Concept design and coupled dynamic response analysis on 6-MW spar-type floating offshore wind turbine

Tower, Spar platform and mooring system are designed in the project based on a given 6-MW wind turbine. Under wind-induced only, wave-induced only and combined wind and wave induced loads, dynamic response is analyzed for a 6-MW Spar-type floating offshore wind turbine (FOWT) under operating conditions and parked conditions respectively. Comparison with a platform-fixed system (land-based system) of a 6-MW wind turbine is carried out as well. Results demonstrate that the maximal out-of-plane deflection of the blade of a Spar-type system is 3.1% larger than that of a land-based system; the maximum response value of the nacelle acceleration is 215% larger for all the designed load cases being considered; the ultimate tower base fore-aft bending moment of the Spar-type system is 92% larger than that of the land-based system in all of the Design Load Cases (DLCs) being considered; the fluctuations of the mooring tension is mainly wave-induced, and the safety factor of the mooring tension is adequate for the 6-MW FOWT. The results can provide relevant modifications to the initial design for the Spar-type system, the detailed design and model basin test of the 6-MW Spar-type system.


Introduction
The wind turbine is a kind of equipment that can convert wind energy into electric energy. With the fossil fuels depletion, the wind turbine has been developed rapidly. Due to the restriction of development of the land-based wind turbine, the floating offshore wind turbine (FOWT) has become the focus of research. The FOWT can be divided into floating spar buoy, tension-leg-type and semisubmersibletype according to the supporting structure. To maintain its stability, catenary, tendon and anchor are needed in FOWT compared with the land-based system. Thus, the dynamic response performance of FOWT under the combined wind and wave loads has become the focus of study. However, all the types of the FOWT have some things in common from the fact that the station keeping and the vertical and rotational oscillation control of them are secured by the combined use of the buoyancy force and the tension of mooring lines or tension legs (Jeon et al., 2013). For Spar-type FOWT, a good stability performance of Spar platform is obtained by a smaller waterline surface area, deeper drafts and a large ballast at the platform bottom. In case of Spar-type FOWT, the buoyancy force produced by Spar plat form supports the whole offshore wind turbine and the tension of mooring lines keeps the station position of Spar-type floating substructure. Surge, sway and yaw are largely influenced by the mooring system, while the other degrees of freedom of heave, roll and pitch are mainly affected by the floating platform characteristics. The research with respect to the FOWT is multidisciplinary, involving aerodynamics, hydrodynamics, multi-structure dynamics (elastic) and automatic control (Namik and Stol, 2010;Wang and Sweetman, 2013;Jeon et al., 2014;Salehyar and Zhu, 2015;Nejad et al., 2015), and so that it is of great importance to reveal the nature of dynamic response characteristics. Model test is the most important method to reveal the FOWT characteristics. However, the cost of basin model test is more expensive than other methods. Simulation can also reveal the dynamic response characteristics of the FOWT to a certain extent. And it is also an indispensable method to study the dynamic response. Simulation is carried out and some results can be obtained, which are beneficial to the following basin model test. Simulation can also reflect some phenomena that the basin model test cannot reveal.
Some characteristics are found in the paper. Firstly, compared with the NREL (National Renewable Energy Laboratory) 5 MW, the 6-MW wind turbine has longer blades and a larger output power, and it is in line with the development trend of the FOWT. Also, the 6-MW wind turbine belongs to multiple megawatt levels and the 6-MW Spar-type FOWT is the significant advanced FOWT domestically. Secondly, tower, Spar platform and mooring system are designed based on a given 6-MW wind turbine and thus the 6-MW Spar FOWT integrated model is put forward. In addition, the 6-MW Spar FOWT integrated model is established in the FAST (Fatigue, Aerodynamics, Structures, and Turbulence) code. Furthermore, coupled dynamic responses of the 6-MW Spar FOWT integrated model are studied more systematically. A complete research process is presented in the paper.

Wind turbine
The wind turbine is an important equipment installed at the upper side of FOWT, which can transfer wind energy into electrical energy. And thus, wind turbine is the primary consideration during the FOWT designing process. In the paper, the wind turbine is a conventional three-bladed, upwind, variable-speed, variable-blade-pitch turbine. The most important performance parameters of the 6-MW horizontal axis wind turbine are given in Table 1.

Tower
The tower is key equipment which connects the upper equipment and lower part of the FOWT. Consequently, the selection of tower is vital critical. In the paper, a tower is designed according to the upper wind turbine of the FOWT. Fig. 1 presents the tower cross section.
By taking into account the connection with Spar platform, the tower bottom section is designed with the wall thickness of 40 mm and the diameter of 8 m at the tower bottom. An amplification factor is added into the tower density considering the existence of bolts and welds. The factor takes 1.05-1.1 under normal conditions, and it is 1.08 in the paper, which means the density is 8500 kg/m 3 . Table 2 is the tower performance parameters.

Spar platform
Spar platform is an important support structure of the FOWT, and its performance seriously affects the overall FOWT performance. The top diameter of the Spar platform is designed to be 8 m, and the detailed information is shown in Fig. 2. Spar platform performance parameters are shown in Table 3.

Mooring system
The heave, roll and pitch motion of the Spar platform, due to the hydrostatic effect, has the restoring force and the moment, and the stable static equilibrium position is in ex-    istence. After the deviation from the balanced position as the external force, the motion can automatically return to the balance point when the external force eliminates. The surge, sway and yaw motion cannot automatically return to the balance point after the deviation from the balanced position as the motion has no resilience. Consequently, mooring systems must be used to maintain the equilibrium position for the FOWT. The mooring system layout diagram is shown in Fig. 3, and three catenary cables are used in the mooring system. The mooring system performance parameters are given in Table 4.

Theoretical background and numerical modeling
3.1 Spar platform motion and equations of the motion In the paper, the Spar platform is considered as a rigid body with six degrees of freedom (DOFs): three translation-al and three rotational, as shown in Fig. 4. The right handed coordinate system has a positive z running vertically upward through the COG of the FOWT with the origin in the plane of the mean sea level. The complete nonlinear timedomain equations of the motion of the coupled wind turbine, tower, Spar platform and mooring system are shown in Eq. (1) (Jonkman and Matha, 2011). Dynamic response of the FOWT is obtained by solving the equation of the motion using FAST code (Jonkman and Buhl, 2005).
where, x is the representative displacement, c is the control input, and t is time.

Aerodynamic loads
In the paper, BEM, based on the blade momentum theory and blade element theory, is applied in the FAST code. The thrust and torque of each blade section are calculated and superimposed to obtain the thrust and torque acting on the whole blade, and then the thrust and power of the wind turbine can be calculated (Burton et al., 2011). Fig. 5 illustrates a transverse cut of the blade element viewed beyond the tip of the blade (Bossanyi, 2005). To obtain the maximum power, Eq. (2) (Hansen, 2008) must be satisfied. The thrust and torque of the blade section can be obtained according to the BEM theory and the formulae are shown as Eqs. (3) and (4) (Burton et al., 2011). Thrust, torque and    power acting on the whole blade are illustrated in Eqs.
(5)-(7) (Hansen, 2008). Air loss phenomenon occurs as uneven distribution of the pressure on the blade tip during the wind turbine operation, and the definition of the tip loss coefficient is shown in Eq. (8) (Manwell et al., 2002). Because the tower has certain obstruction to the air, the velocity of the upstream and the downstream of the tower is reduced, and the equation of wind speed for the tower shadow effect is given as Eqs. (9) and (10) (Hansen, 2005).
where, a and a′ are the axial and angular induction factors, respectively; C L and C D are the lift force coefficient and drag force coefficient, respectively; ϕ is the relative angle of wind; v is the upstream wind velocity; ∆r is the radial length of the blade sections; Ω is the angular velocity (rad/s); r is the distance of the airfoil section from the blade root; c is the airfoil chord length; B is the number of the blade; V 0 is the spatial mean wind speed; V h is the wind speed at the hub height; r tower is the radius of tower; x and y are the distance in the X-direction and Y-direction from the blade element to the axial line the of tower, respectively; v 1 (x, y) is the disturbance influence of the tower shadow effect on the wind speed.

Hydrodynamic loads
The total hydrodynamic loads and moments on the six DOFs of the Spar platform can be split into three separate loads: static restoring force, hydrodynamic force and wave excitation force. The total hydrodynamic loads can be expressed by Eq. (11). The motion equation of the rigid body can be established applying the linear momentum equation and the angular momentum equation. For the simple harmonic motion of steady state, Eq. (11) can be expressed as Eq. (12). By taking the symmetry of the Spar platform into account, Eqs. (13) and (14) are the additional mass matrix and restoring force coefficient matrix, respectively (Jonkman, 2007). In this paper, the Spar platform model is established by using the GeniE module in SESAM, and then the Wadam frequency domain analysis in the HydroD module is conducted to obtain the hydrodynamic coefficients such as the additional mass and potential damping coefficient.
where, F k is the total hydrodynamic loads; f k is the hydrodynamic loads per mass; M kj is the mass matrix; A kj is the additional mass matrix; B kj is the damping coefficient matrix; C kj is the restoring force coefficient matrix; I xx , I yy and I zz are the moments of inertia of the roll, pitch, and yaw, respectively; ρ is the density of seawater; g is the gravitational acceleration; A w is the area at the waterline of the Spar platform; V 0 is the drainage volume of the Spar platform; z COB is the COB of the Spar platform.
3.4 Mooring model In this paper, the Finite Element Anchor Mooring (FEAM) model is introduced into the mooring line, which takes the inertial force and fluid resistance into account. The mooring line is regarded as the elastic rod in the FEAM model as shown Fig. 6. The force balance equation and the torque balance equation of the mooring line are Eqs. (15) and (16) (Bae, 2014). Taking mooring line gravity, hydrostatic and hydrodynamic forces into consideration, the equation of motion can be written as Eq. (17). The governing equations of the rod model are established by Eqs. (17) and (18). Since the governing equations are nonlinear and difficult to solve, the finite element method is introduced and the differential equations are converted into algebraic equations as Eqs. (19) and (20).
where, is the rod acceleration; is the rod acceleration normal to its centerline; is the mean hydrodynamic force; λ is the Lagrangian multiplier; EI is the bending stiffness; is the unit tangent vector at the two end nodes of the elements; A is the cross-sectional area of rod; q is the force per unit length of mooring line; ρ is the mass per unit length; m is the torque per unit length; F and M are the force and torque along the rod centerline; T is the rod tension; ϖ is the mass of the rod in the water.

Coupled dynamic response simulations
In this paper, the turbulence wind is applied, and Kaimal wind spectrum is used with the vertical shear index of 0.14. Wind seed of the wind turbulence is generated by the NREL TurbSim software. JONSWAP irregular waves are applied. The IEC 61400-1 design standard (International Electrotechnical Committee, 2005) is selected here as a guide for the land-based system. The IEC 61400-3 design standard (International Electrotechnical Committee, 2009) is chosen for the FOWT system. Two different sets of DLCs, accounting for operating and parked conditions, are considered here as shown in Table 5 (Zhao et al., 2016a(Zhao et al., , 2016b. DLC1 to DLC5 consider the power production under normal operation with the control system fully enabled over a range of wind speeds and wave conditions. DLC6 and DLC7 consider the parked conditions with the control system being shut down under extreme load cases with 1and 50-year return periods. All simulations for the operational and parked conditions lasted 10 min and 30 min, respectively, and an additional 30 s ramp time was applied during the simulations to eliminate any start-up transient behavior (Zhao et al., 2016c). Fig. 7 shows the wind speed at the hub of DLC2. Wind load is low frequency load obtained from the wind power spectrum. Fig. 8 depicts the wave height of DLC2 and wave elevation spectrum.

Rotor thrust
In the paper, tower, Spar platform and mooring system are designed based on a given 6-MW wind turbine. Therefore, the thrust of the 6-MW wind turbine can be used as the    Table 6 illustrates the reliability of the Spar-type system model and the accuracy of simulation results. It shows the comparison of the rotor thrust between reference values and simulation results, and the maximum deviation is smaller than 4%. Although differences between the reference values and simulation values exist, the simulation results can be accepted. The rotor thrust is simulated for both the land-based system and the Spar-type system, as shown in Fig. 9, and the maximum value is obtained at the rated wind speed under the operational condition (DLC2). The results show that the Spar-type system with the combined wind and wave induced case and the land-based system have approximately the same mean rotor thrust output during the operating status. By virtue of the mooring system and reasonable design scheme, the Spar-type system has a small dynamic motion response to environmental loads and thus has less effect on the mean rotor thrust. For the Spar-type system, the wind-induced only case and the combined wind and wave induced case also have approximately the same mean rotor thrust output, and the phenomenon shows that the mean rotor thrust is primarily induced by wind gusts. For the Spar-type system, the standard deviations of the thrust under the combined wind and wave induced case are higher than those in the land-based system due to the Spar platform motion.

Out-of-plane blade deflection
The out-of-plane deflection of blade 1 during the turbine operation (DLC1 to DLC5) is shown in Fig. 10. The mean response is mainly induced by wind loads as the trend is in great agreement with the mean thrust and it shows the peak response at the rated wind speed due to the peak rotor thrust. An increasing trend is found for both systems in the Fig. 10. Out-of-plane deflection of Blade 1.   standard deviation of the out-of-plane blade deflection. And the standard deviation is mainly induced by the combination of the Spar platform motions and wave loads. As observed, the out-of-plane deflection of Blade 1 is mainly dominated by wind loads. However, wave loads also influence the deflection response in a certain degree. The maximum responses for both systems occur at DLC2, with the maximum deflection for the Spar-type system being 3.1% larger than that of the land-based system. The maximum response for the Spar-type system is the result of the wind and wave combination. More stringent requirements on the blades in the design and manufacture are required for the Spar-type system.

Nacelle acceleration
The modeled nacelle surge acceleration (NSA) for both systems is shown in Fig. 11. It appears overall higher for the Spar-type system with the combined wind and wave induced case than that for the land-based system both during operation and when being parked. Under the operating condition, the standard deviation of the combined wind and wind induced case of the Spar-type system is close to that of the land-based system, but it is larger than that of the windinduced only case. The phenomenon illustrates that oscillation of the NSA of Spar-type system is affected by wind and wave loads, in which wind loads play a dominant role in the oscillation phenomenon. However, under the parked condition, the standard deviation of the combined wind and wind induced case of the Spar-type system is larger than that of the land-based system and wind-induced only case. It shows that oscillation of NSA of the Spar-type system is mainly affected by wave loads under the parked condition.
The maximum NSA of the land-based system is 1.93 m 2 /s and the value is obtained under the operating condition. The maximum NSA of the Spar-type system is 2.55 m 2 /s and 6.08 m 2 /s under the working and parked conditions, respectively. Under the operating condition, the maximum response value of the NSA of the Spar-type system is 32.1% larger than that of the land-based wind turbine. However, the maximum NSA of the Spar-type system is 215% larger than that of the land-based wind turbine during all the DLCs considered. Under the operating condition, although the wind loads play a major role in the NSA, wave loads also have a certain contribution to the oscillation of the nacelle. Consequently, the response of the Spar-type system is larger than that of the land-based system. Under the parked condition, the blade pitch angle becomes 90°, and the wind turbine is no longer in operation situation for both systems. Thus, the motion of the nacelle is dominated by the platform. For the land-based system, the response of NSA is very small. However, the response of the platform is controlled by wave loads for the Spar-type system, and a large response of the NSA is obtained. Fig. 12 is the statistical characteristics of the fore-aft bending moment of the tower base (using M instead of "fore-aft bending moment of the tower base" in the paper) for both the land-based system and the Spar-type system. M for both systems shows similar monotonically increasing trends below the rated wind speed under operating conditions. For the speed larger than the rated wind speed, as the significant wave height increases, the Spar-type system with the combined wind and wave-induced case exhibits larger standard deviations than the land-based system. The mean value of M is almost equal for the wind-induced only case and the combined wind and wave induced case of the Spartype system, and both cases of the Spar-type system are higher than land-based system under the operating conditions. In contrast, under the parked conditions, the mean value of M is almost equal for the two systems. It implies that the wave excitation force only has a small effect on the mean value of M for the Spar-type system under the operating conditions, and it is mainly wind induced. However, under the parked conditions, the mean value of M for the Spartype system is mainly wave induced. As observed, the max- Fig. 11. Statistics of the nacelle surge acceleration. Fig. 12. Fore-aft bending moment statistics of the tower base.

Fore-aft bending moment of the tower base
imum M for the land-based system and the Spar-type system with wind-induced case occurs under operating conditions, whereas for the Spar-type system with the combined wind and wave induced case, it occurs under the parked conditions. The ratio of the maximum M for the Spar-type system with the combined wind and wave induced case versus the land-based system during all the DLCs considered can be as high as 1.92. Under the operating conditions, the thrust generated by the rotor acts on the tower. However, under the parked conditions, the thrust is gener-ated no more, and M is mainly controlled by wave loads. Fig. 13 and Fig. 14 are M spectra at the rated wind speed under the operating conditions of the land-based system and the Spar-type system, respectively. For the Spar-type system, a combined effect can be observed in the bending moment spectrum, which appears as a complex combination of the wind frequency response, pitch resonant response and wave frequency response. However, for the land-based system, the low-frequency wind-excitation load governs the M response. Fig. 15 and Fig. 16 present the statistical characteristics of the platform surge and pitch responses subjected to the combined wind and wave induced, wind-induced only and wave-induced only actions, respectively. As observed, the mean platform surge and pitch responses are wind-induced. However, the standard deviation of the platform surge and pitch are governed by the wave-induced action and monotonically increases with the significant wave height. For the DLC7, the maximum surge and pitch responses are 17.14 m and 10.49° under the combined wind and wave induced, respectively. However, the maximum surge response is 17.6 m and 10.82° under the wave-induced only. The phenomenon implies that the existence of wind load plays a certain degree stabilizing effect on the surge and pitch motions, and the damping of the surge and pitch motions are increased.

Platform motion
The surge and pitch time series and the associated surge spectra when the platform is subjected to the combined wind and wave actions near the cut-out wind speed (DLC5) are illustrated in Fig. 17 and Fig. 18, respectively. The platform surge resonant response is excited by the low-frequency wind force due to its compliant nature. The pitch spectrum shows the maxima at the surge resonant response frequency, which implies that the platform pitch motion is mainly surge-induced. Fig. 19 illustrates the statistics of the mooring line tension (Mooring line 1) subjected to the combined wind and wave induced, wind-induced only and wave-induced only  actions. The mean mooring line tension is wind-induced under the operation conditions and wave-induced under the parked conditions. Its maximum value (for Mooring line 1) is approximately 2.462 MN, including the initial pre-tension. This value gives a safety factor of 4.87. It indicated that the mooring system has a sufficient safety factor. Fig. 20 shows the time series and response spectrum of the Spar-type mooring line tension at the rated wind speed (DLC2). The mooring line tension is nonlinearly coupled with the platform motions. This coupling effect can be clearly observed in the tension spectrum, which appears as a complex combination of the surge resonant response and heave resonant response. As a peak of the mooring line tension spectrum exhibits at the surge resonant response frequency, the fluctuations of the mooring line tensions are mainly surge-induced under the conditions.

Conclusions
The dynamic behaviors of the Spar-type system under normal operation and parked conditions are presented. Quantitative comparisons between the land-based system and the Spar-type system are performed. The dominant ex-   MENG Long et al. China Ocean Eng., 2017, Vol. 31, No. 5, P. 567-577 575 citation loads of the selected response variables are identified by performing DLCs consisting of the wind-induced only, wave-induced only and combined wind and wave induced cases, respectively. Results indicate that: (1) Out-of-plane blade deflection of the Spar-type system is 3.1% larger than that of the land-based system at the maximum deflection. An increasing trend is existed in the standard deviation which is induced by the combination of Spar platform motions and wave loads.
(2) For the Spar-type FOWT, the nacelle surge acceleration is dominated by wind loads under the operational conditions and by wave loads under the parked condition. The maximum value is 215% larger than that of the land-based wind turbine during all the DLCs considered.
(3) The fore-aft bending moment of the tower base of the Spar-type system with the combined wind and wave can be more than 92% as high as that of the land-based system during all the DLCs considered.
(4) The mean platform surge and pitch responses are wind-induced. However, the standard deviation is governed by wave-induced for the Spar-type FOWT. To a certain extent, wind loads can play the stabilizing effect in the surge and pitch motions and increase the damping of the surge and pitch motions.
The results presented herein characterize the coupled dynamic response of a Spar-type FOWT. And it will help elucidate the dynamic characteristics of the Spar-type system, and thus help inform relevant modifications to the initial design of the Spar-type FOWT. Future work will focus on a more thorough investigations on the Spar-type FOWT, assessing the structural strength and performing a scaled model test in a wave tank. By analyzing these variables behaviors, the inherent reasons for some particular phenomena can be more clearly revealed. And the corresponding predictions can also be further employed.