One promising design solution for increasing the efficiency of modern horizontal axis wind turbines is the installation of curved tip extensions. However, introducing such complex geometries may move traditional aerodynamic models based on blade element momentum (BEM) theory out of their range of applicability. This motivated the present work, where a swept tip shape is investigated by means of both experimental and numerical tests. The latter group accounted for a wide variety of aerodynamic models, allowing us to highlight the capabilities and limitations of each of them in a relative manner. The considered swept tip shape is the result of a design optimization, focusing on locally maximizing power performance within load constraints. For the experimental tests, the tip model is instrumented with spanwise bands of pressure sensors and is tested in the Poul la Cour wind tunnel at the Technical University of Denmark (DTU). The methods used for the numerical tests consisted of a blade element model, a near-wake model, lifting-line free-wake models, and a fully resolved Navier–Stokes solver. The comparison of the numerical and the experimental test results is performed for a given range of angles of attack and wind speeds, which is representative of the expected conditions in operation. Results show that the blade element model cannot predict the measured normal force coefficients, but the other methods are generally in good agreement with the measurements in attached flow. Flow visualization and pressure distribution compare well with computational fluid dynamics (CFD) simulations. The agreement in the clean case is better than in the tripped case at the inboard sections. Some uncertainties regarding the effect of the boundary layer at the inboard tunnel wall and the post-stall behavior remain.

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 scale must be overcome through innovative turbine design and control strategies

Traditional-aircraft-related bibliography (e.g., see

Example tip shape applied on a wind turbine blade

In the present work, the aerodynamics of a curved tip shape is investigated via wind tunnel experiments and numerical modeling. The considered swept tip shape is the result of design optimization, focusing on locally maximizing power performance within load constraints compared to an optimal straight tip, for testing in an outdoor rotating test rig (RTR). The tip model is instrumented with spanwise bands of pressure sensors and is tested in the Poul la Cour wind tunnel at the Technical University of Denmark (DTU), for a range of angle of attack and wind speed. Aerodynamic models of different fidelities are utilized to simulate the wind tunnel cases and are compared with the measurement data, namely a blade element model, a near-wake model, lifting-line free-wake models, and a fully resolved Navier–Stokes solver.

The tip shape presented in this work is the result of an aeroelastic optimization for maximizing power performance within load constraints for a tip mounted on DTU's rotating test rig (RTR)

A predefined length of 3 m was used as a design constraint for an outdoor rotating test rig and where the tip is mounted on a 8 m cylindrical boom. The chord and twist distributions of the straight tip were determined from BEM performance for optimal power coefficient in operation at 30 rpm and 6 m/s inflow wind speed. The resulting aeroelastically optimized tip utilizing sweep achieved a 19.58 % increase in power with the same ultimate flapwise bending moment at the boom root and tip connection as the baseline. The design was evaluated with the near-wake model in the aeroelastic code HAWC2

Centerline of the tip design.

Planform of the tip design.

The geometry of the optimal tip is scaled with a factor of 0.5 compared to the RTR tip dimensions in order to be accommodated in the Poul la Cour wind tunnel (PLCT) at DTU (Fig.

Three-dimensional geometry of the tip (in meters), indicating the four sections where pressure taps are located.

The PLCT is a closed return tunnel with a closed test section. When testing the tip, the test section uses an aerodynamic setup with hard walls. The rectangular test section has the dimensions of height,

The tip model mounted in the test section of the Poul la Cour wind tunnel.

The pressures measured from surface pressure taps in the model are numerically integrated to determine the normal and tangential force components. The data acquisition (DAQ) system is based upon the CompactRIO system from National Instruments and a DTU in-house made LabView program. The pressures are measured with Scanivalve MPS4264 scanners with full-scale ranges from 6.9 to 69 kPa (the highest ranges are used close to the leading edge). The accuracy for all scanners is 0.06 % of the full-scale range (0.0041 to 0.041 kPa). The actual accuracy is in practice much better, especially for the higher ranges. In previous studies, the standard deviation of the pressures for attached flow was found to be small, and it is assumed that this is the case for the current measurements as well.

Each of the four sections is equipped with 32 pressure taps. The same normalized chordwise positions are used on all four sections. In the leading edge region (the first 10 % of the chord) 14 taps are distributed evenly along the arc length. On the remaining 90 % of the chord, nine taps are distributed on each side. Again, they are equally distributed along the arc length. The last tap is located at approximately 90 % of the chord on each side. In the post-processing a point at 100 % of the chord is added where the pressure is assumed to be the average of the pressures at the last tap on each side. The present method is used as a first estimation due to its simplicity and robustness. In any case, the influence from the extrapolation method on the normal force is minor, whereas the effect on the tangential force can be larger but still within acceptable limits.

The tip is tested in a range of wind speeds, angles of attack, and surface conditions, as shown in Table

Test configurations. Tripped; zz tape (zz: turbulator zigzag tape; 0.205 mm height, 6 mm wide, 70

The different aerodynamic models used for the numerical simulations, together with the corresponding setups, are described in this section.
Based on the labels used in the present document, those could be ordered in terms of fidelity as HAWC2 (blade element model), HAWC2 near wake, MIRAS (free wake lifting line), and EllipSys3D (CFD). In addition to these models, a different lifting-line code, LLTunnel, was utilized as part of this work for evaluating the effect of the wind tunnel, which was not fully included in any of the previous models. In terms of fidelity, LLTunnel could be thought of as lying between HAWC2 near wake and MIRAS, because it is not a free-wake method. However, it does model the full interference effect of the tunnel on the aerodynamic response.
Both EllipSys3D and MIRAS correspond to independent fluid dynamics solvers. Those two codes were run in the present study through the external coupling framework referred to as

The tunnel wall at the root section is 43 cm away from the innermost instrumented section on the model. In the tunnel, this wall will (1) prevent the formation of a strong root vortex and (2) create a boundary layer at the root wall which will cause the velocity to decrease towards zero in its vicinity. To model the first effect of the wall on the trailed vorticity behind the tip, a mirrored tip is simulated in all codes except for LLTunnel. This is achieved by mirroring the tip geometry at the root section in HAWC2 near wake and MIRAS. A flat plane with a symmetry condition is added in EllipSys3D. The blade element method in HAWC2 will not see any effect of mirroring due to the missing cross-sectional aerodynamic coupling. In contrast to the other codes, LLTunnel models the effect of all four tunnel walls using the method of mirror images.

BEM, which can otherwise be used to compute the induced velocity at a rotor disc, is not applicable in the present study. The single-tip configuration resembles more closely a blade in standstill than a rotor in operation. In this case only the blade element part of blade element momentum theory is applicable. The wind speed is projected into the airfoil cross sections; relative velocity and angle of attack are computed; and lift, drag, and moment coefficients are interpolated from airfoil polar tables. A tip loss model typically used in BEM is not relevant, because no rotor induction is present, and all the sections are radially independent. Results from this basic blade element approach are labeled “HAWC2” in the following.

The near-wake model, a simplified lifting-line model

Simulations with the multi-fidelity vortex solver MIRAS

In what follows, a description of the LL free-wake model employed in all the HAWC2–MIRAS simulations is detailed. In the model, the blades are represented by discrete vortex rings along the span. These elements account for the bound vortex strength and release vorticity into the flow. The bound vortex is discretized with 80 equally spaced straight segments in the mirrored c-shaped configuration. The leading segments of the bound vortex rings are placed along the blade quarter chord line, with the collocation point located at the three-quarter chord.

The strength of these vortex ﬁlaments is calculated via the Kutta–Joukowski theorem,

The motion of the rest of the filaments is described by Lagrangian ﬂuid markers placed at the filament end points. The ﬁlaments are therefore convected downstream with a velocity, which includes the contribution from the freestream, the bound vorticity, and the wake induction. The induced velocities are calculated directly by evaluating the Biot–Savart law. To desingularize the Biot–Savart law, the

Pitch angles from

MIRAS simulation of the c-shape configuration with the free-wake filament-based model.

The key elements of the LLTunnel lifting-line model are essentially identical to those in MIRAS. However, three main points set LLTunnel and MIRAS apart. (1) LLTunnel solves directly for the steady state solution, whereas the MIRAS solution evolves an unsteady solution. (2) LLTunnel is not a free-wake model. The trailed vorticity is assumed to convect downstream directly in the wind/tunnel direction, whereas MIRAS solves for the true time evolution of the force free wake. (3) MIRAS does not have the possibility to enforce walls in the domain in its present version, so the effect of the wall on which the wing is mounted is effectively modeled by modeling also the mirror image of the wing on the other side of the wall. This way there is no flow through the mirror plane, effectively making it a slip wall. This is treated differently in LLTunnel, where any walls in the vicinity of the blade simulated in LLTunnel are simulated using mirror images of the blade and wake vorticity when setting up the influence coefficients of the method (see

Illustration of the use of mirror image model walls.

In the code only the 20 nearest mirror images in each direction were included. The total number of mirrored vortex systems is then

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

A common grid was used for all the EllipSys3D simulations. It was generated in two consecutive steps. First, a structured mesh of the tip surface was generated with the openly available Parametric Geometry Library (PGL) tool

Visualization of the EllipSys3D mesh. For clarity, only one out of every four grid lines is shown, and half of the semi-spherical domain is not depicted.

In this section, the main results of the present work are presented. The first subsection lays the foundation for the rest of the investigations by quantifying the difference in aerodynamic forces between the blade mounted on a symmetry wall and a blade mounted between four tunnel walls, like the wind tunnel tests. All following sections contain a comparison of test and simulation results in a progressive manner, going from the most qualitative observations to a quantified comparison. In this way, Sect.

Before the results from the simulation methods can be compared to wind tunnel measurements, we need to quantify the difference in aerodynamic loading between the wing mounted on a wall, like it is modeled in the majority of the computational methods employed in the present study, and the wing mounted in the wind tunnel, which is what is being measured in the experiments.
This section uses LLTunnel to assess this difference.
Figure

The graphs show MIRAS and LLTunnel

The results in the figure show that there is a good agreement between LLTunnel and MIRAS results for the single-wall version of the LLTunnel. The relatively small differences between the results can be explained by modeling differences for the two codes. MIRAS includes the free-wake effects, which are not included in LLTunnel. On the other hand LLTunnel extends the wake further downstream of the airfoil than MIRAS. The good agreement between the results show that the LLTunnel code is working as intended.
The LLTunnel results in the figure also highlight the difference between the wing on a single wall compared to the wing in the full-tunnel setup. The results show that the effect of the tunnel is to increase the normal force coefficient slightly for all four sections. This is a result of the upwash caused by the additional mirror images in the tunnel case. The effect of the additional tunnel walls on

The difference in

The

Figure

Surface flow visualization. Left column: 0

At an angle of attack of 0

Figure

Pressure coefficient

It is then concluded that the EllipSys3D predictions are in generally good agreement with the experimental tests. In Sect.

The measured and simulated normal force coefficients are compared in Fig.

The results from the pure blade element method denoted HAWC2 overpredict the normal loading at all sections. As described in Sect.

The EllipSys3D results in attached flow are in very close agreement with the MIRAS results except for the most outboard region S4, where the slope predicted by EllipSys3D is significantly smaller. This could be explained by the smaller chord lengths and Reynolds numbers outboard, which lead to worse airfoil performance in EllipSys3D but are not taken into account in the airfoil data input to MIRAS.

In almost all cases EllipSys3D and the measurements both qualitatively predict increased maximum normal force coefficients when comparing to the 2D airfoil data read by HAWC2. An exception is section S2 in the tripped configuration where the maximum measured

For the two inboard sections S1 and S2 all models overpredict

As mentioned before, a plausible explanation for the differences between EllipSys3D and the rest of the numerical models was the fact that the latter group used a fixed set of polar data at

Comparison of measured and simulated

Comparison of measured and simulated

Wind tunnel tests of an optimized swept tip shape are described. A range of fidelity of aerodynamic models is utilized to simulate the wind tunnel test cases, and they are compared with the measurement data, namely a blade element model, a near-wake model, a lifting-line free-wake model, and a fully resolved RANS model. In addition to this, the tunnel effects are assessed with a different lifting-line code. Results show qualitative agreement of the surface flow in flow visualization and CFD. Comparing the surface pressure it is seen that there is better agreement for the clean than tripped case at the inboard sections.

When comparing tunnel velocity normalized normal force coefficients as function of geometric root section AOA, important 3D effects cannot be predicted by the blade element model. There is generally good agreement between near-wake model, MIRAS, CFD, and experiments in attached flow. However, the near-wake model predicts the outboard section less accurately because the curved geometry is not taken into account, and all codes share an uncertainty close to the root due to the neglected tunnel wall boundary layer. CFD and experiments indicate stall delay, but the quantitative agreement in the post-stall region is only fair. The clean measurements are generally in better agreement with the simulations than the tripped measurements, indicating again a too aggressive tripping.
Investigations of the tunnel effect show that the

This work has illustrated the challenges associated with testing and modeling a curved tip shape, even at a 2D setup, and quantified the validity of different aerodynamic modeling fidelities. It also serves as a building block for the work on the full-scale rotating field test of the curved tip on the RTR, which will appear soon. Future investigations could focus on clarifying the influence of the wind tunnel wall boundary layer at the root.

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

TB performed the tip design optimization, wind tunnel model preparation, instrumentation, and testing. GRP contributed to the tip design optimization and performed model simulations. NRG and SGH performed model simulations. RFM contributed to the preparation of the experiments and their instrumentation. ASO contributed to the wind tunnel model testing and data post-processing. MG performed the study on the wind tunnel corrections. All authors contributed to the writing of this paper.

The contact author has declared that neither they nor their co-authors have 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 have also contributed to the presented work: Sigurd L. Ildvedsen, Jimmie S. Beckerlee, Helge Aa. Madsen, 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 Mingming Zhang and reviewed by Joerg Alber and one anonymous referee.