Introduction
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 . 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 . These include methods of reducing
the axial induction of an upstream turbine and thus also mean and turbulent
gradients in the wake as well as wake
redirection techniques . 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 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
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
, 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 . The inflow turbulence
level was observed to influence the shape and deflection of the wake, in
contrast to a moderate shear in the inflow.
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 . 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 .
Moreover, various research has investigated the potential of overall wind farm
power gains through intentional yaw misalignment. An experimental study by
on two aligned model wind turbines (x/D=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 measured a combined power
increase of about 4 % for an upstream turbine yaw angle of -18∘.
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 , who measured a
combined power increase of 21 % for a lateral offset of Δz/D=0.45
between the turbines. Comprehensive studies on yaw misalignment for optimized
full wind farm control haven been presented by and
. They analyzed wake mitigation strategies by using both
the LES code SOWFA and a parametric wake model. A comprehensive
full-scale study by 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
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 . Their comparisons revealed modeling deficiencies,
while shedding light on complex unsteady-flow phenomena during yaw. In a
recent paper by 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 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
. Using a computational framework of a wake model, a blade element momentum (BEM)
model for power and loads, and a gradient-based optimizer,
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 Δz/D and turbine yaw settings
γT1 and γT2 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 , this study
completes the link between detailed wake flow characteristics and power, yaw
moments and thrust forces on a turbine operated in the wake.
Experimental setup
Wind turbine models
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=0.894m. 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 λT1=λT2=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
, while T2's characteristics can be found in
. 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 2.71m in width, 1.81m in height
and 11.15m in length. The turbine models are operated at a blade tip
Reynolds numbers of approximately Retip≈105.
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 . 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 .
For high blockage ratios, correction models (e.g., by , or
) 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.
Inflow conditions
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 TIA=0.23% (inflow A) as well as high turbulence
intensity TIB=10.0% (inflow B). Inflow B is generated by a static grid at
the wind tunnel inlet (x/D=-2) and is measured to the amount TIB=10.0 %
at the location of the upstream turbine (x/D=0). The grid-generated
turbulence decays with increasing downstream distance to about TIB=5.5%
at x/D=3 and to TIB=4.0% at x/D=6. The profiles of streamwise mean
velocity and turbulence intensity measured in the empty wind tunnel for
different downstream positions are presented in .
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=0 for inflow B,
as the footprint of the grid's single bars is still detectable. At x/D=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 uref=10.0ms-1.
Measurement techniques
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.
Statistical measurement uncertainties
The statistical measurement uncertainties for power coefficients, thrust
coefficient and normalized yaw moments have been calculated following the
procedure described by . 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., γT1=0∘, x/D=3, Δz/D=0) with previous results (e.g., by ) has been
checked for consistency.
For the purpose of clarity, error bars are not shown
in the resulting graphs in Sect. . 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
γT1=30∘. 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 ±40∘, respectively. The uncertainty in
normalized yaw moments My* is 0.0032, which corresponds to almost 15 %
of the absolute measurement value at γT1=30∘. 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
γT1=30∘ and T2 is located at x/D=3 and operated at
γT2=0∘. The total uncertainties in power and thrust
coefficient are 0.0060 (2.5 % of the absolute CP value) and 0.0070 (0.9 %
of the absolute CT value), respectively. The normalized yaw moment of the
downstream turbine for this case amounts to 0.0019 (about 8 % of the absolute
value).
Overview of test cases.
Test case
Parameter
Inflow
Yaw angle
Streamwise
Lateral
Yaw angle
variation
turbulence
γT1
separation x/D
offset Δz/D
γT2
1a
Aligned turbines
γT1 & x/D
0.23 %
[-40, …, +40∘]
3 & 6
0
0∘
1b
Aligned turbines
γT1 & x/D
10.0 %
[-40, …, +40∘]
3 & 6
0
0∘
2a
Offset turbines
Δz/D
10.0 %
0∘
3
[-0.5, … +0.5]
0∘
2b
Offset turbines
Δz/D
10.0 %
+30∘
3
[-0.5, … +0.5]
0∘
3a
Downstream turbine yaw
Δz/D & γT2
10.0 %
0∘
3
[-0.5, … +0.5]
[-30, …, +30∘]
3b
Downstream turbine yaw
Δz/D & γT2
10.0 %
+30∘
3
[-0.5, … +0.5]
[-30, …, +30∘]
Test case definition
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
γT1=0∘). The upstream turbine's yaw angle is then
systematically varied at nine different values γT1=[-40,-30,-20,-10,0,+10,+20,+30,+40∘]. Moreover, the streamwise separation distance
between the turbines is varied from x/D=3 to x/D=6.
Finally, the inflow turbulence intensity is varied from TIA=0.23% (inflow A) to TIB=10.0% (inflow B).
In the second test case, the effect of the lateral offset position Δz/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 Δz/D=[-0.50,-0.33,-0.16,0,+0.16,+0.33,+0.50]. This is done for two upstream turbine yaw angles:
γT1=0∘ and γT1=+30∘. The turbine separation
distance is kept constant at x/D=3, and only the highly turbulent inflow
condition (inflow B) is investigated.
In the third and final test case the downstream turbine yaw angle γT2
is varied as an additional parameter while it is operated at different
lateral offset positions Δz/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 γT2=[-30,…,+30∘]. An overview of all investigated test cases is presented
in Table .
For all test cases the power coefficient CP,
thrust coefficient CT and normalized yaw moment My* are assessed on T1
and T2. Note that the coefficients for both turbines are normalized with the
reference inflow velocity Uref measured far upstream of the turbine
array at x/D=-2. The power coefficient is the measured mechanical power
normalized with the kinetic power of the wind in a streamtube of the same
diameter:
CP=P1/8ρπD2Uref3.
The thrust coefficient is defined as the thrust force normal to the rotor plane normalized with the momentum of the wind in a streamtube:
CT=FT1/8ρπD2Uref2.
The yaw moment My 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:
My*=My1/8ρπD3Uref2.
Results
Operating characteristics of T1
At first the yaw-angle-dependent operating characteristics of the upstream
wind turbine are presented for two inflow conditions in Fig. .
The model turbine is operated at a tip speed ratio of λT1=6.0 for
all yaw angles. There, the power coefficient is assessed to be maximum at
λT1=6.0 for all yaw angles from γT1=0 to
±30∘. A slight shift towards a lower optimum tip speed ratio of
λT1=5.5 is measured for γT1=±40∘ (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 λT1=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 λT1, the interested reader is referred to .
(a) Power coefficient CP,T1, (b) thrust
coefficient CT,T1 and (c) normalized yaw moment My,T1* of
the undisturbed upstream turbine T1 for different inflow conditions. The
turbine is operated at λopt,T1=6.0 for all yaw angles.
At
γT1=0 the upstream turbine reaches a power coefficient of about
CP,T1=0.460 for both inflow conditions. It is observed that an increase
in inflow turbulence results in the same performance characteristics. As
discussed by , the decrease in power coefficient can
be approximated CP,γT1=0⋅cos3(γT1) when the
turbine yaw angle is varied. The thrust coefficient's reduction through
yawing is observed to match well with CT,γT1=0⋅cos2(γT1). Despite the commonly assumed exponent of α=3
for the power coefficient CP(γ)=CP,γ=0⋅cosα,
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
and another experimental study on a smaller rotor by
. Another recent experimental study on a very small rotor by
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 (TIA=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
. 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.
Top view of the aligned downstream turbine operated in the wake of an
upstream turbine at the two different positions: x/D=3 and x/D=6. The wake
flow is indicated for (a) γT1=0∘ and (b) γT1=30∘.
Downstream turbine (a) power coefficient, (b) thrust
coefficient and (c) normalized yaw moment as a function of
its tip speed ratio λT2 for different upstream turbine yaw angles
γT1. The downstream turbine T2 is located at x/D=3. The turbines
are exposed to inflow B.
Test case 1: aligned turbines
In the first test case both rotors are installed in the center of the wind
tunnel at (y,z)=(0,0) aligned with the main inflow direction. The
downstream turbine position is varied from x/D=3 to x/D=6, while the
upstream turbine yaw angle is systematically changed in steps of
ΔγT1=10∘ in the range of γT1=[-40,…,+40∘]. Figure shows two example cases, in which
the downstream turbine is operated in the upstream turbine's wake for
γT1=0∘ and γT1=30∘. Positive yaw is defined
as indicated in Fig. . 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 . The results
for the downstream turbine CP,T2, CT,T2 and My,T2* at inflow
B dependent upon its tip speed ratio λT2 are shown in Fig. .
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 λT2 the more kinetic
energy is available in the wake. As the downstream turbine power coefficient
refers to the constant far-upstream reference velocity Uref, 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
, 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 , 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 (TIA=0.23% versus
TIB=10.0%) on the downstream turbine's CP,T2, CT,T2 and
My,T2* is shown in Fig. . The results are presented for
varying upstream turbine yaw angle γT1. The downstream turbine T2
is operated at a λT2, for which CP,T2 was maximum for the
specific conditions. Note that for x/D=6 neither thrust nor yaw moments
were measured.
Downstream turbine (a) power coefficient, (b) thrust
coefficient and (c) normalized yaw moment as a function of
the upstream turbine's yaw angle γT1. The downstream turbine T2 is
located at x/D=3 and x/D=6. The turbines are exposed to
inflows A and B.
The downstream turbine's power coefficient CP,T2 is in general observed
to be higher for a higher inflow turbulence (inflow B). As previously
observed in , 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 γT1.
At high yaw angles γT1≥30∘, however, the power
coefficient CP,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 . 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 γT1 than at high inflow turbulence (inflow B).
Especially for x/D=6, the downstream turbine power CP,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 . 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 γT1=±40∘, T2's power
coefficient reaches levels of CP,T2=0.45–0.46, which is about the same
magnitude as CP,T1 at γT1=0∘. These high downstream
power coefficients CP,T2 can be explained by increased velocity levels
of u/uref=1.10 in the freestream outside of the wake as a result of
wind tunnel blockage . The downstream turbine power
coefficient, however, still refers to the undisturbed far-upstream
reference velocity uref. 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
CP,T2 (Fig. b), where higher thrust forces are measured
for the higher turbulence level in inflow B. Inflow A implicates a higher
asymmetry in CT,T2 with respect to γT1. As previously
discussed, the downstream turbine yaw moments My,T2* are observed to
increase with larger upstream turbine yaw angles γT1. For both
inflow cases, the yaw moments' absolute values are seen to be higher for
positive γT1 than for negative γT1. 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 My,T2* on the downstream turbine located at x/D=3 have
approximately the same magnitude as the yaw moments measured on the upstream
turbine My,T1*. Consequently, an intentional upstream turbine yaw
misalignment implicates significant yaw moments on the upstream turbine
itself as well as an aligned downstream turbine.
Combined relative power PT1+T2* of two turbines for different
upstream turbine yaw angles γT1. The downstream turbine T2 is
located at x/D=3 and x/D=6. The turbines are exposed to
inflows A and B.
Top view of two lateral offset positions ((a) Δz/D=-0.16 and (b) Δz/D=+0.33) of the downstream turbine
while operated in the wake of an upstream turbine at x/D=3. The upstream
turbine is operated at (a) γT1=0∘ and (b) γT1=30∘.
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.
yawing the upstream turbine reduces its power output, while
Fig. 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:
PT1+T2*=PT1(γT1)+PT2(γT1)PT1,γT1=0+PT2,γT1=0.
The results for the combined relative power are presented in Fig.
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
γT1=-30∘. 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
γT1. Moreover, the combined relative power is seen to be asymmetric
with higher values for negative yaw angles γT1. Both upstream
turbine power CP,T1 and downstream turbine power CP,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 γT1=-30∘. Asymmetries in the combined
power output have been previously observed in a computational study by
and a similar experimental setup by
. In a recent follow-up study,
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.
Test case 2: offset turbines
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=3, while different
offset positions Δz/D=[-0.50,-0.33,-0.16,±0,+0.16,+0.33,+0.50] are
investigated. This is done for inflow B (TIB=10.0%) only, while upstream
turbine yaw angles of γT1=0∘ and γT1=+30∘
are investigated. In Fig. two example positions of the
downstream turbine are sketched, illustrating two different wake impingement
situations.
Downstream turbine (a) power coefficient, (b) thrust
coefficient and (c) normalized yaw moment as a function of
its tip speed ratio λT2 for different lateral offset positions
Δz/D. The upstream turbine yaw angle is kept constant at
γT1=0∘. The downstream turbine T2 is located at x/D=3. The
turbines are exposed to inflow B.
Figure shows the downstream turbine's CP,T2, CT,T2 and
My,T2* while operated in the wake of the upstream turbine at
γT1=0∘ dependent upon its tip speed ratio λT2
and lateral offset position Δz/D. As expected, the power coefficient
is seen to increase with increasing lateral offset Δz/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=3 as indicated in
. An analysis of the available kinetic energy
contained in the wake at x/D=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
λT2 with increasing kinetic energy being available in the wake.
Similar trends are observed for the downstream turbine thrust coefficient
CT,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
Δz/D=±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
γT1=0∘ to γT1=30∘ on the downstream
turbine's characteristics in different lateral offset positions is presented
in Fig. . For the shown results the downstream turbine T2 is
operated at its optimum λT2, which differs for each offset
position.
The red curves summarize the results for γT1=0∘ already
shown in Fig. for their optimum operating point, while the
blue curves represent a setup in which T1 is operated at
γT1=30∘ (see Fig. ). For this upstream
turbine yaw angle, the wake center is shifted to Δz/D=-0.167
, and correspondingly the blue curves minima in
CP,T2 and CT,T2 are shifted to Δz/D=-0.16 (Fig. a and b).
The yaw moment My,T2* as depicted in Fig. c 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 Δz/D=+0.16 to Δz/D=+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 Δz/D=+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
CP,T2>0.50 can be explained by increased freestream velocity levels of
u‾/uref=1.10 caused by wind tunnel
blockage. The power and thrust coefficient still refer to uref
measured x/D=-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.
Downstream turbine (a) power coefficient, (b) thrust coefficient
and (c) normalized yaw moment as a function of
its lateral offset position Δz/D. The downstream turbine yaw angle is
kept constant at γT2=0∘. The downstream turbine T2 is
located at x/D=3. The turbines are exposed to inflow B.
Combined relative power PT1+T2* of the two-turbine array for
different lateral offset positions Δz/D. The combined power is
calculated for a change of upstream turbine yaw angle from
γT1=0 to +30∘ for each position. The downstream
turbine T2 is located at x/D=3. The turbines are exposed to inflow B.
The combined relative power output of the two-turbine array is in this case
calculated for a change of upstream turbine yaw angle from
γT1=0 to +30∘. 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
PT1+T2*=PT1,γT1=30+PT2,γT1=30(z/D)PT1,γT1=0+PT2,γT1=0(z/D).
Figure shows the resultant combined relative power output. For
an offset position of Δz/D=+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 Δz/D=+0.50 are measured to be smaller, amounting to about 6 %. This can be
explained by significantly larger CP,T2 values in the non-yawed case for
Δz/D=+0.50 than for Δz/D=+0.33, allowing smaller relative
gains. For zero lateral offset, about 5 % in combined power is lost when
yawing T1 to γT1=+30∘ as previously observed in Fig. .
In the case of the downstream turbine being located at negative
offset positions Δz/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 .
Test case 3: downstream turbine yawing
The third and final test case investigates whether a variation in downstream
turbine yaw angle γT2 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
γT2=-30∘ to γT2=+30∘ in steps of 5∘ for
all seven lateral offset positions and upstream turbine yaw angles
γT1=[0,+30∘]. A sketch of two downstream turbine
yaw angles at two offset positions is presented in Fig. .
(a) Top view of the downstream turbine T2 operated at a
lateral offset position Δz/D=+0.50 and a yaw angle of
γT2=-20∘ in the wake of an upstream turbine T1 operated at
γT1=0∘. (b) Top view of the downstream turbine T2
operated at a lateral offset position (Δz/D=+0.16) and a yaw angle of
γT2=-15∘ in the wake of an upstream turbine T1 operated at
γT1=30∘.
Downstream turbine (a) power coefficient, (b) thrust coefficient and
(c) normalized yaw moment as a function of
its yaw angle γT2 for different lateral offset positions Δz/D. The upstream turbine yaw angle is kept constant at
γT1=0∘. The downstream turbine T2 is located at x/D=3. The
turbines are exposed to inflow B.
The resulting CP,T2, CT,T2 and My,T2* of the downstream
turbine dependent upon its yaw angle γT2 and lateral offset
position Δz/D for a constant upstream turbine yaw angle of
γT1=0∘ are shown in Fig. . The points for
γT2=0∘ correspond to the previously shown red lines in
Fig. . If the downstream turbine rotor is fully impinged
by the upstream turbine's wake, i.e., Δz/D=0, a variation of its yaw
angle γT2 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 γT2≠0∘. At a
lateral offset position of Δz/D=+0.16, for instance, the maximum
CP,T2 is assessed for γT2=-10∘. 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
, 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 , 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 γT2=-10∘ at larger lateral offsets of Δz/D=+0.33 and Δz/D=+0.50. The slope of the power curves in Fig. a
and yaw moment curves in Fig. c are
observed to be even steeper for larger lateral offsets. The power gains when
yawing the turbine from γT2=0∘ to γT2=-10∘
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 γT2. The power output and yaw moment
distribution, however, are not completely symmetrical with respect to yaw angle
γT2 and offset position Δz/D.
Downstream turbine (a) power coefficient, (b) thrust
coefficient and (c) normalized yaw moment as a function of
its yaw angle γT2 for different lateral offset position Δz/D. The upstream turbine yaw angle is kept constant at
γT1=30∘. The downstream turbine T2 is located at x/D=3.
The turbines are exposed to inflow B.
Combined relative power PT1+T2* of two turbines as a function
of the downstream turbine yaw angle γT2 for different lateral
offset positions Δz/D. The upstream turbine yaw angle is kept
constant at (a) γT1=0∘ and
(b) γT1=30∘. The downstream turbine T2 is located
at x/D=3. The turbines are exposed to inflow B.
The concept of downstream turbine yawing in partial-wake-impingement
situations is moreover investigated for an upstream turbine yaw angle of
γT1=+30∘. The wake flow features a significantly higher
asymmetry in this case. The results for CP,T2, CT,T2 and
My,T2* are shown in Fig. . As previously observed, an
offset of Δz/D=-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 γT2. The
yaw moments are observed to be rather low for this offset position and around
zero for γT2=0. For partial-wake-impingement situations at Δz/D≥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 γT2±10∘.
Power gains
by downstream turbine yawing are assessed by a relative combined power of the
two-turbine array:
PT1+T2*=PT1+PT2(γT2,z/D)PT1,γT1=0,z/D=0+PT2,γT1=0,γT2=0,z/D=0.
As a reference of the power measured for the non-yawed upstream turbine, a
non-yawed downstream turbine in an aligned setup (Δz/D=0) is used.
The results are shown in Fig. . For an upstream turbine yaw
angle of γT1=0∘ (Fig. a) combined power
gains of approximately 3 % are measured for moderate downstream turbine yaw
angles (γT2±10 to ±15∘). 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
γT1=+30∘ (Fig. b). A maximum power gain of
about 5 % is measured for offset positions Δz/D=0 and +0.16, and a
downstream turbine yaw angle between γT1=-10 and
-15∘. Note that the downstream turbine's tip speed ratio
λT2 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
γ=±30∘ 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.
Conclusions
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=6 and
low inflow turbulence levels (TIA=0.23%). At a higher inflow turbulence
of TIB=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.