Energy Loss and *Q-H* Stability in Reversible Pump Turbine as Pump with Different Guide Vane Opening Angles. *Water*. 2022; 14(16):2526.
https://doi.org/10.3390/w14162526

**Chicago/Turabian Style**

Yan, Wei, Di Zhu, Ran Tao, and Zhengwei Wang.
2022. "Analysis of the Flow Energy Loss and *Q-H* Stability in Reversible Pump Turbine as Pump with Different Guide Vane Opening Angles" *Water* 14, no. 16: 2526.
https://doi.org/10.3390/w14162526