Numerical Modeling of Hydrodynamic Performance on Porous Slope Type Floating Breakwater Numeričko modeliranje hidrodinamičke izvedbe na poroznom kosom tipu plutajućeg lukobrana

A fl oating breakwater is a coastal building that aims to break up or withstand wave energy that enters the beach so that the characteristics of the incoming waves are by calculations and can reduce abrasion on the shoreline. Designing a fl oating breakwater is very complicated because it depends on many aspects. These fundamental aspects depend on each other, so if one of these aspects changes, the integrity of the fl oating breakwater structure will also change. One of these aspects is the magnitude of the transmission and refl ection coeffi cients generated by the fl oating breakwater. This research will study the hydrodynamic performance of fl oating breakwater due to variations in slope and porosity in reducing and refl ecting waves with computational fl uid dynamics (CFD). The slope-porous fl oating breakwater dimension is based on previous experimental data, including a constant water depth of 0.75 m, a wave height of 0.05 - 0.125 m, and a wave period of 1.1 - 2 sec on regular waves. The results of the numerical model validation and experiments on all variations of the fl oating breakwater model are quite good, which is less than 10% for both wave transmission and refl ection. Analysis of the infl uence of changes in the mooring line angle, the simulation is carried out at an angle of 30 deg to 90 deg and produces an average transmission coeffi cient of 0.79 and a refl ection of 0.21. While the eff ect of changes in water level elevation (0.85 m, 0.75 m, and 0.65 m) gives a reasonably signifi cant average transmission coeffi cient of 0.85 and a refl ection of 0.13. The mooring line angle will be gentler at high tide


INTRODUCTION / Uvod
The propagation of waves to the coast can be diff raction, refraction, shoaling, transmission, and refl ection processes that will aff ect changes in wave energy on the beach.Wave energy has a broad spectrum, so its comprehensive treatment is often complicated, and this is an exciting aspect for coastal engineers.Many coastlines experience coastal de-stabilization conditions due to erosion and sedimentation.These two factors will endanger the potential of coastal areas by disrupting coastal resources and wealth and economic activities in coastal areas, such as tourism, aquaculture, housing, mangroves, sandy beaches, infrastructure, ponds, and others [1][2][3][4][5].In addition, the propagation of high waves can also aff ect the mooring of ships and loading and unloading activities at the port.Calm sea wave conditions are needed so that activities at the port can run smoothly.
Regional planning for coastal activities requires consideration of factors of natural conditions and the surrounding environment and other economic factors.So often, coastal activity areas are selected based on topographical conditions that can provide natural protection in planning, such as an island-protected beach.In some cases, wave protection with natural topography often does not meet the required protection demands, so an artificial coastal protection structure is needed that can absorb the waves [6].The natural condition of the waves and the desired level of wave protection will determine the type and design of the breakwater, the dimensions, and the configuration required [7].
The rubble-mound or caisson-type breakwater off ers the advantage of excellent wave energy damping and has been widely used [8][9][10][11].However, this type of coastal protection becomes uneconomical for relatively steep and deep coastal waters and large waves because construction costs will increase drastically [12].In addition, the average steep coast has rough and poor seabed conditions that aff ect the stability of the structure [13], as well as frequent changes in water fl ow circulation, which can cause erosion and sedimentation in the surrounding area [14].
Floating Breakwaters off er the protection needed when working in deeper waters with more vital natural forces than fi xed breakwaters.The Structure uses the visions of refl ection, dissipation, and transformation to dampen the wave energy to attenuate the incident wave [15].Floating breakwaters provide primary or additional protection against waves where reefs, shallow seabeds, or conventional fi xed structures support wave protection.These structures are generally installed in marinas, ports, tourist areas, and aquaculture facilities.Floating breakwater has several advantages [12,15,16], namely, it can be easily moved, and its layout can be rearranged because of its transportability and fl exibility in design.It can be applied to soil conditions on the seabed with poor systems.Mooring ropes do not interfere with water circulation, sediment transport, and fi sh migration, low current circulation in conventional breakwaters will result in an accumulation of sediment concentration in the area, and construction time is relatively short.Floating breakwaters also off er a low and economical alternative to construction costs compared to conventional breakwaters, especially in water depths of more than 3.05m [17].Apart from the primary function as a wave absorber, this structure can also function as a walkway, marine habitat, seawall, and ship dock.
In addition to the advantages of the fl oating breakwater, it also poses several disadvantages that require careful evaluation.The design and development of fl oating breakwaters for coastal areas is a signifi cant challenge for engineering engineers.The structure design at the specifi ed location should carefully consider wave height analysis.Some drawbacks include limitations for short fetch lengths, structure life (10-20 yrs), and part of the transmitted incident wave [16].Hales [17] stated there was uncertainty about the magnitude and type applied to the system and the insuffi ciency of information on maintenance expenses.So being conservative in design practice will increase construction costs.The main disadvantage of fl oating breakwaters is that these structures always move in reaction to waves, making the system more easily fatigued.
Wave energy can be reduced by taking care of refl ecting waves and destroying the motion of wave particles by fl oating breakwaters.Their refl ectivity and interference depend on the structure's shape, dimensions, surface, and design confi guration.Floating breakwaters can cause wave diff raction, i.e., waves coming from diff erent directions will break apart when they hit the structure.In this process, the wave energy will be transformed into the motion energy of the structure.The greater the wave energy absorbed by the structure, the higher the intensity of the motion of the structure.The amount of energy absorbed depends on the cross-sectional area of the structure to the direction perpendicular to the wave.So that in the fl oating breakwater design, the minimum cross-section and the interaction eff ect become an essential reference to produce a fl oating breakwater with the slightest motion response [18].The study of the shape of the porous structure is very benefi cial because, in addition to being able to dampen waves, the wave energy received by the structure and the mooring line becomes small [19,20].
This research studies a porous slope fl oating breakwater anchored in the sea.The pore shape of this structure aims to reduce the excessive wave load that impacts its performance.In the impermeable form, the structure will cause a maximum structural motion response, increasing the mooring line stress.Based on experimental results [21], researchers will examine the hydrodynamic performance of fl oating breakwater due to the infl uence of slope and porosity by computing fl uid dynamics.
This study aims to determine the optimum floating breakwater performance by comparing the reflection and transmission coefficients based on experimental and numerical results.This paper is organized with the following steps: Step 1 is numerical modeling (computational fluid dynamics) based on previous experimental data.
Step 2 analyzes and validates the transmission and reflection of the numerical model and experiment results.
Step 3 studies the effect of the mooring line angle and water level elevation.Steps 2 and 3 are included in the results and discussion, and the last step contains conclusions and suggestions from this research.

LITERATURE REVIEW / Pregled literature
Research on fl oating breakwaters was initially investigated by Nece and Richey [22].Floating breakwaters objects are in the form of twin-hull pontoons and pontoon boxes.Along with industrial developments in structure module manufacturing, many fl oating breakwaters are chain-moored rectangular caissons with two vertical plates protruding downwards from the sides, such as the Π-type shape.Furthermore, various forms and confi gurations of fl oating breakwaters were investigated by several researchers.Blumberg and Cox [23] conducted experiments on fl umes of various confi gurations (box, T-shape, and catamaran).Based on his research, the curve of transmission coeffi cient and maximum horizontal wave load was obtained.Neelamani and Rajendran [24,25] focused on examining T-type and Ʇ-type fl oating breakwaters.Transmission, refl ection, and energy dissipation were experimentally tested on regular and random waves-the transmission coeffi cient decreases as the steepness of the waves and the relative water depth d/L increase.Two fl oating breakwaters are very effi cient at reducing incident wave energy.T-type fl oating breakwater is better than Ʇ-type by about 20-30%.Dong et al. [26] tested three types of fl oating breakwaters with a physical model: box shape, double box, and plank net.The results found that the board-net fl oating breakwater is a simple and cheap structure that can be applied to deep-water aquaculture.Koutados et al. [27] investigated four forms of fl oating breakwaters.In this study, it can be found that the effi ciency of the fl oating breakwater will increase if the plate is installed in front of the structure.
In addition to experimental research, the behavior of floating breakwaters is also studied numerically.Several researchers, including Fuguzza and Natale [28], built a combined linear model, namely the movement of the structure and wave diffraction, to describe a floating breakwater in the form of a box on a regular wave.The results of the numerical model show conformity with the physical model test.Sannasiraj et al. [29] tested a 2-D numerical model to evaluate the coefficients and hydrodynamic forces on angular waves in a floating breakwater in the form of a pontoon.The 2-D model can be applied to study wavestructure interaction problems.Rahman et al. [30] verified the numerical model with experiments for rectangular floating breakwaters.The results represent water level elevation at different offshore and onshore locations and the dynamic displacement of the floating structure.The forces on the mooring line and the hydrodynamic coefficients are compared to the experimental results.Gesraha [31] proved numerical studies and experiments on the rectangular-type floating breakwater with two thin sideboards vertically downwards, Π-type.The results show that for the angular wave to the structure, the highest wave transmission occurs compared to the rectangular type.
The study of extreme loads that occur in the ocean on fl oating breakwaters has also been investigated by Cox et al. [32] tested the performance of the box type on regular and random waves, namely transmission, refl ection, and dissipation of waves, motion, and structural stability due to wave forces.Ruol and Martinelli [33] tested various mooring lines on the fl oating breakwater type Π, chains with diff erent initiating tension or pile.The analysis concentrated on mooring line forces, chain shock loads, and wave transmission.Furthermore, The performance of type Π fl oating breakwater in diff erent incident wave directions was studied by Martinelli et al. [34].The results of this test show that an increased wave incident angle will reduce wave transmission and mooring forces due to shock loads on the chain will also decrease, and the binding force will slightly increase.
In recent research, several researchers investigated the sensitivity of the floating breakwater transmission coefficient as a dimensionless parameter, namely relative draft and relative width.Compared to the experimental data, the numerical model predicts the hydrodynamics around the double-floating breakwater.The transmission coefficient decreases with increasing relative width for all relative distances [35].Mani [36] investigated the transmission coefficients on pontoons, mats, and moored breakwaters.Murani and Mani [37] tested performance on a cage-type due to wave effects and wave-current interaction.Analysis of pontoon-type behavior experimentally, theoretically, and the dynamic response of motion, mooring force, and wave attenuation were investigated by Sannasiraj et al. [29], Duan et al. [38] determined the transmission coefficient based on the ratio of the width of the structure to the wavelength of F-type.Experimental analysis of floating breakwaters of piled and moored types with various configurations of mooring angles was investigated by Sujantoko et al. [39].Analysis of mooring line tension on saw type [40], wave transmission on the hexagonal type [41], the effect of stability of concrete anchor block on steep-floating breakwater [42], and effect of dynamic response behavior on structure [18,43].
In general, the floating breakwater will decrease wave energy by reflecting waves, destroying the movement of water particles, and lowering water viscosity.If an ocean wave hits the structure, the wave energy will be reflected and scattered and will cause the motion structure.This induced structural motion will generate waves, which the mooring system will limit.[40].Based on the concept of maximum wave energy dissipation, floating breakwater research will continue to develop to produce effective and efficient performance.Some researchers have conducted studies of floating breakwaters in the porous form in various types, namely porous pontoons [44,45], porous boxes [19,46], porous plate [47][48][49], porous pipe/cylinder [50][51][52], and saw porous [18,20].
The study of slope-porous shapes with various variations of slope and porosity has been carried out experimentally at the model scale of 1:20 [21,53] in Figure 1.The floating breakwater models are moored at an angle of 45 degrees with a position of 10.2 m from wave probe 1 (wp1) with a fixed water depth of 0.75 m.The reflected waves are recorded in two wave probes, mounted 1.5m (wp2) and 1.0m (wp3) in front of the model.In contrast, the transmitted wave was measured in wp4, set at 1.0m behind the model.This research shows that the pore shape can reduce the load on the mooring rope, but the transmission becomes more significant than the impermeable shape.Vice versa, the reflection of the wave is small.This approach uses a statistical approach to derive the average equation for turbulence quantities, such as turbulent kinetic energy and dissipation rate.The RNG model generally has a broader application than the standard k-e model [55].The RANS equation is stated as follows: (1) Where fl uid velocity on the axis (u, v, w), fractional open volume at open fl ow (V F ), the fractional open area of the fl uid fl ow in the axis (A x , A y , A z ), acceleration due to gravity on the axis (G x , G y , G z ), the viscous acceleration (f x , f y , f z ), loss of fl ow in a porous medium or across a porous insulating plate (b x , b y , b z ), and the fi nal term is the mass of the geometric component.
CFD is a numerical modeling method that can be used in experiments or modeling related to fl uid fl ow.This research is modeling the fl oating breakwater in the wave tank.The expected output is the water level before and after being exposed to the structure.However, as needed, other outputs are also obtained in addition to the surface height value, such as water pressure conditions, wave-particle velocity, turbulence, and many more.This CFD also has several advantages.It has an easy-to-understand display in making input confi gurations for a model, observations of the results of running models can be seen visually in every position required, and the output is displayed in the form of images and videos.

Numerical Modeling / Numeričko modeliranje
The fl oating breakwater model for numerical modeling is done with SolidWorks software.Good numerical modeling results can be achieved by arranging the dimensions of the waves according to the conditions during the experiment at a water depth of 0.75 m.After modeling the wave tank, the next step is to arrange the number of meshes.The meshing used in the modeling is 0.05-0.08m (Figure 2).The next step is to set up the physical model of CFD's fl oating breakwater and mooring lines.The structure is placed facing the Xmax direction, or the positive x-axis, with the mooring rope coordinates adjusting to the slope angle of the fl oating breakwater (Figure 3).
The hydrostatic input properties include the fl uid density of 1000 kg/m3, the gravity of 9.8 kg/m2 towards the negative z-axis, and the turbulent motion used is laminar.The boundary conditions in this modeling are as follows: a) Waves (Wv).In this boundary condition, waves can enter the computational area and propagate in the expected direction to other boundary conditions.Data on the wave type, wave period, wave amplitude, and water depth are entered in this boundary condition.This boundary condition is defi ned on the right (XMax).b) Symmetry is a boundary condition with no scalar fl ux fl ow along the boundary.c) Walls (W).Boundary conditions where a watertight wall surrounds the mesh tank, and d) Outfl ow (O) is a boundary condition used for the modeled wave fl ow to escape to prevent fl uid from accumulating behind the wave tank.In this boundary condition, a wave absorber is also modeled so that no refl ection occurs behind the structure.After setting the boundary conditions (Figure 4), the next step is to place the history probe by the experimental results, which retrieve water level elevation data at specifi c predetermined points.The type of history probe used is a fl uid probe: Stationary or attached, which allows this probe to remain in position.Examples of free surface elevation results can be seen in Figures 5 and 6 7 and 8. Generally, the fl ow velocity at the structure's surface is more signifi cant than after passing through the structure.Based on this phenomenon, the pore shape is also very effi cient in reducing the water content.In addition, it can absorb wave energy not entirely, so the mooring force received due to wave energy can be reduced.

Wave Transmission and Refl ection Analysis / Analiza transmisije i refl eksije vala
The hydrodynamic performance of the fl oating breakwater is defi ned by the transmission (K t ) and refl ection (K r ) coeffi cient.K t is expressed as the ratio of the height of the transmission wave H t to the incident wave H i .When the K t value is small, the structure can reduce the wave well.At the same time, K r is the result of comparing the height of the refl ected wave Hr with the income wave H i .The fl oating structure is an eff ective antirefl ective structure with a low K r value.
The incident and refl ected waves due to marine structures can be determined using Goda and Suzuki methods [56].Two wave probes record changes in water level simultaneously.This method works by separating the incoming and refl ected waves to determine K r .

Mooring Line System / Sustav užadi za privezivanje
The mooring system is used to hold the fl oating structure in place.This study used mooring ropes with a taut system (Figure 9).The taut system utilizes the mooring system's tension to withstand the structure's buoyancy so that it has a lower mooring radius.The length of the mooring line (l) can be determined analytically.
Motion in fl oating structures due to the infl uence of wave forces will cause tension (T) in the mooring line.The stresses on the mooring line can be divided into a) Mean tension, the tension Figure 9 Confi guration of mooring lines with a taut system on a fl oating breakwater Slika 9. Konfi guracija užadi za privezivanje sustavom napinjanja na plutajućemu lukobranu According to Faltinsen [57], the calculation of the maximum tension of the mooring rope can use the equation below: Where T max maximum mooring rope tension (tonnes), T H horizontal pre-tension (tonnes), w chain weight in water (tonnes/m), and h water depth (m).
In this study, fl oating breakwaters were moored with mooring lines with a confi guration of 45 deg [21] [53] as the initial analysis.Furthermore, to see the mooring angle's infl uence on transmission and refl ection coeffi cients, the mooring angle was varied at an angle of 30, 45, 60, and 90 deg.In this study, mooring ropes used springs to substitute the chains generally utilized in mooring techniques.The spring wire has a diameter of 2 mm, an outer diameter of 6.5 mm, a length of 820 mm, and a stiff ness of 4.28 N/mm 2 .

Wave Transmission Coeffi cient Validation / Validacija koefi cijenta transmisije vala
The results of the transmission coeffi cient analysis for each model are plotted to determine the eff ect of the wave parameter number (H/gT²) on the transmission coeffi cient using a linear equation.It was found that linear variation gave the most signifi cant R 2 value.Based on the data from the analysis of the transmission coeffi cient, it is possible to compare each model with the results of previous experimental tests [21].The following is a comparison graph of the transmission coeffi cient of each model (Figure 10).Based on the picture above, it can be shown that the trendline of numerical simulation results and experiments is relatively the same.The diff erence in error between the results of the numerical model and the experiment average transmission coeffi cient (K t ) of each model is shown in Table 2.The error values in models 1 to 5 are 7.9%, 4.54%, 5.98%, 6.97%, and 6.88%, respectively.The overall result between numerical and experimental modeling is still below 10%, so the modeling is quite good.In the results of numerical and experimental modeling, there are slight diff erences in values where the CFD modeling has a smaller K t than the experimental results.Several causes exist for these diff erences, including human factors in the experiment; excessive surge fl oating breakwater motion can also increase the transmission coeffi cient.This excess motion can occur because of diff erences when modeling the fl oating breakwater and its mooring rope.Not all phenomena during the physical model test can be modeled numerically.
The analysis of the results of K t shows that the gentler the slope of the fl oating breakwater will be, the smaller the K t will be, and the more impermeable the slope of the structure will be, the smaller the value of K t will be.The results of the analysis of the numerical model of the refl ection coeffi cient K r are summarized in Figure 11.Table 3 shows the average refl ection coeffi cient error for each model.The refl ection coeffi cient values in Models 1 to 5 are 5%, 6.79%, 10.24%, 4.07%, and 5.45%, respectively.By making comparisons based on the shape of impermeable and porous structures (see Figure 1), it can be explained that the more gentle the slope of the fl oating breakwater, the smaller the refl ection coeffi cient, and conversely, the steeper the slope of the fl oating breakwater, the larger the refl ection coeffi cient.A comparison of refl ection coeffi cients shows that the simulation and experimental results diff er.This diff erence occurs because, during the experimental test, there was a refl ection from the walls of the fl ume tank, which caused the water elevation read on the wave probe to rise.Based on research by Mansard and Funke [58], to get good results on the Goda and Suzuki method [56], the distance between the wave probes that record the water level elevation data due to refl ections from the structure must be changed every diff erent period.So this method does not produce the maximum refl ection coeffi cient.After the calibration process, the coeffi cients of transmission and refl ection of the fl oating breakwater are determined using CFD simulation due to the infl uence of changes in the mooring rope angle.In this exploration model, model 2 is used because it is considered the most optimal in reducing waves and has the slightest error than other models.Simulations were carried out at wave periods, T=2 seconds, and wave heights H= 5cm, 7.5cm, 10cm, and 12.5cm with the confi guration of the mooring rope angles of 90°, 60°, 45°, and 30°.The simulation results of the mooring line angle on the transmission and refl ection coeffi cients are shown in Figures 12  and 13.It can be shown that the more upright a mooring rope angle is, the higher the transmission and refl ection coeffi cients will be.That can occur because the fl oating breakwater moves more freely, and there is a pulling eff ect from the mooring rope at an angle of 90°, which causes the transmission coeffi cient to be higher.

Eff ect of Water Level Elevation on K t and K r / Učinak podizanja razine mora na K t i K r
The eff ect of changes in water level elevation (d= 85 cm, 75 cm, and 65 cm) on coeffi cients of transmission and refl ection of the fl oating breakwater structure was carried out by numerical simulations in model 2. The simulations were carried out with variations in wave periods of 1.1 seconds to 2.0 seconds and wave heights of 12.5 cm.The mooring rope angle is 30° with a rope length of 150 cm.Figures 14 and 15 show the infl uence of water level elevation on the transmission and refl ection coeffi cients.The water levels of 85 cm (high tide), 75 cm (seawater line), and 65 cm (low tide) gave an average K t of 0.86, 0.89, and 0.92.At the same time, the average K r is 0.16, 0.13, and 0.11, respectively.The graph shows that changes in water level elevation aff ect the transmission and refl ection coeffi cients.At a depth of 85 cm, it produces a minor wave transmission and has the highest wave refl ection rate.This condition occurs because the length of the mooring rope is designed when the water conditions when the tide is 85cm with a mooring rope length of 150 cm.So for water levels of 75 cm and 65 cm, the mooring rope will be loose and not tense, which causes the fl oating breakwater to move more quickly and eliminate the function of the fl oating breakwater itself.The phenomenon of high and low tides must be considered by engineers when designing the structure in the coastal area.

CONCLUSIONS / Zaključci
Numerical modeling has been carried out on the fl oating breakwater model with variations in height and wave period on regular waves.The model validation results between numerical and experimental showed quite good results, namely a maximum of 10% for wave transmission and refl ection.Several causes for these diff erences include excessive surge fl oating breakwater motion, which can increase the transmission coeffi cient.This excess motion can occur because of diff erences when modeling the fl oating breakwater and its mooring rope.
Besides that, there is also a wave refl ection from the wall of the wave fl ume, causing the water elevation read by the wave probe to be high.Based on research by Mansard and Funke, to get good results on the Goda and Suzuki method, the distance between the wave probes that record the water level elevation data due to refl ections from the structure must be changed every diff erent period.So this method does not produce the maximum refl ection coeffi cient.Analysis of the infl uence of changes in the mooring line angle, the simulation is carried out at 30 deg to 90 deg and produces an average transmission coeffi cient of 0.79 and a refl ection of 0.21.While the eff ect of changes in water level elevation of 0.85 m, 0.75 m, and 0.65 m gives a reasonably signifi cant average transmission coeffi cient of 0.85 and a refl ection of 0.13.The mooring line angle will be gentler at high tide, and the transmission and refl ection coeffi cients will be higher.However, the mooring line will loosen at low tide, causing the structure to move more freely and eliminating the function of the fl oating breakwater itself.The tidal phenomenon becomes a challenge for coastal experts in designing structures to produce eff ective and eff ective and effi cient hydrodynamic performance.
This slope-porous fl oating breakwater research needs to be studied further on other aspects, such as motion response and interconnection module, either by experiment or numerical model.

Figure 12 Figure 13
Figure 12 Comparison of K t due to changes in mooring line angle at various wave heights in model 2 Slika 12. Usporedba K t zbog promjena u kutu užeta za privezivanje prema različitim visinama vala na modelu 2

Figure 14
Figure 14 Comparison of K t due to changes in water level elevation in model-2 Slika 14. Usporedba K t zbog podizanja morske razine -model 2

Figure 15
Figure 15 Comparison of K r due to changes in water level elevation in model 2 Slika 15.Usporedba K r zbog promjena u podizanju morske razine -model 2