The second-order wave force on a vertical cylinder

Influence of second-order wave force and focusing position on dynamic responses of tension leg platform under a freak wave

The main difficulty in second-order diffraction analysis stems from the contribution of the second-order potential, which obeys an inhomogeneous free-surface boundary condition. In some applications it is sufficient to know the second-order hydro-dynamic force, which can be calculated without explicitly evaluating this second-order potential. This technique cannot however be used for calculating other quantities such as the hydrodynamic pressure at any point, the sectional force and bending moment in the cylinder or the free-surface elevation due to the second-order effects. This paper provides a detailed analysis of the second-order diffraction problem of a uniform vertical circular cylinder in regular waves. This furnishes results not only on the cylinder surface, but also on the free surface, and in principle in the fluid domain surrounding the body. The analysis may help to throw some light on the physical interpretation of the second-order theory and its mathematical description. Moreover, this information is intended to complement the development of general numerical methods for arbitrary bodies.

Numerical analysis of the wave forces acting on ships can be complex primarily because of the interactions between incident waves and structures. In this paper, the three-dimensional frequency domain Rankine panel method is used to study the seakeeping and second-order wave drift forces of a ship in waves. The model considers second-order wave forces acting on the ship hull and therefore accounts for slow drift ship motions and the added resistance. The second-order wave forces are evaluated using the pressure integral method, also known as the near-field approach. The unsteady velocity potential is divided into three parts namely (a) incident, (b) diffraction and (c) radiation to satisfy the Laplace equation. To avoid wave reflection the Rayleigh’s artificial friction is used in way of the free surface boundary. This method is equivalent to introducing a numerical damping beach for energy dissipation. The numerical results are compared with those of experiments for Wigley-III hull in head waves and the SCb-84 hull in oblique waves. Good agreement is obtained.

In this paper, the second-order long period wave forces acting on a two-dimensional fixed obstacle of arbitrary shape in bichromatic waves in a finite depth water are investigated. In the evaluation, the second-order effect of a wave maker is included to satisfy the precise boundary condition in an experimental tank. The solution of the second-order diffraction problem is obtained by using hybrid type boundary integral equation method. One of the merit of this method is that the complicated second-order free surface condition can be treated easily by using the analytical form of second-order velocity potential which was derived in 1st report.Computations are done for a half immersed circular cylinder and the calculated results are compared with the results obtained from Green's second identity. These results are also compared with experimental values and the validity of the present method is discussed.

A complete semi-analytical solution is given for second-order diffraction of monochromatic waves by a truncated vertical circular cylinder in water of uniform finite depth. The methodology presented in detail elsewhere (Eatock Taylor & Huang 1996) is adopted to find a particular solution which exactly satisfies the governing equation, the inhomogeneous free-surface condition and the seabed condition. In order to satisfy the boundary condition on the cylinder bottom, the fluid domain around the cylinder is divided into two regions. First- and second-order velocity potentials are described separately in the two regions and matched on the interface by the pressure and normal-velocity continuity conditions. Based on the formulation, the second-order wave field in the vicinity of the cylinder and the corresponding wave forces and overturning moments on the cylinder are studied in detail. Numerical results for the double frequency forces obtained by using the present semi-analytical approach are compared with those computed with a higher-order boundary element method (Eatock Taylor & Chau 1992). As well as the exact solution, an approximate solution is also given for the second-order potential and the corresponding forces. Numerical results show that the approximate solution possesses excellent accuracy for the total second-order heave force over a wide range of conditions. When kb > 1.2 (where k, b are the incident wavenumber and the draught of the cylinder respectively), the accuracy for total second-order surge force and pitch moment is also satisfactory. These results could lead to the development of very efficient solutions and corresponding algorithms for the analysis of second-order wave diffraction by more complicated structures such as tension leg platforms. Numerical results based on the present solution show that in many cases, both the first- and the second-order-free surface elevation in the vicinity of a truncated cylinder is very close to that of a bottom-seated cylinder. For waves with larger amplitudes, the maximum free-surface elevation around a vertical cylinder predicted with the second-order theory can significantly exceed that given by linear theory. There is also a considerable difference in the location of the maximum elevation predicted by the linear and nonlinear theories.

A numerical method for solving 3D unsteady potential flow problem of ship advancing in waves was put forward. The flow field was divided into an inner and an outer domain by introducing an artificial matching surface. The inner domain was surrounded by a ship-wetted surface and a matching surface as well as part of the free surface. The free-surface condition for the inner domain was formulated by perturbation about the double-body (DB) flow assumption. The outer domain was surrounded by a matching surface and the rest had a free surface as well as an infinite far-field radiation boundary. The free-surface condition for the outer domain was formulated by perturbation of the uniform incoming flow. The simple Green function and transient free-surface Green function were used to form the boundary integral equation (BIE) for the inner and outer domains, respectively. The Taylor expansion boundary element method (TEBEM) was adopted to solve the DB flow and inner-domain and outer-domain unsteady flow BIE. Matching conditions for the inner-domain flow and outer-domain flow were enforced by the continuity of velocity potential and normal velocity on the matching surface. Direct pressure integration on the ship-wetted surface was applied to obtain the first- and second-order wave forces. The numerical prediction on the displacement, acceleration and added resistance of the 14000-TEU container ship at different forward speeds were investigated by the proposed TEBEM method. Reynolds-Averaged Navier–Stokes (RANS) equations based on Computational Fluid Dynamics (CFD) method were adopted to compare with TEBEM method. The physical tank experiment results also validated the accuracy of the numerical tank results. Compared with the experimental solutions, TEBEM obtained good agreement with the RANS CFD method. TEBEM, however, was much more efficient and robust.

The diffraction of water waves by a vertical circular cylinder is considered in the regime where the wave amplitude A and cylinder radius a are of the same order, and both are small compared to the wavelength. The wave slope is small, and a conventional linear analysis applies in the outer domain far from the cylinder. Significant nonlinear effects exist in the complementary inner domain close to the cylinder, associated with the free-surface boundary condition. Using inner coordinates scaled with respect to a, it is shown that the leading-order nonlinear contribution to the velocity potential includes terms proportional to both A2a and A3. The wave load which acts on the cylinder near the free surface includes second- and third-harmonic components which are proportional respectively to A2a2 and A3a. In a conventional perturbation analysis, where A [Lt ] a, these components would be ordered in magnitude corresponding to the different powers of A, but here they are of the same order. The second- and third-order components of the total force are of comparable magnitude for practical values of the wave slope.

Wave force analysis of the two vertical cylinders by boundary element method

The formal solutions to the three‐dimensional problem of scattering and diffraction due to an impulsive acoustic point source in a fluid half‐space, in which a semiinfinite vertical soft cylinder is embedded, have been obtained in integral forms. The early time‐displacement velocities have been evaluated (1) in the shadow region by the Residue–Cagniard method and (2) in the illuminated region by the saddle‐point–Cagniard method. In the shadow region, there are two types of diffracted waves, i.e., the diffracted waves without and the diffracted waves with the reflection from the free surface. In the illuminated region, there are four types of waves: the direct wave, the reflected wave from the free surface, the reflected wave from the cylinder without reflection from the free surface, and the reflected wave from the cylinder with reflection from the free surface. Numerical results for the early time displacement velocities in the shadow region and in the illuminated region for the cases r = a, z = 5a, ϑ − ...

The diffraction of waves by three bottom fixed vertical circular cylinders is investigated by using the boundary element method. This method has been successfully applied to the isolated vertical circular cylinder and now is used to study the interaction between waves and multiple vertical cylinders. In this paper, a numerical analysis by the boundary element method is developed by the linear potential theory. The numerical analysis by the boundary element method is based on Green's second theorem and introduced to an integral equation for the fluid velocity potential around the vertical circular cylinders. To verify this method, the results obtained in present study are compared with the results computed by the multiple scattering method. The results of the comparisons show strong agreement. Also in this paper, several numerical examples are given to illustrate the effects of various parameters on the wave exciting force such are the separation distance, the wave number and the incident wave angle. This numerical computation method might be used broadly for the design of various offshore structures to be constructed in the future.

Numerical simulation of wave interaction with vertical circular cylinders of different submergences using immersed boundary method

Hydrodynamic interactions of cnoidal waves with a vertical cylinder

Motion responses of a moored barge in shallow water

Shallow-water mooring chains of floating offshore wind turbines pose challenges such as nonlinear tension characteristics, high cost and prominent fatigue issues, which seriously hinder the large-scale use of floating wind power. Based on the hydrological and meteorological data of an offshore wind farm in the South China Sea, a sensitivity analysis of the mooring chain fatigue of a semi-submersible floating offshore wind turbine in shallow water was conducted with different environmental loads and mooring chain design parameters. It was found that mooring fatigue is mainly caused by the wave condition within diagonal distribution of the wave dispersion diagram. The mooring chain fatigue calculated using the main monochromatic wave was more conservative than that calculated using the wave scatter diagram with a difference of about 28%. The mooring fatigue calculated using turbulent wind spectrum was greater than that calculated using steady wind. In contrast, waves are the main source of mooring fatigue, and the second-order wave force has an undeniable impact on the mooring fatigue of a semi-submersible floating offshore wind turbine, which accounts for approximately 26% of wave-induced mooring fatigue. In addition, the current-induced mooring fatigue should not be neglected, although its effect is not as large as that caused by the wave or wind loads. An increase in the cross-sectional diameter and the length of a mooring chain, as well as a reasonable clump weight arranged, all contribute to improving the fatigue life of mooring chains in shallow water, which provide useful technical references for the optimization of mooring lines fatigue in shallow-water areas.

The fully coupled aerodynamic-hydrodynamic-mooring numerical model of floating offshore wind turbine(FOWT) has been established. The complex conditions such as second-order wave force, full-field turbulent wind, and mooring break have been taking into account. Using OrcaFlex and FAST to calculate the dynamic response of FOWT under the combined action of wind, wave and current. The time-domain response of floating foundation, mooring tension, blade root contact force, aerodynamic power, and wind rotor thrust are obtained. And the effect of the turbulent wind and mooring break at different positions on the FOWT are studied. The results show that compared with the platform motion and mooring tension, the aerodynamic power and rotor thrust are more sensitive to the turbulent wind, and there are fluctuations in amplitude and multiple peaks in the frequency spectrum. Compared with the leeward side, the mooring break on the windward side is a more dangerous situation, and it is easy to cause the collapse of platform and the break of the remaining mooring. The mooring break on the leeward side is relatively safe, and it will produce a drift in the sway direction, and have little impact on the safety of the wind turbine.