Wave diffraction from a concentric truncated cylinder system with a porous ring plate fixed inside

Highlights

• The wave diffraction from a concentric truncated cylinder system was studied.

• The theory and program were validated by similar models in previous works.

• The effect of some parameters on the hydrodynamic performance was discussed.

Abstract

The diffraction problem of a concentric truncated cylinder system with a porous ring plate fixed inside is studied in the framework of linear potential theory. The system consists of a porous exterior cylinder and an impermeable interior cylinder, which are connected by an impermeable top and bottom plate, and a porous ring plate arranged below the free surface. Darcy’s law is applied to the porous boundaries under the assumption of fine pores. The velocity potential of the whole fluid domain is analytically derived by the method of variable separation and eigen-function expansion. The hydrodynamic loads of the system are obtained by integrating the pressure on the wet surface. The calculation results of the present paper are compared with the previous works with similar models to verify the correctness of the model. The effect of the dimensionless porous effect parameter of the ring plate and of the exterior cylinder, the draft–depth ratio of the ring plate, the draft–depth ratio of the system, the ratio of the interior and exterior radii are discussed. The results show that appropriate permeability and structural scale parameters can improve the hydrodynamic performance of the structure, which will provide directive guidance for engineering design.

Introduction

Porous structures have extensive application prospects in the field of ocean engineering (e.g. floating airport, semi-submersible platform, breakwater, net cage and etc.) due to their ability to reduce hydrodynamic loads acting on the coastal structures. In recent decades, researchers have carried out substantial theoretical and experimental studies on various types of porous structures, especially the porous plate and porous cylinder.

The analytical solution of wave interaction with submerged porous plate was first given by Chwang and Wu (1994), where the method of eigen-function expansion was used in the framework of linear potential theory. The thickness of the porous plate was assumed to be zero, and Darcy’s law was applied to the boundary condition of the plate. Their results showed that the porous plate with appropriate porosity could reduce the wave surface elevation near the plate, which is similar to the behavior of wave absorbers. Later, many scholars used this method to study various types of porous plate, for example, a pitching porous plate (Yip and Chwang, 1998), a submerged horizontal porous plate with a finite thickness (Liu et al., 2012), etc. The complex wave number is involved in the above problems. For the purpose of avoiding the trouble of complex wave number, some researchers (Liu et al., 2011, Liu and Li, 2011, Cho and Kim, 2013, Zhao et al., 2017) used the method of expanding the vertical derivative of velocity potential along the radial direction to study the submerged plate. A detailed review of the early work on the interaction between wave and a submerged plate can be found in Yu (2002).

On the other hand, many researchers are interested in the interaction between the water wave and the porous cylinder. Wang and Ren (1994) investigated the protective effect of the porous exterior cylinder on the impermeable interior cylinder in a concentric cylinder system. The results show that the porous exterior cylinder can significantly reduce the hydrodynamic loads and wave run-up of the interior cylinder. Williams and Li (2000) researched an array of bottom-mounted surface-piercing porous cylinders. The results further confirmed that the porous cylinder has stronger survivability than the impermeable cylinder. To find the structure with better hydrodynamic performance, many scholars (Park et al., 2010, Mandal et al., 2013, Park and Koo, 2015, Ning et al., 2017, Sarkar and Bora, 2019, Behera et al., 2020) have studied various types of porous compound cylinder system.

It is worth noting that Bao et al. (2009) investigated a semi-submerged porous circular cylinder, which combines a porous plate with a porous cylinder. Later, Zhao et al. (2010) studied the interaction of wave and a porous cylinder with an inner horizontal porous plate in theory and carried out a series of experiments in a wave basin. It was found that the porous plate can make the wave dissipation more effectively. Their research is not the first case in which porous plates are combined with other wave absorbing structures. Wu and Chwang (2002) studied the wave diffraction by a vertical cylinder with a porous ring plate. Liu et al. (2007) examined the hydrodynamic loads of a perforated wall breakwater with a submerged horizontal porous plate. Their research showed that careful design of the size and porosity of the compound structures with plates will lead to significant reduction of hydrodynamic loads.

In this paper, the wave diffraction from a concentric truncated cylinder system with a porous ring plate fixed inside is studied. The model consists of an interior cylinder, an exterior porous cylinder, a porous ring plate, an impermeable top plate and an impermeable bottom plate. The interior cylinder and exterior cylinder are connected by the impermeable top and bottom plate, and a porous ring plate below the free water surface. We assume that the ratio of the thickness of the porous ring plate and the exterior cylinder to the incident wavelength is very small, so the thickness of them can be ignored. This structure makes full use of the wave attenuation ability of the porous ring plate and the porous cylinder, which is expected to obtain better hydrodynamic performance. Simultaneously, the porous ring plate in this model adds another connection to the interior and exterior cylinders, which can enhance the ability of the system to resist wave attack. Therefore, compared with the composite truncated cylinder system without the ring plate, this structure has better connection performance due to the reinforcement effect of the ring plate. In this paper, based on the linear potential theory, the analytical solution of diffraction from a concentric porous truncated cylinder system with a porous ring plate fixed inside is derived by the method of eigen-function expansion. According to the solution, the influence of various wave parameters and structural parameters on wave load is studied.

The governing equations and boundary conditions are introduced in Section 2. The derivation method of the diffraction analytical solution and the calculation method of the hydrodynamic loads are presented in Section 3. Some numerical results are given in Section 4. The last section summarizes the conclusion of this paper.