Wave attenuation by multiple slotted barriers with a zig-zag arrangement -A physical and numerical approach

Abstract

In the present study, scattering of surface gravity waves by multiple slotted vertical barriers arranged in a zig-zag manner is analyzed by employing Computational Fluid Dynamics (CFD) and validated with physical model tests. The porosity of the vertical slotted barrier is varied from 10% to 40%, and the number of slotted barriers varied from 1 to 6. The results from CFD correlate well with the laboratory measurements on the scattering coefficients for a wide range of input conditions giving a high level of confidence. For relatively short waves ($h/\lambda$ > 0.3, $h$- water depth and $\lambda$- wave length), slotted barriers up to 3 numbers and porosity from 20% to 30% are required to achieve wave transmission coefficient in the range of 0.2 to 0.3. For relatively long waves ($h/\lambda$ < 0.3), slotted barriers of 5 to 6 numbers and porosity in the range of 10% to 20% are needed to obtain wave transmission of 0.2 to 0.3. The results presented in this study can be used for a wide range of wave damping applications in the field of coastal engineering.

Introduction

Rubble mound offshore breakwater is widely used around the world as breakwaters and for damping of gravity waves in the coastal area Hudson (1959), Van der Meer (1987), Van der Meer and Daemen (1994). Rubble mound breakwaters are efficient for wave damping. However, one of the main issues is that the volume of rocks required with an increase in water depth is disproportionate, and the project becomes prohibitively expensive. For example, the volume of stone needed for 4 m and 8 m water depth (with a 1:1.5 seaward and leeward slope and 4 m crest width) increases the volume of rocks from 112 m³/m to 160 m³/m. Quarrying rocks from mountains is also considered an environmentally degrading activity. The engineers are looking for solutions that help reduce the volume of natural resources for sustaining the development of coastal space development activities Schoonees (2019). Marine space development is expensive due to the long construction activities due to limited weather windows available every year and high mobilization costs to retain the machines and construction logistics such as floating barges, cranes, divers, construction quality assurance personnel, etc. The pressure on the seabed due to the self-weight of rubble increase with water depth. Kumaran et al. (2021) studied the assessment of dynamic wave pressure on the vertical breakwater in the transitional depth of waters and made a comparison study with empirical approaches. Beyond specific depths, the pressure may exceed the bearing capacity of the local seabed and becomes challenging to construct unless significant settlement is allowed or the bearing capacity is increased. Recently, coastal engineers also look for visually elegant solutions. To satisfy all these requirements, it is required to develop a new type of wave barrier. A series of vertical porous walls built using suitable materials (reinforced concrete, fibre-reinforced plastics, etc.) can be used as wave barriers. The primary scientific requirement is to assess wave transmission, reflection, and dissipation characteristics by such wave barriers. Studies on wave transmission and wave energy dissipation of vertical slotted/perforated breakwaters have been an exciting area for the past five to six decades Terret et al. (1968),Bergman and Oumeraci (1999), Grune and Kohlhase (1974), Isaacson et al., 1998, Kriebel, 1992, Kakuno, 1983. A detailed review of the wave damping and wave loading on perforated barriers is revealed by Huang et al. (2011) in their review article. Hydrodynamic performance of up to three rows of porous vertical walls is reported by Hagiwara (1984) and by Ji and Suh (2010). It is proved that two- and three-row porous barriers have performed better than a single-slotted barrier.

Ahmed and Schlenkhoff (2014) investigate the hydrodynamic performance of a permeable breakwater in the form of a double vertical slotted barrier in FLOW-3D, VOF. There are many studies on such slotted barrier based on analytical and numerical methods, and some of the promising studies are by Chen et al. (2006), Molin and Remy (2015), Liu and Li (2017), Zhao et al. (2018), Venkateswarlu et al. (2021) and Valizadeh et al. (2018). Elahi et al. (2015) established a 2-Dimensional numerical model considering the free surface displacement, liquid viscosity, and surface tension to investigate liquid sloshing phenomenon using the Volume of Fluid method. George and Cho (2020) studied the hydrodynamic performances of vertical slotted barriers with the combination of impermeable upper, lower parts and a permeable middle part theoretically. And also, a comparative study is performed with experimental data and in StarCCM + . The combination of large eddy simulation and Volume of Fluid is performed to analyze the solitary waves propagating on single and double rows of vertical slotted piles Yao et al. (2018). Cabral et al. (2020) investigated the performance of an innovative wave energy converter by combining an oscillating water column and an overtopping device (OWEC) integrated into a Rubble mound breakwater on a geometrical scale of 1:50. Before the physical model study, the performance is numerically optimized using ANSYS Fluent. Poguluri and Cho (2021) investigated the qualitative analytical and numerical model for the efficient design of a horizontal slotted plate fixed to a seawall by reducing the hydrodynamic coefficients. Gong et al. (2020) studied the wave dissipation characteristics with the combination of two inclined plates and one horizontal plate-like mountain-type breakwater. It is revealed that in a wave with a length smaller than four times the test model, the reflected wave amplitude is slightly larger than those of the vertical-plate breakwater. The wave transmission coefficients are all smaller than 0.5, and the wave loss coefficients are smaller are larger than 0.7. To the best of our knowledge, there is no study on porous walls with more than three rows. The wave transmission characteristics of slotted vertical barriers are the functions of porosity, the number of slotted barriers, incident wave height, and wave period. Neelamani and Al-Anjari (2021) have recently carried out detailed experimental investigations on forty-two different SVB configurations by varying the porosity from 5% to 60% and the number of slotted barriers from one to 6 for a wide range of wave heights and wave periods. The technology for prefabrication of concrete panels is well advanced over the last few decades Fernandez-Ordonez (2018). Hence, it is believed that slotted vertical barriers can be prefabricated, assembled, and installed within a short period, especially for sites with narrow annual weather windows. Porous wave barriers also allow easy fish passage and sediment movement between the seaside and lee side Koutandos (2009).

With these motives in mind and to effectively dissipate the wave energy for a wide range of coastal engineering applications, a comprehensive study is carried out on the zig-zag barriers through a numerical model based on the Reynolds Average Navier–Stokes (RANS) equations. The numerical results are then verified with the well-equipped controlled laboratory measurements. The manuscript is organized as follows. The mathematical formulation, the governing equations of the numerical approach using ANSYS-FLUENT, and the selection of mesh size for the computation domain are discussed in Section 2. Section 3 elaborates the experimental setup of the multiple slotted zig-zag barriers in the glass flume of the Hydraulics and Coastal Engineering Laboratory, Kuwait Institute of Scientific Research (KISR). Section 4 focuses on the various results for understanding the effect of relative wave height, the number of slotted barriers, and porosity on the scattering coefficients, namely wave transmission, wave reflection, and energy dissipation. Finally, the main conclusions of the study are drawn in section 5.