THE OPTIMIZATION OF THE HULL FORM WITH THE MINIMUM WAVE MAKING RESISTANCE BASED ON RANKINE SOURCE METHOD

The hull form optimization concerns one of the most important applications of wave making resistance theories. In order to obtain a hull form with the minimum wave making resistance, an optimization design method based on the CFD is proposed, which combines the Rankine source method with the nonlinear programming （NLP）. The bow-body shape is optimized with the minimum wave making resistance as the objective function. A hull form modification function is introduced to represent an improved hull surface, which can be used to generate a new smooth hull surface by multiplying it by the offset data of the original hull surface. The parameters of the hull form modification function are taken as the design variables. Other constraint conditions can also be considered, for example, in optimizing the lines of the bow, appropriate displacements can be taken as the basic constraints. S60 hull form is selected as the original hull. Three improved hulls are obtained by optimal design. Rankine source method proves to be an effective method in ship form optimization based on analysis of the resistance performance and lines of the improved hull.

Shape Optimization of Bow Bulbs with Minimum Wave-Making Resistance Based on Rankine Source Method

The hull form optimization concerns one of the most important applications of wave-making resistance theories.In recent years,scholars can determine the hull form by using the optimization method based on the computational fluid dynamics(CFD)and other mathematical techniques.In this paper,the hull form optimization method based on the Rankine source method and nonlinear programming(NLP)is discussed;in the optimization process,a hull form modification function is introduced to represent an improved hull surface and to generate a new smooth hull surface by changing its frame lines and bow stem profiles under the prescribed design constraints. Numerical example is given for a practical container hull form.Finally,shape optimization of bow bulls is shown for non-protruding and protruding bow bulls.This study presents a simplified and practical design method to the select frame lines of bow bulls.

Numerical Research on Wave-making Resistance of Trimaran

A 3D rankine panel method was developed for calculating the linear wave-making resistance of a tri-maran with Wigley hulls. In order to calculate the normal vector and derivative of the body surface accurately, non-uniform rational B-spline (NURBS) was adopted to represent body surface and rankine source density. The radiation condition is satisfied using the numerical technology of staggered grids. Numerical results show that the linear wave-making resistance of the trimaran can be calculated effectively using this method.

Domain Decomposition and Matching for Time-Domain Analysis of Motions of Ships Advancing in Head Sea

A domain decomposition and matching method in the time-domain is outlined for simulating the motions of ships advancing in waves. The flow field is decomposed into inner and outer domains by an imaginary control surface, and the Rankine source method is applied to the inner domain while the transient Green function method is used in the outer domain. Two initial boundary value problems are matched on the control surface. The corresponding numerical codes are developed, and the added masses, wave exciting forces and ship motions advancing in head sea for Series 60 ship and S175 containership, are presented and verified. A good agreement has been obtained when the numerical results are compared with the experimental data and other references. It shows that the present method is more efficient because of the panel discretization only in the inner domain during the numerical calculation, and good numerical stability is proved to avoid divergence problem regarding ships with flare.

Resistance and Seakeeping Numerical Performance Analyses of a Semi-Small Waterplane Area Twin Hull at Medium to High Speeds

The hydrodynamic analysis of a new semi-small waterplane area twin hull （SWATH） suitable for various applications such as small and medium size passenger ferries is presented. This may be an attractive crossover configuration resulting from the merging of two classical shapes： a conventional SWATH and a fast catamaran. The final hull design exhibits a wedge-like waterline shape with the maximum beam at the stem; the hull ends with a very narrow entrance angle, has a prominent bulbous bow typical of SWATH vessels, and features full stern to arrange waterjet propellers. Our analysis aims to perform a preliminary assessment of the hydrodynamic performance of a hull with such a complex shape both in terms of resistance of the hull in calm water and seakeeping capability in regular head waves and compare the performance with that of a conventional SWATH. The analysis is performed using a boundary element method that was preliminarily validated on a conventional SWATH vessel.

Research on Design Method of the Full Form Ship with Minimum Thrust Deduction Factor

In the preliminary design stage of the full form ships, in order to obtain a hull form with low resistance and maximum propulsion efficiency, an optimization design program for a full form ship with the minimum thrust deduction factor has been developed, which combined the potential flow theory and boundary layer theory with the optimization technique. In the optimization process, the Sequential Unconstrained Minimization Technique（SUMT） interior point method of Nonlinear Programming（NLP） was proposed with the minimum thrust deduction factor as the objective function. An appropriate displacement is a basic constraint condition, and the boundary layer separation is an additional one. The parameters of the hull form modification function are used as design variables. At last, the numerical optimization example for lines of after-body of 50000 DWT product oil tanker was provided, which indicated that the propulsion efficiency was improved distinctly by this optimal design method.

Analytical Solution of Boundary Integral Equations for 2-D Steady Linear Wave Problems

Based on the Fourier transform, the analytical solution of boundary integral equations formulated for the complex velocity of a 2-D steady linear surface flow is derived. It has been found that before the radiation condition is imposed,free waves appear both far upstream and downstream. In order to cancel the free waves in far upstream regions, the eigensolution of a specific eigenvalue, which satisfies the homogeneous boundary integral equation, is found and superposed to the analytical solution. An example, a submerged vortex, is used to demonstrate the derived analytical solution. Furthermore,an analytical approach to imposing the radiation condition in the numerical solution of boundary integral equations for 2-D steady linear wave problems is proposed.

NUMERICAL SIMULATIONS OF WAVE-INDUCED SHIP MOTIONS IN TIME DOMAIN BY A RANKINE PANEL METHOD

A time domain prediction of wave-induced ship motions by a Rankine panel method is investigated. Linear boundary conditions on free surface and mean wetted body surface are adopted, while the numerical damping method is used for the radiation conditions. The motions of two ships in regular head waves are computed by the present method. The related numerical results are compared with the experiment data and those from linear strip theory. The comparison shows satisfactory agreements for pitch and heave transfer functions.

Time domain simulations of radiation and diffraction by a Rankine panel method

The radiation and the diffraction of a ship with a forward speed are studied by using a time domain Rankine panel method. The free surface conditions are linearized onto an undisturbed free surface based on the double body flow. The linearized body boundary condition is applied on the mean wetted hull surface. The fluid domain boundary is discretized by a collection of quadric panels. The unknown quantities, including the free surface elevation, the normal flux over the free surface and the potential on the fluid domain boundary, are determined at each time step. The numerical results are compared with experimental data and other numerical solutions, showing satisfactory agreements.

COMPUTATIONAL RESEARCH ON WAVE MAKING OF MOVING WIGLEY HULL IN TIME DOMAIN

Based on Green＇s theorem, a time domain numerical model was constructed to simulate wave making phenomenon caused by a moving ship. In this article, the Rankine sources and dipoles were placed on boundary surfaces （i.e., the ship surface and free surface）, and a time-stepping scheme was employed. Its unique characteristic is that steady state can be realized from initial value by employing the time-stepping scheme and unsteady free surface conditions. In time domain, if the results of unsteady flow problem tend to data stabilization after many time steps of computation, they could be regarded as the data of steady ones. This model could be employed to steady or unsteady problems. Theoretical reasoning and computational process of this method was described in detail The linear and nonlinear boundary conditions on body surface were studied, and the relative means to realize these boundary conditions in iterative computation were also discussed. Some proper parameters about the model of the Wigley hull were determined by many numerical tests, and their influences on wave making resistance and wave pattern were discussed. According to the comparison between numerical results and data available in relative references, the method used in this work is proven to be a reliable method in time domain. And the lattice reorganization in every time step computation is a feasible numerical approach.

WAVES GENERATED BY A 3D MOVING BODY IN A TWO LAYER FLUID OF FINITE DEPTH

This paper is concerned with the waves generated by a 3 D body advancing beneath the free surface with constant speed in a two layer fluid of finite depth. By applying Green’s theorem, a layered integral equation system based on the Rankine source for the perturbed velocity potential generated by the moving body was derived with the potential flow theory. A four node isoparametric element method was used to treat with the solution of the layered integral equation system. The surface and interface waves generated by a moving ball were calculated numerically. The results were compared with the analytical results for a moving source with constant velocity.

Multiobjective Optimization of Hull Form Based on Global Optimization Algorithm

Rankine source method,optimization technology,parametric modeling technology,and improved multiobjective optimization algorithm were combined to investigate the multiobjective optimization design of hull form.A multiobjective and multilevel optimization design framework was constructed for the comprehensive navigation performance of ships.CAESES software was utilized as the optimization platform,and nondominated sorting genetic algorithm II(NSGA-II)was used to conduct multiobjective optimization research on the resistance and sea-keeping performance of the ITTC Ship A-2 fishing vessel.Optimization objectives of this study are heave/pitch response amplitude and wave-making resistance.Taking the displacement and the length between perpendiculars as constraints,we optimized the profile of the hull.Analytic hierarchy process(AHP)and technique for order preference by similarity to ideal solution(TOPSIS)were used to sort and select Pareto solutions and determine weight coefficient of each navigation performance objective in the general objective.Finally,the hydrodynamic performance before and after the parametric deformation of the hull was compared.The results show that both the wave-making resistance and heave/pitch amplitude of the optimized hull form are reduced,and the satisfactory optimal hull form is obtained.The results of this study have a certain reference value for the initial stage of multiobjective optimization design of hull form.