Nonlinear lifting theory for unsteady WIG in proximity to incident water waves. Part 1: Two-dimension

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

“…Not only does the roll-up effect is considered, but the kinematic boundary condition imposed on the wing surface is nonlinear. As indicated in the previous study [ 19 ], the influence of the roll-up of the shedding vorticity is trivial to the aerodynamic loads exerting on the foil, but the nonlinearity of the kinematic boundary condition is comparatively significant. The proposed approach generalizes the classical unsteady lifting surface theory [ 22 ] to the case of the coupling of WIG and water waves.…”

“…(52) and (53) in [ 19 ] present the velocity potentials in air and water induced by the two-dimensional harmonic progressive water waves. However, for the three-dimensional harmonic progressive water waves, there exists a number of incoming water wave directions, and then the velocity potential in air can be expressed in the form…”

“…For the three-dimensional unsteady nonlinear lifting surface technique, only wing bound vortex elements exist at the moment when the wing suddenly set into motion [ 19 ]. As the time marches, the wake vortex ring elements will be shed.…”

“…The inclination of the vortex ring plan with respect to x -axis and yaxis are τ 1 and τ 2 , respectively. The influences of the still free surface and the incoming regular waves on the vortex ring can be considered separately [ 19 ]. For the vortex ring operating above a free surface, the contribution to the induced velocity components comes from three parts: the velocity components induced by the vortex ring and its image beneath the free surface as well as the contribution of the free-surface disturbance [ 24 ].…”

“…The accurate prediction of the aerodynamic loads acting on the WIG above water waves is essential in the design stage of the WIG craft and helps the aviator maneuver the WIG craft appropriately. The twodimensional foil subject to WIG in the presence of water waves has been studied by authors using the discrete vortex method [ 19 ]. However, three-dimensional WIG in the vicinity of water waves differs widely from the two-dimension.…”