Aero-Elastic-Control-Floater-Mooring Coupled Dynamic Analysis of Floating Offshore Wind Turbines

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1 Proceedings of the Twenty-first () International Offshore and Polar Engineering Conference Maui, Hawaii, USA, June 9-, Copyright by the International Society of Offshore and Polar Engineers (ISOPE) ISBN (Set); ISSN (Set); Aero-Elastic-Control-Floater-Mooring Dynamic Analysis of Floating Offshore Wind Turbines Y.H. Bae*, M.H. Kim*, S.W. Im** and I.H. Chang** * Department of Civil Engineering, Texas A&M University College Station, TX, USA ** Steel Structure Research Laboratory, Research Institute of Industrial Science & Technology (RIST) Incheon, Korea ABSTRACT In the present study, a numerical prediction tool has been developed for the fully coupled dynamic analysis of a FOWT (floating offshore wind turbine) in time domain including aero-loading, blade-rotor dynamics and control, tower elastic responses, mooring dynamics, and platform motions so that their dynamic coupling effects can fully be assessed. The rotor-floater coupled analysis is compared with the uncoupled analysis to identify their coupling effects to the global performance of the whole system. In this regard, Hywind spar design with 5MW turbine is selected as an example. In case of the spar-type floater, it is seen that the maximum offsets and mooring tensions of the coupled analyses are smaller than those of uncoupled analyses. It is also seen that the maximum accelerations at the tower are significantly increased due to the coupling between tower elastic modes and hull 6DOF motions, which will in turn greatly affect the corresponding inertial loading on nacelle and blades. The developed technology and numerical tool are readily applicable to the design of any new offshore floating wind farms in any combinations of irregular waves, dynamic winds, and steady currents. KEY WORDS: Renewable Wind Energy, floating offshore wind turbine, aero-elastic-control-floater-mooring coupled dynamics, spar hull, control-induced motions, tower-blade flexibility, accelerations, comparison with uncoupled analysis, wind farm. INTRODUCTION Wind is the fastest growing clean and renewable energy source. Until recently, most of the wind-farm development has been limited to the land space and shallow water regions. Recently, several countries started to plan offshore floating wind farms. Although they are considered to be more difficult to design, wind farms in deeper waters are in general less sensitive to space availability, noise restriction, visual pollution, and regulatory problems. They are also exposed to much stronger and steadier wind field to be more effective. Furthermore, in designing those floating wind farms, the existing technology and experience of offshore petroleum industry is directly applicable. In this regard, if technology and infrastructure is fully developed, offshore floating wind farms are expected to produce huge amount of clean electricity at a competitive price compared to other energy sources. In deeper (>5m) offshore areas, floating-type wind farms are expected to be more economical than the fixed ones (Tong 998; Henderson et al.,; Musial et al. 3; and Wayman et al. 6). Possible disadvantages of floating type wind farms include more transmission loss, the complexity of blade controls due to body motions, larger inertia loading on tall tower caused by greater floater accelerations, and possibly more expensive/complicated installation processes including mooring lines. They are also directly exposed to the open ocean without any natural protection, so they may have to endure harsher environments. The natural frequencies of 6DOF motions of floating wind turbines are typically much lower than the frequencies of rotating-blade-induced or tower-flexibility-induced excitations, so the possibility of dynamic resonance is much less (e.g. Withee, Jonkman et al 6). One exception is the TLP-type OWT (Bae et al., ; Jagdale & Ma, ), which is much stiffer in the vertical-plane modes compared to other floating wind turbines, and thus the effects of such high-frequency excitations from the tower and blades need to be checked. For other types of floating bases with softer mooring system, such as spar or semi-submersible (Roddier et al., 9), the low-frequency excitations related to blade pitch-angle control may cause large-amplitude slowlyvarying floater motions (Nielsen et al., 6; Bae et al., ). In this regard, the accurate estimation of the coupling effects between the floater dynamics and tower-blade dynamics/control is very important in the optimal design of floating OWTs. The present analysis method integrates rotor dynamics and control, aero-dynamics, tower elasticity, floater dynamics, and mooring-line dynamics to investigate the full dynamic coupling among them in time domain. The corresponding rotor-floater-mooring coupled dynamic analysis computer program is developed by combining respective modules. For the dynamics and control of blade and tower, the primary design code of wind turbines, FAST, promoted by National Renewable Energy Laboratory (NREL), is employed (Jonkman et al., ). The portion of the FAST algorithm is modified to include some features of 9

2 the floater-mooring coupled dynamic analysis program, CHARM3D, and vice versa so that the full coupling of rotor and floater can accurately be achieved. The CHARM3D program has been developed by authors group to analyze the coupling effects between floating platforms and mooring/riser system (e.g. Kim et al., ; Arcandra & Kim, 3; Yang & Kim, ). The CHARM3D program has been verified through numerous comparisons against experiments and field data during the past decade. In this paper, the developed fully coupled dynamic analysis program is applied to a spar-type floating OWT designed for 3-m water depth. NUMIRICAL ANALYSIS OF 5MW FLOATING WIND TUR- BINE IN TIME DOMAIN The time domain analysis tool for rotor-floater-tether fully coupled dynamic system is developed in this study and evaluated for the floating offshore wind turbine system. In order to couple the windturbine motion and tether/floater dynamics, two different analysis modules, CHARM3D and FAST are combined and utilized. The hydrodynamic coefficients including added mass, radiation damping, wave forces, and mean drift forces of floater are obtained by a 3D diffraction/radiation preprocessor WAMIT in frequency domain (Lee et al., 99) and the information is transferred to time-domain-analysis tool, CHARM3D. The mooring dynamics coupled with hull motions are solved at each time step by a generalized-coordinate-based FEM program using high-order elements, the details of which are given in Kim et al. (). The equation of motion in time domain can be expressed as follows: [ MM a ( )] KFI() t Fc(, t ) Fn(, t ) Fm() t () a where M ( ) denotes added mass at infinite frequency, FI () t is wave exciting force, K=hydrostatic coefficients, Fn (, t ) nonlinear drag force from Morison s equation, Fm () t =mooring force, and F (, ) c t radiation force as follows: t F (, t ) R( t ) ( ) d () c,, and represent the six degree of freedom displacements, velocities, and accelerations of the floating body. The retardation function R() t is given by R() t b( )cos( t) d (3) in which b is the linear radiation damping matrix. The complete nonlinear aero elastic equations of motion for the wind turbine model is Mqutq (,, ) f( qquu,,,, t) () d where M is the mass matrix, f is the forcing function, u and ud are the set of wind turbine control inputs and wind inputs, respectively. q, q, and q are the vector of wind turbine motions, velocities, and accelerations, and t is time. The wind turbine dynamics including 6-DOF platform dynamics are computed by FAST, which is developed by NREL. CHARM3D calculates all of the external forces acting on the platform. At each time step, CHARM3D feeds the external forces to FAST, then FAST fills out the forcing function in Eq. () using forces from CHARM3D. The external forces which are derived by CHARM3D include st -order and nd -order (if applicable) wave forces, wave radiation damping force, nonlinear viscous drag force from Morison members, and mooringinduced restoring force. The mooring restoring force can be estimated by the top tension of each mooring line and its directional cosine. Then, FAST solves the equations of motions of all the degrees of freedom. Those updated platform kinematic data, which include displacement, velocity, and acceleration, are then used in CHARM3D side in order to update external forces, which will be fed again to FAST for the next time step. For the present simulation, the time step of CHARM3D-side is.5s and the internal time step for FAST-part is.5s, which means that at every time interval of CHARM3D, the FAST internally calculates steps, and return the resultant data to CHARM3D. The basic concept of rotor-floater coupling is schematically shown in Figure. CHARM3D Forces Displ, Vel, Accel Figure Basic concept of CHARM3D-FAST hybrid model The control system of 5MW wind turbine consists of variable-speed and variable-blade-pitch-to-feather controller. The two control strategies work together to produce quality power outputs and keep the whole system in good condition. The control strategy of land-based turbine is applicable to TLP-type offshore wind turbines without any significant modification. However, for spar platforms, it is necessary to change the control strategy to ensure small floater motions and smooth power generation. Several modification methods are suggested by Larsen, Hansen and J. Jonkman (7), and two of these modifications were applied for the National Renewable Energy Laboratory (NREL) 5MW turbine (Jonkman, 8). NUMIRICAL MODEL FOR 5MW HYWIND SPAR The adopted model of 5MW turbine is the NREL offshore 5MW baseline wind turbine which has been adopted as the reference model for the integrated European UpWind research program. Hywind floating platform in this paper is the OC3-Hywind spar-buoy type platform which is slightly different from the actual turbine used by Statoil of Norway. The detailed specifications of 5MW turbine and Hywind spar hull are summarized in Table and Table. The characteristics of mooring system are tabulated in Table 3. Table Specification of 5MW Turbine FAST Item Unit Specification Tower height m 9. Rotor diameter m 6. Tower diameter (top) m 3.87 Tower diameter (bottom) m 6.5 Elevation to Tower Base above SWL m 3

3 Elevation to Tower Top above SWL m 87.6 Overall Tower mass kg 9,78 Total wind turbine weight (except for platform) kg 599,78 CM Location of Tower above SWL m 3. Tower Structural Damping Ratio (All modes) % Table Specification of Hywind spar platform Item Unit Specification Depth to Platform Base below SWL m. Elevation to Platform Top Above SWL m Depth to Top of Taper Below SWL m Depth to Bottom of Taper Below SWL m Platform Diameter Above Taper m 6.5 Platform Diameter Below Taper m 9. Platform Mass, including Ballast kg 7,66,33 CM Location Below SWL Along Platform Centerline m Platform Roll Inertia about CM kg m,9,3, Paltform Pitch Inertia about CM kg m,9,3, Platform Yaw Inertia about Platform Centerline kg m 6,3, The Hywind spar is moored by three catenary lines. To increase the yaw stiffness of the platform, the lines are attached to the hull via delta connection. This delta-connection effect is included in the time domain simulation by adding the corresponding yaw spring stiffness. Table 3 Specification of Hywind spar mooring system Item Unit Specification Number of Mooring Lines 3 Angle Between Adjacent Lines deg Depth to Anchors Below SWL (Water Depth) m 3 Depth to Fairleads Below SWL m 7. Radius to Anchors from Platform Centerline m Radius to Fairleads from Platform Centerline m 5. Unstretched Mooring Line Length m 9. Mooring Line Diameter m.9 Equivalent Mooring Line Mass Density kg/m Equivalent Mooring Line Weight in Water N/m Equivalent Mooring Line Extensional Stiffness N 38,3, Additional Yaw Spring Stiffness Nm/rad 98,3, Each mooring line is modeled by higher-order finite elements, and its unstretched length is 9.m. Illustrations of mooring line arrangement are shown in Figure. Figure Mooring-line arrangement The flexibility of tower is included by using a linear modal representation as suggested in FAST. As shown in Figure 3, two foreaft and two side-to-side mode shapes of tower and two flap-wise modes and one edgewise mode of blades are used for coupled dynamic analysis. The natural frequencies of those elastic modes are tabulated in Table. Tower base is located at the m height from the MWL which means the flexibility of tower begins from that height. The rated power is 5MW, and the rotor diameter is 6m. In this study, the coupling effects between the rotor and floater on hull motions, tower accelerations, and top tension of mooring lines will be presented st mode nd mode st mode nd mode Flap st mode Flap nd mode Edge mode (c) Figure 3 Normalized mode shapes of tower fore-aft, tower sideto-side and blades Table Natural frequencies of tower and blade Mode rad/s st tower fore-aft mode.33 nd tower fore-aft mode 6. st tower side-to-side mode.3 nd tower side-to-side mode.3 Blade st flapwise.5 Blade nd flapwise.63 Blade st edgewise 6.86 HYDRODYNAMIC COEFFICIENTS IN FREQUENCY DOMAIN Wave forces and hydrodynamic coefficients for the submerged portion of the hull are calculated by using the potential-based 3D diffraction/radiation panel program (Lee et al., 99). Figure shows the discretized panel distribution of the floater. The submerged body has two planes of symmetry and each quadrant has 39 panels. 3

4 z Second-order mean drift forces are also calculated so that it can generate slowly-varying drift forces and motions through Newman s approximation method. The viscous drag force of the hull is included by employing two Morrison members for upper and lower sections. The drag coefficient C D is taken to be.6 which is typical for a cylinder at high Reynolds numbers. - - Table 7 Environmental condition Item Reference Wind Speed at m Mean Wind Speed at Hub Height Water Depth Wave Heading Significant Wave Height Peak Wave Period Specification 3 m/s 7. m/s 3m deg 5. m 8.69 sec y Figure Discretized panel model of floating body The natural frequencies of the Hywind spar platform are tabulated in Table 5. Table 5 Natural frequencies of platform motions Mode rad/s Mode rad/s Surge.5 Sway.5 Heave. Roll. Pitch. Yaw.7 COUPLED DYNAMIC ANALYSIS OF HYWIND FLOATING WIND TURBINE IN TIME DOMAIN In this study, the effects of more rigorous aerodynamic loading, flexible tower/blade, rotating blades, and blade pitch-angle control on floater motions and mooring tensions are investigated in time domain by comparing the coupled and uncoupled numerical models. The coupled analysis is carried out by using CHARM3D-FAST hybrid program, and the tower-blade portion and the floater portion are dynamically interacting at each time step by exchanging dynamic and kinematic information. In the uncoupled analysis, the tower-blade portion is modeled by another rigid body with equivalent wind loading, like the way typical offshore platforms are analyzed. The equivalent mean wind loading on the swept area of blades is determined from that of the coupled analysis by adjusting the blade drag coefficient, as shown in Table 6. Table 6 Wind load for uncoupled dynamics Item Specification Rotor Diameter 6 m Swept Area m Drag Coefficient.68 Mean Wind Load 37.5 kn -- x The wind and wave are collinear and their headings are fixed at degree, and currents are not considered in the present study for convenience. The JONSWAP wave spectrum is used with significant wave height of 5 m and peak wave period of 8.69s. As for wind, -hour mean wind speed (at m height) of 3 m/s is used and time dependent wind velocity is generated from the corresponding API wind spectrum. The environmental condition is summarized in Table 7. During the time-marching procedure, several control methods are working together to maximize and optimize the power capture. In this study, blade-pitch control and variable-speed-torque control methods are adopted. As stated earlier, some modifications of the conventional control strategies typically used for land-based turbines are applied to reduce large resonant motions and eliminate negative damping of the platform pitch mode. Otherwise, unacceptably large resonant motions would occur because the blade-pitch-angle-control-induced excitations act very close to pitch-heave natural frequencies. In Figures 5~, 6-DOF motions of the coupled and uncoupled cases are compared to observe the effects of rotor-tower coupling. Due to the symmetry of the hull geometry and the head-direction of wind and wave, sway-roll-yaw motions of the uncoupled case are zeros, but the corresponding motions of the coupled case show non-zero displacements because of the interaction between hull and wind turbine. Due to the aero-loading on blades and gyro effects of blade rotation, there exist non-zero mean values of sway and roll in coupled analysis. m m Figure 5 Time histories and spectra of the surge motion Figure 6 Time histories and spectra of the sway motion 3

5 m deg deg deg Figure 7 Time histories and spectra of the heave motion Figure 8 Time histories and spectra of the roll motion Figure 9 Time histories and spectra of the pitch motion Figure Time histories and spectra of the yaw motion An interesting phenomenon we can observe is that the uncoupled surge and pitch responses are slightly greater than the corresponding coupled responses. For instance, the maximum surge displacement of the uncoupled case is.7m, but that of the coupled case is only.3m. Similar trend can be observed in pitch responses. As for standard deviations of surge and pitch motions, the uncoupled case is 8% and % higher than those of coupled case respectively. This trend is actually opposite to that of a TLP-type FOWT studied in Bae & Kim (). This phenomenon can be explained by the blade-pitch-control action of the coupled case. Assuming that equivalent winds are applied to the rotor for both cases, the platform of the uncoupled case will fully be actuated by the incident wind. However, in the coupled case, the turbine starts to adjust its blade-pitch angle to regulate the incoming wind effect. This pitch-to-feather action plays a role to mitigate the wind loading and the corresponding platform response. Moreover, in the rotor-floater coupled analysis, the relative wind velocity with respect to the platform motion is used in calculating the wind loading but the relative-wind-velocity effect is ignored in the uncoupled analysis. Also, in the coupled analysis, the instantaneous wind loading is applied at the instantaneous tower-blade position, so acting in all directions including heave direction. On the other hand, in the uncoupled analysis, the wind loading is applied only to the mean position of tower and blade, and thus only horizontal wind loading (and the corresponding pitch moment) is applied at the center of the equivalent disk. Due to this reason, the coupled heave motions are appreciably greater than the uncoupled heave motions, as can be seen in Figure 7. In coupled case, there exist non-zero transverse motions due to the gyro effect of blade rotation and the influence of blade pitchangle control. This phenomenon cannot be obtained from the uncoupled analysis. The statistics of hull responses are tabulated in Table 8. Table 8 Floater-motion statistics (UC:, C: ) Surge (m) Sway (m) Heave (m) Roll (deg) Pitch (deg) Yaw (deg) Max. Min Mean SD UC.7E+.E+.E+ 3.E+ C.3E+ 6.77E+.3E+.6E+ UC 8.6E E-6-7.3E-8.9E-6 C -3.3E- -.5E+ -6.7E-.E- UC.97E E E- 7.5E- C.58E E- -.33E-.68E- UC 3.5E-6-3.6E-6 -.E E-7 C.E-.77E-.96E- 3.7E- UC 6.7E+ -5.6E-.63E+ 8.8E- C 6.35E+ -.E-.76E+ 7.75E- UC 9.7E E-7 -.3E-8.E-7 C 3.39E- -.58E- -8.7E-.7E- The differences in hull motions between the coupled and uncoupled cases directly affect the top-tension statistics of tethers, which are summarized in Table 9. The mooring lines arrangement is depicted in Figure. The upwind-side lines such as line # and #3 will have higher tensions as can be seen in Figures 3~, and the tension of downwind-side line # in Figure will be decreased due to the surge offset. Due to more severe surge slow-drift motions in the uncoupled analysis, the maximum top tensions of lines are increased by 3~6%. Figure Top view of mooring-line arrangement 33

6 Top Tension(N) Top Tension(N) Top Tension(N) x x Figure Top-tension time histories and spectra of Line #. x x.5.5 Figure 3 Top-tension time histories and spectra of Line #. x x.5.5 Figure Top-tension time histories and spectra of Line #3 Table 9 Top-tension statistics (UC:, C: ) Leg (N) Leg (N) Leg 3 (N) Max. Min Mean SD UC 9.5E+5 6.7E E+5 5.3E+ C 8.98E+5 6.E E E+ UC.33E+6 9.5E+5.3E+6 5.6E+ C.9E+6 9.9E+5.3E+6.3E+ UC.33E+6 9.5E+5.3E+6 5.6E+ C.7E E+5.E+6.E+ Fore-aft accelerations at 3-different locations of the tower are also investigated and the coupled and uncoupled cases are compared. For the coupled case, the total acceleration at a given height is calculated by the summation of the local tower acceleration from elastic vibration and the global acceleration due to the hull motion. Phase differences between the local-tower acceleration and global acceleration are considered and included in the calculation of the total acceleration. In the uncoupled analysis, the whole system is treated as a rigid body, so only the global accelerations are considered at the respective heights. m/s m/s m/s Figure 5 Tower-acceleration time histories and spectra at the height of 85.66m from MWL Figure 6 Tower-acceleration time histories and spectra at the height of 58.5m from MWL Figure 7 Tower-acceleration time histories and spectra at the height of.9m from MWL In contrast to the motion results, the accelerations from the coupled analysis are appreciably greater than those from the uncoupled analysis. The differences are greater at higher positions. This means that the acceleration caused by tower elasticity is also important. The large acceleration at the nacelle and blade may cause large inertia loading that may lead to structural or fatigue failure. The statistics of the tower fore-aft accelerations shows that the maximum acceleration of the coupled analysis is increased by 89~ 9% compared to the uncoupled case. This means that the uncoupled analysis, which does not include the tower elasticity and aero-floater-rotor dynamic coupling, is not good enough to reasonably estimate the tower accelerations and the corresponding inertia loadings. Table Tower-acceleration statistics (UC:, C: ) 85.66m (m/s ) 58.5m (m/s ).9m (m/s ) Max. Min Mean SD UC.59E+ -.76E+ -5.E-5.9E- C 3.3E E+ -6.E-5 8.6E- UC.36E+ -.5E+ -.6E E- C.7E+ -.78E+.76E- 7.E- UC 9.77E- -.7E+ -.95E-5.7E- C.85E+ -.9E E-5.89E- 3

7 CONCLUSIONS So far, most of wind farm research has been limited to fixed towers in shallow-water areas. In this paper, a Hywind spar-type floating offshore wind turbine that can be used in deeper areas is studied. The newly developed numerical tool can analyze rotor-floater-tether coupled nonlinear dynamics in time domain and was used for floater-motion, tower-acceleration and mooring-line-tension simulations in a collinear wind-wave environment. The coupled analysis includes time-varying aerodynamic loading, tower-blade elastic deformation, blade-controlinduced loading, and gyro effect of rotating blade in analyzing the global dynamics of the whole system. The rotor-floater coupling effects are assessed through comparisons with the results of uncoupled analysis, in which the whole body is treated as a rigid body. In case of Hywind spar, it is seen that the rotor-floater coupling effects decrease the maximum horizontal offsets and mooring-line tensions but heave motions are increased due to the time-varying wind loading caused by time-varying blade pitch angle and relative wind velocity against moving tower. The tower accelerations are, however, greatly increased due to the effects of tower flexibility, which will in turn greatly affect the corresponding inertial loading on nacelle and blades. It may be of important concern for the structural robustness and fatigue life of the system. The present methodology is directly applicable to any types of new offshore floating wind farms in the future. ACKNOWLEDGEMENTS This study is financially supported by POSCO/RIST (Research Institute of Industrial Science & Technology). This support is gratefully acknowledged. 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