Comparative study on the wake deflection behind yawed wind turbine models

In this wind tunnel campaign, detailed wake measurements behind two different model wind turbines in yawed conditions were performed. The wake deflections were quantified by estimating the rotor-averaged available power within the wake. By using two different model wind turbines, the influence of the rotor design and turbine geometry on the wake deflection caused by a yaw misalignment of 30° could be judged. It was found that the wake deflections three rotor diameters downstream were equal while at six rotor diameters downstream insignificant differences were observed. The results compare well with previous experimental and numerical studies.


Introduction
In order to reduce power losses in wind farms caused by wake effects, different active wake control strategies were investigated in the recent years. One promising approach is an intentional yaw misalignment which is able to deflect the wake deficit laterally and thus reduce its impact on downstream turbines. However, a detailed understanding of a yawed wind turbine's wake trajectory is needed before potentially applying the concept. As full-scale field studies are limited and numeric simulations face modeling uncertainties, wind tunnel experiments are a useful tool for validation purposes. Wakes of yawed model wind turbines have been addressed in multiple wind tunnel studies using different model turbines of varying geometries and rotor designs. For a small model of D = 0.12 m and a yaw angle of γ = 30 • , Medici and Alfredsson [1] found a wake deflection of about z/D ≈ 0.5 at a downstream distance of x/D = 4. For the same yaw angle, Krogstad and Adaramola [2] measured a wake deflection of z/D ≈ 0.2 rotor diameters already at x/D = 1. The model turbine, however, had a rotor diameter of D=0.90 m and thus was significantly larger. A slightly different wake deflection angle for γ = 30 • was found in an experimental PIV study by Bastankhah and Porté-Agel [3], who localized the wake center at z/D ≈ 0.16 for x/D=2 and at z/D ≈ 0.34 for x/D=6 downstream distance for a smaller wind turbine model of D=0.15 m. Howland et al. [4] used a yawed drag disc of D=0.03 m and found a deflection between z/D ≈ 0.4 and z/D ≈ 0.5 at a distance of x/D = 6, dependent on the measurement technique and fitting method. All of these studies qualitatively showed consistent wake deflection effects, that can be generalized. However,  [5]. The installed turbulence grid generates a vertical shear in the inflow velocity, being non-uniform over the rotor area. A common way to describe wind shear is the power law [6] which expresses the wind speed u as a function of height y, given that the wind speed at an arbitrary reference height y ref is known. The coefficient α describes the strength of shear in the profile. The shear grid used here generates a profile that can be approximated by a shear coefficient of α = 0.11, which is a realistic value for offshore boundary layers in stable atmospheric conditions [7]. Table 1 gives an overview of the inflow conditions for each turbine. The turbulence intensity, and the free stream velocity u ∞ refer to the respective turbine's hub height.

Model wind turbines
Two different model wind turbines were used that vary in size, blade design and geometry. The turbines will be denoted NTNU and ForWind, respectively. The ForWind turbine has a rotor diameter of D ForWind = 0.580 m and a hub diameter of 0.077 m. In order to adjust the hub height of the turbine to the center of the NTNU wind tunnel, the turbine tower was extended with four rods of a diameter of 0.02 m attached to the base plate. The rotor blades are based on an SD-7003 airfoil profile, and were manufactured by a vacuum casting method using a MG804 synthetic (isocyanate-polyol) compound. Further details about the blade design and airfoil characteristics can be found in Section 2.3. The rotor is designed for turning in clockwise direction when observed from upstream. The ForWind turbine features an automatic load control, which allows an operation at constant TSR during the experiments. The pitch angle β can be adjusted using a stepper motor (see [8] for details) and was set to have maximum performance in perfect yaw alignment, which resulted in a value of β = 1.8 • for this experiment. The pitch angle and tip speed ratio were then kept constant when the turbine was yawed to an angle of γ = −30 • . Further details about the load control and the turbine design are described by Schottler et al. [8].
The NTNU turbine has a larger rotor of D NTNU = 0.894 m with a hub diameter of 0.090 m. It is a re-design of the turbines used in [5], having a thinner tower and a smaller nacelle in order to minimize their effects on the wake flow behind the turbine. The aluminum blades are based on a NREL S826 airfoil, which was designed by the National Renewable Energy Laboratory (NREL). The NTNU rotor turns in counter-clockwise direction and is driven at by a 400W Panasonic LIQI electric servo motor. The servo motor ensures a rotation at constant tip speed ratio, while the excessive power is burned off in an external resistor. The pitch angle of the turbine has to be adjusted manually and was fixed to β = 0 • for this experiment. Both model turbines were operated at the same TSR of λ = 6. Table 2 gives an overview of the main characteristics of both turbines used, Figure 1 shows scaled sketches of both turbine models.

Rotor and airfoil comparison
The ForWind rotor has a total twist of about 22 • and a chord length distribution varying from about 70 mm at the root to about 20 mm at the tip. The rotor is an upscaled version of the rotor described in Odemark and Fransson [9]. It is build from elements based on the SD-7003 airfoil, which is specifically designed for low Reynolds number operation. A detailed documentation is given by Selig et al. [10] and Counsil et al. [11]. The total twist distribution on the bigger NTNU rotor spans about 38 • from the blade root to the tip, while the chord length varies from 82 mm to 26 mm. The rotor geometry is defined in detail by Saetran & Bartl [12] and is based on the NREL S826 airfoil from the root to the tip. The airfoil was originally designed for full-scale wind turbines operating at Reynolds numbers in the order of 10 6 and is documented by Somers [13]. As the Reynolds number for this model experiment is about one order of magnitude lower, experimental performance data were recorded for low to moderate Reynolds numbers. One comprehensive dataset is provided by Sarmast and Mikkelsen [14], another by Ostovan et al. [15]. The airfoil shapes, on which the two rotors are based, as well as the performance at a Reynolds number of Re = 1 × 10 5 are compared in Figure 2. The drag distribution is observed to be very similar for the two airfoils, while the lift force is seen to be around 20% higher for the NREL S826 airfoil for a wide range of angles of attack. This noteworthy difference in lift is the reason for a lower power output of the ForWind rotor, but also implicates a difference in thrust force between the rotors, having an impact of the wake deflections.

Measurement techniques
Flow velocities in the wake were measured using a DANTEC FiberFlow two-component Laser Doppler Anemometer (LDA) system, recording the u-and v-component of the flow, cf.   Figure 3 illustrates the measurement grid behind the rotors. Based on this grid of physically measured values, a much finer grid of a total of 401×321 ≈ 129000 grid point is interpolated. The distance between the interpolated grid points is thus reduced to 0.005 D. Natural neighbor interpolation is used, which is resulting in a smoother approximation of the distribution of data points [16]. The interpolated values make it possible to calculate a rotor-averaged velocity of approximately 3.16 × 10 4 data points per rotor area for the wake center detection method described in Section 3.1.

Setup
The respective model turbines were positioned on a turning table allowing for a yaw misalignment. The orientation of the yaw angle γ is based on the tunnel geometry, which is sketched in Figure 4 along with the schematic setup. Wake

Wake location detection
As a major motivation for studying wind turbine wakes is the effect on downstream turbines, we use the power of a potential downstream turbine for estimating the wake center position in z-direction. A similar approach was shown by Vollmer et al. [17]. The potential power of a downstream turbine is The rotor area is divided in ten ring segments. A i is the area of the i th ring segment and u i (t) A i ,t denotes the temporally and spatially averaged velocity in main flow direction within the area A i . For simplicity, the power coefficient is assumed to be constant for each ring segment and is not included here. P * is estimated for 50 different hub locations in the range −0.5 D ≤ z ≤ 0.5 D, at the original hub height. We define the wake center in z-direction by the z position resulting in the minimum of P * . The procedure is illustrated in Figure 5.

Operating conditions
Both turbines were operated close to their optimal operation conditions at a yaw angle of γ = 0 • . For γ = −30 • , the TSR was kept constant at λ = 6 based on the u-component of the free stream velocity, resulting in a power decrease of approximately 21 % for the ForWind, and 29 % for the NTNU turbine. The average of both values is 25 %, which corresponds precisely to a cosinesquared relation between the relative power and angle of yaw misalignment as cos 2 (30 • ) = 0.75.  Figure 5. Illustration of the wake center detection method. A i is the area of the i th ring segment of the potential downstream turbine's rotor area, whose hub is located at the red ×. u i (t) A i ,t is the spatially and temporarily averaged u-component of the velocity. The potential power P * is calculated for each ring segment and then added up. This procedure is repeated for various hub locations ×, while the position resulting in the lowest value of P * is interpreted as wake center.

Results
For the wakes of both turbines during a yaw misalignment of γ = −30 • , the deflections in zdirection at x/D = 3 and x/D = 6 were quantified using the approach described in Section 3.1. Figure 6 shows the normalized potential power P * for varying z-positions and both downwind distances. As expected, for both turbines the wake is deflected in z-direction, whereas the magnitude of deflection increases with the downstream distance behind the respective rotor. Table 3 summarizes the results derived from Figure 6 and will be used for further quantification of the wakes' deflections. At x/D=3, the wake deflection magnitude is 0.19 D for both turbines, Table 3. Wake center location and corresponding skew angles based on Figure 6. The wake location corresponds to the value of z resulting in the lowest value of P * , cf. Section 4. nacelle as compared to the NTNU turbine. Further downstream at x/D=6, the deflections are larger, as expected due to the wakes' expansion. However, differences between both turbines become apparent. The wake of the NTNU turbine is located at z/D=0.32, resulting in a slightly smaller skew of approximately 3.0 • . The wake behind the ForWind turbine, on the other hand, is deflected slightly further to z/D=0.40, which corresponds to a skew of nearly 3.8 • and is therewith nearly constant as compared to the distance x/D = 3.

Discussion
The fact that at x/D=3 the same wake deflection in z-direction is observed for both turbines having a different blade design and turbine geometry suggests that those aspects do not influence the wake trajectory at this distance. Further, it is assumed that wind tunnel effects such as blockage or wall-effects are insignificant for both turbines. At x/D=6, however, differences in the wake deflections of both turbines can be observed, the wake behind the ForWind turbine is found to be deflected slightly further. A possible reason for this is a bigger influence of the increased wind tunnel blockage ratio of the 1.5 times bigger NTNU rotor. While the interaction of the flow behind the ForWind rotor with the wind tunnel side walls (blockage ratio 5.4%) is deemed to be insignificant, the considerably higher blockage ratio of 13% for the the NTNU rotor might influence the wake expansion and defection. Chen et al. [18] quantified the influence of blockage effects in a wind tunnel study, suggesting that those can be neglected for a blockage ratio below 10 %. This finding supports the assumption that blockage effects are of greater relevance for the NTNU turbine and might cause the differences in wake deflection at x/D=6 as the blockage ratios of both turbines are on either side of the suggested 10% limit. In general, the observed deflections at x/D=3 and x/D=6 are in very good agreement with large eddy simulations (LES) by Vollmer et al. [17] of a full-scale scenario investigating the wake deflection behind a NREL 5MW turbine in stable atmospheric conditions. There, wake deflections of approximately 0.3 − 0.38 D were observed, depending on the tracking method. Further, an experimental study based on particle image velocimetry (PIV) measurements behind a significantly smaller model wind turbine of 0.15 m rotor diameter showed a very similar wake deflection It should be noted that the thrust force of both turbines is a parameter influencing the wake deflections and trajectories, which is, however, not included in this study.

Conclusion & future work
A comparative study of the wake deflection behind two different model wind turbines operated in γ = −30 • yaw misalignment was realized. A very similar defection behavior of the mean wake flow behind the two turbines was observed, resulting in skew angles of 3.0 − 3.8 • . Only insignificant differences in wake deflection were found at x/D=6, although model turbines of different sizes, rotor designs, and geometries were used. As the deflection magnitudes and skew angles are furthermore observed to fit well with previous experiments on even smaller scale turbines [3] as well as simulations on full-scale turbines [19,17], general estimations for the deflection can be deducted. Further, it can be concluded that the presented experimental setup and methods allow for a systematic investigation of wake details including their trajectories.
In future analyses of the acquired data, the wake shapes and trajectories will be further analyzed in detail. Besides effects of the turbine geometry, the influence of turbulence and shear in the inflow will be investigated. Moreover, a blind test comparison of the wake data with computational wake simulations of the wind tunnel setup is initiated.