A Numerical Ice Load Prediction Model Based on Ice-Hull Collision Mechanism
Abstract
:1. Introduction
2. Ice Load Prediction Model
2.1. Ice-Hull Contact Mechanism and Determination of Impact Load
2.1.1. Ice Crushing
2.1.2. Initial Crack Propagation
2.1.3. Circumferential Ice Breaking
2.1.4. Wedge Shaped Ice Floe with Radial Cracks
2.2. Stochasticity and Discretization in the Present Model
2.3. Model Implementation
3. Ice Load Prediction Sub Models
3.1. Ice Crushing-Shearing Model
3.2. Ice Bending-Breaking Model
4. Model Validation
4.1. Ice Model Test
4.2. Simulation Results
5. Case Study
5.1. Barge Information
5.2. Parameteric Study
6. Discussion and Conclusions
6.1. Ice Crushing and Ice Bending
6.2. Ice Impact Load Prediction Model
6.3. Summary
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
- Lindqvist, G. A straightforward method for calculation of ice resistance of ships. In Proceedings of the 10th Int Port and Ocean Engineering under Arctic Conditions Conference, Luleå, Sweden, 12–16 June 1989. [Google Scholar]
- Keinonen, A.J.; Browne, R.P.R.; Reynolds, A. Ice breaker Characteristics Synthesis; TP 12812 E; Transportation Development Centre: Calgary, AL, Canada, 1996. [Google Scholar]
- Riska, K.; Patey, M.; Kishi, S.; Kamesaki, K. Influence of ice conditions on ship transit times in ice. In Proceedings of the Int Port and Ocean Engineering under Arctic Conditions Conf, Ottawa, ON, Canada, 12–17 August 2001; Volume 2, pp. 729–745. [Google Scholar]
- Rahman, M.S.; Taylor, R.S.; Kennedy, A.; Ré, A.S.; Veitch, B. Probabilistic Analysis of Local Ice Loads on a Lifeboat Measured in Full-Scale Field Trials. J. Offshore Mech. Arct. 2015, 137, 041501. [Google Scholar] [CrossRef] [Green Version]
- Taylor, R.S.; Jordaan, I.J.; Li, C.; Sudom, D. Local Design Pressures for Structures in Ice: Analysis of Full-Scale Data. J. Offshore Mech. Arct. 2010, 132, 031502. [Google Scholar] [CrossRef]
- Zhang, M.; Cheemakurthy, H.; Ehlers, S.; von Bock und Polach, F.; Garme, K.; Burman, M. Ice Pressure Prediction Based on the Probabilistic Method for Ice-Going Vessels in Inland Waterways. J. Offshore Mech. Arct. 2019, 41, 021501. [Google Scholar] [CrossRef]
- Daley, C. Energy based ice collision forces. In Proceedings of the 15th International Conference on Port and Ocean Engineering under Arctic Conditions, Helsinki, Finland, 24–29 May 1999. [Google Scholar]
- Kerr, A. The Bearing Capacity of Floating Ice Plates Subjected to Static or Quasi-Static Loads. J. Glaciol. 1976, 17, 76. [Google Scholar]
- Lubbad, R.; Løset, S. A numerical model for real-time simulation of ship–ice interaction. Cold Reg. Sci. Technol. 2011, 65, 111–127. [Google Scholar] [CrossRef] [Green Version]
- Valanto, P. The resistance of ships in level ice. SNAME Trans. 2001, 109, 53–83. [Google Scholar]
- Enkvist, E.; Varsta, P.; Riska, K. The Ship-Ice Interaction. In Proceedings of the International Conference on Port and Ocean Engineering under Arctic Conditions, Trondheim, Norway, 13–18 August 1979. [Google Scholar]
- Lu, W.; Lubbad, R.; Løset, S. In-plane fracture of an ice floe: A theoretical study on the splitting failure mode. Cold Reg. Sci. Technol. 2015, 110, 77–101. [Google Scholar] [CrossRef]
- Kerr, A.D. The Bearing Capacity of Floating Ice Plates Subjected to Static or Quasistatic Loads, a Critical Survey; Research Report; Cold Regions Research and Engineering Laboratory: Hanover, NH, USA, 1975; Volume 333. [Google Scholar]
- Su, B.; Riska, K.; Moan, T. A numerical method for the prediction of ship performance in level ice. Cold Reg. Sci. Technol. 2010, 60, 177–188. [Google Scholar] [CrossRef]
- Popov, Y.; Faddeyev, O.; Kheisin, D.; Yalovlev, A. Strength of Ships Sailing in Ice; Sudostroenie Publishing House: Leningrad, The Netherlands, 1967. [Google Scholar]
- Trafi. Finnish-Swedish Ice Class Rules 2010. In Ice Class Regulations 2010; Report No. TRAFI 31298; Finnish Transport Safety Agency: Espoo, Finland, 2010. [Google Scholar]
- Daley, C.; Liu, J. Assessment of Ship Ice Loads in Pack Ice; ICETECH: Anchorage, AK, USA, 2010. [Google Scholar]
- Croasdale, K.R. Ice Forces on fixed, rigid structures. In CRREL Special Report 80–26, Working Group on Ice Forces on Structures. A State-of-the-art Report; U.S. Army: Hanover, Germany, 1980. [Google Scholar]
- Kerr, A.D.; Palmer, W.T. The Deformations and Stresses in Floating Ice Plates. Acta Mech. 1972, 15, 57–72. [Google Scholar] [CrossRef]
- Kerr, A.D.; Kwak, S.S. The semi-infinite plate on a Winkler base, free along the edge, and subjected to a vertical force. Arch. Appl. Mech. 1993, 63, 210–218. [Google Scholar]
- Nevel, D.E. The Theory of a Narrow Infinite Wedge on an Elastic Foundation. Trans. Eng. Inst. Can. 1958, 2, 132–140. [Google Scholar]
- Nevel, D.E. The narrow free infinite wedge on elastic foundation. CRREL Res. Rep. 1961, 79, 24. [Google Scholar]
- Aker Arctic Technology Inc. Ice Model Test with a Passenger Ferry for SSPA Sweden; AARC Report A-555; Aker Arctic Technology Inc.: Helsinki, Finland, 16 June 2017. [Google Scholar]
- ITTC. General Guidance and Introduction to Ice Model Testing; Technical Report; International Towing Tank Committee: Wuxi, China, September 2017. [Google Scholar]
- Croasdale, K.R.; Cammaert, A.B.; Metge, M. A method for the calculation of sheet ice loads on sloping structures. IAHR 94. In Proceedings of the 12th International Symposium on Ice, Trondheim, Norway, 23–26 August 1994; The Norwegian Institute of Technology: Trondheim, Norwegian, 1994; Volume 2, pp. 874–885. [Google Scholar]
- ISO/CD 19906. Petroleum and Natural Gas Industries—Arctic Offshore Structures; ISOTC 67/SC 7/WG 8 International Standard; International Standardization Organization: Geneva, Switzerland, 2010. [Google Scholar]
- Sodhi, D.S.; Takeuchi, T.; Nakazawa, N.; Akagawa, S.; Saeki, H. Medium-scale indentation tests on sea ice at various speeds. Cold Reg. Sci. Technol. 1998, 28, 161–182. [Google Scholar] [CrossRef]
- Sodhi, D.S. Crushing failure during ice–structure interaction. Eng. Fract. Mech. 2001, 68, 1889–1921. [Google Scholar] [CrossRef]
- Blanchet, D.; Kivisild, H.R.; Grinstead, J. Equations for local ice energy dissipations during ship ramming. Cold Reg. Sci. Technol. 1990, 18, 101–115. [Google Scholar] [CrossRef]
- Liu, J.; Lau, M.; Williams, F.M. Mathematical Modeling of Ice-Hull Interaction for Ship Maneuvering in Ice Simulations. ICE Tech. 2006, 845, 1–8. [Google Scholar]
Parameters | Description | Parameters | Description |
L | Waterline plane length | β | Frame angle |
B | Waterline plane beam | Β’ | Normal frame angle |
T | Draft | γ | Sheer(buttock) angle |
D | Depth | φ* 1 | Rake angle |
x, y, z | The collision point on the hull or the ice sheet | Block coefficient | |
cg | Centre of gravity | Water plane area coefficient | |
α | Waterline angle | Midship section coefficient |
Full-Scale Ship | Model | ||
---|---|---|---|
(m) | 26.155 | Scale factor | 8.333 |
(m) | 7.5 | (m) | 3.18 |
(m) | 2.3 | (m) | 0.9 |
φ1 (deg) | 25 | (m) | 0.276 |
α (deg) | 30 | (1) | 0.05 |
(1) | 0.549 | E (kPa) | 77,979 |
(1) | 0.896 | (kPa) | 53.6 |
Displacement (kg) | 247,091 | E/ | 1456 |
No. | [m/s] | [N] | [N] | |||
---|---|---|---|---|---|---|
1 | 0.41 | 26 | 58.7 | 16.6 | 67.2 | 31.4 |
2 | 0.92 | 26.8 | 51 | 44.8 | 157.6 | 84.75 |
3 | 1.38 | 30.8 | 55.1 | 77.6 | 240.7 | 146.8 |
Case No. | [m/s] | Model Test Data [N] | Average [N] | Error [%] | Standard Deviation [N] | Error [%] | |
---|---|---|---|---|---|---|---|
1 | 0.41 | 26 | 31.4 | 44.1 | 40.4 | 58.9 | 87.58 |
1.1 | 0.41 | 26 | 31.4 | 34 | 8.3 | 33.6 | 7.01 |
2 | 0.92 | 26.8 | 84.75 | 83.1 | 1.9 | 81.3 | 4.07 |
3 | 1.38 | 30.8 | 146.8 | 134 | 8.7 | 153.7 | 4.7 |
Bow | Shoulder (at B/4) | |||
---|---|---|---|---|
No. | ||||
1 | 0.287 | 0.113 | 0.295 | 0.113 |
2 | 0.300 | 0.116 | 0.291 | 0.116 |
3 | 0.34 | 0.128 | 0.323 | 0.128 |
Displacement [t] | α [deg] | ||||||
---|---|---|---|---|---|---|---|
135 | 11.45 | 3.4 | 3938 | 73 | 55 | 45 | 0.2 |
Density [kg/m3] | ||||
---|---|---|---|---|
900 | 109 | 500 | 2000 | 0.32 |
Rake Angle | Ship Speed | Ice Thickness |
---|---|---|
15–75 [deg] | 1–5 [m/s] | 0.1–0.5 [m] |
© 2020 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/).
Share and Cite
Zhang, M.; Garme, K.; Burman, M.; Zhou, L. A Numerical Ice Load Prediction Model Based on Ice-Hull Collision Mechanism. Appl. Sci. 2020, 10, 692. https://doi.org/10.3390/app10020692
Zhang M, Garme K, Burman M, Zhou L. A Numerical Ice Load Prediction Model Based on Ice-Hull Collision Mechanism. Applied Sciences. 2020; 10(2):692. https://doi.org/10.3390/app10020692
Chicago/Turabian StyleZhang, Meng, Karl Garme, Magnus Burman, and Li Zhou. 2020. "A Numerical Ice Load Prediction Model Based on Ice-Hull Collision Mechanism" Applied Sciences 10, no. 2: 692. https://doi.org/10.3390/app10020692
APA StyleZhang, M., Garme, K., Burman, M., & Zhou, L. (2020). A Numerical Ice Load Prediction Model Based on Ice-Hull Collision Mechanism. Applied Sciences, 10(2), 692. https://doi.org/10.3390/app10020692