# 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 |

## References

- Vartdal, B.; Gjestland, T.; Arvidsen, T. Lateral Propeller Forces and their effects on Propeller Shafts Bearings. In Proceedings of the Symposium on Marine Propellers and Propulsion, Trondheim, Norway, 22–24 June 2009. [Google Scholar]
- Sverko, D.; Sestan, A. Experimental Determination of Stern Tube Journal Bearing Behaviour. Brodogradnja/Shipbuilding
**2010**, 61, 130–141. [Google Scholar] - Broglia, R.; Dubbioso, G.; Durante, D.; Di Mascio, A. Simulation of Turning Circle by CFD: Analysis of different propeller models and their effect on manoeuvering prediction. Appl. Ocean Res.
**2013**, 39, 1–10. [Google Scholar] [CrossRef] - Broglia, R.; Dubbioso, G.; Durante, D.; Di Mascio, A. Turning ability analysis of a fully appended twin screw vessel by CFD. Part I: Single rudder configuration. Ocean Eng.
**2015**, 105, 275–286. [Google Scholar] [CrossRef] - Dubbioso, G.; Broglia, R.; Durante, D.; Di Mascio, A. Turning ability analysis of a fully appended twin screw vessel by CFD. Part II: Single rudder vs Twin rudder configuration. Ocean Eng.
**2016**, 117, 259–271. [Google Scholar] [CrossRef] - Grigoropoulos, G.; Campana, E.; Diez, E.; Serani, A.; Goren, O.; Sarioz, K.; Danisman, D.; Visonneau, M.; Queutey, P.; Abdel-Maksoud, M.; et al. Misson–based hull form and propeller optimization of a transom stern destroyer for best performance in the sea environment. In Proceedings of the 7th VII International Congress on Computational Methods in Marine Engineering MARINE, Nantes, France, 15–17 May 2017. [Google Scholar]
- Taskar, B.; Steen, S. Effect of waves on cavitation and pressure pulses. Appl. Ocean Res.
**2016**, 60, 61–74. [Google Scholar] [CrossRef] - Taskar, B.; Steen, S.; Eriksson, J. Effect of waves on cavitation and pressure pulses of a tanker with twin podded propulsion. Appl. Ocean Res.
**2017**, 65, 206–218. [Google Scholar] [CrossRef] - Taskar, B. The Effects of Waves on Marine Propellers and Propulsion. Ph.D. Thesis, Norwegian University of Science and Technology, Trondheim, Norwegian, 2017. [Google Scholar]
- Amini, H.; Steen, S. Theoretical and experimental analysis of propeller shaft loads in oblique flow. J. Ship Res.
**2011**, 55, 268–288. [Google Scholar] [CrossRef] - Gutsche, F. The Study of Ships’ Propellers in Oblique Flow; Technical Report; Volume 4306 DRIC Translation; Defense Research Information Centre: New Delhi, India, 1975. [Google Scholar]
- Cassella, P.; Mandarino, M.; Scamardella, A. Systematic tests with B—Wageningen screw propellers in non-axial flow: Presentation and analysis of the experimental results. In Proceedings of the 4th International Symposium on Practical Design of Ships and Floating Structures (PRADS), Varna, Bulgaria, 23–28 October 1989. [Google Scholar]
- Amini, H.; Steen, S. Theoretical and experimental investigation of propeller shaft loads in transient condition. Int. Shipbuild. Progress
**2012**, 59, 55–82. [Google Scholar] - Krasilinov, V.; Zhang, Z.; Hong, F. Analysis of Unsteady Propeller Blade Forces by RANS. In Proceedings of the First International Symposium on Marine Propulsors (SMP’09), Trondheim, Norway, 22–24 June 2009. [Google Scholar]
- Liu, P.; Islam, M.; Veitch, B. Unsteady Hydrodynamics of a steering podded propeller unit. Ocean Eng.
**2009**, 36, 1003–1014. [Google Scholar] [CrossRef] - Dubbioso, G.; Muscari, R.; Di Mascio, A. Performance of a marine propeller in oblique flow. Comput. And Fluids
**2013**, 39, 1–10. [Google Scholar] - Dubbioso, G.; Muscari, R.; Di Mascio, A. Analysis of a marine propeller operating in oblique flow. Part 2: Very high incidence angles. Comput. Fluids
**2014**, 92, 56–81. [Google Scholar] [CrossRef] - Yao, J. Investigation on hydrodynamic performance of a marine propeller in oblique flow by RANSE computations. Int. J. Naval Arch. Ocean Eng.
**2015**, 7, 56–69. [Google Scholar] [CrossRef] - Muscari, R.; Felli, M.; Di Mascio, A. Analysis of the Flow Past a Fully Appended Hull with Propellers by Computational and Experimental Fluid Dynamics. J. Fluids Eng.
**2011**, 133, 061104. [Google Scholar] [CrossRef] - Castro, A.M.; Carrica, P.M.; Stern, F. Full scale self-propulsion computations using discretized propeller for the KRISO container ship KCS. Comput. Fluids
**2011**, 51, 35–47. [Google Scholar] [CrossRef] - Mofidi, A.; Carrica, P.M. Simulations of zigzag maneuvers for a container ship with direct moving rudder and propeller. Comput. Fluids
**2014**, 96, 191–203. [Google Scholar] [CrossRef] - Carrica, P.M.; Sadat-Hosseini, H.; Stern, F. CFD analysis of broaching for a model surface combatant with explicit simulation of moving rudders and rotating propellers. Comput. Fluids
**2012**, 53, 117–132. [Google Scholar] [CrossRef] - Sadat-Hosseini, H.; Carrica, P.; Stern, F.; Umeda, N.; Hashimoto, H.; Yamamura, S.; Mastuda, A. CFD, system-based and EFD study of ship dynamic instability events: Surf-riding, periodic motion, and broaching. Ocean Eng.
**2011**, 38, 88–110. [Google Scholar] [CrossRef] - Coraddu, A.; Dubbioso, G.; Mauro, S.; Viviani, M. Analysis of twin screw ships’ asymmetric propeller behaviour by means of free running model tests. Ocean Eng.
**2013**, 68, 47–64. [Google Scholar] [CrossRef] [Green Version] - Ortolani, F.; Mauro, S.; Dubbioso, G. Investigation of the radial bearing force developed during actual ship operations. Part 1: Straight ahead sailing and turning maneuvers. Ocean Eng.
**2015**, 94, 67–87. [Google Scholar] [CrossRef] - Ortolani, F.; Mauro, S.; Dubbioso, G. Investigation of the radial bearing force developed during actual ship operations. Part 2: Unsteady maneuvers. Ocean Eng.
**2015**, 106, 424–445. [Google Scholar] [CrossRef] - Dubbioso, G.; Muscari, R.; Ortolani, F.; Di Mascio, A. Analysis of propeller bearing loads by CFD. Part I: Straight ahead and steady turning maneuvers. Ocean Eng.
**2017**, 130, 241–259. [Google Scholar] [CrossRef] - Muscari, R.; Dubbioso, G.; Ortolani, F.; Di Mascio, A. Analysis of propeller bearing loads by CFD. Part II: Transient maneuvers. Ocean Eng.
**2017**, 146, 217–233. [Google Scholar] [CrossRef] - Muscari, R.; Dubbioso, G.; Ortolani, F.; Di Mascio, A. CFD analysis of the sensitivity of propeller bearing loads to stern appendages and propulsive configurations. Appl. Ocean Res.
**2017**, 65, 205–219. [Google Scholar] [CrossRef] - Di Mascio, A.; Muscari, R.; Dubbioso, G. On the wake dynamics of a propeller wake operating in drift. J. Fluid Mech.
**2014**, 754, 263–307. [Google Scholar] [CrossRef] - Muscari, R.; Di Mascio, A.; Verzicco, R. Modelling of vortex dynamics in the wake of a marine propeller. Comput. Fluids
**2013**, 73, 65–79. [Google Scholar] [CrossRef] - Di Mascio, A.; Broglia, R.; Muscari, R. On the Application of the One-Phase Level Set Method for Naval Hydrodynamic Flows. Comput. Fluids
**2007**, 36, 868–886. [Google Scholar] [CrossRef] - Favini, B.; Broglia, R.; Di Mascio, A. Multi-grid Acceleration of Second Order ENO Schemes from Low Subsonic to High Supersonic Flows. Int. J. Num. Meth. Fluids
**1996**, 23, 589–606. [Google Scholar] [CrossRef] - Di Mascio, A.; Broglia, R.; Favini, B. A Second Order Godunov–Type Scheme for Naval Hydrodynamics. In Godunov Methods: Theory and Applications; Kluwer Academic/Plenum Publishers: Dordrecht, the Netherlands, 2001; pp. 253–261. [Google Scholar]
- Phillips, W.F.; Anderson, E.A.; Kelly, Q.J. Predicting the Contribution of Running Propellers to Aircraft Stability Derivatives. J. Aircraft
**2003**, 40, 1107–1114. [Google Scholar] [CrossRef] - Amini, H.; Sileo, L.; Steen, S. Numerical calculations of propeller shaft loads on azimuth propulsors in oblique inflow. J. Mar. Sci. Technol.
**2012**, 17, 403–421. [Google Scholar] [CrossRef] - Jeong, J.; Hussain, F. On the identification of a vortex. J. Fluid Mech.
**1995**, 285, 69–94. [Google Scholar] [CrossRef] - Carlton, J. Marine Propellers and Propulsion, 2nd ed.; Butterworth-Heinemann: New York, NY, USA, 2006. [Google Scholar]
- Kerwin, S.; Hadler, J. Principles of Naval Architecture ‘Series’-Propulsion, 1st ed.; SNAME: New York, NY, USA, 2010. [Google Scholar]
- Krasilinov, V.; Zhang, Z.; Hong, F. Nominal vs Effective Wake Fields and their influence on Propeller Performance. In Proceedings of the First International Symposium on Marine Propulsors (SMP’09), Trondheim, Norway, 22–24 June 2009. [Google Scholar]

**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 |

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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