Speed In Regular Waves Research Articles

TEBEM for springing responses of a container ship with forward speed and nonlinear effects in time domain

In this paper, springing responses of a container ship with forward speed in regular waves are studied by a time-domain TEBEM which is generalized to elastic modes. TEBEM is used principally to solve the steady and unsteady flow and the infinity radiation condition is achieved by the Damping Zone Method. In the structure part, the Transfer Matrix Method is used to get the generalized structural mass, damping, stiffness and principal mode of displacement and rotation of vertical oscillation modes which will participate in the subsequent hydrodynamic calculation. In the hydrodynamic part, the fourth-order Runge–Kutta method is used to solve the hydroelasticity equations. The effects of forward speed and 2nd order wave forces generated by 1st order velocity potential in head sea are analyzed. Meanwhile, the variation of different load components against wave direction for corresponding different stations and contribution of different part of ship for different load components in head sea are studied. Compared with the experimental results, the motions and loads of a 6750-TEU container ship with different forward speeds predicted by TEBEM show an acceptable agreement.

An alternative linear flow model and boundary integral flow representation for ship motions in regular waves

The basic issue of formulating a linear flow model for the analysis of potential flow around a ship advancing at a constant speed in regular waves is considered. Specifically, the ‘rigid-waterplane flow model’, previously considered for diffraction–radiation of regular waves by offshore structures, is applied to analyze flows around ships advancing in regular waves. A straightforward application of Green’s fundamental identity to the rigid-waterplane flow model yields a remarkable new boundary integral flow representation. Indeed, this flow representation does not involve a line integral around the mean waterline of the ship hull surface, is weakly singular, does not involve a distribution of dipoles over the ship-hull surface, and is free from irregular frequencies. In the particular case of flow around a ship steadily advancing in calm water, the boundary integral flow representation obtained in the study via an analysis based on the rigid-waterplane flow model is identical to the flow representation associated with the Neumann–Michell theory, which is based on a different linear flow model that only considers the flow region strictly outside the ship but consistently accounts for the linear contribution of the thin band of water between the wave profile along the ship hull surface and the undisturbed free surface. This result strongly suggests that the classical application of Green’s basic identity to analyze linear potential flow around a ship advancing in regular waves or in calm water, which yields a notoriously troublesome line integral around the ship waterline, may be questionable due to possible incompatibilities between the Neumann boundary condition at the ship hull surface and the linear free surface boundary condition associated with flows around ships advancing in calm water or in regular waves. This fundamental difficulty may be alleviated in the rigid-waterplane flow model, which imposes a compatibility condition between the Neumann boundary condition at the rigid lid that artificially closes the open ship hull surface and the linear boundary condition at the free surface above the waterplane-lid. The boundary integral flow representation given in the study also holds for diffraction–radiation of regular waves by offshore structures. Thus, this new flow representation provides a common mathematical basis, which fundamentally differs from the basis steadfastly adopted over the past fifty years, for the analysis of three basic classes of flows in ship and offshore hydrodynamics, and indeed can be applied more generally to other boundary-value problems such as those associated with flexural-gravity waves for ice sheets or very large floating structures.

Hydrodynamic Analysis and Motions of Ship with Forward Speed via a Three-Dimensional Time-Domain Panel Method

A new three-dimensional (3D) time-domain panel method is developed to solve the ship hydrodynamic problem and motions. For an advancing ship with a constant forward speed in regular waves, the ship’s hull can be discretized and processed into a number of quadrilateral panels. Based on Green’s theorem, an analytical expression for Froude–Krylov (F–K) forces evaluation on the quadrilateral panels is derived without accuracy loss. Within the linear potential theory, the transient free surface Green function (TFSGF) is applied to solve the boundary value problem. To improve the efficiency and numerical stability of TFSGF evaluation, a precise integration method with variable parameters setting for extended identity matrix is developed to compute the TFSGF in the computation domain. Then, radiation and diffraction forces can be evaluated by means of the impulse response function method. The Wigley I hull form is taken as a study case, and the computed hydrodynamic coefficients, wave exciting forces, and motions by the present method are compared with previous literature experimental data and prior published results. It manifests that the three-dimensional time-domain panel method proposed in this paper has good accuracy.

A time-domain prediction method of ship motions

A time-domain analysis is used to predict wave loading and motion responses for a ship traveling at a constant speed in regular oblique waves. Considered as a distribution of normal velocities on the wetted hull surface, the combined diffraction and radiation perturbations caused by the forward moving ship and her motions are determined simultaneously. This way, the ship-hull boundary condition is exactly fulfilled. The 3-D time domain Green's function is used to express the combined diffraction/radiation potential in terms of impulsive and memory potentials. Application of the Bernoulli equation yields the pressure distribution and accordingly, the necessary hydrodynamic forces. The equations of motion of the ship are then developed and solved in the time domain. Forces and motions at forward speed are predicted for a Wigley ship-hull in head waves and for a catamaran-ferry in oblique waves. Comparison is made with published theoretical and experimental results for the Wigley ship-hull, and the agreement is good. For the catamaran, a self-propelled model is built and tested both in a large towing tank and in a seakeeping basin in order to measure the six-degrees-of-freedom forces, moments and motions at forward speed in regular waves of different directions. For the longitudinal motions, the agreement between measurements and predictions is generally good. For the transverse motions, however, acceptable discrepancy exists. The discrepancy is thought to be mainly due to the exclusion from the analysis of the rudder forces and viscous damping. The inclusion of such nonlinear effects in the time domain simulation involves complex analysis and this problem is left to a future research.

Numerical Analysis of Sloshing Problems for the Middle-sized Double Hull Tanker

This paper deals with numerical analysis of sloshing problems for the middle-sized double hull tanker. A numerical simulation method for non-linear liquid sloshing in the cargo oil tank is proposed by making up a new sloshing cord based upon the SOLA-SURF scheme and a simple two-dimensional sloshing cord. The new sloshing cord has many functions for analyzing sloshing liquid violence motions in the octagon-shaped tank fitted with centre girder, deck centre girder, deck side girder, horizontal girder etc. A series of numerical simulations are executed for cargo oil tanks of a middle-sized double hull tanker and of a single hull tanker sailing at forward speed in regular waves, and numerical calculations are executed for four model tanks in order to compare with experimental results too. By numerical simulations, it is confirmed that the sloshing cord is useful for analyzing non-linear sloshing and for estimating sloshing pressure in liquid cargo tanks of a double hull tanker.

Prediction of motion and wave loads of twin-hull ships

A three-dimensional linearised potential theory associated with a cross-flow approach for taking viscous effects into account is presented for the prediction of motion and dynamic structural responses of twin-hull vessels travelling with forward speed in regular waves. Comparisons between theoretical and experimental results are shown for the motion responses and lateral wave loads of an ASR (anti-submarine rescue) catamaran and 3000-ton SWATH (small waterplane area twin-hull) ship. In general, good agreement between theory and experiment is found except for some discrepancies that are believed to be caused by neglect of forward speed effects on free surface.

Vertical Motions and Longitudinal Strength of Large-Sized High-Speed Ships with Hydrofoils

In this paper, the authors present a new method for calculating vertical motions of large-sized high-speed ships with hydrofoils. It is very important for this calculation to predict correctly the dynamic lift of the submerged hydrofoils which travel close to the free surface under the waves. Measurements were made of the dynamic lift of the hydrofoils moving at constant speed in regular waves. Using these experimental results, we propose a method for estimating the dynamic lift of the hydrofoils travelling beneath the waves. The ship motion is predicted by the strip method taking account of the effects of the nonlinear hydrodynamic forces and dynamic lift of the hydrofoils.To verify the present method, the authors compare the computational results with the experimental ones of HC2000. HC2000 is a new type of hydrofoil catamaran having a displacement of 2000 tons and composed of twin V-hulls and four rectangular hydrofoils. The computational results in still water and head seas agree very well with the experimental ones of the 1/50 model of HC2000.

On the Added Resistance Acting on a Circular Cylinder with Low Forward Speed in Regular Waves

The added resistance acting on a circular cylinder with low forward speed in regular waves are provided numerically and experimentally. The velocity potential is calculated by making use of the source distribution method which is considered not only the singularity distribution over the hull but also a line singularity distribution. And in order to investigate the effect of the forward speed, it is also shown a few approximate numerical methods in which it is assumed that the forward speed is very small. These calculations are made for a circular cylinder and the results are compared with the experimental ones. It is observed that the calculated values are in fairly good agreement with those of experiments.

Ship motions and sea loads in restricted water depth

The influence of the sea bottom on ship motions and sea loads is examined. It is described how to calculate the vertical motions and loads for a ship with non-zero forward speed in regular waves by use of sttip theory and fluid finite element method. Results of such calculations are shown. The effects of shallow water are significant as is seen from several figures.

Ship Model Study of Incidence of Shipping Water Forward

Panel H-7 (Seakeeping Characteristics) of the SNAME T&R Program over the past several years has sponsored a number of projects in its investigation of the seakeeping behavior of merchant ships. As one phase in this continuing program to formulate design guidelines for the naval architect and operational information for the shipowner, Panel H-7 funded the preparation of the following report presenting the results of an investigation of a technique for predicting the incidence of shipping water in irregular waves, involving a comparison of predictions with the actual behavior of a Mariner ship model. The investigation included determination of the model's relative bow motion amplitude operator for one forward speed in regular waves, as well as the generation and analysis of irregular waves and model motions in the Webb Institute towing tank. It was found that with only simple corrections for bow wave build-up, sinkage and trim, a good approximate prediction can be made of the bow submergence in irregular waves, provided that the results of several runs are averaged; if a correction is also made for dynamic wave buildup, a more accurate prediction can be expected. It is the hope of the Panel that this report will stimulate additional efforts of this type to the benefit of the naval architect and ship-owner.