# Investigations of Hydrodynamic Force Generated on the Rotating Cylinder Implemented as a Bow Rudder on a Large-Scale Ship Model

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Test Setup

#### 2.2. Program of Model Tests

_{R}at three distances l measured from the rotor axis in forward direction in bollard-pull conditions (stationary model, calm water) and trials of initial turning with different model speeds and rotor RPM carried out for RC1 and RC2 and rudder angle 0°.

## 3. Results

#### 3.1. Rotor-Generated Velocity in Bollard-Pull Conditions

#### 3.2. Steady Course Keeping Trials

#### 3.3. Turning Circle Trials

_{RC})/X,

## 4. Discussion

_{real scale}= 24 · δ

_{A}· A

_{RC,}

_{A}· A

_{RC}related to the ship length are presented in Table 9, they are equal from 0.3 to 1.8 ship lengths.

#### 4.1. Comparison of Tactical Diameters Obtained for the Tested Model with RC and Model of a Push Train

#### 4.2. Comparison of the Lift Forces Generated by Bow RC and Stern Rudder

_{LRC}obtained from [21].

_{R}is rudder generated lift force, C

_{LR}is the lift coefficient of NACA airfoil, ρ = 1000 kg/m

^{3}is water density, v (m/s) is inflow velocity, A

_{R}is the rudder area.

_{LRC}lift coefficient is dependent on Reynolds number (5) and rotation rate α (6).

^{−6}m

^{2}/s is water kinematic viscosity.

^{5}. The lift force coefficient for the rotation rate α = 1.88, is equal to 3.5 [21].

_{RC}calculated from equation (2) is equal to 196 N (2700 kN in real scale).

_{0}is efflux velocity, c is the propeller type coefficient, f is the ratio of engine power used, P (W) is the maximum engine power, ρ (kg/m

^{3}) is water density, D

_{P}(m) is propeller diameter.

^{3}, D

_{P}= 0.37 m is equal to 1.8 m/s.

_{LR}= 0.6, inflow velocity 1.8 m/s, and A

_{R}= 0.19 m

^{2}is equal to 184 N (2540 kN in real scale).

## 5. Conclusions

- there was no strong influence of free surface and the bow wave on the RC-generated steering force,
- RC vibrations appeared at rotational speeds greater than 400 RPM,
- the RC steering force depends on the drift angle at the bow,
- the lift force generated by the tested RC is of the same magnitude as the lift force of the stern rudder,
- the results of the presented research are comparable to the results obtained from model tests of 1:20 scale push train model, showing the same trend in increased controllability,
- the main problem with the development of the commercial application of the bow steering system is the prediction hydrodynamic force generated by the rotating cylinder in dependence on rotational speed and inflow velocity in operational conditions, necessary to control the steering force.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The new bow with RC attached to the ship model: (

**a**) scheme of the construction of the new bow with rotor and drive; (

**b**) ship model with the new bow.

**Figure 2.**Control panel with indicators of speed, course, rate of turn, rudder angle, and engine telegraph on the model bridge.

**Figure 4.**Flow around RC1: (

**a**) model velocity 0.5 m/s, RC2 rotational speed 200 RPM, (

**b**,

**c**) model velocity 0.5 m/s, RC1 rotational speed 300 RPM, (

**d**) model velocity 0.92 m/s, RC1 rotational speed 300 RPM.

**Figure 5.**Course keeping trial parallel to the leading lights, view from the bridge of the ship model.

**Figure 6.**The trajectory of the model plotted during the steady course trial: A—advance, T—transfer.

**Figure 8.**Turning circle of push train model: (

**a**) turning circle trial with use of bow RCs; (

**b**) maneuvering space of the model using bow RCs (red), stern rudders and bow RCs (green), stern rudders, bow RCs, and dynamical coupling system (black) [1]; L—model length.

Parameter | Description |
---|---|

A (m) | advance |

A_{R} (m^{2}) | rudder area |

B (m) | breadth |

B_{B} (m) | breadth of the bow |

C_{LR} | lift coefficient of rudder |

C_{LRC} | lift coefficient of rotating cylinder |

c | propeller type coefficient |

D (m) | cylinder diameter |

d (m) | cylinder screen diameter |

D_{P} (m) | propeller diameter. |

f | ratio of engine power used |

H (m) | height of rotating cylinder |

v_{R} (m/s) | rotor generated flow velocity |

l (m) | distances from the rotor in forward direction |

L_{OA} (m) | length over all |

L_{B} (m) | length of the bow |

N_{RC} (W) | rotating cylinder drive power |

P (W) | engine power |

r (rad/s) | rotational speed |

Re | Reynolds number |

T_{B} (m) | draft of the bow |

TD (m) | tactical diameter |

U_{0} (m/s) | efflux velocity |

v (m/s) | inflow velocity |

Y_{R} (N) | rudder generated lift force |

Y_{RC} (N) | rotor generated lift force |

α | rotation rate |

ΔA_{real scale} (m) | change in advance due to RC operation |

δ | difference between turning circle trial parameters |

ν (m^{2}/s) | kinematic viscosity |

ρ (kg/m^{3}) | water density |

Parameter | Ship | Model |
---|---|---|

L_{OA} (m) | 292.90 | 12.20 |

B (m) | 48.00 | 2.00 |

T (m) | 15.33 | 0.64 |

Bow parameter | Value |
---|---|

L_{B} (m) | 2.20 |

B_{B} (m) | 2.00 |

T_{B} (m) | 0.64 |

Parameter | RC1 | RC2 |
---|---|---|

H (m) | 0.60 | 0.60 |

D (m) | 0.22 | 0.11 |

d (m) | 0.30 | 0.19 |

r (RPM) | 0–570 | 0–570 |

N_{RC} (W) | 1000 | 1000 |

**Table 5.**Program of model tests. Tests in bollard-pull conditions. Tests at Full Ahead model speed: turning circle and steady course keeping trials. Tests at Half Ahead model speed: turning circle trial.

Bollard-Pull v _{R} Measurement | Full Ahead | Half Ahead Turning Circle | |||||
---|---|---|---|---|---|---|---|

Turning Circle | Steady Course | ||||||

l (m) | RC1 RPM | Ruder Angle | RC2 RPM | Ruder Angle | RC2 RPM | Ruder Angle | RC2 RPM |

1 | 0–570 | 35° | 0 | 8°–10° | 300 | 35° | 0 |

20° | 0 | 20° | 0 | ||||

0.5 | 10° | 0 | 10° | 0 | |||

0° | 300 | 0° | 300 | ||||

0.32 | 35° | 300 | 35° | 300 | |||

20° | 300 | 20° | 300 | ||||

10° | 300 | 10° | 300 |

l (m) | v_{R} (m/s) |
---|---|

1 | 0.080 |

0.5 | 0.094 |

0.32 | 0.990 |

**Table 7.**Turning circle trial at Full Ahead and Half Ahead engine settings, rudder angles set to starboard, and clockwise rotation of RC2.

Ruder Angle | RC2 RPM | Full Ahead | Half Ahead | ||||||
---|---|---|---|---|---|---|---|---|---|

Turning Circle | A | T | TD | Turning Circle | A | T | TD | ||

35° | 0 | 34 | 17 | 38 | 31 | 12 | 30 | ||

20° | 0 | 48 | 23 | 52 | 48 | 19 | 47 | ||

10° | 0 | 58 | 30 | 68 | 51 | 30 | 66 | ||

0° | 300 | 44 | 26 | 55 | 27 | 21 | 46 | ||

35° | 300 | 25 | 13 | 31 | 25 | 13 | 30 | ||

20° | 300 | 27 | 15 | 34 | 25 | 14 | 32 | ||

10° | 300 | 32 | 17 | 38 | 26 | 19 | 40 |

**Table 8.**Difference between turning circle parameters for two engine settings: Full Ahead and Half Ahead, rudder angles set starboard, and clockwise rotational speeds of RC2 trial.

Rudder Angle | δ (%) | |||||
---|---|---|---|---|---|---|

Full Ahead | Half Ahead | |||||

A | T | TD | A | T | TD | |

35° | 26 | 24 | 18 | 19 | −8 | 0 |

20° | 44 | 35 | 35 | 48 | 26 | 32 |

10° | 45 | 43 | 44 | 49 | 37 | 39 |

**Table 9.**Nondimensional advance in turning circle trial for engine setting Full Ahead and Half Ahead, rudder angles set to starboard, and clockwise direction of RC2 rotational speeds RPM.

Rudder Angle | Full Ahead | Half Ahead | ||
---|---|---|---|---|

A/L | ΔA/L | A/L | ΔA/L | |

35° | 2.4 | 0.6 | 1.7 | 0.3 |

20° | 3.3 | 1.5 | 1.9 | 0.9 |

10° | 4.0 | 1.8 | 2.2 | 1.1 |

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**MDPI and ACS Style**

Abramowicz-Gerigk, T.; Burciu, Z. Investigations of Hydrodynamic Force Generated on the Rotating Cylinder Implemented as a Bow Rudder on a Large-Scale Ship Model. *Sensors* **2022**, *22*, 9137.
https://doi.org/10.3390/s22239137

**AMA Style**

Abramowicz-Gerigk T, Burciu Z. Investigations of Hydrodynamic Force Generated on the Rotating Cylinder Implemented as a Bow Rudder on a Large-Scale Ship Model. *Sensors*. 2022; 22(23):9137.
https://doi.org/10.3390/s22239137

**Chicago/Turabian Style**

Abramowicz-Gerigk, Teresa, and Zbigniew Burciu. 2022. "Investigations of Hydrodynamic Force Generated on the Rotating Cylinder Implemented as a Bow Rudder on a Large-Scale Ship Model" *Sensors* 22, no. 23: 9137.
https://doi.org/10.3390/s22239137