Motion Responses Analysis for Tidal Current Energy Platform: Quad-Spar and Catamaran Types

One approach to support floating tidal current turbines is by using a moored catamaran, a barge type platform. Considering its low draft, one might expect that it performs best at typical straits with sea states of small wavelets to small waves. The problem is that the high rotational motion responses of the catamaran due to wave loads tend to reduce the turbine performance. This paper looks for a possibility to deteriorate these rotational responses by introducing a platform with four buoyant legs referred to as a quad-spar considering its good stability performance. The platforms are moored by four catenary cables as their mooring system. The motion response modeling was undertaken by Computational Fluid Dynamic (CFD) simulation based on three-dimensional potential flow theory. Considering sea states of straits with typical tidal current energy potentials, the environmental load was set on random wave with the significant wave height, Hs, of about 0.09 to 1.5 m and the wave period, T, of about 1.5 to 6 s corresponding to the wave frequency, ω, of about 1.1 to 4.2 rad/s. This study found that lower motion responses can be satisfied by the quad-spar, in which its yaw, roll and pitch responses are on average about 5%, 44%, and 38%, respectively, compared to those of the catamaran. This result indicates that the quad-spar is more effective in reducing rotational motion responses needed to keep a high performance of the tidal current energy system.


Introduction
In recent years there has been a rapid development of tidal current energy system to extract kinetic energy in the body of seawater into useful energy in the form of electricity with a help of mechanical turbines and electrical generators (Melo and Jeffrey, 2018). One of the conversion technologies uses a floating system to utilize the tidal current energy near the seawater surface, e.g. Zhang et al. (2015), Mukhtasor et al. (2018), Junianto et al. (2018) and Mutsuda et al. (2019). A choice of types of the floating system requires their performance to work under environmental conditions of the potential sites.
Many sites of tidal current energy potentials are typically at straits. Among others, examples are Larantuka and Alas Straits in Indonesia (Blunden et al., 2013;Orhan and Mayerle, 2017), Dover Strait in France (Thiébaut and Sentchev, 2016), Gibraltar Strait in Spain (Sammartino et al., 2014), Qiongzhou Strait in China (Wu et al., 2016), John-stone Strait in Canada (Sutherland et al., 2007), and Messina Strait in Italy (Coiro et al., 2013). Yu et al. (2018) used satellite altimetry data to provide with a global map of significant wave heights. Their map (Yu et al., 2018) shows that the significant wave heights of many straits might be estimated, ranging from 0 m to about 1.5 m. These wave conditions might be classified using Chakrabarti (2005) as sea states of small wavelets to small waves.
Among marine vehicles on the small waves, a catamaran has a low vertical motion sickness incidence (Fang and Chan, 2007;Piscopo and Scamardella, 2015). In line with this advantage, studies have been carried out in order to modify the catamaran, from a marine vehicle into a supporting platform of tidal current turbine, e.g. Jing et al. (2013) and Qasim et al. (2018). The problem with the catamaran-typed platform is that its rotational motions seriously cause a disruption to the turbine rotation, i.e. roll, pitch and yaw (Li et al., 2019). Furthermore, a study confirms that the amplitudes of roll motion give an influence in capturing the tidal current energy (Wang et al., 2017). Yawing motion changes tidal current distribution around the turbine, which leads to deteriorate the turbine performance (Wang et al., 2016). For this reason, there is a need to look at alternative options of floating platform to support the tidal current turbines while maintaining rotational motion responses.
Selection of platform types may adopt technology of oil and gas. For this purpose, an investigation is required to consider motion responses, particularly by considering the tidal current turbines as an additional deadweight (Ji et al., 2018). Rho et al. (2014) simulated motion responses of four platforms with horizontal axis turbines, i.e. barge, single buoyant leg, tension leg platform and semisubmersible, in which their dimensions were scaled down to suit the site of tidal current energy potentials. The simulation of the four platforms confirms that the buoyant leg type has the lowest rotational responses.
The problem with the buoyant leg type is that its configuration may not be used to prop the vertical axis turbines because of a limited horizontal area of the structure. On the other hand, the buoyant leg type produces low motion responses in receiving the wave load because it has a small water plan area and a symmetry body (Jain and Agarwal, 2003;Pham and Shin, 2019). These advantages may be explored in developing alternative platforms for supporting the turbines.
For the above reasons, in this paper, the single buoyant leg is modified to be four buoyant legs jointed to a deck. This modified type is referred to as a quad-spar type. The deck size of the quad-spar, which is used to support the turbines, is comparable to that of the catamaran. Because of this configuration, the quad-spar has arm moments which may result in rotational motion responses when it is subject to the wave load. The objective of this paper is to investigate the rotational motion responses of the quad-spar and to compare these responses to those of the catamaran.
The analysis in this paper was undertaken numerically by Computational Fluid Dynamic (CFD) based on a threedimensional potential flow theory on the regular and random waves. The platforms with four catenary cables are loaded by deadweight of the twin turbines in order to improve turbine performance (Antheaume et al., 2008;Li, 2014). The results are presented in terms of rotational motion responses which might be expected to affect the turbines performance (Wang et al., 2016(Wang et al., , 2017Li et al., 2019). As a supplementary result, the required steel-plates for construction may be obtained by considering the area of the supporting platform. By these considerations, a choice of a more effective and efficient platform may be suggested.

Governing Equations
CFD calculates the rotational motion responses using the potential flow theory. These simulations have been done by hydrodynamic diffraction and hydrodynamic response. Under regular wave, hydrodynamic diffraction produces rotational-degrees-of-freedom (3-DOF) of Response Amplitude Operator (RAO) using motion equation in Eq.
(1) (Kim et al., 2015). The subscript i in Eq. (1) describes mode of motions such as roll, pitch and yaw. The equation can be written as: The parameters of motion response are showed in Eq.
is the regular waves amplitude, is the wave frequency (in rad/s), is the wave phase angle (in radians) relative to the origin of the fixed reference axes. The RAOs in Eq. (3) are the ratio between the amplitude of the 3-DOF, to the amplitude of incident wave.
The motion responses are further analyzed in random wave conditions by hydrodynamic response. Wave spectrum, , of International Towing Tank Conference (ITTC) in Eq. (4) and RAO are considered to define the motion spectral density. This step produces significant responses in rotational motions. . (4)

Numerical verification in regular wave
Before analyzing motion responses of the quad-spar and catamaran, a verification process of numerical modeling has been carried out in this section. Eqs. (1)−(3) in the previous section are employed in this step. The verification may be undertaken by the considerations on variety of settings of the input parameters (Altiok and Melamed, 2007;Sargent, 2011). The result of this verification is a percentage of difference rate from the numerical simulation compared to available experimental data. Ma et al. (2016) performed an experiment in a towing tank with a catamaran scale of 3:40 with four mooring cables (Fig. 1). In the experimental test, there were two wave conditions namely regular waves and random waves.
A catamaran model has been tested with and without single turbine rotations. In this paper, the verification of CFD has chosen the regular wave loading and without turbine rotation in order to find uncoupled motion responses of the supporting platforms. In the regular wave experiment (Ma et al., 2016), the catamaran was loaded with a wave velocity of 0.7 m/s and a wave height of 0.06 m which carried out by variations of the ratio of wavelength to catamaran length. The result was reported in the maximum value of the pitch RAO. There are nine maximum of pitch RAO values which are used as the verification data following the number of wavelength ( ) and catamaran length variations (L), , of 0.8, 1.0, 1.2, 1.5, 1.8, 2.0, 2.2, 2.5, and 3.
The conditions of numerical modeling in this verification follow those of the experiment (Ma et al., 2016). The numerical model has the same size as that of the experiment. The numerical and experimental results are recorded by the time response method. Then, the maximum value of each RAO is presented in Table 1. As seen in the table, the percentages are expressed in terms of difference between those from experimental and numerical calculations, ranging from 2.9% to 6.7%. Fig. 2 indicates that there is only slightly difference between the results of the CFD and the the experimental method. More specifically, all points lay above the line of equality indicating that there is little overestimate in numerical calculation in the range of about 3% to 7%. The difference might arise partly from the uncertain wave velocity assumption. This small deviation is considered acceptable and therefore the approach of the numerical calculations may be acceptable for further analyses.

Geometry and model of platforms
This study investigates the rotational motion responses of quad-spar and catamaran-typed platform with turbines. The catamaran is developed from the base platform of experiment of Ma et al. (2016) in full scale. This platform has been studied by widening the distance of demi-hull separation in order to generate low RAO .
The study reports that the least RAO can be satisfied at the demi-hull separation by 1.45 times of base catamaran. Fig. 3 is pitch RAO comparison between base catamaran and widening catamaran. For a comparison purpose, the appearance of twin turbines-loaded catamaran (Fig. 4) is the widening catamaran compared to that of Ma et al. (2016).
The geometry parameters of the catamaran and the quad-spar are explained in Table 2. Twin turbines-loaded catamaran has two floaters of barge type. The quad-spar has been modified in order to give a wide horizontal area with four floaters of buoyant leg type (Fig. 5). The leg size of quadspar is adjusted to the straits with typical tidal current energy potentials. In other words, this type is simulated at sea state   Sony JUNIANTO et al. China Ocean Eng., 2020, Vol. 34, No. 5, P. 677-687 679 of small wavelets to small waves with water depth of 35 m. The platforms are similar in deck size, weight load, and displacement which are designed for supporting vertical axis turbines because of the advantage in response to tidal current energy from every direction (Bachant and Wosnik, 2015;Satrio et al., 2018). The turbines are arranged in sideby-side where the turbine shafts are ordered in a straight line and perpendicular to the incoming flow. The distance of the turbines is about 1.5D between of the rotor shaft axis (Antheaume et al., 2008). The closer the turbine arrangement is in the side-by-side, the better the turbine performance. This condition arises because hydrodynamic interactions are constructive in all the turbines (Li, 2014).
The numerical solution has computational domain with hexahedron mesh, as shown in Fig. 6. Table 3 describes the performance parameter. Defeaturing tolerance and maximum element size are the determinant of the number of elements. The catamaran type has 29 721 elements and 29 658 nodes and the quad-spar type has 30 821 elements and 30 769 nodes. The growth rate type is exponential set at 1.2. To get the solution, the simulation has been set in time response analysis with time step of 0.5 s for 13 500 s. The other parameters are described as total weight and radius gyration for rolling ( ), pitching ( ) and yawing ( ).

Mooring system configuration
The platforms in this study are moored by four catenary cables using a similar specification. Therefore, the motion responses and the mooring tensions of the platforms can be analyzed and compared. This mooring type is suitable for shallow water, e.g. straits (Ma et al., 2019). The mooring points are about 1 m above water. The mooring layouts are shown in Fig. 7 for catamaran and Fig. 8 for quad-spar. The mooring properties are presented in Table 4 and Table 5.

Environmental condition
The turbines are designed to generate power of about 50 kW in a current speed of about 1.3 m/s from 0° (head seas) direction in order to have a good angle of attack. The strait waters environment under consideration in this study is represented by random waves with significant wave heights, of about 0.09 to 1.5 m, wave periods, T of about 1.5 to 6 s corresponding to wave frequencies, of about 1.1 to 4.2 rad/s, coming from head seas (0°) and quartering seas (45°) as illustrated in Fig. 9. The directions are the main incident wave in this simulation because they are predominantly oc-curred at the strait waters (Blunden et al., 2013).

Configuration effects of supporting platforms
Motion responses of quad-spar and catamaran-typed platforms are analyzed under two loading conditions, i.e. without turbines and with turbines. The characteristics of the platforms without turbines provide a conventional motion response. The analysis of the motion responses is continued by giving the turbine load in order to obtain the degree of motion which might influence the turbine power extraction. . In this study, the significant wave height is 0.09−1.5 m where the tidal current energy potential is predominantly in the strait area (Orhan et al., 2015). The use of samples of significant wave height is based on the sea state, from the level of small wavelets to small waves.     Sony JUNIANTO et al. China Ocean Eng., 2020, Vol. 34, No. 5, P. 677-687 ant leg. However, the degree of roll responses is lower than those of catamaran under all conditions. Fig. 10a shows that the maximum roll response of quad-spar without turbines is 2.3 times higher than that of quad-spar with turbines. Fig. 10b shows that the roll response of catamaran without turbines is 2.17 times higher than that of catamaran with tur- Fig. 11. Effect of the presence of the turbines on pitch response of quad-spar (a) and catamaran-typed (b) platforms.

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Sony JUNIANTO et al. China Ocean Eng., 2020, Vol. 34, No. 5, P. 677-687 H s bines on the same . H s Fig. 11 presents the degree of pitch responses of quadspar and catamaran-typed platform on of 1.16 m. Fig. 11a is the responses of quad-spar with and without turbines. The graph shows that the pitch response of quad-spar without turbines is 2.75 times higher than that of quad-spar with turbines at the maximum response. Furthermore, in Fig. 11b, the maximum pitch response of catamaran with turbines is 0.69 times lower than that of catamaran without turbines. The existence of four buoyant legs of the quad-spar gives the effect of pitch response even though it is not as high as that of the catamaran-typed platform.

H s
Yaw responses in Fig. 12 arise because of an incident wave from quartering seas. Quad-spar has lower yaw response than catamaran on the same . According to the graph in Fig. 12a, yaw responses of the quad-spar with turbines are close to zero compared to those of quad-spar without turbines. Fig. 12b presents yaw response of catamaran with turbines which is 0.41 times lower than that of catamaran without turbines in maximum value.

H s
The quad-spar rotational responses are consistently lower than those the catamaran under conditions with and without turbines. These may be caused by the quad-spar floater configuration in the form of four buoyant legs, which have a deeper immersed body than the catamaran. The rotational response graphs above show that the platforms with turbines have a lower degree than those without turbines because the presence of the turbines increases the damping of the structures. Furthermore, the responses in time domain are calculated in order to investigate the significant degree of rotational responses by the highest third responses. The significant response analysis is done on the ranging from 0.09 m to 1.5 m.
H s H s The significant response of roll motion is shown in Fig. 13. The graph shows the motion quality of quad-spar and catamaran-typed platform. In the range of in this study, the quad-spar has smaller degree of roll motion than the catamaran, in all cases of with and without turbines conditions. For example, at =1.16 m, the degree of the quad-spar motion reaches the significant response of 0.22° under the condition with turbines and 0.55° under the condition without turbines, while the catamaran reaches the significant re-sponse of 0.49° under the condition with turbines and 0.81°u nder the condition without turbines. The configuration of the turbines has reduced the roll response of quad-spar and catamaran-typed platform on average about 61% and 39%, respectively.
H s H s Fig. 14 shows the degree of pitch motion in significant responses which is influenced by significant wave height. The larger the incoming , the larger the pitch of the two platforms. The quad-spar has lower pitch responses than that of the catamaran. The difference in the degree of pitch response is an average of 63% under the condition with turbines and 40% under the condition without turbines. When the potential location has of 1.16 m, the quad-spar has degree of pitch response of 0.28° under the condition with turbines and 0.75° under the condition without turbines. Then, the catamaran has degree of pitch response of 0.76°u nder the condition with turbines and 1.25° under the condition without turbines.

H s
The last investigation of rotational response is yaw. This response pattern is shown in Fig. 15. The yaw of the catamaran has higher degree than that of the quad-spar. The difference reaches average value of 95% under the condition with turbines and 44% under the condition without turbines. On =1.16 m, the catamaran has the yaw response degree of 0.38° under the condition without turbines and 0.18° under the condition with turbines. Then, the quad-spar has the yaw response degree of 0.009° under the condition with turbines and 0.22° under the condition without turbines.
H s At =0.09−1.16 m, the rotational motion of the quadspar is consistently smaller than that of the catamaran. The very significant difference of motion responses is influenced by the configuration of the floaters which gives great damping to the platforms. The following analysis is about the maximum tension of the mooring system of the platforms with turbines.
A maximum tension of mooring is caused by the wave frequency motion. In the beginning of the incident, the mooring cables receive more external force. When the external force is no longer working, the viscosity of the fluid reduces the oscillation of the platforms and the tension of the mooring cables. The tensions are presented in Fig. 16a for mooring cables of the catamaran and Fig. 16b for moor-Fig. 15. Significant wave height effect on yaw response. Sony JUNIANTO et al. China Ocean Eng., 2020, Vol. 34, No. 5, P. 677-687 H s ing cables of the quad-spar. For these graphs, the cable tensions of the quad-spar are smaller than those of the catamaran. This condition follows the value of response amplitude where the responses increase, the cable tensions increase. According to these graphs, the highest maximum tension is in Cable 3 because this cable gets more thrust than the others. Table 6 shows the percentage of the maximum tension difference in Cable 3 between the quad-spar and the catamaran. The percentage of the difference increases from 7.87% to 32.7% in line with the increasing .

Random wave effects on spectral responses
This section explains the spectral response due to random wave in order to analyze a peak spectrum position before the platforms are installed. A peak of the spectral responses informs the wave frequency which must be avoided while the platform is being operated. Resonance may occur when the platform operated on the ocean waves with critical frequency. The quad-spar and catamaran with turbines have a specific pattern in roll, pitch and yaw. These graphs show an area below the spectral responses which are affected by the wave significant height in the range of the wave frequency. Fig. 17 shows the wave spectra which are calculated by ITTC with Eq. (4) and influence the rotational spectral density. The wave spectra have one peak which occurs in the wave frequency of about 1.02 rad/s. The increase of the wave spectra follows the increase of H s . The area under the curve is formed in a wide frequency range. The condition makes it possible to create more than one peak of spectral responses, for example, roll and yaw spectral responses ( Fig. 18 and Fig. 20).
H s Fig. 18 shows the spectral response of roll motion. The catamaran has a different pattern compared to that of the quad-spar. The peak value of the catamaran roll response is higher than that of the quad-spar. For example, on =1.16 m, the catamaran has a peak response roll value of 0.000 2 rad·s whereas the quad-spar has a peak value of 0.000 1 rad·s. In other words, the use of four buoyant legs as supporting platform can reduce the spectral response of the roll motion in the order of 50%. H s Fig. 19 explains the peak position of pitch spectral response. When =1.16 m, the catamaran has the peak spectral response value of 0.002 rad·s. The quad-spar has the spectral response peak value of 0.000 7 rad·s. The spectral response of catamaran has the sleek graphs. This condition explains that the length of the deck affects the stability of the twin quad-spar, where the length of the deck becomes the factor of the return arm of the pitch moment caused by  the wave. The configuration may give a high spectral response with high significant wave height. Therefore, the spectral response of pitch motion on the catamaran is higher than that of the quad-spar.
The rotational motion of yaw has significant difference in spectral response between the catamaran and the quadspar. Fig. 20 shows that the peak values of the spectral motion response of the catamaran are averaged 10 5 times larger than that of the quad-spar. Where =1.16 m, the catamaran has the peak value of 0.000 1 rad·s, while the quadspar has the peak value of rad·s. The use of four buoyant legs and a deck as supporting structure may significantly reduce yaw motion.
The spectral response of rotational motion on the quad spar and catamaran has different peak values with wave spectra (Fig. 10). In other words, this response is influenced by the resonance frequency of its configuration and is produced by a small frequency range. The quad-spar and catamaran cannot be used directly as a reference to select the type of platform with a low rotation response.

Supplementary study of supporting platform configurations
The main topic of this paper is about motion response of the moored quad-spar and catamaran. As a reinforcement of the results, this section explains the economic impact as the second effect of the platform configuration. The quad-spar and catamaran have the different buoyant structures which have the own area. Therefore, the stuctures require a steel plate according to the dimension of those.   Sony JUNIANTO et al. China Ocean Eng., 2020, Vol. 34, No. 5, P. 677-687 685 The analysis is continued by calculating the number of steel plate requirement which will be produced. Based on Table 7, the quad-spar surface area is smaller than the catamaran. Therefore, there is less need for steel plates on the quad-spar and has lower purchase cost. According to industrial condition, the assumption is in a basic calculation with steel plate size of 4.7 mm×1.52 m× 6.1 m and a price of US$171.32 per unit.

Conclusions
In this paper, the moored quad-spar and catamaran are analyzed with and without turbines. This study provides result that the quad-spar has lower motion response than the catamaran. The motion response is analyzed based on the frequency domain on random wave which gives attention to roll, pitch and yaw.
Low degrees of rotational motion can lessen interference with the tidal current turbine performance. Numerical simulation produces roll motion of the quad-spar about of 44% of the catamaran. In pitch motion, the result of this analysis shows that the quad-spar has the response about of 38% of the catamaran. Furthermore, the quad-spar also has a yaw motion response about of 5% of the catamaran.
The mooring system of quad-spar and catamaran has a varying tension because of different motion responses and incident waves. The quad-spar has smaller cable tension than the catamaran under all conditions. For the mooring cable 1 to cable 4, the tension of the quad-spar mooring cables are on average about 71%, 70%, 77%, and 79%, respectively, compared to those of the catamaran.  Sony JUNIANTO et al. China Ocean Eng., 2020, Vol. 34, No. 5, P. 677-687