Dynamic Performance Investigation of A Spar-Type Floating Wind Turbine Under Different Sea Conditions

Both numerical calculation and model test are important techniques to study and forecast the dynamic responses of the floating offshore wind turbine (FOWT). However, both the methods have their own limitations at present. In this study, the dynamic responses of a 5 MW OC3 spar-type floating wind turbine designed for a water depth of 200 m are numerically investigated and validated by a 1:50 scaled model test. Moreover, the discrepancies between the numerical calculations and model tests are obtained and discussed. According to the discussions, it is found that the surge and pitch are coupled with the mooring tensions, but the heave is independent of them. Surge and pitch are mainly induced by wave under wind wave conditions. Wind and current will induce the low-frequency average responses, while wave will induce the fluctuation ranges of the responses. In addition, wave will induce the wavefrequency responses but wind and current will restrain the ranges of the responses.


Introduction
As the traditional energy has been increasingly exhausted over the past decades, clean and environmental friendly renewable energy, especially offshore wind energy, has attracted more attentions than ever before. Nowadays, there exist many fixed-bottom offshore wind turbines. However, the further developments of such kind of wind turbine are restricted by the complaints of noise pollution and unstable power supply. Besides, considering the fixedbottom offshore wind turbine economic cost grows rapidly with the increase of water depth, offshore floating wind turbine is hoped to replace fixed-bottom offshore wind turbine and dominate the development of offshore wind power in the future. Nevertheless, the dynamic responses of floating wind turbines are more complex than those of fixed-bottom ones because they will suffer from wind, wave, current and complicated motion responses. Thus, it has significant engineering application values to choose appropriate methods to study the dynamic responses of floating wind turbines.
Recently, a great deal of researches and concepts of floating offshore wind turbine (FOWT) have been carried out and proposed by scholars all over the world. A 5 MW baseline wind turbine was developed in National Renewable Energy Laboratory (NREL) . In phase of the Offshore Code Comparison Collaboration (OC3), a spar floating platform called OC3-Hywind was designed for the 5MW baseline wind turbine (Jonkman, 2010). In phase of the Offshore Code Comparison Collaboration Continuation (OC4), a semi-type platform was designed (Robertson et al., 2014). In 2013, a combination of a spartype floating wind turbine and a floating wave energy converter, i.e. a new concept called Spar Tours Combination (STC) was proposed in NTNU (Muliawan et al., 2013).
In order to verify the dynamic properties of the above concept models, several simulation codes have been developed. By adding the module of HydroDyn and mooring to the fixed wind turbine analysis code-Fatigue, Aerodynamics, Structures, and Turbulence (FAST), a fully coupled aero-hydro-servo-elastic simulation tool was developed (Jonkman, 2007). Then, the dynamic responses of OC3-Hywind under different sea conditions were calculated by FAST and other six codes, such as HAWC2, 3Dfloat and Simo . The dynamic responses of OC3-Hywind were also calculated by HAWC2-DeepC (Karimirad and Moan, 2012) and HydroD-DeepC-TDH-MILL3d (Thomas, 2010). SIMO/RIFLEX and AeroDyn were combined to study the coupled dynamic responses of WindFloat semi-type platform (Kvittem et al., 2012). MLT-SIM-FAST code was developed to calculate the TLP floating wind turbine in DeepCwind Project (Koo et al., 2013). A coupled time domain simulation code -DARwind which considers the high-order rigid-flexible coupled term in the multi-body model was developed (Hu et al., 2017).
However, single numerical analysis method cannot accurately predict the dynamic responses. Model test is another method for predicting dynamic responses and validating numerical analysis code. In 2006, a 1:47 scaled model test of Hywind was conducted at Marintek (Nielsen et al., 2006). University of Maine used to unite MARIN to organize 1:50 scaled model tests of spar, semi and TLP floating platforms to predict the dynamic responses of these three floating wind turbine concepts (Martin et al., 2012;Koo et al., 2012;Goupee et al., 2014;Kimball et al., 2012). In 2004, a thrust-matched blade system was developed by MARIN and a new MARIN Stock Wind Turbine (MSWT) model was also proposed . Then, the MSWT model was tested by a 1:130 scaled model in The University of Maine . A 1:100 scaled model test was conducted to predict the dynamic response of a spar floating wind turbine with four mooring lines (Sethuraman and Venugopal, 2013). In 2016, a 1:50 scaled model test of a 5 MW OC3 spar-type floating wind turbine designed for a water depth of 200 m was carried out at Shanghai Jiao Tong University. The dynamic responses under different sea conditions were recorded (Duan et al., 2016) and researches were conducted based on the model test results.
This paper studies the dynamic responses of the 5 MW OC3 spar-type floating wind turbine under different sea conditions through numerical calculations using the fully coupled time domain FAST code (Jonkman and Buhl, 2005). The numerical results are validated by the model tests. Also, the differences between them are discussed and the reasons are analyzed. It is expected that this study can bring valuable guidelines for engineering applications in the future.

Coupled dynamic analysis theory
In consideration of the rotation effect of blades, floating wind turbine is not only affected by wave forces, but also wind loads. The blades-nacelle-tower-platform coupled system is nonlinear and should be solved in the time domain, which is different from the traditional offshore structures calculated by linear theories and methods.
In order to study the dynamic responses of a floating wind turbine in the time domain, the platform can be re-garded as a rigid body and its motion equation can be given as: where is the generalized displacement of the platform in the time domain; and are the generalized velocity and acceleration, respectively; is the mass matrix; and are the added mass matrix and damping coefficient matrix, which are caused by the wave radiation and can be calculated by WAMIT (Lee, 2013); is the hydrostatic restoring force matrix, which can also be calculated by WAMIT; is the incident-wave induced force; is the wind loads acting on the blades and tower; is the mooring tension; while is the drag force caused by fluid viscosity. Wave-induced force in the frequency domain predicted by WAMIT based on the potential flow theory will be transformed to load in the time domain by FAST. The load in the j-th direction can be calculated as (Jonkman and Sclavounos, 2006): where ω is the frequency of incident wave, is the Fourier transform of a realization of a White Gaussian Noise time series process with unit variance, is twosided wave spectrum which depends on ω.
is a wave induced force array normalized per unit wave amplitude, which depends on the geometry of the floating platform, frequency and direction of the incident wave .
The aerodynamic load on the blades is regarded as external load acting on the platform and can be calculated by the blade element momentum theory (Hansen, 2008), the normal force and the torque on the control volume of the thickness dr are: where ρ is the air density, B is the number of the blades, is the wind speed, c is the chord of the airfoil, is the relation flow angle which equals the blades twist adding the angle of the attack , and are the coefficients for the normal force and thrust force which can be calculated by the lift coefficient and drag coefficient , respectively: a a ′ and are the axial induction factor and the tangential induction factor, respectively. They can be calculated as follows: σ where is the fraction of the annular area in a control volume.
is regarded as another external load, which can be divided into the vertical tension and horizontal tension . They are solved by the catenary equation using the iteration method. Since no section of the mooring line rests on the seabed, and can be analyzed as follows (Jonkman, 2009): x F z F where and are respectively the horizontal and vertical coordinates of the fairlead position relative to the anchor, w is the mass of the mooring line per unit length, L is the unstretched length of the total mooring line, and EA is the sectional stiffness of the mooring line.
Besides, the flow separation behind the cylindrical structures will induce the viscous drag force, which can be estimated by the Morison equation: where is drag coefficient, is the velocity of water and is the velocity of strip.

Model test
The 5 MW OC3 spar-type floating wind turbine is based on OC3-Hywind and it is modified to fit the water depth of 200 m. The taut mooring system is connected by a delta connection. The results used in this paper are based on a 1:50 scaled model test conducted at Shanghai Jiao Tong University. More details of the test can be found in the research of Duan et al. (2016). The main parameters are listed in Table 1, in which the negative sign indicates an elevation below the still water line.

Numerical simulation model
The simulation model of the whole floating wind turbine system can be divided into five modules in FAST, i.e. aerodynamic module, structural dynamic module, hydrodynamic module, mooring module and control module. Each module is calculated independently and coupled by equivalent additional mass and load.
Blade element momentum theory considering dynamic stall is applied in the aerodynamic module. Multi-body-dynamics formulation and FEM are used in the structural dynamic module. Quasi-static catenary equation is applied in the mooring module. That is to say the taut mooring system used in the model test is simulated by the catenary mooring system, which can be implemented by modifying the stiffness of the mooring system in FAST. In the hydrodynamic module, the hydrostatic restoring force, added mass and linear damping caused by the wave radiation, wave exciting force, and drag force are considered. The hydrostatic restoring force, added mass and linear damping, as well as the wave exciting can be solved and output in the frequency domain by WAMIT based on the potential flow theory. Then, the output of WAMIT will be used as the input for FAST. The panel model of the spar-type platform below the waterline built in WAMIT is shown in Fig. 1. The control module is imported to simulate the form of a dynamic link library (DLL) to adjust the generator torque and blade pitch angle.

Cases definitions
In order to study the dynamic responses of the spar-type floating wind turbine, several cases shown in Table 2 are conducted. In which, the cases with steady wind only (LC1-LC3), steady wind combined irregular waves (LC4-LC6) and the combination of steady wind, irregular waves and current (LC7-LC9), free decay in still water (LC10) are included. The prototype wind speeds vary from H s T p the rated speed 11.4 m/s to 23 m/s. The prototype irregular wave is one-year return period irregular wave. For which, the significant wave height is 7.1 m, spectral peak wave period is 12 s and spectral peak parameter γ is 2.2. The current speeds vary from 0.50 m/s to 1.20 m/s.

Assumptions for the model test and numerical simulation
In the model test, the parameters of environment and the experimental model are scaled based on Froude similarity rule. Additionally, the scale effect caused by the dissimilarity of the Reynolds number has been revised. Assuming that the lift coefficient and resistance coefficient of the blade airfoil are insensitive to the Reynolds number, the tip speed ration similarity is adopted. In the model test, the active wave elimination device is installed on two adjacent sides of the basin, thus, the reflection effect of wave is regarded as nonexistent. More importantly, the quality of the wind field determines the accuracy of the aerodynamic load. To guarantee the wind environment quality for steady wind speeds, a wind generation system which is consisted of nine independently controllable axial fans in a 3×3 stacked square configuration is applied and a honeycomb screen is attached to the front of the wind generation system. Thus, in the model test, the wind field was assumed to be steady.
In the numerical simulation, it is assumed that the floating wind turbine is a rigid-flexible multi-body. In the hydrodynamic module, the linearization assumption of the classical marine hydrodynamic load is adopted and the viscousdrag term is considered by the Morison equation. In the mooring module, the inertia and damping of the mooring system is ignored. Moreover, the delta connection is ignored. More details can be found in the paper of Jonkman (2007).

Free decay
Comparing the free decay results from numerical calculation and model test can verify both methods preliminarily. It can be found from Table 3 that the results from numerical calculation and model test match well, which indicates that using the catenary mooring system by modifying the stiffness of mooring system to simulate taut mooring system can guarantee the accuracy of free decay.

Surge, pitch and heave motions
The surge and pitch responses of the platform are obvious motion modes of the whole system. Wind, wave and current have different effects on the surge and pitch. Comparisons are conducted in statistics of results in the time domain and shown in Table 4. It can be found that when wind speed is increasing over the rated speed, the responses of the surge and pitch reduce with the decreasing of axial thrust. Besides, the average responses of the surge and pitch change observably when wind speed changes. By comparing the wind only load cases (LC1-LC3) with wind-wave cases (LC4-LC6), it can be found that the average responses of the surge and pitch change lightly, but the fluctuation ranges of the surge and pitch vary significantly. Take the surge response in model tests for example, the average value of surge in LC1 and LC4 are respectively 8.67 m and 8.68 m, which are much similar. However, the fluctuation range of surge is 1.73 m in LC1 while 8.23 min LC4 for the effects of wave. Through comparing the wind-wave cases (LC4-LC6) with the combination of wind, wave and current load cases (LC7-LC9), it is found that current increases the average motion responses, but has little influence on the motion fluctuation ranges. Also, taking the surge response in the model tests for example, the average response in LC4 is 8.68 m, while it increases to 9.24 m in  LC7 for the effect of current. Thus, the average responses of the surge and pitch are mainly induced by wind, while the current will magnify the induction effect. But the ranges of the surge and pitch are mostly dominated by wave. By considering the results from the numerical calculations and model tests, and taking the surge response in LC1 for example, the fluctuation range of the model test is 1.73 m, while that of the numerical calculation is only 0.11 m. Also, it can be found that the fluctuation ranges of the numerical calculations in other load cases are smaller than those of the model tests. The smaller fluctuation range of the numerical calculation is mainly due to less consideration of the instability of wind and this phenomenon is particularly obvious with wind only. The average response of the numerical calculation is bigger than that of the model test at the rated wind speed of 11.4 m/s, but is smaller than those of the model tests at 18 and 23 m/s. The discrepancy is mainly due to the influence of the modeling of the mooring system. The catenary model of FAST hardly supplies the great mooring tension as the taut mooring of the model test is under great deflection condition. When the wind speed reaches the rated wind speed of 11.4 m/s, the floating wind turbine will subject to a great wind load. With smaller restoring force supplied by the mooring tension, the total environment load on the platform is greater. Thus, the deflection calculated by FAST is larger than that in the model test. With the wind speed increasing, the total environment load and average response in the simulation become smaller than that in the model test.
Analyses in the frequency domain are also conducted. The left figures in Fig. 2 and Fig. 3 show power the spectral density curves of the surge and pitch respectively for FAST, while the right ones are for the model test.
From the frequency response results of FAST and the model test, it can be seen that both the surge and pitch can be resolved into the low frequency response and wave frequency response under a combination of wind, wave and current condition. Furthermore, the wave frequency response induced by wave plays a dominating role.
In Fig. 2, it indicates that the peak of the low frequency surge response of the model test is at 0.154 rad/s, which is close to the natural frequency of the surge at 0.155 rad/s. In Fig. 3, it can be observed that the peak frequency of the low frequency pitch response of the model test is at 0.160 rad/s, which is lower than the natural frequency of the pitch at 0.185 rad/s. As the natural frequency of the surge is 0.155 rad/s, it indicates that the pitch response is coupled with the surge response. From the power spectral density curves, it can be observed that the peaks of LC4 are higher than those of LC7 and the curves of LC1 are close to zero. It indicates that the surge and pitch frequency responses are mainly induced by wave and will be restrained by wind and current. This is because wave has periodic characteristics and it will lead to periodic motions of the surge and pitch, but wind and current loads are regarded as constant external forces and they will restrain the periodic motions of the surge and pitch.
Though the general regularities for the results of FAST and the model test are similar, the power spectral density curves for FAST and the model test show noticeable differences. FAST underestimates the frequencies of the surge and pitch low frequency responses. This phenomenon is believed to be caused by the unsteadiness of the wind turbine system in the simulations. Besides, the peaks in different load cases calculated by FAST are higher than those calculated by the model test, which can be attributed to the aerodamping.
Heave is another important motion response of the platform. From Table 5, it can be found that the average responses of the heave will noticeably decrease with the increase of the wind speed, but the fluctuation ranges will not change much when the wind speed varies. Fig. 4 shows that heave frequency response can also be resolved into the low frequency response and wave frequency response under a combination of wind and wave condition. The peak of the low frequency response appears at 0.226 rad/s, which is exactly the natural frequency of the heave and far away from the natural frequencies of the surge and pitch. Thus, it can be concluded that the heave is not coupled with the surge or pitch. Also, it can be seen that the peak values for FAST and model test at the heave natural frequency differ greatly. The higher peak at the heave natural frequency of the model test shows that the heave response is affected greatly not only by the wave frequency, but also by its natural frequency. The model test conducted in MARIN  also shows the similar result. But the lower peak of the numerical calculation at the natural frequency indicates that the heave response is mainly affected by the wave frequency. The discrepancy of FAST can be attributed to two main reasons. One of them is the differences in the mooring system models. For the catenary mooring system, the mooring tension has little effect on the heave response. However, the mooring tension of the taut mooring system in the model tests is comparatively bigger, and affects the heave observably under the wind-wave conditions. The other reason is that, for the wind field in the model test is not perfectly steady, the low-frequency turbulent wind loads may increase the low frequency resonance response.

Yaw and tower top bending moment
Different from the traditional floating platforms, the yaw of floating turbines is mainly caused by the rotor's rotations. The responses of the whole floating wind turbine system are closely related to the yaw. Furthermore, the tower top bending moment is mainly induced by the yaw.   . It can be seen that the free decay curve from the numerical calculation in the time domain almost coincides with that from the model tests, indicating that FAST can simulate free decay of the yaw response well. Fig. 6 shows the yaw and tower top bending moment responses of LC4 in the time domain. It can be seen that the response of the yaw from the numerical calculations is small, which differs greatly from the result from the model tests. Also, the response of the tower top bending moment from the numerical calculations is much smaller than those from the model tests. This means that FAST has the limitation on simulating the yaw and tower top bending moment under wind-wave conditions. Fig. 7 is the power spectral density curves of the yaw and tower top bending moment for LC4. Fig. 7a is for the yaw and Fig. 7b is for the tower top bending moment.
The spectrum of the yaw in the model test has two peaks. One peak is at 0.5 rad/s, which is induced by incident wave. The other peak is at the high frequency of 1.45 rad/s. The peak at the wave frequency almost can be ignored compared with the peak at the high frequency. As the rotation speed of the rotor is 14.4 rpm at the wind speed of 11.4 m/s (Duan et al., 2016), and the corresponding rotor rotation frequency is 1.51 rad/s, it can be known that the peak at 1.45 rad/s is induced by the rotor rotation. The rotating rotor will cause the angular momentum that is parallel to the rotating axis. However, due to the motion of the platform, the direction of the rotation axis changes. Thus, the rotor rotation will excite an extra load -gyroscopic moment that excites the yaw motion of the platform. In fact, the rotor will not speed up to 14.4 rpm for the existence of the drift angle. Thus, the resonant frequency is lower than 1.51 rad/s. Similarly, the tower top bending moment is mainly induced by the rotor rotation as well. However, the spectra for FAST have no peak at 1.45 rad/s, which are different from the spectra for the model tests. The reason for this deviation could be that FAST might have some limitations on simulating the yaw and tower top bending moment under windwave conditions. Nevertheless, it can also be the modeling reason for the simulation of the yaw rigidity in the model test, which proves the importance of simulating the yaw ri-    gidity through delta lines deploying way. Therefore, it is needed to make further investigation on the yaw stiffness simulation.

Mooring system response
Mooring tension is considered as the external load acting on the platform, which has important effects on the responses of the whole floating wind turbine system. The mooring line along the wind direction was chosen in the following research. Analyses are conducted based on the power spectral density curves as plotted in Fig. 8. Fig. 8a is the spectrum from FAST and Fig. 8b is the spectrum from the model test. There is a distinct peak at 0.51 rad/s for both FAST and the model test. The irregular wave spectrum peak period is 12.1 s, which means that the frequency of incident wave is 0.52 rad/s. Thus, the peak at 0.51 rad/s is mainly induced by incident wave. There is another peak at 0.156 rad/s, which can be regarded as the resonant frequency corresponding to the natural frequency of some motion of the floating wind turbine system. But the peak values of LC1, LC4 and LC7 at the natural frequency for FAST are smaller than those for the model test. This phenomenon is similar to the heave responses for similar reasons as analyzed above.
Besides, it can be found that 0.156 rad/s is nearly the same with the natural frequency of 0.155 rad/s for the surge, which indicates that the surge has an obvious coupling effect on the dynamic response of the mooring system under wave or wind-wave conditions. That is to say 0.156 rad/s is the resonant frequency corresponding to the surge.

Rotor thrust and tower top shear force
Rotor thrust is related closely to the whole floating wind turbine system and the tower top shear force influences the structural safety greatly. The study of the rotor thrust and tower top shear force under different conditions is of crucial importance. The average values of the rotor thrust and tower top shear force in the time domain are summarized in Table 6.
From Table 6, it can be found that the numerical results show the similar tendencies as the results of the model test. Rotor thrust and tower top shear force will reach the maximal values at 11.4 m/s and will decrease with the wind speed increase. This indicates that the area of the blades exposed to wind will decrease with wind speeding up and the axial thrust will consequently decrease. From Table 6, it can also be found that the average values of the rotor thrust and tower top shear force under the combination of wind and irregular wave conditions (LC4-LC6) are smaller than those under wind only conditions (LC1-LC3). As the rated power reached at higher wind speed under the combination of wind and wave condition, it indicates that the average relative velocity of incident wind will decrease under the periodic action of wave.
Besides, the results from FAST are always smaller than the values given by the model tests. The rotor thrust calcu- lated contains neither the rotor thrust acting on the hub only, nor the inertial force acting on it. Thus, the discrepancy mainly consisted of two parts. On one hand, the angle between the incident wind and shaft will cause the decrease of the relative wind speed, which will reduce the rotor thrust acting on the hub. On the other hand, the pitch angles in simulation are smaller than those in the model test, which will reduce the rotor thrust acting on the hub calculated by FAST even further. In order to compare the results of the numerical calculation and model test, the power spectral density curves are plotted in Fig. 9. The power spectral density curves of the model test have five peaks under wind-wave condition and the reasons causing these five peaks have been explained in the paper of Duan et al. (2016): The first peak is caused by the unsteadiness of the wind generation system, the second peak is induced by incident wave, the third peak is caused by the rotor rotation, the fourth peak is induced by the firstmode tower vibration and the fifth peak appears near the 3P frequency. But the spectral curves of the numerical results under wind-wave condition only have two peaks. One peak is caused by the unsteadiness of the wind generation system, while the other is induced by incident wave. It indicates that FAST has limitations on simulating the responses of rotor thrust and tower top shear force induced by the vibration of tower and the rotation of the rotor. On contrast, the peaks of FAST and the model test at wave frequency match well, which indicates that FAST can simulate the responses of the rotor thrust and tower top shear force induced by wave well. Besides, from Fig. 9, it can be found that the maximum peaks are induced by wave, which means that the rotor thrust and tower top shear are both mainly influenced by wave.

Conclusions
In this paper, the dynamic responses of a 5 MW OC3 spar-type floating wind turbine under different conditions are researched by the FAST code and a 1:50 scaled model test, and the results are analyzed in both the time domain and frequency domain. The discrepancies between the numerical calculations and model tests are compared and discussed. Several conclusions can be drawn as follows.
On the basis of the comparisons of the numerical calculation and model test, it can be found that the results of FAST are credible in general. However, there are some discrepancies between the results of FAST and the model test as well. Though the yaw responses in free decays for FAST and the model test match well, there are still noticeable differences between them under wind-wave conditions. Compared with the model test, FAST will underestimate the impact of the low frequency on the heave and mooring tension and it has limitation on simulating the responses of the rotor thrust and tower top shear force induced by the vibration of tower and the rotation of the rotor.
According to the comparisons of the numerical calculation and model test, several motion characteristics are concluded. Surge and pitch are coupled with the mooring tension, but the heave is independent of them. Surge, pitch, ro-tor thrust and tower top shear force are mainly induced by wave under wind-wave conditions, yaw and tower top bending moment are mainly induced by the rotor rotation.
Besides, the impacts of wind, wave and current on the responses of the spar-type floating wind turbine are also discussed. Wind and current will induce the low-frequency average responses, while wave will induce the fluctuation ranges of the responses. Besides, wave will induce the wave-frequency responses, but wind and current will restrain the ranges of the responses.