Generalized Weissinger’s L-method for prediction of curved wings operating above a free surface in subsonic flow

The classical Weissinger’s L-method is generalized to the lifting problem for steadily advancing curved wings subject to the wing-in-ground (WIG) effect above a large body of water in subsonic flow, and the free surface defines the boundary between the air and water. Unlike the traditional analysis of the lifting problem, the essential techniques focus on finding the three-dimensional free surface Green’s function generated by the isolated horseshoe vortex in the upper layer of the stratified fluid where the air is regarded as weakly compressible and the water is incompressible. The numerical calculation is implemented using Weissinger’s L-method. Finally, the effects of the curved geometry on WIG effect in the vicinity of a free surface in subsonic flow are discussed. Extensive numerical examples are carried out to show the lift properties for three-dimensional swept and dihedral wings operating in the vicinity of a free surface as a function of the sweep or dihedral angle for different clearance-to-chord ratios and Mach numbers. Interestingly, for high Froude numbers, the free surface effectively becomes rigid, and it can safely be treated as a solid surface.