**1. Introduction**

An excellent, natural energy resource is the Kuroshio strong current flowing along the east of Taiwan, which has an estimated electricity capacity of 4 GW [1]. Ocean current is one of the potential energy sources to be developed. However, the seabed beneath the Kuroshio current is almost over 1000 m in the area mentioned above. Moreover, several typhoons strike Taiwan every year. These two disadvantages must be solved before a current power generation system is constructed.

Investigation of fluid–structure interaction (FSI) is important for marine engineering, aircraft, engines, bridges and biotechnology. FSI is the interaction of some movable or deformable structures with an internal or surrounding fluid flow. Fluid–structure coupling can be simply divided into one-way coupling and two-way coupling. One-way coupling ignores the change of flow field space caused by structural deformation, so the calculation is more simplified. Anagnostopoulos [2] investigated the dynamic response analyses of offshore platforms under wave loadings and predicted the wave forces by means of Morison's equation. Therefore, the equation of motion for the lumped mass idealization of the platform was presented. The system was one-way coupling. It was found that the

**Citation:** Lin, S.-M.; Liauh, C.-T.; Utama, D.-W. Design and Dynamic Stability Analysis of a Submersible Ocean Current Generator Platform Mooring System under Typhoon Irregular Wave. *J. Mar. Sci. Eng.* **2022**, *10*, 538. https://doi.org/10.3390/ jmse10040538

Academic Editor: Eugen Rusu

Received: 13 February 2022 Accepted: 10 April 2022 Published: 14 April 2022

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importance of fluid–structure interaction increased with higher dynamic amplifications. The effect of viscous damping due to the relative velocity between fluid and structure significantly decreased the resonant response. Istrati and Buckle [3] investigated the effect of FSI on connection forces in bridges caused by tsunami loads by using LS-DYNA software. It was found that the flexibility and the dynamic characteristics of the bridge structure significantly influenced the external tsunami loads on the bridge and the connection forces.

Xiang and Istrati [4] investigated the solitary wave–structure interaction of complex coastal deck geometries by using the Lagrangian–Eulerian (ALE) method with a multiphase compressible formulation. It was found that, for small wave heights, the horizontal and uplift forces increased with the number of girders (Ng), while, for large waves, the opposite happened. Moreover, if the Ng was small, the wave particles accelerated after the initial impact on the offshore girder, leading to more violent slamming and larger pressures and forces on the deck. Conversely, if the Ng was large, unsynchronized eddies were formed in each chamber, which dissipated energy and resulted in weaker impacts on the deck. Obviously, if the surfaced structure is too large, the two-way coupling effect of wave– structure interaction needs to be considered. In addition, the multi-phase flow simulation needs to be considered in the numerical analysis, which is a very challenging problem and important in marine engineering. Some literature [4–6] is devoted to this research. Peregrine et al. [5] found that the breaking/broken waves and bores were dominated by significant turbulence effects and air entrapment. The hydrodynamic loads caused by the breaking wave on the marine decks were totally different from unbroken waves [6].

Firouz-Abadi et al. [7] investigated the stability analysis of shells conveying fluid. The boundary element method was applied to model the potential flow. It was found that the eigenvalues and mode shapes of the flow in the shell were strongly related to the unsteady pressure that induced the shell vibration. Bose et al. [8] investigated the flow-induced dynamic stability of a fluid–structure interaction (FSI) system comprising of a symmetrical NACA 0012 airfoil supported by non-linear springs. Lin et al. [9] investigated the wave propagation of an artery. A mathematical model was proposed to describe the wave propagation through an isotropic, elastic, thick tube filled with viscous and incompressible fluid. The tube is supported by the elastic muscle and simulated as the viscoelastic foundation. The flexural Young and Lamb wave modes through a tube wall are presented simultaneously. The dispersion curves and the energy transmissions of the three modes were investigated. It was found that the effect of the viscoelastic foundation constant on the wave speed and the transmission was significant.

The numerical method is usually used to investigate the dynamic behavior of the two-way-coupled FSI. In general, the numerical methods include the boundary element method [10], the finite volume method [11], the finite-element-based, arbitrary Lagrangian– Eulerian method [12], particle-based methods, such as smoothed particle hydrodynamics [13], and hybrid methods, such as coupled SPH-DEM [14] and coupled SPH-FEM [15].

There have been two cases where the performance of ocean current turbines was tested in seas: (1) One 50 kW ocean current turbine, developed by the Wanchi company (Kaohsiung City, Taiwan), was successfully moored to the 850 m deep seabed near the offshore of Pingtung County, Taiwan, by Chen et al. [1]. The current turbine generated about 26 kW under the current speed of 1.0 m/s; (2) An experimental 100-kW-class ocean current turbine was located off the coast of Kuchinoshima Island, Kagoshima Prefecture, and demonstrated by IHI and NEDO [16]. The current turbine generated about 30 kW under the current speed of 1.0 m/s. The turbine system 50 m below the sea surface was connected to the mooring foundation on the seabed at the depth of 100 m. The above experiments were conducted under the condition of small waves, and the influence of waves on the dynamic stability of the mooring system was not studied.

Zwieten et al. [17] investigated the C-plane prototype of an ocean current turbine with a hydrodynamic platform that was connected to the seafloor with a rope. This turbine, using its wingtips and canard to manipulate its depth and orientation in a temporally and spatially varying current, could generate maximum energy production. This study did not

take the problem of turbine damage due to excessive water pressure when diving too deep into consideration. It also did not consider the disadvantages of the deeper ocean current, the lower flow rate and the smaller power generation. The effect of waves was also not considered.

One of the most challenging tasks for the ocean current turbine system is to develop a deep mooring technology because the targeted seabed is at a depth of almost 1000 m, as mentioned. To monitor the performance of the ocean turbine, the dynamic stability of the mooring system under the coupled effect of the ocean current and wave is needed [18–24]. Lin et al. [25] used the ocean current turbine system developed by the Wanchi company to investigate the dynamic stability of the system subjected to regular wave and current forces. The mooring system was composed of a turbine, a floating platform, traction ropes and a mooring foundation. Results showed that the effects of several parameters of the system on the dynamical stability of the ocean current turbine system were significant. However, the dynamic tension of the rope was not investigated in the study.

As the mooring foundation is set on the seabed over 1000 m deep, a long mooring rope is required. Consider the strength of the rope: lightweight, high-strength PE mooring ropes are more beneficial than chain and steel ropes. Lin and Chen [26] found that, when the ocean current velocity was 1 m/s and the rope length was about 2900 m, the drag force was 15 tons, and the rope was almost straight. In other words, the bending deformation of the PE rope was negligible. The deformation of the rope was longitudinal only. Accordingly, the mooring system is simulated in the linear elastic model to analyze the problem of dynamic stability. Consider an ocean current power generation system composed of a surfaced turbine, a floating platform, a towing rope and a mooring foundation [25]: whenever a typhoon hits, the turbine generator is towed back to the shore to avoid any possible damage, leaving the mooring system in the sea. Lin and Chen [26] proposed a protection method to protect the mooring system that avoids the damage caused by typhoon wave current. The principle of the design is that the platform generates a negative buoyancy to dive by letting water flow into its inner tank, and the pontoon is used to create a positive buoyancy. When the two elements are connected by a rope to achieve static equilibrium, the floating platform is submerged at a fixed depth determined by the rope length. Furthermore, the linear elastic model is used to construct the coupled motion equation of the system under a regular wave. The analytical solutions of the coupled equations are derived. It is theoretically verified that the proposed protection procedure can avoid the damage of the floating platform and the mooring line due to typhoon wave impact.

Lin et al. [27] simulated a mooring system for ocean current generation during nontyphoon periods and proposed a system that keeps the turbine statically stable at a designed underwater depth to ensure that the ocean current generator can generate electricity effectively. In their design, the turbine generator is connected to a surfaced platform, the platform is anchored to the deep mooring foundation by lightweight, high-strength polyethylene ropes and a pontoon is connected to ocean current turbines with rope. The static balance of the ocean current turbine is formed. Therefore, the depth of the current turbine can be determined by the length of the rope. Additionally, the linear elastic model is used to simulate the motion equation of the overall mooring system under a regular wave. The theoretical solution of the static and dynamic stability analysis of the mooring system is proposed. The dynamic displacements of the components and the dynamic tensions of ropes under the regular wave and ocean current are investigated. It is found that the effect of the wave phase on the dynamic response of the system is significant. The length of the rope can be adjusted to avoid resonance and reduce the tension of the rope. In addition, a buffer spring is used to reduce the dynamic tension of the rope to increase the safety and lifespan of the rope significantly.

To simplify the actual ocean waves, which are irregular, three approaches are commonly adopted: (1) the approximation of the wave field by a single, sinusoidal component with a given height, period and direction (regular waves); (2) the use of a limited number of harmonics of a primary wave to approximate non-sinusoidal properties (irregular waves); and (3) the representation of the water surface by an infinite summation of Fourier

components (wave spectrum) [28]. Pierson and Moskowitz [29] presented the Pierson and Moskowitz wave spectrum. The assumption was that, if the wind blows steadily over a large area for a long time, the waves will reach equilibrium with the wind. This is the concept of a fully developed sea, which requires winds of a sea that continuously blow over hundreds of miles for several days to reach full development. Hasselmann et al. [30] experimentally found that the wave spectrum can never be fully developed. The wave spectrum continues to develop due to wave-to-wave interactions, even over long periods of time and distances. Therefore, the Pierson–Moskowitz spectrum is modified to add an additional and somewhat artificial factor to it to make the wave spectrum and experimental measurements more closely matched. The Jonswap wave spectrum is presented.

This study proposes a mooring design in which the ocean current generator still generates electricity when typhoon waves hit without interruption. To prevent the typhoon waves from invading the ocean current generator set, a process is adopted whereby the system dives below 60 m to avoid the damage of the typhoon waves. At the same time, to prevent diving too deep from damaging the turbine, the turbine is in a static balance at a predetermined depth underwater, and it must be able to maintain the a not-too-large dynamic displacement. The surface velocity of the Kuroshio in eastern Taiwan is relatively fast, and the deeper the water depth, the smaller the velocity. Therefore, the ocean current generator group should not be placed too deep. This study proposes a safe and efficient mooring system design and a linear elastic model to simulate the motion of the entire mooring system. Results for analyzing the static and dynamic stability of mooring systems, the dynamic displacements of turbines, floating platforms, pontoons and the dynamic tension of ropes under the action of typhoon waves and ocean currents are studied. The effects of several parameters on the dynamic behavior of the system are presented.
