# Numerical prediction of ship manoeuvring in regular waves by a 2.5D approach

• Shi He

Student thesis: Doctoral Thesis

### Abstract

This thesis intends to study the manoeuverability of a single ship advancing in regular waves which is believed to be important for ship navigation safety as the situation is much more common experienced by a seagoing ship in real seaways instead of the calm water environment for traditional manoeuverability analysis.For this purpose, a so called two time scales model is applied to study the problem, according to the difference of the motion frequencies between the two involved sub-problems. That is to say, the total ship motions are consist of two parts, namely the wave induced motions analysed in a rapidly varying time scale system and the manoeuvring motions associated with a slowly varying time scale system. The two systems exchange data with each other at specific time intervals to reflect the interaction between two sub-motions. By this means, the analysis for an advancing ship executing a maneuver in waves can be achieved.To make concrete analysis of the sub-problems, a boundary element method (BEM) based on the 2.5 dimensional (2.5D) potential flow theory is adopted to solve the 5 degrees of freedom (DOF) rapidly varying wave induced motions, i.e., the seakeeping problem of slender ships advancing at speeds from moderate to relatively high is determined by interactively solving the discrete boundary integrate equation, kinematic and dynamic boundary conditions on the free surface in cross sections from bow to stern in time domain. Besides, this method is also used for the estimation of the manoeuvring derivatives required by the manoeuvring analysis.A numerical scheme called Multi-Transmitting Formula (MTF) is imposed on an artificial boundary to satisfy the radiation condition. The lift force, regarded as a consequence of the 3 dimensional (3D) flow effect which is important to manoeuvring motions but normally be neglected in the 2.5D theory, is taken into account for the evaluation of the total hydrodynamic forces acting on the ship during lateral motions. Furthermore, Non-Uniform Rational B-Spline (NURBS) is used for modelling the body plans of the ship and expressing the unknown quantities on the boundary elements to give more accurate and smoother solutions for the boundary value problems (BVP).To validate the established numerical tool, computations are carried out on a WigleyIII hull, a Series 60 hull and a container ship S175 hull respectively. The results are compared with the available experimental data.Regarding the manoeuvring motion simulations, the model is established based on the modular concept proposed by the Japanese Mathematical Modelling Group (MMG). The forces and moments induced by the propulsion system, the rudder system and the nonlinear viscous effect are estimated separately by empirical formulae or directly obtained from experimental measurements. The mean second order wave drift force is determined by direct pressure integration depending on the solved linear velocity potential from the seakeeping module.Simulations of the standard free running maneuvers, namely turning circle motion and Zig-zag motion, are carried out on the S175 ship in calm water and different regular waves successively. The results are compared with experimental measurements for validation which demonstrates that the present numerical tool can reasonably predict the manoeuvring motions of a slender ship in regular waves.
Date of Award 5 Jun 2017 English University Of Strathclyde Atilla Incecik (Supervisor) & Sandy Day (Supervisor)

'