Steady Flow Approximations in Three-Dimensional Ship Motion Calculation

Abstract

When a ship advances at constant speed in waves, the steady flow interacts with the unsteady wave field generated by the ship's motion. The interaction between the steady flow and the unsteady wave field appears in so-called mj terms. The three different steady flow models, that is, free stream, double body flow, and steady wave flow, are considered for the realization of the mj terms. For completeness in a linear sense, the steady flow contributions are retained in a consistent manner in the expressions for the hydrodynamic and restoring forces, which can be derived from the integration of the linearized pressure over the mean wetted part of the hull surface. The steady trim and sinkage are also considered important in determining the mean wetted position. The numerical results are obtained using a three-dimensional panel method based on a translating and pulsating Green function approach. An efficient numerical method is applied for the accurate evaluation of the mj terms without deriving the second derivatives of the Green function. Numerical calculations have been made for a submerged sphere and a Wigley hull. It is found that the steady flow has strong influence on added masses and damping forces in heave and pitch at relatively low encounter frequencies, while its effect is not observed as significant in wave exciting forces. The importance of the steady flow effect is also pronounced in the peak values of heave and pitch motion responses. In comparison with semiana-lytical and experimental results, the double body and steady wave flows are found to be the proper choices for the steady flow approximation.