A three-dimensional linear analysis of steady ship motion in deep water

Abstract

The investigation of steady ship motion in calm water is a classic problem in ship hydrodynamics, where ship waves and wave resistance are subjects of unquestionable importance. Despite considerable efforts in the past a satisfactory solution of the steady ship motion problem has not been achieved so far. The application of three-dimensional potential flow theory results in an essentially nonlinear problem formulation due to the unknown position of the disturbed free surface. In this thesis consistent linearisation schemes are discarded in favour of the inconsistent Neumann-Kelvin theory. This approximation implies that nonlinear free surface effects are neglected entirely, but the three-dimensional features of the fluid flow and hull geometry are otherwise fully retained. The Kelvin wave source potential, otherwise known as the wave resistance Green's function, is analysed in great detail. Solutions to the disturbance potential of the steady perturbed ship flow are obtained by means of a Kelvin wave source distribution method. The exact source strength is the solution of a Fredholm integral-equation of the second kind. An explicit source strength approximation, valid for sufficiently slender ships operating at fairly low speeds, is investigated. Particular emphasis is placed on computational aspects. Highly accurate and efficient methods for the evaluation of the Kelvin wave source potential are proposed. The developed theory is applied to five different ship forms, viz. a submerged prolate spheroid, Wigley's parabolic ship, a tanker, a fast destroyer and a cruiser. Over a wide range of ship speeds experimental data are compared with theoretical predictions of the steady flow parameters such as wave resistance, wave profiles, pressure signatures and lift force distributions.