Transmission Coefficient Analysis of Notched Shape Floating Breakwater Using Volume of Fluid Method : A Numerical Study H )

’'Department of Ocean Engineering, Institut Teknologi Sumatera, South Lampung 35365, Indonesia 2) Department of Ocean Engineering, Faculty of Marine Technology, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia 3) Department of Naval Architecture, Faculty of Marine Technology, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia *' Corresponding Author : asfarur.ridlwan@kl.itera.ac.id


Introduction
The breakwater is one of the coastal structures designed to protect ships, marine ecosystems, port facilities, and coastal protection against waves. The conventional breakwater is generally applied in shallow water, and its geometry is a bottomfounded structure. The unconventional breakwater is known as the floating breakwater for deep water. It is found that there are several advantages of the floating breakwater, such as more environmentally friendly to pollution and sedimentation problems because it does not inhibit water circulation [1] and easy to relocate to another location [2], When seawater level (SWL) rises due to tides or climate change, floating breakwater can adjust, which is more economical than a bottom-founded structure. Further, floating breakwater may be the only solution for high load structures to poor soil conditions [3], Scientists and engineers did a tremendous development of floating breakwater research either experimentally, numerically, or a combination of both. Most research has usually been conducted to analyze various geometric shapes, configurations, or bilge keels of the floating breakwater on the wave characteristics. Recently, the interest in both numerical and experimental studies of floating breakwaters is increasing. Christensen and Bingham [2] conducted physical experiments and numerical modeling to evaluate transmission, reflection, and performances of regular pontoon (RG), wing plate (WP), and porous media (WP-P100). The study showed that wing plates (WP) reduced the floating breakwater motions, while WP and (WP-P100) reduced the refection and transmission more effectively. An experimental study for a dual rectangular pontoon floating breakwater with two treatments (single-row and double-row) is conducted by [4], The result indicated that double-row floating breakwater significantly reduced transmission, especially for short-period waves, compared to the single-row floating breakwater. Moreover, Cho [5] investigated the transmission of incident waves interacting with vertical porous side plates using the matched eigenfunction expansion method (MEEM). Wang and Sun [6] conducted an experimental study of a porous floating breakwater with large fabricated numbers of diamond-shaped blocks to reduce transmitted wave height and mooring force. Furthermore, the review by [7], [8], [9] conducted an experimental new type of floating breakwater. The result showed that a new type of floating breakwater's transmission coefficient had better than the traditional regular pontoon. A numerical study of a single pontoon floating breakwater to estimate the nonlinear dynamics using the volume of fluid (VOF) method is investigated in [10], Lastly, a numerical simulation of wave overtopping performance above caisson breakwaters utilizing the VOF method is reviewed [11], The hydrodynamics performance of cylindrical floating breakwater using the VOF method is investigated in [12], The result showed that the transmission coefficient is sensitive, especially in small wave height for regular and random waves. Subsequently, a wing box-type and four typical box-type floating breakwaters have been studied by [13], [14] using SPH numerical simulation. The numerical results show that the protruding plate can reduce wave energy [13], The floating breakwaters have better performance in the larger and lighter breakwaters and greatly sensitive to the immersion depth [14], The energy dissipating performances and motion responses of floating breakwaters under regular or irregular waves are investigated using numerical simulation [15], Under regular waves, the wave transmission (CT) decreases with H/L and B/L when B/L < 0.35, while under irregular waves observed the negative correlation between pitch motion and wave transmission. Also, numerical simulations of three kinds of floating breakwaters are examined in regular waves to compare the performance by [16], Furthermore, based on the previous studies, there is no investigation regarding the optimal transmission coefficient of floating breakwater using a basic geometric shape applied to the floating breakwater's front side to reduce wave energy.
They only examined the basic geometry as the floating breakwater body, not used to the front side (porous). Whereas, based on previous research, porous breakwaters are very effective in reducing the transmission coefficient.
This study aims to develop floating breakwater models by optimizing the wave transmission coefficient (CT) due to the wave force. The study is expected to contribute to the development of ocean floating breakwater in Indonesia's coastline. In this analysis, a numerical study is calculated by CFD based on the VOF method using Flow 3D Software. The basic model (regular ponton (RG) floating breakwater) is modified into several notched shapes. Three floating breakwater models, such as square notch (SQ.), circular notch (CN), and triangular notch (VN), were developed. Data parameters and numerical models were validated by the result of experiments conducted by [2], The CFD model development will be explained in detail in the next section. 42 2. Materials and Methods

Floating Breakwater Simulation
Floating breakwater geometry was based on the regular pontoon experiment test [2], The experiment conducted a twodimensional physical model test where cross-sections were tested and analyzed in the wave flume. The data parameter of regular pontons is shown in Table 1, and the basic cross-section of the regular pontoon is illustrated in Figure 1. Furthermore, the experimental model will be developed on a porous shape on the side plates with numerical simulations using CFD to optimize wave transmission. The variation of the developed model floating breakwater can be seen in Figure 2.

Data Parameter
The data were composed of wave parameters that were scaled using Froude scaling by 1:65. Froude scaling was considered valid as long as viscous effects are negligible. The 2nd stokes wave was used in this simulation because the relationship betweenvs -(see Table 2) gets the 2nd order stokes area in the wave theory (see Figure 4). Table 2 shows the condition of the wave data parameter for numerical simulations.

Wave Flume
The flume dimensions are 28 m in length, 0.6 m in width, 0.8 m in height, and 0.615 m in the initial surface elevation. The flume was filled with fresh water with a density of 1000 kg/m3. The flume was equipped with a wavemaker at one side and a wave absorber at the other side. The floating breakwaters were placed almost cover the entire width of the flume to reduce the sidewalls' effect. The illustration of the wave flume can be seen in Figure 6.

Wave Measurement and Analysis
The motion response of floating breakwaters is not described in six degrees of freedom (DOF). The objective of this study is to obtain the transmission coefficient (CT), the ratio of transmitted wave height (HT) to incident wave height (Hi).
The transmission coefficient can be shown in Eq. 1 as follow: (1) Measurement of transmitted and incident wave heights was represented by surface elevation using wave gauges. A total of four-wave gauges were placed on the incident side, while three-wave gauges were placed on the left side, as illustrated in Figure 7.

Stokes Wave Theory
The 2nd order Stokes wave can be generated at a mesh boundary. The 2nd order Stokes wave theory is used to simulate the model developed by Fenton [17], The Stokes wave theory is a nonlinear wave with higher wave amplitude than the Airy wave theory. Figure 3 described the stokes wave entering the left side of the computational domain where the wave train is assumed to come from the flat bottom reservoir to the computational domain by crossing the mesh boundary. The free surface elevation (x,t), and the velocity in x and z directions u(x,z,t) and w(x,z,t) of the 2nd order stokes wave theory is as follow: ( , ) = + cos also known as wave steepness, X=x-ct, and kX=kxt, k is the wave number, and is the angular frequency. The coefficient A_(i,j), B_(i,j), and C_0 are nonlinear functions of kd and are presented in [18], Figure 4 shows the selection of wave theory based on the dimensionless ratio ofand -.

Where
The wave is assumed to come from a flat bottom reservoir, which is outside the computational domain.

CFD Modelling
In this research, CFD modeling has been used using Flow 3D software. In Flow 3D, the fluid flow environment is limited by boundary conditions to simulate the particular investigation area's surrounding effects. The principle of Flow 3D described the behavior of fluid flow in which the equation of fluid motion was solved by RANS (Reynolds Averaged Navier-Stokes) equation, as shown in Eq. 5. The solution of the equation of motion of fluid flow for control volume was carried out on a staggered and structured finite-difference grid [12], The simulation was conducted by preparing a computational grid in Flow 3D using a rectangular grid. The free surface was tracked by combining the VOF method with the Reynolds Averaged Navier-Stokes (RANS) equation. In the computation of turbulence flows, Renormalization-Group (RNG) turbulence was used because it has a low Reynold number effect [19] and has the most accurate for the best real-world problems [17], The RNG group model uses equations similar to the equations for the k-e model. This approach applied statistical methods to derivate ( , , ) Kapal: Jurnal Ilmu Pengetahuan dan Teknologi Kelautan, 18(1) (2021): 41-50 the average equations for turbulence quantities, such as turbulent kinetic energy and dissipation rate. Generally, the RNG group model has wider applicability than the standard k-e model [17], The equations of motion for the fluid velocity components Stokes equations with some additional terms. The equation is as follow: 45 in the three coordinate directions are the Navier- (5) are flow losses in porous media or across porous baffle plates, and the final terms account for the injection of mass at a source represented by a geometry component Where are body accelerations, are viscous accelerations, and

Boundary Condition
The simulation was used by Flow-3D software. The simulation was firstly conducted by modeling the floating breakwater geometry in the stereolithographic format (.stl format). Then, the .stl file format was imported into the Flow-3D software. Then, the computational domain wave flume as a boundary condition set was arranged. The boundary condition was used to assume the solution at the boundaries (boundary condition setting) and initial time (initial conditions) and also to use these values to solve the partial differential equation (PDE) governing in the domain [17], The purpose of boundary conditions was to determine model conditions that represented the experimental condition. The view of the model can be seen in Figure 5. Boundary conditions used in the model are as follow: Wave: A wave boundary condition was defined at left (X Min). A surface wave entered the computational domain and propagated in the direction normal to the boundary. The wave was set 2nd stokes as wave generator represent the physical wave conditions at the boundary.
Outflow: The outflow boundary condition was defined at right (X Max). It allowed users to investigate the effects of wave interactions with structures numerically. The capability permitted a reduction in the extent of the computing mesh needed for accurate computations. A wave-absorbing layer was used to reduce the reflection of the periodic wave at an open boundary.
Symmetry: The symmetry condition was defined at the front (Y Min), behind (Y Max), below (Z Min), and up (Z Max).
No-slip conditions were imposed using the wall shear-stress options described in the Prandtl Mixing Length model. The symmetry condition can be specified as free-slip conditions that have a non-zero wall shear-stress.

Meshing
Mesh block was used to determine the modeled area. The smaller mesh will be more detailed, but the output files will be larger, and the simulation run longer. Floating breakwater modeling used one mesh block with a meshing size of 0.04 m at a total length (X-axis) of 28 m, total width (Y-axis) of 0.6 m, and total height (Z-axis) of 0.8 m. See Figure 8

Model validation
Validation was conducted by comparing the experimental results of the transmission coefficient by [2] with the numerical study of the CFD aided with Flow 3D Software. Christensen has surveyed three floating breakwater shapes, but only one Regular Pontoon (RG) was validated in this study. The purpose of validation was to find out whether the numerical analysis was suitable for the experimental result. Further, when the verification was conducted, the model's development can be explored for other optimal shapes.
In this study, validation is conducted based on comparing the transmission coefficient between numerical test and experimental test. The error rate refers to the Mean Absolute Percentage Error (MAPE) theory [20], The MAPE theory can be seen in detail in Table 3. The validation results can be seen in Figure 10 and Table 4. Based on the MAPE theory, this study can be validated with good agreement because the error rate between CT of experiment and CT of numeric is still below 10%. Therefore, it can be developed with more optimal shapes. Regular Pontoon (RG) is one type of floating breakwater that was examined by [2] and validated with a numerical model. Figure 9 is the shape of the wave profile and the distribution of the current velocity through the structure in one wave variation with time series. The reduction in wave height at the rear of the structure can be seen with the transmission wave profile that is more gentle than the incident waves. A decrease follows the decrease in wave height in the current velocity, which is indicated by the change in the velocity contour's gradation. When the waves are higher and directly in front of the structure, the current tends to be faster. When the waves are lower and behind the structure, the current speed tends to be slower. Both of these can be seen by changing the current velocity contours. Therefore, the fluid flow velocity is also affected by a structure's presence and directly proportional to the wave height. The velocity pattern can be seen Figure 9, and the validation of the transmission coefficient of numerical simulation results can be seen in Table 4. The transmission coefficient is obtained from the analysis of the output surface elevation results in Flow 3D software, as shown in Figure 10. Surface elevation data used to analyze the transmission coefficient are obtained from wave gauge 1 (in front of the structure) and wave gauge 5 (behind the structure). Surface elevation data is converted into wave height using Wave Analysis (WAVAN) coding. Then, to get the transmission coefficient, the calculation is according to Eq. 1. The results of regular pontoon coefficient transmission are shown in Table 4.

Transmission Coefficient Development Notched Shape
The wave transmission coefficient (CT) due to the wave force to the structure is estimated. There are several factors that influence it; one of them is wave steepness (H/gT2). The modeling results obtained free surface elevation data for each wave observation point and velocity magnitude data for each current velocity observation point.
The wave data used in the transmission coefficient (CT) analysis is based on the processed free surface elevation data for all predetermined observation points. The data obtained is in water level vs. time series data in meters and seconds. The wave data is then analyzed with WAVAN coding to determine the average period (T) and average wave height (H) for each observation point. This is done for the wave observation points at the front and back of the structure. The wave height in front of and behind the structure is then used to determine the transmission coefficient (CT), which is represented by CT on X-axis and the wave steepness (H/gT2) in Y-axis There are three notched shapes of the floating breakwater, as illustrated in Figure 2. In this analysis, Flow 3D software is used to obtain the transmission coefficient of Regular Pontoon. The results of coefficient transmission of three different notched shapes are shown in Table 5. The average value of the transmission coefficient each of 0.6248, 0.6886, and 0.6735. The smaller the transmission coefficient value, the more optimal. It can be summarized that the square notch (SQ.) model is the most optimal floating breakwater structure.

Conclusion
The study presents a numerical analysis to analyze optimum transmission coefficients of three different notched models of the floating breakwater. Numerical simulation was validated with the experimental test. The result shows lower limits of error with an error rate of 8.5%. So, it can be developed for more optimum notched shape models. Some models are overestimated, which may be common as a numerical approach and can be tolerated. It is a high prediction approaching experimental trial results.
Simulation results show the transmission coefficient created by the wave parameters, specifically wave period and high wave. To minimize the value of the transmission coefficient, it can use the developed notched model in front of the floating breakwater structure. Three development models: square notch (SQ.), circular notch (CN), and triangular notch (VN), have an average transmission coefficient of 0.6248, 0.6886, and 0.6735, respectively. It can be summarized that the smaller the transmission coefficient value, the more optimal the model. The square notch (SQ) model is the most optimal floating breakwater structure.
Based on the research results, the square notch (SQ) model is the most optimal floating breakwater in reducing wave energy. The experimental study can be carried out using the square notch (SQ) model as the optimum breakwater notch shape in further research. The square notch (SQ) model's motion can be analyzed and compared with a numerical approach.