Keh-Han Wang

Wave interaction with a concentric porous cylinder system

Abstract This is a theoretical investigation of wave interaction with a concentric surface-piercing two-cylinder system. The exterior cylinder is porous and considered to be thin in thickness and the interior cylinder is impermeable. Both cylinders are rigidly fixed at the sea bed. The fluid motion is idealized as a linearized potential flow. The free-surface elevation and the total net hydrodynamic forces acting on both cylinders are determined analytically. The wave-induced overturning moments are also evaluated. It is found that, with the existence of the exterior porous cylinder, the hydrodynamic force acting on the interior cylinder is reduced if compared to the force exerted on the interior cylinder by a direct wave impact. The reduction of the wave amplitude around the leeward side of the outer porous cylinder is shown from the free-surface computations. In this paper, results are also presented to illustrate the effects of wave parameter and structural porosity on this wave and cylinder interaction problem. The role played by the ratio of radii of the inner and outer cylinders is duscussed.

Water wave interaction with a floating porous cylinder

Abstract The interaction of water waves with a freely floating circular cylinder possessing a side-wall that is porous over a portion of its draft is investigated theoretically. The porous side-wall region is bounded top and bottom by impermeable end caps thereby resulting in an enclosed fluid region within the structure. The problem is formulated based on potential flow and linear wave theory and assuming small-amplitude structural oscillations. An eigenfunction expansion approach is then used to obtain semi-analytical expressions for the hydrodynamic excitation and reaction loads on the structure. Numerical results are presented which illustrate the effects of the various wave and structural parameters on these quantities. It is found that the permeability, size and location of the porous region may have a significant influence on the horizontal components of the hydrodynamic excitation and reaction loads, while its influence on the vertical components in most cases is relatively minor.

Wave motion over a breakwater system of a horizontal plate and a vertical porous wall

A two-dimensional analytical solution is presented to study the reflection and transmission of linear water waves propagating past a submerged horizontal plate and through a vertical porous wall. The velocity potential in each fluid domain is formulated using three sets of orthogonal eigenfunctions and the unknown coefficients are determined from the matching conditions. Wave elevations and hydrodynamic forces acting on the porous wall are computed. Reflection and transmission coefficients are presented to examine the performance of the breakwater system. The present analytical solutions are found in fairly good agreement with the available laboratory data. The results indicate that the plate length, the porous-effect, the gap between plate and porous wall, and the submerged depth of the plate all show a significant influence on the reflected and transmitted wave fields. It is also interesting to note that the submerged plate plays an important role in reducing the transmitted wave height, especially for long incident waves.

Wave motion over a group of submerged horizontal plates

Abstract Wave reflection and transmission over a group of submerged horizontal plates is investigated analytically based on the linear potential wave theory. The velocity potential in each fluid domain is formulated and the unknown coefficients are determined from the matching conditions using three sets of orthogonal eigenfunctions. The reflection and transmission coefficients are obtained to evaluate the performance of the multiple plates as a breakwater. The variations of reflection and transmission coefficients vs the plate length, incident wave length, submergence of the top plate and the gap between plates are examined and discussed.

AN EFFECTIVE WAVE-TRAPPING SYSTEM

Abstract This is a theoretical study of a breakwater-seawall wave-trapping system. The breakwater, being flexible, porous and thin beam-like, is held fixed in the sea bed and idealized as one-dimensional beam of uniform flexural rigidity and uniform mass per unit length. The seawall, being vertical, rigid and impermeable, is located behind the breakwater by a distance of L . The velocity potentials of the wave motion are coupled with the equation of motion of the breakwater. Analytical solutions in closed forms are obtained for the reflected and transmitted velocity potentials together with the displacement of the breakwater. The free-surface elevation, hydrodynamic forces acting on both the breakwater and the seawall are determined. It is found that the values of L , at which the minimum reflected-wave amplitudes reach, are in the range of 2n+1 4 λ to 3n+2 6 λ for breakwaters with different rigidity and permeability. It is shown that, when the spacing L maintains values in the range of 2n+1 4 λ to 3n+2 6 λ, the resultant amplitudes in both regions can be reduced to a favorable amount for any wave and structural parameters. It is also shown that the hydrodynamic forces on the breakwater decrease as the structural flexibility and porosity increase. However, with increases of the structural porosity and flexibility, the seawall experiences an increase of the hydrodynamic forces. Various results are presented in this paper to illustrate the effects of the structural and perous parameters together with the spacing on the response and efficiency of the breakwater-seawall wave-trapping system.

Interactions of cnoidal waves with cylinder arrays

The three-dimensional scattering of cnoidal waves by cylinder arrays are studied numerically by using the generalized Boussinesq equations. The boundary-fitted coordinate transformation and a dual-grid technique are used to simplify the finite-difference computation. Also, a set of open boundary conditions and an incident cnoidal wave are incorporated for time-domain simulation. The free-surface elevation and hydrodynamic forces on each cylinder are calculated to illustrate the evolution of nonlinear waves and their interactions with large cylinder arrays. Comparisons are made between the present nonlinear wave loads and those obtained from linear diffraction theory. The sheltering role played by the neighboring cylinders and the feature of wave interference are discussed.

A Boussinesq model for simulating wave and current interaction

A new formulation of a pair of Boussinesq equations for three-dimensional nonlinear dispersive shallow-water waves is presented. This set of model equations permits spatial and temporal variations of the bottom topography and the presence of uniform currents. The newly derived equations are used to simulate the propagation of cnoidal waves and their interactions with a uniform current in a wave channel. The modified Eulers predictor-corrector algorithm for time advancing and a central difference representation for the space derivatives are applied to the computation of the basic equations. A set of open boundary conditions is developed to effectively transmit the cnoidal waves out of the computational domain. It is found that, as expected, the wave length decreases with an opposing current and increases with a following current. The wave height increases in magnitude with an opposing current and decreases with a following current. The Mach reflection due to oblique cnoidal waves propagating into an open channel with an opposing current is also investigated. Due to the opposing current, the wave patterns are compressed into smaller saddle-like regions in comparison with the Mach reflection without current effect.

Hydrodynamic interactions of cnoidal waves with a vertical cylinder

This paper describes a study of the diffraction of periodic nonlinear shallow water waves around a vertical cylinder. The generalized Boussinesq (GB) numerical model is used to effectively simulate the propagation of cnoidal waves and the associated three-dimensional nonlinear interactions. The numerical computation is based on an Euler predictor-corrector algorithm in a curvilinear coordinate system. An approximate second-order cnoidal wave solution for the GB equations is derived and used to provide the initial and incident wave conditions. The temporal and spatial evolution of an incident cnoidal wave after interacting with a cylinder is presented. The maximum force acting on the cylinder is also computed. The GB model simulation predicts strong nonlinear and three-dimensional effects on the forces which cannot be predicted by linear theories.

Modeling propagation of pressure surges with the formation of an air pocket in pipelines

Abstract In this study, a computational model that combines the method of characteristics and the shock wave theory is developed to simulate the propagation of pressure surges in pipelines. The surge velocity and pressure change under the conditions of pressurization and depressurization are calculated. The model results show good agreement with measured data. The transient flow model is also extended to study the movement of an entrapped air pocket between interfaces. It is found the air pressure changes greatly during the early stage of formation of an air pocket. For the case of an air pocket trapped between two positive interfaces, an open surge front may be emerged from the upstream interface and eventually reverses the upstream surge to propagate upstream as a negative wave.

Mooring lines connected to floating porous breakwaters

Abstract An analytical study is conducted to investigate the behavior of a flexible, porous, floating breakwater consisting of a compliant, beam-like porous structure anchored to the sea bed and kept under tension by a small buoyancy chamber at the tip. Additional stiffness is provided by mooring lines. The velocity potentials of the wave motion are coupled with the equation of motion of the breakwater. Analytical solutions in closed forms are obtained for the reflected and transmitted velocity potentials together with the displacement of the breakwater. The free-surface elevation, hydrodynamic force acting on the breakwater, and the overturning moment are determined. The dynamic response of the breakwater in terms of bending moment and shear force are also evaluated. For an impermeable flexible floating breakwater, the agreement between the present solutions and the existing numerical results is fairly good. The results also indicate that, for any finite rigidity breakwater, the transmission coefficient increases as porous effect increases whereas the reflection coefficient decreases. The hydrodynamic force on the breakwater increases as structural rigidity increases and the force decreases as porosity increases. It is found that the reflection coefficient and the hydrodynamic force on the breakwater increase with increases of the mooring line stiffness and angle. It is also found that the role played by the axial force is negligible.