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The interaction of water waves with partially porous-surfaced circular cylinders was investigated. A three-dimensional numerical modeling was developed based on the complete mathematical formulation of the eigenfunction expansion method in the potential flow. Darcy’s law was applied to describe the porous boundary. The partial-porous cylinder is composed of a porous-surfaced body near the free surface, and an impermeable-surfaced body with an end-capped rigid bottom below the porous region. The optimal ratio of the porous portion to the impermeable portion can be adopted to design an effective ocean structure with minimal hydrodynamic impact. To scrutinize the hydrodynamic interactions in

Since a circular cylinder has the advantage of a hydrodynamic effect without directivity, an array of vertical circular cylinders is commonly used for coastal and offshore structures. Examples include floating airports, bridges, semisubmersibles, and wave power-conversion systems. In order to design a reliable marine structure that will withstand severe environmental conditions, accurate prediction of hydrodynamic interactions with multibodied structures must be considered. Therefore, research in the area of hydrodynamics has primarily been focused on optimizing systems to avoid significant hydrodynamic impacts. The fundamental idea of dampening the hydrodynamic impact directly on the structure has recently been introduced. One concept involves using porous-surfaced bodies, which can reduce the influence of wave-body interaction through pores on the body surface.

The following is a brief summary of previous research on multibodied circular cylinders with impermeable or porous surfaces. Under the assumption of potential flow and linear wave theory, Spring and Monkmeyer [

For the analysis of

In the present study, with complete mathematical formulations, a three-dimensional potential-flow-based numerical method for an array of surface-piercing, partial-porous cylinders was developed using the eigenfunction expansion method and Darcy’s law. The partial-porous cylinder is composed of a porous-surfaced body located near the free surface and a rigid-surfaced body with a rigid end-capped bottom below the porous region. This new type of structure can be used for a variety of marine applications, which require minimum hydrodynamic impact coupled with maximum buoyancy of the submerged module. Using the numerical method, the dynamic response of the new structure due to wave excitation and seismic forces was calculated by Park et al. [

In order to verify the developed numerical method, the results for an array of truncated full-body porous cylinders are compared with the experimental data of Zhao et al. [

The boundary value problem for an array of partial-porous circular cylinders can be described using linear potential theory. The fluid in the computational domain is assumed to be an incompressible, inviscid, and irrotational flow. The water particle velocity in the fluid domain can be described using the gradient of the velocity potential

Coordinate system for an array of surface-piercing partial-porous cylinders.

The array of surface-piercing partial-porous stationary cylinders is subjected to a train of regular waves of height

As a governing equation, the Laplace equation is satisfied for the entire fluid domain of the present boundary value problem:

For solving the governing equation, the following boundary conditions for the free surface (

The incident wave potential in the

The scattered wave potential from the cylinder

When combining the incident wave potential (equation (

Using Graf’s addition theorem for Bessel functions [

The wave potential of the

The wave potential beneath the

In order to account for the porous-body boundary condition, the circular cylinder near the free surface has a thin-surfaced wall containing small pores, which allow water particles to pass through, where Darcy’s law (

Substituting (

In the case of

In the case of

For the second matching condition between regions 2 and 3 in (

In the case of

In the case of

Applying the orthogonal property to the first and third matching conditions in (

In the case of

By applying (

In the case of

In order to calculate the potential coefficients

Using a standard matrix technique, the

After solving the velocity potentials, the wave excitation forces on each cylinder can be obtained from integrating the pressure on the wetted surface. Surge (

In order to verify the wave forces on a single porous cylinder, the calculated results are compared with given experimental results of Zhao et al. [

Comparison of numerical results with experimental results for

Figure

Comparison of total wave forces on four cylinders with

In order to examine the effect of porosity strength, the respective wave forces on four full-porous and partial-porous cylinders for various porosity parameters (

Wave forces on four cylinders with

Heave forces on partial-porous bodies are much greater than those on full-body porous cylinders, regardless of porosity strength. For the vertical wave loads observed in Figures

Figure

Wave forces on four partial-porous cylinders with

In order to evaluate the wave forces on each cylinder at different locations with an incident wave angle of 45°, the horizontal and vertical forces on full-rigid and partial-porous cylinders are compared in Figure

Comparison of wave force on each cylinder with

Figure

Comparison of wave run-up on each cylinder for various porosity depths with

In order to evaluate the effect of the porous wall-depth

Comparison of maximum wave run-up at two locations with

In Figure

Comparison of maximum wave run-up on four cylinders with

Figure

Snapshot of free surface elevations for four partial-porous cylinders with

Figure

Comparison of wave forces on four partial-porous cylinders for various cylinder gap distances (

The average wave forces for four-cylinder and nine-cylinder structures are compared in Figure

Comparison of average wave forces for four-cylinder and nine-cylinder cases with

Under the assumption of potential flow and linear wave theory, a 3D numerical method for an array of surface-piercing partial-porous stationary cylinders was developed using the eigenfunction expansion method and Darcy’s law, with a complete form of the mathematical formulations. This model was used to scrutinize the hydrodynamic properties of

The greatest wave run-up for the four rigid bodies was observed at the rear of the foremost cylinder against wave propagation direction, implying that the hydrodynamic interaction between four cylinders can magnify the wave run-up. The run-up for the partial-porous cylinder was less influenced by the cylinder location, however, because of the reduction in wave-body interaction. The role of porosity in diminishing the run-up height may be retained when the porous-surfaced wall is installed to only a quarter of the total body draft. Finally, this method for an array of partial-porous cylinders can be used to optimize the design of structures in order to reduce the wave loads to which they are subjected.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This study was supported by Korea Institute of Marine Science and Technology Promotion through the research project “Safety evaluation of concrete substructure systems for offshore wind power (20120093).” This work was also financially supported by the Ministry of Trade, Industry and Energy (MOTIE), Korea Institute for Advancement of Technology (KIAT), and DongNam Institute for Regional Program Evaluation (IRPE) through the Leading Industry Development for Economic Region.