# Experimental and Numerical Investigation of Propeller Loads in Off-Design Conditions

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## Abstract

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## 1. Introduction

## 2. Test Case

#### 2.1. Experimental Set-Up

#### 2.2. Numerical Set-Up

## 3. Models and Methodologies

## 4. Results

#### Experimental Results

## 5. Discussion

## 6. Semi Empirical Method for Full Scale Prediction of in-plane loads

#### 6.1. Effect of Reynolds Number

#### 6.2. Effect of Cavitation Number

- the cavitation lenght ${l}_{CAV}$ is overestimated because the linear theory does not account for thickness
- the maximum value of the cavity length is ${l}_{CAV}=0.75$; in fact, Equation (6) admits two solutions, a long and a short bubble. The long cavity is unstable and physically unacceptable. For this reason, the iteration loop for the solution of Equation (6) was stopped when the bubble length achieved this limit
- during off-design conditions, the higher angle of incidences experienced by the blade sections may give rise to types of cavitation other than the attached sheet cavity assumed in linear theory (cloud cavitation, bubble cavitation)

#### 6.3. Further Remarks on the Scale Factors in Cavitating Conditions

## 7. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

ITTC | International Towing Tank Conference |

CFD | Computational Fluid Dynamics |

BEMT | Blade Element Momentum Theory |

RANSE | Reynolds Averaged Navier Stokes |

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**Figure 5.**(

**a**) hub and blade reference system. (

**b**) Inflow and forces generated on a generic blade section.

**Figure 14.**(

**a**) imbalance of thrust on the upper/lower half of the disk. (

**b**) imbalance of thrust on the left/right half of the disk.

**Figure 15.**(

**a**) imbalance of side force on the upper/lower half of the disk. (

**b**) imbalance of vertical force on the left/right half of the disk.

**Figure 16.**Ratio between forces and moments in cavitating and non cavitating conditions. (

**a**) forces. (

**b**) moments.

**Figure 17.**Cavitation extent, $BEMT$ solution via the linearized theory. (

**a**) $\delta ={15}^{\circ}$, internal propeller. (

**b**) $\delta ={35}^{\circ}$, external propeller.

**Figure 18.**Correlation between blade loads and cavitation volume. (

**a**) $\delta ={15}^{\circ}$, internal propeller. (

**b**) $\delta ={35}^{\circ}$, external propeller.

HULL | |
---|---|

L/B | 7.5 |

B/T | 3.25 |

${C}_{B}$ | 0.5 |

PROPELLER | |

N. blades, Z | 5 |

P/D, Pitch to diam. ratio | 1.35 |

Expanded area ratio | 0.79 |

Hub ratio | 0.25 |

Free Running Tests | ||
---|---|---|

Test | Speed | Rudder Angle [deg] |

self–propulsion | $0.05<{F}_{N}<0.45$ | $\delta $ = 0${}^{\circ}$ |

turning circle (with pull–out) | ${F}_{N}$ = 0.218, 0.31 | $\delta $ = $\pm {15}^{\circ}$, $\pm {25}^{\circ}$, $\pm {35}^{\circ}$ |

turning circle (with pull–out) | ${F}_{N}$ = 0.35 | $\delta $ = $\pm {35}^{\circ}$ |

zig–zag | ${F}_{N}$ = 0.218, 0.31, 0.35 | $\delta $ = $\pm {10}^{\circ}$, $\pm {20}^{\circ}$, $\pm {35}^{\circ}$ |

Domain | Cells | Percent |
---|---|---|

HULL | 2.81 M | 27.52% |

BILGE KEELS | 1.42 M | 13.90% |

PROP. SHAFT | 1.50 M | 14.69% |

FORWARD BRACKETS | 0.33 M | 3.20% |

ASTERN BRACKETS | 1.35 M | 13.20% |

SKEG | 0.80 M | 16.70% |

STERN REFINEMENT | 1.54 M | 7.80% |

BACKGROUND BUFFER | 0.36 M | 3.50% |

BACKGROUND | 0.11 M | 0.10% |

TOTAL | 10.21 M |

Free Running Tests | ||
---|---|---|

Rudder | Yaw Rate $\xb7\frac{{\mathit{L}}_{\mathit{pp}}}{{\mathit{V}}_{\mathit{ref}}}$ | Drift Angle [deg] |

$\delta ={15}^{\circ}$ | 0.236 | 7.5 |

$\delta ={25}^{\circ}$ | 0.333 | 12.5 |

$\delta ={35}^{\circ}$ | 0.363 | 13.5 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Ortolani, F.; Dubbioso, G.; Muscari, R.; Mauro, S.; Di Mascio, A. Experimental and Numerical Investigation of Propeller Loads in Off-Design Conditions. *J. Mar. Sci. Eng.* **2018**, *6*, 45.
https://doi.org/10.3390/jmse6020045

**AMA Style**

Ortolani F, Dubbioso G, Muscari R, Mauro S, Di Mascio A. Experimental and Numerical Investigation of Propeller Loads in Off-Design Conditions. *Journal of Marine Science and Engineering*. 2018; 6(2):45.
https://doi.org/10.3390/jmse6020045

**Chicago/Turabian Style**

Ortolani, Fabrizio, Giulio Dubbioso, Roberto Muscari, Salvatore Mauro, and Andrea Di Mascio. 2018. "Experimental and Numerical Investigation of Propeller Loads in Off-Design Conditions" *Journal of Marine Science and Engineering* 6, no. 2: 45.
https://doi.org/10.3390/jmse6020045