Minimum Wave Resistance Research Articles

Ship Forebody Optimization Based on Rankine Source Method

Abstract The shape of the ship’s forebody has a greater impact on the ship’s resistance, and a reasonable optimization of the forebody can play a role in reducing the propulsion power and optimizing the resistance performance. Under the premise of Rankine source method of potential flow wave theory as the theoretical basis, SHIPFLOW software is used as the calculation tool, and CAESES software is used as the optimization tool to study the optimal design of the ship with minimum wave resistance. In the optimization process, a real ship is taken as the object, and the optimal solution of the rising wave resistance coefficient is calculated with the rising wave resistance coefficient as the objective function and the ship speed and displacement as the constraints. The real ship is selected as the mother ship, the parameters of the hull shape are taken as the design variables, and the shape of the forebody is optimized by the Lackenby shift method, so as to obtain a ship shape with less wave resistance at the same speed and within the displacement limit. The results show that the improved ship shape has obvious effect of reducing the wave resistance, which verifies the effectiveness and feasibility of this method for ship shape optimization

Study on the design method of an automatic outrigger layout control system for variable outrigger layout trimaran

During the navigation of a trimaran, its wave resistance is influenced by both sailing speed and outrigger layout. In the case of a variable outrigger layout trimaran, due to the adjustability of its outrigger layout according to different speeds, its wave resistance will be lower than that of traditional trimarans. In this paper, an automatic outrigger layout control system is figured out for a variable outrigger layout trimaran. The system can control and regulate the position of outriggers according to the traveling speed in order to reduce the wave resistance during navigation. The slender ship theory based resistance calculation program is applied as the solver in this system to evaluate the wave resistance of the trimaran and further determine the optimal outrigger layout under a specific speed. In order to improve the calculation accuracy, NURBS (Non-Uniform Rational B-Splines) method is introduced to modeling the hull surface. Model tests for trimaran with 6 different outrigger layouts are conducted to obtain the resistance of the trimaran in order to validate the numerical method. The steepest descent method is applied to solve the problem of searching the outrigger layout with minimum wave resistance efficiently. On this basis, an open-loop control system for trimaran outrigger layout is designed based on PID (Proportional Integral Derivative) algorithm with the control objective derived by the solver. Finally, a outrigger layout adjustment simulation (when speed changes from Fr=0.4 to Fr=0.35) is conducted on the experimental trimaran model. By comparing the resistance results obtained by numerical method utilized in this paper to the results obtained by CFD (Computational Fluid Dynamics) simulations, the effectiveness of the proposed system is validated.

Study on fast interference wave resistance optimization method for trimaran outrigger layout

The configuration of outriggers has a significant influence on the wave resistance of a trimaran. In this paper, slender ship theory is applied to calculate the wave resistance of trimarans. In order to improve the calculation accuracy, NURBS (Non-Uniform Rational B-Splines) method is introduced to molding the hull surface and the relative ideal results are obtained. On this basis, a series of 3D color maps of interference resistance (between main hull and outriggers) under different speeds and different displacement ratios are given to study the influence of the outrigger layout on the interference resistance. The results show that within an appropriate range, there is only one valley point of interference resistance exists in each 3D color map. For this reason, in combination with the characteristic of linear wave resistance has analytic expression, the steepest descent method can be applied to solve the problem of searching the outrigger layout with minimum wave resistance efficiently. Based on the above aspects, this paper proposes a fast trimaran outrigger layout resistance optimization method. By means of selecting an appropriate initial outrigger layout position, using trimaran wave resistance formula combined with steepest descent method, the minimum interference resistance layout in specific speed can be obtained efficiently. The results show a good precision of the optimal solution and an obvious promotion in computing efficiency compared to typical enumeration method.

The Minimum Wave Resistance of Hull Form Design Method Based on CFD Method

To reduce the resistance of the ship in actual navigation, a hull form optimization design method for minimum wave resistance is proposed. A numerical wave tank of regular waves is established based on the CFD (Computational Fluid Dynamics) theory. Overlapping grid technology is adopted to mesh the hull form and free surface. The new hull offsets are generated by using the parameters of modified function as design variables. The geometric expression and reconstruction of optimized hull form is determined through the three-dimensional CAD (Computer Aided Design) modeling technology. The displacement limit was used as the basic constraint, and other additional constraints were considered; nonlinear programming quadratic line search algorithm was used to set up a mathematical model of hull form optimization on the ISIGHT platform. The optimization calculations of Wigley hull form and surface ship DTMB5415 are carried out. Compared with the parent hull, the wave resistance of the optimized hull form is significantly reduced, and the feasibility of this method is confirmed. The research results can provide technical support for the development of "green ship"design.

Mathematical programming basis for ship resistance reduction through the optimization of design waterline

It has been more than a decade since Calisal et al. (J Ship Res 46(3):208–213, 2002) presented their concept of wave resistance reduction by allowing an increase in the beam of a ship accompanied by smoothing the shoulders. Since then a series of computational and experimental studies have been performed to provide evidence for the design idea that an increase in the beam with waterline parabolization may give reduced wave resistance for moderate Froude numbers in most cases in contrast to the common understanding among naval architects. The procedure in the design concept mentioned has been based on a systematic search supported by computational work and validated by experimental studies. The present study attempts to rationalize the introduced design concept by establishing a mathematical programming basis which employs the thin-ship approximation for wave resistance and a quadratic programming in finding the optimal shape of the design waterline (DWL), for minimum wave resistance, for the given design constraints. In this case, the shape of the DWL and in turn the hull shape in accordance with DWL is determined by a well-defined optimization procedure, which is dictated by the mathematical programming routine. Computational tools are employed to check the hydrodynamic characteristics of the hull form determined by the optimization routine, before tank testing. An experimental work is carried out to confirm the computational results and to validate the proposed methodology. Both the computational and the experimental work point out that the present design approach is effective particularly for Froude numbers greater than 0.21 and less than 0.4 where the ship-generated wavelength along the hull is less than the body length.

Study for the Development of an Optimum Hull Form using One Minus Prismatic

This study investigates the analysis algorithm for developing an optimum hull form with minimum wave resistance by using the practical application of one minus prismatic. In this algorithm the potential- based panel method was adopted to get the wave resistance coefficient as the objective function and SQP method was applied as an optimizer to get the optimum hull form. As an target ship, the series 60(CB=0.6) was taken into account and LBP(length between perpendiculars) of the ship was changed in the direction including a central parallel portion. To verity the validity of this study, the results of the numerical analyses were compared with experimental data.

SQP법을 이용한 최적선형개발에 대한 연구

본 연구에서는 최적화기법과 전산유체역학의 기술을 이용하여 저항의 관점에서 최적의 형상을 가지는 선형을 개발하는 알고리즘을 개발하였다. 최적화기법으로는 SQP(sequential quadratic programming)을 사용하였으며, 목적함수인 저항을 구하기 위하여 먼저 조파저항은 비선형 자유수면 경계조건을 고려한 선체주위 포텐셜유동을 계산할 수 있는 수치해석기법인 상 방향 패널이동법을 사용하였고, 선체에 미치는 전 저항을 구하기 위하여 ITTC 1957년 모형선-실선상관곡선을 이용하였다. 선형최적화 과정 중의 선체의 변경이나 계산 격자의 생성은 NURBS(Non-Uniform Rational B-Spline)기법을 사용하여 구현하였다. 이와 같은 방법을 사용하여 개발된 선형최적화 기법의 타당성을 검증하기 위하여 선형이 비교적 잘 알려진 건형인 Wigley선형과 Series 60(CB=0.6)선형에 대하여 설계속도 Fn=0.316에서 선형최적화를 위한 수치해석을 수행하고 그 결과를 초기선형과 서로 비교하였다. This paper presents the method for developing an optimum hull form with minimum wave resistance using SQP(sequential quadratic programming) as an optimization technique. The wave resistance is evaluated by a Rankine source panel method with non-linear free surface conditions and the ITTC 1957 friction line is used to predict the frictional resistance coefficient. The geometry of the hull surface is represented and modified using NURBS(Non-Uniform Rational B-Spline) surface patches. To verity the validity of the developed program the numerical calculations for Wigley hull and Series 60( <TEX>$C_B=0.6$</TEX>) hull have been performed and the results obtained by the numerical calculations have been compared with the original hulls.

Study on the Development of an Optimal Hull Form

This paper presents the method for developing an optimum hull form with minimum wave resistance using SQP( sequential quadratic programming) as an optimization technique. The wave resistance is evaluated by a Rankine source panel method with non-linear free surface conditions and the ITTC 1957 friction line is used to predict the frictional resistance coefficient. The geometry of the hull surface is represented and modified using NURBS(Non-Uniform Rational B-Spline) surface patches. To verify the validity of the developed program the numerical calculations for Wigley hull and Series 60 Cb=0.6 hull are performed and the results obtained after the numerical calculations are compared with the initial hulls.

최소 조파저항을 가지는 컨테이너선의 선형최적화 기법에 대한 연구

This paper presents the method for developing an optimum hull form with minimum wave resistance using SQP(sequential quadratic programming) as an optimization technique. The wave resistance is evaluated by a Rankine source panel method with non-linear free surface conditions and the ITTC 1957 friction line is used to predict the frictional resistance coefficient. The geometry of the hull surface is represented and modified using B-spline surface patches. The optimization method is applied to Series 60 hull and KCS(KRISO 3600 TEU Container Ship). The obtained results prove that the method is appropriate for preliminary hull form design.

An Adjoint Formulation for Shape Optimization in Free-Surface Potential Flow

This paper is a step towards the application of automatic shape optimization techniques to the hydrodynamic design of marine vehicles. The flow is assumed to be irrotational and free-surface conditions are linearized. Several objective functionals of relevance to free-surface flow are proposed, and adjoint formulations for the determination of their gradients are derived. The accuracy of the gradient using the adjoint formulations has been verified by comparisons with direct calculations using second-order finite differences. The method is then used to obtain an optimal solution to the inverse problem for a three-dimensional body submerged near a free surface, and to design a minimum wave resistance body.

Free-surface pressure distributions with minimum wave resistance

The wave resistance of distributions of excess pressure over a rectangular region on the surface of a steady stream is minimised by choice of spatial variation in pressure. Both unconstrained and constrained (non-negative) pressures are studied. Results with impressive resistance reductions are provided, both via discretisation to a large number of step pressures, and via optimisation within a low-order continuous family.

Slowly moving hull forms in short waves

The purpose of this paper is to provide a mathematical tool to improve the optimal design of ship forms. It is common practice that hull forms are designed such that they have minimum wave resistance in calm water. In this paper a theory is described by which the effect of short waves may be incorporated.

Fundamental Studies on Hull Form Design by Means of Nonlinear Programming (6 th Report)

The author has investigated the application of the wave resistance theory to the hull form design by means of nonlinear programming. In this study two problems are discussed, one of which is the problem of hull form improvement, and the other is the problem of minimum wave resistance. The present paper concerns the concluding result of these series, and the feasibility of this approach has been proved by showing the high performance hull form of SR 138 container ship being improved further as an example.We can regard the hull form design as a kind of the problem of nonlinear programming, because the objective function is generally specified as the nonlinear functional of design variables and many constraints of equalities or inequalities are needed in the practical design stage. The nonlinear programming technique provides a rational method for the determination of lines of practical hull forms.

Optimal Ship Forms for Minimum Total Resistance

A numerical scheme is developed by using the "tent" function to compute the hull surface area and then the ship frictional resistance in a quadratic form in terms of ship offsets. Combining with the wave resistance, a total ship resistance formula is derived in a standard quadratic form. With a set of linear-inequality constraints, the optimal solution of ship offsets for minimum total resistance can be obtained by applying a quadratic programming method to the problem. Computations have been carried out for three conditions which have exactly the same constraints as those required to obtain the optimal forms for minimum wave resistance shown in an earlier work [1].3 The optimal forms found for minimum total resistance also have either bow or midship bulbs. The new optimal bulbs have a relatively small size, higher vertical slope to the baseline, and less curvature at the tip of the bulb.

An Application of Mathieu Function Expansions to Hull Form Improvement

Mathieu-function-expansion method is proposed for evaluating and improving performance of ship hull forms. Medium speed ships, the design Froude number somewhere between 0.20 and 0.25, are mainly discussed.The present method is based on minimum wave resistance theory (Maruo and Bessho, 1963) for infinite draft wall-sided ships. When the half breadth curve is expanded by Mathieu functions, the coefficient of the higher order term has by far the greater effect upon the value of the wave resistance than the coefficients of the lower order terms. Using this fact the performance of the ship hull form is evaluated from the standpoint of the wave resistance and the information, how to improve the ship hull form is gotton.The tank tests are carried out to verify it and the results show that the present method is very powerful for improvement of practical ship hull forms.

Fundamental Studies on Hull Form Design by Means of Nonlinear Programming (3rd Report)

The minimum wave resistance problem based on Michell's thin ship theory has been investigated by means of variational approach so far. In this paper, a kind of the fairing constraint to hull form is introduced into the minimum wave resistance problem, and the optimization technique is applied instead of the variational approach.Two formulations are shown for the present problem and optimized by means of SUMT (Sequential Unconstrained Minimization Technique) as in the 1st & 2 nd reports. Numerical examples are given under several kinds of design conditions. As the fairing constraint is considered, the minimum wave resistance hull forms without swan necks are obtained.

Optimal Ship Forms for Minimum Wave Resistance

By introducing a set of "tent" functions to approximate the ship hull function, the Michell integral for wave resistance is reduced to a standard quadratic form in terms of ship offsets. With linear-inequality constraints of the type 0 ≤ H(x, z) ≤ B;C ≤ Hx(x,z) ≤ D(where H(x,z) is the hull function and B, C, D are constants), we are able to find various optimal ship forms of minimum wave resistance by applying quadratic programming techniques to the problem. Three optimal forms have been chosen among a number of computed results for tests in the ship-model towing tank. All three models have afterbodies identical with that of Series 60, Block 60, a standard merchant ship hull of good quality. Although the experimentally determined residuary resistance is in no better agreement with the theoretically predicted results than is usual in such comparisons, the order of "goodness" of the hull-forms as predicted and as measured was the same for Fn ≥ 0.36 and also for 0.20 ≤ Fn ≤ 0.26.

Free Surface Shock Waves and Methods for Hull Form Improvement

A new method of designing hull forms of minimum wave resistance is developed in which two major components of wave resistance, i.e., one due to free surface shock waves and the other due to linear waves are taken into account. A procedure of extracting wave profiles due to free surface shock waves is proposed, which is utilized as a quantitative measure of the magnitude of free surface shock waves. The relation between hull form and resistance coefficient due to free surface shock waves is empirically derived and it is incorporated into the wave-analytical procedure of obtaining hull forms of minimum wave pattern resistance, so that the sum of wave pattern resistance (linear wave resistance) and resistance due to free surface shock waves (nonlinear wave resistance) is minimized. The effectiveness of the new method is demonstrated by experiments.

An Application of Wave Resistance Theory to Hull Form Design

The objective of this paper is to apply linearized wave resistance theory and wave analysis to the hull form design for high speed ships. The paper consists of two parts. One is related to the method of estimation of wave resistance. The other is related to the method of hull form design.We start from the simplification of framelines while we do not vary the sectional area curve, and obtain the calculation formula of wave resistance for simplified hull forms by using Michell's theory. Next we consider a systematic series of parent models, and obtain the estimation formula of wave resistance of the models by comparing between calculation and wave analysis. The hull form of a high speed ship is made by superposing a thin hull form on that of a parent model. Then the amplitude functions of the high speed ship are obtained by superposing the amplitude functions of both hull forms on the basis of the principle of linear superposition.Concerning the method of hull form design, we propose the method to determine sectional area curve and load water line of minimum wave resistance by applying Ritz's method to the estimation formula of wave resistance. Moreover we propose a method to determine principal particulars from a viewpoint of wave resistance.

A Trial of Determining High Speed Practical Hull Forms by the Aid of the Minimum Wave Resistance Theory

An application of the theory of minimum wave resistance to the practical design of high speed ship forms is introduced. Use is made of the theory, indicated by Krein and Bessho, of the variation of hull forms without change in wave resistance. Tank experiments are conducted with a series of high speed container ship models, of which the hull forms are derived from the theoretical form of minimum wave resistance. The result can well prove the feasibility of the design method proposed here.