Nonlinear lifting theory for unsteady WIG in proximity to incident water waves. Part 2: Three-dimension

Abstract

a b s t r a c tThe present article presents a nonlinear analysis for determining the three-dimensional unsteady potentialflow characteristics about a wing subject to wing-in-ground effect (WIG) operating above progressive water waves. By means of the time-domain Green's function for the three-dimensional dipole moving above the free surface satisfying the dynamic and kinematic boundary conditions on the mean free surface, the influence of the free surface on the vortex ring is considered. Then, the nonlinear unsteady lifting surface theory is developed to study the lifting problem for a three-dimensional wing operating above progressive water waves. Furthermore, the roll-up shed from the wing in the presence of a free surface and water waves is taken into account. With the computed results, the non-dimensional force coefficients (including the lift coefficient, induced drag coefficient and lift-to-drag ratio) are presented with the variation of different geometry and water wave parameters. The data reported in the literature are presented to validate the present approach.Crown

Higher-order derivatives of the Green function in hyper-singular integral equations

“…According to [35,37], a constant dipole distribution can be represented by a closed vortex ring comprising segments of the edge of the panel, and the induced velocity vector can be calculated by the Biot-Savart law which is widely used in the hydrofoil theory [38,39,40,41]. The velocity vector is written as:…”

Dynamic Lift Characteristics of a Water-Borne Wigcraft

“…These studies essentially rely on earlier proposed approximate ground effect dynamic force prediction expressions derived from implementing the method of images in the thin airfoil theory and lifting line theory, or experimental data to estimate the values of the stability derivatives (Liang et al, 2013a(Liang et al, , 2013bZong et al, 2012;Wieselsberger, 1922).…”