One promising design solution for increasing the energy production of modern horizontal axis wind turbines is the installation of curved tip extensions. However, since the aeroelastic response of such geometrical add-ons has not been characterized yet, there are currently uncertainties in the application of traditional aerodynamic numerical models. The objective of the present work is twofold. On the one hand, it represents the first effort in the experimental characterization of curved tip extensions in atmospheric flow. On the other hand, it includes a comprehensive validation exercise, accounting for different numerical models for aerodynamic load prediction. The experiments consist of controlled field tests at the outdoor rotating rig at the Risø campus of the Technical University of Denmark (DTU), and consider a swept tip shape. This geometry is the result of an optimized design, focusing on locally maximizing power performance within load constraints compared to an optimal straight tip. The tip model is instrumented with spanwise bands of pressure sensors and is tested in atmospheric inflow conditions. A range of fidelities of aerodynamic models are then used to aeroelastically simulate the test cases and to compare with the measurement data. These aerodynamic codes include a blade element momentum (BEM) method, a vortex-based method coupling a near-wake model with a far-wake model (NW), a lifting-line hybrid wake model (LL), and fully resolved Navier–Stokes computational fluid dynamics (CFD) simulations. Results show that the measured mean normal loading can be captured well with the vortex-based codes and the CFD solver. The observed trends in mean loading are in good agreement with previous wind tunnel tests of a scaled and stiff model of the tip extension. The CFD solution shows a highly three-dimensional flow at the very outboard part of the curved tip that leads to large changes of the angle of the resultant force with respect to the chord. Turbulent simulations using the BEM code and the vortex codes resulted in a good match with the measured standard deviation of the normal force, with some deviations of the BEM results due to the missing root vortex effect.

The trend of reducing the levelized cost of energy (LCOE) of horizontal axis wind turbines through increasing rotor size has long been established. To achieve this, the challenges of scaling must be overcome through innovative turbine design and control strategies

Existing bibliography relevant to wind turbine applications typically focuses on winglets and aerodynamic tip shapes, with limited testing of generalized curved shapes in controlled or atmospheric conditions

Previous related work by the authors focused on the aeroelastic optimization of curved tip extensions

The tip shape presented in this work is an aeroelastically optimized tip which is mounted on DTU's rotating test rig (RTR)

Design variables range and optimized values.

Three-dimensional geometry of the tip indicating the measurement sections.

Pareto front of the optimization objectives (horizontal axis: change in flapwise bending moment at tip connection compared to baseline, vertical axis: change in aerodynamic power compared to baseline, color bar: summed difference in power and flapwise moment).

In-plane and out-of-plane coordinate of the centerline of the optimized tip design compared to the reference.

Planform of the optimized tip design compared to the reference.

Mass and flapwise stiffness distributions of the tip compared to the reference.

Internal structure of the mid-span section of the tip compared to the reference.

In order to fill in the gap between full-scale MW experiments and wind tunnel tests, the 95 kW Tellus turbine

The tip mounted on the RTR and nearby met mast.

The tip as seen from the boom-mounted camera.

Four chordwise bands of 1 mm inner diameter pressure taps are installed on the tip at spanwise locations of 9.09, 9.79, 10.49, and 11.18 m from the boom root (15 %, 35 %, 55 %, and 75 % of the tip span, respectively). The 32 taps on each section are connected via tubing to one 1 psi and one 5 psi range DMT pressure scanners with an accuracy of 0.05 psi located on the joint piece inboard of the tip root. Sets of strain gauges are installed at the sides of the spar cap and leading edge and trailing edge at two sections at spanwise locations of 9.8 and 10.6 m from the boom root. A 6-hole Pitot tube is also mounted at the joint piece inboard of the tip root, measuring the local inflow. The data acquisition (DAQ) system is based on cRIO from National Instruments. Finally, two cameras are mounted inboard of the joint piece connected to the end of the boom.

The pressure distributions from the surface taps are numerically integrated into normal and chordwise aerodynamic forces on the local airfoil section reference frame, while an average pressure from the two nearby points is added to the trailing edge (Fig.

Example of measured average pressure coefficient at section S2 of the tip for one case at 5

The target result is the statistical distribution of the aerodynamic forces at each section for a set of statistical distributions of operation (wind speed, yaw, pitch). The parameters of the measured 300 s cases are shown in Table

Parameters of all measured cases.

Parameters of measured cases averaged based on pitch angle.

The time domain aeroelastic simulations performed within the framework of the present study were orchestrated by the multi-body finite-element code HAWC2. All the computations shared the same structural modeling, which is described in Sect.

Distribution of aerodynamic sections along the planform.

All the presented methods were coupled with a common multi-body finite-element HAWC2 model. For simplicity, the tower was considered to be stiff (the maximum tower deflection is estimated to be within 10 cm, with the ratio of its first natural frequency to the rotational frequency of around 1.2). Together with the ensemble of the boom and the tip, which was considered to be a single body, the shaft and the counterweight were also modeled. The mechanical properties of the latter two components of the model are further described in

The BEM method in the present study corresponds to the model described in

The coupled near- and far-wake model

Medium-fidelity simulations were carried out with the in-house vortex solver MIRAS

Higher-fidelity simulations were performed with the three-dimensional computational fluid dynamics software EllipSys3D

The deflections of the boom centerline and the mounted-tip centerline, computed by HAWC2, were introduced in the CFD solution during run time. These deflections were subsequently applied to the surface grid through a spline interpolation. The surface grid deflection was then smoothed into the inner domain through a mesh-deformation algorithm based on the distance to the blade surface. Rotation was simulated by applying a rotational motion to the full computational grid as a solid body. At every time step, the CFD loading was computed and injected into the HAWC2 solution. This was done by integrating the pressure and frictional loads (including forces and moments) in a series of sectional planes which are normal to the local blade axes. The location of such sectional cuts was forced to correspond to the position of the aerodynamic sections that were defined in the rest of the methods included in this work (see Fig.

The grid was generated in two consecutive steps. First, a structured mesh around the cylindrical boom and the tip surfaces was generated with the Parametric Geometry Library (PGL) tool

Visualization of the EllipSys3D mesh. For clarity, only one out of every four grid lines is shown. Left: overview of the boundary conditions distribution. Half of the spherical domain is not depicted and the freestream velocity vector is aligned with

This section contains the comparison of measured loads with the aeroelastic loads predicted using the aerodynamic models of varying fidelity. Because no wake rake was mounted on the rotating rig, only the measured forces normal to the chord based on surface pressures are used. Insufficient wind speed measurements were available to accurately estimate shear coefficients, so no mean shear profile is present in the simulations. The effect of shear is, however, assumed to be minor, due to the small rotor diameter of the rotating test rig. All the simulations shown here use transitional polars. Since the state of the boundary layer during operation in the field is unknown, the transitional polars have been selected, since these were closer to the results. It has been shown that the comparison of fully turbulent CFD and LL using fully turbulent polars is consistent, and this is briefly demonstrated. But generally, the loading was found to be underpredicted using fully turbulent polars and fully turbulent CFD. These results are omitted here for brevity.

The section is organized as follows: in Sect.

Unless otherwise stated, the results shown here are averaged from four simulations at the four slightly different operating conditions for each pitch angle, see Table

The averaged normal force from measurements and simulations and the averaged simulated chordwise force are shown in Fig.

Comparison of normal (left panels) and chordwise (right panels) load distribution obtained from simulations and measurements. Results shown are averaged from four simulations per pitch angle, see Table

At 5

At 10

The purpose of Fig.

Comparison of normal force from simulations and experiment as a function of pitch angle. Results shown are averaged from four simulations per pitch angle, see Table

At sections S2 and S3, the experiment shows indications of stall occurrence towards 10

The generally very good agreement between NW and LL computations in attached flow was also observed in the previous comparison with wind tunnel measurements. At section S4, the agreement is improved in the present work because the swept tip shape is taken into account by the NW model due to the modifications described briefly in Sect.

Comparison of mean deflections for case 3 and case 4. The torsional deflection is given about the pitch axis.

The torsional and flapwise deflections for cases 3 and 4 are shown in Fig.

Comparison of resultant force magnitude (left panels) and angle (right panels) between LL and CFD for cases 3, 9, and 13 from Table

Figure

Surface-restricted stream lines computed with the CFD method for case 3 corresponding to a pitch of

LL is unable to predict the near-tip direction change of the load, and actually, these angles and forces would not be possible to achieve based on airfoil data, because there is a significant spanwise flow in the CFD simulations. Along these lines, it could be speculated that one of the factors explaining why all the other methods showed higher loading when compared to CFD could also lie in this three-dimensional behavior.

As already mentioned, there seems to be generally larger tip loss in the CFD simulations than in the LL simulations. This is in part due to the rounded tip geometry (see Fig.

Simulations accounting for an inflow turbulence that matches the measured one during the experimental campaign were carried out. The averaged cases based on pitch angle defined in Table

First of all, the turbulence generator of

Cases 1 to 3 in Table

In MIRAS, the turbulent boxes are transformed into a particle cloud by computing the curl of the velocity field. The turbulent particles are released one diameter upstream of the rotor plane and interact freely with the turbine wake, if existent. The vortex solver accounts for turbulence development as it convects downstream towards the rotor plane. In the simulations without a turbine, the local velocities are calculated in every time step at the rotor plane position, and a

All codes (BEM, NW, and LL) simulate each seed for 900 s at a time step of 0.01 s. The initial 100 s are discarded in the postprocessing.

In the following, the mean and standard deviation of the loads from the turbulent simulations are compared to the experimental values.

Comparison of normal and chordwise force from turbulent simulations and the experiment. Results shown are averaged from four turbulent seeds per pitch angle, using the mean operating conditions as shown in Table

The spanwise mean loading in the normal and chordwise directions obtained from measurements and simulations is shown in Fig.

Comparison of standard deviations of normal force from turbulent simulations and the experiment. Results shown are averaged from four turbulent seeds per pitch angle, using the mean operating conditions as shown in Table

The shaded area in Fig.

Generally, the spread between the results for different turbulence seeds indicates that a large part of the deviation between experiments and simulations may be explained by variations between turbulence realizations, with an exception of the outmost section at a pitch of

The distribution of the standard deviations of the normal loading and chordwise loading are shown in Fig.

The measured standard deviation of the normal force is generally similar to the simulated standard deviation. An exception is case 2 at roughly 0

The shaded area, which represents the spread in standard deviations between turbulence seeds, agrees very well between LL and NW, with the BEM predicting a much larger spread in case 3 (5

The aeroelastic response of a swept tip is investigated for application to wind turbine tip extensions by controlled field testing in the outdoor rotating rig at the Technical University of Denmark (DTU). The swept tip shape in focus is the result of design optimization focusing on locally maximizing power performance within load constraints compared to an optimal straight tip. The tip model is instrumented with spanwise bands of pressure sensors and is tested in atmospheric inflow conditions. A range of fidelities of aerodynamic models are used to simulate the test cases and results are compared with the measurement data, namely a blade element momentum (BEM) model, a coupled near- and far-wake model (NW), a lifting-line hybrid wake model (LL), and fully resolved Navier–Stokes computational fluid dynamics (CFD) simulations. The first simulations tackled a series of idealized inflow conditions that were obtained by averaging several time windows of the experimental data. Results show that the measured mean normal loading can be captured well with the vortex-based codes and the CFD solver. The CFD solver seemed to generally underpredict the measured mean loading for these idealized conditions in attached flow. However, this higher-fidelity method computed a similar stall delay to that seen in the measurements at a high angle of attack. Similar trends to those seen in earlier wind tunnel measurements were observed when plotting the measured and simulated loading against the pitch angle. The CFD solution shows a highly three-dimensional flow at the very tip that leads to large changes in the angle of the resultant force with respect to the chord at the very outboard part of the curved tip. These angle changes cannot be predicted by any model using 2D airfoil data. No measurements were available at these outboard stations and, therefore, we were not able to validate this phenomenon with measurements. In a second stage of the analysis, the influence of turbulence on the definition of the ideal cases was addressed. Simulations with four different turbulence realizations indicated that a large part of the deviations between measured and simulated mean loading by the higher-fidelity codes can be due to seed-to-seed variations. These turbulent simulations show that the measured standard deviations of the normal force match those predicted by the vortex codes well. There are some deviations when comparing to the BEM simulations, especially towards the root section. Future work should focus on full-scale validation of aeroelastically optimized tip shapes, with focus on further enabling structural tailoring features and topologies, and possible combination with active aerodynamic add-on features.

Pre-/post-processing scripts and datasets are available upon request. The codes HAWC2, MIRAS, and EllipSys3D are available with a license.

TB performed the tip design optimization, contributed to model preparation, performed the tests, and contributed to the model setup and comparison. GP contributed to the tip design optimization and model setup and comparison. NRG contributed to the model setup and comparison. SGH contributed to the model setup and comparison. AL developed and implemented the updated near-wake model used in this work and contributed to the comparison. HAM contributed to the tip design optimization and model preparation and testing.

The contact author has declared that none of the authors has any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This research was supported by the project Smart Tip (Innovation Fund Denmark 7046-00023B), in which DTU Wind Energy and Siemens Gamesa Renewable Energy explore optimized tip designs. The following persons also contributed to the presented work: Flemming Rasmussen, Niels N. Sørensen, Frederik Zahle, Peder B. Enevoldsen, and Jesper M. Laursen.

This research has been supported by the Innovationsfonden (grant no. 7046-00023B).

This paper was edited by Sandrine Aubrun and reviewed by Vasilis A. Riziotis and one anonymous referee.