Lifting Theories For Wing-in-Ground Effect And Hydrofoils In The Vicinity Of A Free Surface

The wing-in-ground effect (WIGE) vessel and hydrofoil-supported vessel belong to new type of high-speed marine vehicles. The speed of them is much higher than that of usual vessels, and they have good anti-wave performance, which indicates that they are of practical significance in both military and civilian fields. WIGE and hydrofoil are the most important devices to provide the lift force to support hulls of WIGE vessels and hydrofoil-supported vessels. Therefore, the accurate prediction of lift force produced by WIGE and hydrofoil in proximity to a free surface has guiding significance for the preliminary design of WIGE vessels and hydrofoil-supported vessels.The present thesis is focused on 2D and 3D lifting problems for WIGE and hydrofoil in proximity to a free surface within the framework of the potential-flow theory. The classical Prandtl lifting line theory and lifting surface theory are generalized to cases more than infinite fluid. In order to model the influence of the free surface, the free-surface Green function satisfying the linearized free-surface boundary condition and radiation condition is taken as the fundamental solution of the governing equation herein. The calculated results are verified by available theoretical, numerical and experimental results documented in the literature.First of all, the lift properties of 2D and 3D WIGE are investigated. In the problem of a WIGE operating in proximity to a free surface, both air and water are disturbed. Following this, the free-surface boundary conditions for this kind of problem are derived, and the linearization procedure is carried out. Then, the vortex distribution method is adopted to study the lift behavior of a 2D WIGE steadily operating above a free surface. On the basis of the 2D problem, the 3D lift problem for WIGE is investigated using the Prandtl lifting line theory. For a foil with complicated configuration, including the biplane, the foil with winglets and tandem arrangement, the vortex lattice method is developed to tackle these kinds of foils steadily translating over the free surface. It is found that there is no propagating waves on the free surface and only local disturbance occurs at a high speed. In addition, the lift of a WIGE near a free surface is slightly lower than that in the presence of a rigid wall when the forward speed is high. Furthermore, the foils with dihedral angle and winglets can achieve higher lift.Due to the propagation of surface waves, the flight process of a WIGE above water waves is unsteady. The discrete vortex method incorporating the 2D time-domain Green function for a singularity moving above a free surface with an arbitrary trajectory is applied to study the lift performance of a 2D WIGE translating above progressive water waves. In addition, the unsteady evolution of the wake vorticity is taken into consideration. As a sequel to the 2D problem, the unsteady vortex lattice method combining with the time-domain Green function for a singularity moving above a free surface is developed to investigate the lifting problem of a 3D WIGE flying above water waves. It indicates that the lift coefficient increases when the wing flies over the convex wave shape, and it reaches up to the maximal value as the wave slope takes the positive maximum. Apart from that, the oblique wave and transverse wave can lead to the transverse oscillation of the pressure center of a WIGE.Finally, the 2D and 3D free-surface Green functions for singularities with steady translation including the viscosity and surface tension effects are investigated, and the asymptotic analysis on the dispersion relation and dispersion curves is conducted. Based on that, a kind of free surface Green function for a horseshoe vortex is developed. Taking these two kinds of free-surface Green functions as the fundamental solution, the hydrodynamic loads acting on a 2D steady hydrofoil is computed using the vortex distribution method. Then, the classic Prandtl lifting line theory and vortex lattice method are generalized to the lift calculation of a 3D hydrofoil steadily operating beneath a free surface, respectively. In addition, an approach combining the boundary element method and the Green function including the viscosity and surface tension effects to compute hydrodynamic loads on a 3D hydrofoil is introduced. It is found that, under the influence of the surface tension, upstream capillary waves are always present. Apart from the discovered critical value of the forward speed 0.232m/s, another critical value 0.450m/s is found. When the forward speed is between two critical values, divergent waves disappear. The thickness effect of a hydrofoil exerts an influence on the lift behavior. Besides, the lift force of the rear hydrofoil varies severely with the Froude number under the influence of the free-surface waves generated by the front hydrofoil.