Numerical Study on the Dynamic Characteristics of a Coupled Wind–Wave Energy Device

Abstract

A wind–wave coupled device integrating an offshore fixed wind turbine and an OWC (oscillating water column) wave energy device is proposed in this study. Its dynamic characteristics under extreme environmental conditions are analyzed for practical design and development using a numerical model established based on the commercial finite element method platform ANSYS-Workbench, which is then validated using experimental data for an offshore fixed wind turbine model. The modal analysis results indicate that installing the OWC system does not modify the basic dynamic characteristics of the original wind turbine. Under different extreme environmental conditions at different design water levels, stress concentration can be observed at different locations on the structures. Although the gap between the sub-chambers of the OWC system can be increased to reduce stress on the chamber and piles, an excessively large gap will enhance structural complexity and increase construction costs. An appropriate relative size for the gap between the sub-chambers is recommended for practical design.

1. Introduction

Ocean renewable energy has become increasingly critical for social and economic development. As individual energy resources currently face limitations in widespread utilization, developments in integration have become inevitable. The characteristics associated with wind and wave energies make their joint utilization an innovative solution for electricity generation in terms of application. With their development, wind turbines are becoming larger in size and being operated at greater water depths [1]. Wind turbine foundations for offshore sites in shallow waters comprise the gravity base, monopile, jacket-frame, semi-submersible, and tension-leg platforms [2]. Wave energy is another renewable energy source in the ocean, characterized by abundance, high flux density, and wide distribution. Based on the operation principle of a prime mover, wave energy converters (WECs) can be classified as oscillating water column (OWC), overtopping, and oscillating body [3]. Different types of wave energy converters can be employed according to the power output requirements and environmental conditions.

Various coupled wind and wave energy devices with fixed foundations have recently been proposed. For instance, a joint device integrating an OWC WEC and monopile and jacket-frame foundations was proposed by a research team from the University of Plymouth [4], and a wave treader consisting of a monopile wind turbine foundation and oscillating wave surge converters was reported on by Green Ocean Energy [5]. In addition, a research team from the Ocean University of China proposed coupled devices integrating a hinged heaving-body WEC and a jacket-frame wind turbine foundation [6]. A device typically used for floating wind turbines is a semi-submerged wind turbine platform integrating an OWC WEC called the Mermaid multi-use platform [7]. A marine offshore renewable energy lab in Italy proposed a mixed platform coupling a spar-buoy wind turbine and three OWC WECs [8]. Other integrated devices include a wind–wave float coupling a semi-submerged wind turbine platform and a spherical WEC [9], a device coupling a semi-submersible wind turbine and a flap-type WEC [10], and a spar torus combining a spar wind turbine and a ring-type oscillating body WEC [11,12].

In the existing studies, offshore wind turbines have primarily been coupled with OWC and oscillating body WECs. Since OWC devices employ simple structures without any underwater movers and have good stability and reliability, there are good prospects for further developments involving the integration of wind turbines and OWC devices, which can effectively increase the quality and quantity of power output, mitigate harmful dynamic platform responses, and enhance the stability and cost-effectiveness of the system [13]. However, integrated platforms have more complex dynamic characteristics that present huge challenges. Such platforms are more sensitive to incident winds and waves, increasing the uncertainty through possible structural failures, and the force and dynamic responses of the coupled platform should thus be analyzed [14]. In addition, since the foundation of the wind turbine is compact, its installation and integration with an OWC device might cause a change in the inherent dynamic characteristics of the original structure leading to possible safety risks, which should be considered during design [15].

Offshore wind turbines are affected by different environmental loads, and analyzing the dynamic response under varying loads is meaningful for turbine design [16]. Most existing studies have focused on the effects of environmental excitations on the dynamic response of offshore wind turbines and the identification of modal parameters [17]. Monopile platforms are the most widely used supporting structures for offshore wind turbines [18] and have become a research hotspot. Cong et al. integrated four fan-shaped sub-chambers on a monopile, and an OWC device was co-axial with the monopile. The results indicated that the wave forces on the OWC and monopile could be balanced, obtaining a nearly zero net wave force [19]. Zhou et al. conducted numerical and experimental studies on an OWC coupled with a fixed monopile for offshore wind turbines and investigated the hydrodynamic performances of this OWC system [20]. The results showed that the OWC system could absorb wave power and thereby reduce the wave force on the monopile. In an actual sea state, the external loads on the wind turbine could generate the excited responses in the upper structure and induce vibrations in the pile foundation because of inertia [21]. The soil body vibrates because of the dynamic loads from the pile foundation, resulting in a reaction force from the soil body. Consequently, pile–soil interactions should be considered because of the characteristics of fixed foundations. Ding et al. studied the coupled effects of wind and waves on the monopile of an offshore wind turbine, considering the interactions between the monopile and soil body [22]. Their results indicated that the inherent structural frequency of the wind turbine decreased due to soil–monopile interactions, and the soil energy dissipation was the greatest under the wind–wave coupling load. Iqbal et al. explored the effects of the pile wall thickness, water depth, and wave height on nonlinear monopile–soil dynamic responses and found that when the pile diameter and wall thickness were increased, the dynamic impedance increased horizontally and vertically as the pile approached its tip [23]. The method most commonly used for dynamic response analysis is the finite element method (FEM). Pezeshki et al. studied the effects of free-surface elevation on the natural frequency of wind turbine vibration using nonlinear Stokes wave theory and considering wave–structure and soil–foundation interactions [24]. It was found that unreasonable simplification might cause a larger error in the natural frequency of vibration, with a peak value of 16.8%. Karpenko et al. proposed a numerical model that combines FEM and experimental measurements, which was used to investigate the dynamic characteristics of a laminated composite structure with nonlinear properties [25].

The technology underlying fixed foundations for wind turbines is relatively mature. The original fixed foundations could not support wind turbines with a rated power exceeding 2.0 MW because of insufficient structural strength [18]. A foundation in which multiple high piles are used to connect a cap was proposed for supporting turbines with larger rated powers and has been widely used in South China [26]. In terms of the offshore high-pile-cap foundation structure, piles were installed in the soil to reduce foundation settlement and minimize underwater operations [27]. A high-pile-cap foundation has larger vertical, horizontal, and bending bearing capacities compared to a foundation based on monopiles [28]. Furthermore, the high piles have varied bearing capacities, and more offsets could be used for piles experiencing larger forces, which might cause instability of the wind turbine foundation that affects system operation [29]. Thus, it is necessary to analyze the force characteristics of the high piles.

From the existing studies, it can be determined that the foundations of wind–wave coupled systems might have complex dynamic responses under the reciprocating loads from the wind and waves. There is sufficient area in the high-pile-cap foundation to deploy and install an OWC WEC. Although OWC WECs can absorb some wave power, they impact the stability of the foundation. There have yet to be any studies focusing on this type of wind–wave coupled device. Therefore, it is necessary to establish an FEM model of the coupled structure consisting of the foundation, wind turbine, tower, soil body, and OWC WEC for analyzing the dynamic response and stress distribution characteristics, ensuring that the natural frequency of the foundation structure does not match the excitation frequency from environmental loads and thereby suppressing the dynamic responses of the structure. In this study, an FEM model is established to analyze the OWC wind–wave coupled device using the ANSYS platform. Modal and quasi-static analysis is conducted to investigate the effects of the environmental loads and the gap between the sub-chambers on the natural characteristics of the device and the strain and stress at critical parts. The stability of the system is evaluated for checking safety and further optimization.

2. Coupled Wind and Wave Energy Device

The coupled wind and wave energy device is designed based on an offshore fixed wind turbine in the offshore wind farm located in the Haitan Strait in Fujian, China. At the location of the wind turbine, the mean water level is 17.7 m. The foundation is a high-rise pile cap with a diameter of 17.0 m and a height of 4.8 m. There are eight socketed steel-pipe piles with a diameter of 2.0 m and slope ratio of 5:1. Solid joints are employed for connections between the piles and the cap. The wind turbine has a rated power of 7.0 MW, rotor diameter of 158.0 m, and hub mounting center height of 100.9 m. The total mass of the nacelle and turbine rotor is 456.0 t. The supporting tower cylinder comprises four sections with bottom and top diameters of 7.0 m and 4.05 m.

The coupled wind and wave energy device is an integrated device in which an OWC WEC is attached to the foundation of the wind turbine such that the two devices operate together, and the electricity generated from the WEC is transmitted to the electrical system of the wind turbine for further processing, as shown in Figure 1. A steel foundation frame is designed for installing and attaching the OWC WEC to the wind turbine foundation. The frame has eight supporting rods each on two sides, which can help to resist the bending effects caused by the waves and currents. The welding points on the side frames and the anchoring plates on the cap at the two ends are connected through supporting rods. These supporting rods, installed on the piles by a hoop, are in turn connected to the steel plate on the third/fourth levels by welding. The steel plates in the frame generate eight sub-chambers arranged in two rows with varying drafts. The sub-chambers have a width of W = 1.8 m, and the gap between the sub-chamber D can be nondimensionalized as the relative gap D/W. The tops of the sub-chambers are covered by a shared chamber for cumulation of the reciprocating airflows generated by the sub-chambers. The air ducts are installed on top of the shared chamber and extended into an integrated container fixed on the first-level plane of the cap. The air turbines and electrical system are installed in this container.

The chamber heights are designed to adapt to different water levels to guarantee the operating duration. Based on local environmental conditions and existing studies, the bottom levels of the sub-chambers in two rows are set as −0.60 m and 0.70 m, respectively, with a bottom level difference of 1.30 m. The top level of the sub-chambers is fixed at 6.67 m, considering the total weight and submerging range. Therefore, the heights of the sub-chambers in the two rows are 7.27 m and 5.97 m, respectively. The shared chamber has a trapezoidal vertical-section profile and is separated into two parts by a division plate, which ensures that the air remains isolated, as there is no exchange between the two rows of the sub-chambers.

3. Numerical Model Setup and Validation

3.1. Governing Equations

For an inviscid, incompressible and irrotational fluid, the velocity potential ϕ can be written as a function of the time and position of the fluid particles ϕ(x, y, z, t):

$$u={\displaystyle \frac{\partial \varphi }{\partial x}},v={\displaystyle \frac{\partial \varphi }{\partial y}},w={\displaystyle \frac{\partial \varphi }{\partial z}}$$

(1)

where u, v, and w are the velocities of the fluid particle in the x, y, and z directions, respectively.

In addition, the Laplace equation can be expressed as follows:

$${\nabla }^2\varphi ={\displaystyle \frac{{\partial }^2\varphi }{\partial x^2}}+{\displaystyle \frac{{\partial }^2\varphi }{\partial y^2}}+{\displaystyle \frac{{\partial }^2\varphi }{\partial z^2}}=0$$

(2)

For the boundary condition, the seabed surface boundary condition at depth is applied to solve the dynamic equation:

$${\displaystyle \frac{\partial \varphi }{\partial z}}=0,z=-h$$

(3)

where h is the water depth. The free surface boundary condition can be written as:

$${\displaystyle \frac{{\partial }^2\varphi }{\partial t^2}}+g{\displaystyle \frac{\partial \varphi }{\partial z}}=0,z=0$$

(4)

where g is the gravity acceleration. The immersed body surface boundary condition can be described as:

$${\displaystyle \frac{\partial \varphi }{\partial n}}={\displaystyle \sum _{j=1}^6{V}_r}{f}_j(x,y,z)$$

(5)

where n is the normal vector, V_r is the velocity vector of the fluid particle, and f is surface equation of the object.

The dynamic water pressure can be derived from the Bernoulli equation as follows [30]:

$$p_i=-\rho {\displaystyle \frac{\partial \varphi }{\partial t}}-\rho gz-\rho {\omega }^2{\displaystyle \sum _i{\varphi }_j{e}^{i\omega t}}$$

(6)

where p_i is the dynamic water pressure at the monitoring point i; ρ is the fluid density, and ω is the wave angular frequency.

Then the wave force acting on the submerged part of the structure can then be expressed as:

$$F_w={\displaystyle \underset{s}{\iint }\left(p_i\cdot n\right)dS}$$

(7)

where F_w is the wave force and S is the wetted surface of the structure.

As the eigen solutions of the dynamic responses are solved for a specific structure, the structure model is discretized using the FEM technology. Based on the principle of the minimum potential energy, the differential equation of the motion can be derived as follows:

$$M{Q}^{″}+C{Q}^{\prime }+KQ=F$$

(8)

where M is the global mass matrix, K is the global stiffness matrix, and C is the global damping matrix; Q, Q′, and Q″ are the node displacement, velocity, and acceleration matrices, respectively; F is the external load matrix. If F is a null matrix, meaning that no external load is acting on the structure, the structure is in an automatic vibration state, where the natural mode shape of the structure is reflected. The modal analysis is free-vibration analysis, which is a method used for the analysis of structural dynamic characteristics. The natural frequency and vibration mode, which can be derived from modal analysis, are critical parameters for further analyzing the structural dynamic responses of the model under the joint action of wind, currents, and waves.

3.2. Numerical Model Setup

A three-dimensional (3D) numerical model of the coupled wind and wave energy device is established using the ANSYS-Workbench platform, as shown in Figure 2. The model is identical in size to an actual 7 MW offshore fixed wind turbine. The dead weight and center of gravity of each component are modeled according to the data provided by the manufacturer. The center of gravity of the wind turbine and the coupled wind–wave energy device are located 2.1 and 2.3 m below the top of the cap, respectively. To determine the frequencies for each order of the coupled device, the integrated structural model of the soil, steel pipe-piles, concrete cap, supporting tower cylinder, wind turbine, and OWC device is established using FEM.

The pile–soil interactions are calculated following the model proposed in the American Petroleum Institute (API) code [31]. As depicted in Figure 2a, a series of horizontal and vertical nonlinear springs are deployed on the piles with an interval of 1.0 m. The nonlinear springs in the horizontal direction follow the p–y curve in the API code, and the nonlinear springs in the vertical direction follow the t–z curve in the API code. In addition, the bearing capacity at the pile end is calculated using the Q–z curve in the API code. The length of the steel-pipe piles is 42.0 m, and the buried depth is 22.0 m. In the structural model, all materials are assumed to be homogeneous, with identical physical properties in all directions, and the stress–strain relationship follows Hooke’s law. Additionally, relative slip between the structural interfaces is neglected, and all structures are assumed to be rigidly connected without considering the interface setting. The surfaces of the structure are all set as no-penetration boundaries. The details of the finite element meshes generated by the internal grid tool in the ANSYS can be found in Figure 2b,c. Triangular panel meshes are used for the wind turbine blade tip, while quadrilateral panel meshes are employed for the surfaces of other structures, including the fluid–structure coupling interface. Mesh convergence verification was first conducted considering both convergence speed and computational accuracy, and the optimal mesh number for the model was determined to be 32100. In the simulations, the wind turbine blades are assumed to be stationary and nonrotating.

Quasi-steady analysis of the coupled device under the joint action of the wind, currents, and waves at the interface between the fluid and solid domains is conducted based on fluid–structure coupling using the load transfer method. As the actions of the fluid domain to the solid domain are the focus of this study, the one-way transfer of data from the fluid domain (AQWA module) to the solid domain (Transient Structural module) is used for the data at the interface. Specifically, the wave force loads are solved using the AQWA module, and it is assumed that the waves propagate in one direction. The wind loads are obtained based on the windward area and wind force coefficients, while the current loads are calculated using the projected area in the flow direction and current force coefficients. The resulting loads acting on the device under the combined effects of oceanic environmental conditions are then transferred, via the Workbench platform, to the corresponding wall surfaces in the Transient Structural module, and it is assumed that these loads have been accurately determined and act continuously on the surfaces. The calculation procedures are outlined as follows: (a) creating the environmental load simulation model in the AQWA module; (b) generating meshes using the internal grid tool in the AQWA module; (c) conducting calculations of the environmental loads acting on the coupled device; (d) transferring the environmental load data to the Transient Structural module via the Workbench; (e) conducting quasi-steady analysis using the load data on FEM structural walls. In the AQWA module, the fluid is assumed to be inviscid, incompressible, and irrotational. Random waves based on the JONSWAP spectrum with a simulation period of 2000 s are used. The defeature size of the structure is 0.1 m, and the maximum allowed frequency is 0.681 Hz.

3.3. Numerical Model Validation

The numerical model established in this study is validated using the dynamic response experimental results of an offshore monopile wind turbine under the joint action of extreme wind, current, and wave conditions [32]. In the experimental tests, the monopile wind turbine is simplified to include a model pile, a model tower, and a concentrated mass representing the nacelle. Froude similarity law is applied for the model setup, and the effects of Reynolds number are ignored. The model pile length is 0.9 m and its bury depth in saturated sand is 0.6 m. The peak loads from the wind, currents, and waves, calculated from the local environmental conditions based on theoretical analysis, are applied to the model through a dynamic load loading system according to a specific scale ratio. A comparison of the numerical predictions vs. the results for experimental testing of the peak bending moment on the pile against the bury depth are shown in Figure 3. As the bury depth is less than 0.3 m, a slight overestimation of the peak bending moment in the numerical model can be observed. The main source of this error is the assumption that the soil in the model is homogeneous and isotropic, which leads to a mismatch between the restraining effect on the pile foundation and the experimental conditions, resulting in a higher value for the simulated dynamic response. The average error between the simulation and experimental results at different bury depths is 4.9%. The largest error occurs at a bury depth of 5.4 m, with a value of 9.7%. Overall, the numerical predictions show good agreement with the experimental results for the trend of the peak bending moment on the pile. Therefore, the model can be scaled up to investigate the dynamic characteristics of the full-scale device.

4. Results and Discussions

4.1. Environmental Conditions

The coupled wind and wave energy device can generate complex dynamic responses under the joint action of the wind, currents, and waves. The oceanic environmental conditions with a recurrence interval of five years are listed in

Table 1. Oceanic environmental conditions.

Serial No.	Water Level	Mean Water Depth (m)	Incident Wave Direction	Hm (m)	H10% (m)	Tp (s)	Wind Speed (m/s)
1	EHWL	21.6	S	2.0	4.1	7.8	22.0
2	DHWL	19.8	S	1.8	3.6	7.3	22.0
3	EHWL	21.6	SE	1.2	2.5	6.1	14.5
4	DHWL	19.8	SE	1.2	2.4	6.0	14.5
5	EHWL	21.6	E	1.4	2.9	6.6	23.3
6	DHWL	19.8	E	1.3	2.7	6.3	23.3
7	EHWL	21.6	NE	1.9	3.8	7.7	28.7
8	DHWL	19.8	NE	1.8	3.6	7.4	28.7

. Two water levels are employed for the calculations: Extreme High Water Level (EHWL) and Design High Water Level (DHWL). Four incident wave directions are chosen: S, SE, E, and NE. The wave condition employs the mean wave height H_m, the ten percent large wave height H_10%, and the spectral peak period T_p, respectively. For the incident ocean current, the direction perpendicular to the OWC device is taken as the worst incident direction. The maximum current speed is fixed at 1.21 m/s. The geological parameters of different soil layers are listed in

Table 2. Geological parameters of different soil layers.

Layer	Soil Type	Depth of the Layer Bottom (m)	Thickness (m)	Bulk Density (kN/m3)	Cohesive Force (kPa)	Internal Friction Angle (º)
1	Silt	2.5	2.5	16.0	5.0	15.0
2	Silty clay	6.5	4.0	18.0	12.0	16.0
3	Fine sand	11.7	5.2	19.0	6.0	20.0
4	Gravel-bearing medium-coarse sand	14.2	2.5	22.0	35.0	25.0
5	Strong-weathered granite	18.7	4.5	23.2	201.0	27.0
6	Weak-weathered granite	27.1	8.4	25.5	30,950.0	55.0

.

The loads on the structure will become more complex after installing the OWC wave energy device onto the supporting frame of the offshore fixed wind turbine. Therefore, safety assessments of the wave–wind coupled device are conducted to validate the strength of the connecting structures and the safety of the OWC system under extreme environmental conditions. In addition, the influences of the OWC system and its connecting structures on the dynamic responses and stability of the wave–wind coupled device are evaluated. The stress distribution characteristics of the OWC and its connecting structures can be employed for further optimization. Figure 4 shows the installation orientation of the OWC wave energy system, with the underwater mouth facing the direction in which waves most frequently occur. A coordinate system is defined in the figure, with the positive x-direction and y-direction opposed and perpendicular to the most frequently occurring wave direction, respectively. The positive z-direction is defined as perpendicular to the figure. According to the local environmental conditions, four directions are defined for both the incident wave and current: E, NE, S, and SE.

4.2. Modal Analysis

The wind and wave loads acting on the offshore wind turbine are random, and the dynamic loads on the entire wind turbine might be significantly amplified. As the frequency of the excitation load is similar to the natural frequency of the entire structure of the wind turbine, resonance could be observed, which poses a threat to the safety of the structure. Therefore, it is necessary to conduct a modal analysis of the wind–wave coupled device and ensure the natural frequency of the coupled structure satisfies the frequency domain requirements specified by the wind turbine manufacturers.

Installing the multi-tube OWC system on the supporting frame of the wind turbine changes the mass distribution of the entire structure and might result in structure resonance. As this resonance is mostly caused by low-order natural frequencies, modal analysis can be conducted on the original wind turbine structure and the coupled structure for comparison and safety evaluation using the Block Lanczos method. The first six natural vibration frequencies and periods of the original wind turbine structure are listed in

Table 3. Natural vibration frequencies and periods of the original wind turbine.

Order	1	2	3	4	5	6
Natural frequency (Hz)	0.3212	0.3274	0.8094	0.9510	0.9858	1.2567
Natural period (s)	3.1129	3.0547	1.2355	1.0516	1.0144	0.7958

. The first- and second-order frequencies are 0.3212 Hz and 0.3274 Hz, falling in the frequency domain range between 0.3160 Hz and 0.3413 Hz proposed by the wind turbine manufacturers, indicating that the numerical model is reliable.

The first three-order natural vibration modes for the original wind turbine are depicted in Figure 5. The vibration modes of the original wind turbine include the swing and torsion. As shown in Figure 5a, the vibration is the swing in the Y–Z plane with a maximum deformation of 2.62 mm on the top tip of a rotor blade. The deformation is a relative value and is the same in the following. The vibration in the second-order mode in Figure 5b is also the swing, which can be observed in the X–Z plane. The maximum relative deformation of 2.63 mm occurs at the top tip of a rotor blade. The vibration in the third-order mode in Figure 5c is the torsion in the X–Z plane, with a maximum deformation of 6.91 mm at the top tip of a rotor blade.

The first six natural vibration frequencies and periods of the coupled wind–wave device are listed in

Table 4. Natural vibration frequencies and periods of the coupled wind–wave device.

Order	1	2	3	4	5	6
Natural frequency (Hz)	0.3213	0.3275	0.8102	0.9489	0.9846	1.2563
Natural period (s)	3.1128	3.0538	1.2343	1.0539	1.0156	0.7960

. The first- and second-order frequencies are 0.3213 Hz and 0.3275 Hz, and the frequency domain is between 0.3160 Hz and 0.3413 Hz, as proposed by the manufacturers. The frequencies and periods at different orders of the wind–wave coupled device are almost identical to those of the original wind turbine, indicating that the addition of the OWC wave energy system has little influence on the offshore wind turbine structures.

The first three-order natural vibration modes for the coupled wind–wave device are depicted in Figure 6. The natural vibration modes of the coupled device are also almost the same as in the original wind turbine. The maximum deformations for the first three natural vibration modes of the coupled device are observed at the top tip of rotor blades, with values of 2.61 mm, 2.63 mm, and 6.90 mm, respectively. The results indicate that the vibration modes of the coupled device are not evidently different from those of the original structure. This is because the OWC system has far lower mass than the wind turbine structure, resulting in no significant changes in the total mass and gravity center of the structure. Consequently, there are only minor changes to the natural vibration modes after integrating the additional OWC system with the wind turbine.

4.3. Dynamic Load and Response Analysis

The wind, current, and wave loads acting on the offshore wind turbine are random, and the dynamic loads on the entire wind turbine might be significantly amplified. Therefore, a safety check is conducted to evaluate the influence level of the OWC system and its connecting structures on the dynamic response and stability of the coupled device. This is necessary for verifying the safety of the OWC system and the strength of the connecting structures under extreme sea conditions based on detailed insight into the stress distribution on the coupled device, which can serve as valuable information for the practical design. Based on the sub-chamber size, three values are chosen for the relative gap D/W: 0.1, 0.2, and 0.3.

The time histories of the relative loads P/G acting on the OWC system in three typical directions in 100 wave cycles for the incident direction of NE and D/W = 0.2 are depicted in Figure 7, where two water levels are considered: EHWL and DHWL. The instantaneous relative load P/G is defined as the ratio between the instantaneous load acting on the OWC system P and the weight of the system G, where G includes the OWC chamber and the connecting and supporting structures, which is 105.8 kN in this case. As the incident direction of waves and currents is close to the X direction, the loads are significantly larger in this direction than in the other two directions. The dramatic fluctuation of the load acting on the OWC system is caused by irregular incident waves. In addition, the peak amplitude of the loads has a larger impact under EHWL than DHWL conditions. Consequently, it is reasonable to assess safety by calculating the dynamic loads on the system under EHWL conditions.

The components of environmental load amplitudes in the X, Y, and Z directions in four typical incident directions under EHWL conditions are compared in Figure 8, where the load amplitude is represented by P_A and nondimensionalized as the relative load amplitude P_A/G. As shown in Figure 8a, for the incident directions of E, NE, and SE, the relative load amplitudes are negative, indicating the chamber endures large pressure on the wave-ward side. In addition, as the incident direction is S, the relative load amplitude becomes positive because the pressure on the chamber changes to the cap side. In the four incident directions, the largest absolute P_A/G values are obtained in the X direction as D/W = 0.1, and the peak value is 14.4 for the incident direction of S. As the relative gap increases, the absolute value of the relative load amplitude decreases because of the diminished blockage effects of the gap. The smallest absolute P_A/G value can be observed at 2.1 for D/W = 0.3 in the incident direction of SE.

Furthermore, as shown in Figure 8b,c, the numerical predictions indicate that the relative gap has a minor influence on the variations of the relative load amplitudes in the Y and Z directions. For the incident directions of E, NE, S, and SE, the absolute P_A/G values in the Y direction vary in ranges of between 1.8 and 1.9, 0.95 and 0.97, 1.1 and 1.2, and 1.7 and 1.8, respectively. For the four incident directions, the absolute P_A/G values in the Z direction are 0.2, 0.3, 0.4, and 0.2, respectively, indicating there is minor uplift pressure. Generally, as the included angles of the incident directions of SE and E are close to the Y direction, the relative load amplitudes are similar. In addition, the peak P_A/G values are observed in the X direction for the incident direction of S, in the Y direction for the incident direction of E, and in the Z direction for the incident direction of S.

Under EHWL conditions, the environmental loads acting on the OWC system decrease as the gap between the sub-chambers increases. The peak P_A/G values are obtained when D/W = 0.1. According to the integration plan of the OWC and the high-rise pile cap, the environmental loads acting on the OWC system can be transmitted to the supporting framework of the wind turbine. From the dynamic load analysis, it can be concluded that the environmental loads are larger in the incident directions of NE and S. For the incident direction of NE, the supporting framework and chamber walls of the OWC system bear the pressure and relative bending moments; for the incident direction of S, the OWC system bears the tensions and relative bending moments. Consequently, the analysis can be conducted in these two incident directions to evaluate the stress and strain distribution characteristics of the coupled device for system design.

The contours of equivalent (von Mises) stress and elastic strain distributions on the OWC system for the incident direction of NE and D/W = 0.1 are depicted in Figure 9. The peak equivalent stress and strain can be observed near the still water surface, with a maximum stress value of 1.65 × 10⁶ kPa and a maximum strain value of 1.14 × 10⁻². The maximum stress is less than the material ultimate strength of 1.8 × 10⁶ kPa, which demonstrates that the structure is safe under these conditions. The stress decreases on the upper and lower sides because the intensive wave force on the two sides diminishes. This stress can be transmitted through the supporting framework to the fixing framework on the cap, inclined supporters, anchor plates on the cap, and hoops on the piles. Stress concentration can appear in these structures and connections, which have a smaller area. The gradual stress transition to the piles and the cap demonstrates there is effective stress transmission in the OWC system. To guarantee the stability and safety of the entire structure, more attention should be focused on the areas with larger stress levels.

The contours of equivalent (von Mises) stress and elastic strain distributions on the OWC system for the incident direction of S and D/W = 0.1 are depicted in Figure 10. In contrast to the prediction results for the incident direction of NE, the maximum equivalent stress of 1.70 × 10⁶ kPa and strain of 1.22 × 10⁻² are both observed on the sub-chamber at the still water level, which are less than the ultimate strength and yield strength. For the stress and strain distributions, asymmetry is observed in the incident direction of S with a larger high-stress area. In addition, the stress and strain values for sub-chambers No. 1 and No. 4 are larger than those for sub-chambers No. 2 and No. 3. These differences might be due to the presence of piles and their blockage effects. The trend of a gradual transition of the stress from the OWC system to the foundation of the wind turbine also indicates that there is effective transmission of environmental loads. According to the distribution characteristics of the stress and strain on the OWC system in various incident directions, the areas of stress concentration should be strengthened or optimized, such as through increasing the chamber wall thickness or by installing keels in the internal area of the chamber, both of which are expected to effectively reduce stress and strain concentration.

For the wind–wave coupled device, under the joint action of waves and currents, stress concentration can be observed on the hoops, with additional stress on the foundation piles. The piles are the core supporting structures of the foundation of the offshore wind turbine, and additional stress might threaten the safety of the wind turbine. Therefore, further stress analysis on piles is conducted, and the results for the prediction of stress on the piles are listed in

Table 5. Equivalent stresses on the piles for the wind-wave coupled device.

Incident Direction	D/W	Equivalent Stress on the Pile A (kPa)	Equivalent Stress on the Pile B (kPa)
NE	0.1	1.89 × 104	1.65 × 104
	0.2	1.63 × 104	1.44 × 104
S	0.1	1.67 × 104	1.70 × 104
	0.2	1.42 × 104	1.44 × 104

. There is more stress on pile A than on pile B in the incident direction of NE, while there is less stress on pile A than on pile B in the incident direction of S. There is significant asymmetry in the distribution. In addition, the stresses on the piles are smaller for D/W = 0.2, than for D/W = 0.1, because there more space between the sub-chambers for the passage of waves and currents. Although an increase in the distance between the sub-chambers can cause a reduction in the environmental loads acting on the OWC system, an enlargement such that the chamber width exceeds the diameter of the high-rise pile cap results in a more complex structure design for supporting the additional system, with increased construction costs. Consequently, the recommended value for D/W is 0.2, which allows balancing the structural loads and construction expenses.

5. Conclusions

A wind–wave coupled device was proposed that employs an offshore fixed wind turbine and an OWC device with rectangular chambers integrated on the high-rise pile cap of the turbine foundation. The OWC system was installed using connecting rods at two sides of the chamber, anchoring plates, and hoops for welding and attaching the additional structures to the original foundation. The dynamic response characteristics of the wind–wave coupled device under extreme environmental conditions were analyzed using numerical FEM. The numerical model was validated by relevant experimental results, with an average error of 4.9% in dynamic load prediction, which demonstrates the accuracy of the model.

The modal analysis results indicate that the natural vibration frequencies of the original wind turbine and the coupled device are all in the range of 0.3160 Hz to 0.3413 Hz proposed by the manufacturers. The main vibration modes are swing and torsion. The modal analysis results also demonstrate that the dynamic characteristics of the offshore fixed wind turbine will not be significantly changed following installation of the OWC system.

The environmental load acting on the OWC system decreases as the gap between the sub-chambers increases. For the incident direction of NE and the relative gap of 0.1, the maximum equivalent stress of 1.65 × 10⁶ kPa and the maximum equivalent strain of 1.14 × 10⁻² are observed near the still water level of EHWL. For the incident direction of S and the relative gap of 0.1, the stress and strain are asymmetrically distributed because of foundation piles, and the maximum equivalent stress and strain are 1.70 × 10⁶ kPa and 1.22 × 10⁻², respectively. The values for both the maximum stress and strain are below those for the ultimate strength and yield strength, indicating the safety of the system.

The stress and strain transmitted from the OWC system exhibit asymmetric characteristics for the foundation piles under the action of environmental loads in different incident directions. The gap between the sub-chambers can be increased to significantly reduce the stress on the piles. On the other hand, an excessively large gap will enhance the complexity of the entire structure and increase construction costs. Consequently, a relative gap of 0.2 is recommended for the coupled device.