Wake Structure in Actuator Disk Models of Wind
Turbines in Yaw under Uniform Inflow Conditions
Michael F. Howland
1
, Juliaan Bossuyt
1,2
, Luis A. Mart´ınez-Tossas
1
Johan Meyers
2
, and Charles Meneveau
1
12th May 2016
1
Johns Hopkins University, Baltimore, MD 21218
2
KU Leuven, Leuven, B3001, Belgium
Email: mike.howland13@gmail.com
Abstract
Reducing wake losses in wind farms by deflecting the wakes through turbine yawing has been shown
to be a feasible wind farm controls approach. Nonetheless, the effectiveness of yawing depends not only
on the degree of wake deflection but also on the resulting shape of the wake. In this work, the deflection
and morphology of wakes behind a porous disk model of a wind turbine operating in yawed conditions are
studied using wind tunnel experiments and uniform inflow. First, by measuring velocity distributions at
various downstream positions and comparing with prior studies, we confirm that the non-rotating porous
disk wind turbine model in yaw generates realistic wake deflections. Second, we characterize the wake
shape and make observations of what is termed a curled wake, displaying significant spanwise asymmetry.
The wake curling observed in the experiments is also reproduced qualitatively in large eddy simulations
using both actuator disk and actuator line models. Results suggest that when a wind turbine is yawed
for the benefit of downstream turbines, the asymmetric shape of the wake must be taken into account
since it affects how much of it intersects the downstream turbines.
1 Introduction
Considering the U.S. Department of Energy 20% Wind by 2030 plan [1] and similar goals elsewhere in the
world [2], the efficiency and control of wind turbines placed in large wind farms has become an important area
of study. Inevitably, significant power degradation occurs due to strong wake interactions between turbines
downstream of each other [3–6]. Better understanding of these interactions is needed for improved designs
of large, base load supplying wind farms. Currently, wind farms operate on the principle of maximum power
point extraction, which entails each turbine to operate individually in an effort to maximize its own power at
any time [7]. This operation can be considered similar to the control of a single, independent wind turbine
that is not in a wind farm array. However, since such control strategies do not take wake interactions, and
spatial or temporal correlations explicitly into account, they are most likely not the most effective strategy
for an entire wind farm [8, 9]. Recently, there has been a push towards the optimization in the control of
power generated by an entire large wind farm, as opposed to operating each turbine in a maximum power
point tracking manner [10, 11]. In this vane, the wake deflection by operating wind turbines in yaw has been
shown to be an attractive option to control wake deflection and power output [10, 12–16], and has recently
generated significant interest [9, 17, 18].
Nominally, turbines are operated with the rotor perpendicular to the flow, with tip speed ratio and pitch
near optimal values, which are dependent on the turbine and the desired power output. In an effort to reduce
the power losses for downstream wind turbines that reside in the wake of an upstream one, there have been
experimental studies which have considered altering yaw angle, tip speed ratio, and blade pitch [14, 17, 18].
1
Preprint version. Published in Journal of Renewable and Sustainable Energy 8, 043301 (2016)
doi: http://dx.doi.org/10.1063/1.4955091
Ref. [14] used two aligned turbines in a wind tunnel and tested varying the rotor yaw angle, tip speed ratio,
and the blade pitch of the upstream wind turbine only. This study showed that varying the yaw angle of
the wind turbine was of comparable benefit to increasing the streamwise spacing between turbines, with
an optimal power output occurring at 30
◦
. Refs. [17, 18] studied the effects of controlling yaw angle, tip
speed ratio, and the blade pitch of the upstream turbine for scaled model wind turbines, with results also
revealing the benefits of yawing the upstream turbine. Further, yaw misalignment has been shown to reduce
the steady-state blade loading variations by up to 70%, which has lead to the use of yawing to increase
operational life [19]. Ref. [20] studied a rotating wind turbine model in replicated atmospheric boundary
layer conditions to discover a deflection of approximately 0.6D in the far wake.
Refs. [9, 21–23] were computational studies of wake deflection using various yaw angles. Ref. [21] uses
LES with an actuator disk model with turbulent inflow and shows that wake deflection can be reproduced
in such simulations. They also propose a momentum-based model for the deflection which is compared to
LES with reasonable validity in the far wake. Some experimental results are compared, but the authors cite
a need for more experimental verification before a wake controller may be developed.
Ref. [9] studied wake deflection under various conditions using the SOWFA Large Eddy Simulation
(LES) code and using the NREL 5 MW turbine model [24]. When the yaw angle γ was γ = 30
◦
, the study
found the maximum wake deflection to reach about 0.5D in the far wake, where D is the rotor diameter.
Ref. [22] studied the near wake structure of a wind turbine under uniform inflow using Reynolds Averaged
Navier-Stokes flow modeling and the results displayed some strong asymmetries in the near field (up to 2D
downstream). Furthermore, employing an actuator disk model for the turbine under uniform shear, Ref. [23]
found wakes deflected up to 0.7D when γ = 30
◦
. Further LES studies of several yawed turbines have been
carried out in Ref. [25], and they compared the wake deflection with the theoretical model of Ref. [21], which
characterizes the skew angle behind a yawed turbine.
Most of the studies considered only 2D wake deflection in horizontal planes, generally at hub height.
However, the wakes of wind turbines have been shown to exhibit asymmetric properties in yaw, as pointed
out in Ref. [26]. The spanwise forcing imposed by a wind turbine operating in yaw has been shown to be
significant. Additionally, Ref. [26] has noted the importance of free stream turbulence on the structure of
the 3D wake, which influences the high energy mixing downstream.
In general, prior studies have shown that yawing turbines has power reduction for the yawed turbine
(following cos
3
(γ)), but can yield noticeable power increases for downstream wind turbines as a result of
the deflected wake. Even when wind turbines operate nominally in non-yawed conditions, in practice there
always is some yaw misalignment due to the imperfections of the yaw control for aligning the turbine with the
incoming wind. In fact it has been shown with LIDAR measurements that wind turbines typically operate
from 4
◦
to 10
◦
in yaw when the turbine attempts to track the flow to operate with 0
◦
yaw [27]. Therefore,
understanding of the dynamics and implications of a wind turbine operating in yaw are important to the
design and control of wind farms even if traditional yaw alignment controllers are used.
The objectives of this study are to establish whether porous disk wind turbine models exhibit the
phenomenon of wake deflection, whether the degree of deflection is comparable to that of other models and
simulations, and to examine the shape of the resulting deflected wake. For experimental studies of large
wind farms, it is often necessary to use non-rotating porous disk models, in order to accommodate a large
number of small models that may be installed within the physical constraints of typical wind tunnels [28].
As such, the mechanism of wake deflection when using a porous (or actuator) disk model must be established
in order to enable further studies. To our knowledge, there has not been an experimental study of porous
disk models in yaw to study wake deflection. A wind tunnel experiment, described in §2, is performed and
results are presented in §3, where the center of wake is defined and then determined from the data and
compared with prior studies. Also, streamwise and spanwise mean velocity distributions are mapped out at
various downstream cross-sections with particular attention to the shape of the resulting wake, shown in §4.
Traditional wake models assume a symmetric, circular shape but as will be shown, significant asymmetries
develop in yawed wakes. In order to provide further evidence of the particular wake morphology determined
experimentally, we perform large eddy simulations using both actuator disk and actuator line methods and
confirm, qualitatively, the observed wake shapes. Large eddy simulations are presented in §5. Conclusions
2
are presented in §6.
2 Experimental Setup
Experiments are performed in the Corrsin Wind Tunnel at the Johns Hopkins University. It is a closed loop,
two-story facility, with a primary contraction-ratio of 25:1 and a secondary contraction of 1.27:1. The test
section is 10 m long with a cross section of 1 m by 1.3 m. The experiments are performed in laminar, uniform
inflow, with free-stream velocity in the test section of U
∞
= 12 m/s. The free stream turbulence level is
less than 0.12%. To ensure uniform inflow, the drag disk wind turbine model is placed far downstream of
the contraction and in the center of the cross section, far from any walls (the boundary layer thicknesses at
the measurement location are below 8 cm). The single turbine is mounted on a slender cylinder which is
connected to a stepper motor with a step size of 0.1125
◦
allowing precise control of the yaw angle. Overall,
we estimate the systematic yaw uncertainty to be ±0.5
◦
due to uncertainties in turbine placement within
the experimental domain. As will be verified based on velocity measurements in §4, the support structure is
sufficiently far from the turbine and wake region so that no influence on the measurements can be observed.
The x, y, and z coordinate directions are streamwise, spanwise, and height respectively and are shown in
Figure 1.
(a) (b)
Figure 1: Schematic of 3D printed porous drag disk model turbine (a), and photograph of the model turbine
and yaw control stepper motor mounted in the JHU Corrsin Wind Tunnel (b).
Experiments use a porous disk model which was designed to match the far wake properties of a full
scale wind turbine through comparisons to prior models in literature [28]. Figure 1 shows a schematic and
a photograph of the porous disk and the setup in the wind tunnel. The diameter of the model turbine is
3 cm, i.e. a scale ratio of about 4 × 10
3
compared to a large-scale D = 120m utility wind turbine. Such
a scale ratio is needed here to fit 100 models inside the test section. It would be very challenging to build
rotating model turbines of such small diameters that would still produce the correct thrust and induction
coefficients and correct turbine control. These parameters mainly determine the overall properties of the
wake. The turbine model has been designed to match a desired thrust coefficient of C
T
= 0.75 ± 0.04 and
is manufactured using 3D printing. Its properties have been carefully documented in Ref. [28] for the case
3
of non-yawed conditions, showing excellent agreement with the desired thrust coefficient (measured using
strain-gages) and canonical wake defect velocity profiles that agree very well with those of rotating wind
turbines at streamwise distances beyond 3D.
Measurements are performed using hot wire anemometry and a Pitot-static probe. The hot-wire meas-
urements were made with an X-wire probe made in-house as described in Ref. [29]. The probe is mounted on
a three-axis traverse system with spatial location accuracy of ± 0.1 mm. Signals are acquired at a sampling
rate of 10 kHz, with a low pass filter (Nyquist) of 5 kHz, capturing both the mean velocity and the variance
of the velocity signal accurately. Signals are acquired at each measurement location for 26 seconds to ensure
converged mean and second-order flow statistics. The X-wire is oriented such that the u and v components
(streamwise and spanwise components, respectively) of the velocity are measured. In order to compensate
for the temperature drift of the hot-wire probe measurement system, the data are recalibrated to U
∞
when
the probe is in the free stream, with subsequent measurements adjusted using linear interpolation, as done
in Ref. [30]. Measurement locations along YZ and XY planes are shown in Figure 2. XY planes were taken
at hub height in order to characterize the 2D wake deflection. The YZ planes were taken at x/D = 5, 8 for
the hot-wire probe in order to show the development of the wake structure in the far wake. Typical turbine
placement is 5D - 8D, so the wake deflection and structure between these locations is important.
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
-2-1012
(a)
x/D
0 2 4 6 8 10
y/D
-2
-1
0
1
(b)
Figure 2: (a) Distribution of measurement points for the YZ plane experiments for the yawed turbine and
(b) measurement points for the XY plane experiments. The YZ plane is viewed from the negative x direction
and XY plane is viewed from the positive z direction. Red ellipse in (a) and inclined plane in (b) represents
the corresponding two views of the yawed turbine.
The Pitot measurements were carried out with a Pitot static probe with an outside diameter of 2 mm.
The pressure was measured with an 220CD Baratron General Purpose Differential Capacitance Manometer
with measurement uncertainty of ±0.15%, leading to an error of ±2 Pa. The output voltage was measured
with an Omega Instrunet i555. Together, this setup results in an overall velocity measurement uncertainty
of ±0.2 m/s in the case of 7 m/s laminar flow, the lowest velocity measured with the Pitot setup in the
wake of the turbine. This gives a maximum Pitot velocity uncertainty of 3%. While a Pitot static probe
results in very accurate flow measurements in low turbulent flows, added pressure effects due to turbulence
will lead to a measurement offset in the wake of the turbine [31]. The Pitot-static probe was used for an XY
plane at hub height and YZ planes at x/D = 0.5, 1.5, 2, 4, 5, 6, 7, 10, and 12. The Pitot probe is used for the
characterization of the center of the wake, but will not be used for detailed velocity measurements. Pitot
probes were chosen for wake deflection characterization since hot-wire measurements require a significantly
more elaborate construction and calibration process and have a higher sensitivity to temperature drift during
long duration measurements [32]. In the high turbulent wake region, Pitot probes carry higher uncertainty
4
than hot-wires (as seen in §3) yet due to the described time limitations of hot-wire measurements, Pitot
probes were chosen for wake center characterization to allow for measurement of various yaw angles, including
γ = 0
◦
, 5
◦
, 10
◦
, 20
◦
, and 30
◦
. For these cases, however, Pitot-probe measurements of mean velocity were only
performed in XY planes at hub height. In the wake of the turbine, the turbulence intensity is not uniform,
which may alter the uncertainty of the Pitot probe during the experiment. However, the resulting center of
wake positions, being given by a ratio of integrated velocity distributions, are expected to be fairly insensitive
to the inaccuracies of the Pitot probe in turbulence. As further shown below, reasonable agreement between
Pitot and hot-wire probe was observed for the wake deflection characterization.
3 Center of Wake Deflection
With a wind turbine in yawed conditions, the wake is no longer symmetric in the spanwise direction. Further,
when a tower or rotational turbine model is included, the wake is no longer symmetric in height either. As
a result, it becomes necessary to characterize the center of asymmetric wakes in order to compare different
yaw angles and control methods. Several methods have been proposed before, such as fitting a Gaussian
shape [9,21] or using the “center of mass” of the velocity defect [25,33]. Additionally, Ref. [34] has proposed
using particles to track the center of wake for turbines in yaw, yet this study only considers particles deflection
in a horizontal slice, not the 3D wake effects. Since the wake shape will be found to differ significantly from
Gaussian and exhibits 3D properties, here we use the “center of mass” method. The center of the wake
is computed at every streamwise distance in the flow, according to the resolution of the domain. At each
streamwise measurement location x, mean streamwise velocity data on a YZ plane is considered. The center
of wake coordinates y
c
(x) and z
c
(x) are computed according to
y
c
(x) =
RR
y ∆U(x, y, z) dydz
RR
∆U(x, y, z) dydz
, and z
c
(x) =
RR
z ∆U(x, y, z) dydz
RR
∆U(x, y, z) dydz
, (1)
where ∆U(x, y, z) = U
∞
− ¯u(x, y, z), ¯u is the time averaged velocity and U
∞
is, as before, the free stream
velocity. The integration is performed discretely over the available spatial data.
To obtain the center of wake from the XY-plane measurements at the many x locations, we use 1D
integration in the y-direction only and neglect the z-dependence of the wake
y
0
c
(x) =
R
y ∆U(x, y, z = 0) dy
R
∆U(x, y, z = 0) dy
, (2)
In Figure 3, filled circles represent y
c
(x) from Pitot data in successive YZ planes at the various
(x − x
0
) /D distances downstream where x
0
/D is the downstream location where y
c
(x) = 0. In some cases
the deflection measured from simulations at x=0 is not exactly zero. Hence, in order to compare the deflec-
tion with respect to where y
c
vanishes initially, a virtual origin x
0
is subtracted from the reported x-positions
in the cases in which y
c
is measured at the turbine location. The value of x
0
/D is shown in the legend of
Figure 3. The cross markers show the y
0
c
(x) computed from Pitot data from an XY plane measurement
at hub height. The open circles represents y
0
c
(x) for hot-wire probe results for which data was available in
an XY plane measurement at hub height. All measurements obtained at the measurement locations shown
in the point map in Figure 2. The experimentally measured wake deflection downstream for the γ = 30
◦
yawing case is compared with results from literature. Specifically, in Figure 3 we compare the center of
wake computed from Eq. 2 with Pitot and hot-wire measurements and the center of wake computed from
Eq. 1 from Pitot measurements with wind tunnel results from EPFL [20] and with numerical simulations
from National Renewable Energy Laboratory (NREL) [9] and Danish Technical University (DTU) [23]. New
simulations were also performed with the in-house JHU LES code using actuator disk (ADM) and actuator
line (ALM) models, shown with solid and dashed black lines respectively. Details about the LES are provided
in §5. The conditions for the different cases shown in Figure 3 are summarized in Table 1.
Estimating the experimental uncertainty associated with the Pitot and hot-wire probe measurements
is challenging. For the Pitot probe, we choose the maximum measured deviation of y
0
c
(x) for a case in which
5
![Table 1: Comparison of the turbine models [9, 21,23,28].](/figures/table-1-comparison-of-the-turbine-models-9-212328-3d6a4i5p.webp)
