On Wave Diffraction of a Two-Dimensional Moonpool in a Two-Layer Fluid in Finite Water Depth

This paper studies the wave diffraction of a two-dimensional moonpool in a two-layer fluid in finite water depth by using a domain decomposition scheme and an eigenfunction matching method. The formulae of the wave exciting forces, the free surface and internal wave elevations at zero-frequency are derived. Numerical convergence has been assessed by repeating the computations for increasing values of the truncation orders. The present model has been validated by comparing a limiting case with a single-layer fluid case and the comparisons are in general satisfactory. Although the wave exciting forces and free surface wave elevations around resonance frequency are overestimated, the piston mode resonance frequency is well predicted. Two typical configurations with different moonpool widths are selected for computations in both free surface and internal wave modes. It is found that, the wave exciting forces, free surface and internal wave elevations in internal wave mode are much smaller than those in free surface wave mode. In addition, the wave exciting forces in internal wave mode attenuate to zero quickly as incident wave frequency increases. For moonpool with small width, only piston mode resonance can be observed. The piston mode resonance frequencies identified in free surface and internal wave modes are the same. The characteristics of piston mode resonance can also be observed in the horizontal and vertical wave exciting forces. Around the piston mode resonance frequency, the wave exciting forces reach their local maximums. It is revealed that, as moonpool width increases, the piston mode resonance frequency decreases. Meanwhile, it shows that more asymmetric and symmetric sloshing mode resonances appear alternately and occur at higher frequencies than the piston mode resonance. Moreover, the predicted sloshing mode resonance frequencies are compared with those estimated by a simple approximate formula.

Wave-Body Interactions Among an Array of Truncated Vertical Cylinders

A semi-analytical method is developed to investigate water-wave radiation and diffraction by an array of truncated vertical cylinders as a model for a point-absorber wave farm. Each cylinder can have independent movements in six modes. The method of matched eigenfunction expansions is applied to obtain the velocity potential for the fluid. To achieve fast computation, the effects of evanescent modes of locally scattered waves from one cylinder are neglected in the near fields of the neighboring cylinders. Wave-exciting forces and moments on an individual cylinder or a group of cylinders, situated among an array, are evaluated by a new, generalized form of Haskind relation that is applicable to an array configuration. In results, hydrodynamic coefficients and wave-exciting loads are presented for arrays of different configurations. Comparisons between wave-exciting loads obtained from the generalized Haskind relation and those from direct diffraction solutions show excellent agreements.

Numerical Analysis of Pontoon Effect on Flow-Induced Forces of the Deep Draft Semisubmersible in a Cross-Flow

Deep draft semisubmersible (DDS) concepts have been developed recently in order to improve the vertical motion characteristics of the platform, due to the smaller wave exciting forces on the pontoons than a conventional semisubmersible. However, the DDS may experience critical vortex-induced motions (VIM) stemming from the fluctuating forces in a strong current environment. Aiming to investigate the excitation loads and the mechanism of VIM, Computational Fluid Dynamics (CFD) analyses are performed to study the flow around the DDS in a cross-flow. Special attentions are paid to the effect of the pontoon and the heading angle. Good agreement between CFD simulations and model test results for the current loads of a DDS is observed. Detailed computational results including hydrodynamic loads and flow patterns are presented.

Optimum Distance Between Two Advancing Ships Arranged Side by Side

The hydrodynamic interaction between two advancing ships is very important. Because of the hydrodynamic interactions, even relatively small waves can induce large motions of the smaller ship due to the proximity of the larger ship. The aim of this paper is to develop a method to optimize the spacing between two advancing ships, in order to minimize the hydrodynamic interactions. The optimization method is based on the far-field wave patterns produced by a translating and oscillating source point. For values of the parameter τ > 0.25 (τ = ωeu/g) there is a fan-shaped quiescent region in front of the vessel. As τ increases, the range of the fan-shaped quiescent region will be expanded. It can be supposed that if the two ships are located in each other’s fan-shaped quiescent region, the hydrodynamic interactions can be minimized. This assumption was validated through the numerical simulation, which was based on a 3-D Rankine source panel method. We calculated and compared the wave exciting forces and wave patterns of two Wigley hulls advancing in waves side by side. The numerical results were consistent with our theoretical assumption.

Wave Exciting Forces of a Free Floating Semi Submersible in Regular Waves

Drilling and production of oil by semi submersible take place in many locations throughout the world. Generally, floating structures play an important role in exploring the oil and gas from the sea. The force and motion prediction of offshore structures may be carried out using time domain or frequency domain models or model tests. In this paper the frequency domain analysis used because it is the simplified and linearized form of the equations of motion. The time domain analysis, unlike frequency domain models, is adequate to deal with non-linearities such as viscous damping and mooring forces, but it requires sophisticated solution techniques and it is expensive to employ. In this paper, the wave exciting forces of a free floating semi-submersible were carried out using 3D source distribution method within the scope of the linear wave theory. The results obtained from computations were also compared with the results obtained using commercial software MOSES and WAMIT.

Wave Drift Forces and Resonance Analysis on Two Ships Arranged Side by Side

In recent years, with the development of new ships and further utilization of marine resources, multi-body floating systems are widely used in practice. Compared with the single floating body, the movement in multi-body floating system is not only affected by the external environment, but the interaction between the bodies cannot be neglected. So analysis of hydrodynamic performance of a multi-body floating system is of great importance. In this paper, a multi-body system consisting of two side-by-side ships is studied. The code AQWA® is used for its hydrodynamic performance analysis in frequency domain. Its hydrodynamic parameters are compared with those of the related single-ship system and the difference is obvious. The two-ship system shows a peak in motion different from single-ship system at some frequencies and its wave exciting forces have period effects. Also, negative values appear in added masses, which never occur for a single-body floating system. When the gap between the two ships is changed, there is a significant trend that the wave frequency of the peak value decreases with the gap size between the two ships. In addition, this paper also discussed the length of wave and distance of ships ratio that the motion resonance usually happens. Through the analysis of this dimensionless parameter, a conclusion about resonance between two parallel ships is deducted.

An Analytical Solution of Wave Exciting Loads on CALM Buoy with Skirt

Linearized potential wave theory is applied to calculate the wave exciting loads on a CALM buoy in water of finite depth. The solution is based on the domain decomposition method and the unknown constants in the velocity potentials are determined by matched eigenfunction expansions. A comparison of the analytical solution with published experimental results on a vertical truncated cylinder is performed as part of the validation process. The effects of the disk on the wave exciting forces are discussed.

Experimental Investigation of the First and Second Order Wave Exciting Forces on a Restrained Body in Long Crested Irregular Waves

The paper presents an experimental investigation of the first order and second order wave exciting forces acting on a body of simple geometry subjected to long crested irregular waves. The body is axis-symmetric about the vertical axis, like a vertical cylinder with a rounded bottom, and it is restrained from moving. Second order spectral analysis is applied to obtain the linear spectra, coherence spectra and cross bi-spectra of both the incident wave elevation and of the horizontal and vertical wave exciting forces. Then the linear and quadratic transfer functions (QTF) of the exciting forces are obtained. The QTF obtained from the analysis of irregular wave measurements are compared with results from experiments in bi-chromatic waves and with numerical predictions from a second order potential flow code.

The Motions of a Ship on a Sloped Seabed

In standard diffraction theory it is assumed that the water depth is constant and that the seabed is infinitely large. To account for a local varying bathymetry in shallow water (as it can occur for offshore LNG terminals) it is sometimes considered to introduce a second fixed body on the seabed representing this bathymetry in diffraction theory. Based on the results presented in this paper it can be concluded that this is (without special measures) not possible. The refraction and interference effects are too strong and affect the wave exciting forces on the LNG carrier in an incorrect way. A large size of the second body and smoother edges of this body do not improve the situation. However, a second body in diffraction theory, when chosen properly with respect to size and shape, can contribute to the correct calculation of the added mass and damping of vessels on sloped seabeds as this varies with the local water depth over the length of the vessel. This will clearly affect the motion response of the vessel. This can be seen for instance in the pitch-heave coupling. This will influence the motions of the ship in waves, as well as the resulting drift forces and related mooring loads.