The analysis of wind turbine aerodynamics requires accurate information about the axial and tangential wake induction as well as the local angle of attack along the blades. In this work we present a new method for obtaining them conveniently from the velocity field. We apply the method to the New Mexico particle image velocimetry (PIV) data set and to computational fluid dynamics (CFD) simulations of the same turbine. This allows the comparison of experimental and numerical results of the mentioned quantities on a rotating wind turbine. The presented results open up new possibilities for the validation of numerical rotor models.

The wake induction and the angle of attack (AoA) are crucial quantities for the design and analysis of wind turbines. Several methods
have been proposed for their estimation

In order to address the mentioned issues, this work aims to provide a simple method for obtaining the wake induction and the AoA from the velocity field in the rotor plane. The required flow data can be captured experimentally e.g. by means of particle image velocimetry (PIV) or numerically with computational fluid dynamics (CFD) models. The new method is not only straightforward in its application but also independent from user-defined input parameters. Furthermore, it takes advantage of the high resolution of PIV and CFD results for obtaining detailed spanwise distributions of the quantities searched.

A brief description of the most common methods for the determination of the wake induction and the AoA is presented in
Sect.

The main challenge for determining the local wake induction and the AoA is to obtain the local velocity in the rotor plane
without blade bound circulation influences. Once the local undisturbed velocity components are known, the axial and tangential
induction factors (

As seen above, the determination of the wake induction and the AoA requires detailed information about the rotor flow
without blade induction. A comparison of several methods for obtaining them concluded that three out of four methods were reasonably
consistent and reliable

In our method, the velocities are directly probed at a location in the rotor plane at which the induction of the blades is counterbalanced
and cancelled out. With axial, uniform inflow, this condition is fulfilled at the bisectrix between two consecutive blades (this
applies for both two-bladed and three-bladed rotors). This probing location is represented in Fig.

Schematic representation of the probing location (red line) of the new method for computing the wake induction and the AoA on a rotor operating under axial, uniform inflow. The bound circulation is represented around the blades. Along the red line, the downwash of the blade located at the 11 o'clock position is cancelled out by the upwash of the blade located at the 6 o'clock position. The blade located at the 3 o'clock position does not induce any velocity along the red line. As a result, the velocities obtained along the red line are free of blade induction influences.

The difference between the free-stream velocity and the probed axial velocity corresponds to the axial wake induction. The probed
tangential velocity corresponds to the tangential wake induction with opposite sign. Equations (

In the case of yawed or non-uniform inflow conditions, the new method can still be applied, but it becomes considerably more complex. In that case, the location at which the blade-induced velocities are counterbalanced must be computed by equalizing the induction of all the blades, which must be computed with the law of Biot–Savart. This requires calculating the local bound circulation along each blade beforehand. The simplest way to do this is to compute the line integral of the velocity field along a closed contour located around the blade section and outside the boundary layer.

In the following section, the wake induction and the AoA is computed from experimental (PIV) and numerical results of the MEXICO turbine.

PIV windows located just upstream and downstream of the rotor plane are available for the whole blade span

Schematic representation of the set of PIV windows located at the 3 o'clock position upstream and downstream of the rotor
plane. Between both sets of PIV windows there is a gap of approximately 30

The PIV windows were located in a fixed horizontal plane. In this work, we use phase-locked measurements at the azimuth angle

Axial, uniform inflow conditions with three different wind speeds are considered in this work: 10, 15 and 24

The numerical results used in this work have been extracted from Reynolds-averaged Navier–Stokes simulations of the MEXICO turbine,
which were validated against experimental results in

The results presented in this section have been computed applying the AAT (see
Sect.

Figure

Axial induction factor along the rotor radius.

At 15

The results obtained from the CFD and PIV results using the new method compare reasonably well, although clear discrepancies appear in
the tip region at 10

The computed tangential induction factor is displayed in Fig.

Tangential induction factor along the rotor radius.

As shown in Fig.

Angle of attack distribution along the rotor radius comparing three different methods (new method, azimuthal averaging
technique and Shen). The results from Shen have been extracted from

The comparison between the method proposed by

In Fig.

The method proposed in this work for computing the wake induction and the angle of attack allows the accurate extraction of those quantities
from numerical as well as experimental results of the velocity field in the rotor plane. The method is easy to use and automatize for
uniform axial inflow. Furthermore, it does not require any user-defined input parameters. The main limitation of the current method,
which also applies to other methods, is that it cannot capture the influence of the local trailed and shed vorticities accurately. In
principle, this could be an issue at the tip, where the influence of the tip vortex should not be disregarded. However, it has been
shown that the method proposed by

In the case of yawed or non-uniform inflow, our method can still be used, but it becomes considerably more complicated because of the dependence of the blade bound circulation on the azimuthal blade position.

CFD simulations have been shown to be capable of quite accurately predicting the AoA distribution along the blade span. Therefore, combining the AoA extracted from CFD results with experimental blade pressure measurements can be considered a reliable approach for obtaining realistic lift and drag blade characteristics. Nevertheless, slight deviations with respect to the purely experimental results should be expected in the root region at stall conditions.

The prediction of the wake induction with CFD is much more challenging than the prediction of the AoA, especially in the tip and root regions. This is especially noticeable at operating conditions involving complex, three-dimensional flows.

The direct extraction of the wake induction and the AoA from PIV measurements provides valuable information for the validation of numerical models. Another possible application of the new method is the extraction of 100 % of experimental blade section characteristics (as long as pressure distributions are also available). This, in turn, can contribute to the development or enhancement of engineering correction models for different aerodynamic effects.

The employed measurements are available for all participants of the IEA Wind Task 29 MexNext. For more information please contact the third author (schepers@ecn.nl).

The new method proposed in this work for computing the wake induction and the angle of attack on the rotor blades of wind turbines is based on the assumption that for axisymmetric, homogeneous inflow conditions, the induction from the blades bound circulation is counterbalanced at the bisectrix between two blades. In the following, this will be demonstrated for a three-bladed rotor.

At a given point, the velocity induced by the bound circulation of each blade can be computed using the theorem of Biot–Savart:

Biot–Savart's integrand from Eq. (

Now plotting the fraction of the integrand of Eq. (

IH proposed the new method for estimating the angle of attack and the wake induction, performed the calculations, analysed the results and wrote the paper, except the appendix, which was written by ED. JGS and ED contributed with detailed discussions about the method and the results.

The authors declare that they have no conflict of interest.

This article is part of the special issue “Wind Energy Science Conference 2017”. It is a result of the Wind Energy Science Conference 2017, Lyngby, Copenhagen, Denmark, 26–29 June 2017. Edited by: Jens Nørkær Sørensen Reviewed by: two anonymous referees