# Analysis of Bulb Turbine Hydrofoil Cavitation

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## Abstract

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## Featured Application

**Bulb water turbine blades with improved cavitation properties.**

## Abstract

^{2}values above 0.95. The results of the cavitation length regression model also confirm that the modified hydrofoil exhibits improved the cavitation properties.

## 1. Introduction

## 2. Hydrofoil

#### Hydrofoil Modifications

## 3. Experiment

#### 3.1. Turbine Measurements

^{−1}) is the rotational frequency, while D (m) is the discharge ring diameter of the bulb turbine. The turbine rotational frequency N (1000 min

^{−1}) was the same for all measuring points. Both runners had the same nominal diameter D (m). The guide vane opening coefficient A

_{0}was the same for each pair of measuring points used in the comparison:

_{v}(mm) is the guide vane’s opening and z (/) is the number of guide vanes. D

_{v}(mm) is the guide vane pivot diameter. Important manufacturing methods and characteristics were kept the same for reliable comparison between both runners. Control of runner tip gaps to the discharge ring and clearances of guide vanes to the guide vane pressure rings are very important for reliably estimating model turbine runners. Both runners were manufactured from the same material and using the same production methods and procedures. As such, for both runners, the tip gaps, guide vane clearances, and surface finishes were the same.

^{3}/s) represented in its nondimensional form as flow number φ [18] is:

#### 3.2. Cavitation Tunnel Measurements

_{abs}was measured on the suction side using an ABB 2600T 264NS pressure transducer. The temperature was measured by a Pt-100 4 wire temperature transducer, connected to the Agilent 34970A data acquisition unit. Valves in front of and behind the test section were fully open during experiments and they were only used during installation. Suction pressure was set using a vacuum pump, located on the top of a tank with a free water surface.

_{v}(N/m

^{2}) is the water evaporation pressure and p

_{abs}(N/m

^{2}) is absolute pressure. Water evaporation pressure was estimate using the Equation

_{w}(°C) is water temperature. Equation (6) provides for a maximum difference of 0.2%, with a negligible influence on the measurements.

_{abs}was set as constant at the inlet of the cavitation tunnel. To decrease the cavitation number σ we increased the flow Q (m

^{3}/s) and flow velocity. Several such operating points were measured for increasingly lower absolute pressure p

_{abs}in the test section. This enabled comparison between both hydrofoils and among different absolute pressures.

#### 3.3. Cavitation Image Analysis

_{g}(i,j,t) and standard deviation were calculated as explained below.

_{g}(i,j,t) was acquired by processing intervals of 256 grey levels (8-bit camera image depth) from black (intensity = 0) to white (intensity = 255). The averaged grey level series were calculated in observation region. The standard deviation was estimated using the equation below:

_{g}(i,j)〉 is time and spatially averaged grey level, which is proportional to the average void fraction of the cavitation structure’s.

^{3}/h; σ = 2.27) and in Figure 9 for the modified hydrofoil (p = 0.15 bar; Q = 61.7 m

^{3}/h; σ = 2.27). Cavitation length for the selected operating points was estimated to L = 22.74 mm for existing hydrofoil and L = 11.27 mm for modified hydrofoil. Such a method of estimating cavitation length was used for all operating points for both hydrofoils and later for regression cavitation length modelling.

#### 3.4. Regression Cavitation Length Model

_{0}, β

_{1}, and β

_{2}were calculated using the minimum mean square error method.

## 4. Results and Discussion

#### 4.1. Cavitation Dependence on the Cavitation Number σ

_{abs}= 0.65 bar are shown in Figure 10. Cavitation structures (void fraction) start to appear on the modified hydrofoil at cavitation number around σ = 3.65. The cavitation starts behind the leading edge as an attached cavitation. With the further decrease of the cavitation number to around σ = 3.1 we observed an increase in the cavitation intensity and the quasiperiodic shedding of cavitation clouds. On the other hand, cavitation was observed on the original hydrofoil at cavitation numbers around σ = 4.45. At cavitation number σ = 3.65 we observed some cavitation cloud shedding, and at cavitation σ = 3.1 more than two-thirds of the hydrofoil was cavitating. At cavitation σ = 3.1, with the modified hydrofoil, the cavitation length was only 1/3 of the hydrofoil length. Since the hydrofoils in both cases were attached at the same angle of attack, we assume that the difference in cavitation occurrence is due to the shape and curvature of the leading edge. A sharp leading edge cuts through the flow such that it cannot follow the hydrofoil shape immediately downstream from the leading edge. The resulting flow separation induces cavitation inception due to the low absolute pressure and high velocity.

_{abs}= 0.45 bar are shown in Figure 11. The cavitation on the modified hydrofoil profile starts behind the leading edge as an attached cavitation around σ = 3.45, and p

_{abs}= 0.65 bar. At cavitation σ = 3 we again observed cavitation cloud shedding as in Figure 10. The cavitation is much more intense for the case of the existing hydrofoil. We observed cavitation inception already at around σ = 4.5, while almost the entire hydrofoil was cavitating around σ = 3.

_{abs}= 0.30 bar are shown in Figure 12. Measurements commenced around σ = 3.55; at this operating point the incipient cavitation is already present. Incipient cavitation here is present as an attached cavitation. For the modified hydrofoil, the attached cavitation formed only at around σ = 3; it covered up to around half of the hydrofoil length. With the original hydrofoil, the cavitation inception began around the same cavitation number (σ = 3.55) as for the modified hydrofoil, although with slightly higher intensity. A remarkable difference in the intensity of cavitation was observed at cavitation number σ = 3.0. Here, the cavitation cloud is much larger for the existing hydrofoil. Below the cavitation number σ = 2.6 most of the hydrofoil is covered by a thick cavitation cloud in the case of the existing hydrofoil.

_{abs}= 0.15 bar are shown in Figure 13. With modified hydrofoil, no cavitation was observed around cavitation number σ = 2.85, while with the modified hydrofoil the cavitation cloud at around σ = 2.25 covers up to one-third of the hydrofoil length. At around σ = 1.82 the cavitation cloud is again more intense than at cavitation number σ = 2.25. Below around cavitation number σ = 1.45 both hydrofoils are fully covered with supercavitation.

#### 4.2. Cavitation Length Model

_{0}is modest at around 6% in favor of existing hydrofoil. The modified hydrofoil’s dependence on the parameter β

_{1}shows that the cavitation length of the modified hydrofoil is lower than that of the existing one. The most important improvement of the modified hydrofoil over the existing one is hidden in the dependence on cavitation number σ (achieving a value at parameter β

_{2}of −3.4, improving over the original −2.93). The results of the cavitation length model confirm the modified hydrofoil’s superior cavitation characteristics over the existing one.

^{2}> 0.95. The high values of both coefficients of determination confirm the validity of the cavitation length model.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

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**Figure 8.**Original hydrofoil, a sample image of cavitation (

**top**), spatially averaged grey level (

**middle**), and standard deviation of grey level (

**bottom**), operating point p = 0.15 bar, Q = 61.7 m

^{3}/h, and σ = 2.27.

**Figure 9.**Modified hydrofoil, a sample image of cavitation (

**top**), spatially averaged grey level (

**middle**), and standard deviation of grey level (

**bottom**), operating point p = 0.15 bar, Q = 61.7 m

^{3}/h, and σ = 2.27.

**Figure 15.**Cavitation model for the modified hydrofoil, coefficient of determination R

^{2}= 0.9858.

Parameter | Modified | Unmodified |
---|---|---|

Runner diameter D_{0} | ø 350 mm | ø 350 mm |

Number of runner blades Z | 4 | 4 |

Location of reference hydrofoil R_{h} | 95% D_{0} | 95% D_{0} |

Blade angle β_{0} | 25° | 25° |

Blade chord line length at 95% R | 180.7 mm | 180.7 mm |

Location of maximum thickness l_{1} | 27.11 mm | 72.28 mm |

Ratio l_{1}/l | 15% | 40% |

Location of maximum curvature l_{2} | 54.2 mm | 81.3 mm |

Ratio l_{2}/l | 30% | 45% |

Leading edge radius r_{0} | 1.63 mm | 1.27 mm |

Parameter | Modified Hydrofoil | Existing Hydrofoil |
---|---|---|

Hydrofoil chord length l | 60 mm | 60 mm |

Maximum hydrofoil thickness d_{max} | 2.55 mm | 2.55 mm |

Maximum thickness position l_{1} | 9 mm | 24 mm |

Maximum thickness position ratio l_{1}/l | 15% | 40% |

Maximum hydrofoil curvature s_{max} | 0.87 mm | 0.87 mm |

Maximum curvature position l_{2} | 18 mm | 27 mm |

Maximum curvature position ratio l_{2}/l | 30% | 45% |

Radius at the Leading edge r_{0} | 0.54 mm | 0.42 mm |

Parameter | |||
---|---|---|---|

β_{0} | β_{1} | β_{2} | |

Existing hydrofoil | 2.81 × 10^{−8} | 1.88 | −2.93 |

Modified hydrofoil | 2.99 × 10^{−8} | 1.86 | −3.40 |

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**MDPI and ACS Style**

Podnar, A.; Hočevar, M.; Novak, L.; Dular, M.
Analysis of Bulb Turbine Hydrofoil Cavitation. *Appl. Sci.* **2021**, *11*, 2639.
https://doi.org/10.3390/app11062639

**AMA Style**

Podnar A, Hočevar M, Novak L, Dular M.
Analysis of Bulb Turbine Hydrofoil Cavitation. *Applied Sciences*. 2021; 11(6):2639.
https://doi.org/10.3390/app11062639

**Chicago/Turabian Style**

Podnar, Andrej, Marko Hočevar, Lovrenc Novak, and Matevž Dular.
2021. "Analysis of Bulb Turbine Hydrofoil Cavitation" *Applied Sciences* 11, no. 6: 2639.
https://doi.org/10.3390/app11062639