Unlocking the Wave's Potential: Dynamic Numeric Simulation Response of Hexagon Buoy and Ring Heave Plate in a Shared Wave Environment

. Wave electricity extraction technology in advanced international locations holds to advance. One of the strategies used is a point absorber, which extracts electricity from the response of its system. The essential machine includes a floating buoy and a response management tool referred to as a heave plate. This look discusses the impact of the heave plate's floor location variant at the hydrodynamic parameters of a hexagonal-fashioned buoy (heave and pitch Response Amplitude Operator (RAO), brought mass, and radiation damping). The evaluation changed into performed the usage of the industrial software program ANSYS AQWA. The effects of the evaluation display that the presence of the heave plate at the buoy version affects the RAO values, mainly for the heave and pitch modes. Increasing the ratio of the heave plate's floor location results in a growth withinside the RAO heave price however decreases the RAO pitch price. Additionally, the presence of the heave plate influences the values of brought mass and radiation damping. The maximum ratio of heave plate location effects withinside the maximum brought mass price. This price gradually decreases because the ratio of the heave plate location decreases, and the buoy without a heave plate has the bottom price. This is reversed for the radiation damping price, wherein the best heave plate ratio corresponds to the bottom damping price. The damping price will gradually increase because the heave plate ratio decreases, with the buoy without a heave plate having the best price. The presence of the heave plate in the buoy model influences the RAO values, particularly in the observed motion modes of heave and pitch.


Introduction
As outlined in the Electricity Supply Business Plan (RUPTL) for the period 2018-2027 by PT Perusahaan Listrik Negara (PLN) Persero, the Indonesian government has established a goal of attaining a 23% portion of Renewable Energy (RE) within the overall energy composition by the year 2025 [1].However, as of 2020, the percentage only reached 19.5%, which indicates a significant gap to be bridged by 2025 [2].This is primarily due to the suboptimal utilization and development of renewable energy sources [3].
Given that the majority of Indonesia's territory consists of oceans, there is a significant potential for harnessing wave energy.One of the mechanisms to convert ocean wave potential energy into electrical energy is known as a Wave Energy Converter (WEC).Various methods can be employed to convert wave energy, including utilizing heave, pitch, pitch-heave, surge, or heave-surge motion systems [4].
Among these WEC types, the self-reacting WEC utilizes the reaction of its system without requiring interaction with the seabed.The buoy, also known as a pontoon, acts as the point of reaction to the incoming wave energy and undergoes vertical movement (heave) at the water surface.The addition of a heave plate is used * Corresponding author: ekosasmitohadi@lecturer.undip.ac.id to absorb the reaction forces between the buoy and the water.Positioned underwater, the heave plate tends to have a relatively static motion.The relationship between the buoy and the heave plate is utilized to extract wave energy and convert it into electrical energy.
Heave plates are commonly employed in offshore structures, particularly in oil drilling.They can reduce excessive heaving motion by increasing the added virtual mass and providing viscous damping [5].
Several studies have been conducted to investigate the factors influencing energy absorption efficiency and the hydrodynamic characteristics of heave plates.Research conducted by [6] indicates that the shape and dimensions of the heave plate affect the hydrostatic coefficient when used in WEC applications.Furthermore, research by [7] adds that the thickness, corner radius, shape, and hole ratio of the heave plate influence the added mass and damping coefficient.Experimental studies on the interaction forces between the buoy and the heave plate, with the addition of a vertical plate, have been conducted by [8].
Both numerical and experimental methods have been employed to study the heaving motion, added mass, and damping force of box-shaped plates [9]. the numerical analysis conducted by [10] to solve Laplace's equation in diffraction theory using ANSYS/AQWA software.This demonstrates that numerical methods have a good analytical capability and yield results that are consistent with experimental findings.
The scope of this study is a hexagonal-shaped buoy and a circular heave plate, along with variations in their dimensions.The focus of this research is to analyze the influence of the presence of a heave plate and its varying surface area on the heave and pitch motions, added mass, and damping force.

Research Outline 2.1 Research Object
The concept and technology of Wave Energy Converters (WECs) encompass a wide range of variations.More than 1000 wave energy conversion techniques have been patented in Japan, North America, and Europe.However, they can generally be grouped into two categories: based on their placement location and based on their type [11].Point absorber is one of the types of conversion technique.This type of device is relatively smaller in size compared to the wavelength of the ocean.
The research object consists of a hexagonal-shaped buoy as the floating component, a heave plate as the reaction control device, and a spar as the connecting element between them.Testing conducted by [12] has shown that a polygon-shaped buoy can effectively reduce wave excitation forces and pitching moments by orienting its corner sides towards the incoming waves.The buoy model to be used in this research is illustrated in Figure 1.

Fig. 1. Buoy Model
The variations applied to the heave plate are based on diameter ratios, as shown in Table I and Figure 2. The selection of these variations is based on the ratio of the heave plate's surface area to the buoy's frontal area.The heave plate is connected to the buoy through a cylindrical spar with a diameter of 10 mm and a length of 30 mm (0.3 times the buoy's height, H).

Research Preparation
The buoy, various heave plate variations, and the spar have been modeled using 3D numerical modeling software in the form of surfaces.The coordinate (0, 0, 0) in the x, y, z axes is located on the waterline of the buoy (0.5H).To perform hydrodynamic simulations, it is important to know the mass inertia properties.The inertia mass properties data for each model variation are shown in Table 2.The Base Model is the main model of the buoy without any additional heave plate, as shown in

Wave Induction on an Object
The forces acting on a floating structure due to hydrodynamics result from the movement of water particles in waves, the motion of the floating entity, and the interplay between the waves and the floating structure.In waves with small amplitudes, the wave excitation loads consist of the incident wave forces (Froude-Krylov forces) and the diffraction forces generated by the disturbed waves due to the presence of the floating object.The wave inertia loads (radiation loads) are caused by the wave disturbances resulting from the motion of the floating object.
The 3D panel method is the most common numerical method used to analyze the hydrodynamic behavior of a floating object in waves.This method is based on potential theory and represents a series of diffracting panels.The numerical approach is employed to describe the wave loads on the floating object.
In real-world conditions, waves are not linear in shape, and the forces vary with time.However, in this study, the waves are assumed to be simple and harmonic [10].

Common Equations
The first-order diffraction potential theory and wave radiation potential are used to analyze diffraction and radiation forces.Therefore, the linear superposition theory can be employed to formulate the velocity potential in the fluid domain.The fluid flow field surrounding the floating object with the velocity potential can be determined by: where a_w is the amplitude of the incident wave and ω is the wave frequency.
Adopting the notation from the 6-degrees-offreedom rigid body motion in seakeeping theory, the translational and rotational motions of the object with respect to the Center of Gravity caused by the incident wave are expressed in the following units: The potential equations due to the incident wave, diffraction wave, and radiation wave can be written as follows: where 1 is the first-order incident wave potential,  is the diffraction wave potential, and j is the radiation wave potential due to the motion denoted by j.
In the case of water with finite depth, the incident wave potential 1 at a point  ⃗ =(X, Y, Z) in Equation 3can be expressed as shown in Equation 4.
where d is the water depth, and g is the acceleration due to gravity.
When the wave velocity potential is known, the distribution of first-order hydrodynamic pressure can be calculated using the Bernoulli equation.
p (1) Various fluid forces can be calculated by integrating the pressure over the surface of the submerged object based on its pressure distribution.When the object is partially or fully submerged in water, the volume or weight of the displaced water can be obtained by integrating over the entire submerged surface area.

∇= ∫ Zn 3 ds
S o (6) where S0 is the wetted surface area of the object in calm water conditions,  ⃗⃗ = (1, 2, 3) is the unit vector normal to the wetted surface of the object, and Z is the vertical coordinate of the surface point (in global coordinates).
To obtain the general form of the equations for the forces and moments acting on the object, it is necessary to introduce vector notation for the 6 components corresponding to the basic motions of the rigid body.
(n 1 n 2 n 3 )=n ⃗⃗ (n 4 n 5 n 6 )=r ⃗×n ⃗⃗ (7) where  ⃗ =  ⃗ −  ⃗  is the position vector of a point on the surface of the body with respect to the CoG in global coordinates.
Using the notation in Equation 7, the components of the first-order hydrodynamic forces and moments can be expressed as follows: F j e -iωt =-∫ p (1) Based on Equation 3, the total first-order hydrodynamic force can be written as follows: ] where j=1,6 (9) The equation for the Froude-Krylov force due to the incident wave in j mode, can be written as follows: (10) The equation for the diffraction force in J mode, due to the diffracted wave can be written as follows: Then, the radiation force in J mode due to the radiation wave induced by the rigid body motion with unit amplitude in mode k can be written as follows: The radiation wave potential can be expressed in terms of real and imaginary parts.Continously, it is substituted into Equation 12to obtain the added mass coefficient and the damping coefficient.
=  2   +   Therefore, the added mass and damping can be expressed as follows: It should be noted that all the fluid force equations calculated are functions of the wetted surface geometry of the object and do not depend on the mass of the object.
A series of linear algebraic equations is solved to obtain the harmonic response of the object to regular waves.These characteristics are often referred to as Response Amplitude Operators (RAOs), where their values are proportional to the wave amplitude.The linear motion equations for the structural hydrodynamic interaction M in the frequency domain can be obtained through the equation: where MS is the structural mass matrix of size 6M x 6M, Ma = [Ajm,kn] and C = [Bjm,kn] are the respective 6M x 6M added mass and damping matrices, and Khys is the combined hydrostatic stiffness matrix of size 6M x 6M.
Equation 15 can also be expressed in the following form: Where, referred to as a transfer function that relates the input force to the output response.

Hydrostatic and Mesh Information
The hydrostatic and the mesh results are shown in

Influence of the Heave Plate on Added Mass and Damping
The comparison of added mass values along the Z-axis for the various test models is presented in Figure 5.This graph is used to observe the influence of the heave plate on the added mass of the system along the Z-axis.
Based on Figure 5, it can be observed that all four simulation models exhibit a similar trend.However, each model has different values.The highest value is obtained in Model 1, followed by Model 2, Model 3, and the smallest value is in the Base Model.These findings are consistent with the research conducted by [5].Based on Figure 6, it can be observed that all four models exhibit similar curve trends.The highest peak value is obtained in the Base Model, followed by Model 3, Model 2, and finally Model 1.This provides an indication that the heave plate has an impact on reducing the damping value of the buoy.Additionally, the size of the heave plate affects the frequency position of the peak damping value.A larger heave plate leads to a lower frequency position of the peak damping value.However, further adjustments are necessary and require further research.

Influence of the Heave Plate on Heave and Pitch RAO
The comparison of the analysis results for Heave and Pitch RAOs is presented in Figures 7 and 8, respectively.These graphs provide an overview of the differences in the influence of the heave plate on Heave RAO and Pitch RAO.Based on Figure 7, it can be observed that the highest peak value for Heave RAO is obtained in Model 1, followed by Model 2, Model 3, and the Base Model in decreasing order.Based on Figure 8, it can be observed that the highest peak value for Pitch RAO is obtained in the Base Model, followed by Model 3, Model 2, and Model 1 in decreasing order.Based on both graphs, it can be understood that the presence of the heave plate has contrasting effects on Heave RAO and Pitch RAO.
A larger heave plate has a positive impact on increasing Heave RAO and decreasing Pitch RAO.Conversely, a narrower heave plate has a negative impact on decreasing Heave RAO and increasing Pitch RAO.
The presence of the heave plate also has an impact on the frequency position of the peak response.This effect is the same for both Heave RAO and Pitch RAO.It should be noted that the occurrence of peaks in the RAO curves is due to the resonance between the natural frequency of the buoy and the wave frequency.
A larger heave plate shifts the peak position towards the left, towards lower frequencies.This can be explained by considering the formulas for the natural frequencies of heave and pitch motion, where both the mass and added mass are in the denominator [13].

Conclusion
An analysis of the dynamic response of the hexagonal buoy and its variations with the heave plate has been conducted.The presence of the heave plate in the buoy model influences the RAO values, particularly in the observed motion modes of heave and pitch.Increasing the ratio of heave plate area leads to an increase in the heave RAO value, but a decrease in the pitch RAO value.
Furthermore, the presence of the heave plate affects the values of added mass and damping.The highest ratio of heave plate area results in the highest added mass value.Subsequently, the values decrease in ascending order towards the smallest ratio of heave plate area, with the smallest value obtained for the buoy without a heave plate.This is in contrast to the damping values.The highest ratio of heave plate area leads to the lowest damping value.The values increase sequentially towards the smallest ratio of heave plate area, with the highest value obtained for the buoy without a heave plate.

Figure 3 .Fig. 3 .
Fig. 3. Base model assembled with one of the heave plate variationsThe wave used in this simulation is a regular sinusoidal wave based on Airy Wave Theory.Each model is tested at 36 frequencies within the wave frequency range of 0.1 rad/s to 12 rad/s.The presented data only includes the wave incidence angle of 180º (head sea).The selection of a single wave direction is based on the geometry of the hexagonalshaped model, assuming symmetry along the X and Y axes.The analysis is conducted under no forward speed conditions (no forward motion) and free-floating conditions.The simulation tank dimensions are 2 m in length, 2 m in width, and 2 m in depth, as shown in Figure4.

Fig. 5 .
Fig. 5. Comparison of Mass Added Values on the Z-Axis.

Fig. 7 .Fig. 8 .
Fig. 7. Comparison of RAO (Response Amplitude Operator) Values for The results obtained from both methods align with each other.The Boundary Element Method was utilized in

Table 1 .
Heave Plate Model Variation Fig. 2. Heave plate surface area variations

Table 3 Table 3 .
Hydrostatic Analysis and Mesh Information