**1. Introduction**

Although coal is the earliest type of fossil fuel used by human beings, it has always a serious air pollution impact. The nuclear waste treatment and the warm drainage are the major environmental impact issues. Therefore, at present, most countries have started to use renewable energy. Taiwan is an island located in the eastern part of Asia and on the west side of the Pacific Ocean. Taiwan's imported energy accounted for 98.16% of its total energy usage in 2018. It is urgen<sup>t</sup> for the Taiwanese governmen<sup>t</sup> to develop and increase its renewable energy percentage. Taiwan's northeast monsoon is very strong, especially in the Taiwan Strait. According to the 4C Offshore reported in 2014, the world's 23-year average wind speed observation found that the Taiwan Strait has accounted for 16 places of the world's 20 most windy offshore wind farms. For this reason, the Taiwanese governmen<sup>t</sup> approved the "Thousand Sea and Land Wind Turbines". The goal is to complete the land wind farm installation with a capacity of 1200 MW. In addition to land farm, the offshore wind farm project is expected to be completed in 2025 with a capacity of 3000 MW and 1000 wind turbines will be installed in the near west coast of Taiwan.

Taiwan is located in the volcanic belt of the Pacific Rim, and it is in the active seismic zone. High seismic activity and frequent typhoon attacks are the threats to offshore structures. Therefore, the offshore structure is usually equipped with a damping device to suppress the vibration of the

structure under extreme loading conditions and reduce the fatigue damage caused by the long-term cyclic loading, thereby prolonging the service life of the o ffshore structure.

#### *O*ff*shore Wind Turbine (OWT)*

O ffshore wind turbines are developing rapidly in recent years because the OWTs have higher wind speeds, less noise, and less land occupation than on-land WTs. The OWTs may generate large amounts of energy as the extreme wind and wave loads act on the OWTs, which usually have a slender supported tower and a monopile foundation. Therefore, the damping device is needed to reduce the dynamic response of OWTs. Structural control includes active, semi-active, and passive control, and the passive control is the simplest control method. The tuned mass damper (TMD) is a passive control that absorbs structural vibration by mass swing. For example, the control system of the top floor of Taipei 101 is a tuned mass damper. Murtagh et al. [1] applied TMD to control the vibration of the OWT, and two TMDs were placed in the cabin of OWT to reduce the vibration in the fore-aft and side-to-side directions. Sun and Jahangiri [2] designed a three-dimensional pendulum tuned mass damper (3d-PTMD) to control the multi-directional vibration of the OWT, and it has 10% more damping e ffect than double TMDs have. Hemmati and Oterkus [3] developed a semi-active TMD for the vibration reduction of OWTs; they used a short-time Fourier transform to adjust the damping system to the instantaneous frequency of the system to achieve a better damping e ffect. The results showed that the performance of a semi-active TMD with a mass ratio (the ratio of mass of TMD to mass of the structure) of 1% is better than a passive TMD with a mass ratio of 4%. Since the installation and maintenance costs of TMD are quite expensive, in order to reduce the cost, the tuned liquid damper (TLD) has been developed. The sloshing liquid counteracts with the externally applied force to achieve the shock absorption e ffect. The working principle of TLD is based on sloshing of the liquid to absorb a portion of the dynamic energy of the structure subjected to dynamic loadings and thus controls the structural vibration.

As early as 1950, the TLD has been used to stabilize ships. Modi and Welt [4] used the liquid sloshing in the annular tank to dissipate the sloshing energy and evaluate whether the damper can attenuate the low-frequency vibrations of the structure in aerodynamics, and that damper can e ffectively suppress the vibration of the structure under wind loads. Fujii et al. [5] developed multi-layer tuned liquid dampers (TLDs), which were used in the Nagasaki Airport Building (42 m high) and the Yokohama Marine Building (101 m high) under strong winds, which can reduce structural vibration by about 50%. Kareem [6] avoids calculating complex free liquid levels by converting the sloshing of the liquid into a particle spring system, and then simulated the e ffect of TLD installation in high-rise buildings. Sun et al. [7] established a rectangular nonlinear TLD model, using the shallow water wave theory to consider the damping e ffect and breaking waves of the liquid, and then using fluid–solid coupling to obtain the e ffect of TLD on the structure. Wakahara et al. [8] studied the optimization of TLD design on high-rise buildings, explored the parameters of changing TLD design, and developed new methods to predict the suppression of high-rise buildings by TLDs. Tamura et al. [9] set up TLDs on buildings to verify the motion reduction e ffect of the TLD. It turns out that the TLD can significantly improve the durability of the building.

Sakai [10] proposed another TLD-based damping method, tuned liquid column damper (TLCD), which used a U-tube as a container for liquids, and the vibration of the structure is reduced by the sway of the liquid in the tube. Colwell and Basu [11] used a TLCD to reduce the vibration of OWTs under wind and wave loads, and they applied Miner's law in their fatigue analysis. They reported that TLCD can e ffectively reduce the vibration generated by strong winds and waves, and it can also reduce the fatigue damage caused by wind waves. However, because the OWT is a long and narrow structure, the performance of the TLCD depends on the width of the bottom and the total length proportion. The greater the proportion of the bottom width, the better the shock absorption performance, but the width of the OWT is limited (cannot be large), and the performance of the container is limited as well. On the other hand, the TLCD can only absorb vibration in one direction, but the direction of the wind

and waves on the sea does not necessarily coincide, so the load action on the OWT is not only in one direction. Colwell suggests that it can install multiple sets of TLCDs in different directions or use TLD to achieve multi-directional damping. Jin et al. [12] used a cylindrical TLD to control the vibration of the offshore platform, and they used the lumped mass method to simulate the effect of the TLD on the structure. The results are consistent with the experiment, and they concluded that the TLD could effectively reduce the structure motion during earthquakes. However, the earthquakes were the only loads considered in their study.

In the previous studies, not all the environmental loads, such as wind, waves, and earthquakes, were considered. Therefore, this study proposed setting multiple TLDs on the top of OWTs to reduce the motion of OWTs under various environmental load conditions including wind, waves, and earthquakes. The most recent reported study of Chen and Yang [13] indicated once the natural frequency (ωl) of a TLD is equal to the exciting frequency (ωx), the TLD may have the best motion reduction effect. As a result, the natural frequency of the TLD may be tuned to the natural frequency (ωs) of the OWT, and good motion reduction of the OWT can be expected. The study mainly refers to the International Electrotechnical Commission (IEC) and the internationally renowned certification unit DNV (Det Norske Veritas) [14] for the environmental load simulation and analysis. The supported tower, monopile foundation, and wind turbine models refer to the 5 MW WTs designed by Jonkaman et al. [15] and Jonkman and Musial [16]. Wind and wave loads are generated by the FAST program, which was developed by the National Renewable Energy Laboratory (NREL). The FAST program can perform the wind analysis of the wind turbine during operation, startup, parked, shutdown, and standby states. The turbulent wind field simulation was made by the TurbSim program, which was also developed by NREL. The wind and wave conditions refer to the results of the feasibility study of Taipower's second phase offshore wind power project. The wave conditions are the appropriate wave height and period at the water depth of 20 m in the Changbin offshore project wind field in Taiwan, and the corresponding wind speed is at 90 m elevation. The required wind field and wave conditions were determined according to IEC 61400-3 design load (Design load case) regulations [17].

Turbsim simulates the wind field in the frequency domain using single-point power spectral density, spatial correlation function, and Taylor turbulence hypothesis. The FAST uses the blade element momentum theory to calculate the force of the wind acting on the blade. In this study, the hydrodynamic load evaluation of the supporting structure is referred to the above relevant specifications, and it considered the regular wave and the irregular wave models. After obtaining the dynamic characteristics of the wave particles, the hydrodynamic load can be calculated by using the Morison equation.

The TLDs were set at the top of the tower, and the two-way fluid-solid coupling module of ANSYS was used to simulate the interaction between the TLD and the structure. This study also designed simple experiments to verify the accuracy of numerical simulation. Then, this study explored the effect of TLD on offshore wind turbines under various wind and wave conditions. We also used the rainflow-counting method and the Miner's rule to do the fatigue analysis. Section 2 introduces the methods used in this study and they include FAST and Turbsim, as well as ANSYS-Fluent and ANSYS-Mechanical modules. The environmental loads according to IEC 61400-3 were also described in the section. Section 3 reports the simulation results and experimental measurements and numerical results validation. The effects of multiple TLDs on structural motion control were investigated in the section. The fatigue analysis of OWT with TLDs was also reported in this section. The final section lists the concluding remarks found in this study.

#### **2. Methods Used**

FAST is a computer-aided engineering (CAE) software developed by NREL, which is mainly used to simulate the dynamic responses of a wind turbine. FAST incorporates aerodynamic models (AeroDyn), hydrodynamic models of offshore structures (HydroDyn), control and motor system

dynamic models (ServoDyn), and structural dynamic model (ElastoDyn and SubDyn). FAST can simultaneously couple air, fluid, motors, and structures in the same time domain.

#### *2.1. Environmental Loads*

The environmental conditions included wind, waves, and current. A full field wind speed above mean sea level (MSL) was established based on the field data measured by the Central Weather Bureau, Taiwan. Regarding hydrodynamic loading, the ocean conditions considered in this study include waves, ocean currents, and water levels.

#### 2.1.1. Wind Model

This study selects the wind speed and wind field model of the wind field according to the IEC 61400-3 specification, and then it uses the TurbSim to simulate the wind field. TurbSim is a random, global, turbulent wind field simulator. Simulating the time series of three wind speed vectors on two-dimensional orthogonal grid points, TurbSim generates the wind spectrum frequency by wind speed, turbulence model, wind field model, etc. Then obtains the time history of the wind field by inverse Fourier transform. The data generated by TurbSim can be used by inputting AeroDyn in FAST. Then, it inputs TurbSim's two-dimensional wind field data in AeroDyn, converts it into a three-dimensional wind field by Taylor's frozen turbulence hypothesis, linearly interpolates the wind speed on the node, and converts it into an external force on the node. The force on the blade is theoretically analyzed by blade element momentum theory, and the blade tip loss correction factor is also considered. The FAST simulation procedure is shown in Figure 1.

**Figure 1.** The simulation procedure of FAST (National Renewable Energy Laboratory, or NREL).

The wind load of the rotor nacelle assembly (RNA) and the structure (the tower and substructure are included) were evaluated separately. The wind load of the support structure is based on DNV-RP-C205 (DNV 2014) [18], while FAST analysis provides the wind load of RNA. According to the IEC 61400-1 specification (IEC 2005) [19], the relevant parameters of the standard wind-turbine (WT) class are shown in the Table 1.

**Table 1.** Wind related parameters of the wind-turbine (WT) classes.


Vref is the 10-min average wind speed at RNA, and Iref is the turbulence intensity within 10 min.

According to IEC 61400-1, the WT class I-A was adopted, and the reference wind speed Vref and turbulence intensity Iref were set as 50 m/s and 0.16, respectively. The longitudinal turbulence scale parameter Λ1 is shown in Equation (1) as

$$\Lambda\_1 = \begin{cases} \ 0.7z, \ z\_{ref} \le 60 \ m \\\ \ 42, \ z\_{ref} > 60 \ m \end{cases} \tag{1}$$

where *z* is the height above the still water level, and *zref* is the height at the RNA center.

The longitudinal standard deviation of the normal turbulence model is the standard deviation of 90% of the average wind speed at the height of the hub (nacelle), and it can be estimated by

$$\sigma\_1 = I\_{ref}(0.75V\_{ref} + b), \text{ b} = 5.6 \text{ m/s}.\tag{2}$$

The turbulent extreme wind speed model has a 10-min average wind speed of *V*50 and *V*1, respectively, in the 50-year and 1-year regression periods:

$$V\_{50} = V\_{ref} \left( z / z\_{ref} \right)^{0.11} \tag{3}$$

$$V\_1 = 0.8V\_{50}.\tag{4}$$

The standard deviation of the longitudinal turbulence is:

$$
\sigma\_1 = 0.11 V\_{ref}.\tag{5}
$$

The annual data for buoys and tidal observations provided by the Central Weather Bureau, Taiwan were used in this paper, and monthly wind speed statistics and hourly wave records were obtained from the Hsinchu Buoy Station and monthly tidal statistics were obtained from the Waipu Tide Station in the Taiwan Strait.

#### 2.1.2. Wave Model

According to the design load case of IEC 61400-3 (IEC 2009) [17], regular waves and irregular waves can be used. Regular waves include linear and nonlinear waves, and the linear wave is applicable when the wave height is small. When the wave height increases or the water depth becomes shallow, the wave peaks become sharp, and the troughs become flat. At this time, the linear wave theory is not enough to describe the waveform and the movement of water particles, so the nonlinear wave should be used, and one can use the streamline function theory to describe nonlinear waves in the most water depths. Once the water depth, period, and wave height were determined, the required wave theory can be determined accordingly (DNV OSJ101, 2014) [18]. Irregular waves usually describe in terms of their spectra, and the JONSWAP and Pierson–Moskowitz spectra are the most commonly used spectra. In this study, the water depth of 20 m was assumed, the stream wave function was used in the regular wave model, and the JONSWAP spectrum was applied to the stochastic irregular wave model.

#### 2.1.3. Current Model

Ocean currents always vary in space and time, but they are usually defined as a uniform horizontal flow field with a direction and flow rate that varies only with water depth. According to IEC 61400-3, the current model is divided into three types: sub-surface currents, near surface currents, and surf underflow currents. In this study, the sub-surface current model was used and they can be expressed as:

$$\mathcal{U}\_{\mathfrak{sl}}(z) = \mathcal{U}\_{\mathfrak{sl}}(0) \left( \frac{z+d}{d} \right)^{1/7}. \tag{6}$$

The free surface current speed *Uss* (0) was measured at the OWT site. After selecting the wave theory and current model, the speed and acceleration of water particles can be obtained, and Morison's equation was used to calculate the forces acting on the structure by the waves and currents.

#### *2.2. ANSYS Fluent*

ANSYS Fluent is a CFD (Computational Fluid Dynamics) software developed by ANSYS. To study TLDs on the motion reduction for OWT, we combined the fluent and structural analysis modules of ANSYS to simulate the fluid–structure interaction between TLDs and OWTs. We adopted Reynolds-Average Navier–Stokes Equation Models (RANS) and a standard *k*-<sup>ε</sup> model to solve the flow passing marine turbines. The detailed description of the model is as follows:

The RANS momentum equations can be written as

$$
\rho \left( \frac{\partial \overline{u}\_i}{\partial t} + \mathcal{U}\_k \frac{\partial \overline{u}\_i}{\partial \mathbf{x}\_k} \right) = -\frac{\partial p}{\partial \mathbf{x}\_i} + \frac{\partial}{\partial \mathbf{x}\_j} \left( \mu \frac{\partial \overline{u}\_i}{\partial \mathbf{x}\_j} \right) + \frac{\partial \mathcal{R}\_{ij}}{\partial \mathbf{x}\_j} \tag{7}
$$

where ρ is fluid density, μ is dynamic viscosity, *p* is pressure, *ui* is velocity component, *xi* is coordinate, *t* is time, and *Rij* is the Reynolds stress. The eddy viscosity model was used, and the Reynold shear stress can be written as

$$R\_{i\bar{j}} = -\rho \overline{u'\_i u'\_{\bar{j}}} = \mu\_l \left(\frac{\partial \overline{u}\_i}{\partial \mathbf{x}\_{\bar{j}}} + \frac{\partial \overline{u}\_{\bar{j}}}{\partial \mathbf{x}\_{\bar{i}}}\right) - \frac{2}{3} \mu\_l \frac{\partial \overline{u}\_k}{\partial \mathbf{x}\_k} \delta\_{i\bar{j}} - \frac{2}{3} \rho k \delta\_{i\bar{j}} \tag{8}$$

δ*ij* = 1 when *i* = *j* and 0 when *i* - *j*. Lai et al. (2016) used three turbulence models to investigate the optimal turbine blades, and they are the "Realizable *k*-<sup>ε</sup> two layer", "standard *k*-<sup>ε</sup>", and "*k*-<sup>ε</sup> SST". They found that the results of three different models are about the same. Then, we chose the "standard *k*-ε" model. Then, we have μ*t* = f(ρ*k*<sup>2</sup>/ε), where *k* and ε are the turbulent kinetic energy and turbulent kinetic energy dissipation rate, and they can be defined as

$$\delta k \equiv \overline{u'\_i u'\_j}/2 \text{ and } \varepsilon \equiv \nu \overline{\partial u'\_i/\partial \mathbf{x}\_j (\partial u'\_i/\partial \mathbf{x}\_j + \partial \mathbf{u'}\_j/\partial \mathbf{x}\_x)}. \tag{9}$$

Turbulent energy equation of the standard *k*-<sup>ε</sup> model equations:

$$\frac{D(\rho\varepsilon)}{Dt} = \frac{\partial}{\partial \mathbf{x}\_j} \left[ \left( \mu + \frac{\mu\_l}{\sigma\_\varepsilon} \right) \frac{\partial \varepsilon}{\partial \mathbf{x}\_j} \right] + \mathbf{C}\_{\varepsilon 1} \frac{\varepsilon}{k} \mathbf{G}\_k - \rho \mathbf{C}\_{\varepsilon 2} \frac{\varepsilon^2}{k} \tag{10}$$

where *Gk* can be defined as

$$\mathbf{G}\_k = \rho \nu\_t \frac{\partial \overline{u}\_i}{\partial \mathbf{x}\_j} \left( \frac{\partial \overline{u}\_i}{\partial \mathbf{x}\_j} + \frac{\partial \overline{u}\_j}{\partial \mathbf{x}\_i} \right). \tag{11}$$

The values of all the constants are empirically as *C*μ = 0.09, *C*ε<sup>1</sup> = 1.44, *C*ε<sup>2</sup> = 1.92, and σ*k* = 1.0.
