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**Research articles**
15 Aug 2018

**Research articles** | 15 Aug 2018

Combined power output and yaw moments of two yaw-controlled model wind turbines

^{1}Department of Energy and Process Engineering, Norwegian University of Science And Technology, Trondheim, Norway^{2}Faculty of Environmental Sciences and Natural Resource Management, Norwegian University of Life Sciences, Ås, Norway

Abstract

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In this experimental wind tunnel study the effects of intentional yaw misalignment on the power production and loads of a downstream turbine are investigated for full and partial wake overlap. Power, thrust force and yaw moment are measured on both the upstream and downstream turbine. The influence of inflow turbulence level and streamwise turbine separation distance are analyzed for full wake overlap. For partial wake overlap the concept of downstream turbine yawing for yaw moment mitigation is examined for different lateral offset positions.

Results indicate that upstream turbine yaw misalignment is able to increase the combined power production of the two turbines for both partial and full wake overlap. For aligned turbine setups the combined power is increased between 3.5 % and 11 % depending on the inflow turbulence level and turbine separation distance. The increase in combined power is at the expense of increased yaw moments on both the upstream and downstream turbine. For partial wake overlap, yaw moments on the downstream turbine can be mitigated through upstream turbine yawing. Simultaneously, the combined power output of the turbine array is increased. A final test case demonstrates benefits for power and loads through downstream turbine yawing in partial wake overlap. Yaw moments can be decreased and the power increased by intentionally yawing the downstream turbine in the opposite direction.

How to cite

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How to cite.

Bartl, J., Mühle, F., and Sætran, L.: Wind tunnel study on power output and yaw moments for two yaw-controlled model wind turbines, Wind Energ. Sci., 3, 489-502, https://doi.org/10.5194/wes-3-489-2018, 2018.

1 Introduction

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In wind farms the individual wind turbines interact aerodynamically through their wakes. Besides significant power losses, rotors exposed to upstream turbines' wakes experience higher unsteady loading (Kim et al., 2015). The reduced power and increased rotor loads are dependent on the downstream turbine's lateral and streamwise location in the wake, the upstream turbine's control settings and the characteristics of the incoming wind. The inflow characteristics are governed by the atmospheric stability, in which the turbulence level and the degree of shear and veer are important parameters. In combination with the wind farm layout, the site-dependent wind statistics, such as wind speed and direction distributions, define the occurrence for downstream turbines to be fully or partially exposed to the upstream turbine's wake.

In order to mitigate power losses and wake-induced loads on downstream turbines, different upstream turbine control strategies have recently been suggested (Gebraad et al., 2015; Knudsen et al., 2014). These include methods of reducing the axial induction of an upstream turbine and thus also mean and turbulent gradients in the wake (Annoni et al., 2016; Bartl and Sætran, 2016) as well as wake redirection techniques (Fleming et al., 2015). The most discussed wake deflection mechanisms include individual pitch angle control, tilt angle variation and yaw angle actuation. In a computational fluid dynamics (CFD) study Fleming et al. (2015) compare these techniques with regards to power gains and out-of-plane blade bending loads using a two-turbine setup. Individual pitch control was observed to cause high structural loads. Most current turbine designs do not feature tilt mechanisms, while yaw actuation is concluded to be a promising technique due to its simple implementability. As all modern wind turbines are equipped with yaw actuators, intentional yaw misalignment can be used to laterally deflect the wake flow and potentially increase the wind farm power output.

A number of recent studies have focused on the wake characteristics behind a yawed wind turbine. In a combined experimental and computational study Howland et al. (2016) measured the wake of yawed small drag disc and conducted a large-eddy simulation (LES) behind an actuator-disc/line-modeled rotor. They discussed different quantifications for wake deflection and characterized the formation of a curled wake shape due to a counter-rotating vortex pair. A similar wake shape was found in a LES study by Vollmer et al. (2016), who found a significant variation of wake shape and deflection depending on the atmospheric stability. The yawed wake characteristics' dependency on inflow turbulence and shear were investigated in an experimental study by Bartl et al. (2018). The inflow turbulence level was observed to influence the shape and deflection of the wake, in contrast to a moderate shear in the inflow. Schottler et al. (2018) highlight the importance of considering non-Gaussian distributions of velocity increments in wind farm control and layout optimizations. A ring of strongly intermittent flow is shown to surround the mean velocity deficit locations, suggesting a much wider wake expansion as based on the mean velocity. An extensive theoretical and experimental study on yaw wakes was performed by Bastankhah and Porté-Agel (2016). They presented a theoretical description for the formation of the counter-rotating vortex pair in the wake and developed a sophisticated analytical model for the far wake of a yawed turbine. Including inflow turbulence as an additional input parameter makes Bastankhah and Porté-Agel's model a favorable alternative to the wake deflection model by Jiménez et al. (2010).

Moreover, various research has investigated the potential of overall wind farm
power gains through intentional yaw misalignment. An experimental study by
Adaramola and Krogstad (2011) on two aligned model wind turbines ($x/D=\mathrm{3}$)
demonstrated an increase in combined efficiency with increasing upstream
turbine yaw angle. For a yaw angle of 30^{∘}, they measured an increase
of 12 % in combined power compared to the reference case at 0^{∘}. For
the same separation distance Schottler et al. (2016) measured a combined power
increase of about 4 % for an upstream turbine yaw angle of $-\mathrm{18}{}^{\circ}$.
Their experimental study on two aligned model turbines furthermore pointed
out clear asymmetries of the downstream turbine power output with regards to
the upstream turbine yaw angle. Another experimental study on three model
wind turbines was presented by Campagnolo et al. (2016), who measured a
combined power increase of 21 % for a lateral offset of $\mathrm{\Delta}z/D=\mathrm{0.45}$
between the turbines. Comprehensive studies on yaw misalignment for optimized
full wind farm control haven been presented by Fleming et al. (2014) and
Gebraad et al. (2016). They analyzed wake mitigation strategies by using both
the LES code SOWFA and a parametric wake model. A comprehensive
full-scale study by McKay et al. (2013) investigated the connection of yaw
alignment and power output of a downstream turbine operated in the wake of an
upstream turbine. They found a power increase for downstream turbines, which
independently misaligned their yaw angle from the main wind direction when
operated in a partial wake.

Most of these studies focus on the possibilities for power optimization through yaw control; however, the discussion of increased structural loads is often left open. Yet yaw misalignment of an undisturbed turbine was observed to increase unsteady loading on the yawed rotor. In a simulation by Kragh and Hansen (2014) these loads are quantified for different inflow conditions. It is furthermore shown that load variations due to wind shear can potentially be alleviated by yaw misalignment. Load characteristics on a yawed model turbine rotor were compared to various computational approaches by Schepers et al. (2014). Their comparisons revealed modeling deficiencies, while shedding light on complex unsteady-flow phenomena during yaw. In a recent paper by Damiani et al. (2018) damage equivalent loads and extreme loads under yaw misalignment are measured and predicted for a fully instrumented wind turbine. They observed rather complex, inflow-dependent load distributions for yaw angle offsets. In a computational setup of 10 aligned turbines Andersen et al. (2017) investigated the influence of inflow conditions and turbine spacing on yaw moments of downstream turbines operated in the wake. The study shows unexpected load peaks for every second or third downstream turbine in below-rated operating conditions. A way to utilize measured rotor loads such as yaw moments to estimate rotor yaw misalignment, inflow shear or partial wake rotor operation is investigated by Schreiber et al. (2016). Using a computational framework of a wake model, a blade element momentum (BEM) model for power and loads, and a gradient-based optimizer, (van Dijk et al., 2017) investigated the effects of yaw misalignment on power production and loads in full and partial wake overlap. They found that upstream turbine yaw misalignment is able to increase the total power production of their modeled wind farm, while reducing the loads in partial wake overlap.

The
objective of the present study is to analyze potentials of yaw control for
the often contradicting goals of combined power gains and load mitigation.
Balancing the benefits of power gains and costs of increased rotor loads is
of utmost importance for the design of cost-effective wind farm control
strategies. For this purpose the parameters turbine separation distance
*x*∕*D*, lateral turbine offset Δ*z*∕*D* and turbine yaw settings
*γ*_{T1} and *γ*_{T2} are systematically varied in this wind tunnel
experiment. Aside from power output and rotor thrust, the yaw moments acting
on the individual rotors are measured. Yaw moments are a representation of
the imbalance of the forces acting on a rotor blade during the course of one
rotation. High values of yaw moments thus indicate increased unsteady blade
loading at a frequency corresponding to the rotational speed. Special focus
is given to the concept of downstream turbine yawing in partial-wake
situations for the purpose of load reduction and combined power gains.
Together with the inflow-dependent wake flow measurements using the same
experimental setup presented in Bartl et al. (2018), this study
completes the link between detailed wake flow characteristics and power, yaw
moments and thrust forces on a turbine operated in the wake.

2 Experimental setup

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Two wind turbine models of exactly the same rotor geometry were used for this
study. The rotor was designed based on the NREL S826 airfoil and has a total
diameter of *D*=0.894 m. The tower and nacelle structure of the upstream
turbine (T1) is slightly slimmer than that of the downstream turbine (T2), in
order to minimize the effect on the wake flow behind the yawed upstream
turbine. The maximum power point of both turbines is reached at a tip speed
ratio of ${\mathit{\lambda}}_{\mathrm{T}\mathrm{1}}={\mathit{\lambda}}_{\mathrm{T}\mathrm{2}}=\mathrm{6.0}$ in undisturbed inflow. In this
experiment T2 is controlled to its optimum power point, which strongly varies
for different positions and upstream turbine operational parameters. The
exact geometry and detailed performance curves of T1 are described in
Bartl et al. (2018), while T2's characteristics can be found in
Bartl and Sætran (2017). In contrast to most other turbines, the investigated model
turbines rotate counterclockwise.

The experiments were performed in the closed-loop wind tunnel at the
Norwegian University of Science and Technology (NTNU) in Trondheim, Norway.
The tunnel's cross-section measures 2.71 m in width, 1.81 m in height
and 11.15 m in length. The turbine models are operated at a blade tip
Reynolds numbers of approximately *Re*_{tip}≈10^{5}.

Moreover,
about 12.8 *%* of the wind tunnel's cross sectional area is blocked by the
turbines' rotor-swept area. The wind tunnel width measures about 3 times
the turbine's rotor diameter, which leaves sufficient space for lateral wake
deflection and offset positions for T2. However, a speed-up of the flow in
freestream areas around the rotors is observed due to blockage effects as
described in detail in Bartl et al. (2018). The impact of the wind
tunnel blockage on the wake expansion behind the same model turbine rotor has
furthermore been investigated in a computational study by Sarlak et al. (2016).
For high blockage ratios, correction models (e.g., by Sørensen et al., 2006, or
Ryi et al., 2015) for the power output are available. In this study, however,
no correction models have been applied, in order not to add another dimension
of modeling uncertainty to the results.

The influence of different inflow turbulence levels is investigated in this
study. For this purpose the turbines are exposed to an inflow of low
turbulence intensity TI_{A}=0.23 *%* (inflow A) as well as high turbulence
intensity TI_{B}=10.0 *%* (inflow B). Inflow B is generated by a static grid at
the wind tunnel inlet ($x/D=-\mathrm{2}$) and is measured to the amount TI_{B}=10.0 %
at the location of the upstream turbine ($x/D=\mathrm{0}$). The grid-generated
turbulence decays with increasing downstream distance to about TI_{B}=5.5 *%*
at $x/D=\mathrm{3}$ and to TI_{B}=4.0 *%* at $x/D=\mathrm{6}$. The profiles of streamwise mean
velocity and turbulence intensity measured in the empty wind tunnel for
different downstream positions are presented in Bartl et al. (2018).
Inflow A is assessed to be uniform within ±0.8 *%* over the rotor-swept
area. A velocity variation of ±2.5 *%* is measured at $x/D=\mathrm{0}$ for inflow B,
as the footprint of the grid's single bars is still detectable. At $x/D=\mathrm{3}$,
however, the grid-generated turbulent flow is seen to be uniform within
±1.0 *%*. Both test cases were performed at the constant reference velocity
of ${u}_{\mathrm{ref}}=\mathrm{10.0}\phantom{\rule{0.125em}{0ex}}\mathrm{m}\phantom{\rule{0.125em}{0ex}}{\mathrm{s}}^{-\mathrm{1}}$.

The mechanical power of both rotors was measured in separate steps with an HBM torque transducer of the type “T20WN/2NM”, which is installed in the nacelle of the downstream turbine T2. The transducer is connected to the rotor shaft through flexible couplings. An optical photo cell inside the nacelle makes the rotor's rotational speed assessable. On the test rig of T1 the rotational speed is controlled via a servo motor, ensuring the same power and load characteristics as for T2.

For the purpose of thrust force and yaw moment measurements the model turbines are separately installed on a six-component force balance by Carl Schenck AG. By constantly recording signals obtained from the three horizontal force cells, the yaw moments referring to the rotor center can be calculated. For the assessment of the rotor thrust, the drag force on tower and nacelle is measured isolated and then subtracted from the total thrust. No such correction is applied for the assessment of the yaw moments.

The statistical measurement uncertainties for power coefficients, thrust coefficient and normalized yaw moments have been calculated following the procedure described by Wheeler and Ganji (2004). Random errors are computed from repeated measurements of various representative measurement points based on a 95 % confidence interval. Furthermore, the match of power and thrust values of the baseline cases (e.g., ${\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=\mathrm{0}{}^{\circ}$, $x/D=\mathrm{3}$, $\mathrm{\Delta}z/D=\mathrm{0}$) with previous results (e.g., by Bartl and Sætran, 2016, 2017) has been checked for consistency.

For the purpose of clarity, error bars are not shown
in the resulting graphs in Sect. 3. Instead, a short overview
of uncertainties for the different measures is given here. The total
uncertainty in T1's power coefficient is 0.011 (1.9 %) for non-yawed
operation, rising up to about 0.017 (3.9 %) for a yaw angle of
${\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=\mathrm{30}{}^{\circ}$. The uncertainty in T1's thrust coefficient is
assessed to be very similar, varying from 0.013 (1.4 %) to 0.018 (3.1 %) for
yaw angles 0^{∘} and $\pm \mathrm{40}{}^{\circ}$, respectively. The uncertainty in
normalized yaw moments ${M}_{\mathrm{y}}^{*}$ is 0.0032, which corresponds to almost 15 %
of the absolute measurement value at ${\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=\mathrm{30}{}^{\circ}$. Due to very
small absolute values of the yaw moments, the relative uncertainty is rather
high. In the case of T2, the uncertainties are presented representatively for
the aligned test case, in which the upstream turbine is operated at
${\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=\mathrm{30}{}^{\circ}$ and T2 is located at $x/D=\mathrm{3}$ and operated at
${\mathit{\gamma}}_{\mathrm{T}\mathrm{2}}=\mathrm{0}{}^{\circ}$. The total uncertainties in power and thrust
coefficient are 0.0060 (2.5 % of the absolute *C*_{P} value) and 0.0070 (0.9 %
of the absolute *C*_{T} value), respectively. The normalized yaw moment of the
downstream turbine for this case amounts to 0.0019 (about 8 % of the absolute
value).

Three main test cases are investigated in this study. In the first test case
the two model turbines are installed in an aligned arrangement in the wind
tunnel; i.e., T2 is immersed in the full wake of T1 (for
${\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=\mathrm{0}{}^{\circ}$). The upstream turbine's yaw angle is then
systematically varied at nine different values ${\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=[-\mathrm{40},-\mathrm{30},-\mathrm{20},-\mathrm{10},\mathrm{0},+\mathrm{10},+\mathrm{20},+\mathrm{30},+\mathrm{40}{}^{\circ}]$. Moreover, the streamwise separation distance
between the turbines is varied from $x/D=\mathrm{3}$ to $x/D=\mathrm{6}$.
Finally, the inflow turbulence intensity is varied from TI_{A}=0.23 *%* (inflow A) to TI_{B}=10.0 *%* (inflow B).

In the second test case, the effect of the lateral offset position Δ*z*∕*D*
of the downstream turbine T2 in the wake of an upstream turbine T1 is
investigated. That means that T2 is in most cases exposed to partial-wake
situations. For this purpose, the lateral offset is set to seven different
positions in the range of $\mathrm{\Delta}z/D=[-\mathrm{0.50},-\mathrm{0.33},-\mathrm{0.16},\mathrm{0},+\mathrm{0.16},+\mathrm{0.33},+\mathrm{0.50}]$. This is done for two upstream turbine yaw angles:
${\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=\mathrm{0}{}^{\circ}$ and ${\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=+\mathrm{30}{}^{\circ}$. The turbine separation
distance is kept constant at $x/D=\mathrm{3}$, and only the highly turbulent inflow
condition (inflow B) is investigated.

In the third and final test case the downstream turbine yaw angle *γ*_{T2}
is varied as an additional parameter while it is operated at different
lateral offset positions Δ*z*∕*D*. This concept intends to demonstrate
the possibility for yaw moment mitigation in partial-wake situations by
opposite-direction yawing of the downstream turbine. In this test case T2 is therefore
operated at 13 different yaw angles in the range of ${\mathit{\gamma}}_{\mathrm{T}\mathrm{2}}=[-\mathrm{30},\mathrm{\dots},+\mathrm{30}{}^{\circ}]$. An overview of all investigated test cases is presented
in Table 1.

For all test cases the power coefficient *C*_{P},
thrust coefficient *C*_{T} and normalized yaw moment ${M}_{\mathrm{y}}^{*}$ are assessed on T1
and T2. Note that the coefficients for both turbines are normalized with the
reference inflow velocity *U*_{ref} measured far upstream of the turbine
array at $x/D=-\mathrm{2}$. The power coefficient is the measured mechanical power
normalized with the kinetic power of the wind in a streamtube of the same
diameter:

$$\begin{array}{}\text{(1)}& {C}_{\mathrm{P}}={\displaystyle \frac{P}{\mathrm{1}/\mathrm{8}\mathit{\rho}\mathit{\pi}{D}^{\mathrm{2}}\phantom{\rule{0.125em}{0ex}}{U}_{\mathrm{ref}}^{\mathrm{3}}}}.\end{array}$$

The thrust coefficient is defined as the thrust force normal to the rotor plane normalized with the momentum of the wind in a streamtube:

$$\begin{array}{}\text{(2)}& {C}_{\mathrm{T}}={\displaystyle \frac{{F}_{\mathrm{T}}}{\mathrm{1}/\mathrm{8}\mathit{\rho}\mathit{\pi}{D}^{\mathrm{2}}\phantom{\rule{0.125em}{0ex}}{U}_{\mathrm{ref}}^{\mathrm{2}}}}.\end{array}$$

The yaw moment *M*_{y} is normalized in a similar way to the thrust
force with an additional rotor diameter *D* to account for the normalization of the yaw moment's lever:

$$\begin{array}{}\text{(3)}& {M}_{\mathrm{y}}^{*}={\displaystyle \frac{{M}_{\mathrm{y}}}{\mathrm{1}/\mathrm{8}\mathit{\rho}\mathit{\pi}{D}^{\mathrm{3}}\phantom{\rule{0.125em}{0ex}}{U}_{\mathrm{ref}}^{\mathrm{2}}}}.\end{array}$$

3 Results

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At first the yaw-angle-dependent operating characteristics of the upstream
wind turbine are presented for two inflow conditions in Fig. 1.
The model turbine is operated at a tip speed ratio of *λ*_{T1}=6.0 for
all yaw angles. There, the power coefficient is assessed to be maximum at
*λ*_{T1}=6.0 for all yaw angles from *γ*_{T1}=0 to
$\pm \mathrm{30}{}^{\circ}$. A slight shift towards a lower optimum tip speed ratio of
*λ*_{T1}=5.5 is measured for ${\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=\pm \mathrm{40}{}^{\circ}$ (not shown
in graph). As the difference in total power coefficient is observed to be
very small, the upstream turbine is also constantly operated at *λ*_{T1}=6.0 for these yaw angles. The downstream turbine shows exactly the same
operating characteristics when operated in undisturbed inflow. For
measurements showing the power and thrust coefficient depending on the tip
speed ratio *λ*_{T1}, the interested reader is referred to Bartl et al. (2018).

At
*γ*_{T1}=0 the upstream turbine reaches a power coefficient of about
${C}_{\mathrm{P},\mathrm{T}\mathrm{1}}=\mathrm{0.460}$ for both inflow conditions. It is observed that an increase
in inflow turbulence results in the same performance characteristics. As
discussed by Bartl et al. (2018), the decrease in power coefficient can
be approximated ${C}_{\mathrm{P},{\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=\mathrm{0}}\cdot {\mathrm{cos}}^{\mathrm{3}}\left({\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}\right)$ when the
turbine yaw angle is varied. The thrust coefficient's reduction through
yawing is observed to match well with ${C}_{\mathrm{T},{\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=\mathrm{0}}\cdot {\mathrm{cos}}^{\mathrm{2}}\left({\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}\right)$. Despite the commonly assumed exponent of *α*=3
for the power coefficient ${C}_{\mathrm{P}}\left(\mathit{\gamma}\right)={C}_{\mathrm{P},\mathit{\gamma}=\mathrm{0}}\cdot {\mathrm{cos}}^{\mathit{\alpha}}$,
Micallef and Sant (2016) refer to different values of *α* between 1.8 and 5
measured in different full-scale tests. The measured relations of our study,
however, correspond well to previous measurements on the same rotor by
Krogstad and Adaramola (2012) and another experimental study on a smaller rotor by
Ozbay et al. (2012). Another recent experimental study on a very small rotor by
Bastankhah and Porté-Agel (2017) confirmed the *α*=3 for the power coefficient
but found a slightly smaller exponent of *β*=1.5 for the thrust
coefficient.

The normalized yaw moment shows an almost linear behavior around
the origin. However, minor asymmetries between positive and corresponding
negative yaw angles are observed. These asymmetries are slightly stronger for
inflow A (TI_{A}=0.23 *%*). Although it is not entirely clear where these stem
from, the only reasonable source for an asymmetric load distribution in an
uniform inflow is the rotor's interaction with the turbine tower. In the
course of a revolution, the blades of a yawed turbine experience unsteady-flow
conditions, i.e., fluctuations in angle of attack and relative velocity.
When superimposing an additional low-velocity zone, tower shadow or shear for
example, the yaw symmetry is disturbed. Asymmetric load distributions for
turbines exposed to sheared inflow were recently reported by
Damiani et al. (2018). They showed that vertical wind shear causes asymmetric
distributions of angle of attack and relative flow velocity in the course of
a blade revolution. They link these to rotor loads and conclude further
consequences on wake characteristics and wind farm control strategies.

In the first test case both rotors are installed in the center of the wind
tunnel at $(y,z)=(\mathrm{0},\mathrm{0})$ aligned with the main inflow direction. The
downstream turbine position is varied from $x/D=\mathrm{3}$ to $x/D=\mathrm{6}$, while the
upstream turbine yaw angle is systematically changed in steps of
$\mathrm{\Delta}{\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=\mathrm{10}{}^{\circ}$ in the range of ${\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=[-\mathrm{40},\mathrm{\dots},+\mathrm{40}{}^{\circ}]$. Figure 2 shows two example cases, in which
the downstream turbine is operated in the upstream turbine's wake for
${\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=\mathrm{0}{}^{\circ}$ and ${\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=\mathrm{30}{}^{\circ}$. Positive yaw is defined
as indicated in Fig. 2. The sketched wake flow contours in
the *x*–*z* plane at hub height are included for illustrative purposes. The location
of the wake flow as sketched in gray is roughly estimated from previously
performed measurements as presented in Bartl et al. (2018). The results
for the downstream turbine *C*_{P,T2}, *C*_{T,T2} and ${M}_{\mathrm{y},\mathrm{T}\mathrm{2}}^{*}$ at inflow
B dependent upon its tip speed ratio *λ*_{T2} are shown in Fig. 3.
The downstream turbine's power is observed to increase with an
increasing absolute value of the upstream turbine yaw angle. As the wake is
laterally deflected, the downstream turbine is partly exposed to higher flow
velocities of the inflow. The power output of the downstream turbine is
observed to be asymmetric with respect to the upstream turbine yaw angle.
Higher downstream turbine power coefficients are measured for negative
upstream turbine yaw angles. The optimum downstream turbine T2's operating
point shifts to higher tip speed ratios *λ*_{T2} the more kinetic
energy is available in the wake. As the downstream turbine power coefficient
refers to the constant far-upstream reference velocity *U*_{ref}, the
optimum operating conditions are measured for higher tip speed ratios as soon
as the local inflow velocity increases. A corresponding asymmetry between
positive and negative upstream turbine yaw angles is also observed in T2's
thrust coefficient, showing higher values for negative upstream turbine yaw
angles. The yaw moments experienced by the downstream turbine are observed to
grow with increasing upstream turbine yaw angle. As expected, downstream
turbine yaw moments are positive for positive upstream turbine yaw angles and
vice versa. For low tip speed ratios, i.e., while approaching stalled flow conditions, the yaw moments are
seen to be small and below 0.01. As soon as the flow is attached, the absolute
value of the yaw moments is observed to strongly rise. Again, an asymmetry
between negative and positive upstream turbine yaw angles is observed. The
asymmetric wake deflection for positive and negative yaw angles is considered
to be the main reason for the asymmetric distribution of T2's yaw moments. As
discussed in an analysis of the wake flow behind a yawed turbine by
Bartl et al. (2018), the overall wake displacement for positive and
negative yaw angles was observed to be slightly asymmetric. The interaction
of the rotor wake with the turbine tower is identified to be the main
contributor for the asymmetric wake flow. This finding is supported by a
previous study on the non-yawed wake by Pierella and Sætran (2017), in which they
attributed a significant displacement of the wake center to the interaction
with the turbine tower.

The effect of a variation in inflow turbulence level (TI_{A}=0.23 *%* versus
TI_{B}=10.0 *%*) on the downstream turbine's *C*_{P,T2}, *C*_{T,T2} and
${M}_{\mathrm{y},\mathrm{T}\mathrm{2}}^{*}$ is shown in Fig. 4. The results are presented for
varying upstream turbine yaw angle *γ*_{T1}. The downstream turbine T2
is operated at a *λ*_{T2}, for which *C*_{P,T2} was maximum for the
specific conditions. Note that for $x/D=\mathrm{6}$ neither thrust nor yaw moments
were measured.

The downstream turbine's power coefficient *C*_{P,T2} is in general observed
to be higher for a higher inflow turbulence (inflow B). As previously
observed in Bartl et al. (2018), the wake flow recovers at a higher
rate, leaving more kinetic energy for the downstream turbine to extract. The
difference in T2's power extraction between the two inflow turbulence levels
is observed to be highest at small upstream turbine yaw angles *γ*_{T1}.
At high yaw angles ${\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}\ge \mathrm{30}{}^{\circ}$, however, the power
coefficient *C*_{P,T2} is very similar for the two different inflow
turbulence levels. For these high yaw angles the wake's mean velocity deficit
has the largest lateral deflection, exposing about half of T2's rotor-swept
area to the freestream (Bartl et al., 2018). The kinetic energy content
in the freestream is about the same for both inflows, which brings T2's power
levels closer together. Moreover, the downstream turbine's power output at
low inflow turbulence (inflow A) is observed to be more asymmetric with
respect to *γ*_{T1} than at high inflow turbulence (inflow B).
Especially for $x/D=\mathrm{6}$, the downstream turbine power *C*_{P,T2} is strongly
asymmetric for inflow A. This observation corresponds well to the asymmetry
in the mean streamwise wake flow measured for positive and negative yaw
angles reported in Bartl et al. (2018). Therein, the wake flow behind a
positively and negatively yawed turbine exposed to inflow A was observed to
feature a higher degree of asymmetry than for the same turbine exposed to
inflow B. For extreme yaw angles ${\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=\pm \mathrm{40}{}^{\circ}$, T2's power
coefficient reaches levels of ${C}_{\mathrm{P},\mathrm{T}\mathrm{2}}=\mathrm{0.45}$–0.46, which is about the same
magnitude as *C*_{P,T1} at ${\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=\mathrm{0}{}^{\circ}$. These high downstream
power coefficients *C*_{P,T2} can be explained by increased velocity levels
of $u/{u}_{\mathrm{ref}}=\mathrm{1.10}$ in the freestream outside of the wake as a result of
wind tunnel blockage (Bartl et al., 2018). The downstream turbine power
coefficient, however, still refers to the undisturbed far-upstream
reference velocity *u*_{ref}. Although a considerable part of the downstream
turbine rotor is impinged by T1's wake, higher wind speeds outside of the
wake lift the downstream turbine's power to these levels.

Similar trends are observed for the downstream turbine thrust coefficient
*C*_{P,T2} (Fig. 4b), where higher thrust forces are measured
for the higher turbulence level in inflow B. Inflow A implicates a higher
asymmetry in *C*_{T,T2} with respect to *γ*_{T1}. As previously
discussed, the downstream turbine yaw moments ${M}_{\mathrm{y},\mathrm{T}\mathrm{2}}^{*}$ are observed to
increase with larger upstream turbine yaw angles *γ*_{T1}. For both
inflow cases, the yaw moments' absolute values are seen to be higher for
positive *γ*_{T1} than for negative *γ*_{T1}. Larger yaw moments
are measured for inflow A than for inflow B, which possibly stems from
stronger mean velocity gradients in the wake flow in inflow A. The yaw
moments ${M}_{\mathrm{y},\mathrm{T}\mathrm{2}}^{*}$ on the downstream turbine located at $x/D=\mathrm{3}$ have
approximately the same magnitude as the yaw moments measured on the upstream
turbine ${M}_{\mathrm{y},\mathrm{T}\mathrm{1}}^{*}$. Consequently, an intentional upstream turbine yaw
misalignment implicates significant yaw moments on the upstream turbine
itself as well as an aligned downstream turbine.

A main goal of this study is to find out if upstream turbine yawing can positively affect the total power output. As observed in Fig. 1 yawing the upstream turbine reduces its power output, while Fig. 4 shows that the downstream turbine's power increases simultaneously. In order to quantify if the gain in T2 power can make up for the losses in T1, we define the combined relative power output of the two-turbine array:

$$\begin{array}{}\text{(4)}& {P}_{\mathrm{T}\mathrm{1}+\mathrm{T}\mathrm{2}}^{*}={\displaystyle \frac{{P}_{\mathrm{T}\mathrm{1}}\left({\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}\right)+{P}_{\mathrm{T}\mathrm{2}}\left({\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}\right)}{{P}_{\mathrm{T}\mathrm{1},{\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=\mathrm{0}}+{P}_{\mathrm{T}\mathrm{2},{\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=\mathrm{0}}}}.\end{array}$$

The results for the combined relative power are presented in Fig. 5
for both inflow conditions and two turbine separation distances.
In all of these four setups a maximum increase in combined power between
3.5 % and 11 % was measured for upstream turbine yawing. For both turbine
spacings, the maximum combined efficiencies were measured for
${\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=-\mathrm{30}{}^{\circ}$. The combination of a larger wake deflection and a
progressed wake recovery at higher separation distances is seen to shift the
optimum of the energy balance between T1 and T2 to higher yaw angles
*γ*_{T1}. Moreover, the combined relative power is seen to be asymmetric
with higher values for negative yaw angles *γ*_{T1}. Both upstream
turbine power *C*_{P,T1} and downstream turbine power *C*_{P,T2} are observed
to be asymmetrically distributed. The larger portion can, however, be
ascribed to the power extraction of downstream turbine, which is exposed to
asymmetric wake flow fields for positive and negative yaw angles.
Furthermore, the relative power gains are observed to be significantly larger
for lower inflow turbulence levels (inflow A). Relative power gains of about
11 % were measured for inflow A, while only 8 % were obtained for inflow B at
the same yaw angle of ${\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=-\mathrm{30}{}^{\circ}$. Asymmetries in the combined
power output have been previously observed in a computational study by
Gebraad et al. (2016) and a similar experimental setup by
Schottler et al. (2016). In a recent follow-up study,
Schottler et al. (2017) attributed the asymmetry to a strong shear in
the inflow to the two-turbine setup. As the inflow in the present study was
measured to be spatially uniform, inflow shear is not a reason for the
observed asymmetries.

The power and loads of the downstream turbine T2 are dependent on many
different parameters, such as the inflow conditions, the operating point of
the upstream turbine T1, its relative streamwise and lateral position with
respect to T1, and its operating point. In the second test case we
therefore investigate the downstream turbine's performance in lateral offset.
That means that T2 experiences partial-wake situations. The turbine
separation distance is in this test case fixed to $x/D=\mathrm{3}$, while different
offset positions $\mathrm{\Delta}z/D=[-\mathrm{0.50},-\mathrm{0.33},-\mathrm{0.16},\pm \mathrm{0},+\mathrm{0.16},+\mathrm{0.33},+\mathrm{0.50}]$ are
investigated. This is done for inflow B (TI_{B}=10.0 *%*) only, while upstream
turbine yaw angles of ${\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=\mathrm{0}{}^{\circ}$ and ${\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=+\mathrm{30}{}^{\circ}$
are investigated. In Fig. 6 two example positions of the
downstream turbine are sketched, illustrating two different wake impingement
situations.

Figure 7 shows the downstream turbine's *C*_{P,T2}, *C*_{T,T2} and
${M}_{\mathrm{y},\mathrm{T}\mathrm{2}}^{*}$ while operated in the wake of the upstream turbine at
${\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=\mathrm{0}{}^{\circ}$ dependent upon its tip speed ratio *λ*_{T2}
and lateral offset position Δ*z*∕*D*. As expected, the power coefficient
is seen to increase with increasing lateral offset Δ*z*∕*D* as the
downstream turbine is partly exposed to a flow of higher kinetic energy. T2's
power coefficient is observed not to be entirely symmetric with respect to
its lateral position in the wake. Slightly higher power coefficients are
measured for negative offset positions. The reason for this is deemed to be a
not perfectly axis-symmetric velocity deficit at $x/D=\mathrm{3}$ as indicated in
Bartl et al. (2018). An analysis of the available kinetic energy
contained in the wake at $x/D=\mathrm{3}$ behind a non-yawed upstream turbine
confirmed a higher kinetic energy over an imaginary rotor-swept area for
negative lateral offsets *z*∕*D* than for positive offsets. As observed
earlier, T2's optimum operating point shifts to higher tip speed ratios
*λ*_{T2} with increasing kinetic energy being available in the wake.

Similar trends are observed for the downstream turbine thrust coefficient
*C*_{T,T2}, which was measured to be slightly higher for negative offset
positions. The yaw moments experienced by the downstream turbine are seen to
increase for larger lateral offsets as the rotor is impinged by stronger mean
velocity gradients. The largest increases are detected for a change from
$\mathrm{\Delta}z/D=\pm \mathrm{0}$ to ±0.16 and from ±0.16 to ±0.33, while a
position change from ±0.33 to ±0.50 only causes a small increase in
yaw moment. The curves are generally observed to be almost symmetric with
respect to the offset position but also show slightly higher absolute values
for negative offset positions.

The effect of a variation in upstream turbine yaw angle from
${\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=\mathrm{0}{}^{\circ}$ to ${\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=\mathrm{30}{}^{\circ}$ on the downstream
turbine's characteristics in different lateral offset positions is presented
in Fig. 8. For the shown results the downstream turbine T2 is
operated at its optimum *λ*_{T2}, which differs for each offset
position.

The red curves summarize the results for ${\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=\mathrm{0}{}^{\circ}$ already
shown in Fig. 7 for their optimum operating point, while the
blue curves represent a setup in which T1 is operated at
${\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=\mathrm{30}{}^{\circ}$ (see Fig. 6). For this upstream
turbine yaw angle, the wake center is shifted to $\mathrm{\Delta}z/D=-\mathrm{0.167}$
(Bartl et al., 2018), and correspondingly the blue curves minima in
*C*_{P,T2} and *C*_{T,T2} are shifted to $\mathrm{\Delta}z/D=-\mathrm{0.16}$ (Fig. 8a and b).
The yaw moment ${M}_{\mathrm{y},\mathrm{T}\mathrm{2}}^{*}$ as depicted in Fig. 8c is observed to be around zero for this offset position, as
the rotor is approximately impinged by a full wake. For an offset position
around $\mathrm{\Delta}z/D=+\mathrm{0.16}$ to $\mathrm{\Delta}z/D=+\mathrm{0.33}$ the yaw moments reach a
maximum level, as roughly half the rotor-swept area is impinged by the
low-velocity region of the wake. At a lateral offset of $\mathrm{\Delta}z/D=+\mathrm{0.50}$ the
yaw moments on T2 are observed to decrease again. A large part of the rotor
is exposed to the freestream flow; however, the wake is not yet entirely
deflected away from T2. For this offset position the power and thrust
coefficient are seen to reach very high levels as the rotor is exposed to a
large portion of high-kinetic-energy freestream flow. A power coefficient of
${C}_{\mathrm{P},\mathrm{T}\mathrm{2}}>\mathrm{0.50}$ can be explained by increased freestream velocity levels of
$\stackrel{\mathrm{\u203e}}{u}/{u}_{\mathrm{ref}}=\mathrm{1.10}$ (Bartl et al., 2018) caused by wind tunnel
blockage. The power and thrust coefficient still refer to *u*_{ref}
measured $x/D=-\mathrm{2}$ upstream of T1. Unfortunately, it is not possible to
correct for blockage effects on the downstream turbine power, thrust and yaw
moments with simple correction models. The influence of wind tunnel blockage
on the highly complex inflow to the downstream turbine operated in a partial
wake would have to be quantified by dedicated experiments or high-fidelity
simulations.

The combined relative power output of the two-turbine array is in this case
calculated for a change of upstream turbine yaw angle from
*γ*_{T1}=0 to $+\mathrm{30}{}^{\circ}$. It has to be kept in mind that the
upstream turbine power is constant, independent of the downstream turbine
position. The combined power for each offset position is calculated as

$$\begin{array}{}\text{(5)}& {P}_{\mathrm{T}\mathrm{1}+\mathrm{T}\mathrm{2}}^{*}={\displaystyle \frac{{P}_{\mathrm{T}\mathrm{1},{\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=\mathrm{30}}+{P}_{\mathrm{T}\mathrm{2},{\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=\mathrm{30}}(z/D)}{{P}_{\mathrm{T}\mathrm{1},{\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=\mathrm{0}}+{P}_{\mathrm{T}\mathrm{2},{\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=\mathrm{0}}(z/D)}}.\end{array}$$

Figure 9 shows the resultant combined relative power output. For
an offset position of $\mathrm{\Delta}z/D=+\mathrm{0.33}$ a maximum combined power increase of
13 % is measured, as a major part is deflected away from the downstream
rotor. Surprisingly, the relative power gains measured for an offset $\mathrm{\Delta}z/D=+\mathrm{0.50}$ are measured to be smaller, amounting to about 6 %. This can be
explained by significantly larger *C*_{P,T2} values in the non-yawed case for
$\mathrm{\Delta}z/D=+\mathrm{0.50}$ than for $\mathrm{\Delta}z/D=+\mathrm{0.33}$, allowing smaller relative
gains. For zero lateral offset, about 5 % in combined power is lost when
yawing T1 to ${\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=+\mathrm{30}{}^{\circ}$ as previously observed in Fig. 5.
In the case of the downstream turbine being located at negative
offset positions Δ*z*∕*D*, the wake is deflected directly on T2's rotor,
significantly reducing its power output and consequently also the combined
power.

In conclusion, it has been demonstrated that intentional upstream turbine yaw control is favorable in offset situations when considering both the power output and yaw moments on a downstream turbine. Depending on the downstream turbine's streamwise and lateral position, the wake can be partly or even fully deflected away from its rotor-swept area. This finding experimentally confirms results of a similar test case recently computed with a model framework by van Dijk et al. (2017).

The third and final test case investigates whether a variation in downstream
turbine yaw angle *γ*_{T2} contributes to a yaw load mitigation and
power optimization. As previously seen, both partial wake impingement and
turbine yaw misalignment are possible sources for increased yaw moments. An
intentional yaw misalignment opposed to the partial wake impingement is
therefore considered to cancel out yaw loading on the turbine. For this
purpose, the downstream turbine yaw angle is systematically varied from
${\mathit{\gamma}}_{\mathrm{T}\mathrm{2}}=-\mathrm{30}{}^{\circ}$ to ${\mathit{\gamma}}_{\mathrm{T}\mathrm{2}}=+\mathrm{30}{}^{\circ}$ in steps of 5^{∘} for
all seven lateral offset positions and upstream turbine yaw angles
${\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=[\mathrm{0},+\mathrm{30}{}^{\circ}]$. A sketch of two downstream turbine
yaw angles at two offset positions is presented in Fig. 10.

The resulting *C*_{P,T2}, *C*_{T,T2} and ${M}_{\mathrm{y},\mathrm{T}\mathrm{2}}^{*}$ of the downstream
turbine dependent upon its yaw angle *γ*_{T2} and lateral offset
position Δ*z*∕*D* for a constant upstream turbine yaw angle of
${\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=\mathrm{0}{}^{\circ}$ are shown in Fig. 11. The points for
${\mathit{\gamma}}_{\mathrm{T}\mathrm{2}}=\mathrm{0}{}^{\circ}$ correspond to the previously shown red lines in
Fig. 8. If the downstream turbine rotor is fully impinged
by the upstream turbine's wake, i.e., $\mathrm{\Delta}z/D=\mathrm{0}$, a variation of its yaw
angle *γ*_{T2} reduces its power output and increases uneven yaw
moments. During a lateral offset, however, the maximum power output and
minimum yaw moments are found for yaw angles ${\mathit{\gamma}}_{\mathrm{T}\mathrm{2}}\ne \mathrm{0}{}^{\circ}$. At a
lateral offset position of $\mathrm{\Delta}z/D=+\mathrm{0.16}$, for instance, the maximum
*C*_{P,T2} is assessed for ${\mathit{\gamma}}_{\mathrm{T}\mathrm{2}}=-\mathrm{10}{}^{\circ}$. Simultaneously, the yaw
moment is measured to be around zero at this yaw angle. The potential of load
reductions of a single turbine by yawing has been previously discussed by
Kragh and Hansen (2014), in situations where the rotor was exposed to vertically
sheared inflows. In the present test case, however, the partial wake
impingement on the rotor represents a situation of a strongly horizontally
sheared flow. Whether the shear in the incoming wind field is horizontal or
vertical obviously makes a big difference, but mitigation of loads and
maximization of power might be possible with yaw adjustments in both cases.
As the downstream turbine operated in the partial wake is exposed to a
strongly sheared inflow, yaw moments can be mitigated by actively yawing the
rotor in the opposite direction to the incoming shear. The simultaneous power
increase for the oppositely yawed downstream rotor is a positive side effect,
although the exact reasons for the power increase are not entirely clear at
this stage. A power increase by downstream turbine yawing has previously been
reported in a full-scale data evaluation by McKay et al. (2013), who found an
offset in the downstream turbine's yaw alignment for the purpose of
optimized power output when operated in a partial wake of an upstream
turbine. The downstream turbine yaw angle was observed to adjust itself
opposed to the velocity gradient in the partial wake impinging the downstream
rotor. These findings are in total agreement with the optimal downstream
turbine yaw angle measured in our wind tunnel experiment. Higher power
outputs and decreased yaw moments are also measured for moderate yaw angles
around ${\mathit{\gamma}}_{\mathrm{T}\mathrm{2}}=-\mathrm{10}{}^{\circ}$ at larger lateral offsets of $\mathrm{\Delta}z/D=+\mathrm{0.33}$ and $\mathrm{\Delta}z/D=+\mathrm{0.50}$. The slope of the power curves in Fig. 11a
and yaw moment curves in Fig. 11c are
observed to be even steeper for larger lateral offsets. The power gains when
yawing the turbine from ${\mathit{\gamma}}_{\mathrm{T}\mathrm{2}}=\mathrm{0}{}^{\circ}$ to ${\mathit{\gamma}}_{\mathrm{T}\mathrm{2}}=-\mathrm{10}{}^{\circ}$
are larger for higher lateral offsets. At the same time, the relative yaw
moment reduction is larger, implying that yawing of the downstream
turbine in the opposite direction is
expected to be even more effective for higher lateral offsets.

For negative lateral offset positions, the opposite trends are observed;
i.e., maximum power and smallest absolute yaw moments are measured for positive
downstream turbine yaw angles *γ*_{T2}. The power output and yaw moment
distribution, however, are not completely symmetrical with respect to yaw angle
*γ*_{T2} and offset position Δ*z*∕*D*.

The concept of downstream turbine yawing in partial-wake-impingement
situations is moreover investigated for an upstream turbine yaw angle of
${\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=+\mathrm{30}{}^{\circ}$. The wake flow features a significantly higher
asymmetry in this case. The results for *C*_{P,T2}, *C*_{T,T2} and
${M}_{\mathrm{y},\mathrm{T}\mathrm{2}}^{*}$ are shown in Fig. 12. As previously observed, an
offset of $\mathrm{\Delta}z/D=-\mathrm{0.16}$ approximately corresponds to an impingement of
the full wake. Thus, the power coefficient has an almost symmetric
distribution with respect to downstream turbine yaw angle *γ*_{T2}. The
yaw moments are observed to be rather low for this offset position and around
zero for *γ*_{T2}=0. For partial-wake-impingement situations at $\mathrm{\Delta}z/D\ge \mathrm{0}$, negative downstream turbine yaw angles are again seen to reduce
the yaw moments acting on the rotor. The gradients in yaw moment reduction
per degree of yaw angle are observed to be steeper for larger lateral
offsets. The maximum power coefficients are again measured for moderate
downstream turbine yaw angles around ${\mathit{\gamma}}_{\mathrm{T}\mathrm{2}}\pm \mathrm{10}{}^{\circ}$.

Power gains by downstream turbine yawing are assessed by a relative combined power of the two-turbine array:

$$\begin{array}{}\text{(6)}& {P}_{\mathrm{T}\mathrm{1}+\mathrm{T}\mathrm{2}}^{*}={\displaystyle \frac{{P}_{\mathrm{T}\mathrm{1}}+{P}_{\mathrm{T}\mathrm{2}}({\mathit{\gamma}}_{\mathrm{T}\mathrm{2}},z/D)}{{P}_{\mathrm{T}\mathrm{1},{\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=\mathrm{0},z/D=\mathrm{0}}+{P}_{\mathrm{T}\mathrm{2},{\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=\mathrm{0},{\mathit{\gamma}}_{\mathrm{T}\mathrm{2}}=\mathrm{0},z/D=\mathrm{0}}}}.\end{array}$$

As a reference of the power measured for the non-yawed upstream turbine, a
non-yawed downstream turbine in an aligned setup ($\mathrm{\Delta}z/D=\mathrm{0}$) is used.
The results are shown in Fig. 13. For an upstream turbine yaw
angle of ${\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=\mathrm{0}{}^{\circ}$ (Fig. 13a) combined power
gains of approximately 3 % are measured for moderate downstream turbine yaw
angles (*γ*_{T2}±10 to $\pm \mathrm{15}{}^{\circ}$). The combined power
characteristics are observed to be quite symmetrical with respect to
downstream turbine offset and its yaw angle. Slightly higher relative power
gains are obtained for the case of an upstream turbine yaw angle of
${\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=+\mathrm{30}{}^{\circ}$ (Fig. 13b). A maximum power gain of
about 5 % is measured for offset positions $\mathrm{\Delta}z/D=\mathrm{0}$ and +0.16, and a
downstream turbine yaw angle between ${\mathit{\gamma}}_{\mathrm{T}\mathrm{1}}=-\mathrm{10}$ and
$-\mathrm{15}{}^{\circ}$. Note that the downstream turbine's tip speed ratio
*λ*_{T2} is kept constant when the downstream turbine is yawed. As no
change in optimum tip speed ratio was measured for yaw angle variations up to
$\mathit{\gamma}=\pm \mathrm{30}{}^{\circ}$ in undisturbed inflow, it is assumed at this stage
that no further adjustments of the tip speed ratio in a partial wake are
needed for an optimal downstream turbine power output.

In conclusion, this third test case demonstrates that moderate downstream turbine yawing can be an effective method of mitigating yaw moments acting on the rotor in partial-wake situations, while simultaneously obtaining slight power gains.

4 Conclusions

Back to toptop
A wind tunnel experiment studying the effects of intentional yaw misalignment on the power production and yaw moments of a downstream turbine was presented. Both full wake impingement and partial wake overlap were investigated. For partial wake overlap, the concept of downstream turbine yawing for the purpose of yaw moment mitigation is examined.

It is demonstrated that upstream turbine yaw misalignment is able to increase
the combined power production of the two turbines for both partial and full
wake overlap setups. For aligned turbines the combined array power was
increased up to a maximum of 11 % for a separation distance of $x/D=\mathrm{6}$ and
low inflow turbulence levels (TI_{A}=0.23 *%*). At a higher inflow turbulence
of TI_{B}=10.0 *%*, however, the relative power increase was assessed to be
only 8 %. For smaller turbine separation distances, combined power gains were
assessed to be even smaller. The distribution of combined power gains
dependent upon the upstream turbine yaw angle was observed to be rather
asymmetrical. The formation of not entirely symmetric velocity deficit shapes
in the wake was deemed to be the main reason for that finding.

The obtained power gains were assessed to be at the cost of increased yaw moments on the upstream rotor. The yaw moments on the upstream rotor are observed to increase roughly linearly with increasing yaw angle but are not entirely symmetrical distributed. Upstream turbine yaw control is moreover seen to directly influence the yaw moments on a downstream rotor. For aligned turbine positions, the downstream turbine yaw moments are observed to increase to magnitudes similar to those for the upstream turbine. These results highlight the importance of also taking loads into account when optimizing layout and control of a wind farm.

Further, we demonstrate advantages of upstream turbine yaw control for load reduction and power increases on an offset downstream turbine. For situations in which the downstream turbine is impinged by a partial wake, upstream turbine yaw control can redirect the wake either on or away from the downstream rotor. If the wake is directed onto the downstream turbine's rotor-swept area, its yaw moments and power production reduce. If the lateral offset between the turbines is large enough, the wake can be deflected entirely away from the downstream turbine, maximizing its power and canceling out yaw moments.

Moreover, a final test case proved the concept of yaw control for yaw moment mitigation on a downstream turbine operated in partial wake overlap. While yaw moments are observed to decrease when yawing the rotor opposed to the shear layer in the incoming wake flow, the turbine's power output is also seen to increase. These results illustrate the importance for combined power and load optimization on all turbines in a wind farm.

Data availability

Back to toptop
Data availability.

The experimental dataset is available on request to the corresponding author.

Author contributions

Back to toptop
Author contributions.

The experiments were prepared and executed by JB and FM under supervision of LS. The paper was written by JB and revised by FM and LS.

Competing interests

Back to toptop
Competing interests.

The authors declare that they have no conflict of interest.

Acknowledgements

Back to toptop
Acknowledgements.

A special thank-you to Jannik Schottler for lots of discussions on the topic and for
proofreading the manuscript.

Edited by: Raúl Bayoán Cal

Reviewed by: three anonymous referees

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