Propulsion of a foil moving in water waves.

Abstract

Propulsion of a foil moving in the water close to a free surface is examined. The foil moves with a forward speed U and is subjected to heaving and pitching motions in calm water, head waves or following waves. The model is two-dimensional and all equations are linearized. The fluid is assumed to be inviscid and the motion irrotational, except for the vortex wake. The fluid layer is infinitely deep.The problem is solved by applying a vortex distribution along the centreline of the foil and the wake. The local vortex strength is found by solving a singular integral equation of the first kind, which appropriately is transformed to a non-singular Fredholm equation of the second kind. The vortex wake, the forward thrust upon the foil and the power supplied to maintain the motion of the foil are investigated. The scattered free surface waves are computed. For moderate values of Uσ/g (U is forward speed of the foil, σ is frequency of oscillation, g is acceleration due to gravity) it is found that the free surface strongly influences the vortex wake and the forces upon the foil. When the foil is moving in incoming waves it is found that a relatively large amount of the wave energy may be extracted for propulsion. As an application of the theory the propulsion of ships by a foil propeller is examined. The theory is compared with experiments.