A Prediction Method and Model Experiments on Surf-Riding and Broaching in Stern-Quartering Waves
Abstract
:1. Introduction
2. Mathematical Model
2.1. Coordinate Systems
2.2. 6DOF Motion Equations
2.3. Hull Forces in Still Water
2.4. Propeller Thrust
2.5. Rudder Forces
2.6. Wave Forces
2.7. Heave and Pitch Motions
3. Experiments
4. Simulations and Discussions
4.1. The Effect of Ship Speed
4.2. The Effect of the Instantaneous Wetted Surface of the Hull
4.3. The Effect of Rudder Exposure
4.4. The Effect of Heave and Pitch Motions
5. Conclusions
- (1)
- Through comparing the results of the calculations and experiments, it can be concluded that the recommended 6DOF coupled mathematical model can effectively predict broaching and pure loss of stability in stern-quartering waves. This prediction method can be used for the direct stability assessment of broaching and pure loss of stability. Combined with the criteria of the direct stability assessment, the prediction method can also be used to evaluate the stability of ships to guide ship design and evaluate the navigational performance of ships to guide ship maneuvering in waves.
- (2)
- From the experiments and calculations, it can be seen that under the same wave condition and heading, as the speed increases, the motion mode of the ship transitions from pure loss of stability to broaching, which indicates that there is cross-coupling between the speed range of the occurrences of broaching and pure loss of stability. In addition, the significant roll caused by pure loss of stability can severely expose one side of the rudder in waves, which can result in a decrease in course-keeping capability. The significant roll induced by pure loss of stability is a key factor leading to broaching.
- (3)
- The calculation considering the instantaneous wetted surface of the ship can effectively simulate the nonlinearity of roll motion, especially the large roll during broaching. The nonlinearity of roll has a significant effect on the prediction of broaching, which affects the final motion mode of the ship.
- (4)
- The rudder exposure in waves is one of the key factors in predicting broaching.
- (5)
- The heave and pitch affect the prediction accuracy of roll motion, and are also key factors affecting rudder exposure, which can reduce the course-keeping capability of rudders and result in broaching.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
Rudder force increase factor | |
After section and forward section of the hull | |
The port and starboard rudders normal forces | |
The port and starboard rudders lifting slope coefficients | |
Gravitational acceleration | |
Moment of inertia in roll and yaw | |
The port and starboard propellers advanced ratios | |
Wave number | |
Rudder gain coefficient | |
Thrust coefficient of the propeller | |
Mean correction factor for flow-straightening due to yaw | |
Ship mass | |
Ship-added mass in surge direction | |
Ship-added mass in sway direction | |
Propeller revolution | |
Roll rate | |
Yaw rate | |
Wetted hull surface area in still water | |
Thrust deduction factor | |
Steering resistance deduction factor | |
The time constant for the steering gear | |
The time constant for differential control | |
Surge and sway velocity of the ship hull | |
Inflow velocity to the port and starboard rudders in surge direction | |
Inflow velocity to the rudder in sway direction | |
Wake fraction at propeller position | |
Longitudinal and vertical positions of additional sway force due to the rud-der | |
Longitudinal and vertical positions of the rudder | |
Effective inflow angles to the port and starboard rudders | |
Rudder angle | |
The ratio of propeller diameter to rudder span | |
The ratio of wake fraction at the propeller and rudder position | |
Propeller-induced flow velocity factor | |
Wavelength | |
Ruder aspect ratio | |
The real-time port and starboard rudders aspect ratio | |
Mean flow-straightening effect coefficient | |
Water density | |
Wave frequency and encounter frequency | |
Wave amplitude |
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Items | Full Scale | Model Scale |
---|---|---|
Length (LPP) | 154.0 m | 3.800 m |
Draft (d) | 5.494 m | 0.136 m |
Breadth (B) | 18.8 m | 0.464 m |
Depth (D) | 14.5 m | 0.358 m |
Displacement (W) | 8507 ton | 0.128 ton |
Block coefficient CB | 0.535 | 0.535 |
Metacentric height GM | 2.068 m | 0.051 m |
Vertical position of the center of gravity KG | 7.672 m | 0.189 m |
Natural roll period Troll | 11.14 s | 1.75 s |
Roll inertia radius Kxx | 0.44 B | 0.44 B |
Pitch inertia radius Κyy | 0.25 LPP | 0.25 LPP |
Rudder area | 23.74 m2 | 0.0145 m2 |
Propeller diameter | 5.22 m | 0.129 m |
No. | Experiments Conditions | Experiments Results | ||||
---|---|---|---|---|---|---|
λ/Lpp | H/λ | Fn | Maximum Roll Angle (Degree) | Maximum Yaw Angle (Degree) | Motion Modes | |
1 | 1.25 | 0.05 | 0.250 | 19.6 | 8.3 | Pure loss of stability |
2 | 1.25 | 0.05 | 0.300 | 28.0 | 11.3 | Pure loss of stability |
3 | 1.25 | 0.05 | 0.325 | 32.6 | 9.5 | Pure loss of stability |
4 | 1.25 | 0.05 | 0.350 | 35.3 | 13.2 | Pure loss of stability |
5 | 1.25 | 0.05 | 0.400 | 43.4 | 26.9 | Broaching |
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Chu, J.; Gu, M.; Lu, J.; Zhang, P. A Prediction Method and Model Experiments on Surf-Riding and Broaching in Stern-Quartering Waves. J. Mar. Sci. Eng. 2024, 12, 1538. https://doi.org/10.3390/jmse12091538
Chu J, Gu M, Lu J, Zhang P. A Prediction Method and Model Experiments on Surf-Riding and Broaching in Stern-Quartering Waves. Journal of Marine Science and Engineering. 2024; 12(9):1538. https://doi.org/10.3390/jmse12091538
Chicago/Turabian StyleChu, Jilong, Min Gu, Jiang Lu, and Peijie Zhang. 2024. "A Prediction Method and Model Experiments on Surf-Riding and Broaching in Stern-Quartering Waves" Journal of Marine Science and Engineering 12, no. 9: 1538. https://doi.org/10.3390/jmse12091538