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

The present article presents a nonlinear analysis for determining the three-dimensional unsteady potential-flow 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.

• The unsteady effect of the three-dimensional wing-in-ground effect is studied.
• The nonlinear lifting surface theory is utilized, and the influence of roll-up is considered.
• The Green’s function is used to represent the effect of the free surface reducing the number of grid.