Abstract
Prandtl’s lifting line theory was generalized to the lifting problem of a three-dimensional hydrofoil in the presence of a free surface. Similar to the classical lifting theory, the singularity distribution method was utilized to solve two-dimensional lifting problems for the hydrofoil beneath the free surface at the air-water interface, and a lifting line theory was developed to correct three-dimensional effects of the hydrofoil with a large aspect ratio. Differing from the classical lifting theory, the main focus was on finding the three-dimensional Green function of the free surface induced by the steady motion of a system of horseshoe vortices under the free surface. Finally, numerical examples were given to show the relationship between the lift coefficient and submergence Froude numbers for 2-D and 3-D hydrofoils. If the submergence Froude number is small free surface effect will be significant registered as the increase of lift coefficient. The validity of these approaches was examined in comparison with the results calculated by other methods.
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Foundation item: Supported by the National Natural Science Foundation of China under Grant No.50921001 and 973 Program under Grant No. 2010CB83270.
Hui Liang, born in 1988, is currently an undergraduate student at the School of Naval Architecture Engineering, Dalian University of Technology. His research interests include hydrodynamics, aerodynamics and fluid-structure interaction.
Zhi Zong, born in 1964, is a professor at Dalian University of Technology. His research interests are hydrodynamics, underwater explosion and fluid-structure interaction. He authored two monographs in English published by Elsevier Science in 2006 and CRC Press in 2009, respectively.
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Liang, H., Zong, Z. A lifting line theory for a three-dimensional hydrofoil. J. Marine. Sci. Appl. 10, 199–205 (2011). https://doi.org/10.1007/s11804-011-1038-5
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DOI: https://doi.org/10.1007/s11804-011-1038-5