Wind-Wave Misalignment Effects on Floating Wind Turbines: Motions and Tower Load Effects

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1 Erin E. Bachynski 1 Centre for Ships and Ocean Structures, NOWITECH, Centre for Autonomous Marine Operations and Systems, Trondheim NO-7491, Norway erin.bachynski@ntnu.no Marit I. Kvittem Centre for Ships and Ocean Structures, NOWITECH, Centre for Autonomous Marine Operations and Systems, Trondheim NO-7491, Norway marit.irene.kvittem@ntnu.no Chenyu Luan Centre for Ships and Ocean Structures, NOWITECH, Centre for Autonomous Marine Operations and Systems, Trondheim NO-7491, Norway chenyu.luan@ntnu.no Torgeir Moan Professor Centre for Ships and Ocean Structures, NOWITECH, Centre for Autonomous Marine Operations and Systems, Trondheim NO-7491 Norway torgeir.moan@ntnu.no Wind-Wave Misalignment Effects on Floating Wind Turbines: Motions and Tower Load Effects The dynamic responses of a spar, tension leg platform (TLP), and two semisubmersible floating wind turbines (FWTs) in selected misaligned wind and wave conditions are investigated using numerical simulation with an aero-hydro-servo-elastic computational tool. For a range of representative operational conditions, the platform motions and short-term fatigue damage in the tower base and tower top are examined. Although some misalignment conditions result in increased motions both parallel and perpendicular to the wave direction, aligned wind and waves cause the largest short-term tower base fatigue damage for the studied platforms and conditions. Several factors which lead to larger fatigue damage for certain platforms in particular conditions are identified, such as tower resonance due to the 3p blade passing frequency in low wind speeds; surge and pitch motions, particularly in the wave frequency range; and the variations in first-order hydrodynamic loads due to wave direction. A semisubmersible platform with large displacement suffers the least damage at the base of the tower. [DOI: / ] 1 Introduction There is an increasing interest in using wind turbines offshore, and in deeper water. FWT concepts, such as spar, semisubmersible, and TLP wind turbines, may be able to harness the offshore deep water resource. Analysis of these concepts is a fairly young field, and much of the research has been limited to environmental conditions (ECs) where wind and waves arrive from the same direction. It is not uncommon, however, for the wind and waves to be significantly misaligned, particularly in stable atmospheric conditions [1 3]. In general, there are misalignments between the wind and waves at all wind speeds: small misalignments at large wind 1 Corresponding author. Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received December 10, 2013; final manuscript received July 4, 2014; published online August 13, Assoc. Editor: Ron Riggs. speeds and large misalignments at lower wind speeds [3]. The largest misalignments are associated with stable atmospheric conditions [1]. Observations from the North Sea suggest that misalignment of up to 30 deg is common, while misalignment larger than 60 deg occurs less than 5% of the time [2]. Misalignment is expected to influence both ultimate and fatigue loads. Increased extreme side side tower base loads on a spar FWT, for example, were previously observed in numerical simulations by Barj et al. [4]. These loads were nonetheless smaller than the fore-aft loads in corresponding conditions with aligned wind and waves. Because the aerodynamic damping is less effective at mitigating wave-induced loading when the waves come from a different direction than the wind, increased tower fatigue damage has been predicted for monopile wind turbines subjected to misaligned wind and waves. Observations of an installed monopile at Bockstigen suggest increased side side loads during 90 deg misalignment conditions, but the results are difficult to Journal of Offshore Mechanics and Arctic Engineering NOVEMBER 2014, Vol. 136 / Copyright VC 2014 by ASME

2 Table 1 Floating platform models Table 2 Tower dimensions (as in Ref. [7]) Spar TLP Semi 1 Semi 2 Water depth (m) Displacement (tonnes) ,260 Hull mass (tonnes) ,473 Draft (m) Waterline diameter (m) a 12.0/6.5 b Surge natural period (s) Sway natural period (s) Heave natural period (s) Roll natural period (s) c Pitch natural period (s) c Yaw natural period (s) Tower bending period (s) d a Single column. b Single offset column/center column. c Includes significant tower bending, see Refs. [11,15,16]. d Second tower bending/platform pitch mode. interpret due to the lack of information about the ECs [5]. The nature of the tower loading is somewhat different for floating and fixed platforms, however, as the platform motions can both cause inertial loads and mitigate certain wave-induced loads. In order to better inform designers and design standards, the current work compares the dynamic response of four 5 MW FWT designs in selected misaligned wind and wave conditions. Numerical simulations in irregular waves and turbulent wind were carried out using the SIMO-RIFLEX-AeroDyn coupled solver, which is an aero-hydro-servo-elastic computational tool. Representative operational conditions were chosen in order to directly investigate the effects of misalignment on motions and on short-term fatigue predictions for the tower. The results show the sensitivity of the predicted motion and tower fatigue responses of different platforms to misalignment. In addition to investigating the effects of misalignment, the results screen a range of typical operational conditions for severe fatigue issues, and provide some comparisons between platforms. 2 FWT Models Four FWTs were studied: a spar platform, a TLP, and two semisubmersibles, as summarized in Table 1 and depicted in Fig. 1. The platforms were considered in the water depth for which they were designed: 150 m for the TLP, 320 m for the spar and semisubmersible 1, and 200 m for semisubmersible 2. All of the models were assumed to support the NREL 5 MW wind turbine [6] with the OC3 Hywind tower [7]. The tower dimensions are presented in Table 2. The effects of blade pitch controller faults on similar models were studied previously [8]. Length Base diameter Base thickness Top diameter Top thickness 77.6 m 6.5 m m 3.87 m m The blade pitch and generator torque control routines for FWTs are generally modified from those used on land-based turbines in order to avoid negative feedback [9,10]. In the present work, the OC3-Hywind control parameters were applied to the spar and semisubmersible wind turbines. Although the natural frequencies of the TLP are quite high, an intermediate control system was applied for the TLP wind turbine to avoid negative feedback in the wave frequency range. The control system parameters are given in Table 3. The hydrodynamic models of the concepts included a combination of potential flow and Morison s equation. The first-order potential flow solution for each concept was computed using a panel model. The resulting added mass, radiation damping, and wave excitation were applied in the time domain using convolution. Additional viscous forces on large-volume components were included through Morison s equation (Table 4). Morison s equation (including added mass and the Froude Krylov forces) was also applied to slender elements which were not included in the potential flow model (Table 4). Sections describe each of the platforms and their respective numerical models in greater detail. The coefficients come originally from Refs. [7], [11 13]. The present paper did not attempt to adjust these coefficients. 2.1 Spar Platform. The spar platform considered here was the OC3 Hywind hull, as defined by Jonkman [7]. In addition to the first-order and viscous hydrodynamic forces, mean wave drift forces were applied and Newman s approximation was used to estimate the difference-frequency wave excitation. Drag and added mass coefficients were applied as specified by Jonkman [7] (Table 4). The hull was modeled as a rigid body, while the tower, blades, and mooring lines consisted of flexible components. A chain mooring system with delta lines and clump weights was applied to approximate the mooring system stiffness described in Ref. [7]. The mooring lines were modeled using bar elements and connecting joints, allowing for a full dynamic solution. 2.2 TLP. The TLP model was an approximately half-scale version of the original sea star oil platform [14]. Additional details regarding this design are available from Ref. [11], where it is identified as tension leg platform wind turbine (TLPWT) 3. In the numerical model, the hull was modeled as a single rigid body, while all other components were modeled as flexible beams. The tendons were modeled using axisymmetric beam elements. Hydrodynamic forces on the tendons were applied using Morison s equation. The tendons are somewhat stiffer than those described in, for example, Refs. [15] and [16], giving the platform very short natural periods in heave and pitch. In addition to the first-order and viscous forces, differencefrequency forces using Newman s approximation and Table 3 Control system parameters (as in Refs. [6] and [7]). K I and K P are given for the minimum blade pitch setting, the final row gives the above-rated strategy. Land-based TLP Spar, Semisubs 1 and 2 Fig. 1 Floating platform designs: spar, TLP, semisubmersible 1, and semisubmersible 2. Hull mass includes ballast. K I K P s s s x wn 0.6 rad/s 0.4 rad/s 0.2 rad/s const. power const. torque const. torque / Vol. 136, NOVEMBER 2014 Transactions of the ASME

3 Table 4 Morison coefficients in the hydrodynamic models. PF indicates that frequency-dependent potential flow results were used. Platform Component C D C m Spar [7] Hull 0.6 PF Mooring lines TLP [11] Main column 0.7 PF Pontoons 0.7 PF Tendons Semisub 1 [12] Columns 1.0 PF Mooring chain Mooring poly. rope Main beam, pontoons Braces Heave plates 7.5 PF Semisub 2 [13] Main column 0.56 PF Upper column 0.61 PF Base column, trans PF Base column, axial 4.8 PF Braces Mooring lines sum-frequency forces due to the full second-order potential solution were also applied. Due to limitations in the present version of the software, difference-frequency forces due to the full secondorder potential solution could not be applied simultaneously with the sum-frequency forces. Since the sum-frequency forces are more critical for the platform response [17,18], approximations were used for the difference-frequency components. The importance of second-order forces in misaligned wind and wave conditions is documented in Ref. [19]. 2.3 Semisubmersible Platform 1. The first of two semisubmersible designs had the turbine placed on one of the three columns. The platform specifications and mooring system were similar, but not identical, to the WindFloat platform. The geometry and the original mass model are identical, and the mooring system gives natural periods similar to the generic WindFloat specification [20]. WindFloat has an active ballast system that counteracts the rotor s thrust force and makes the platform float upright. The reaction time of this system is 20 min according to Ref. [20]. The ballast system was included in the numerical model by making the mass model a function of the mean wind speed, i.e., by giving different mass and restoring matrices for each EC. The mass and restoring matrices were kept constant throughout each time domain simulation because the mean wind speed remained constant throughout the simulation. The ballast model also counteracted the rotor torque moment. The semisub 1 platform was studied using a multibody hull model. The columns and heave plates were treated as rigid bodies, while the braces were modeled by flexible beams, following Ref. [21]. A long-term fatigue analysis of this concept is presented in Ref. [12]. As shown in Table 4, the damping coefficients for this concept are somewhat higher than those of the other concepts, but the effect of reducing these coefficients to C D ¼ 0.7 was found to have less than 0.5% effect on the fatigue damage. 2.4 Semisubmersible Platform 2. The second semisubmersible concept was the OC4 DeepCWind semisubmersible, as described in detail in Ref. [13]. The wind turbine is located on the center column. There are three offset columns with pontoons around the center column, each of which has an attached catenary mooring line. Braces are used to connect all of the columns as an integrated body. The large waterplane area moment of inertia provides good stability and stiffness, thus limiting the platform pitch angle in wind and waves. In this study, the orientation of the platform with respect to the wind is opposite that described by Robertson et al. [13,22]. In the present work, this concept was also modeled using a multibody hull [21]. The four columns were modeled as rigid bodies, with first-order and viscous hydrodynamic forces applied, while the braces were modeled as flexible beams with Morison-type loads. The tower, blades, and mooring lines were also modeled using flexible elements. The Morison coefficients were applied as specified by Robertson et al. [13]. 3 Numerical Simulations Numerical simulations were carried out in order to investigate the effect of wind-wave misalignment on FWTs. A limited number of wind-wave misalignment conditions were considered, as illustrated in Fig. 2. All concepts were studied for 0 degree wind (b wind ¼ 0 deg) and four wave directions (b wave : 0 deg, 30 deg, 60 deg, and 90 deg). For the semisub 1 concept, which is not symmetric about the rotor, b wind ¼ 90 deg was also studied. In all cases, the rotor was aligned with the wind, and the wave directions were defined with respect to the wind direction. Using the analysis tool described in Sec. 3.1, ten 1 h simulations (after transients) for each of the six ECs (Sec. 3.2) were carried out for each concept and set of wind-wave directions. Based on a study of the long-term fatigue damage to semisubmersible 1, ten 1 h simulations were found to be sufficient to capture the contribution of a given EC to the lifetime (20 yr) tower fatigue damage within 2% [12]. 3.1 Dynamic Analysis Tool. Three integrated computer codes were used to model the coupled behavior of the FWT systems in the time domain: SIMO, which models the rigid body hydrodynamics of the hull [23]; RIFLEX, which includes the finite element solver, flexible elements for the mooring lines (or tendons), tower, shaft, blades, and braces, and the link to an external controller [24]; and AeroDyn, which provides the forces and moments on the blades based on blade element/momentum or generalized dynamic wake theories, including dynamic stall, tower shadow, and skewed inflow correction [25]. The generator torque and blade pitch control system was written in Java. This combination provided a stable nonlinear finite element solver, sophisticated hydrodynamics, well-tested aerodynamics, and control logic. The SIMO-RIFLEX wind turbine module has been previously verified [26,27], and the SIMO-RIFLEX-AeroDyn combination has been documented [28]. 3.2 ECs. A numerical hindcast model from the National and Kapodistrian University of Athens was used to generate 10-yr statistics for several locations in the North Sea, Atlantic Ocean, and Mediterranean Sea for the Marina Platform project [29]. Six ECs based on the conditions near the Cabo Silleiro buoy off the coast of Spain were selected. Table 5 describes the characteristics of the waves (significant wave height H s and peak period T p ) and wind (hub-height mean speed U and turbulence intensity I). These conditions represent a range of operational conditions for the turbine, including low wind speeds which are likely to be encountered often. Table 5 also includes the 1p and 3p rotor periods (T 1p and T 3p, respectively) and mean thrust (F thrust ) corresponding to the mean wind speeds [6]. T 3p, which is the blade passing period, is an important forcing period for the tower. As discussed in Sec , relatively benign wind and wave periods can become important in terms of fatigue due to the interaction between T 3p and the structural natural periods. ECs 3 and 4 are close to the rated wind speed, where F thrust is at a maximum. Finally, Table 5 also shows the probability of encountering the given conditions, where the probability P is given for a (0.73 m/s, 0.5 m, and 0.5 s) box in the (U, H s, and T p ) space [12]. It should be noted that the chosen wave conditions represent relatively large Journal of Offshore Mechanics and Arctic Engineering NOVEMBER 2014, Vol. 136 /

4 Fig. 2 Top view of wind-wave misalignment conditions. In order to conserve space, only the first few meters of the catenary mooring lines are shown. waves for the given wind speeds, such that these conditions have relatively small probabilities. Conditions with relatively large waves were expected to show the most important effects of windwave misalignment. The JONSWAP wave model was used to generate the wave history with time step Dt ¼ 0.2 s and frequency resolution Dx ¼ rad/s. The wind field was generated according to the Kaimal spectrum in TurbSim [30], using points in the rotor plane with horizontal time step 0.05 s, and the normal turbulence model was applied for class C turbines [31]. A power law vertical wind speed profile with exponent 0.14 was applied to the mean wind speed [32]. 3.3 Stress and Fatigue Calculation. The dynamic simulation results give the time history of loads at various cross sections. These loads are denoted N x (axial force), V y and V z (shear forces), M x (torsional moment), and M y and M z (bending moments). Based on the coordinate system in Fig. 3, the axial stress (r x ) and shear stress (s xy ) at a given point (r, h) on the hollow circular cross section (with outer radius r) are given by the following equations: the cross section computed about the y and z axes, respectively. In this case, the positive direction for r x is tension (aligned with N x ) and the positive direction for s h is with h. Note that this sign convention implies that positive shear stress is defined opposite the direction of positive M x and that these coordinates do not directly correspond to RIFLEX output coordinates. Based on the time history of the stress, the number of load cycles at different stress levels must be computed. The rainflow counting technique was proposed by Matsuishi and Endo [33] and is generally considered to be the best method for fatigue damage estimation for metal structures [34]. Effective stress ranges are counted based on the time history of peaks and valleys. In the present work, the implementation of rainflow cycle counting in WAFO was employed [35]. Finally, the 1 h fatigue damage (D RFC ) was found by Palmgren Miner s rule [34] with a small modification to allow for bilinear stress versus cycles to failure (S-N) curves. Representative S-N curves were selected for the tower based on Det Norske Veritas (DNV) recommendations, as shown in Table 6. Curves from Table 2-1 are for steel in air, and t ref ¼ 25 mm [36]. r x ¼ N x A þ M y r sinðhþþ M z r cosðhþ I y I z (1) s h ¼ M xr J þ 2V y A sinðhþþ2v z cosðhþ A (2) In Eqs. (1) and (2), A is the cross-sectional area, J is the polar moment of area, and I y and I z are the second moment of area for Table 5 Wind-wave misalignment ECs. The mean wind speed U is reported for the hub height (90 m). Condition EC1 EC2 EC3 EC4 EC5 EC6 H s (m) T p (s) U (m/s) I T 1p (s) T 3p (s) F thrust (kn) P(EC) (10 4 ) (-) Fig. 3 Coordinate system for sectional loads, tower base as seen from above / Vol. 136, NOVEMBER 2014 Transactions of the ASME

5 Since fatigue damage occurs in welds rather than in the base material, SN curves for girth welds were used. In order to obtain a first measure for comparison, the base metal cross sections of the members were used in stress calculation with a stress concentration factor of 1. Furthermore, axial and shear stresses were considered separately. More detailed studies may consider different stress concentration factors for different load types, more detailed geometry of the joints between structural members, and address the combined stress state. 4 Results Table 6 S-N curves for tower fatigue analysis [36] m 1 log ðk 1 Þ Maximum N 1 m 2 log ðk 2 Þ S-N curve r x , D s h , C1 4.1 Platform Motions. The standard deviations of several rigid body motions are shown as a function of the wind-wave misalignment in Fig. 4. The rigid body motions of the semisubmersible hulls were defined by the motions of the hull component which supports the wind turbine. The global x (surge) direction was aligned with the wind. While translations and yaw motions were reported in the global coordinate system, the pitch and roll rotations were reported in the yawed local coordinate system. The global surge (g 1 ) and local pitch (g 5 ) motions were therefore nearly aligned with the wind, while the global sway (g 2 ) and local roll (g 4 ) motions were perpendicular to the wind. The global yaw (g 6 ) motion is also shown in Fig. 4. Although the wave excitation in surge decreased with increasing b wave, the surge standard deviation (r(g 1 )) increased with increasing b wave in ECs 2 5 for the spar and semisubmersible platforms. The frequency content of the surge response, exemplified in Fig. 5 for one realization of the spar response in EC 4, showed an increase in the low-frequency response and a decrease in the wave frequency response for increasing b wave. For the TLP, the decrease in surge motion at the wave frequency was more significant than the increased surge at the natural frequency, such that r(g 1 ) decreased. The reason for the increase in low-frequency surge motion with increasing b wave is related to a decrease in aerodynamic damping: Fig. 4 Platform motion standard deviations as a function of b wave, b wind 5 0 deg, all ECs Journal of Offshore Mechanics and Arctic Engineering NOVEMBER 2014, Vol. 136 /

6 Fig. 5 Spar surge spectrum, EC 4. Low-frequency and wave frequency effects are shown with different scales on the vertical axis. The same effect was observed regardless of the presence of viscous hydrodynamic forces, but the same effect was not seen when the thrust force from an isolated rotor was applied as an external force. That is, there was no increase in the low-frequency surge motion with b wave when there was no feedback from the rotor velocity to the thrust force. Nevertheless, the mechanism by which the wave frequency motions contribute to the aerodynamic damping is difficult to isolate. The relative velocity of the rotor contributes nonlinearly to the thrust load, which can be approximated as F thrust C T q air ðu þ V rotor ÞjU þ V rotor ja (3) where C T is the instantaneous thrust coefficient, q air is the air density, U is the wind speed in the x-direction, V rotor is the rotor velocity in the x-direction (including contributions from pitch, surge, and tower bending), and A is the rotor disc area. This simple model highlights the fact that difference-frequency components of the rotor velocity may be present in the thrust force. The standard deviation of platform pitch motions, shown in the second subplot of Fig. 4, tended to decrease slightly with increasing b wave. The pitch motions are important due to their relation to tower loads (and tendon tension for the TLP). As with the surge motions, the wave frequency pitch motions decreased for increasing b wave while low-frequency pitch motions increased. For the TLP, the pitch motions at the first pitch/bend natural frequency also decreased with increasing b wave. It should be noted that the small pitch motions of the TLP are associated with a large mooring system cost. The sway motions were more straightforward: The increased wave excitation resulted in increased wave frequency sway motions for increasing b wave. There was negligible low-frequency sway motion. For the spar and semisubmersibles, the standard deviations of the roll motions also increased with increasing b wave. While the wave frequency roll motions increased as the misalignment increased, the low-frequency roll motions (induced in part by rotor torque variations) did not seem to depend strongly on wave direction. The TLPWT showed larger standard deviation in roll than in pitch, even in aligned wind and wave cases, although both motions were quite small in terms of absolute value (on the order of deg). In general, larger roll motion than pitch motion was seen at low frequencies, while the wave direction determined whether wave frequency roll or pitch was larger. In aligned wind and wave conditions, the high-frequency (natural frequency) pitch motions were larger, but the high-frequency roll motions for b wave ¼ 90 deg were larger than the high-frequency pitch motions for b wave ¼ 0 deg. This can be explained by noting that aerodynamic damping is not strongly present for roll motions. Furthermore, roll motions are coupled to yaw motions through the thrust force. The first-order yaw force transfer function is nonzero for 30 deg and 90 deg waves due to the orientation of the pontoons. Significant roll motions were seen at the yaw natural frequency, and increased roll motions in 30 deg waves occurred in the upper half of the wave frequency range. The final subplot of Fig. 4 shows the yaw standard deviation. Yaw motions are induced by wind speed variations on the rotor, the gyroscopic moment due to the rotor, coupling to roll via the thrust force, and direct wave excitation. Increased yaw motions were observed for b wave ¼ 30 deg and b wave ¼ 90 deg for the TLP and semisubmersible concepts: This is due to the first-order wave force. Based on the shape of the given structures, there was nonzero wave excitation for those wave directions. For the axially symmetric spar platform, the yaw motions (which were primarily at the wind frequency) did not vary as significantly with wave direction. The spar yaw motions at the wave frequency increased with increasing b wave. 4.2 Tower Fatigue Damage. After examining the platform motions, the 1 h fatigue damage at several points on the tower was computed for all of the platforms. First, the distribution of damage around the tower base and top cross sections for b wind ¼ 0 deg and b wave ¼ 0 90 deg is examined in Sec The effects of misalignment on tower base fatigue damage for different ECs are discussed in Sec Distribution of Tower Damage. The damage was computed for 24 points around the tower cross section at the base and the tower top, as defined by the angle h in Fig. 6 for the b wind ¼ 0 deg cases. Two distinct patterns in the distribution of the expected fatigue damage at the tower base were observed: The tower base fatigue in the spar and TLPWT generally behaved as in the example shown in Fig. 7; the tower base fatigue in the semisubmersibles is exemplified in Fig. 8. For simplicity, the distribution is only shown for EC 3, with b wind ¼ 0 deg. The upper and lower portions of each figure show the damage due to axial and shear stress, respectively. Several observations can be made about the tower base fatigue damage distribution, as exemplified in Figs. 7 and 8: The damage due to axial stress (D RFC (r x )) had two approximately equal peaks separated by 180 deg. The damage due to the shear stress (D RFC (s h )) had two peaks separated by 180 deg, but these were not necessarily equal due to the combination of shear force and torsion. Fig. 6 Fatigue damage locations for the tower for all wave directions and concepts (top view) / Vol. 136, NOVEMBER 2014 Transactions of the ASME

7 aligned wind and wave condition. For semisubmersible 1, 30 deg and 90 deg wave conditions resulted in similar or slightly larger D RFC (s h ) compared to the b wave ¼ 0 deg condition. For the spar and TLPWT, the two peaks in D RFC (r x ) were nearly (within 15 deg) aligned with the wave direction. Exception: in EC 1, the peak tower damage for the TLPWT was aligned with the wind regardless of wave direction, since the T 3p response was large. For the semisubmersibles, the two peaks in D RFC (r x ) were aligned with the wind direction, except in the 60 deg wave case, where the peaks were aligned with the wave direction. For b wave ¼ 30 deg and 90 deg, low-frequency stress cycles were dominant, while there were increased wave-induced loads for the b wave ¼ 60 deg case (due to the alignment of the columns relative to the waves and each other). D RFC (s h ) << D RFC (r x ). Fig. 7 Tower base 1 h expected fatigue damage as a function of cross section location: spar platform, EC 3, b wind 5 0 deg, b wave deg. Twenty-four cross-sectional locations are considered. The maximum D RFC (r x ) and maximum D RFC (s h ) were separated by 90 deg. The maximum D RFC (r x ) occurred for the aligned wind and wave condition. For the spar, TLPWT, and semisubmersible 2 platforms, the maximum D RFC (s h ) also occurred for the Similarly, several observations about the tower top fatigue damage can be made. Figure 9 shows the tower top fatigue damage due to axial and shear stress for the spar in EC 3. Although only the spar results are presented in Fig. 9, both the spar and TLPWT generally behaved as shown in Fig. 9. The semisubmersible platforms showed similar, but slightly different, patterns compared to the spar and TLPWT for both D RFC (r x ) and D RFC (s h ). The key observations about the tower top fatigue damage were as follows: At the tower top, D RFC (r x ) had two approximately equal peaks separated by 180 deg, aligned with the wind direction. For the spar and TLPWT platforms, the maximum D RFC (r x ) occurred for the aligned condition, but 30 deg and 60 deg waves gave similar or slightly larger D RFC (r x ) for the semisubmersible platforms. D RFC (r x ) at the tower top did not vary significantly among different platforms. D RFC (s h ) at the tower top had two peaks separated by 180 deg, but these were not necessarily equal. The peak Fig. 8 Tower base 1 h expected fatigue damage as a function of cross section location: semisubmersible 2 platform, EC 3, b wind 5 0 deg, b wave deg. Twenty-four cross-sectional locations are considered. Fig. 9 Tower top 1 h expected fatigue damage as a function of cross section location: spar platform, EC 3, b wind 5 0 deg, b wave deg. Twenty-four cross-sectional locations are considered. Journal of Offshore Mechanics and Arctic Engineering NOVEMBER 2014, Vol. 136 /

8 D RFC (s h ) followed the wave direction for the spar and TLPWT, while the peak D RFC (s h ) followed a pattern similar to the second subplot of Fig. 8 for the semisubmersibles. D RFC (s h ) < D RFC (r x ) at the tower top. D RFC (s h ) was larger at the tower top than at the tower base. Based on the results presented in this section, D RFC (r x ) at the tower base was chosen for further study. Despite the thrust force, the damage due to shear stress was relatively small at both the tower top and tower base. The tower top damage was dominated by wind forces and was not significantly affected by the wave direction Fatigue Damage Variation Due to Wave Direction and EC. Having examined the distribution of short-term fatigue damage around the cross section, it is then interesting to look at the dependence of the damage on the wave direction and EC. Figure 10 shows the variation of the expected maximum short-term tower base damage due to axial stress as a function of b wave. The expected maximum is computed as the average of the maximum value for each of ten seeds. The value of D RFC (r x ) is shown for the point on the cross section where it was maximum for each condition; this is not necessarily the same point for all wave directions or ECs. Although the aligned wind and wave condition consistently caused the maximum damage, the absolute value and slope of the decrease in damage with increasing b wave depended on the platform and on the EC. Note that Fig. 10 includes all four platforms in the b wind ¼ 0 deg conditions, as well as semisubmersible 1 in the b wind ¼ 90 deg conditions, and that the vertical scales differ. As shown in the first subplot of Fig. 10, the spar platform generally suffered the most damage, and it was seen to be particularly sensitive to the wave height. This can be observed by noting that the ECs with the largest wave heights caused the most damage for the spar. The fatigue damage decreased consistently with increasing b wave. For the TLP (the second subplot of Fig. 10), the decrease in D RFC (r x ) as a function of b wave depended significantly on the EC. In EC 1, the damage was primarily driven by T 3p excitation (which matched the first platform pitch/tower fore-aft bending natural period) and did not depend on b wave. For ECs 2 and 3, there was little dependence on b wave, while there was a sharper decrease in fatigue damage up to b wave ¼ 60 deg for ECs 4 6. For b wave ¼ 90 deg, the results were similar to b wave ¼ 60 deg. Based on the stress spectra (see also Figs. 13 and 14), it was observed that vibrations at the combined platform pitch and tower bending natural frequency became more important as b wave increased [19]. As shown in the third subplot of Fig. 10, semisubmersible 1 showed decreasing fatigue damage up to b wave ¼ 60 deg for all ECs, with flattening or a small increase for b wave ¼ 90 deg. Semisubmersible 1 was relatively sensitive to ECs 2 and 5. In EC 2, the T 3p blade passing period coincided with the tower natural fore-aft bending period. In EC 5, there was significant first-order wave excitation of platform pitch (T p ¼ 10 s). Compared to the TLP, semisubmersible 1 showed fairly similar tower base fatigue damage. Semisubmersible 2, shown in the fourth subplot of Fig. 10, suffered the least fatigue damage of all of the platforms. As with semisubmersible 1, EC 2 caused significant fatigue damage to the tower of semisubmersible 2 due to the coincidence of the T 3p excitation with the tower fore-aft bending natural period. Furthermore, although there was a significant decrease in fatigue damage for b wave ¼ 30 deg compared to b wave ¼ 0 deg, the fatigue damage was relatively flat or slightly increased for b wave ¼ 60 deg and 90 deg. It should be noted that the location of maximum stress was different for b wave ¼ 60 deg compared to all other directions (see Fig. 8). The wave frequency component of the stress tended to increase for b wave ¼ 60 deg, since two of the main columns then had the same phase relationship to the incoming waves, resulting in increased wave forcing. For the other wave directions, the Fig. 10 Tower base fatigue damage due to axial stress (caused by bending) as a function of wave direction. Note that the expected fatigue damage is plotted for the cross section location with the largest damage for each combination of EC and b wave. The vertical scale varies among different platforms. low-frequency component of the stress was most significant for semisubmersible 2. Finally, semisubmersible 1 in the b wind ¼ 90 deg conditions (the last subplot of Fig. 10) showed less fatigue damage to the tower than in the b wind ¼ 0 deg conditions (the third subplot of Fig. 10). The same sensitivity to wave periods around 10 s was observed for b wind ¼ 90 deg as for b wind ¼ 0 deg. Furthermore, for b wind ¼ 90 deg, an increase in first-order wave pitch forcing at b wave ¼ 90 deg was seen (since two columns then had the same phase relationship to the incoming long-crested waves, as shown in Fig. 2). Even so, the aligned wind and wave condition (b wave ¼ 0 deg, b wind ¼ 90 deg, see Fig. 2) remained most the critical condition for fatigue damage. A more direct comparison of the tower base damage due to axial stress for different ECs is presented in Fig. 11. In Fig. 11, the damage is multiplied by the probability of encountering each condition (P(EC)), as given in Table 5. D RFC (r x ) is shown for the aligned wind-wave case, where it is a maximum. Figure 11 is also useful for more direct comparison of the D RFC (r x ) at the tower base for different concepts. The difference / Vol. 136, NOVEMBER 2014 Transactions of the ASME

9 Fig. 11 1h expected fatigue damage multiplied by P(EC) for different ECs. The maximum value from the cross section for the aligned wind and waves case is shown. between semisubmersible 2 and the other concepts is particularly noticeable. Except for EC 2, where the blade passing frequency excited the first tower bending mode, semisubmersible 2 showed significantly lower damage than the other concepts. The spar tended to suffer the most fatigue damage, while the TLP and semisubmersible 1 showed more similar fatigue damage. The differences between different concepts can also be examined by looking at the spectra of tower base stress at the point where the maximum damage occurred. The spectrum of the stress variation is not a direct measure of fatigue: It does not show the effects of the number of cycles at different frequencies. Nonetheless, the spectrum of stress can show how the stress variation depends on the concept under study. Figures show stress spectra from one simulation of each of three selected conditions: EC 3, b wave ¼ 0 deg; EC 5, b wave ¼ 0 deg; and EC 5, b wave ¼ 60 deg. For clarity, the spectra are divided into lowfrequency, wave frequency, and tower natural frequency ranges; the vertical scales differ. Although the stress spectra may be small at the tower natural frequency, this stress can contribute to fatigue due to the large number of cycles. In EC 3 with aligned wind and waves (Fig. 12), semisubmersible 1 and the TLP suffered similar total fatigue damage (see also Figs. 10 and 11). Semisubmersible 1 and the spar platform showed significant stress variations in the low-frequency range: This can come from the thrust force, low-frequency pitch motions or accelerations, or surge accelerations. The spar also showed large wave-induced stresses, while semisubmersible 2 had much less wave-induced stress variation. The tower-frequency stress (due to vibrations at the tower natural frequency, which are primarily excited by rotor forces and, for the TLP, second-order sumfrequency wave forces) was small compared to the low- and wave frequency stress for all concepts. Figure 12 shows that high- and low-frequency stress variations cannot be neglected in the fatigue calculation: Even though the wave frequency stress standard deviation for the TLP was 30% higher than for semisubmersible 1, semisubmersible 1 had marginally larger fatigue damage. Figures 13 and 14 show how the stress spectrum changes for two different values of b wave in EC 5. In the aligned wind and wave case (Fig. 13), the spar and semisubmersible 1 showed very similar fatigue damage, while the TLP was less susceptible to fatigue. Comparing the stress spectra for the spar and semisubmersible 1, semisubmersible 1 had more low-frequency stress variation, while the spar had larger high-frequency stress variation. Despite the larger peak in the semisubmersible 1 response at the wavefrequency, the areas underneath the spectra in that region were quite similar. Furthermore, the spar wave frequency response included more of the upper range of wave-frequencies than that of semisubmersible 1. At the tower-frequency, the spar had much larger response. Considering the area underneath the curve, the TLP showed even more stress variation at the wave frequency than the spar and semisubmersible 1, but the TLP s low- and high-frequency variations were significantly smaller, resulting in lower expected fatigue damage. Fig. 12 Spectrum of axial stress at the tower base, EC 3, b wave 5 0 deg, b wind 5 0 deg Fig. 13 Spectrum of axial stress at the tower base, EC 5, b wave 5 0 deg, b wind 5 0 deg Journal of Offshore Mechanics and Arctic Engineering NOVEMBER 2014, Vol. 136 /

10 Fig. 14 Spectrum of axial stress at the tower base, EC 5, b wave 5 60 deg, b wind 5 0 deg Figure 14 shows the stress spectra for EC 5 with b wave ¼ 60 deg. In this condition, approximately the same point on the cross section experienced the maximum fatigue damage for all platforms, so the results can be fairly compared. Compared to the aligned wind-wave results in Fig. 13, the low-frequency component of the stress in Fig. 14 decreased for all of the concepts (to approximately 50% of the standard deviation of stress in the aligned case for the spar and semisubmersibles, 25% for the TLP). The wave-induced component of the stress decreased more significantly for the TLP and semisubmersible 1 than the spar and Fig. 15 Expected maximum tower base bending moments (fore-aft, M FA and side side, M SS ) and axial stress (r x, see Eq. (1)) as a function of b wave for b wind 5 0 deg / Vol. 136, NOVEMBER 2014 Transactions of the ASME

11 semisubmersible 2, but the same general pattern could be seen in the response. For the TLP, second-order sum-frequency wave forces excited part of the tower-frequency response. For increasing wind-wave misalignment, the decreased aerodynamic damping of these vibrations can be seen quite clearly [19]. The towerfrequency responses of the other platforms were primarily induced by rotor forces: These responses decreased when examining a point on the cross section away from the global x-axis (as in Fig. 14, which refers to the point of maximum fatigue damage). 4.3 Maximum Tower Base Bending Moments and Stresses. In addition to the fatigue damage, the maximum loads and stresses are of interest when studying the effects of misalignment. Figure 15 shows the expected maximum absolute values of the tower base fore-aft bending moment (M FA ), tower base side side bending moment (M SS ), and tower base axial stress (r x ). It should, however, be noted that none of the studied ECs are extreme conditions. The maximum M FA occurred for aligned wind-wave conditions, while the maximum M SS occurred for b wave ¼ 90 deg for the TLP and spar and b wave ¼ 60 deg for the semisubmersible concepts. Furthermore, for a given EC, the maximum M SS (for b wave ¼ 90 deg or 60 deg) was slightly smaller than the maximum M FA (for b wave ¼ 0 deg). The results for the spar are consistent with those of Barj et al. [4]. As shown in the third subplot of Fig. 15, the maximum expected r x occurred for the aligned wind and wave condition. An approximately linear decrease in maximum stress with increasing misalignment was seen for all platforms up to b wave ¼ 60 deg. The maximum stress for b wave ¼ 90 deg, however, was often larger than the maximum axial stress observed for b wave ¼ 60 deg. For b wave ranging from 0 deg to 60 deg, the maximum stress occurred at the same location (615 deg) where the maximum damage was observed (see Figs. 7 and 8). Of the two peaks in Figs. 7 and 8, the maximum stress occurred on the downwind (compression) side (h 180 deg, see Fig. 6). The location of maximum stress varied more significantly among different realizations of the b wave ¼ 90 deg conditions, except for semisubmersible 2 (where the maximum stress consistently occurred for h in the range deg for b wave ¼ 90 deg). The combined wind-induced pitch motions and wave-induced roll motions caused the maximum base bending moment to occur at different locations. For all concepts, the expected absolute value of the maximum stress for b wave > 0wassmallerthan in the aligned wind and wave conditions. 5 Conclusions The effects of misaligned wind and waves on several FWTs in selected operational conditions were investigated. Although increased platform motions were observed in misaligned conditions, the short-term fatigue due to axial stress in the tower base was smaller than in corresponding conditions with aligned wind and waves. The maximum axial stress in the tower base also occurred for b wave ¼ 0 deg, given b wind ¼ 0 deg. The study was limited to a small number of ECs based on the joint wind-wave probability distribution for an area off the coast of Spain. This work focused on conditions with large waves for the given wind speed. These conditions were expected to show the most important effects of wind-wave misalignment. Furthermore, results were restricted to platform motions and tower load effects: The effects of misalignment on the mooring systems and the internal braces of the semisubmersibles were not shown. Within the tower results, the tower base axial stress was found to be most critical, and was therefore studied in most detail. Second-order sum-frequency forces were applied to the TLPWT. Mean drift and slowly varying forces according to Newman s approximation were applied to the spar. No second-order drift forces were applied to the semisubmersibles. Differencefrequency forces are expected to increase the low-frequency platform responses and may be important for mooring system design and fatigue calculations. Despite these limitations, and the fact that the most severe load condition for all of the platforms was the b wave ¼ 0 deg condition, several interesting effects were noted in the results. The distribution of stress around the cross section of the tower base followed two distinct patterns: The maximum damage due to axial stress followed the waves for the spar and TLPWT, but the maximum damage tended to be in the wind direction for the semisubmersibles, except for b wave ¼ 60 deg. The results for b wave ¼ 60 deg highlight the effect of platform orientation on wave loads: When two of the semisubmersible columns had the same relative phase with the wave, the excitation moment amplitude increased. Low-frequency surge and pitch motions tended to increase with increasing b wave given b wind ¼ 0 deg. This effect was attributed to aerodynamic damping, but the exact mechanism by which wavefrequency motions induced low-frequency aerodynamic damping was not isolated. It was found that T 3p (blade passing) excitation of the first tower fore-aft natural frequency in low wind speeds could have a large effect on fatigue damage. In the present study, a reference tower design was used for all of the platforms. In order to improve the fatigue life, the tower fore-aft and side side modes on each floating platform should be considered, and the tower should be redesigned such that the first frequency falls outside the range of potential T 3p excitation. Improvements to the wind turbine control system may also lead to improved fatigue life for these concepts. Finally, this study compares the tower fatigue life for several FWT concepts in a limited range of ECs. The fatigue damage to the tower base of semisubmersible 2 was much smaller than for the other concepts. There was relatively little stress variation in the tower base at low, wave-, and tower-frequencies for this concept, which mitigated wave loads through its large platform inertia. Furthermore, despite the TLPWT s small pitch and surge motions, it suffered fatigue damage due to both wave frequency and high-frequency stress variations. The low-frequency surge and pitch accelerations of semisubmersible 1 were non-negligible in computing the fatigue life. Further studies of misalignment including slow-drift forces on the semisubmersibles, additional ECs and wave directions, and consideration of the mooring system should be pursued in order to determine whether or not such conditions are necessary for design checks. Full long-term studies of fatigue damage are needed in order to extend the present results to a wider range of conditions. Misalignment effects in severe ECs, when the turbine may be parked or idling, should also be studied. Acknowledgment The authors gratefully acknowledge the financial support from the Research Council of Norway granted through the Centre for Ships and Ocean Structures, and Norwegian Research Centre for Offshore Wind Technology (NOWITECH), NTNU. Erin E. Bachynski acknowledges support from Statoil through an MIT-NTNU Gemini cooperative research project. The authors are grateful to MARINTEK for support in the development of the coupled computer code. References [1] Barth, S., and Eecen, P. 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