In this paper, a method to determine the angle of attack on a wind turbine rotor blade using a chordwise pressure distribution measurement was applied. The approach used a reduced number of pressure tap data located close to the blade leading edge. The results were compared with the measurements from three external probes mounted on the blade at different radial positions and with analytical calculations. Both experimental approaches used in this study are based on the 2-D flow assumption; the pressure tap method is an application of the thin airfoil theory, while the probe method applies geometrical and induction corrections to the measurement data.

The experiments were conducted in the wind tunnel at the Hermann Föttinger Institut of the Technische Universität Berlin. The research turbine is a three-bladed upwind horizontal axis wind turbine model with a rotor diameter of 3 m. The measurements were carried out at rated conditions with a tip speed ratio of

Results show that the pressure tap method is suitable and provides a similar angle of attack to the external probe measurements as well as the analytical calculations. This is a significant step for the experimental determination of the local angle of attack, as it eliminates the need for external probes, which affect the flow over the blade and require additional calibration.

The angle of attack (AoA) is, by definition, a 2-D concept. Nevertheless, on a wind turbine, the rotating system, i.e., a blade, is under 3-D effects such as tip and root vortices, yaw misalignment and velocity inductions, among others that render the precise determination of the AoA difficult

The AoA can be calculated according to its geometrical definition using the velocity triangle defined by the wind velocity and the rotational speed. Unfortunately, this estimation relies on well-known free-stream conditions and does not take into account induction effects. Therefore, if a more reliable estimation is required, it is necessary to use on-blade measurement tools.

Most of the on-blade measurements use external probes to measure the local pressure. Various methods have been used, while they follow the same principle: apply a correction due to the upwash induced by the presence of the blade itself. Including a stagnation pressure hole leaves the three-hole probe as required minimum. Additional holes (five, six, seven) allow the cross flow derivation and provide better accuracy. However, the number of calibration curves increases; thus the determination of the inflow becomes more difficult

Several field measurements have been conducted using probes as one of the estimation methods for the AoA.

Angle-of-attack estimation methods on wind turbine rotor blades.

These methodologies have been applied over wind turbine models on tunnel experiments.

In general, according to the published literature, external probes can be used to determine the AoA. However, in the case of wind turbine models, such probes are intrusive and significantly disturb the flow over the blade section where they are mounted.

Other complementary tools used on research turbines are surface pressure sensors, located along the blade chord. These sensors are used to record the pressure distribution along the blade chord at a desired radial position and to calculate the aerodynamic loads. Different computational methods use this information as a source to estimate the AoA.

The inverse blade element momentum (BEM) method is probably the most common. From the surface pressure sensors, the normal and tangential forces are calculated, assuming that they are uniform over an annulus containing the blade section. The wake-induced velocities are calculated according to momentum theory, yielding the effective velocity vector and subsequently the AoA

The NREL suggested an algorithm to estimate the AoA from pressure distribution values under axial

The surface pressure measurements also allow experimental estimations.

Moreover,

Furthermore,

Therefore, the pressure distribution over a rotating section can be used to relate the AoA, if it is comparable with nonrotating conditions, where the AoA is known. Several investigations showed a relation between 2-D and 3-D pressure distribution.

Overall, it is generally agreed that static 2-D wings and rotating blades have a good agreement in surface pressure measurements, at least for attached flow conditions. This opens up the possibility of using methods based on the blade chord pressure distribution to estimate the AoA, in the range of agreement.

To the authors' knowledge, this method has not been applied on a rotating blade yet. Given the good agreement between 2-D and 3-D pressure distributions away from the root region, this paper presents an alternative method of determining the AoA by means of pressure tap measurements. The present investigation aims at providing experimental verification for one such surface pressure method

Today, new technologies such as passive fiber optic pressure sensors presented by

The Technical University of Berlin has developed a scaled wind turbine model, BeRT, equipped with three-hole probes and pressure taps on one of its blades

In the remainder of the paper, the facilities and the research turbine model are described, followed by the methodology to determine the AoA and to assess the validity of the Gaunaa method on the rotating plane. The results are presented in Sect.

The tests were conducted at the Hermann Föttinger Institut of the Technische Universität Berlin in the GroWiKa (large wind tunnel), a closed-loop wind tunnel driven by a 450 kW fan and a cross-sectional area

Outline of GroWiKa, modified from

At the same time, the inflow showed some heterogeneity, i.e., was not fully uniform as is depicted in Fig.

Axial inflow. Dashed lines: tip and tower positions. Colored lines: radial positions at

Additionally, the dynamic pressure is monitored by two Prandtl tubes located at the walls at 0.43R upstream the turbine at 2.7 m height. Based on the Prandtl tubes, all test cases were conducted with a free-stream velocity of

BeRT, Fig.

Angle definition. Azimuth,

A slightly modified Clark Y airfoil profile is used along the entire blade span and there is no cylindrical root section. The airfoil modification was necessary in order to account for a realistic trailing edge thickness with respect to manufacturing requirements. Aerodynamically, the design intended to avoid stall while continuing to offer optimal performance and the maximum internal space to include instrumentation

In this way, the specific airfoil profile was chosen as it performs well at low Reynolds numbers (

Twist and chord distribution along span

The turbine rotor area (

One blade was equipped with pressure taps and three three-hole probes at different radial positions, as shown in Fig.

Tubing details between pressure taps and sensors.

The three-hole probes were located at

Three-hole probes mounted in the equipped blade

All pressure transducers were installed in such a way that their membranes were parallel to the plane of rotation to minimize the centrifugal effect on them. More information about the sensors can be found in previous work by

The blade was also provided with three trailing edge flaps with

Rotating (NI cRIO-9068) and nonrotating (NI cDAQ-9188) measurement systems were synchronized and located in the hub and the external control cabinet, respectively. The measurement data were recorded using NI 9220 modules with an acquisition frequency of 10 kHz.

The pressure data from the blade were recorded through the rotating system, while the free-stream dynamic pressure was recorded through the nonrotating system. The blade position was recorded through a Hall effect sensor located in the nacelle. Each measurement was recorded and phase averaged until 100 rotations were completed, with an azimuth step of

In this section, the methodology of this research is described. The main idea is to compare the results obtained by the method proposed by

According to the BeRT design specification, the combination of chord and twist distribution achieves an optimal shape

The calibration of the sensors, the applied corrections and the description of the methods used to determine the AoA follow, while the test cases and their uncertainty are summarized at the end of this section.

Differential pressure sensors were used for both experimental methods, the pressure taps (HCL0025E) and the three-hole probes (HCL0075E). During the calibration of the sensors, the turbine was in a static position and a constant pressure was provided to achieve 11 calibration pressure points using the external calibrator, Halstrup KAL 84. All calibrations were linear and the fitting curves showed a coefficient of determination value of

The three-hole probes were calibrated in a small wind tunnel. The calibration range was from

The pressure sensors measure the differential pressure (

The structural design of BeRT results in eigenfrequencies of the blades of

Frequency spectrum of one pressure sensor of the three-hole probe at

The dynamic response of the taps–tubes system was evaluated theoretically following the model proposed by

Scheme of the model to apply

In the case of the pressure taps, the centrifugal effect was quantified and corrected, Eq. (

The hydrostatic correction has less impact since all the sensors are located in the hub and was consequently neglected.

The method to determine the AoA from the three-hole probes was based on previous work with the same setup. It is outlined here for completeness, while further details can be found in

The AoA relative to the probe,

Schematic of the reference system for a probe, modified from

As the turbine was set under yaw misalignments, it is important to verify the effectiveness of the 2-D probe. The range of the AoA, in the probe stations, is

Moreover,

The determination of the AoA from the pressure distribution on the blade section was based on the unsteady model developed by

Aiming at simpler solutions to estimate airfoil loads that can be applied to active load control, and based on the considerations mentioned above,

It is important to note that this summary neglects the chord streamwise degree of freedom, i.e.,

On the right side of Eq. (

The remaining contributions in Eq. (

The formulation allows the calculation of the effect of a flap on the airfoil, with

The term

Equation (

Several studies conducted by

In order to obtain the constants

Finally the AoA was calculated using Eq. (

Figure

XFOIL (

Since there are no pressure taps in the exact

The relative dynamic pressure,

The introduction of a yaw misalignment produces an expected change in the AoA distribution along the blade span due to the crossflow, i.e., depends on the azimuth angle variations. Therefore, a geometrical approach was used to compare the experimental methods under these operational points, as pressure tap and three-hole-probe locations differ in radial position.

The normal velocity contribution is a function of the yaw angle, Eq. (

The blockage effect must be considered. Consequently, the inflow velocity (

Equation (

Several operational conditions were analyzed, three yaw angles

The measurement uncertainty, for all quantities, was taken into account in order to quantify the error magnitude over the results. Both AoA estimation approaches have the same iteration in the error propagation, based on the following steps:

nominal error of each sensor;

the standard deviation of the averaged measurements, which was calculated with the same azimuth step as the phase average;

conversion to AoA and thus the error propagation after applying Eqs. (

Table

Measurement uncertainty summary.

During the measurement campaign, while the changes on the pitch or yaw angle were made between test cases, the tunnel was left open to allow for fresh air to enter the tunnel circuit. As a result, the temperature and relative humidity were kept within

The results are presented in this section, starting from the pressure distributions and the relative dynamic pressure along the chord at the span position of

The AoA estimation based on the surface pressure measurements depends on the relative dynamic pressure (

Results from pressure taps at

For the aligned case,

Initially,

This behavior agrees qualitatively with computational results made by

With the introduction of yaw misalignment

For the case of yaw angle

In terms of the measurement range, the relative pressure is

The magnitude of the dynamic pressure,

Pressure contours over the pressure side at

It can be seen that for the case of a yaw angle

The pressure taps are located at discrete points on the blade surface. For this reason, the sensor that estimates the stagnation point, i.e., the values of the relative dynamic pressure, fluctuates in location. The latter explains the sharp changes present in yaw angle

Normalized relative dynamic pressure at radial position

Regarding the drop in relative dynamic pressure for the misalignment cases, this can be explained with the geometrical velocities. Equation (

Figure

Figures

AoA results for yaw angle

Figure

The explanation is due to the heterogeneity of the inflow. These variations,

Although the AoA over the azimuthal variation is not constant, both methods estimate a similar AoA range. The AoAs for both pressure tap and three-hole-probe methods are slightly lower than previous experimental results show by

On previous work by

Additionally, Table

AoA from the pressure taps and three-hole-probe methods at a yaw angle of

Figure

AoA results for yaw angle

From Fig.

The same behavior is presented in the case of analytical AoA, Fig.

For this yaw misalignment, it is shown that the three-hole probe has a trend less pronounced than the pressure tap approach between

Figure

AoA results for yaw angle

The behavior of the AoA results from the pressure tap method, Fig.

The analytical AoAs, Fig.

Overall, the pressure tap method presents good results, qualitatively and quantitatively. In the aligned case, the average difference between three-hole probes and analytical AoA is below 1

AoA estimations from pressure tap and three-hole-probe methods and variations with pitch angle. Three yaw cases

A comparison between the AoA estimations from both approaches through the pitch angle cases, at a fixed azimuth position,

A linear fit

A method to determine the AoA based on the pressure difference between the pressure and suction side on a wind turbine blade was tested. The method was compared with the AoA results from three three-hole probes in simultaneous wind tunnel measurements together with analytical calculations. Several conditions were studied regarding the introduction of yaw misalignment and different pitch angles for the blades.

The pressure distribution on the blade at

The application of the method can be summarized as follows.

Perform computational calculations or 2-D airfoil measurements to obtain the pressure distribution

Get a fit equation between the pressure difference of the lower and upper sides

Perform pressure distribution measurements at a blade section with similar characteristics of the 2-D airfoil. Only pressure taps at

Identify the relative dynamic pressure,

Estimate the AoA through the inverse equation from the 2-D calculations:

The results show that in the aligned case,

With the introduction of yaw misalignment, the AoA results from the pressure tap method show, as expected, the crossflow influence in a more pronounced curve than the three-hole probe, in agreement with the analytical results. The crossflow impact is more dominant than the tower effects, and the pressure tap method is not able to predict its influence, from where an AoA overestimation in the azimuth region of

Regarding the pitch angle changes in the blades, the AoA results from the pressure tap approach present a linear behavior with a slope value of

Overall, it is found that the pressure tap method applied here to determine the AoA provides reliable data, with good performance for both aligned and misaligned cases. Hence, the presented method is a promising alternative to the use of external probes, which affect the flow over the blade and require additional calibration.

AoA results from the pressure tap and three-hole-probe approaches with their uncertainties. The pitch angles

AoA results from the pressure tap and three-hole-probe approaches. In columns are shown the yaw angles:

AoA results from the pressure tap and three-hole-probe approaches. In columns are shown the yaw angles:

Pressure measurement data and results can be provided by contacting the corresponding author.

RSV carried out the measurement campaign with the support of JA and SB. RSV worked in the implementation of the pressure tap method, performed the calculations and analysis, and wrote the paper. SB provided the code for the three-hole-probe method. JA, SB, MM, CNN and COP contributed with comments and discussions about each section in the manuscript.

The authors declare that they have no conflict of interest.

This article is part of the special issue “Wind Energy Science Conference 2019”. It is a result of the Wind Energy Science Conference 2019, Cork, Ireland, 17–20 June 2019.

The authors would like to acknowledge Joseph Saverin for providing valuable feedback.

This research has been supported by the ANID PFCHA/Becas Chile-DAAD/2016 (grant no. 91645539).This open-access publication was funded by Technische Universität Berlin.

This paper was edited by Katherine Dykes and reviewed by Uwe Paulsen and one anonymous referee.