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**Wind Energy Science**
The interactive open-access journal of the European Academy of Wind Energy

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**Research article**
16 May 2018

**Research article** | 16 May 2018

Wind tunnel experiments on wind turbine wakes in yaw: redefining the wake width

^{1}ForWind, University of Oldenburg, Institute of Physics, Oldenburg, Germany^{2}Department of Energy and Process Engineering, Norwegian University of Science and Technology, Trondheim, Norway^{3}Faculty of Environmental Sciences and Natural Resource Management, Norwegian University of Life Sciences, Ås, Norway^{4}Fraunhofer IWES, Oldenburg, Germany

^{1}ForWind, University of Oldenburg, Institute of Physics, Oldenburg, Germany^{2}Department of Energy and Process Engineering, Norwegian University of Science and Technology, Trondheim, Norway^{3}Faculty of Environmental Sciences and Natural Resource Management, Norwegian University of Life Sciences, Ås, Norway^{4}Fraunhofer IWES, Oldenburg, Germany

**Correspondence**: Jannik Schottler (jannik.schottler@forwind.de)

**Correspondence**: Jannik Schottler (jannik.schottler@forwind.de)

Abstract

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This paper presents an investigation of wakes behind model wind turbines,
including cases of yaw misalignment. Two different turbines were used and
their wakes are compared, isolating effects of boundary conditions and
turbine specifications. Laser Doppler anemometry was used to scan full planes
of wakes normal to the main flow direction, six rotor diameters downstream of
the respective turbine. The wakes of both turbines are compared in terms of
the time-averaged main flow component, the turbulent kinetic energy and the
distribution of velocity increments. The shape of the velocity increments'
distributions is quantified by the shape parameter *λ*^{2}. The results
show that areas of strongly heavy-tailed distributed velocity increments
surround the velocity deficits in all cases examined. Thus, a wake is
significantly wider when two-point statistics are included as opposed to a
description limited to one-point quantities. As non-Gaussian distributions of
velocity increments affect loads of downstream rotors, our findings impact
the application of active wake steering through yaw misalignment as well as
wind farm layout optimizations and should therefore be considered in future
wake studies, wind farm layout and farm control approaches. Further, the
velocity deficits behind both turbines are deformed to a kidney-like curled
shape during yaw misalignment, for which parameterization methods are
introduced. Moreover, the lateral wake deflection during yaw misalignment is
investigated.

How to cite

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How to cite.

Schottler, J., Bartl, J., Mühle, F., Sætran, L., Peinke, J., and Hölling, M.: Wind tunnel experiments on wind turbine wakes in yaw: redefining the wake width, Wind Energ. Sci., 3, 257–273, https://doi.org/10.5194/wes-3-257-2018, 2018.

1 Introduction

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Due to the installation of wind turbines in wind farm arrangements, the turbine wakes become inflow conditions of downstream rotors, causing wake effects. Those include a reduced wind velocity and an increased turbulence level. The former causes power losses of up to 20 % (Barthelmie et al., 2010) in wind farms, while the latter is linked to increased loads of downstream turbines, affecting fatigue and lifetime (Burton et al., 2001). In order to mitigate wake effects, various concepts of active wake control strategies have been proposed and investigated. One concept is an active wake steering by an intentional yaw misalignment, where the velocity deficit behind a rotor is deflected laterally by misaligning it with the mean inflow direction. The possibility of wake re-direction by yawing was observed and investigated by means of numeric simulations (Fleming et al., 2014b; Jiménez et al., 2010), in wind tunnel experiments (Campagnolo et al., 2016; Medici and Alfredsson, 2006) and in full-scale field measurements by Trujillo et al. (2016). Further, the potential of increasing the power yield in a wind farm configuration has been explored experimentally (Schottler et al., 2016), numerically (Fleming et al., 2014b; Gebraad et al., 2014) and in a field test in a full-scale wind farm (Fleming et al., 2017), showing promising results as the total power yield could be increased in the mentioned studies. As the applicability of the concept to future wind farms requires a thorough understanding of the wakes behind yawed wind turbines, this study examines the wakes behind model wind turbines during yaw misalignment. Experimental studies are necessary to validate numeric results, to tune engineering models and to gain a deeper understanding of the present effects in a controlled laboratory environment. However, when examining wake effects experimentally, varying turbine models are used. Those models strongly differ in their complexity and design, including blade design, geometry or control concepts. The simplest model is a drag disc concept, where a wind turbine is modeled by a porous disk in the flow as done by España et al. (2012) and Howland et al. (2016). Moreover, rotating turbine models have been used in numerous studies, where the design and complexity of the models vary significantly. Examples include Medici and Alfredsson (2006), Bottasso et al. (2014), Abdulrahim et al. (2015), Rockel et al. (2016) or Bastankhah and Porté-Agel (2016). In contrast to numerical studies, where the vast majority of the research community uses consistent turbine models (NREL 5 MW (Jonkman et al., 2009) or DTU 10 MW (Bak et al., 2013) reference turbines for example), experiments lack certain systematics and comparability due to varying turbine models, facilities and measurement techniques. The present study aims to compare the wakes of two different model wind turbines in the same facility, using comparable boundary conditions as far as possible. In doing so, a separation between general wake effects and turbine specific observations can be achieved.

We present wake analyses ranging from mean quantities to higher-order statistics. Average mean flow components are of relevance when assessing the energy yield of potential downstream turbines. An investigation of turbulence parameters such as the turbulent kinetic energy (TKE) is linked to fluctuating inflow conditions, which is important for loads of downstream turbines and thus their lifetime (Burton et al., 2001). To gain a deeper insight, we extend our analyses to two-point statistics. More precisely, velocity increments are analyzed, allowing for a scale-dependent analysis of flows. Non-Gaussianity of the distributions of velocity increments has been reported not only in small-scale turbulence (Frisch, 1995) but also in the atmospheric boundary layer (Boettcher et al., 2003; Liu et al., 2010; Morales et al., 2012). To what extent statistical characteristics of velocity increments are transferred to wind turbines is of current interest throughout the research community (van Kuik et al., 2016). Schottler et al. (2017c) found a transfer of intermittency from wind to torque, thrust and power data in a wind tunnel experiment using a model wind turbine. Similarly, Mücke et al. (2011) found a transfer of intermittency to torque data using a generic turbine model. Milan et al. (2013) reported intermittent power data in a full-scale wind farm. We thus believe that distributions of velocity increments in wakes are of importance for potential downstream turbines as non-Gaussian characteristics are likely to be transferred to wind turbines in terms of fluctuating loads and power output. Consequently, investigations of velocity increments in wakes are extremely relevant for active wake control concepts as well as for wind farm layout optimization approaches. A further elaboration on the connection between non-Gaussian velocity increments and loads as well as power fluctuations is given in Sect. 4.

This work is organized as follows. Section 2 introduces the methods used throughout the study, including the experimental methods, a concept for quantifying a wake's deflection and a definition of the examined parameters. Section 3 shows the results of the study. First, results of the non-yawed rotors are investigated and compared in Sect. 3.1. Wakes during yaw misalignment are analyzed in Sect. 3.2, including a quantification of the wake deflection. Section 4 discusses the findings before Sect. 5 summarizes this work and states the conclusions. This work is part of a joint experimental campaign by the Norwegian University of Science and Technology (NTNU) in Trondheim and ForWind in Oldenburg, Germany. While this paper compares the wakes behind two different model wind turbines, a second paper by Bartl et al. (2018) examines the influence of varying inflow conditions on the wake of one model wind turbine.

2 Method

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The experiments were performed in the wind tunnel of the NTNU in Trondheim, Norway. The closed-loop wind tunnel has a closed test section of 2.71 m × 1.81 m × 11.15 m (width × height × length). The inlet to the test section was equipped with a turbulence grid having a solidity of 35 % and a mesh size of 0.24 m. Further details on the grid are described by Bartl and Sætran (2017).

Two different model wind turbines were used that vary in geometry, blade design and direction of rotation. Those deliberate distinctions allow for an isolation of general effects of wake properties. The turbines will be denoted NTNU and ForWind. Table 1 summarizes the main features and differences of both turbines, further details are described by Schottler et al. (2017b). Figure 1 shows technical drawings. As can be seen, the ForWind turbine was placed on four cylindrical poles to lift the rotor above the wind tunnel boundary layer to a hub height of 820 mm above the wind tunnel floor.

One turbine at a time was placed on a turning table allowing for yaw
misalignment, denoted by the angle *γ*, which is positive for a
clockwise rotation of the rotor when observed from above as sketched in
Fig. 2.

For the NTNU turbine, the reference velocity measured in the empty wind
tunnel was ${u}_{\mathrm{ref},\phantom{\rule{0.125em}{0ex}}\mathrm{NTNU}}=\mathrm{10}$ m s^{−1} at a turbulence intensity of
TI $={\mathit{\sigma}}_{u}/\langle u\rangle =\mathrm{0.1}$. For the ForWind turbine, the inflow
velocity was ${u}_{\mathrm{ref},\phantom{\rule{0.125em}{0ex}}\mathrm{ForWind}}=$7.5 m s^{−1} and TI =0.05. In both
cases, *u*(*t*) was homogeneous within ±6 *%* and the TI within ±3 *%*
on a vertical line at the turbine's position.

In this study we consider two-dimensional cuts through the wake, normal to
the main flow direction at a downstream distance of $x/D=\mathrm{6}$ for both turbines
as illustrated in Fig. 2. Data were acquired using a Dantec
FiberFlow two-component laser Doppler anemometer (LDA) system, recording the
*u* and *v* component of the flow. The accuracy is stated to be 0.04 % by
the manufacturer. During turbine operation, the LDA system was traversed in
the *y*–*z* plane, normal to the main flow direction. Each measured plane
consists of 357 points, 21 in the *z* direction ranging from −*D* to +*D* and 17
points in the *y* direction ranging from −0.8 *D* to 0.8 *D*; see Fig. 3. The resulting distance separating two points of
measurement is thus 0.1 *D*. For one location, 5×10^{4} samples were
recorded, resulting in time series of varying lengths of approximately 30 s.
As can be seen, the NTNU turbine has a slimmer tower and nacelle relative to
its rotor diameter than the ForWind turbine.

The grid of physically measured values was interpolated to a grid of $\mathrm{401}\times \mathrm{321}\approx $ 129 000 points for further
analyses. The distance between the interpolated grid points is thereby reduced to 0.005 *D*.
Natural neighbor interpolation is used, resulting in a smoother approximation of the distribution
of data points (Amidror, 2002).

In order to quantify the lateral wake position, we compute the power of a potential downstream turbine as described by Schottler et al. (2017b). A similar approach was shown by Vollmer et al. (2016). We define the potential power of a downstream turbine to be

$$\begin{array}{}\text{(1)}& {P}^{*}=\sum _{i=\mathrm{1}}^{\mathrm{10}}\mathit{\rho}{A}_{i}\phantom{\rule{0.125em}{0ex}}\langle {u}_{i}\left(t\right){\rangle}_{{A}_{i},t}^{\mathrm{3}}\phantom{\rule{0.33em}{0ex}}.\end{array}$$

The rotor area is divided into 10 ring segments. *A*_{i} is the area of the
*i*th ring segment, and $\langle {u}_{i}\left(t\right){\rangle}_{{A}_{i},t}$ denotes the
temporally and spatially averaged velocity in mean flow direction within the
area *A*_{i}. *P*^{*} is estimated for 50 different hub locations in the range
$-\mathrm{0.5}\phantom{\rule{0.125em}{0ex}}D\le z\le \mathrm{0.5}\phantom{\rule{0.125em}{0ex}}D$, at hub height. We define the horizontal wake
center as the *z* position resulting in the minimum of *P*^{*}. The procedure
is illustrated in Fig. 4.

TKE is defined by the fluctuations of the three velocity components as

$$\begin{array}{}\text{(2)}& k=\mathrm{0.5}\left(\langle {u}^{\prime}(t{)}^{\mathrm{2}}\rangle +\langle {v}^{\prime}(t{)}^{\mathrm{2}}\rangle +\langle {w}^{\prime}(t{)}^{\mathrm{2}}\rangle \right)\phantom{\rule{0.33em}{0ex}},\end{array}$$

where *u*^{′}(*t*) is the fluctuation around the mean of *u*(*t*) so that

$$\begin{array}{}\text{(3)}& u\left(t\right)=\langle u\left(t\right)\rangle +{u}^{\prime}\left(t\right)\phantom{\rule{0.33em}{0ex}}.\end{array}$$

For briefness, we write 〈*u*〉 instead of 〈*u*(*t*)〉.
As the third flow component *w* was not recorded, we assume $\langle {w}^{\prime}(t{)}^{\mathrm{2}}\rangle \approx \langle {v}^{\prime}(t{)}^{\mathrm{2}}\rangle $ so that Eq. (2) becomes

$$\begin{array}{}\text{(4)}& {k}^{*}=\mathrm{0.5}\left(\langle {u}^{\prime}(t{)}^{\mathrm{2}}\rangle +\mathrm{2}\langle {v}^{\prime}(t{)}^{\mathrm{2}}\rangle \right)\phantom{\rule{0.33em}{0ex}},\end{array}$$

which will be used in further analyses. This approximation is discussed in
Sect. 4 and supported by Fig. 15. For a
thorough analysis of the wake turbulence, we examine velocity changes during
a time lag *τ* and refer to them as velocity increments:

$$\begin{array}{}\text{(5)}& {u}_{\mathit{\tau}}\left(t\right):=u\left(t\right)-u(t+\mathit{\tau}).\end{array}$$

Investigating their probability density function (PDF) allows for
scale-dependent analyses of turbulent flows, including all higher-order
moments of *u*_{τ}, and hence all structure functions of order *n*,
${S}_{\mathit{\tau}}^{n}=\langle {u}_{\mathit{\tau}}^{n}\rangle $ of a velocity time series
(Frisch, 1995). The impact of certain properties of velocity increment
PDFs on wind turbines is to date a widely discussed topic in wind energy
research (Berg et al., 2016; Milan et al., 2013; Mücke et al., 2011; Schottler et al., 2017c). For
more details, we refer the reader to Morales et al. (2012) or
Schottler et al. (2017c). Following Chillà et al. (1996), the shape parameter

$$\begin{array}{}\text{(6)}& {\mathit{\lambda}}^{\mathrm{2}}\left(\mathit{\tau}\right)={\displaystyle \frac{ln\left(F\left({u}_{\mathit{\tau}}\right)/\mathrm{3}\right)}{\mathrm{4}}}\phantom{\rule{0.33em}{0ex}}\end{array}$$

is used to quantify the shape of the distribution *p*(*u*_{τ}). *F*(*u*_{τ}) is
the flatness of the time series of velocity increments:

$$\begin{array}{}\text{(7)}& F\left({u}_{\mathit{\tau}}\right)={\displaystyle \frac{\langle ({u}_{\mathit{\tau}}-\langle {u}_{\mathit{\tau}}\rangle {)}^{\mathrm{4}}\rangle}{\langle {u}_{\mathit{\tau}}^{\mathrm{2}}{\rangle}^{\mathrm{2}}}}\phantom{\rule{0.33em}{0ex}}.\end{array}$$

Equation (6) becomes zero for a Gaussian distribution; larger values correspond to broader, more heavy-tailed PDFs.

*λ*^{2} is of practical relevance as it provides an analytical expression
for the shape of *p*(*u*_{τ}). A discussion about the interpretation is given
in Sect. 4. In this analysis, we compute *λ*^{2}
for timescales *τ* that relate to the rotor diameter *D* of the
respective turbine. Using Taylor's hypothesis of frozen turbulence
(Mathieu and Scott, 2000), the length scale *r*=*D* is converted to the
timescales *τ*:

$$\begin{array}{}\text{(8)}& \mathit{\tau}=r/\langle u\rangle =D/\langle u\rangle \phantom{\rule{0.125em}{0ex}},\end{array}$$

whereas 〈*u*〉 refers to the respective time series, resulting
in varying values of *τ* within a wake. In order to compute *u*_{τ}(*t*)
using Eq. (5), evenly spaced data are needed. The
procedure applied to uniformly resample the non-uniform LDA data is
described in Appendix A. The approach results in a constant
sampling rate for each wake.

3 Results

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At first, we investigate wakes without yaw misalignment, *γ*=0^{∘}.
Figure 5 shows the contour plots of the velocity
component in mean flow direction 〈*u*〉∕*u*_{ref} for both
turbines 6*D* downstream.

The velocity deficits behind both turbines show a circular shape as expected, exceeding the rotor area, indicating a slight wake expansion. For both wakes, the minimum velocity is $\langle u\rangle /{u}_{\mathrm{ref}}=\mathrm{0.64}$. Besides those general similarities, some differences are apparent. Both graphs show the tower wake, which is more strongly pronounced for the ForWind turbine. This can be explained by the larger tower diameter relative to the rotor diameter as shown in Fig. 3. Similarly, the four poles the ForWind turbine is placed on (cf. Fig. 1) are likely to enhance this effect. Figure 5 also reveals that the wake behind the ForWind turbine is slightly displaced vertically towards the ground. This effect can be linked to the tower wake, creating an uneven vertical transport of momentum as recently demonstrated by Pierella and Saetran (2017). Next, the NTNU wake shows areas of velocities exceeding $\langle u\rangle /{u}_{\mathrm{ref}}=\mathrm{1.1}$ at the edges of the velocity deficit, especially in the corners of the contour plot. Very likely, this is a blockage effect as the measurement plane is significantly larger for the NTNU turbine, having a higher blockage ratio (13 % for the NTNU rotor, 5.4 % for the ForWind rotor). As suggested by Chen and Liou (2011), blockage effects are expected for a cross-sectional blockage ratio exceeding 10 % when using model wind turbines, which is confirmed here for wake velocities. In order to better compare both contour plots, values exceeding $\langle u\rangle /{u}_{\mathrm{ref}}=\mathrm{1.1}$ are masked. To further analyze the wake flows, Fig. 6 shows the contour plots of the TKE behind both turbines.

The contours of the TKE appear as circular shape, slightly larger than the rotor area. Behind the NTNU
rotor, an outer ring of high TKE values appears more pronounced than in the center region.
This observation is significantly less distinct for the ForWind turbine.
The differences of the pronounced ring arise most likely from the different
blade geometries. The airfoil of the NTNU turbine (NREL S826) has higher lift
coefficients for the relevant angles of attack and Reynolds numbers than
the ForWind rotor (SD7003 airfoil). A comparison of both airfoils is given
by Schottler et al. (2017b). As a result, larger pressure differences between
suction and pressure side of the blades are expected, resulting in more
pronounced tip vortices shed from the NTNU rotor. Although those are already
decayed at $x/D=\mathrm{6}$ (Eriksen and Krogstad, 2017), the tip vortices are likely to be the
origin for a pronounced TKE at blade tip locations behind the NTNU rotor.
Further increasing in complexity and completeness of the wakes' stochastic
description, Fig. 7 shows the contour plots of the shape
parameter *λ*^{2} behind both turbines.

The length scale *τ* is related to the rotor diameter *D* of the respective turbine.
The scale is transferred from space to time using Taylor's hypothesis; cf. Eq. (8).
In both cases, the contours of *λ*^{2} show a circular ring, whose diameter is significantly
larger than the rotor diameter.

In order to quantify the qualitative shapes of the contours shown in Fig. 7, Fig. 8 shows the increment PDFs
of the respective time series, *p*(*u*_{τ}), at the positions indicated by the
red marks
($\circ /\times $) in
Fig. 7. *u*_{τ} is normalized by the standard deviation,
*σ*_{τ}, for better visual comparison.

As shown in black, the positions behind the rotor tips, where
*λ*^{2}≈0, reveal increment PDFs very close to a Gaussian
distribution, which holds for both turbines. For *z*=*D*, which lies within the
ring of large *λ*^{2} values, *p*(*u*_{τ}) strongly deviates from a
Gaussian, showing a heavy-tailed distribution. Figure 8 further shows *p*(*u*_{τ}) based on the model
proposed by Castaing et al. (1990). Those distributions were evaluated based on
the *λ*^{2} values computed by Eq. (6) at *z*=*D*,
visualizing exemplarily how well the distributions' shapes are grasped by
*λ*^{2}. Our results show that, depending on the examined quantity,
different radial wake regions are of interest. To compare the varying spatial
extensions of the three quantities' significant areas, Fig. 9 shows diagonal cuts through the
respective contour plots for the non-yawed cases along the line *y*=*z*.

The area of pronounced TKE approximately coincides with the rotor area. The
notable peaks are separated by ≈0.86 *D* (NTNU) and ≈0.77 *D*
(ForWind) and are significantly less pronounced behind the
ForWind rotor as previously described. Clearly, the *λ*^{2} peaks span
a much larger distance: approximately 1.7 *D* (NTNU) and 2.0 *D*
(ForWind). At their location, the velocity deficit has recovered to
≥90 % of the free-stream velocity in all cases. Thus, for a thorough
description of wind turbine wakes, a much larger radial area is of interest
as compared to a description restricted to mean values and the turbulent
kinetic energy as often done in literature and wake models. An approximation
of the lateral extension of high TKE and *λ*^{2} values based on a
Gaussian fit through the velocity deficit is given by *μ*±1*σ*_{u} and
*μ*±2*σ*_{u}, respectively, with *μ* being the mean value and
*σ*_{u} the standard deviation of the fit. For illustration, the dotted
lines in Fig. 9 mark the respective
locations. It is shown that the radial areas of TKE and *λ*^{2} can be
related in this way to the velocity deficit. To get a feeling of the impact
on potential downstream turbines, Fig. 10 compares
*p*(*u*_{τ}) in absolute terms at a free-stream position ($y/D=\mathrm{0.8}$, $z/D=\mathrm{1}$)
and at a position featuring high *λ*^{2} values ($y/D=\mathrm{0}$, $z/D=\mathrm{1}$),
exemplary for the ForWind turbine. It becomes clear that velocity increments
exceeding 3 m s^{−1} occur much more frequently within the ring of high
*λ*^{2} values than in the free stream. Hereby we show that this radial
position of the wake features significantly different flows than the free
stream. To compare more visually, Fig. 11 shows
the corresponding time series *u*_{τ}(*t*). Clearly, the spiky signature of
extreme events becomes obvious in Fig. 11b,
confirming that no free-stream condition is reached at $z/D=\mathrm{1}$.

During a yaw misalignment of $\mathit{\gamma}=\pm \mathrm{30}$^{∘}, the velocity deficits
behind both rotors are deflected and deformed as shown in Fig. 12 by the contours of the main flow component 〈*u*〉∕*u*_{ref}.

The wakes are deflected sideways behind both turbines, whereas the lateral direction is dependent on the yaw angle's sign. This is expected due to a lateral thrust component of the rotor as a result of yaw misalignment, which has been observed and described in numerous studies, including Medici and Alfredsson (2006), Jiménez et al. (2010), Vollmer et al. (2016) and Trujillo et al. (2016). The deflection of the velocity deficit is quantified using the approach described in Sect. 2.2; the results are listed in Table 2, including the resulting wake skew angles.

As Table 2 shows, the skew angles behind the ForWind
turbine are equal apart from their sign for both directions of yaw
misalignment. The NTNU rotor, however, shows slightly different deflection
angles for *γ*=30^{∘} and $\mathit{\gamma}=-\mathrm{30}$^{∘}, which is likely caused
by blockage effects, which play a more significant role for the NTNU rotor due
to the larger blockage ratio. This can also be seen in Fig. 12, where speed-up effects are visible in the corners. In
Schottler et al. (2017b), where the same setup was used^{1}, the skew angle for the NTNU
rotor decreased from $x/D=\mathrm{3}$ to $x/D=\mathrm{6}$, which is a further indication for
wall effects due to blockage, especially during yaw misalignment.
Furthermore, both values show smaller angles as for the ForWind turbine.

In Fig. 12, minimum 〈*u*〉 values are marked, showing a vertical transport of momentum in all cases. For *γ*=30^{∘},
the wake is moved upwards behind the NTNU turbines and downwards behind the ForWind rotor.
Directions are reversed for $\mathit{\gamma}=-\mathrm{30}$^{∘}.
Similar observations have been made by Bastankhah and Porté-Agel (2016). The vertical
transport is related to an interaction of a wake's rotation with the tower
shadow/ground. Our results isolate this effect, as the direction of vertical
transport is opposite comparing both turbines, having an opposite direction
of rotation. The fact that the vertical transport is stronger behind the
ForWind rotor further supports this explanation as the tower wake is more
pronounced due to the larger tower diameter and the structure the turbine is
placed on. A deformation of the velocity deficit to a curled
“kidney” shape is observed for both
turbines during yaw misalignment, whereas it is slightly more pronounced
behind the ForWind turbine. The curled shape behind a wind turbine model in
yaw has previously been observed by Howland et al. (2016) using a drag disc of
30 mm diameter and by Bastankhah and Porté-Agel (2016) using a rotating turbine model
of 150 mm diameter. Figure 12 confirms these findings on two
further scales. For a better comparison of the curled shape of the velocity
deficit during yaw misalignment, we apply the following parametrization,
exemplarily shown in Fig. 13a for the ForWind
turbine at *γ*=30^{∘}: data points of horizontal cuts through the
wake, $\langle u{\rangle}_{y=\mathrm{const}.}$, are fitted by a polynomial. The
procedure is repeated for values of *y* ranging from −0.4 *D* to 0.4 *D*.
The positions of the polynomials' minima (green marks) are fitted by a
quadratic function (red line). Figure 13b
shows the comparison of both turbines for $\mathit{\gamma}=\pm \mathrm{30}$^{∘}.

As already seen in Fig. 12, the wakes behind the ForWind
turbine are deflected further and the curled shape is more strongly pronounced,
which can be attributed to blockage effects. Figure 13b also shows that the wakes behind both
turbines are slightly tilted. Looking at the black curves (ForWind turbine),
an asymmetry can be noticed as the curves are tilted towards the left, while
the red curves are tilted towards the right. This is illustrated by the gray
dashed lines in Fig. 13b which connect the
points of intersection for $\mathit{\gamma}=\pm \mathrm{30}$^{∘}. Not shown in detail here,
the same effect was observed for different inflow conditions and other
downstream distances, using the same setup and methods as in this study.
Similar asymmetries have been observed by Bastankhah and Porté-Agel (2016) for positive
and negative yaw angles, which is explained by an interaction of a wake's
rotation with the tower wake and the ground. By using turbines of opposite
rotation direction, we can attribute the asymmetries in vertical transport
and tilt in opposite direction for $\mathit{\gamma}=\pm \mathrm{30}$^{∘} to the rotation of
rotor and wake.

Adding TKE and *λ*^{2} contours during yaw misalignment, Fig. 14
shows all three examined quantities, exemplary at a yaw misalignment of $\mathit{\gamma}=-\mathrm{30}$^{∘},
for both turbines. The shapes of the TKE contours are deformed similarly to 〈*u*〉.
A curled shape evolves, and the differences between both turbines as described for $\mathit{\gamma}=\mathrm{0}{}^{\circ}$
are still notable during yaw misalignment.

Similarly, the circular rings of high *λ*^{2} values are deformed to a curled shape at $\mathit{\gamma}=\pm \mathrm{30}$^{∘}.
Thus, the general effect of heavy-tailed increment PDFs surrounding the
velocity deficit in a wake is stable against yaw misalignment and the
resulting inflow variations at the rotor blades. Further, this finding is
confirmed in large-eddy simulations (LES) performed at the Universidad de la
República, Uruguay, shown in Appendix B.

It is found to be a general effect as it is observed for all wakes considered, independent of yaw misalignment or turbine design.

The red markings in Fig. 14 show the approximation of the
radial extension of the TKE and *λ*^{2} based on *μ*±1*σ*_{u} and
*μ*±2*σ*_{u}. *μ* and *σ*_{u} correspond to Gaussian fits of the
velocity deficits at various horizontal cuts (*y* is a constant) from $y/D=-\mathrm{0.5}$ to
$y/D=\mathrm{0.5}$, with *μ* being the fit's mean value and *σ*_{u} the standard
deviation. It is shown that the method results in quite good first-order
approximations, even during yaw misalignment.

4 Discussion

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In this study the characterization of yawed and non-yawed wind turbine wakes
is investigated and extended by taking into account a further turbulence
measure, namely the intermittency parameter *λ*^{2}. We find
heavy-tailed distributions of velocity increments in a ring area
surrounding the velocity deficit and areas of high TKE in a wind
turbine wake. Thus, the definition of a wake width strongly depends on the
quantities taken into account as the ring area features significantly
different statistics than the free stream. The heavy-tailed distributions are
the statistical description of large velocity changes over given timescales
and are transferred to turbines in terms of loads and power output. This has
been shown experimentally (Schottler et al., 2017c), numerically
(Mücke et al., 2011) and in a field study by Milan et al. (2013). Consequently,
our findings should be considered in wind farm layout optimization
approaches, where a wake's width is a crucial parameter for radial turbine
spacing. As layouts are being optimized regarding power and loads, the latter
might be significantly affected by taking into account intermittency and the
resulting increased wake width. Possibly, the ring of non-Gaussian velocity
increments is a result of instable flow states, where the flow switches
between a wake and free stream state. Behind a rotor, the wake
characteristics dominate the flow. Outside the wake, free-stream properties
are dominant. In the transition zone, a switching between both flow states is
believed to result in heavy-tailed velocity increments and therefore high
*λ*^{2} values. Generally, *λ*^{2} will be larger for smaller
scales *τ*, which is a known feature of turbulence (Frisch, 1995).
Care should be taken when interpreting *λ*^{2} as an indicator for an
increment PDF's shape. Here, we use the shape parameter as a qualitative
indicator. For a more quantitative analysis, one has to consider the
increment PDF of a time series directly. This is done in Fig. 8 exemplarily for chosen points; however, in order
include all time series of a wake, using *λ*^{2} allows for a much better
visualization and comparison.

Figure 14 shows that the velocity deficit is deflected
laterally during yaw misalignment, so that a potential in-line downstream
turbine would exhibit a power increase as more undisturbed flow hits the
rotor area at $z/D\approx -\mathrm{0.5}$. Looking at the *λ*^{2} contours,
however, shows that areas of non-Gaussian velocity increments are now deflected onto
the rotor area. This becomes important when assessing the applicability of
active wake steering approaches, as a gain in power has to be balanced with a
potential load increase, affecting maintenance costs and the lifetime of
turbines overall. It should be noted that it is to date not clear to what
extent high TKE levels and intermittent force data are affecting common ways
of fatigue and extreme-load calculations. This important aspect needs to be
addressed in future works. It might depend quite strongly on details such as
considered timescales. In our opinion, it is likely that non-Gaussian inflow
is linked to drive train, gear box or pitch system failures, especially
because those inflow characteristics are not accounted for in standard models
used in the design process of wind turbines.

The velocity deficit in mean flow direction 〈*u*〉 deforms to a
curled kidney shape during yaw
misalignment. Consequently, horizontal cuts through the wake are insufficient
when characterizing wakes behind yawed rotors, resulting in misleading and
incomplete conclusions when quantifying wake deflections by yaw misalignment.
The parametrization of the wake's curl shown in Fig. 13 should not be interpreted as a quantification.
Instead, we use the described approach to better compare multiple curled
wakes as done in Fig. 13b. Our analyses
include the velocity deficit in mean flow direction, the turbulent kinetic
energy and the shape parameter *λ*^{2}. The turbulence intensity in the
wakes revealed very comparable results to the TKE, which is why we restrict
our analyses to the TKE. For the majority of wakes considered, only two flow
components were recorded. For one exemplary wake, however, all three
components are available, allowing the assumption of $\langle {v}^{\prime}(t{)}^{\mathrm{2}}\rangle \approx \langle {w}^{\prime}(t{)}^{\mathrm{2}}\rangle $ to be examined;
cf. Eq. (4). Figure 15 shows the contours of *k* and
*k*^{*} as well as 〈*v*^{′}(*t*)^{2}〉 versus 〈*w*^{′}(*t*)^{2}〉
for all measurement positions. Both contour plots show neglectable
differences, confirming the approximation. This is further supported by a
high correlation coefficient of 0.94 between 〈*v*^{′}(*t*)^{2}〉 and
〈*w*^{′}(*t*)^{2}〉.

Besides the lateral deflection, a vertical transport of the velocity deficit is observed for both turbines during yaw misalignment. Using counter-rotating turbines, this effect could be attributed to the wake's rotation and its interaction with the tower wake. In full-scale scenarios, the ground, wind shear and rotor tilt would further contribute to the effect. For potential floating turbines, a pitch motion will deflect the wake upwards; see Rockel et al. (2014). This vertical deflection will interact with the vertical transport shown in Fig. 12. Consequently, the direction of yaw misalignment is believed to be of importance when applying the concept of wake steering to wind farm controls. This confirms findings by Fleming et al. (2014a) and Schottler et al. (2017a), reporting an asymmetric power output of a two-turbine case with respect to the upstream turbine's angle of yaw misalignment. One should bear in mind that the inflow turbulence intensities are different regarding both turbines. We want to point out that the influence of inflow turbulence on the wake deflection is investigated by Bartl et al. (2018), showing no significant effects.

5 Conclusions

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This work shows an experimental investigation of wind turbine wakes, using
two different model wind turbines. The analyses include the main flow
component, the turbulent kinetic energy and two-point statistics of velocity
increments, quantified by the shape parameter *λ*^{2}. Yaw angles of
$\mathit{\gamma}=\mathit{\{}\mathrm{0}{}^{\circ},\pm \mathrm{30}{}^{\circ}\mathit{\}}$ are considered at a downstream distance of
$x/D=\mathrm{6}$. Generally, the results of 〈*u*〉, the TKE and
*λ*^{2} compare well for both model turbines. Minor differences could be
ascribed to the more prominent blockage (12.8 vs. 5.4 %) in the NTNU setup,
confirming findings by Chen and Liou (2011) even for wake velocity measurements,
who state blockage effects can be neglected for a blockage ratio
≤10 %. An outer ring of heavy-tailed velocity increments surrounds the
velocity deficit and areas of high TKE in a wind turbine wake. The wake
features significantly non-Gaussian velocity increment distributions in
areas where the velocity deficit recovered nearly completely. For
*γ*=0^{∘}, the ring has a diameter of approximately 1.7*D*–2*D*,
depending on the turbine. Based on a Gaussian fit through the velocity
deficit, the radial location of intermittent increments can be approximated
by *μ*±2*σ*_{u} (*μ* being the mean value, *σ*_{u} the standard
deviation of the fit), making a wake considerably wider when taking two-point
statistics into account. This observation becomes important in wind farm
layout optimization and active wake steering approaches through yaw
misalignment. During yaw misalignment, the circular shape of a wake is
deformed to a curled kidney shape. A method for parameterizing the curl shape
was introduced. The lateral wake deflection was quantified, resulting in skew
angles of ±3.6^{∘} at ±30^{∘} for the smaller rotor and
3.0 and −2.6^{∘} for the larger rotor. Furthermore, vertical
momentum transport in the wake during yaw misalignment was observed. The
direction of vertical transport is dependent on the direction of yaw
misalignment. Using counter-rotating turbines, the effect could be attributed
to an interaction of a wake's rotation with the tower wake in this study.

Data availability

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Data availability.

The experimental data sets along with further documentation are available at https://doi.org/10.5281/zenodo.1193656 (Schottler et al., 2018). We encourage researchers to use the data for validation purposes or any other scientific use.

Appendix A: Data preprocessing

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In order to study intermittency using the shape parameter *λ*^{2},
uniformly sampled data are needed when applying Eq. (5). As the LDA measurement result in non-uniformly sampled
data points, appropriate preprocessing is necessary. In the following, the
procedure is described that results in uniformly sampled data points. It is
exemplarily applied to the data of an arbitrarily chosen wake. The time
separating two samples of a time series is Δ*t*. For one time series,
(Δ*t*)^{−1} is plotted for all samples in Fig. A1a.
The corresponding histogram is shown in Fig. A1b. The
point corresponding to 40 % of all events is marked by the red dashed line
and is referred to as *F*_{S}. In this example, *F*_{S}≈1.17 kHz.

This procedure is repeated for all 357 time series contained in one plane of
measurement. Figure A2 shows *F*_{S} for all time series, with
the mean value indicated.

The mean value of all *F*_{S} values in one plane will be used as the sampling
frequency to resample the time series in one plane uniformly; an exemplary
result is shown in Fig. A3.

Data points are interpolated linearly onto a vector of uniformly spaced
instants defined by the new sampling rate 〈*F*_{S}〉. It should be
noted that the analyses of velocity increments were performed for different
constant sampling rates without showing any significant effect on the
results.

Appendix B: LES simulations

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Within the scope of the blind test 5 project, LES simulations of the
ForWind turbine in a very comparable setup were performed, where the inflow
features a vertical shear as opposed to the experiments shown in this paper.
The incompressible flow solver caffa3d.MBRi as described by
Mendina et al. (2014) and Draper et al. (2016) was used to obtain the results
shown in Fig. B1. The turbine was modeled by
actuator lines. The top row shows $x/D=\mathrm{3}$; $x/D=\mathrm{6}$ is shown beneath. The
contours of 〈*u*〉∕*u*_{ref} and *λ*^{2} reveal very
similar results to the experimental data. Qualitatively, it can be
concluded that the outer ring of high *λ*^{2} values and thus
heavy-tailed distributions of velocity increments that surrounds the
velocity deficit of a wake can be correctly predicted in LES simulations.

Competing interests

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Competing interests.

The authors declare that they have no conflict of interest.

Acknowledgements

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Acknowledgements.

The authors thank Marín Draper and Andrés Guggeri, Universidad de la
República, Uruguay, for performing the LES simulation and providing the
data. Parts of this project are funded by the Ministry for Science and Culture
of Lower Saxony through the funding initiative “Niedersächsisches Vorab”. The authors also thank the Reiner
Lemoine Foundation for further funding.

Edited by: Gerard J. W. van Bussel

Reviewed by: three
anonymous referees

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In Schottler et al. (2017b), the quantification was carried out for a sheared inflow. Other aspects of the setup were equal.

Short summary

In this work, the wake flows behind two different model wind turbines were investigated in wind tunnel experiments user laser Doppler anemometry. It was found that the width of the wake flow is significantly dependent on the quantities examined, becoming much wider when taking higher-order statistics into account. This effect is stable against yaw misalignment and thus affects not only wind farm layout optimizations but also the applicability of active wake steering methods.

In this work, the wake flows behind two different model wind turbines were investigated in wind...

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