The objective of Phase III of the Offshore Code Comparison Collaboration, Continued, with Correlation and unCertainty (OC6) project is to evaluate the accuracy of aerodynamic load predictions by offshore wind modeling tools for a floating offshore wind turbine (FOWT). FOWT platforms can experience significant translational and rotational motions, affecting the system dynamics and loads (Veers et al., 2022).

The OC6 project is part of an ongoing effort under the International Energy Agency Wind Technology Collaboration Programme (IEA Wind) Task 30 to verify and validate offshore wind turbine modeling tools (IEA Wind, 2022). To validate the aerodynamic loading on the wind turbine under large motions, participants in OC6 Phase III modeled a 1:75 scaled version of the Technical University of Denmark (DTU) 10 MW reference wind turbine (RWT) (Bak et al., 2013) examined in the Unsteady Aerodynamics for FLOating Wind (UNAFLOW) project (Fontanella et al., 2021a, b) and a follow-on experimental campaign. For such configuration, the group ran a series of simulations, including steady and unsteady wind conditions due to the platform motion, and compared the resulting rotor loads and wake behavior from the experiments and the different modeling tools. The rotor loads were also compared between different modeling approaches to assess the potential advantages and disadvantages of models of different fidelities. This paper summarizes the work done within the OC6 Phase III project.

The organization of the remainder of the paper is as follows: Sect. 2 provides a definition of the scaled model and testing performed. Section 3 provides a description of the active participants involved in OC6 Phase III and their modeling approaches. Section 4 then summarizes the load cases that were performed for the verification and validation. Finally, Sects. 5 and 6 provide some example results from the project and the conclusions drawn.

To validate the accuracy of the rotor loads for an FOWT, measurement data from two wind tunnel experimental campaigns were used. Both campaigns were conducted in the Politecnico di Milano wind tunnel (13.84 m wide by 3.84 m high by 35 m long) and used a 1:75 scaled version of the DTU 10 MW RWT. The blades were straight, without a cone angle, and rigid. The blade properties can be found in Table 1. The aerodynamic center of the different radial stations is coincident with the blade pitch axis. Its position along the chord, as measured from the leading edge, is given in Table 1.

Two-dimensional sectional-model experiments were conducted in the DTU red wind tunnel to characterize the airfoil polars with smooth- and rough-surface conditions (Fontanella et al., 2021b). The airfoil polars, with the lift and drag coefficients for the different angles of attack at the 20 radial stations shown in Table 1 for rough-surface conditions, were provided to the participants. Each airfoil polar contains seven sets of lift and drag coefficients for Reynolds numbers ranging between 5E4 and 2E5 (Robertson et al., 2023).

The rest of the model geometry (e.g., tower, rotor overhang) was dependent on the testing campaign being studied. The first data set was developed during the UNAFLOW project (Fontanella et al., 2021a). The testing was similar to that performed during the LIFES50+ project (Bayati et al., 2017). However, for the UNAFLOW test the tower was considered rigid and included a negative tilt angle of 5∘ to offset the wind turbine tilt angle, resulting in a rotor perpendicular to the wind tunnel floor. The second data set is from a follow-on testing campaign performed during 2021 in the same wind tunnel. It used the same rotor but a different nacelle and tower length (also rigid) than the one used in the UNAFLOW project.

Figure 1 shows the scaled DTU 10 MW RWT during the two testing campaigns. For simplicity, the UNAFLOW campaign is described as Experiment 1, and the follow-on campaign is described as Experiment 2. An air density of 1.177 kg m-3 is considered for both campaigns.

Figure 2 shows a schematic representation of the wind turbine tested in both campaigns and the two coordinate systems used in this project. Table 2 provides the geometrical properties for these two campaigns.

Experiment 1 includes steady and unsteady wind conditions. The unsteady wind conditions were induced by means of forced harmonic oscillations in the surge direction (i.e., fore–aft translation). The forced motion was achieved through two hydraulic actuators at the tower base. This campaign includes load measurements with a 6 degree of freedom (DOF) load cell at the tower-top location, a 6 DOF load cell at the tower base, hot-wire probes to measure the wind speed along and across the wake, and particle image velocimetry (PIV) to study the blade-tip vortex behavior.

Experiment 2 used a 6 DOF robot at the base instead of the two hydraulic actuators used for the fore–aft translation in Experiment 1. During this testing, some of the conditions studied during Experiment 1 were tested again. In addition, for the unsteady wind cases, equivalent tests resulting in the same rotor apparent wind were tested but using platform pitch motion instead of surge motion. Equivalent measurements for tower-top loads were recorded during this test campaign, but information about the wind turbine wake was not recorded (i.e., hot-wire and PIV measurements are not available).

During Experiment 1, the rotor was kept rotating at a constant speed. However, Experiment 2 used a different rotor speed controller, resulting in some rotor speed oscillations. These rotor speed variations can impact the amplitude and phase of the rotor loads, which could have important implications for the torque due to the rotor inertia. Politecnico di Milano tried to remove these rotor speed variations by means of an analytical postprocessing.

The hub height in both experiments is also slightly different. The relatively small distance (close to 0.5 m or 0.2 rotor diameter) between the blade tip and the wind tunnel ceiling might affect the wake expansion in the vertical direction and thus the induction in the rotor area.

During the testing campaigns, the wind turbulence intensity in the region covered by the rotor was close to 2 % (Bayati et al., 2018). Moreover, the wind speed was fairly constant over the rotor-swept area (Bayati et al., 2018). For the numerical models, it was decided to use a spatially uniform steady inflow.

Finally, Politecnico di Milano performed a postprocessing of the load measurements to remove the inertial loads (Mancini, 2020). The loads studied in this paper are purely aerodynamic. Participants modeled a rigid tower and a rigid rotor and extracted the rotor aerodynamic loads.

A total of 29 academic and industrial partners from 10 different countries participated in OC6 Phase III. Those actively involved were Bureau Veritas (BVMO, France), the Centro Nacional de Energías Renovables (CENER, Spain), the China General Certification Center (CGC, China), the China State Shipbuilding Corporation (CSSC, China), Det Norsk Veritas (DNV, United Kingdom), the Technical University of Denmark (DTU, Denmark), the Dalian University of Technology (DUT, China), Électricité de France (EDF, France), eureka! (EURE, Spain), the Institute for Energy Technology (IFE, Norway), IFP Energies nouvelles (IFPEN, France), the Maritime Research Institute Netherlands (MAR, the Netherlands), the National Renewable Energy Laboratory (NREL, USA), Newcastle University (NU, United Kingdom), the Office National d'Etudes et de Recherches Aérospatiales (ON, France), Politecnico di Milano – the POLI-Wind Laboratory (POLI-W, Italy), Politecnico di Milano (POLIMI, Italy), PRINCIPIA (PRI, France), Shanghai Jiao Tong University (SJTU, China), Tecnalia (TECN, Spain), the Netherlands Organization for Applied Scientific Research (TNO, the Netherlands), Technische Universität Berlin (TUB, Germany), Hamburg University of Technology (TUHH, Germany), Università degli Studi di Firenze (UNIFI, Italy), Universitat Politècnica de Catalunya (UPC, Spain), the University of Stuttgart (USTUTT, Germany), the University of Strathclyde (UoS, United Kingdom), Vulcain Engineering (VULC, France), and WyndTek (WTEK, the Netherlands).

The participants used modeling approaches of different fidelities to study the system: blade element momentum (BEM) theory, dynamic BEM (DBEM) that accounts for a dynamic inflow effect, generalized dynamic wake (GDW), free-vortex wake (FVW), and blade-resolved or actuator-line-based computational fluid dynamics (CFD).

The BEM, DBEM, GDW, some FVW, and the actuator-line-based CFD approaches are based on the lifting-line theory. In these approaches, the airfoil polar data are used as an input for the model. The airfoil polar provides information about the lift and drag coefficients as a function of the angle of attack. Participants can use the airfoil polar information as a look-up table (static polar approach) or to account for unsteady airfoil aerodynamics. The unsteady airfoil aerodynamics accounts for the flow hysteresis in the lift and drag coefficients under unsteady wind and wind turbine operating conditions (e.g., blade pitch actuations). The flow hysteresis can occur during attached flow (e.g., linear region in the airfoil polar) or flow separation, including dynamic stall (e.g., nonlinear region in the airfoil polar). These unsteady effects are computed by the modeling tools and depend on the underlying theory considered. The lifting surface and three-dimensional panel FVW as well as the blade-resolved CFD do not use the airfoil polar data as input. Instead, they use a surface mesh based on the blade geometry. One computer-aided design (CAD) file of the blade was provided to the participants. In this case, it may be challenging to reproduce the airfoil polars' behavior due to the relatively small Reynolds numbers during the experiment (mainly below 1E5). Small Reynolds numbers may increase the boundary-layer thickness, resulting in larger drag and smaller lift coefficients.

Sectional aerodynamic loads are computed on the basis of the local inflow velocity. The local inflow velocity is the sum of the relative velocity (e.g., due to the incoming wind, the rotor rotation, and the platform motion) and the induced velocity (i.e., the velocity change due to the interaction with the rotor). The steady BEM theory assumes that the wake reacts instantaneously. In this equilibrium wake assumption, the induced velocities (based on the axial and tangential induction factors) are quasi-steady. However, in reality, it takes time (delay) for the wake to respond to a change in the flow conditions. This change in the flow conditions can be due to changes in the incoming wind or the turbine response (e.g., rotor speed variations, blade pitch variations, and platform motions). The BEM theory with a dynamic inflow model (also referred to as dynamic wake) tries to capture the unsteady aerodynamic response from this delayed wake response by means of a correction consisting of low-pass filters over the quasi-steady induced velocities. In GDW, dynamic inflow is explicitly calculated by representing the induced velocity in terms of series expansion of radial and azimuthal basis functions within a governing equation that takes into account an apparent mass. Dynamic inflow is intrinsically captured by FVW because induction is calculated directly from the time-dependent trailing and shed vorticity and by CFD because of the explicit solving of the momentum and continuity equations.

A list of the participants is provided in Table 3, which also shows the modeling approaches adopted and the codes used. Some participants decided to use more than one modeling approach, and some used different codes. A total of 54 numerical models were involved in this validation.

EDF, EURE, and NREL used two different modeling approaches based on the lifting-line theory within the same code. The models denoted with “1” use a static polar approach, while the models denoted with “2” account for unsteady airfoil aerodynamics.

Other participants using a lifting-line approach with static polars were BVMO, IFE (DBEM), MAR, NU, ON, POLI-W, POLIMI, TUHH, UNIFI (FVW), UPC (BEM), and VULC. Other participants using a lifting-line approach with unsteady airfoil aerodynamics were CENER (FVW), CGC, CSSC, DNV, DTU1, DTU2, DUT, IFE (GDW), IFPEN, PRI, TECN, TNO, TUB, UNIFI (DBEM), UPC (FVW), and WTEK.

All FVW models used by participants are based on the lifting-line theory. For the CFD models, three participants used an actuator-line-based approach (DTU1, POLIMI, and UNIFI), and four participants used a blade-resolved approach (CENER, SJTU, USTUTT, and UoS).

A stepwise validation procedure was performed in the OC6 Phase III project, taking advantage of the two experimental campaigns carried out in the Politecnico di Milano wind tunnel.

Table 4 provides a summary of the simulations that are presented in Sect. 5, including one steady wind condition (Load Case 1.1) and unsteady wind conditions under platform surge (Load Cases 2.X) and platform pitch motion (Load Cases 3.X). For the pitch motion, the equivalent longitudinal amplitude can be approximated by multiplying the sine of the platform pitch angle by the distance from the hub to the tower base. Load Cases 3.5 and 3.7 result in the same rotor apparent wind (horizontal component) as Load Cases 2.5 and 2.7, respectively. The rotor apparent wind in Load Case 3.1 is slightly lower than in Load Case 2.1 due to a limitation in the 6 DOF robot motion range.

Three additional load cases (2.12, 2.16, and 2.17) were included to examine conditions that might create more impactful unsteady aerodynamic responses due to changes in the flow conditions. There are no experimental data available for these conditions; thus, they are used as verification cases only. Load Case 2.12 includes a platform surge oscillation at the same frequency as Load Case 2.7 but with an amplitude that is 1 order of magnitude higher. Finally, Load Cases 2.16 and 2.17 are based on Load Case 2.12 but include some rotor speed and blade pitch variations.

Some numbers are skipped in the load case numbering sequence because there were more load cases that did not provide additional insight and are therefore left out of the results of Sect. 5.

The studied wind speed of 4.19 m s-1 and rotor speed of 240 rpm in these load cases is representative of the near-rated condition for the DTU 10 MW RWT at a model scale (tip-speed ratio of 7.1). This wind speed was already corrected to account for the wind tunnel blockage (Robertson et al., 2023). The presence of the scaled wind turbine in the test section reduces the flow area compared to an unrestricted freestream. This flow area reduction results in an increased wind velocity in the rotor disk area. The blockage ratio between the rotor disk area and the wind tunnel cross area was close to 8 % during the experiments. This corrected value of 4.19 m s-1 was used by participants using BEM, DBEM, GDW, and FVW approaches. Most participants using the CFD approach (POLIMI, UNIFI, USTUTT, and UoS) included the wind tunnel walls, ceiling, and floor in their numerical models, reproducing the confined system conditions. These boundary conditions were introduced in the CFD models by means of slip walls. A wind speed of 4 m s-1 was used by these participants.

In the study of unsteady aerodynamics, it is common to use reduced frequencies (Ferreira et al., 2022; Mancini et al., 2020). The reduced frequency is a dimensionless number with higher values, indicating a greater degree of unsteadiness. The rotor's reduced frequency (k) is related to the motion frequency (f), the rotor diameter (Ø), and the freestream wind (U0) as stated in Eq. (1). The platform motion frequencies shown in Table 4 result in the rotor's reduced frequencies of 0.071, 0.568, and 1.137. 1k=f⋅ØU0 The platform motion amplitudes shown in Table 4 correspond to oscillations ranging from 0.6 to 9.375 m at a full scale (i.e., from 0.003 to 0.05 rotor diameter). In terms of periods at a full scale, the tests cover the range from 12.5 to 20 s (Mancini et al., 2020). Most FOWT testing is done with Froude-scaled models. However, in the two testing campaigns considered in this study, the scaling was based on the reduced frequency to try to preserve the relationship between the wind and the platform velocity. In this case, the wind velocity was scaled by a factor of 3 and the physical dimensions by 75 (Mancini et al., 2020). These amplitudes and periods are considered representative of different FOWT support structures.

The loads measured at the tower top during the experiments were oriented according to the tilted tower (x′–y′–z′ coordinate system in Fig. 2). These loads were first rotated according to the tilt angle and then translated to the hub location (x–y–z coordinate system in Fig. 2) to make the comparison between the numerical models and the experiments easier.

During the processing of the experimental data, a significant 1P response corresponding to the blade-passing frequency was observed. This frequency was due to a rotor asymmetry. The three blades were weighted, and one of the blades had a significant mass imbalance (∼10 %). Moreover, a 2P was also present in the response. This could imply an aerodynamic imbalance (e.g., one blade pitch error or blades with different aerodynamic performances). This aerodynamic imbalance would result in loads with a different mean value as well as the presence of a 1P in the response and the corresponding harmonics (e.g., 2P). To avoid the dynamic influence of this rotor asymmetry, the data from the experiments were low-pass filtered at 3 Hz. This cutoff frequency was a compromise to include the fastest platform motion in the experiments (2 Hz in Load Cases 2.7 and 3.7) and exclude the rotor asymmetry (1P frequency is 4 Hz for a rotational speed of 240 rpm). The low-pass filter also removes the tower shadow effect (e.g., the 3P excitation and the corresponding harmonics). Accordingly, participants did not include the tower's influence on the wind in their numerical models, or they filtered it out in the case it was included.

In this section, a comprehensive overview of the studied load cases shown in Table 4 is presented and explained.

In the frame of the OC6 Phase III project, participants modeled a scaled version of the DTU 10 MW RWT and studied the system response under steady and unsteady wind conditions. The results of numerical models with different fidelity levels were compared against two testing campaigns, performed at Politecnico di Milano, for platform surge and pitch harmonic motions. A good agreement was observed between the numerical models and the experiments for the platform frequencies and amplitudes considered. For reference, these tests correspond to periods between 12.5 and 200 s at a full scale and nacelle motion amplitudes between 0.6 and 9.375 m. No significant differences between the numerical models of different fidelities were observed during the forced platform motions. For these tests, the aerodynamic rotor load was linearly proportional to the rotor apparent wind, denoting a quasi-steady aerodynamic response. Only a small hysteresis in airfoil performance undergoing angle of attack variations in attached flow was observed by participants using unsteady airfoil aerodynamics. This introduced a small phase shift in the rotor loads, but the impact was limited.

Additional load cases were also included to understand if other conditions could produce a significant unsteady aerodynamic behavior. It was observed that the change in the flow conditions due to rotor speed and blade pitch variations combined with the platform motion resulted in such an unsteady aerodynamic response. While there were no measurement data available for these conditions, the numerical models showed significant differences based on the modeling approach used. Those that did not include dynamic inflow effects predicted rotor load variation amplitudes 9 % smaller under rotor speed variations and load variation amplitudes 18 % higher when there were blade pitch actuations. The dynamic inflow also had a limited impact on the phase of the rotor loads. Thus, this work has shown that while the motion of the turbine itself does not require an unsteady aerodynamic modeling approach to accurately predict the loads in the turbine (at least for the design and forced motion studied in this project), a realistic condition where generator torque control and blade pitch angle control are included will need unsteady aerodynamic models (both airfoil unsteady aerodynamics and dynamic inflow models) for accurate load prediction.