Dynamic analysis of a 5-MW tripod offshore wind turbine by considering fluid–structure interaction

Fixed offshore wind turbines usually have large underwater supporting structures. The fluid influences the dynamic characteristics of the structure system. The dynamic model of a 5-MW tripod offshore wind turbine considering the pile–soil system and fluid structure interaction (FSI) is established, and the structural modes in air and in water are obtained by use of ANSYS. By comparing low-order natural frequencies and mode shapes, the influence of sea water on the free vibration characteristics of offshore wind turbine is analyzed. On basis of the above work, seismic responses under excitation by El-Centro waves are calculated by the time-history analysis method. The results reveal that the dynamic responses such as the lateral displacement of the foundation and the section bending moment of the tubular piles increase substantially under the influence of the added-mass and hydrodynamic pressure of sea water. The method and conclusions presented in this paper can provide a theoretical reference for structure design and analysis of offshore wind turbines fixed in deep seawater.


Introduction
In recent years, against the background of rapidly increasing demand for clean energy, a good opportunity has been being created to construct high-power offshore wind turbines. However, in consideration of the high construction cost and complex working environment involved in the case of offshore wind turbines, their safety is immensely important. Offshore wind turbines fixed in water at the depths of 10-60 m usually have large supports, and seawater causes vibrations in this support and reacts with the structure when the system vibrates. The water-added mass and the hydrodynamic pressure influence the dynamic characteristics of the structures system. Therefore, it is essential to analyze the dynamic performance accurately and ensure safety operation of high-power wind turbines in the marine environment.
Fluid-structure interaction (FSI) has been extensively researched worldwide as well as in China, and a lot of useful data have been accumulated. Fish et al. (1980) studied the FSI using Morison's equation for the experimental and theoretical design of offshore structures, and proposed a simplified method to calculate wave force on piles. Tao et al. (1997) calculated the addi-tional mass of moving structures in water using Morrison's equation and obtained the natural vibration characteristics and dynamic response of the structure by considering the fluid effect by using a numerical method. Huang and Zhang (2011) analyzed the coupled modes and identified the dynamic characteristics of the tension leg platform for offshore wind turbine supports by adopting the strong-interaction method. Deng (2015) simulated the stochastic wave using the harmonic wave superposition method and calculated the wave force by using the modified Morison's equation, and then examined the responses of monopole offshore wind turbines considering FSI. Sun (2013) researched the seismic responses of bridge pier systems in deep water by a numerical method and through shaking table tests. Sun reported that the structural responses in water are greater than those in air. Song et al. (2015) researched the seismic responses of offshore wind towers considering the effects of tide level and hydrodynamic pressure and showed that the changes in the dynamic performance indicators caused by shallow water hydrodynamic pressure are negligible. Tian et al. (2015) analyzed the natural dynamic characteristics and seismic responses of the supporting systems of offshore wind turbines by considering the complicated interaction of water, soil, and the supporting system, and the results indicated that water caused a reduction in the high-order frequencies and in the system seismic responses, such as displacements, peak acceleration, and effective stress; these observations were not in agreement with the conclusions of the aforementioned studies.
Thus, at present, studies on the dynamic characteristics of the fixed offshore wind turbines considering FSI seem to be lacking, and further research is quite necessary. This paper presents the theoretical model for the dynamic analysis of a 5-MW tripod offshore wind turbine. The influence of seawater on the natural frequencies and seismic responses was analyzed by using ANSYS, which will provide a project reference for the structure design and analysis of the fixed offshore wind turbines.

Theory of FSI
Under the assumption that the fluid is inviscid, vortexfree, and incompressible, and by neglecting the surface fluctuations and fluid damping, the fluid movement equation is described as follows (Xue et al., 2015): where, P stands for the pressure vector of fluid domain; M F , the fluid mass matrix; K F , the fluid stiffness matrix; F F , external load of fluid; and R F , the coupling surface load matrix. (2) N where ρ is the fluid density; c is the sound velocity in fluid; N F is the shape function matrix of fluid elements; is the transformation matrix between displacement vector in outer normal of fluid boundary and the degree of structure freedom D. R F in Eq. (1) represents the interaction between the fluid and structure, and the fluid pressure load on the structure is expressed as follows: In consideration of the fluid pressure load, the structural dynamic governing equation with structure damping is described below: In Eq. (7), Rayleigh damping is considered as the struc-C s tural damping , which can be described by Eqs. (8)- (10): where α and β are scale factors; ω 1 and ω 2 stand for the first-and second-order natural frequencies; and ζ is the corresponding damping ratio. The dynamic responses considering the fluid loading effect will be obtained by solving Eqs.
(1) and (7). In this method, the motion equations of fluid and structures are developed independently and the descriptions of the physical fields are consistent with the actual situation. This model has a good accuracy despite the huge amount of calculations. With the improvement in the computer performances, the application of this method will become increasingly easy.

Design parameters of the 5-MW wind turbine
The design parameters of the offshore wind turbine rated 5 MW in this study refer to the published data of the U.S. Department of Energy's (DOE's) National Renewable Energy Laboratory (NREL) (Jonkman et al., 2009), except for the data of the support. The specific parameters of the rotor and nacelle are presented in Table 1. Q345D is the main material of the tower and the substructure, which are designed independently, as shown in Fig. 1. Young's module E=2.06×10 5 MPa, Poisson's ratio μ=0.3, and steel density ρ=7800 kg/m 3 .The design parameters of the tower, tripod, and tubular piles are listed in Table 2.

Parameters of soil
The geologic exploration data of the offshore wind farm (Chen, 2010) were referred for the foundation design of the 5-MW wind turbine. These data are presented in Table 3.

FEA model
The dynamic properties of the 5-MW wind turbine were analyzed by using ANSYS. In the finite element model, the hub, blades, and nacelle were reduced to mass elements mass21, and they were connected by a mass-less rigid beam MCP184. In order to evaluate the effect of FSI, the tower and substructure were meshed with shell181, and the fluid field was meshed with FLUID30, which has eight nodes wherein every node has three displacement arguments and one pressure argument. The coupled actions between the fluid and the structure were achieved by FSI method provided by ANSYS. That is, the fluid nodes and adjacent structure nodes had the same normal speed. The fluid elements had a one-to-one mapping relationship with the structure elements, and the nodes on the coupled surface were shared.
The fluid field was designed as a cylinder with a height of 42 m and a diameter of 60 m. The hydrodynamic pressure of the outer boundary was assumed to have no fluctuations because the fluid field was sufficiently large. The pressure on the top surface was set zero, while that on the bottom was 0.42 MPa, and that on the medium surface was in accordance with the linear interpolation. The density of seawater was assumed ρ=1026 kg/m 3 , and the sound velocity in water c=1450 m/s.
The distributed spring-mass model was used to simulate the coupled performance of the foundation piles and soil. Every pile was meshed into 40 segments using PIPE16, and two horizontal springs were perpendicular to each other and a vertical spring was present at each node of PIPE16 elements. The stiffness of the vertical springs was calculated using the axial force transfer t-z curve (Chen, 2010), while that of the horizontal springs was calculated using the lateral force-deflection p-y curve (Wang, 2012). The completed finite element models of the 5-MW offshore wind turbine are shown in Figs. 2-4.

Modal analysis
In the design of the wind turbine, the low-order natural frequencies must diverge from the rotor rotation frequency 1P and blades frequency 3P; else, resonance may occur, endangering the structure. For the 5-MW offshore wind turbine considered in this study, the cut-in speed and rated rotor speed are 6.9 rpm and 12.1 rpm, respectively, and the corresponding 1P is 0.115-0.2 Hz, and 3P is 0.345-0.6 Hz. Table 4 presents the first 10 order dominant frequencies.
The first-and second-order frequencies in air and in water are 0.28 Hz. The difference between 1P and the low-order frequencies is sufficiently large to ensure no resonance.
The first 10 order mode shapes of the wind turbine structure in air and in water are shown in Figs. 5 and 6. The mode shapes in water are almost identical to those in air, except for the third to fifth order, which are also listed in Table 4.
Comparison of the frequencies of the same mode shape in air and in water shows that seawater has little influence on the frequencies of the primary swing vibration and twist vibration. However, in the case of the foundation sway and surge, the frequencies of the structure in water are lower than those of the same mode shapes in air. This is because for the primary swing and twist, vibrations mainly occur in  ZHANG Li-wei, LI Xin China Ocean Eng., 2017, Vol. 31, No. 5, P. 559-566 the superstructures, and the lateral deflection of the substructures is very small. However, for vibrations such as the foundation sway and surge, the displacement of the substructure is relatively large, and the movement of the substructure is influenced by water; in other words, the equivalent mass of the substructure and the vibration period increased because of the influence of water. Therefore, the bottom loads such as wave, current, and earthquake excitation and the coupling effect must be considered in the design and analysis of wind turbines fixed in the sea.

Seismic response analysis
The seismic responses of the studied wind turbine were analyzed by using the time-history analysis method. The El-   Centro waves, which are commonly used in seismic research, were applied for excitation. The original wave and its Fourier spectrum are shown in Fig. 7. Following the seismic requirements of a wind farm, the seismic peak acceleration was set as 0.15g, and the acceleration spectrum was adjusted accordingly. One time of seismic acceleration in the X direction and 0.5 of seismic acceleration in the Z direction were combined as the acceleration inputs. The loading coordinate system is shown in Fig. 8. Fig. 9 shows the curves of the displacement responses of the tower top in the X direction. Under two conditions, the displacement responses of the tower top change with the same tendency, and the peak displacement in water is only slightly higher than that in air. Secondly, the two displacement curves have identical frequencies and equilibrium positions, demonstrating that water has little effect on the vibrations of the superstructure. Fig. 10 shows the curves of the displacement responses of the pile top (bottom of the casing pipe) in the X direction. The pile top displacement in water is much larger than that in air, and the curve is similar to that of the acceleration input. Therefore, it seems that the foundation vibrates with a high frequency and is greatly affected by water. Fig. 11 shows the maximum bending moments of piles at different depths. In two situations, the moments increase at first and then decrease with the depth, and the peaks are observed at a depth of 8 m. The maximum moment of the piles in water is 13903 kN·m, which is approximately 2.87 times that of the piles in air. Fig. 12 shows the curves of section moments with time at a depth of 8 m, and the curves can be divided into two stages, with the peaks at 2.2 s.
Figs. 10-12 all show that water causes an increase in the dynamic responses of the substructure. Fig. 13 shows the changes in the hydrodynamic pressure on the interaction surface of the bottom segment of the main barrel. The curve of the hydrodynamic pressure is similar to that of the pile top displacements, and they have the same phase, demonstrating that the hydrodynamic pressure fluctuation at the interaction surface plays an important role in increasing the dynamic responses under seismic excita-  ZHANG Li-wei, LI Xin China Ocean Eng., 2017, Vol. 31, No. 5, P. 559-566 563 tion. Fig. 14 shows the contour plot of the hydrodynamic pressure of the bottom segment of the main barrel at 2.2 s, when the pile top undergoes the maximum displacement. At this time, the pressure on the right side (+X direction) increases, while that on the other side decreases, creating a pressure difference in the same direction as the displacement of the pile top to amplify it. Figs. 15 and 16 give the von Mises stress of the tripod and piles in water corresponding to the maximum tower top displacement and the maximum pile top displacement, respectively. The maximum equivalent stresses of the tripod and piles are 218.06 MPa and 83.42 MPa, respectively, which meet the strength requirement of Q345.

Conclusions
The theoretical and numerical models of the dynamic analysis of a 5-MW tripod offshore wind turbine were established. The influence of seawater on the natural frequencies and seismic responses were analyzed by using ANSYS. Based on the results, the following conclusions are drawn:       (1) The difference between the low-order frequency and the rated rotation frequency of the 5-MW offshore wind turbine is sufficiently large to ensure that there will be no resonance during normal operation.
(2) Comparison of the frequencies of the same order in air and in water shows that the influence of water on the natural frequencies of the structure depends on the order and the mode shapes. Water has very little influence on the frequencies of the tower swing and twist vibration. However, for vibrations such as the foundation sway and surge, the structure frequencies in water are lower than those of the same modes in air. The equivalent mass of the substructure is considered to increase under the influence of water. Therefore, the bottom loads such as wave, current, and earthquake excitation and the coupling effect must be considered in the design of tripod offshore wind turbines.
(3) Under excitation by seismic waves, the displacement responses of the tower top in two situations change with the same tendency; the peak displacement in water is only slightly higher than that in air. In addition to the amplitude, the displacement curves have identical low frequency and equilibrium positions, demonstrating that seawater has little effect on the vibrations of the superstructure. However, with regard to the substructure, the foundation vibrates at a high frequency and appears to be greatly affected by water. The pile top displacement and maximum moment of piles in water are much higher than those in air.
(4) The curve of the hydrodynamic pressure is similar to that of the pile top displacement, and the curves have the same phase, demonstrating that the hydrodynamic pressure fluctuation at the interaction surface plays an important role in increasing dynamic responses under seismic excitation.  ZHANG Li-wei, LI Xin China Ocean Eng., 2017, Vol. 31, No. 5, P. 559-566 565