# Influence of Radial Installation Deviation on Hydraulic Thrust Characteristics of a 1000 MW Francis Turbine

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## Abstract

**:**

## 1. Introduction

## 2. Research Object and Methodology

## 3. Calculation Setup and Results Analysis

- (a)
- The CFD calculation used the mesh with 5 million elements. The mesh independence verification had been done previously, and the subsequent deviation model only changed the clearance mesh division and size on this basis.
- (b)
- The total pressure was set as the inlet conditon, and the static pressure was set as outlet condition.
- (c)
- The calculated steps were 2000, and the residual converges were limited to ${10}^{-4}$. We use a convergence criterion of ${10}^{-4}$ instead of higher orders, because the gap size in the mesh was much smaller than that of the impeller, which made it difficult to converge in the calculations. Multiple calculations only converged to ${10}^{-4}$, so we set the criterion at this value.

- (a)
- Regardless of whether wall velocity was added or not, the radial force increased with the increase in deviation in any part.
- (b)
- The radial force on the crown chamber was the largest.
- (c)
- Compared to with and without the wall velocity, the radial force trend with the wall velocity added was more realistic.

#### 3.1. Steady-State Calculation

- (1)
- The radial hydraulics force increased with the increase in deviation in different fluid domains.
- (2)
- The radial hydraulics force on the crown chamber was the largest, and the second largest was the runner.

#### 3.2. Unsteady Computation

#### 3.2.1. Analysis of the Radial Force Fluctuations

- 1.
- The crown chamber

- (1)
- The force received by the crown chamber was the smallest. Although there are large force fluctuations, the average force value was the lowest among all the components.
- (2)
- The direction of the crown chamber force mostly focused on the direction from −50${}^{\circ}$ to −150${}^{\circ}$ showed in Figure 15. This was consistent with the position change of the high-pressure area we later observed.

- 2.
- The runner

- 3.
- The bottom ring

- 1.
- Under influence by radial deviation, the primary frequency of the hub, blade, and shroud was large, and the secondary frequency was the second. In addition, the third frequency of the bottom ring was obvious. The effect of the blade was greater than the other two.
- 2.
- In addition to the primary frequency and secondary frequency of the bottom ring, there were 0.75, 1.25, and 1.5 times the frequency, and other parts were not as large.
- 3.
- In addition, fluctuations could be seen in the curves of all components. It can be seen that radial deviation will cause great vibrations to the unit, among which the influence of the crown chamber would be the most obvious.

#### 3.2.2. Pressure and Pressure Fluctuations

- 1.
- The crown chamber

- 2.
- The runner

- 3.
- The bottom ring chamber

## 4. Conclusions

- 1.
- With the increase in radial deviation, the radial force on the component also increased linearly.
- 2.
- After comparison with the steady calculation, it was necessary to add wall velocity, although it caused instability in the unsteady calculation.
- 3.
- The greater the deviation was, the greater the pressure was in the region, within a certain deviation value. However, when the maximum value was exceeded, the high-pressure region generated by the deviation moved in the direction where the maximum value of the radial deviation existed because of the fluid flowing harder.
- 4.
- Near the runner, the pressure pulsations vibrated periodically along the direction of deviation, but, as the flow continued, the influence of the wall velocity was introduced, and the pressure pulsations moved in the opposite direction of the runner rotation, just like in the high-pressure area.
- 5.
- Different parts were affected by different degrees of radial deviation, with the crown chamber having the greatest influence, followed by the lower ring and, finally, the runner.
- 6.
- The affected parts were mainly produced at four frequencies: 7 Hz, 28 Hz, 42 Hz, and 56 Hz which are the 0.25 times frequency, the primary frequency, the 1.5 times frequency and the secondary frequency, respectively. Additionally, the bottom ring chamber also had the tertiary frequency, and as the space became more narrow, the percentage of the high frequency increased.
- 7.
- The addition of wall velocity intensified the influence of the radial deviation, thus resulting in the characteristics of high deviation at a low deviation.

## 5. Discussion

- 1.
- We added the condition of wall velocity, which only considers the case of large-scale hydro turbines, as many literature sources do not include this condition. While our study shows that this condition better reflects actual situations, further verification is needed to determine its applicability to hydro turbines of different sizes.
- 2.
- The radial deviation value used in the steady-state calculation was actually higher than the value that is likely to occur during the operation of large-scale hydro turbines, where a deviation of 2.5 mm is almost impossible. We calculated this value mainly to consider the performance of the turbines under the worst-case scenario. However, we have started to calculate smaller deviations upon the writing of this paper.
- 3.
- Due to time and length constraints, we only calculated the non-steady-state part for a deviation of 0.5 mm. To summarize the overall pattern, we also need to provide results for deviations of 1.5 mm and 2.5 mm, which will be calculated in our future studies.
- 4.
- There is very little research on the radial installation deviation of large-scale mixed-flow and axial-flow hydro turbines, and even less research on the combination of these two types of turbines. We only found relevant studies on the radial deviation of fans and axial-flow turbines, so this direction is still in its exploratory stage and lacks sufficient reference materials.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 6.**The differences in the radial forces between the radial deviation model with speed or without.

**Figure 7.**Pressure distributions of the crown chamber with the 0.5 mm (

**top-left**), 1.5 mm (

**top-right**), and 2.5 mm (

**lower**) radial installation deviation models with speed.

**Figure 8.**Velocity distributions of the crown chamber with the 0.5 mm (

**top-left**), 1.5 mm (

**top-right**), and 2.5 mm (

**lower**) radial installation deviation models.

**Figure 9.**Pressure distributions of the bottom ring with the 0.5 mm (

**top-left**), 1.5mm (

**top-right**), and 2.5 mm (

**lower**) radial installation deviation models with speed.

**Figure 10.**Velocity distributions of the bottom ring with the 0.5 mm (

**top-left**), 1.5 mm (

**top-right**), and 2.5 mm (

**lower**) radial installation deviation models.

**Figure 11.**Pressure distributions of the runner with the 0.5 mm (

**top-left**), 1.5 mm (

**top-right**), and 2.5 mm (

**lower**) radial installation deviation models with speed.

**Figure 12.**Velocity distributions of the runner of the 0.5 mm (

**top-left**), 1.5 mm (

**top-right**), 2.5 mm (

**lower**) radial installation deviation model.

**Figure 13.**The monitoring points of the crown chamber (

**top-left**), the runner (

**top-right**), and the bottom ring chamber (

**lower**).

Parameters | Value |
---|---|

Rated Power | 1000 MW |

Runner blade number | 15 |

Guide vane number | 24 |

Stay vanes number | 23 |

Rated Conditions | Relative Opening (%) | Rated Head (%) | Relative Efficiency (%) |
---|---|---|---|

Meshes with 5 million elements | 100 | 100 | 99.6 |

Meshes with 10 million elements | 100 | 100 | 100 |

Flow Domain | Number of Elements |
---|---|

Spiral case | $3.92\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{6}$ |

Stay vane | $3.79\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{6}$ |

Guide vane | $7.12\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{6}$ |

Runner | $1.42\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{7}$ |

Crown chamber | $2.68\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{6}$ |

Bottom ring chamber | $1.77\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{6}$ |

Balance tubes × 4 | $1.04\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{7}$ |

Runner cone | $1.31\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{6}$ |

Draft tube | $5.63\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{6}$ |

Total | $5.08\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{7}$ |

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## Share and Cite

**MDPI and ACS Style**

Wang, Y.; Jin, K.; Huang, X.; Lin, P.; Wang, Z.; Wang, W.; Zhou, L.
Influence of Radial Installation Deviation on Hydraulic Thrust Characteristics of a 1000 MW Francis Turbine. *Water* **2023**, *15*, 1606.
https://doi.org/10.3390/w15081606

**AMA Style**

Wang Y, Jin K, Huang X, Lin P, Wang Z, Wang W, Zhou L.
Influence of Radial Installation Deviation on Hydraulic Thrust Characteristics of a 1000 MW Francis Turbine. *Water*. 2023; 15(8):1606.
https://doi.org/10.3390/w15081606

**Chicago/Turabian Style**

Wang, Yifan, Kun Jin, Xingxing Huang, Peng Lin, Zhengwei Wang, Wenliang Wang, and Lingjiu Zhou.
2023. "Influence of Radial Installation Deviation on Hydraulic Thrust Characteristics of a 1000 MW Francis Turbine" *Water* 15, no. 8: 1606.
https://doi.org/10.3390/w15081606