Numerical And Experimental Transient Tests For Ship Seakeeping

Abstract

A potential flow model for linearized ship seakeeping in time domain is presented. The numerical algorithm is briefly sketched. The transient test technique, based on the interaction of a mathematical wave packet with the advancing ship, is numerically simulated and allow to recover the efficiency of frequency domain models. Solutions are presented for a frigate, a container-ship and a mathematical tri-hull. A set of experiments, also of transient type, have been performed to support the numerical findings. I N T R O D U C T I O N Practical ship motion simulation tools have to be efficient enough to provide results in a relatively short time. On this ground, linearized frequency domain strip theories are largely employed because of the good compromise between simplicity, accuracy and computer requirements. On the other hand, the fully nonlinear three dimensional simulation in time domain is the natural avenue to deal with extreme wave conditions. For ship motions, the fully nonlinear approach is pioneered by the group led by R. Beck at University of Michigan through a desingularized Rankine panel method (see Scorpio et al. (1996)). The (weakly) nonlinear code SWAN2 developed at M.I.T. (see Sclavounos 1996) is the most extensively tested time domain code documented in literature. Here we present our attempt to develop a time domain algorithm for ship of arbitrary geometry and speed (Colagrossi and Landrini 1999). To recover the efficiency of two-dimensional (Salvesen et al. 1970) and three-dimensional (Bertram 1998) frequency domain methods we determine the ship behavior by studying the response to incoming wave packets (Ciauss and Vannahme 1999). Three categories of ships have been considered. The first one is representative of modern frigate ship: DDG 51. The second ship is a well known container vessel, S 175, for which experimental data are available both for head and following seas. Finally, a tri-hull ship made by assembling Wigley models is considered. For the combatant and the trimaran, we have also performed an extensive set of experiments based both on the transient test technique and on more conventional tests in regular and irregular waves. The good agreement between experimental data and numerical results validates the computational procedure as well as presents the latter as a useful alternative tool to seakeeping tests. NUMERICAL TREATMENT OF THE PROBLEM The unsteady motion of a ship in a seaway is studied by an inviscid model. In this framework, the nonlinear problem is stated in Newman (1978). Here, we consider the case of small oscillations ot = ~ + f~ x R with respect to the mean trim and sinkage attained by the ship when advancing in calm sea, with constant forward velocity U in the z-direction. In the following, W denotes the basis-flow. The perturbation velocity potential cp satisfies the Laplace equation v2~ = o (1) together with the standard no-penetration boundary condition on the mean wetted hull/3: ~p, = ( a , + V x ( a x W ) ) . n ~po., (2) and with the linearized kinematic and dynamic free surface conditions on the mean free surface level .T: = <pz -Vr / W + r / W ~ . k + v w 2 2g • V~o = 9 r i W • Vcp (3) In eqs. (3), 9 is the gravity acceleration, p is the fluid density, ~7 is the wave height and t the time. Lower suffices stand for partial derivatives. The above problem describes the induced motion a of the ship under the action of incoming waves with potential ~0. The fluid dynamic problem is coupled with the body motion through