Mathematical Modeling of Moored Ship Motion in Arbitrary Harbor utilizing the Porous Breakwater

The motion of the moored ship in the harbor is a classical hydrodynamics problem that still faces many challenges in naval operations,such as cargo transfer and ship pairings between a big transport ship and some small ships.A mathematical model is presented based on the Laplace equation utilizing the porous breakwater to investigate the moored ship motion in a partially absorbing/reflecting harbor.The motion of the moored ship is described with the hydrodynamic forces along the rotational motion(roll,pitch,and yaw)and translational motion(surge,sway,and heave).The efficiency of the numerical method is verified by comparing it with the analytical study of Yu and Chwang(1994)for the porous breakwater,and the moored ship motion is compared with the theoretical and experimental data obtained by Yoo(1998)and Takagi et al.(1993).Further,the current numerical scheme is implemented on the realistic Visakhapatnam Fishing port,India,in order to analyze the hydrodynamic forces on moored ship motion under resonance conditions.The model incorporates some essential strategies such as adding a porous breakwater and utilizing the wave absorber to reduce the port’s resonance.It has been observed that these tactics have a significant impact on the resonance inside the port for safe maritime navigation.Therefore,the current numerical model provides an efficient tool to reduce the resonance within the arbitrarily shaped ports for secure anchoring.

Hydrodynamic Performance of Vertical Porous Structures Under Regular Waves

The hydrodynamic efficiency of the vertical porous structures is investigated under regular waves by use of physical models. The hydrodynamic efficiency of the breakwater is presented in terms of the wave transmission （kt）, reflection （kr） and energy dissipation （ka） coefficients. Different wave and structural parameters affecting the breakwater efficiency are tested. It is found that, the transmission coefficient （kt） decreases with the increase of the relative water depth （h/L）, the wave steepness （Hi^L）, the relative breakwater widths （B/L, B/h）, the relative breakwater height （D/h）, and the breakwater porosity （n）. The reflection coefficient （kr） takes the opposite trend of kt when D/h=l.25 and it decreases with the increasing h/L, HJL and B/L when D/h〈1.0. The dissipation coefficient （kd） increases with the increasing h/L, HilL and B/L when D/h〈_l.O and it decreases when D/h=l.25. In which, it is possible to achieve values ofkt smaller than 0.3, k~ larger than 0.5, and kd larger than 0.6 when D/h=1.25, B/h=0.6, h/L〉0.22, B/L〉O. 13, and H/L 〉0.04. Empirical equations are developed for the estimation of the transmission and reflection coefficients. The results of these equations are compared with other experimental and theoretical results and a reasonable agreement is obtained.

不均匀海底地形影响下柔性板与斜向来浪的相互作用

The present work analyzes the interaction of oblique waves by a porous flexible breakwater in the presence of a step-type bottom.The physical models for both scattering and trapping cases are considered and developed within the framework of small amplitude water-wave theory.Darcy’s law is used to model the wave interaction with the porous medium.It is assumed that the varying bottom extends over a finite interval,connected by a finite length of uniform bottom near an impermeable wall,and a semi-infinite length of bottom in the open water region.The boundary value problem is solved using the eigenfunction expansion method in the uniform bottom regions,while a modified mild-slope equation(MMSE)is used for the region with the varying bottom.Additionally,a mass-conserving jump condition is employed to handle the solution at slope discontinuities in the bottom.A system of equations is derived by matching the solutions at interfaces.The reflection coefficient and force on the breakwater and impermeable wall are plotted and analyzed for various parameters,such as the length of the varying bottom,depth ratio,angle of incidence,and flexural rigidity.It is observed that moderate values of flexural rigidity and depth ratio significantly contribute to an optimum reflection coefficient and reduce the wave force on the wall and breakwater.Remarkably,the outcomes of this study are assumed to be applicable in the construction of this type of breakwater in coastal regions.

Direct Numerical Simulation of Interaction Between Wave and PorousBreakwater Based on N-S Equation

In this paper, a numerical model is established. A modified N-S equation is used as a control equation for the wave field and porous flow area. The control equations are discreted and solved by the finite difference method. The free surface is tracked by the VOF method. The pressure field and velocity field of the whole flow area are solved by the reiterative iteration method. Finally, compared with the physical model test results of wave flume, the numerical model established in the present study is validated.

Hydrodynamic Performance of A Porous-Type Land-Fixed Oscillating Water Column Wave Energy Converter

A hybrid, porous breakwater-Oscillating Water Column(OWC) Wave Energy Converter(WEC) system is put forward and its hydrodynamic performance is investigated using the fully nonlinear, open-source computational fluid dynamics(CFD) model, OpenFOAM. The permeable structure is positioned at the weather side of the OWC device and adjoined to its front wall. A numerical modelling approach is employed in which the interstices within the porous structure are explicitly defined. This permits the flow field development within the porous structure and at the OWC front wall to be observed. The WEC device is defined as a land-fixed, semi-submerged OWC chamber. A range of regular incident waves are generated at the inlet within the numerical tank. The OWC efficiency and the forces on the structure are examined. Results are compared for the simulation cases in which the porous component is present or absent in front of the OWC chamber. It is found that the incorporation of the porous component has minimal effect on the hydrodynamic efficiency of the OWC, reducing the efficiency by less than 5%. Nevertheless,the forces on the front wall of the OWC can be reduced by up to 20% at the higher wave steepness investigated,through inclusion of the porous structure at the OWC front wall. These findings have considerable implications for the design of hybrid OWC-breakwater systems, most importantly in terms of enhancing the durability and survivability of OWC WECs without significant loss of operational efficiency.

Wave Damping and Refraction-Diffraction Due to Variable Depth Porous Bottom

The refraction-diffraction of surface waves due to porous variable depth has been the subject of many investigations. In the present study, we extend the boundary-value problem of impermeable varying topography to that of a variable depth porous seabed, which is the situation most likely to be encountered in practical prob-lems of coastal engineering. A wave-induced fluid motion is applied to the porous bottom, while the well-known linear potential theory is applied to the free-water above the bottom. Eigenfunction expansions are employed to derive the matching condition and the so-called modified dispersion relation. As a result of the porous bottom, the wavenumber becomes a complex value, of which the real part represents the spatial periodicity while the imagi-nary part refers to the energy dissipation. The characteristics of water waves over a porous bottom are studied in detail. By neglecting the non-propagating modes which only have a local effect and damp exponentially with dis-tance, we derive a mathematical model to represent the characteristics of both the wave refraction-diffraction and wave-damping. The developed model is applied to the damping problem of waves over submerged porous breakwaters.