Numerical Study of Viscous Wave-Making Resistance of Ship Navigation in Still Water

The prediction of a ship＇s resistance especially the viscous wave-making resistance is an important issue in CFD applications. In this paper, the resistances of six ships from hull 1 to hull 6 with different hull forms advancing in still water are numerically studied using the solver naoe-FOAM-SJTU, which was developed based on the open source code package OpenFOAM. Different components of the resistances are computed and compared while considering two speed conditions （12 kn and 16 kn）. The resistance of hull 3 is the smallest while that of hull 5 is the largest at the same speed. The results show hull 3 is a good reference for the design of similar ships, which can provide some valuable guidelines for hull form optimization.

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.

A BOUNDARY ELEMENT METHOD FOR STEADY SHIP WAVE-MAKING POTENTIAL PROBLEMS

A boundary element method for three-dimensional steady ship wave-making potential problems is established with the Rankine source function as its fundamental solution. In the treatment of the linearized free surface condition, one-sided, upstream finite difference operator (FDO) is used to suppress the upstream waves, and the equation of the disturbance velocity is established so that the first order FDO can be used in place of the second order FDO. Compared with the method with the second order FDO, the current method gives better precision and stability. Numerical examples are presented for verification.

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 Wave Channel with Absorbing Wave-Maker

The numerical wave channel has been developed based on the volume of fluid method (VOF) in conjunction with the Navier-Stokes equations. The absorbing wave-maker boundary on the left side of the channel is presented by prescribing velocity reference to linear wave-maker theory. The principle of which is that the numerical wave-maker is designed to move in a way that generates the required incident wave and cancels out any reflected wave that reach it at the same time. On the right side of the channel, the open boundary is set to permit incident waves to be transmitted freely. The parametric studies have been carried out at a range of ratios of water depth to wave length d/ L from 0.124 to 0.219, with wave height in the front of paddle/water depth ratio (H0 / d) from 0.1 to 0.3. Wave height, wave pressure distribution along the channel and velocity field are obtained for both open boundary condition and reflective boundary condition at the other end of the channel. For a reflective case, it is shown that the absorbing wave-maker is very effective in canceling out the reflected wave that reaches the numerical paddle and highly repeatable waves can be generated.

An Irregular Wave Maker of Active Absorption with VOF Method

A numerical irregular wave flume with active absorption of re-reflected waves is simulated by use of volume of fluid （VOF） method. An active ＇absorbing wave-maker based on linear wave theory is set on the left boundary of the wave flume. The progressive waves and the absorbing waves are generated simultaneously at the active wave generating-absorbing boundary. The absorbing waves are generated to eliminate the waves coming back to the generating boundary due to reflection from the outflow boundary and the structures. SIRW method proposed by Frigaard and Brorsen （1995） is used to separate the incident waves and reflected waves. The digital filters are designed based on the surface elevation signals of the two wave gauges. The corrected velocity of the wave-maker paddle is the output from the digital filter in real time. The numerical results of regular and irregular waves by the active absorbing-generating boundary are compared with the numerical results by the ordinary generating boundary to verify the performance of the active absorbing-generator boundary. The differences between the initial incident waves and the estimated incident waves are analyzed.

Efficient computation method for two-dimensional nonlinear waves

The theory and simulation of fully-nonlinear waves in a truncated two-dimensional wave tank in time domain are presented. A piston-type wave-maker is used to generate gravity waves into the tank field in finite water depth. A damping zone is added in front of the wave-maker which makes it become one kind of absorbing wave-maker and ensures the prescribed Neumann condition. The efficiency of numerical tank is further enhanced by installation of a sponge layer beach (SLB) in front of downtank to absorb longer weak waves that leak through the entire wave train front. Assume potential flow, the space- periodic irrotational surface waves can be represented by mixed Euler-lagrange particles Solving the integral equation at each time step for new normal velocities, the instantaneous free surface is integrated following time history by use of fourth-order Runge- Kutta method. The double node technique is used to deal with geometric discontinuity at the wave- body intersections. Several precise smoothing methods have been introduced to treat surface point with high curvature. No saw-tooth like instability is observed during the total simulation. The advantage of proposed wave tank has been verified by comparing with linear theoretical solution and other nonlinear results, excellent agreement in the whole range of frequencies of interest has been obtained.

Experimental Study of Wave Energy Spectrum in Shallow Water

Wave energy spectrum in shallow water can be studied in wind wave channel in combination with irregular wave- maker. Fetch length is successfully extended and by 'Relay' method the corresponding spectrum pattern and the wind velocity scale are obtained.

Coupling model for waves propagating over a porous seabed

The wave-seabed interaction issue is of great importance for the design of foundation around marine infrastructures. Most previous investigations for such a problem have been limited to uncoupled or one- way coupled methods connecting two separated wave and seabed sub models with the continuity of pressures at the seabed surface. In this study, a strongly coupled model was proposed to realize both wave and seabed processes in a same program and to calculate the wave fields and seabed response simultaneously. The information between wave fields and seabed fields were strongly shared and thus results in a more profound investigation of the mechanism of the wave-seabed interaction. In this letter, the wave and seabed models were validated with previous experimental tests. Then, a set of application of present model were discussed in prediction of the wave-induced seabed response. Numerical results show the wave-induced liquefaction area of coupled model is smaller than that of uncoupled model.

A numerical piston-type wave-maker toolbox for the open-source library OpenFOAM

A novel numerical piston-type wave-maker toolbox for the OpenFOAM is developed and demonstrated in this paper. This toolbox is implemented in C++ for improving the solutions of nonlinear wave problems in the field of hydrodynamics. As a toolbox that generates waves using the piston-type method only, it contains several frequently used functions, including the generation and the absorption of waves of various forms, an active absorption system and the porous media flow. Furthermore, to illustrate the operability of the toolbox, some validations and applications are presented, including the regular waves, the irregular waves, and the solitary waves. In each case, a satisfactory agreement is obtained in comparison with the published experimental or theoretical results,so this toolbox may be applied with a considerable confidence.

A fully nonlinear approach for efficient ship-wave simulation

This paper presents an efficient time-domain method for simulating nonlinear ship waves.The proposed method,implemented in an earth-fixed coordinate system,integrates a compact boundary element domain within a high-order spectral layer,enabling accurate modeling of both near-field and far-field ship waves.An overset mesh method and an attention mechanism are employed to track the moving ship.The effectiveness of the method is validated through simulations of Wigley and Series 60 ships sailing at various speeds.The numerical results,including the nonlinear wave run-up at the ship bow,surface pressure distribution on the hull,and the ship resistance,agree well with experimental data and published numerical results,confirming that the method is capable of accurately simulating the nonlinear ship waves.

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.

Method to Calculate Resistance of High-Speed Displacement Ship Taking the Effect of Dynamic Sinkage and Trim and Fluid Viscosity into Account

A method is presented to calculate the resistance of a high-speed displacement ship taking the effect of sinkage and trim and viscosity of fluid into account.A free surface flow field is evaluated by solving Reynolds averaged Navier-Stokes(RANS) equations with volume of fluid(VoF) method.The sinkage and trim are computed by equating the vertical force and pitching moment to the hydrostatic restoring force and moment.The software Fluent,Maxsurf and MATLAB are used to implement this method.With dynamic mesh being used,the position of a ship is updated by the motion of "ship plus boundary layer" grid zone.The hull factors are introduced for fast calculating the running attitude of a ship.The method has been applied to the ship model INSEAN2340 for different Froude numbers and is found to be efficient for evaluating the flow field,resistance,sinkage and trim.

Numerical computations of resistance of high speed catamaran in calm water

In this paper, the in-house multifunction solver naoe-FOAM-SJTU is applied to study the resistance and wave-making performance of a high-speed catamaran sailing at different velocity in calm water. The volume of fluid（VOF） method is used to capture the free interface and the finite volume method（FVM） is adopted as the discretization scheme. The hull model is fixed with initial trim and sinkage. The numerical results of the presented paper agree very well with the measurement data of model test. Wave making and vortex field are well simulated to analyze the hydrodynamic performance of a catamaran.

Research on Numerical Wave Tank Based on the Improved Moving-Particle Semi-Implicit Method with Large Eddy Simulation

Moving-particle semi-implicit(MPS) method is a new mesh-free numerical method based on Lagrangian particle. In this paper, MPS method is applied to the study on numerical wave tank. For the purpose of simulating numerical wave, we combine the MPS method with large eddy simulation(LES) which can simulate the turbulence in the flow. The intense pressure fluctuation is a significant shortcoming in MPS method. So, we improve the original MPS method by using a new pressure Poisson equation to ease the pressure fluctuation. Divergencefree condition representing fluid incompressible is used to calculate pressure smoothly. Then, area-time average technique is used to deal with the calculation. With these improvements, the modified MPS-LES method is applied to the simulation of numerical wave. As a contrast, we also use the original MPS-LES method to simulate the wave in a numerical wave tank. The result shows that the new method is better than the original MPS-LES method.

Experimental investigation of the generation of large-amplitude internal solitary wave and its interaction with a submerged slender body

A principle of generating the nonlinear large-amplitude internal wave in a stratified fluid tank with large cross-section is pro- posed according to the ＇jalousie＇ control mode. A new wave-maker based on the principle was manufactured and the experi- ments on the generation and evolution of internal solitary wave were conducted. Both the validity of the new device and ap- plicability range of the KdV-type internal soliton theory were tested. Furthermore, a measurement technique of hydrodynamic load of internal waves was developed. By means of accurately measuring slight variations of internal wave forces exerted on a slender body in the tank, their interaction characteristics were determined. It is shown that through establishing the similarity between the model scale in the stratified fluid tank and the full scale in the numerical simulation the obtained measurement re- suits of internal wave forces are confirmed to be correct.