THEORETICAL MEAN WAVE RESISTANCE OF PRECURSOR SOLITON GENERATION IN TWO-LAYER FLOW

A new concept of pseudo mean wave resistance is introduced to find theoretical mean wave resistances of the precursor soliton generation in two-layer how over a localized topography at near-resonance in this paper. The pseudo mean wave resistance of the precursor soliton generation of two-layer how is determined in terms of the AfKdV equation. From the theoretical results it is shown that the theoretical mean wave resistance is equal to the pseudo mean wave resistance times 1/m(1), where m(1) is the coefficient of the fKdV equation. From the regional distribution of the energy of the precursor soliton generation at the resonant points, it is shown that ratios of the theoretical mean wave resistance and regional mean energy to the total mean energy are invariant constants, i.e. <(E)over circle (1)>/(E) over circle : <(E)over circle (2)>/(E) over circle: <(E)over circle (3)>(E) over circle :< D > /(E) over circle = (1/2) : (-1/2) : 1 : 1, in which <(E)over circle 1>,<(E)over circle (2)> and <(E)over circle (3)> are the mean energy of the generating regions of the precursor solitons, of the depression and of the trailing wavetrain at the resonant points respectively, (E) over circle and < D > are the total energy of the system and the theoretical mean wave resistance at the resonant points. A prediction of the theoretical mean wave resistances of two-layer how over the semicircular topography is carried out in terms of the theoretical results of the present paper. The comparison shows that the theoretical mean wave resistance is in good agreement with the numerical calculation.

Flexural-gravity wave resistances due to a surface-moving line source on a fluid covered by a thin elastic plate

Analytical solutions for the flexural-gravity wave resistances due to a line source steadily moving on the surface of an infinitely deep fluid are investigated within the framework of the linear po- tential theory. The homogenous fluid, covered by a thin elastic plate, is assumed to be incompressible and inviscid, and the motion to be irrotational. The solution in integral form for the wave resistance is obtained by means of the Fourier transform and the explicitly analytical solutions are derived with the aid of the residue theorem. The dispersion relation shows that there is a minimal phase speed cmin, a threshold for the existence of the wave resistance. No wave is generated when the moving speed of the source V is less than emin while the wave resistances firstly increase to their peak values and then decrease when V ~〉 Crnin. The effects of the flexural rigidity and the inertia of the plate are studied. @ 2013 The Chinese Society of Theoretical and Applied Mechanics. [doi：10.1063/2.1302202]

RESEARCH ON THE METHOD AND CALCULATION OF THE NEW SLENDER-SHIP WAVE RESISTANCE THEORY

Analyses of the new slender-ship theory of wave resistance were made and corresponding calculation methods were proposed. Based on these theoretical methods, the calculations of wave resistance of near surface submersible, Wigley hull and vertical/canted strut SWATHs were conducted. In the single and double integral parts of Green's function, the method of special function expansion and Chebyshev polynomial approach were adopted respectively. The formulas for zeroth-first-and second-order wave-making resistance were derived. In a towing tank, the calm water resistance experiment of SWATH model ASW-2 with canted strut was conducted and researched. The influences of waterline integral term, the surface mesh number, element node number, range of the integration and truncation of special function expansions on velocity potential and numerical results of resistance were investigated, and the difference between the zeroth-order and first-order wave resistance was analyzed. The theoretical calculation results agree well with the well-found model experimental results.

Flexural-gravity wave resistances due to a moving point source on 2-D infinite floating beam

The flexural-gravity wave responses due to a load steadily moving or suddenly accelerated along a rectilinear orbit are analytically studied within the framework of the linear potential theory. A thin viscoelastic plate model is used for a very large floating structure. The initially quiescent fluid in the ocean is assumed to be homogenous, incompressible, and inviscid, and the disturbed motion be irrotational. A moving line source on the plate surface is considered as a moving point in the two-dimensional coordinates. Under the assumptions of small-amplitude wave motion and small plate deflection, a linear fluid-plate coupling model is established. The integral solutions for the surface deflections and the wave resistances are analytically obtained by the Fourier transform method. To study the dynamic characteristics of the flexural-gravity wave response, the asymptotic representations of the wave resistances are derived by the residue theorem and the methods of stationary phase. It shows that the steady wave resistance is zero when the speed of moving load is less than the minimal phase speed. The wave resistances due to the accelerate motion consist of two parts, namely the steady and transient wave responses. Eventually the transient wave resistance declines toward zero and the wave resistance approaches the steady component as the time goes to the infinity. Furthermore, the effect of the strain relaxation time for this viscoelastic plate is studied and it exhibits more influence for a high-speed motion.

Ship hull optimization based on wave resistance using wavelet method

The ship hull surface optimization based on the wave resistance is an important issue in the ship engineering industry. The wavelet method may provide a convenient tool for the surface hull optimization. As a preliminary study, we use the wavelet method to optimize the hull surface based on the Michel wave resistance for a Wigley model in this paper. Firstly, we express the model＇s surface by the wavelet decomposition expressions and obtain a reconstructed surface and then validate its accuracy. Secondly, we rewrite the Michel wave resistance formula in the wavelet bases, resulting in a simple formula containing only the ship hull surface＇s wavelet coefficients. Thirdly, we take these wavelet coefficients as optimization variables, and analyze the main wave resistance distribution in terms of scales and locations, to reduce the number of optimization variables. Finally, we obtain the optimal hull surface of the Wigley model through genetic algorithms, reducing the wave resistance almost by a half. It is shown that the wavelet method may provide a new approach for the hull optimization.

Numerical Modelling of Wash Waves Generated by Ships Moving over An Uneven Bottom

Unsteady wash waves generated by a ship with constant speed moving across an uneven bottom topography are investigated by numerical simulations based on a Mixed Euler–Lagrange(MEL) method. The transition is accomplished by the ship traveling from the depth h1 into the depth h2 via a step bottom. A small tsunami would be created after this transition. However, the unsteady wave-making resistance induced by this new phenomenon has not been well documented by literature. Therefore, the main purpose of the present study is to quantify the effects of an uneven bottom on the unsteady wash waves and wave-making resistance acting on the ship. An upwind differential scheme is commonly used in the Euler method to deal with the convection terms under free-surface condition to prevent waves in the upstream. Evidently, it cannot be applied to the present problem due to upstream waves generated by the ship would be dampened by the upwind scheme. The central differential scheme provides more accurate results,but it is not unconditionally stable. An MEL method is therefore employed to investigate the upstream wave generated by the ship moving over the uneven bottom. Simulation results show that the hydrodynamic interaction between the ship and the uneven bottom could initiate an upstream tsunami, as well as unsteady wave-making resistance on ships.The unsteady wave-making resistance oscillates periodically, and the amplitude and period of the oscillations are highly dependent on speed and water depth.

NUMERICAL SIMULATION OF WAVE RESISTANCE OF TRIMARANS BY NONLINEAR WAVE MAKING THEORY WITH SINKING AND TRIM BEING TAKEN INTO ACCOUNT

Up to now, there are no satisfactory numerical methods for simulating wave resistance of trimarans, mainly due to the difficulty related with the strong nonlinear features of the piece hull wave making and their interference. This article proposes a numerical method for quick and effective calculation of wave resistance of trimarans to be used in engineering applications. Based on Wyatt＇s work, the nonlinear free surface boundary condition, the time domain concept, and the full nonlinear wave making theory, using the Rankine source Green function, the 3-D surface panel method is expanded to solve the trimaran wave making problems, with high order nonlinear factors being taken into account, such as the influence of the sinking and trim, transom, and ship wave immersed hull surface. And the software is successfully developed to implement the method, which is validated. Several trimaran models, including a practical trimaran with a sonar dome and the transom, are used as numerical calculation samples, their wave making resistance is calculated both by the present method and some other methods such as linear （Dawson） methods. Moreover, sample model resistance tests were carried out to provide data for comparison, validation and analysis. Through the validation by model experiments, it is concluded that present method can well predict the wave making resistance, sinking and trim, and the accuracy of wave making resistance calculation is significantly improved by taking the trim and sinking into account, especially at high speeds.

Study on Wave Added Resistance of a Deep-V Hybrid Monohull Based on Panel Method

In this paper, a panel method based on three dimensional potential flow theory is used to study the problem of wave added resistance. The time-domain motion response of Wigely III ship in head waves is calculated by AQWA, and then the wave added resistance of ship is obtained by near-field pressure integration method. By comparing the calculated results with the experimental data in literature, it is shown that the variation trend and peak value are in good agreement, and the accuracy and efficiency meet the research requirements. Based on the above mentioned method, the wave added resistance of a deep-V hybrid monohull in head waves is studied. The motions and wave added resistances of the deep-V hybrid monohull and the deep-V original ship advancing in head waves with various forward speed and wave frequencies are calculated and analyzed. The results show that the longitudinal motion response of the deep-V hybrid monohull is effectively suppressed and the wave added resistance is obviously reduced, the new type of ship has good engineering application prospects. The present method provides an approach of satisfactory accuracy and efficiency to predict wave added resistance of ships voyaging in waves.

Study on Wave Added Resistance of Ships in Oblique Waves Based on Panel Method

When the ship is sailing at sea,wave added resistance has great influence on the rapidity and economy of the ship.With the increasing pressure of energy and environmental protection,IMO has proposed the EEDI formula of the newly built ships,which restricts the energy consumption standard of civil ships more strictly.Therefore,a panel method based on three dimensional potential flow theory is proposed to study the problem of wave added resistance in this paper.Firstly,the method solves the motion responses of the ship in the time domain,and then calculates the wave added resistance of the ship by near-field pressure integration method.The wave added resistance of S175 container ship in head and oblique waves are calculated and compared with the experimental data,and the accuracy of the proposed method are verified.At last,the influence of Froude number and wave direction angle on wave added resistance is studied.The proposed method provides an approach of satisfactory accuracy and efficiency for the development of high-performance new ship forms,optimization of ship hull lines,comprehensive performance evaluation of ships and practical navigation guidance.

Analysis of Wave Added Drag and Motion Response of Mid-high-speed Ship against Waves

In order to accurately predict the on-wave resistance and responses to hull motions of ships in actual sea conditions,the k-εmethod of the RNG model is adopted on the basis of the unsteady RANS method.The two-formula turbulence model deals with the viscous flow,the VOF method captures the free surface,the velocity boundary method makes waves,the artificial damping method is used to eliminate waves,and the nested grid technology is used to deal with the motion response of ships on waves.Combined with the 6-DOF motion formula,a three-dimensional numerical wave cell for regular waves is established.For one example,taking a KCS Container ship and fishing boat sailing at a mid-high-speed,the increase of wave resistance and motion response at different wavelengths are analyzed,and the simulation results are compared with the experimental value,the content of strip theory in potential flow theory and the panel method to prove the reliability of CFD method in predicting ship motion.

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.

静水和波浪中阻力最小的集装箱船参数化船型优化

This paper described the process of generating the optimal parametric hull shape with a fully parametric modeling method for three containerships of diferent sizes.The newly created parametric ship hull was applied to another ship with a similar shape,which greatly saved time cost.A process of selecting design variables was developed,and during this process,the infuence of these variables on calm water resistance was analyzed.After we obtained the optimal hulls,the wave added resistance and motions of original hulls and optimal hulls in regular head waves were analyzed and compared with experi-mental results.Computations of the fow around the hulls were obtained from a validated nonlinear potential fow boundary element method.Using the multi-objective optimization algorithm,surrogate-based global optimization(SBGO)reduced the computational efort.Compared with the original hull,wave resistance of the optimal hulls was signifcantly reduced for the two larger ships at Froude numbers corresponding to their design speeds.Optimizing the hull of the containerships slightly reduced their wave added resistance and total resistance in regular head waves,while optimization of their hulls hardly afected wave-induced motions.

Prediction of added resistance of a ship in waves at low speed

This paper presents predictions of the added resistance of a ship in waves at a low speed according to the IMO minimum propulsion power requirement by a hybrid Taylor expansion boundary element method(TEBEM).The flow domain is divided into two parts:the inner domain and the outer domain.The first-order TEBEM with a simple Green function is used for the solution in the inner domain and the zero order TEBEM with a transient free surface Green function is used for the solution in the outer domain.The TEBEM is applied in the numerical prediction of the motions and the added resistance in waves for three new designed commercial ships.The numerical results are compared with those obtained from the seakeeping model tests.It is shown that the prediction of the ship motions and the added resistance in waves are in good agreement with the experimental results.The comparison also indicates that the accuracy of the motion estimation is crucial for the prediction of the wave added resistance.In general,the TEBEM enjoys a satisfactory accuracy and efficiency to predict the added resistance in waves at a low speed according to the IMO minimum propulsion power requirement.

船舶航线优化中任意浪向的航速损失预测模型

This paper proposes a semi-empirical model to predict a ship’s speed loss at arbitrary wave heading.In the model,the formulas that estimate a ship’s added resistance due to waves attacking from different heading angles have been further developed.A correction factor is proposed to consider the nonlinear effect due to large waves in power estimation.The formulas are developed and verified by model tests of 5 ships in regular waves with various heading angles.The full-scale measurements from three different types of ships,i.e.,a PCTC,a container ship,and a chemical tanker,are used to validate the proposed model for speed loss prediction in irregular waves.The effect of the improved model for speed loss prediction on a ship’s voyage optimization is also investigated.The results indicate that a ship’s voyage optimization solutions can be significantly affected by the prediction accuracy of speed loss caused by waves.

An iterative Rankine BEM for wave-making analysis of submerged and surface-piercing bodies in finite water depth

A 3-D iterative Rankine Boundary Element Method （BEM） for seakeeping problem in time domain is developed in the framework of linear potential theory. Waves generated by both submerged and surface-piercing bodies moving at a constant forward speed in otherwise calm water, and the resultant steady wave pattern, wave profile and resistance are computed to validate this newly-developed code. A rectangular computational domain moving with the same forward speed as the body is introduced, in which an artificial damping beach is installed at an outer portion of the free surface except the downstream side for satisfying the radiation condition. The velocity potential on the ship hull and the normal velocity on the free surface are obtained directly by solving the boundary integral equation, with the Rankine source used as the kernel function. An iterative time-marching scheme is employed for updating both kinematic and dynamic free surface boundary conditions to stabilize the calculation. Extensive results including the wave patterns, wave profiles and wave resistances for a submerged spheroid and a Wigley hull with forward speed are presented to validate the efficiency of the proposed 3-D time-domain higher-order approach. Finally, the sensitivity of ship-generated waves to the water depth is investigated. Computed results show satisfactory agreement with the corresponding experimental data and other numerical solutions.

COMPARISON OF RESISTANCE FOR SEVERAL DISPLACEMENT HIGH PERFORMANCE VEHICLES

According to the linear wave resistance theory, a comparison among the ship resistance for the high speed round bilge ships, the deep “Vee” vessels, the wave-piercing catamarans, and the high speed trimarans was given by using the high-speed round-bilge ship as a benchmark. And the optimal speed range of each ship form was also suggested by using the analysis of the research results.

OPTIMIZATION OF A WAVE CANCELLATION MULTIHULL SHIP USING CFD TOOLS

A simple CFD tool, coupled to a discrete surface representation and a gradient based optimization procedure, is applied to the design of optimal hull forms and optimal arrangement of hulls for a wave cancellation multihull ship. The CFD tool, which is used to estimate the wave drag, is based on the zeroth order slender ship approximation. The hu ll surface is represented by a triangulation, and almost every grid point on the surface can be used as a design variable. A smooth surface is obtained via a si mplified pseudo shell problem. The optimal design process consists of two steps . The optimal center and outer hull forms are determined independently in the fi rst step, where each hull forms are determined independently in the first step, where each hull keeps the same displacement as the original design while the wav e drag is minimized. The optimal outer hull arrangement is determined in the se cond step for the optimal center and outer hull forms obtained in the first step . Results indicate that the new design can achieve a large wave drag reduction i n comparison to the original design configuration.

Numerical study on ship-generated unsteady waves based on a Cartesian-grid method

The added resistance of a ship in waves can be related to ship-generated unsteady waves.In the present study,the unsteady wave-pattern analysis is applied to calculate the added resistance in waves for two modified Wigley models using a Cartesian-grid method.In the present numerical method,a first-order fractional-step method is applied to the velocity-pressure coupling in the fluid domain,and one of volume-of-fluid(VOF)methods is adopted to capture the fluid interface.A ship is embedded in a Cartesian grid,and the volume fraction of the ship inside the grid is calculated by identifying whether each grid is occupied by liquid,gas,and solid body.The sensitivity to the location of measuring position of unsteady waves as well as the number of solution grids is examined.The added resistance computed by direct pressure integration and wave pattern analysis is compared with experimental data.In addition,nonlinear characteristics of the added resistance in waves are investigated by detailed analyses of unsteady flow field and resulting wave pattern.

Numerical simulation of dynamic characteristics of a water surface vehicle with a blended-wing-body shape

The blended-wing-body shape vehicle is a new type of water surface vehicle with a large square coefficient. The interference of the wave systems under a high speed condition is more significant for the blended-wing-body shape vehicle and the dynamic characteristics of the new type vehicle are very different from that of a traditional vehicle. In this paper, the implicit volume of fluid（VOF） method is adopted to simulate the wave resistance of the high speed blended wing body vehicle, and a semi-relative reference frame method is proposed to compute the maneuvering coefficients. The effects of the navigation speed, the drift angle and the rotating radius are studied. The dimensional analysis method is used to assess the influence of Fr and L/R on the results. The wave making resistance coefficient against the speed sees a large fluctuation because of the serious wave interference. The lateral rotation maneuvering characteristics under the surface navigation condition is nonlinear and more complex than under the under water condition, which is quite different to control.