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 wa...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.展开更多
A joint probability density function (PDF) for surface slopes in two arbitrary directions is derived on the basis of Longuet Higgins's linear model for three-dimensionol (3-D) random wave field. and the correlatio...A joint probability density function (PDF) for surface slopes in two arbitrary directions is derived on the basis of Longuet Higgins's linear model for three-dimensionol (3-D) random wave field. and the correlation moments of surface slopes. as parameters in the PDF, are expressed in terms of directional spectrum of ocean waves. So long as the directional spectrum model is given, these parameters are determined. Since the directional spectrum models proposed so far are mostly parameterized by the wind speed and fetch, this allows for substituting these parameters with thc wind speed and fetch. As an example, the wind speed and fetch are taken to be 14 m ' s and 200 km, and the Hasselmann and Donclan directional spectra are, respectively, use to compute these parameters. Some novel results a reobtained. One of the increasing interesting results is that the variances of surface slope in downwind and cross-wind directions determined by the Donclan directional spectra are close to those measured by Cox and Munk (1954). Some discussions are made on these results.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.50921001973 Program under Grant No. 2010CB83270
文摘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.
基金This work is financially supported by the National Natural Science Foundation of China(No.49676277)863-818 Project(05-02)
文摘A joint probability density function (PDF) for surface slopes in two arbitrary directions is derived on the basis of Longuet Higgins's linear model for three-dimensionol (3-D) random wave field. and the correlation moments of surface slopes. as parameters in the PDF, are expressed in terms of directional spectrum of ocean waves. So long as the directional spectrum model is given, these parameters are determined. Since the directional spectrum models proposed so far are mostly parameterized by the wind speed and fetch, this allows for substituting these parameters with thc wind speed and fetch. As an example, the wind speed and fetch are taken to be 14 m ' s and 200 km, and the Hasselmann and Donclan directional spectra are, respectively, use to compute these parameters. Some novel results a reobtained. One of the increasing interesting results is that the variances of surface slope in downwind and cross-wind directions determined by the Donclan directional spectra are close to those measured by Cox and Munk (1954). Some discussions are made on these results.
