A porous-wavemaker theory is developed to analyse small-amplitude surface waves on water of finite depth, produced by horizontal oscillations of a porous vertical plate. Analytical solutions in closed forms are obtained for the surface-wave profile, the hydrodynamic-pressure distribution and the total force on the wavemaker. The influence of the wave-effect parameter C and the porous-effect parameter G, both being dimensionless, on the surface waves and on the hydrodynamic pressures is discussed in detail.

A porous wavemaker theory

Hydrodynamic analysis of floating breakwater with perforated structure based on the Taylor expansion boundary element method

In order to improve the understanding of hydrodynamic performances of spar-type Floating Offshore Wind Turbines (FOWTs), in particular the effect of wave-current-structure interaction, a moored 6MW spar-type FOWT in regular waves and uniform current is considered. The wind loads are not considered at this stage. We apply the potential-flow theory and perturbation method to solve the weakly-nonlinear problem up to the second order. Unlike the conventional formulations in the inertial frame of reference, which involve higher derivatives on the body surface, the present method based on the perturbation method in the non-inertial body-fixed coordinate system can potentially avoid theoretical inconsistency at sharp edges and associated numerical difficulties. A cubic Boundary Element Method (BEM) is employed to solve the resulting boundary-value problems (BVPs) in the time domain. The convective terms in the free-surface conditions are dealt with using a newly developed conditionally stable explicit scheme, which is an approximation of the implicit Crank–Nicolson scheme. The numerical model is firstly verified against three reference cases, where benchmark results are available, showing excellent agreement. Numerical results are also compared with a recent model test, with a fairly good agreement though differences are witnessed. Drag loads based on Morison’s equation and relative velocities are also applied to quantify the influence of the viscous loads. To account for nonlinear restoring forces from the mooring system, a catenary line model is implemented and coupled with the time-domain hydrodynamic solver. For the considered spar-type FOWT in regular-wave and current conditions, the current has non-negligible effects on the motions at low frequencies, and a strong influence on the mean wave-drift forces. The second-order sum-frequency responses are found to be negligibly small compared with their corresponding linear components. The viscous drag loads do not show a strong influence on the motions responses, while their contribution to the wave-drift forces being notable, which increases with increasing wave steepness.

/pdf/hydrodynamic-responses-of-a-6-mw-spar-type-floating-offshore-5bsema5ppt.pdf

Hydrodynamic Responses of a 6 MW Spar-Type Floating Offshore Wind Turbine in Regular Waves and Uniform Current

Potential flow theory-based analytical and numerical modelling of porous and perforated breakwaters: A review

A novel solution to the second-order wave radiation force on an oscillating truncated cylinder based on the application of control surfaces

Second-order Taylor expansion boundary element method for the second-order wave radiation problem

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.

J.K. Chen

Papers

Second-order Taylor expansion boundary element method for the second-order wave radiation problem

Hydrodynamic analysis of floating breakwater with perforated structure based on the Taylor expansion boundary element method

Time-domain TEBEM method for wave added resistance of ships with forward speed

The numerical study of viscous drag force influence on low-frequency surge motion of a semi-submersible in storm sea states

Time domain TEBEM method of ship motion in waves with forward speed by using impulse response function formulation